Patent Publication Number: US-2023132715-A1

Title: Irak degraders and uses thereof

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional App. No. 62/875,258, filed on Jul. 17, 2019, U.S. Provisional App. No. 62/913,037, filed on Oct. 9, 2019, U.S. Provisional App. No. 62/959,332, filed on Jan. 10, 2020, and U.S. Provisional App. No. 63/041,255, filed on Jun. 19, 2020, the content of each of which is hereby incorporated by reference. 
    
    
     TECHNICAL FIELD OF THE INVENTION 
     The present invention relates to compounds and methods useful for the modulation of one or more interleukin-1 receptor-associated kinases (“IRAK”) via ubiquitination and/or degradation by compounds according to the present invention. The invention also provides pharmaceutically acceptable compositions comprising compounds of the present invention and methods of using said compositions in the treatment of various disorders. 
     BACKGROUND OF THE INVENTION 
     Ubiquitin-Proteasome Pathway (UPP) is a critical pathway that regulates key regulator proteins and degrades misfolded or abnormal proteins. UPP is central to multiple cellular processes, and if defective or imbalanced, it leads to pathogenesis of a variety of diseases. The covalent attachment of ubiquitin to specific protein substrates is achieved through the action of E3 ubiquitin ligases. 
     There are over 600 E3 ubiquitin ligases which facilitate the ubiquitination of different proteins in vivo, which can be divided into four families: HECT-domain E3s, U-box E3s, monomeric RING E3s and multi-subunit E3s. See generally Li et al. (PLOS One, 2008, 3, 1487) titled “Genome-wide and functional annotation of human E3 ubiquitin ligases identifies MULAN, a mitochondrial E3 that regulates the organelle&#39;s dynamics and signaling.”; Berndsen et al. (Nat. Struct. Mol. Biol., 2014, 21, 301-307) titled “New insights into ubiquitin E3 ligase mechanism”; Deshaies et al. (Ann. Rev. Biochem., 2009, 78, 399-434) titled “RING domain E3 ubiquitin ligases.”; Spratt et al. (Biochem. 2014, 458, 421-437) titled “RBR E3 ubiquitin ligases: new structures, new insights, new questions.”; and Wang et al. (Nat. Rev. Cancer., 2014, 14, 233-347) titled “Roles of F-box proteins in cancer.” 
     UPP plays a key role in the degradation of short-lived and regulatory proteins important in a variety of basic cellular processes, including regulation of the cell cycle, modulation of cell surface receptors and ion channels, and antigen presentation. The pathway has been implicated in several forms of malignancy, in the pathogenesis of several genetic diseases (including cystic fibrosis, Angelman&#39;s syndrome, and Liddle syndrome), in immune surveillance/viral pathogenesis, and in the pathology of muscle wasting. Many diseases are associated with an abnormal UPP and negatively affect cell cycle and division, the cellular response to stress and to extracellular modulators, morphogenesis of neuronal networks, modulation of cell surface receptors, ion channels, the secretory pathway, DNA repair and biogenesis of organelles. 
     Aberrations in the process have recently been implicated in the pathogenesis of several diseases, both inherited and acquired. These diseases fall into two major groups: (a) those that result from loss of function with the resultant stabilization of certain proteins, and (b) those that result from gain of function, i.e. abnormal or accelerated degradation of the protein target. 
     The UPP is used to induce selective protein degradation, including use of fusion proteins to artificially ubiquitinate target proteins and synthetic small-molecule probes to induce proteasome-dependent degradation. Bifunctional compounds composed of a target protein-binding ligand and an E3 ubiquitin ligase ligand, induced proteasome-mediated degradation of selected proteins via their recruitment to E3 ubiquitin ligase and subsequent ubiquitination. These drug-like molecules offer the possibility of temporal control over protein expression. Such compounds are capable of inducing the inactivation of a protein of interest upon addition to cells or administration to an animal or human, and could be useful as biochemical reagents and lead to a new paradigm for the treatment of diseases by removing pathogenic or oncogenic proteins (Crews C, Chemistry &amp; Biology, 2010, 17(6):551-555; Schnnekloth J S Jr., Chembiochem, 2005, 6(0:40-46). 
     An ongoing need exists in the art for effective treatments for disease, especially hyperplasias and cancers, such as multiple myeloma. However, non-specific effects, and the inability to target and modulate certain classes of proteins altogether, such as transcription factors, remain as obstacles to the development of effective anti-cancer agents. As such, small molecule therapeutic agents that leverage E3 ligase mediated protein degradation to target cancer-associated proteins such as interleukin-1 receptor-associated kinases (“IRAK”) hold promise as therapeutic agents. Accordingly, there remains a need to find bifunctional compounds that are IRAK degraders useful as therapeutic agents. 
     SUMMARY OF THE INVENTION 
     The present application relates novel bifunctional compounds, which function to recruit IRAK kinases to E3 Ubiquitin Ligase for degradation, and methods of preparation and uses thereof. In particular, the present disclosure provides bifunctional compounds, which find utility as modulators of targeted ubiquitination of IRAK kinases, which are then degraded and/or otherwise inhibited by the bifunctional compounds as described herein. An advantage of the compounds provided herein is that a broad range of pharmacological activities is possible, consistent with the degradation/inhibition of IRAK kinases. In addition, the description provides methods of using an effective amount of the compounds as described herein for the treatment or amelioration of a disease condition, such as cancer, e.g., multiple myeloma. 
     The present application further relates to bifunctional molecules, including bifunctional molecules that link a cereblon-binding moiety to a ligand that binds IRAK kinases that are effective for the modulation of targeted ubiquitination. Such compounds have the general structure: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein each variable is as defined and described herein. 
     It has now been found that compounds of this invention, and pharmaceutically acceptable compositions thereof, targeted degradation of IRAK kinases through the use of bifunctional molecules, including bifunctional molecules that link a cereblon-binding moiety to a ligand that binds IRAK kinases having the following general formula I, I′, or II: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein each variable is as defined and described herein. 
     Compounds of the present invention, and pharmaceutically acceptable compositions thereof, are useful for treating a variety of diseases, disorders or conditions, associated with regulation of signaling pathways implicating IRAK kinases. Such diseases, disorders, or conditions include those described herein. 
     Compounds provided by this invention are also useful for the study of IRAK enzymes in biological and pathological phenomena; the study of intracellular signal transduction pathways occurring in bodily tissues; and the comparative evaluation of new IRAK inhibitors or IRAK degraders or other regulators of kinases, signaling pathways, and cytokine levels in vitro or in vivo. 
    
    
     DETAILED DESCRIPTION OF CERTAIN EMBODIMENTS 
     1. General Description of Certain Embodiments of the Invention 
     Compounds of the present invention, and compositions thereof, are useful as degraders and/or inhibitors of one or more IRAK protein kinases. In some embodiments, a provided compound degrades and/or inhibits IRAK-1/2/3/4. 
     In certain embodiments, the present invention provides a compound of formula I: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein: 
         X 1  is a covalent bond, —CH 2 —, —O—, —NR—, —CF 2 —, 
       
    
     
       
         
         
             
             
         
       
         
         X 2  and X 3  are independently —CH 2 —, —C(O)—, —C(S)—, or 
       
    
     
       
         
         
             
             
         
       
         
         Z 1  and Z 2  are independently a carbon atom or a nitrogen atom; 
         Ring A x  is a fused ring selected from benzo or a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
         L x  is a covalent bond or a C 1-3  bivalent straight or branched saturated or unsaturated hydrocarbon chain wherein 1-2 methylene units of the chain are independently and optionally replaced with —O—, —S—, —C(O)—, —C(S)—, —CR 2 —, —CRF—, —CF 2 —, —NR—, or —S(O) 2 —; 
         each R x  is independently selected from hydrogen, deuterium, R z , halogen, —CN, —NO 2 , —OR, —SR, —NR 2 , —S(O) 2 R, —S(O) 2 NR 2 , —S(O)R, —CF 2 R, —CF 3 , —CR 2 (OR), —CR 2 (NR 2 ), —C(O)R, —C(O)OR, —C(O)NR 2 , —C(O)N(R)OR, —OC(O)R, —OC(O)NR 2 , —C(S)NR 2 , —N(R)C(O)OR, —N(R)C(O)R, —N(R)C(O)NR 2 , —N(R)S(O) 2 R, —OP(O)R 2 , —OP(O)(OR) 2 , —OP(O)(OR)NR 2 , —OP(O)(NR 2 ) 2 , —Si(OR)R 2 , and —SiR 3 ; or
       two R x  groups are optionally taken together to form an optionally substituted 5-8 membered partially unsaturated or aryl fused ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur;   
     
         each R is independently selected from hydrogen, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, a 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or:
       two R groups on the same carbon or nitrogen are optionally taken together with their intervening atoms to form an optionally substituted 4-7 membered saturated, partially unsaturated, or heteroaryl ring having 0-3 heteroatoms, in addition to the carbon or nitrogen, independently selected from nitrogen, oxygen, and sulfur;   
     
         R y  is selected from 
       
    
     
       
         
         
             
             
         
       
         
          or hydrogen; 
         Ring B x  is phenyl, a 4-10 membered saturated or partially unsaturated mono- or bicyclic carbocyclic or heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, wherein Ring B x  is further optionally substituted with 1-2 oxo groups; 
         each R w  is independently selected from hydrogen, deuterium, R z , halogen, —CN, —NO 2 , —OR, —SR, —NR 2 , —S(O) 2 R, —S(O) 2 NR 2 , —S(O)R, —CF 2 R, —CF 3 , —CR 2 (OR), —CR 2 (NR 2 ), —C(O)R, —C(O)OR, —C(O)NR 2 , —C(O)N(R)OR, —OC(O)R, —OC(O)NR 2 , —N(R)C(O)OR, —N(R)C(O)R, —N(R)C(O)NR 2 , —N(R)S(O) 2 R, —OP(O)R 2 , —OP(O)(OR) 2 , —OP(O)(OR)NR 2 , —OP(O)(NR 2 ) 2 , and —SiR 3 ; 
         each R z  is independently selected from an optionally substituted group selected from C 1-6  aliphatic, phenyl, a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
            is a single or double bond; 
         x is 0, 1, 2, 3 or 4; 
         w is 0, 1, 2, 3 or 4; 
         L is a covalent bond or a bivalent, saturated or unsaturated, straight or branched C 1-50  hydrocarbon chain, wherein 0-6 methylene units of L are independently replaced by —C(D)(H)—, —C(D) 2 -, —CRF—, —CF 2 —, -Cy-, —O—, —N(R)—, —Si(R) 2 —, —Si(OH)(R)—, —Si(OH) 2 —, —P(O)(OR)—, —P(O)(R)—, —P(O)(NR 2 )—, —S—, —OC(O)—, —C(O)O—, —C(O)—, —S(O)—, —S(O) 2 —, —N(R)S(O) 2 —, —S(O) 2 N(R)—, —N(R)C(O)—, —C(O)N(R)—, —OC(O)N(R)—, —N(R)C(O)O—, 
       
    
     
       
         
         
             
             
         
       
         
          wherein: 
         each -Cy- is independently an optionally substituted bivalent ring selected from phenylenyl, an 8-10 membered bicyclic arylenyl, a 4-7 membered saturated or partially unsaturated carbocyclylenyl, a 4-11 membered saturated or partially unsaturated spiro carbocyclylenyl, an 8-10 membered bicyclic saturated or partially unsaturated carbocyclylenyl, a 4-7 membered saturated or partially unsaturated heterocyclylenyl having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, a 4-11 membered saturated or partially unsaturated spiro heterocyclylenyl having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, an 8-10 membered bicyclic saturated or partially unsaturated heterocyclylenyl having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, a 5-6 membered heteroarylenyl having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or an 8-10 membered bicyclic heteroarylenyl having 1-5 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each p is independently 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10; and 
         IRAK is an IRAK binding moiety. 
       
    
     In certain embodiments, the present invention provides a compound of formula I′: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, wherein: 
         X 1  is —CR 2 —, —O—, —NR—, —CF 2 —, 
       
    
     
       
         
         
             
             
         
       
         
          —C(O)—, —C(S)—, or 
       
    
     
       
         
         
             
             
         
       
         
         X 2  and X 3  are independently —CH 2 —, —C(O)—, —C(S)—, —CR 2 C(O)—, or 
       
    
     
       
         
         
             
             
         
       
         
         Z 1  and Z 2  are independently a carbon atom or a nitrogen atom; 
         Ring A x  is a fused ring selected from benzo, a 4-6 membered saturated or partially unsaturated carbocyclic or heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
         L x  is a covalent bond or a C 1-3  bivalent straight or branched saturated or unsaturated hydrocarbon chain wherein 1-2 methylene units of the chain are independently and optionally replaced with —O—, —S—, —C(O)—, —C(S)—, —CR 2 —, —CRF—, —CF 2 —, —NR—, or —S(O) 2 —; 
         each R x  is independently selected from hydrogen, deuterium, R z , halogen, —CN, —NO 2 , —OR, —SR, —NR 2 , —S(O) 2 R, —S(O) 2 NR 2 , —S(O)R, —CFR 2 , —CF 2 R, —CF 3 , —CR 2 (OR), —CR 2 (NR 2 ), —C(O)R, —C(O)OR, —C(O)NR 2 , —C(O)N(R)OR, —OC(O)R, —OC(O)NR 2 , —C(S)NR 2 , —N(R)C(O)OR, —N(R)C(O)R, —N(R)C(O)NR 2 , —N(R)S(O) 2 R, —OP(O)R 2 , —OP(O)(OR) 2 , —OP(O)(OR)NR 2 , —OP(O)(NR 2 ) 2 , —Si(OR)R 2 , and —SiR 3 ; or
       two R x  groups are optionally taken together to form an optionally substituted 5-8 membered partially unsaturated or aryl fused ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur;   
     
         each R is independently selected from hydrogen, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, a 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or:
       two R groups on the same carbon or nitrogen are optionally taken together with their intervening atoms to form an optionally substituted 4-7 membered saturated, partially unsaturated, or heteroaryl ring having 0-3 heteroatoms, in addition to the carbon or nitrogen, independently selected from nitrogen, oxygen, and sulfur;   
     
         R y  is selected from 
       
    
     
       
         
         
             
             
         
       
         
          or hydrogen; 
         Ring B x  is phenyl, a 4-10 membered saturated or partially unsaturated mono- or bicyclic carbocyclic or heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, wherein Ring B x  is further optionally substituted with 1-2 oxo groups; 
         each R w  is independently selected from hydrogen, deuterium, R z , halogen, —CN, —NO 2 , —OR, —SR, —NR 2 , —S(O) 2 R, —S(O) 2 NR 2 , —S(O)R, —CFR 2 , —CF 2 R, —CF 3 , —CR 2 (OR), —CR 2 (NR 2 ), —C(O)R, —C(O)OR, —C(O)NR 2 , —C(O)N(R)OR, —OC(O)R, —OC(O)NR 2 , —N(R)C(O)OR, —N(R)C(O)R, —N(R)C(O)NR 2 , —N(R)S(O) 2 R, —OP(O)R 2 , —OP(O)(OR) 2 , —OP(O)(OR)NR 2 , —OP(O)(NR 2 ) 2 , and —SiR 3 ; 
         each R z  is independently selected from an optionally substituted group selected from C 1-6  aliphatic, phenyl, a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
            is a single or double bond; 
         w is 0, 1, 2, 3 or 4; 
         x is 0, 1, 2, 3 or 4; and 
         y is 0, 1, or 2. 
       
    
     In certain embodiments, the present invention provides a compound of formula II: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof wherein L and IRAK are as defined above and described in embodiments herein, wherein:
     X 1  and X 4  are independently a covalent bond, —CR 2 —, —O—, —NR—, —C(O)—, —CF 2 —, or   

     
       
         
         
             
             
         
       
         
         X 2  and X 3  are independently —CR 2 —, —C(O)—, —C(S)—, or 
       
    
     
       
         
         
             
             
         
       
         
         Ring C x  is a spiro-fused ring selected from a 4-10 membered saturated or partially unsaturated mono- or bicyclic carbocyclic or heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, wherein Ring C is optionally further substituted with 1-2 oxo groups; 
         L x  is a covalent bond or a C 1-3  bivalent straight or branched saturated or unsaturated hydrocarbon chain wherein 1-2 methylene units of the chain are independently and optionally replaced with —O—, —S—, —C(O)—, —C(S)—, —CR 2 —, —CRF—, —CF 2 —, —NR—, or —S(O) 2 —; 
         each R x  is independently selected from hydrogen, deuterium, R z , halogen, —CN, —NO 2 , —OR, —SR, —NR 2 , —S(O) 2 R, —S(O) 2 NR 2 , —S(O)R, —CFR 2 , —CF 2 R, —CF 3 , —CR 2 (OR), —CR 2 (NR 2 ), —C(O)R, —C(O)OR, —C(O)NR 2 , —C(O)N(R)OR, —OC(O)R, —OC(O)NR 2 , —C(S)NR 2 , —N(R)C(O)OR, —N(R)C(O)R, —N(R)C(O)NR 2 , —N(R)S(O) 2 R, —OP(O)R 2 , —OP(O)(OR) 2 , —OP(O)(OR)NR 2 , —OP(O)(NR 2 ) 2 , —Si(OR)R 2 , and —SiR 3 ; or
       two R x  groups are optionally taken together to form an optionally substituted 5-8 membered partially unsaturated or aryl fused ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur;   
     
         each R is independently selected from hydrogen, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, a 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or:
       two R groups on the same carbon or nitrogen are optionally taken together with their intervening atoms to form an optionally substituted 4-7 membered saturated, partially unsaturated, or heteroaryl ring having 0-3 heteroatoms, in addition to the carbon or nitrogen, independently selected from nitrogen, oxygen, and sulfur;   
     
         R y  is selected from 
       
    
     
       
         
         
             
             
         
       
         
          or hydrogen; 
         Ring B x  is phenyl, a 4-10 membered saturated or partially unsaturated mono- or bicyclic carbocyclic or heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, wherein Ring B is further optionally substituted with 1-2 oxo groups; 
         each R w  is independently selected from hydrogen, deuterium, R z , halogen, —CN, —NO 2 , —OR, —SR, —NR 2 , —S(O) 2 R, —S(O) 2 NR 2 , —S(O)R, —CFR 2 , —CF 2 R, —CF 3 , —CR 2 (OR), —CR 2 (NR 2 ), —C(O)R, —C(O)OR, —C(O)NR 2 , —C(O)N(R)OR, —OC(O)R, —OC(O)NR 2 , —N(R)C(O)OR, —N(R)C(O)R, —N(R)C(O)NR 2 , —N(R)S(O) 2 R, —OP(O)R 2 , —OP(O)(OR) 2 , —OP(O)(OR)NR 2 , —OP(O)(NR 2 ) 2 , and —SiR 3 ; 
         each R z  is independently selected from an optionally substituted group selected from C 1-6  aliphatic, phenyl, a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
         x is 0, 1, 2, 3 or 4; and 
         w is 0, 1, 2, 3 or 4. 
       
    
     2. Compounds and Definitions 
     Compounds of the present invention include those described generally herein, and are further illustrated by the classes, subclasses, and species disclosed herein. As used herein, the following definitions shall apply unless otherwise indicated. For purposes of this invention, the chemical elements are identified in accordance with the Periodic Table of the Elements, CAS version, Handbook of Chemistry and Physics, 75 th  Ed. Additionally, general principles of organic chemistry are described in “Organic Chemistry”, Thomas Sorrell, University Science Books, Sausalito: 1999, and “March&#39;s Advanced Organic Chemistry”, 5 th  Ed., Ed.: Smith, M. B. and March, J., John Wiley &amp; Sons, New York: 2001, the entire contents of which are hereby incorporated by reference. 
     The term “aliphatic” or “aliphatic group”, as used herein, means a straight-chain (i.e., unbranched) or branched, substituted or unsubstituted hydrocarbon chain that is completely saturated or that contains one or more units of unsaturation, or a monocyclic hydrocarbon or bicyclic hydrocarbon that is completely saturated or that contains one or more units of unsaturation, but which is not aromatic (also referred to herein as “carbocycle,” “cycloaliphatic” or “cycloalkyl”), that has a single point of attachment to the rest of the molecule. Unless otherwise specified, aliphatic groups contain 1-6 aliphatic carbon atoms. In some embodiments, aliphatic groups contain 1-5 aliphatic carbon atoms. In other embodiments, aliphatic groups contain 1-4 aliphatic carbon atoms. In still other embodiments, aliphatic groups contain 1-3 aliphatic carbon atoms, and in yet other embodiments, aliphatic groups contain 1-2 aliphatic carbon atoms. In some embodiments, “cycloaliphatic” (or “carbocycle” or “cycloalkyl”) refers to a monocyclic C 3 -C 6  hydrocarbon that is completely saturated or that contains one or more units of unsaturation, but which is not aromatic, that has a single point of attachment to the rest of the molecule. Suitable aliphatic groups include, but are not limited to, linear or branched, substituted or unsubstituted alkyl, alkenyl, alkynyl groups and hybrids thereof such as (cycloalkyl)alkyl, (cycloalkenyl)alkyl or (cycloalkyl)alkenyl. 
     As used herein, the term “bridged bicyclic” refers to any bicyclic ring system, i.e. carbocyclic or heterocyclic, saturated or partially unsaturated, having at least one bridge. As defined by IUPAC, a “bridge” is an unbranched chain of atoms or an atom or a valence bond connecting two bridgeheads, where a “bridgehead” is any skeletal atom of the ring system which is bonded to three or more skeletal atoms (excluding hydrogen). In some embodiments, a bridged bicyclic group has 7-12 ring members and 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur. Such bridged bicyclic groups are well known in the art and include those groups set forth below where each group is attached to the rest of the molecule at any substitutable carbon or nitrogen atom. Unless otherwise specified, a bridged bicyclic group is optionally substituted with one or more substituents as set forth for aliphatic groups. Additionally or alternatively, any substitutable nitrogen of a bridged bicyclic group is optionally substituted. Exemplary bridged bicyclics include: 
     
       
         
         
             
             
         
       
     
     The term “lower alkyl” refers to a C 1-4  straight or branched alkyl group. Exemplary lower alkyl groups are methyl, ethyl, propyl, isopropyl, butyl, isobutyl, and tert-butyl. 
     The term “lower haloalkyl” refers to a C 1-4  straight or branched alkyl group that is substituted with one or more halogen atoms. 
     The term “heteroatom” means one or more of oxygen, sulfur, nitrogen, phosphorus, or silicon (including, any oxidized form of nitrogen, sulfur, phosphorus, or silicon; the quaternized form of any basic nitrogen or; a substitutable nitrogen of a heterocyclic ring, for example N (as in 3,4-dihydro-2H-pyrrolyl), NH (as in pyrrolidinyl) or NR +  (as in N-substituted pyrrolidinyl)). 
     The term “unsaturated,” as used herein, means that a moiety has one or more units of unsaturation. 
     As used herein, the term “bivalent C 1-8  (or C 1-6 ) saturated or unsaturated, straight or branched, hydrocarbon chain”, refers to bivalent alkylene, alkenylene, and alkynylene chains that are straight or branched as defined herein. 
     The term “alkylene” refers to a bivalent alkyl group. An “alkylene chain” is a polymethylene group, i.e., —(CH 2 ) n —, wherein n is a positive integer, preferably from 1 to 6, from 1 to 4, from 1 to 3, from 1 to 2, or from 2 to 3. A substituted alkylene chain is a polymethylene group in which one or more methylene hydrogen atoms are replaced with a substituent. Suitable substituents include those described below for a substituted aliphatic group. 
     The term “alkenylene” refers to a bivalent alkenyl group. A substituted alkenylene chain is a polymethylene group containing at least one double bond in which one or more hydrogen atoms are replaced with a substituent. Suitable substituents include those described below for a substituted aliphatic group. 
     As used herein, the term “cyclopropylenyl” refers to a bivalent cyclopropyl group of the following structure: 
     
       
         
         
             
             
         
       
     
     The term “halogen” means F, Cl, Br, or I. 
     The term “aryl” used alone or as part of a larger moiety as in “aralkyl,” “aralkoxy,” or “aryloxyalkyl,” refers to monocyclic or bicyclic ring systems having a total of five to fourteen ring members, wherein at least one ring in the system is aromatic and wherein each ring in the system contains 3 to 7 ring members. The term “aryl” may be used interchangeably with the term “aryl ring.” In certain embodiments of the present invention, “aryl” refers to an aromatic ring system which includes, but not limited to, phenyl, biphenyl, naphthyl, anthracyl and the like, which may bear one or more substituents. Also included within the scope of the term “aryl,” as it is used herein, is a group in which an aromatic ring is fused to one or more non-aromatic rings, such as indanyl, phthalimidyl, naphthimidyl, phenanthridinyl, or tetrahydronaphthyl, and the like. 
     The terms “heteroaryl” and “heteroar-,” used alone or as part of a larger moiety, e.g., “heteroaralkyl,” or “heteroaralkoxy,” refer to groups having 5 to 10 ring atoms, preferably 5, 6, or 9 ring atoms; having 6, 10, or 14 π electrons shared in a cyclic array; and having, in addition to carbon atoms, from one to five heteroatoms. The term “heteroatom” refers to nitrogen, oxygen, or sulfur, and includes any oxidized form of nitrogen or sulfur, and any quaternized form of a basic nitrogen. Heteroaryl groups include, without limitation, thienyl, furanyl, pyrrolyl, imidazolyl, pyrazolyl, triazolyl, tetrazolyl, oxazolyl, isoxazolyl, oxadiazolyl, thiazolyl, isothiazolyl, thiadiazolyl, pyridyl, pyridazinyl, pyrimidinyl, pyrazinyl, indolizinyl, purinyl, naphthyridinyl, and pteridinyl. The terms “heteroaryl” and “heteroar-”, as used herein, also include groups in which a heteroaromatic ring is fused to one or more aryl, cycloaliphatic, or heterocyclyl rings, where the radical or point of attachment is on the heteroaromatic ring. Nonlimiting examples include indolyl, isoindolyl, benzothienyl, benzofuranyl, dibenzofuranyl, indazolyl, benzimidazolyl, benzthiazolyl, quinolyl, isoquinolyl, cinnolinyl, phthalazinyl, quinazolinyl, quinoxalinyl, 4H-quinolizinyl, carbazolyl, acridinyl, phenazinyl, phenothiazinyl, phenoxazinyl, tetrahydroquinolinyl, tetrahydroisoquinolinyl, and pyrido[2,3-b]-1,4-oxazin-3(4H)-one. A heteroaryl group may be mono- or bicyclic. The term “heteroaryl” may be used interchangeably with the terms “heteroaryl ring,” “heteroaryl group,” or “heteroaromatic,” any of which terms include rings that are optionally substituted. The term “heteroaralkyl” refers to an alkyl group substituted by a heteroaryl, wherein the alkyl and heteroaryl portions independently are optionally substituted. 
     As used herein, the terms “heterocycle,” “heterocyclyl,” “heterocyclic radical,” and “heterocyclic ring” are used interchangeably and refer to a stable 5- to 7-membered monocyclic or 7-10-membered bicyclic heterocyclic moiety that is either saturated or partially unsaturated, and having, in addition to carbon atoms, one or more, preferably one to four, heteroatoms, as defined above. When used in reference to a ring atom of a heterocycle, the term “nitrogen” includes a substituted nitrogen. As an example, in a saturated or partially unsaturated ring having 0-3 heteroatoms selected from oxygen, sulfur or nitrogen, the nitrogen may be N (as in 3,4-dihydro-2H-pyrrolyl), NH (as in pyrrolidinyl), or  + NR (as in N-substituted pyrrolidinyl). 
     A heterocyclic ring can be attached to its pendant group at any heteroatom or carbon atom that results in a stable structure and any of the ring atoms can be optionally substituted. Examples of such saturated or partially unsaturated heterocyclic radicals include, without limitation, tetrahydrofuranyl, tetrahydrothiophenyl pyrrolidinyl, piperidinyl, pyrrolinyl, tetrahydroquinolinyl, tetrahydroisoquinolinyl, decahydroquinolinyl, oxazolidinyl, piperazinyl, dioxanyl, dioxolanyl, di azepinyl, oxazepinyl, thiazepinyl, morpholinyl, and quinuclidinyl. The terms “heterocycle,” “heterocyclyl,” “heterocyclyl ring,” “heterocyclic group,” “heterocyclic moiety,” and “heterocyclic radical,” are used interchangeably herein, and also include groups in which a heterocyclyl ring is fused to one or more aryl, heteroaryl, or cycloaliphatic rings, such as indolinyl, 3H-indolyl, chromanyl, phenanthridinyl, or tetrahydroquinolinyl. A heterocyclyl group may be monocyclic, bicyclic, bridged bicyclic, or spirocyclic. The term “heterocyclylalkyl” refers to an alkyl group substituted by a heterocyclyl, wherein the alkyl and heterocyclyl portions independently are optionally substituted. 
     As used herein, the term “partially unsaturated” refers to a ring moiety that includes at least one double or triple bond. The term “partially unsaturated” is intended to encompass rings having multiple sites of unsaturation, but is not intended to include aryl or heteroaryl moieties, as herein defined. 
     As described herein, compounds of the invention may contain “optionally substituted” moieties. In general, the term “substituted,” whether preceded by the term “optionally” or not, means that one or more hydrogens of the designated moiety are replaced with a suitable substituent. Unless otherwise indicated, an “optionally substituted” group may have a suitable substituent at each substitutable position of the group, and when more than one position in any given structure may be substituted with more than one substituent selected from a specified group, the substituent may be either the same or different at every position. Combinations of substituents envisioned by this invention are preferably those that result in the formation of stable or chemically feasible compounds. The term “stable,” as used herein, refers to compounds that are not substantially altered when subjected to conditions to allow for their production, detection, and, in certain embodiments, their recovery, purification, and use for one or more of the purposes disclosed herein. 
     Suitable monovalent substituents on a substitutable carbon atom of an “optionally substituted” group are independently halogen; —(CH 2 ) 0-4 R ◯ ; —(CH 2 ) 0-4 OR ◯ ; —O(CH 2 ) 0-4 R ◯ , —O—(CH 2 ) 0-4 C(O)OR ◯ ; —(CH 2 ) 0-4 CH(OR ◯ ) 2 ; —(CH 2 ) 0-4 SR ◯ ; —(CH 2 ) 0-4 Ph, which may be substituted with R ◯ ; —(CH 2 ) 0-4 O(CH 2 ) 0-1 Ph which may be substituted with R ◯ ; —CH═CHPh, which may be substituted with R ◯ ; —(CH 2 ) 0-4 O(CH 2 ) 0-1 -pyridyl which may be substituted with R ◯ ; —NO 2 ; —CN; —N 3 ; —(CH 2 ) 0-4 N(R ◯ ) 2 ; —(CH 2 ) 0-4 N(R ◯ )C(O)R ◯ ; —N(R ◯ )C(S)R ◯ ; —(CH 2 ) 0-4 N(R ◯ )C(O)NR ◯   2 ; —N(R ◯ )C(S)NR ◯   2 ; —(CH 2 ) 0-4 N(R ◯ )C(O)OR ◯ ; —N(R ◯ )N(R ◯ )C(O)R ◯ ; —N(R ◯ )N(R ◯ )C(O)NR ◯   2 ; —N(R ◯ )N(R ◯ )C(O)OR ◯ ; —(CH 2 ) 0-4 C(O)R ◯ ; —C(S)R ◯ ; —(CH 2 ) 0-4 C(O)OR ◯ ; —(CH 2 ) 0-4 C(O)SR ◯ ; —(CH 2 ) 0-4 C(O)OSiR ◯   3 ; —(CH 2 ) 0-4 OC(O)R ◯ ; —OC(O)(CH 2 ) 0-4 SR—, SC(S)SR ◯ ; —(CH 2 ) 0-4 SC(O)R ◯ ; —(CH 2 ) 0-4 C(O)NR ◯ ; —C(S)NR ◯   2 ; —C(S)SR ◯ ; —SC(S)SR ◯ , —(CH 2 ) 0-4 OC(O)NR ◯   2 ; —C(O)N(OR ◯ )R ◯ ; —C(O)C(O)R ◯ ; —C(O)CH 2 C(O)R ◯ ; —C(NOR ◯ )R ◯ ; —(CH 2 ) 0-4 SSR ◯ ; —(CH 2 ) 0-4 S(O) 2 R ◯ ; —(CH 2 ) 0-4 S(O) 2 OR ◯ ; —(CH 2 ) 0-4 OS(O) 2 R ◯ ; —S(O) 2 NR ◯   2 ; —(CH 2 ) 0-4 S(O)R ◯ ; —N(R ◯ )S(O) 2 NR ◯   2 ; —N(R ◯ )S(O) 2 R ◯ ; —N(OR ◯ )R ◯ ; —C(NH)NR ◯   2 ; —P(O) 2 R ◯ ; —P(O)R ◯   2 ; —OP(O)R ◯   2 ; —OP(O)(OR ◯ ) 2 ; SiR ◯   3 ; —(C 1-4  straight or branched alkylene)O—N(R ◯ ) 2 ; or —(C 1-4  straight or branched alkylene)C(O)O—N(R ◯ ) 2 , wherein each R ◯  may be substituted as defined below and is independently hydrogen, C 1-6  aliphatic, —CH 2 Ph, —O(CH 2 ) 0-1 Ph, —CH 2 -(5-6 membered heteroaryl ring), or a 5-6-membered saturated, partially unsaturated, or aryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or, notwithstanding the definition above, two independent occurrences of R ◯ , taken together with their intervening atom(s), form a 3-12-membered saturated, partially unsaturated, or aryl mono- or bicyclic ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, which may be substituted as defined below. 
     Suitable monovalent substituents on R ◯  (or the ring formed by taking two independent occurrences of R ◯  together with their intervening atoms), are independently halogen, —(CH 2 ) 0-2 R ● , -(haloR ● ), —(CH 2 ) 0-2 OH, —(CH 2 ) 0-2 OR*, —(CH 2 ) 0-2 CH(OR ● ) 2 ; —O(haloR ● ), —CN, —N 3 , —(CH 2 ) 0-2 C(O)R ● , —(CH 2 ) 0-2 C(O)OH, —(CH 2 ) 0-2 C(O)OR ● , —(CH 2 ) 0-2 SR ● , —(CH 2 ) 0-2 SH, —(CH 2 ) 0-2 NH 2 , —(CH 2 ) 0-2 NHR ● , —(CH 2 ) 0-2 NR ●   2 , —NO 2 , —SiR ●   3 , —OSiR ●   3 , —C(O)SR ● , —(C 1-4  straight or branched alkylene)C(O)OR ● , or —SSR ●  wherein each R ●  is unsubstituted or where preceded by “halo” is substituted only with one or more halogens, and is independently selected from C 1-4  aliphatic, —CH 2 Ph, —O(CH 2 ) 0-1 Ph, or a 5-6-membered saturated, partially unsaturated, or aryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur. Suitable divalent substituents on a saturated carbon atom of R ◯  include ═O and ═S. 
     Suitable divalent substituents on a saturated carbon atom of an “optionally substituted” group include the following: ═O, ═S, ═NNR* 2 , ═NNHC(O)R*, ═NNHC(O)OR*, ═NNHS(O) 2 R*, ═NR*, ═NOR*, —O(C(R* 2 )) 2-3 O—, or —S(C(R* 2 )) 2-3 S—, wherein each independent occurrence of R* is selected from hydrogen, C 1-6  aliphatic which may be substituted as defined below, or an unsubstituted 5-6-membered saturated, partially unsaturated, or aryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur. Suitable divalent substituents that are bound to vicinal substitutable carbons of an “optionally substituted” group include: —O(CR* 2 ) 2-3 O—, wherein each independent occurrence of R* is selected from hydrogen, C 1-6  aliphatic which may be substituted as defined below, or an unsubstituted 5-6-membered saturated, partially unsaturated, or aryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur. 
     Suitable substituents on the aliphatic group of R* include halogen, —R ● , -(haloR ● ), —OH, —OR ● , —O(haloR ● ), —CN, —C(O)OH, —C(O)OR ● , —NH 2 , —NHR ● , —NR ●   2 , or —NO 2 , wherein each R ●  is unsubstituted or where preceded by “halo” is substituted only with one or more halogens, and is independently C 1-4  aliphatic, —CH 2 Ph, —O(CH 2 ) 0-1 Ph, or a 5-6-membered saturated, partially unsaturated, or aryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur. 
     Suitable substituents on a substitutable nitrogen of an “optionally substituted” group include —R † , —NR †   2 , —C(O)R † , —C(O)ORT, —C(O)C(O)R † , —C(O)CH 2 C(O)R † , —S(O) 2 R † , —S(O) 2 NR †   2 , —C(S)NR †   2 , —C(NH)NR †   2 , or —N(R † )S(O) 2 R † ; wherein each R †  is independently hydrogen, C 1-6  aliphatic which may be substituted as defined below, unsubstituted —OPh, or an unsubstituted 5-6-membered saturated, partially unsaturated, or aryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or, notwithstanding the definition above, two independent occurrences of R † , taken together with their intervening atom(s) form an unsubstituted 3-12-membered saturated, partially unsaturated, or aryl mono- or bicyclic ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur. 
     Suitable substituents on the aliphatic group of R are independently halogen, —R ● , -(haloR ● ), —OH, —OR ● , —O(haloR ● ), —CN, —C(O)OH, —C(O)OR ● , —NH 2 , —NHR, —NR ●   2 , or —NO 2 , wherein each R ●  is unsubstituted or where preceded by “halo” is substituted only with one or more halogens, and is independently C 1-4  aliphatic, —CH 2 Ph, —O(CH 2 ) 0-1 Ph, or a 5-6-membered saturated, partially unsaturated, or aryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur. 
     As used herein, the term “provided compound” refers to any genus, subgenus, and/or species set forth herein. 
     As used herein, the term “pharmaceutically acceptable salt” refers to those salts which are, within the scope of sound medical judgment, suitable for use in contact with the tissues of humans and lower animals without undue toxicity, irritation, allergic response and the like, and are commensurate with a reasonable benefit/risk ratio. Pharmaceutically acceptable salts are well known in the art. For example, S. M. Berge et al., describe pharmaceutically acceptable salts in detail in J. Pharmaceutical Sciences, 1977, 66, 1-19, incorporated herein by reference. Pharmaceutically acceptable salts of the compounds of this invention include those derived from suitable inorganic and organic acids and bases. Examples of pharmaceutically acceptable, nontoxic acid addition salts are salts of an amino group formed with inorganic acids such as hydrochloric acid, hydrobromic acid, phosphoric acid, sulfuric acid and perchloric acid or with organic acids such as acetic acid, oxalic acid, maleic acid, tartaric acid, citric acid, succinic acid or malonic acid or by using other methods used in the art such as ion exchange. Other pharmaceutically acceptable salts include adipate, alginate, ascorbate, aspartate, benzenesulfonate, benzoate, bisulfate, borate, butyrate, camphorate, camphorsulfonate, citrate, cyclopentanepropionate, digluconate, dodecylsulfate, ethanesulfonate, formate, fumarate, glucoheptonate, glycerophosphate, gluconate, hemisulfate, heptanoate, hexanoate, hydroiodide, 2-hydroxy-ethanesulfonate, lactobionate, lactate, laurate, lauryl sulfate, malate, maleate, malonate, methanesulfonate, 2-naphthalenesulfonate, nicotinate, nitrate, oleate, oxalate, palmitate, pamoate, pectinate, persulfate, 3-phenylpropionate, phosphate, pivalate, propionate, stearate, succinate, sulfate, tartrate, thiocyanate, p-toluenesulfonate, undecanoate, valerate salts, and the like. 
     Salts derived from appropriate bases include alkali metal, alkaline earth metal, ammonium and N + (C 1-4  alkyl) 4  salts. Representative alkali or alkaline earth metal salts include sodium, lithium, potassium, calcium, magnesium, and the like. Further pharmaceutically acceptable salts include, when appropriate, nontoxic ammonium, quaternary ammonium, and amine cations formed using counterions such as halide, hydroxide, carboxylate, sulfate, phosphate, nitrate, loweralkyl sulfonate and aryl sulfonate. 
     Unless otherwise stated, structures depicted herein are also meant to include all isomeric (e.g., enantiomeric, diastereomeric, and geometric (or conformational)) forms of the structure; for example, the R and S configurations for each asymmetric center, Z and E double bond isomers, and Z and E conformational isomers. Therefore, single stereochemical isomers as well as enantiomeric, diastereomeric, and geometric (or conformational) mixtures of the present compounds are within the scope of the invention. Unless otherwise stated, all tautomeric forms of the compounds of the invention are within the scope of the invention. Additionally, unless otherwise stated, structures depicted herein are also meant to include compounds that differ only in the presence of one or more isotopically enriched atoms. For example, compounds having the present structures including the replacement of hydrogen by deuterium or tritium, or the replacement of a carbon by a  13 C- or  14 C-enriched carbon are within the scope of this invention. Such compounds are useful, for example, as analytical tools, as probes in biological assays, or as therapeutic agents in accordance with the present invention 
     As used herein, the term “inhibitor” is defined as a compound that binds to and/or inhibits an IRAK kinase with measurable affinity. In certain embodiments, an inhibitor has an IC 50  and/or binding constant of less than about 50 μM, less than about 1 μM, less than about 500 nM, less than about 100 nM, less than about 10 nM, or less than about 1 nM. 
     As used herein, the term “degrader” is defined as a heterobifunctional compound that binds to and/or inhibits both an IRAK kinase and an E3 ligase with measurable affinity resulting in the ubiqitination and subsequent degradation of the IRAK kinase. In certain embodiments, a degrader has an DC 50  of less than about 50 μM, less than about 1 μM, less than about 500 nM, less than about 100 nM, less than about 10 nM, or less than about 1 nM. 
     A compound of the present invention may be tethered to a detectable moiety. It will be appreciated that such compounds are useful as imaging agents. One of ordinary skill in the art will recognize that a detectable moiety may be attached to a provided compound via a suitable substituent. As used herein, the term “suitable substituent” refers to a moiety that is capable of covalent attachment to a detectable moiety. Such moieties are well known to one of ordinary skill in the art and include groups containing, e.g., a carboxylate moiety, an amino moiety, a thiol moiety, or a hydroxyl moiety, to name but a few. It will be appreciated that such moieties may be directly attached to a provided compound or via a tethering group, such as a bivalent saturated or unsaturated hydrocarbon chain. In some embodiments, such moieties may be attached via click chemistry. In some embodiments, such moieties may be attached via a 1,3-cycloaddition of an azide with an alkyne, optionally in the presence of a copper catalyst. Methods of using click chemistry are known in the art and include those described by Rostovtsev et al., Angew. Chem. Int. Ed. 2002, 41:2596-99 and Sun et al., Bioconjugate Chem., 2006, 17:52-57. 
     As used herein, the term “detectable moiety” is used interchangeably with the term “label” and relates to any moiety capable of being detected, e.g., primary labels and secondary labels. Primary labels, such as radioisotopes (e.g., tritium,  32 P,  33 P,  35 S, or  14 C), mass-tags, and fluorescent labels are signal generating reporter groups which can be detected without further modifications. Detectable moieties also include luminescent and phosphorescent groups. 
     The term “secondary label” as used herein refers to moieties such as biotin and various protein antigens that require the presence of a second intermediate for production of a detectable signal. For biotin, the secondary intermediate may include streptavidin-enzyme conjugates. For antigen labels, secondary intermediates may include antibody-enzyme conjugates. Some fluorescent groups act as secondary labels because they transfer energy to another group in the process of nonradiative fluorescent resonance energy transfer (FRET), and the second group produces the detected signal. 
     The terms “fluorescent label”, “fluorescent dye”, and “fluorophore” as used herein refer to moieties that absorb light energy at a defined excitation wavelength and emit light energy at a different wavelength. Examples of fluorescent labels include, but are not limited to: Alexa Fluor dyes (Alexa Fluor 350, Alexa Fluor 488, Alexa Fluor 532, Alexa Fluor 546, Alexa Fluor 568, Alexa Fluor 594, Alexa Fluor 633, Alexa Fluor 660 and Alexa Fluor 680), AMCA, AMCA-S, BODIPY dyes (BODIPY FL, BODIPY R6G, BODIPY TMR, BODIPY TR, BODIPY 530/550, BODIPY 558/568, BODIPY 564/570, BODIPY 576/589, BODIPY 581/591, BODIPY 630/650, BODIPY 650/665), Carboxyrhodamine 6G, carboxy-X-rhodamine (ROX), Cascade Blue, Cascade Yellow, Coumarin 343, Cyanine dyes (Cy3, Cy5, Cy3.5, Cy5.5), Dansyl, Dapoxyl, Dialkylaminocoumarin, 4′,5′-Dichloro-2′,7′-dimethoxy-fluorescein, DM-NERF, Eosin, Erythrosin, Fluorescein, FAM, Hydroxycoumarin, IRDyes (IRD40, IRD 700, IRD 800), JOE, Lissamine rhodamine B, Marina Blue, Methoxycoumarin, Naphthofluorescein, Oregon Green 488, Oregon Green 500, Oregon Green 514, Pacific Blue, PyMPO, Pyrene, Rhodamine B, Rhodamine 6G, Rhodamine Green, Rhodamine Red, Rhodol Green, 2′,4′,5′,7′-Tetra-bromosulfone-fluorescein, Tetramethyl-rhodamine (TMR), Carboxytetramethylrhodamine (TAMRA), Texas Red, Texas Red-X. 
     The term “mass-tag” as used herein refers to any moiety that is capable of being uniquely detected by virtue of its mass using mass spectrometry (MS) detection techniques. Examples of mass-tags include electrophore release tags such as N-[3-[4′-[(p-Methoxytetrafluorobenzyl)oxy]phenyl]-3-methylglyceronyl]isonipecotic Acid, 4′-[2,3,5,6-Tetrafluoro-4-(pentafluorophenoxyl)]methyl acetophenone, and their derivatives. The synthesis and utility of these mass-tags is described in U.S. Pat. Nos. 4,650,750, 4,709,016, 5,360,8191, 5,516,931, 5,602,273, 5,604,104, 5,610,020, and 5,650,270. Other examples of mass-tags include, but are not limited to, nucleotides, dideoxynucleotides, oligonucleotides of varying length and base composition, oligopeptides, oligosaccharides, and other synthetic polymers of varying length and monomer composition. A large variety of organic molecules, both neutral and charged (biomolecules or synthetic compounds) of an appropriate mass range (100-2000 Daltons) may also be used as mass-tags. 
     The terms “measurable affinity” and “measurably inhibit,” as used herein, means a measurable change in an IRAK protein kinase activity between a sample comprising a compound of the present invention, or composition thereof, and an IRAK protein kinase, and an equivalent sample comprising an IRAK protein kinase, in the absence of said compound, or composition thereof. 
     3. Description of Exemplary Embodiments 
     The compounds of the present application include bifunctional molecules that link a cereblon-binding moiety to a ligand that binds IRAK kinases having the following general structure: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein: 
         IRAK is an IRAK binding moiety capable of binding to one or more of IRAK-1, -2, -3, or -4; 
         L is a bivalent moiety that connects IRAK to LBM; and 
         LBM is a ligase binding moiety, such as a cereblon E3 ubiquitin ligase binding moiety. 
       
    
     Ligase Binding Moiety (LBM) 
     As described above, in certain embodiments, the present invention provides a compound of formula I: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, wherein: 
         X 1  is a covalent bond, —CH 2 —, —O—, —NR—, —CF 2 —, or 
       
    
     
       
         
         
             
             
         
       
         
         X 2  and X 3  are independently —CH 2 —, —C(O)—, —C(S)—, or 
       
    
     
       
         
         
             
             
         
       
         
         Z 1  and Z 2  are independently a carbon atom or a nitrogen atom; 
         Ring A x  is a fused ring selected from benzo or a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
         L x  is a covalent bond or a C 1-3  bivalent straight or branched saturated or unsaturated hydrocarbon chain wherein 1-2 methylene units of the chain are independently and optionally replaced with —O—, —S—, —C(O)—, —C(S)—, —CR 2 —, —CRF—, —CF 2 —, —NR—, or —S(O) 2 —; 
         each R x  is independently selected from hydrogen, deuterium, R z , halogen, —CN, —NO 2 , —OR, —SR, —NR 2 , —S(O) 2 R, —S(O) 2 NR 2 , —S(O)R, —CF 2 R, —CF 3 , —CR 2 (OR), —CR 2 (NR 2 ), —C(O)R, —C(O)OR, —C(O)NR 2 , —C(O)N(R)OR, —OC(O)R, —OC(O)NR 2 , —C(S)NR 2 , —N(R)C(O)OR, —N(R)C(O)R, —N(R)C(O)NR 2 , —N(R)S(O) 2 R, —OP(O)R 2 , —OP(O)(OR) 2 , —OP(O)(OR)NR 2 , —OP(O)(NR 2 ) 2 , —Si(OR)R 2 , and —SiR 3 ; or
       two R x  groups are optionally taken together to form an optionally substituted 5-8 membered partially unsaturated or aryl fused ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur;   
     
         each R is independently selected from hydrogen, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, a 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or:
       two R groups on the same carbon or nitrogen are optionally taken together with their intervening atoms to form an optionally substituted 4-7 membered saturated, partially unsaturated, or heteroaryl ring having 0-3 heteroatoms, in addition to the carbon or nitrogen, independently selected from nitrogen, oxygen, and sulfur;   
     
         R y  is selected from 
       
    
     
       
         
         
             
             
         
       
         
          or hydrogen; 
         Ring B x  is phenyl, a 4-10 membered saturated or partially unsaturated mono- or bicyclic carbocyclic or heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, wherein Ring B x  is further optionally substituted with 1-2 oxo groups; 
         each R w  is independently selected from hydrogen, deuterium, R z , halogen, —CN, —NO 2 , —OR, —SR, —NR 2 , —S(O) 2 R, —S(O) 2 NR 2 , —S(O)R, —CF 2 R, —CF 3 , —CR 2 (OR), —CR 2 (NR 2 ), —C(O)R, —C(O)OR, —C(O)NR 2 , —C(O)N(R)OR, —OC(O)R, —OC(O)NR 2 , —N(R)C(O)OR, —N(R)C(O)R, —N(R)C(O)NR 2 , —N(R)S(O) 2 R, —OP(O)R 2 , —OP(O)(OR) 2 , —OP(O)(OR)NR 2 , —OP(O)(NR 2 ) 2 , and —SiR 3 ; 
         each R z  is independently selected from an optionally substituted group selected from C 1-6  aliphatic, phenyl, a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
            is a single or double bond; 
         x is 0, 1, 2, 3 or 4; and 
         w is 0, 1, 2, 3 or 4. 
       
    
     As described above, in certain embodiments, the present invention provides a compound of formula I′: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, wherein: 
         X 1  is —CR 2 —, —O—, —NR—, —CF 2 —, 
       
    
     
       
         
         
             
             
         
       
         
          —C(O)—, —C(S)—, or 
       
    
     
       
         
         
             
             
         
       
         
         X 2  and X 3  are independently —CH 2 —, —C(O)—, —C(S)—, —CR 2 C(O)—, or 
       
    
     
       
         
         
             
             
         
       
         
         Z 1  and Z 2  are independently a carbon atom or a nitrogen atom; 
         Ring A x  is a fused ring selected from benzo, a 4-6 membered saturated or partially unsaturated carbocyclic or heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
         L x  is a covalent bond or a C 1-3  bivalent straight or branched saturated or unsaturated hydrocarbon chain wherein 1-2 methylene units of the chain are independently and optionally replaced with —O—, —S—, —C(O)—, —C(S)—, —CR 2 —, —CRF—, —CF 2 —, —NR—, or —S(O) 2 —; 
         each R x  is independently selected from hydrogen, deuterium, R z , halogen, —CN, —NO 2 , —OR, —SR, —NR 2 , —S(O) 2 R, —S(O) 2 NR 2 , —S(O)R, —CFR 2 , —CF 2 R, —CF 3 , —CR 2 (OR), —CR 2 (NR 2 ), —C(O)R, —C(O)OR, —C(O)NR 2 , —C(O)N(R)OR, —OC(O)R, —OC(O)NR 2 , —C(S)NR 2 , —N(R)C(O)OR, —N(R)C(O)R, —N(R)C(O)NR 2 , —N(R)S(O) 2 R, —OP(O)R 2 , —OP(O)(OR) 2 , —OP(O)(OR)NR 2 , —OP(O)(NR 2 ) 2 , —Si(OR)R 2 , and —SiR 3 ; or
       two R x  groups are optionally taken together to form an optionally substituted 5-8 membered partially unsaturated or aryl fused ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur;   
     
         each R is independently selected from hydrogen, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, a 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or:
       two R groups on the same carbon or nitrogen are optionally taken together with their intervening atoms to form an optionally substituted 4-7 membered saturated, partially unsaturated, or heteroaryl ring having 0-3 heteroatoms, in addition to the carbon or nitrogen, independently selected from nitrogen, oxygen, and sulfur;   
     
         R y  is selected from 
       
    
     
       
         
         
             
             
         
       
         
          or hydrogen; 
         Ring B x  is phenyl, a 4-10 membered saturated or partially unsaturated mono- or bicyclic carbocyclic or heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, wherein Ring B x  is further optionally substituted with 1-2 oxo groups; 
         each R w  is independently selected from hydrogen, deuterium, R z , halogen, —CN, —NO 2 , —OR, —SR, —NR 2 , —S(O) 2 R, —S(O) 2 NR 2 , —S(O)R, —CFR 2 , —CF 2 R, —CF 3 , —CR 2 (OR), —CR 2 (NR 2 ), —C(O)R, —C(O)OR, —C(O)NR 2 , —C(O)N(R)OR, —OC(O)R, —OC(O)NR 2 , —N(R)C(O)OR, —N(R)C(O)R, —N(R)C(O)NR 2 , —N(R)S(O) 2 R, —OP(O)R 2 , —OP(O)(OR) 2 , —OP(O)(OR)NR 2 , —OP(O)(NR 2 ) 2 , and —SiR 3 ; 
         each R z  is independently selected from an optionally substituted group selected from C 1-6  aliphatic, phenyl, a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
            is a single or double bond; 
         w is 0, 1, 2, 3 or 4; 
         x is 0, 1, 2, 3 or 4; and 
         y is 0, 1, or 2. 
       
    
     As described above, in certain embodiments, the present invention provides a compound of formula II: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof wherein L and IRAK are as defined above and described in embodiments herein, wherein:
     X 1  and X 4  are independently a covalent bond, —CR 2 —, —O—, —NR—, —C(O)—, —CF 2 —, or   

     
       
         
         
             
             
         
       
         
         X 2  and X 3  are independently —CR 2 —, —C(O)—, —C(S)—, or 
       
    
     
       
         
         
             
             
         
       
         
         Ring C x  is a spiro-fused ring selected from a 4-10 membered saturated or partially unsaturated mono- or bicyclic carbocyclic or heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, wherein Ring C is optionally further substituted with 1-2 oxo groups; 
         L x  is a covalent bond or a C 1-3  bivalent straight or branched saturated or unsaturated hydrocarbon chain wherein 1-2 methylene units of the chain are independently and optionally replaced with —O—, —S—, —C(O)—, —C(S)—, —CR 2 —, —CRF—, —CF 2 —, —NR—, or —S(O) 2 —; 
         each R x  is independently selected from hydrogen, deuterium, R z , halogen, —CN, —NO 2 , —OR, —SR, —NR 2 , —S(O) 2 R, —S(O) 2 NR 2 , —S(O)R, —CFR 2 , —CF 2 R, —CF 3 , —CR 2 (OR), —CR 2 (NR 2 ), —C(O)R, —C(O)OR, —C(O)NR 2 , —C(O)N(R)OR, —OC(O)R, —OC(O)NR 2 , —C(S)NR 2 , —N(R)C(O)OR, —N(R)C(O)R, —N(R)C(O)NR 2 , —N(R)S(O) 2 R, —OP(O)R 2 , —OP(O)(OR) 2 , —OP(O)(OR)NR 2 , —OP(O)(NR 2 ) 2 , —Si(OR)R 2 , and —SiR 3 ; or
       two R x  groups are optionally taken together to form an optionally substituted 5-8 membered partially unsaturated or aryl fused ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur;   
     
         each R is independently selected from hydrogen, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, a 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or:
       two R groups on the same carbon or nitrogen are optionally taken together with their intervening atoms to form an optionally substituted 4-7 membered saturated, partially unsaturated, or heteroaryl ring having 0-3 heteroatoms, in addition to the carbon or nitrogen, independently selected from nitrogen, oxygen, and sulfur;   
     
         R y  is selected from 
       
    
     
       
         
         
             
             
         
       
         
          or hydrogen; 
         Ring B x  is phenyl, a 4-10 membered saturated or partially unsaturated mono- or bicyclic carbocyclic or heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, wherein Ring B is further optionally substituted with 1-2 oxo groups; 
         each R w  is independently selected from hydrogen, deuterium, R z , halogen, —CN, —NO 2 , —OR, —SR, —NR 2 , —S(O) 2 R, —S(O) 2 NR 2 , —S(O)R, —CFR 2 , —CF 2 R, —CF 3 , —CR 2 (OR), —CR 2 (NR 2 ), —C(O)R, —C(O)OR, —C(O)NR 2 , —C(O)N(R)OR, —OC(O)R, —OC(O)NR 2 , —N(R)C(O)OR, —N(R)C(O)R, —N(R)C(O)NR 2 , —N(R)S(O) 2 R, —OP(O)R 2 , —OP(O)(OR) 2 , —OP(O)(OR)NR 2 , —OP(O)(NR 2 ) 2 , and —SiR 3 ; 
         each R z  is independently selected from an optionally substituted group selected from C 1-6  aliphatic, phenyl, a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
         x is 0, 1, 2, 3 or 4; and 
         w is 0, 1, 2, 3 or 4. 
       
    
     As defined herein and described below, wherein a formula is depicted using square brackets, e.g., 
     
       
         
         
             
             
         
       
     
     L is attached to a modifiable carbon, oxygen, or nitrogen atom within LBM including substitution or replacement of a defined group in LBM. 
     As defined above and described herein X 1  is a covalent bond, —CR 2 —, —O—, —NR—, —CF 2 —, 
     
       
         
         
             
             
         
       
     
     —C(O)—, —C(S)—, or 
     
       
         
         
             
             
         
       
     
     In some embodiments, X 1  is a covalent bond. In some embodiments, X 1  is —CR 2 —. In some embodiments, X 1  is —CH 2 —. In some embodiments, X 1  is —O—. In some embodiments, X 1  is —NR—. In some embodiments, X 1  is —NH—. In some embodiments, X 1  is —NMe-. In some embodiments, X 1  is —CF 2 —. In some embodiments, X 1  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, X 1  is —C(O)—. In some embodiments, X 1  is —C(S)—. In some embodiments, X 1  is 
     
       
         
         
             
             
         
       
     
     In certain embodiments, X 1  is selected from those shown in the compounds of Table 1. 
     As defined above and described herein, X 2  and X 3  are independently —CR 2 —, —C(O)—, —C(S)—, —CR 2 C(O)—, or 
     
       
         
         
             
             
         
       
     
     In some embodiments, X 2  and X 3  are independently —CR 2 —. In some embodiments, X 2  and X 3  are independently —CH 2 —. In some embodiments, X 2  and X 3  are independently —C(O)—. In some embodiments, X 2  and X 3  are independently —C(S)—. In some embodiments, X 2  and X 3  are independently —CR 2 C(O)—. In some embodiments, X 2  and X 3  are independently 
     
       
         
         
             
             
         
       
     
     In certain embodiments, X 2  and X 3  are independently selected from those shown in the compounds of Table 1. 
     As defined above and described herein, X 4  is a covalent bond, —CR 2 —, —O—, —NR—, —CF 2 —, 
     
       
         
         
             
             
         
       
     
     —C(O)—, —C(S)—, or 
     
       
         
         
             
             
         
       
     
     In some embodiments, X 4  is a covalent bond. In some embodiments, X 4  is —CR 2 —. In some embodiments, X 4  is —CH 2 —. In some embodiments, X 4  is —O—. In some embodiments, X 4  is —NR—. In some embodiments, X 4  is —CF 2 —. In some embodiments, X 4  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, X 4  is —C(O)—. In some embodiments, X 4  is —C(S)—. In some embodiments, X 4  is 
     
       
         
         
             
             
         
       
     
     In certain embodiments, X 4  is selected from those shown in the compounds of Table 1. 
     As define above and described herein, Z 1  and Z 2  are independently a carbon atom or a nitrogen atom. 
     In some embodiments, Z 1  and Z 2  are independently a carbon atom. In some embodiments, Z 1  and Z 2  are independently a carbon atom. 
     In certain embodiments, Z 1  and Z 2  are independently selected from those shown in the compounds of Table 1. 
     As defined above and described herein, Ring A x  is a fused ring selected from benzo, a 4-6 membered saturated or partially unsaturated carbocyclic or heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur. 
     In some embodiments, Ring A x  is benzo. In some embodiments, Ring A x  is a 4-6 membered saturated or partially unsaturated carbocyclic or heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, Ring A x  is a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur. 
     In some embodiments, Ring A x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, Ring A x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, Ring A x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, Ring A x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, Ring A x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, Ring A x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, Ring A x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, Ring A x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, Ring A x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, Ring A is 
     
       
         
         
             
             
         
       
     
     In certain embodiments, Ring A x  is selected from those shown in the compounds of Table 1. 
     As defined about and described herein, Ring C x  is a spiro-fused ring selected from a 4-10 membered saturated or partially unsaturated mono- or bicyclic carbocyclic or heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, wherein Ring C x  is optionally further substituted with 1-2 oxo groups. 
     In some embodiments, Ring C x  is a spiro-fused ring selected from a 4-10 membered saturated or partially unsaturated mono- or bicyclic carbocyclic or heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, Ring C x  is optionally further substituted with 1-2 oxo groups. 
     In some embodiments, Ring C x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, Ring C x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, Ring C x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, Ring C x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, Ring C x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, Ring C x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, Ring C x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, Ring C x  is 
     
       
         
         
             
             
         
       
     
     In certain embodiments, Ring C x  is selected from those shown in the compounds of Table 1. 
     As defined above and described herein, L x  is a covalent bond or a C 1-3  bivalent straight or branched saturated or unsaturated hydrocarbon chain wherein 1-2 methylene units of the chain are independently and optionally replaced with —O—, —S—, —C(O)—, —C(S)—, —CR 2 —, —CRF—, —CF 2 —, —NR—, or —S(O) 2 —. 
     In some embodiments, L x  is a covalent bond. In some embodiments, L x  is a C 1-3  bivalent straight or branched saturated or unsaturated hydrocarbon chain wherein 1-2 methylene units of the chain are independently and optionally replaced with —O—, —S—, —C(O)—, —C(S)—, —CR 2 —, —CRF—, —CF 2 —, —NR—, or —S(O) 2 —. 
     In some embodiments, L x  is —C(O)—. 
     In certain embodiments, L x  is selected from those shown in the compounds of Table 1. 
     As defined above and described herein, each R x  is independently selected from hydrogen, deuterium, R z , halogen, —CN, —NO 2 , —OR, —SR, —NR 2 , —S(O) 2 R, —S(O) 2 NR 2 , —S(O)R, —CFR 2 , —CF 2 R, —CF 3 , —CR 2 (OR), —CR 2 (NR 2 ), —C(O)R, —C(O)OR, —C(O)NR 2 , —C(O)N(R)OR, —OC(O)R, —OC(O)NR 2 , —C(S)NR 2 , N(R)C(O)OR, —N(R)C(O)R, —N(R)C(O)NR 2 , —N(R)S(O) 2 R, —OP(O)R 2 , —OP(O)(OR) 2 , —OP(O)(OR)NR 2 , —OP(O)(NR 2 ) 2 , —Si(OR)R 2 , and —SiR 3 , or two R x  groups are optionally taken together to form an optionally substituted 5-8 membered partially unsaturated or aryl fused ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur. 
     In some embodiments, R x  is hydrogen. In some embodiments, R x  is deuterium. In some embodiments, R x  is R z . In some embodiments, R x  is halogen. In some embodiments, R x  is —CN. In some embodiments, R x  is —NO 2 . In some embodiments, R x  is —OR. In some embodiments, R x  is —SR. In some embodiments, R x  is —NR 2 . In some embodiments, R x  is —S(O) 2 R. In some embodiments, R x  is —S(O) 2 NR 2 . In some embodiments, R x  is —S(O)R. In some embodiments, R x  is —CFR 2 . In some embodiments, R x  is —CF 2 R. In some embodiments, R x  is —CF 3 . In some embodiments, R x  is —CR 2 (OR). In some embodiments, R x  is —CR 2 (NR 2 ). In some embodiments, R x  is —C(O)R. In some embodiments, R x  is —C(O)OR. In some embodiments, R x  is —C(O)NR 2 . In some embodiments, R x  is —C(O)N(R)OR. In some embodiments, R x  is —OC(O)R. In some embodiments, R x  is —OC(O)NR 2 . In some embodiments, R x  is —C(S)NR 2 . In some embodiments, R x  is —N(R)C(O)OR. In some embodiments, R x  is —N(R)C(O)R. In some embodiments, R x  is —N(R)C(O)NR 2 . In some embodiments, R x  is —N(R)S(O) 2 R. In some embodiments, R x  is —OP(O)R 2 . In some embodiments, R x  is —OP(O)(OR) 2 . In some embodiments, R x  is —OP(O)(OR)NR 2 . In some embodiments, R x  is —OP(O)(NR 2 ) 2 . In some embodiments, R x  is —Si(OR)R 2 . In some embodiments, R x  is —SiR 3 . In some embodiments, two R x  groups are optionally taken together to form an optionally substituted 5-8 membered partially unsaturated or aryl fused ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur. 
     In some embodiments, R x  is fluoro. In some embodiments, R x  is bromo. In some embodiments, R x  is methyl. In some embodiments, R x  is —OH. In some embodiments, R x  is —NH 2 . In some embodiments, R x  is —NHCH 3 . In some embodiments, R x  is —N(CH 3 ) 2 . In some embodiments, R x  is —NHCH(CH 3 ) 2 . In some embodiments, R x  is —NHSO 2 CH 3 . In some embodiments, R x  is —CH 2 OH. In some embodiments, R x  is —CH 2 NH 2 . In some embodiments, R x  is —C(O)NH 2 . In some embodiments, R x  is —C(O)NHCH 3 . In some embodiments, R x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R x  is 
     
       
         
         
             
             
         
       
     
     In certain embodiments, each R x  is independently selected from those shown in the compounds of Table 1. 
     As defined above and described here, each R is independently selected from hydrogen, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, a 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or two R groups on the same carbon or nitrogen are optionally taken together with their intervening atoms to form an optionally substituted 4-7 membered saturated, partially unsaturated, or heteroaryl ring having 0-3 heteroatoms, in addition to the carbon or nitrogen, independently selected from nitrogen, oxygen, and sulfur. 
     In some embodiments, R is hydrogen. In some embodiments, R is an optionally substituted C 1 -6 aliphatic. In some embodiments, R is an optionally substituted phenyl. In some embodiments, R is an optionally substituted 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, R is an optionally substituted a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, two R groups on the same carbon or nitrogen are optionally taken together with their intervening atoms to form an optionally substituted 4-7 membered saturated, partially unsaturated, or heteroaryl ring having 0-3 heteroatoms, in addition to the carbon or nitrogen, independently selected from nitrogen, oxygen, and sulfur. 
     
       
         
         
             
             
         
       
     
     As defined above and described herein, R y  is selected from or hydrogen. 
     In some embodiment R y  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R y  is hydrogen. 
     In certain embodiments, R y  is selected from those shown in the compounds of Table 1. 
     As defined above and described herein, Ring B x  is phenyl, a 4-10 membered saturated or partially unsaturated mono- or bicyclic carbocyclic or heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, wherein Ring B x  is further optionally substituted with 1-2 oxo groups. 
     In some embodiments, Ring B x  is phenyl. In some embodiments, Ring B x  is a 4-10 membered saturated or partially unsaturated mono- or bicyclic carbocyclic or heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur In some embodiments, Ring B x  is a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, Ring B x  is further optionally substituted with 1-2 oxo groups. 
     In some embodiments, Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In some embodiments Ring B x  is 
     
       
         
         
             
             
         
       
     
     In certain embodiments, Ring B x  is selected from those shown in the compounds of Table 1. 
     As defined above and described herein, each R w  is independently selected from hydrogen, deuterium, R z , halogen, —CN, —NO 2 , —OR, —SR, —NR 2 , —S(O) 2 R, —S(O) 2 NR 2 , —S(O)R, —CFR 2 , —CF 2 R, —CF 3 , —CR 2 (OR), —CR 2 (NR 2 ), —C(O)R, —C(O)OR, —C(O)NR 2 , —C(O)N(R)OR, —OC(O)R, —OC(O)NR 2 , —N(R)C(O)OR, —N(R)C(O)R, —N(R)C(O)NR 2 , —N(R)S(O) 2 R, —OP(O)R 2 , —OP(O)(OR) 2 , —OP(O)(OR)NR 2 , —OP(O)(NR 2 ) 2 , and —SiR 3 . 
     In some embodiments, R w  is hydrogen. In some embodiments, R w  is deuterium. In some embodiments, R w  is R z . In some embodiments, R w  is halogen. In some embodiments, R w  is —CN. In some embodiments, R w  is —NO 2 . In some embodiments, R w  is —OR. In some embodiments, R w  is —SR. In some embodiments, R w  is —NR 2 . In some embodiments, R w  is —S(O) 2 R. In some embodiments, R w  is —S(O) 2 NR 2 . In some embodiments, R w  is —S(O)R. In some embodiments, R w  is —CFR 2 . In some embodiments, R w  is —CF 2 R. In some embodiments, R w  is —CF 3 . In some embodiments, R w  is —CR 2 (OR). In some embodiments, R w  is —CR 2 (NR 2 ). In some embodiments, R w  is —C(O)R. In some embodiments, R w  is —C(O)OR. In some embodiments, R w  is —C(O)NR 2 . In some embodiments, R w  is —C(O)N(R)OR. In some embodiments, R w  is —OC(O)R. In some embodiments, R w  is —OC(O)NR 2 . In some embodiments, R w  is —N(R)C(O)OR. In some embodiments, R w  is —N(R)C(O)R. In some embodiments, R w  is —N(R)C(O)NR 2 . In some embodiments, R w  is —N(R)S(O) 2 R. In some embodiments, R w  is —OP(O)R 2 . In some embodiments, R w  is —OP(O)(OR) 2 . In some embodiments, R w  is —OP(O)(OR)NR 2 . In some embodiments, R w  is —OP(O)(NR 2 ) 2 . In some embodiments, R w  is —SiR 3 . 
     In certain embodiments, R w  is selected from those shown in the compounds of Table 1. 
     As defined above and described herein, each R z  is independently an optionally substituted group selected from C 1-6  aliphatic, phenyl, a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur. 
     In some embodiments, R z  is an optionally substituted C 1-6  aliphatic. In some embodiments, R z  is an optionally substituted phenyl. In some embodiments, R z  is an optionally substituted 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, R z  is an optionally substituted 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur. 
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In some embodiments, R z  is 
     
       
         
         
             
             
         
       
     
     In certain embodiments, R z  is selected from those shown in the compounds of Table 1. 
     As defined above and described herein,   is a single or double bond. 
     In some embodiments,   is a single bond. In some embodiments,   is a double bond. 
     In certain embodiments,   is selected from those shown in the compounds of Table 1. 
     As defined above and described herein, w is 0, 1, 2, 3 or 4. 
     In some embodiments, w is 0. In some embodiments, w is 1. In some embodiments, w is 2. In some embodiments, w is 3. In some embodiments, w is 4. 
     In certain embodiments, w is selected from those shown in the compounds of Table 1. 
     As defined above and described herein, x is 0, 1, 2, 3 or 4. 
     In some embodiments, x is 0. In some embodiments, x is 1. In some embodiments, m is 2. In some embodiments, x is 3. In some embodiments, x is 4. 
     In certain embodiments, x is selected from those shown in the compounds of Table 1. 
     As defined above and described herein, y is 0, 1, or 2. 
     In some embodiments, y is 0. In some embodiments, y is 1. In some embodiments, y is 2. 
     In certain embodiments, y is selected from those shown in the compounds of Table 1. 
     In some embodiments, the present invention provides a compound of formula I′, wherein Ring A x  is benzo, y is 1, X 1  is —CH 2 —, X 2  and X 3  are —C(O)—, and Z 1  and Z 2  are carbon atoms as shown, to provide a compound of formula I-a: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein each of IRAK, L, L x , R x , R y , and x is as defined above and described in embodiments herein, both singly and in combination. 
     In some embodiments, the present invention provides a compound of formula I′, wherein Ring A x  is imidazolyl, y is 1, X 1  is —CH 2 —, X 2  and X 3  are —C(O)—, and Z 1  and Z 2  are carbon atoms as shown, to provide a compound of formula I-b: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein each of IRAK, L, L x , and R y  is as defined above and described in embodiments herein, both singly and in combination. 
     In some embodiments, the present invention provides a compound of formula I′, wherein Ring A x  is imidazolyl, y is 1, X 1  is —CH 2 —, X 2  and X 3  are —C(O)—, and Z 1  and Z 2  are carbon atoms as shown, to provide a compound of formula I-c: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein each of IRAK, L, L x , and R y  is as defined above and described in embodiments herein, both singly and in combination. 
     In some embodiments, the present invention provides a compound of formula I′, wherein Ring A x  is oxazolyl, y is 1, X 1  is —CH 2 —, X 2  and X 3  are —C(O)—, and Z 1  and Z 2  are carbon atoms as shown, to provide a compound of formula I-d: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein each of IRAK and L is as defined above and described in embodiments herein, both singly and in combination. 
     In some embodiments, the present invention provides a compound of formula I′, wherein Ring A x  is benzo, y is 0, X 2  and X 3  are —C(O)—, and Z 1  and Z 2  are carbon atoms as shown, to provide a compound of formula I-e: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein each of IRAK, L, L x , R x , R y , and x is as defined above and described in embodiments herein, both singly and in combination. 
     In some embodiments, the present invention provides a compound of formula I′, wherein Ring A x  is benzo, y is 1, X 1  is —O—, X 2  and X 3  are —C(O)—, and Z 1  and Z 2  are carbon atoms as shown, to provide a compound of formula I-f: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein each of IRAK, L, L x , R x , R y , and x is as defined above and described in embodiments herein, both singly and in combination. 
     In some embodiments, the present invention provides a compound of formula I′, wherein Ring A x  is benzo, y is 1, X 1  is —NR—, X 2  and X 3  are —C(O)—, and Z 1  and Z 2  are carbon atoms as shown, to provide a compound of formula I-g: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein each of IRAK, L, L x , R, R x , R y , and x is as defined above and described in embodiments herein, both singly and in combination. 
     In some embodiments, the present invention provides a compound of formula I′, wherein Ring A x  is benzo, y is 1, X 1  is —CF 2 —, X 2  and X 3  are —C(O)—, and Z 1  and Z 2  are carbon atoms as shown, to provide a compound of formula I-h: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein each of IRAK, L, L x , R x , B y , and x is as defined above and described in embodiments herein, both singly and in combination. 
     In some embodiments, the present invention provides a compound of formula I′, wherein Ring A x  is benzo, y is 1, X 1  is 
     
       
         
         
             
             
         
       
     
     X 2  and X 3  are —C(O)—, and Z 1  and Z 2  are carbon atoms as shown, to provide a compound of formula I-i: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein each of IRAK, L, L x , R x , R y , and x is as defined above and described in embodiments herein, both singly and in combination. 
     In some embodiments, the present invention provides a compound of formula I′, wherein Ring A x  is pyridyl, y is 1, X 1  is —CH 2 —, X 2  and X 3  are —C(O)—, and Z 1  and Z 2  are carbon atoms as shown, to provide a compound of formula I-j: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein each of IRAK, L, L x , R x , R y , and x is as defined above and described in embodiments herein, both singly and in combination. 
     In some embodiments, the present invention provides a compound of formula I′, wherein Ring A x  is pyridyl, y is 1, X 1  is —CH 2 —, X 2  and X 3  are —C(O)—, and Z 1  and Z 2  are carbon atoms as shown, to provide a compound of formula I-k: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein each of IRAK, L, L x , R x , R y , and x is as defined above and described in embodiments herein, both singly and in combination. 
     In some embodiments, the present invention provides a compound of formula I′, wherein Ring A is benzo, y is 1, X 1 , X 2  and X 3  are —C(O)—, y is 1, and Z 1  and Z 2  are carbon atoms as shown, to provide a compound of formula I-l: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein each of IRAK, L, L x , R x , R y , and x is as defined above and described in embodiments herein, both singly and in combination. 
     In some embodiments, the present invention provides a compound of formula I′, wherein Z 1  and Z 2  are carbon atoms and Ring A x  is 
     
       
         
         
             
             
         
       
     
     y is 0, and X 2  and X 3  are —C(O)— as shown, to provide a compound of formula I-m: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein each of IRAK, L, L x , R x , R y , and x is as defined above and described in embodiments herein, both singly and in combination. 
     In some embodiments, the present invention provides a compound of formula II, wherein X 1  and X 4  are —CH 2 —, and X 2  and X 3  are —C(O)— as shown, to provide a compound of formula II-a: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein each of Ring C x , IRAK, L, L x , R x , R y , and x is as defined above and described in embodiments herein, both singly and in combination. 
     In some embodiments, the present invention provides a compound of formula II, wherein X 1  is —CH 2 —, X 4  is a covalent bond, and X 2  and X 3  are —C(O)— as shown, to provide a compound of formula II-b: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein each of Ring C, IRAK, L, L x , R x , R y , and x is as defined above and described in embodiments herein, both singly and in combination. 
     In certain embodiments, the present invention provides a compound wherein LBM is human kelch-like ECH-associated protein 1 (KEAP1), thereby forming a compound of formula 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, both singly and in combination. 
     In certain embodiments, the present invention provides a compound wherein LBM is a KEAP1 binding moiety as recited in Lu et al., Euro. J. Med. Chem., 2018, 146:251-9, thereby forming a compound of formula III-b: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, both singly and in combination. 
     In certain embodiments, the present invention provides a compound wherein LBM is KEAP1-NRF2 binding moiety thereby forming a compound of formula III-c-1 or III-c-2: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, and wherein each of the variables R, R 1 , R 5 , and R 8  is as described and defined in WO 2020/018788, the entirety of each of which is herein incorporated by reference. 
     In certain embodiments, the present invention provides a compound wherein LBM is KEAP1-NRF2 binding moiety as recited in Tong et al., “Targeted Protein Degradation via a Covalent Reversible Degrader Based on Bardoxolone”, ChemRxiv 2020, thereby forming a compound of formula III-d-1 or III-d-2: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, both singly and in combination. 
     IRAK Binding Moiety (IRAK) 
     As defined above and described herein, IRAK is a IRAK-4 binding moiety. 
     As defined herein and described below, wherein a formula is depicted using square brackets, e.g., 
     
       
         
         
             
             
         
       
     
     L is attached to a modifiable carbon, oxygen, or nitrogen atom within IRAK including substitution or replacement of a defined group in IRAK. 
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK-4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-dd-1 or I-dd-2 respectively: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         A is optionally substituted heteroaryl, optionally substituted aryl, optionally substituted heterocycloalkyl, optionally substituted cycloalkyl, optionally substituted (cycloalkyl)alkyl, optionally substituted (heterocycloalkyl)alkyl, optionally substituted aralkyl, optionally substituted heteroaralkyl, optionally substituted cycloalkyl-NR x —, optionally substituted heterocycloalkyl optionally substituted aryl-NR x —, optionally substituted heteroaryl-NR x —, optionally substituted cycloalkyl-O—, optionally substituted heterocycloalkyl-O—, optionally substituted aryl-O— or optionally substituted heteroaryl-O—; e.g., wherein each optional substituent independently represents an occurrence of R z ; 
         B is hydrogen, halogen, cyano, optionally substituted alkyl, optionally substituted alkenyl, optionally substituted alkoxy, —NR a R b , optionally substituted cycloalkyl, optionally substituted aryl, optionally substituted heterocycloalkyl, optionally substituted heteroaryl, optionally substituted (cycloalkyl)alkyl, optionally substituted (heterocycloalkyl)alkyl, optionally substituted aralkyl, optionally substituted heteroaralkyl, optionally substituted cycloalkyl-NR x —, optionally substituted heterocycloalkyl-NR x —, optionally substituted aryl-NR x —, optionally substituted heteroaryl-NR x —, optionally substituted cycloalkyl-O—, optionally substituted heterocycloalkyl-O—, optionally substituted aryl-O—, optionally substituted heteroaryl-O—; e.g., wherein each optional substituent independently represents an occurrence of R y ; 
         Q is absent or optionally substituted heterocycloalkyl, optionally substituted heteroaryl, optionally substituted aryl, optionally substituted cycloalkyl, optionally substituted (heterocycloalkyl)alkyl, optionally substituted (heteroaryl)alkyl, optionally substituted aralkyl, optionally substituted (cycloalkyl)alkyl, —NR 3 R 4 , —O—R 3  or —S—R; e.g., wherein each optional substituent independently represents an occurrence of R z ; 
         W is N or CH; 
         R 1  is hydrogen, optionally substituted alkyl, optionally substituted cycloalkyl, optionally substituted (cycloalkyl)alkyl, optionally substituted (heterocycloalkyl)alkyl, optionally substituted heterocycloalkyl, optionally substituted aralkyl, optionally substituted (heteroaryl)alkyl-, optionally substituted alkoxyalkyl, optionally substituted aminoalkyl, or —(CH 2 ) m —R 2 ; e.g., wherein each optional substituent independently represents halo, hydroxy, alkoxy, amino, nitro, cycloalkyl, aryl, heterocycloalkyl or heteroaryl; 
         R 2  is hydrogen, —NR a R b , alkoxy, hydroxy, optionally substituted heteroaryl or optionally substituted heterocycloalkyl; e.g., wherein each optional substituent independently represents an occurrence of R y ; 
         each R 3  and R 4  is independently selected from optionally substituted aryl, optionally substituted cycloalkyl, optionally substituted heteroaryl, optionally substituted heterocycloalkyl, optionally substituted aralkyl, optionally substituted (cycloalkyl)alkyl, optionally substituted (heteroaryl)alkyl and optionally substituted (heterocycloalkyl)alkyl; e.g., wherein each optional substituent is independently selected from alkyl, halo, haloalkyl, hydroxy, hydroxyalkyl, alkoxy, alkoxyalkyl, amino, nitro, cycloalkyl, (cycloalkyl)alkyl, aryl, aralkyl, heterocycloalkyl, (heterocycloalkyl)alkyl, heteroaryl and (heteroaryl)alkyl; 
         each R a  and R b  is independently selected from hydrogen, alkyl, aminoalkyl, acyl and heterocyclyl; or R a  and R b  are taken together with the nitrogen to which they are attached to form an optionally substituted ring; 
         R x  is hydrogen, alkyl, hydroxy, hydroxyalkyl, acyl or cycloalkyl; 
         each R y  and R z  is independently selected from hydroxy, hydroxyalkyl, halo, alkyl, oxo, haloalkyl, alkoxy, alkenyloxy, amino, nitro, cyano, —SH, —S(alkyl), glycinate, ester, thioester, cycloalkyl, heterocycloalkyl, aryl, heteroaryl, (cycloalkyl)alkyl, (heterocycloalkyl)alkyl, aralkyl, and (heteroaryl)alkyl; optionally wherein the hydroxy, hydroxyalkyl, alkoxy, cycloalkyl, heterocycloalkyl, aryl and heteroaryl are further substituted by one or more substituents selected from alkyl, halo, alkenyl, amino, nitro, cycloalkyl and (cycloalkyl)alkyl; or 
         R y  and R z  taken together with the atoms to which they are attached form an alkyl chain having 1-10 carbon atoms; optionally wherein 1-3 carbon atoms are replaced by O, NH or S; 
         m is 1, 2, or 3; and 
         n is 1 or 2;
 
as defined and described in WO 2017/009798 and US 2018/0201609, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-ee-1, I-ee-2, I-ee-3, or I-ee-4 respectively: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         Ring A is selected from phenyl and 5- or 6-membered heteroaryl; 
         Ring B is selected from phenyl and 5- or 6-membered heteroaryl; 
         n is 0, 1, or 2; 
         p is 0, 1, or 2; 
         one of W and X is N, and the other of W and X is C; 
         Y is N or C—R 2 ; 
         R 1  is selected from C 1-6 alkyl, C 2-6 alkenyl, C 2-6 alkynyl, C 3-6 cycloalkyl, 3- to 6-membered saturated heterocyclyl, halo, —CN, —C(R 1a )═NR(OR 1a ), —C(R 1a )═N(R 1a ), —C(O)R 1a , —C(O) 2 R 1a , —C(O)N(R 1a ) 2 , —NO 2 , —N(R 1a ) 2 , —N(R 1a )C(O)R 1a , —N(R 1a )C(O) 2 R 1a , —N(R 1a )C(O)N(R 1a ) 2 , —N(R 1a )S(O) 2 R 1a , OR 1a —OC(O)R 1a , —OC(O)N(R 1a ) 2 , —SR 1a , —S(O)R 1a , —S(O) 2 R 1a , —S(O)N(R 1a ) 2 , and —S(O) 2 N(R 1a ) 2 , wherein said C 1-6 alkyl, C 2-6 alkenyl, C 2-6  alkynyl, C 3-6  cycloalkyl, and 3- to 6-membered saturated heterocyclyl are optionally substituted with one or more R 10 ; or two R 1  substituents, together with their intervening atoms, form a C 5-7 cycloalkyl or a saturated 5- to 7-membered heterocyclic ring, wherein said C 5-7  cycloalkyl or a saturated 5- to 7-membered heterocyclic ring are optionally substituted with one or more R 15 ; 
         R 1a  in each occurrence is independently selected from H, C 1-6 alkyl, C 2-6 alkenyl, C 2-6 alkynyl, 3- to 6-membered monocyclic carbocyclyl, and 3- to 6-membered monocyclic heterocyclyl wherein said C 1-6 alkyl, C 2-6 alkenyl, C 2-6  alkynyl, 3- to 6-membered monocyclic carbocyclyl, and 3- to 6-membered monocyclic heterocyclyl in each occurrence are optionally and independently substituted with one or more R 10 ; 
         R 10  in each occurrence is independently selected from C 1-6 alkyl, C 2-6 alkenyl, C 2-6 alkynyl, 3- to 6-membered carbocyclyl, 3- to 6-membered heterocyclyl, halo, —CN, —C(R 10a )═NR(OR 10a ), —C(R 10a )═N(R 10a ), —C(O)R 10a , —C(O) 2 R 10a , —C(O)N(R 10a ) 2 , —NO 2 , —N(R 10a ) 2 , —N(R 10a )C(O)R 10a , —N(R 10a )C(O) 2 R 10a , —N(R 10a )C(O)N(R 10a ) 2 , —N(R 10a )S(O) 2 R 10a , —OR 10a , —OC(O)R 10a , —OC(O)N(R 10a ) 2 , —SR 10a , —S(O)R 10a , —S(O) 2 R 10a , —S(O)N(R 10a ) 2 , and —S(O) 2 N(R 10a ) 2 ; 
         R 10a  in each occurrence is independently selected from H and C 1-6 alkyl, wherein said C 1-6 alkyl is optionally substituted with one or more halo; 
         R 15  in each occurrence is independently selected from C 1-6 alkyl, C 2-6 alkenyl, C 2-6 alkynyl, 3- to 6-membered carbocyclyl, 3- to 6-membered heterocyclyl, halo, —CN, —C(R 15a )═NR(OR 15a ), —C(R 15a )═N(R 15a ), —C(O)R 15a , —C(O) 2 R 15a , —C(O)N(R 15a ) 2 , —NO 2 , —N(R 15a ) 2 , —N(R 15a )C(O)R 15a , —N(R 15a )C(O) 2 R 15a , —N(R 15a )C(O)N(R 15a ) 2 , —N(R 15a )S(O) 2 R 15a , —OR 15a , —OC(O)R 15a , —OC(O)N(R 15a ) 2 SR 15a , —S(O)R 15a , —S(O) 2 R 15a , —S(O)N(R 15a ) 2 , and —S(O) 2 N(R 15a ) 2 ; 
         R 15a  in each occurrence is independently selected from H and C 1-6 alkyl, wherein said C 1-6 alkyl is optionally substituted with one or more halo; 
         R 2  is selected from H, C 1-6  alkyl, C 2-6  alkenyl, C 2-6  alkynyl, 3- to 7-membered carbocyclyl, 3- to 7-membered heterocyclyl, halo, —CN, —C(R 2a )═NR(OR 2a ), —C(R 2a )═N(R 2 ), —C(O)R 2a , —C(O) 2 R 2a , —C(O)N(R 2a ) 2 , —NO 2 , —N(R 2a ) 2 , —N(R 2a )C(O)R 2a , —N(R 2a )C(O) 2 R 2a , —N(R 2a )C(O)N(R 2a ) 2 , —N(R 2a )S(O) 2 R 2a , —OR 2a , —OC(O)R 2a , —OC(O)N(R 2a ) 2 , —SR 2a , —S(O)R 2a , —S(O) 2 R 2a , —S(O)N(R 2a ) 2 , and —S(O) 2 N(R 2a ) 2 , wherein said C 1-6 alkyl, C 2-6 alkenyl, C 2-6 alkynyl, 3- to 7-membered carbocyclyl, and 3-7 membered heterocyclyl are optionally substituted with one or more R 20 ; 
         R 2a  in each occurrence is independently selected from H and C 1-6 alkyl, wherein said C 1-6 alkyl in each occurrence is optionally and independently substituted with one or more R 20 ; 
         R 20  in each occurrence is independently selected from C 1-6 alkyl, C 2-6 alkenyl, C 2-6 alkynyl, C 3-7 cycloalkyl, 3- to 7-membered saturated heterocyclyl, halo, —CN, —C(R 20a )═NR(OR 20a ), —C(R 20a )═N(R 20a ), —C(O)R 20a , —C(O) 2 R 20a , —C(O)N(R 20a ) 2 , —NO 2 , —N(R 20a ) 2 , —N(R 20a )C(O)R 20a , —N(R 20a )C(O) 2 R 20a , —N(R 20a )C(O)N(R 20a ) 2 , —N(R 20a )S(O) 2 R 20a , —OR 20a , —OC(O)R 20a , —OC(O)N(R 20a ) 2 , —SR 20a , —S(O)R 20a , —S(O) 2 R 20a , —S(O)N(R 20a ) 2 , and —S(O) 2 N(R 20a ) 2 , wherein said C 1-6 alkyl, C 2-6 alkenyl, C 2-6 alkynyl, C 3-7 cycloalkyl, and 3-7 membered saturated heterocyclyl in each occurrence are optionally and independently substituted with one or more R 25 ; 
         R 20a  in each occurrence is independently selected from H and C 1-6 alkyl, wherein said C 1-6 alkyl is optionally substituted with R 25 ; 
         R 25  is selected from halo and —OR 25a ; 
         R 25a  is selected from H and C 1-6 alkyl; 
         R 3  is selected from C 1-6 alkyl, C 2-6 alkenyl, C 2-6 alkynyl, C 3-6 cycloalkyl, 3- to 6-membered saturated heterocyclyl, halo, —CN, —C(R 3a )═NR(OR 3a ), —C(R 3a )═N(R 3a ), —C(O)R 3a , —C(O) 2 R 3a , —C(O)N(R 3a ) 2 , —NO 2 , —N(R 3a ) 2 , —N(R 3a )C(O)R 3a , —N(R 3a )C(O) 2 R 3a , —N(R 3a )C(O)N(R 3a ) 2 , —N(R 3a )S(O) 2 R 3a , —OR 3a , —OC(O)R 3a , —OC(O)N(R 3a ) 2 , —SR 3a , —S(O)R 3a , —S(O) 2 R 3a , —S(O)N(R 3a ) 2 , and —S(O) 2 N(R 3a ) 2 , wherein said C 1-6 alkyl, C 2 -6alkenyl, C 2-6  alkynyl, C 3-6  cycloalkyl, and 3- to 6-membered saturated heterocyclyl are optionally substituted with one or more R 30 ; 
         R 3a  in each occurrence is independently selected from H, C 1-6 alkyl, 3- to 6-membered carbocyclyl, and 3- to 6-membered heterocyclyl, wherein said C 1-6  alkyl, 3- to 6-membered carbocyclyl, and 3- to 6-membered heterocyclyl in each occurrence are optionally and independently substituted with one or more R 30 ; 
         R 30  in each occurrence is independently selected from C 1-6 alkyl, C 2-6 alkenyl, C 2-6 alkynyl, 3- to 6-membered carbocyclyl, 3- to 6-membered heterocyclyl, halo, —CN, —C(R 30a )═NR(OR 30a ), —C(R 30a )═N(R 30a ), —C(O)R 30a , —C(O) 2 R 30a , —C(O)N(R 30a ) 2 , —NO 2 , —N(R 30a ) 2 , —N(R 30a )C(O)R 30a , —N(R 30a )C(O) 2 R 30a , —N(R 30a )C(O)N(R 30a ) 2 , —N(R 30a )S(O) 2 R 30a , —OR 30a , —OC(O)R 30a , —OC(O)N(R 30a ) 2 , —SR 30a , —S(O)R 30a S(O) 2 R 30a , —S(O)N(R 30a ) 2 , and —S(O) 2 N(R 30a ) 2 , wherein said C 1-6 alkyl, C 2-6 alkenyl, C 2-6  alkynyl, 3-6 membered carboyclyl, 3- to 6-membered heterocyclyl in each occurrence are optionally and independently substituted with one or more R 35 ; 
         R 30a  in each occurrence is independently selected from H and C 1-4 alkyl, wherein C 1-4 alkyl is optionally substituted with one or more R 35 ; 
         R 35  in each occurrence is independently selected from halo and —OR 35a ; 
         R 35a  in each occurrence is independently selected from H and C 1-6 alkyl; 
         R 4  is selected from H, halo, C 1-6 alkyl, N(R 4a ) 2 , and —OR 4 a; and R 4a  in each occurrence is independently selected from H and C 1-6 alkyl;
 
as defined and described in WO 2016/011390 and US 2017/0204093, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-ff-1, I-ff-2, I-ff-3, or I-ff-4 respectively: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         Ring A is selected from phenyl and 5- or 6-membered heteroaryl; 
         Ring B is selected from phenyl and 5- or 6-membered heteroaryl; 
         Ring C is a 3- to 6-membered carbocyclyl, 
         n is 1, 2 or 3; 
         p is 0, 1, or 2; 
         one of W and X is N, and the other of W and X is C; 
         Y is N or C—R 2 ; 
         R 1  is selected from C 1-6  alkyl, C 2-6 alkenyl, C 2-6  alkynyl, halo, —CN, —C(R 1a )═NR(OR 1a ), —C(R 1a )═N(R 1a ), —C(O)R 1a , —C(O) 2 R 1a , —C(O)N(R 1a ) 2 , —NO 2 , —N(R 1a ) 2 , —N(R 1a )C(O)R 1a , —N(R 1a )C(O) 2 R 1a , —N(R 1a )C(O)N(R 1a ) 2 , —N(R 1a )S(O) 2 R 1a , —OC(O)R 1a , —OC(O)N(R 1a ) 2 , —SR 1a , —S(O)R 1a , —S(O) 2 R 1a , —S(O)N(R 1a ) 2 , and —S(O) 2 N(R 1a ) 2 , wherein said C 1-6  alkyl, C 2 -6alkenyl, and C 2-6  alkynyl are optionally substituted with one or more R 10 ; 
         R 1a  in each occurrence is independently selected from H or C 1-6 alkyl wherein said C 1-6 alkyl in each occurrence are optionally and independently substituted with one or more R 10 ; 
         R 10  in each occurrence is independently selected from halo, —CN, —C(R m a)═NR(OR) 10a , —C(R 10a )═N(R 10a ), —C(O)R 10a , —C(O) 2 R 10a , —C(O)N(R 10a ) 2 , —NO 2 , —N(R 10a ) 2 , —N(R 10a )C(O)R 10a , —N(R 10a )C(O) 2 R 10a , —N(R 10a )C(O)N(R 10a ) 2 , —N(R 10a )S(O) 2 R 10a , —OR 10a , —OC(O)R 10a , —OC(O)N(R 10a ) 2 , —SR 10a , —S(O)R 10a , —S(O) 2 R 10a , —S(O)N(R 10a ) 2 , and —S(O) 2 N(R 10a ) 2 ; 
         R 10a  in each occurrence is independently selected from H and C 1-6 alkyl, wherein said C 1-6 alkyl is optionally substituted with one or more halo; 
         R is selected from H, C 1-6 alkyl, C 2-6 alkenyl, C 2-6 alkynyl, 3- to 7-membered carbocyclyl, 3- to 7-membered heterocyclyl, halo, —CN, —C(R 2a )═NR(OR 2a ), —C(R 2a )═N(R 2a ), —C(O)R 2a , —C(O) 2 R 2a , —C(O)N(R 2a ) 2 , —NO 2 , —N(R 2a ) 2 , —N(R 2a )C(O)R 2a , —N(R 2a )C(O) 2 R 2a , —N(R 2a )C(O)N(R 2a ) 2 , —N(R 2a )S(O) 2 R 2a , —OC(O)R 2a , —OC(O)N(R 2a ) 2 , —SR 2a , —S(O)R 2a , —S(O) 2 R 2a , —S(O)N(R 2a ) 2 , and —S(O) 2 N(R 2a ) 2 , wherein said C 1-6 alkyl, C 2-6 alkenyl, C 2-6 alkynyl, 3- to 7-membered carbocyclyl, and 3-7 membered heterocyclyl are optionally substituted with one or more R 20 ; 
         R 2a  in each occurrence is independently selected from H and C 1-6 alkyl, wherein said C 1-6 alkyl in each occurrence is optionally and independently substituted with one or more R 20; 
         R 20  in each occurrence is independently selected from C 1-6 alkyl, C 2-6 alkenyl, C 2-6  alkynyl, C 3-7 cycloalkyl, 3- to 7-membered saturated heterocyclyl, halo, —CN, —C(R 20a )═NR(OR 20a ), —C(R 20a )═N(R 20a ), —C(O)R 20a , —C(O) 2 R 20a , —C(O)N(R 20a ) 2 , —NO 2 , —N(R 20a ) 2 , —N(R 20a )C(O)R 20a , —N(R 20a )C(O) 2 R 20a , —N(R 20a )C(O)N(R 20a ) 2 , —N(R 20a )S(O) 2 R 20a , —OR 20a , —OC(O)R 20a , —OC(O)N(R 20a ) 2 , —S(O)R 2′ , —S(O) 2 R 20a , —S(O)N(R 20a ) 2 , and —S(O) 2 N(R 2′ ) 2 , wherein said C 1-6 alkyl, C 2-6 alkenyl, C 2-6 alkynyl, C 3-7 cycloalkyl, and 3-7 membered saturated heterocyclyl in each occurrence are optionally and independently substituted with one or more R 25 ; 
         R 10a  in each occurrence is independently selected from H and C 1-6 alkyl, wherein said C 1-6 alkyl is optionally substituted with R 25 ; 
         R 25  is selected from halo and —OR 25a ; 
         R 25a  is selected from H and C 1-6 alkyl; 
         R is selected from C 1-6 alkyl, C 2-6 alkenyl, C 2-6 alkynyl, C 3-6 cycloalkyl, 3- to 6-membered saturated heterocyclyl, halo, —CN, —C(R 3a )═NR(OR 3a ), —C(R 3a )═N(R 3a ), —C(O)R 3a , —C(O) 2 R 3a , —C(O)N(R 3a ) 2 , —NO 2 , —N(R 3a ) 2 , —N(R 3a )C(O)R 3a , —N(R 3a )C(O) 2 R 3a , —N(R 3a )C(O)N(R 3a ) 2 , —N(R 3a )S(O) 2 R 3a , —OR 3a , —OC(O)R 3a , —OC(O)N(R 3a ) 2 , —SR 3a , —S(O)R 3a , —S(O) 2 R 3a , —S(O)N(R 3a ) 2 , and —S(O) 2 N(R 3a ) 2 , wherein said C 1-6 alkyl, C 2-6 alkenyl, C 2-6 alkynyl, C 3-6 cycloalkyl, and 3- to 6-membered saturated heterocyclyl are optionally substituted with one or more R 30 ; 
         R 3a  in each occurrence is independently selected from H, C 1-6  alkyl, 3- to 6-membered carbocyclyl, and 3- to 6-membered heterocyclyl, wherein said C 1-6  alkyl, 3- to 6-membered carbocyclyl, and 3- to 6-membered heterocyclyl in each occurrence are optionally and independently substituted with one or more R 30 ; 
         R 30  in each occurrence is independently selected from C 1-6 alkyl, C 2-6 alkenyl, C 2-6 alkynyl, 3- to 6-membered carbocyclyl, 3- to 6-membered heterocyclyl, halo, —CN, —C(R 30a )═NR(OR 30a ), —C(R 30a )═N(R 30a ), —C(O)R 30a , —C(O) 2 R 30a , —C(O)N(R 30a ) 2 , —NO 2 , —N(R 30a ) 2 , —N(R 30a )C(O)R 30a , —N(R 30a )C(O) 2 R 30a , —N(R 30a )C(O)N(R 30a ) 2 , —N(R 30a )S(O) 2 R 30a , —OC(O)R 30a , —OC(O)N(R 30a ) 2 —S(O)R 30a , —S(O) 2 R 30a , —S(O)N(R 30a ) 2 , and —S(O) 2 N(R 30a ) 2 , wherein said C 1-6 alkyl, C 2-6 alkenyl, C 2-6 alkynyl, 3-6 membered carbocyclyl, 3- to 6-membered heterocyclyl in each occurrence are optionally and independently substituted with one or more R 35 ; 
         R 30a  in each occurrence is independently selected from H and C 1-4 alkyl, wherein C 1-4 alkyl is optionally substituted with one or more R 35 ; 
         R 35  in each occurrence is independently selected from halo and —OR 35a ; and 
         R 35a  in each occurrence is independently selected from H and C 1-6 alkyl;
 
as defined and described in WO 2017/127430, the entirety of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-gg-1: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         HET is a heteroaryl selected from pyrrolo[2,3-b]pyridinyl, pyrrolo[2,3-d]pyrimidinyl, pyrazolo[3,4-b]pyridinyl, pyrazolo[3,4-d]pyrimidinyl, imidazolo[4,5-b]pyridinyl, and imidazolo[4,5-d]pyrimidinyl, wherein said heteroaryl is attached to the pyridinyl group in the compound of Formula (I) by a nitrogen ring atom in said heteroaryl and wherein said heteroaryl is substituted with zero to 2 R b ; 
         A is pyrazolyl, imidazolyl, triazolyl, isoxazolyl, oxadiazolyl or dihydroisoxazolyl, each substituted with R a ; 
         R 3  is C 2-3  alkyl, C 2-3  fluoroalkyl, C 3-4  hydroxyalkyl, or a cyclic group selected from C 3-6  cycloalkyl, oxetanyl, tetrahydrofuranyl, tetrahydropyranyl, and pyrazolyl, wherein said cyclic group is substituted with zero to 2 substituents independently selected from F, —OH, C 1-2  alkyl, and —CH 2 CHF 2 ; 
         R a  is: 
         (i) H, F, Cl, —OH, —CN, C 1-6  alkyl, C 1-6  fluoroalkyl, C 1-4  cyanoalkyl, C 1-6  hydroxyalkyl, C 1-5  hydroxy-fluoroalkyl, C 2-4  alkenyl, C 1-6 aminoalkyl, —(CH 2 ) 1-3 NHR y , —(CH 2 ) 1-3 NR y R y , —CH 2 CH(OH)(phenyl), —CH(CH 2 OH)(phenyl), —CH 2 CH(OH)CH 2 (phenyl), —CH 2 CH(OH)CH 2 O(methoxyphenyl), —CH 2 CH(NH 2 )CH 2 (phenyl), —(CH 2 CH 2 O) 4 H, —(CH 2 ) 1-3 O(C 1-3  alkyl), —CH 2 CH(OH)CH 2 O(C 1-3 alkyl), —CH 2 C(O)(C 1-3  alkyl), —CH 2 C(O)NR y R y , —(CH 2 ) 1-3 NR y C(O)(C 1-3  alkyl), —CH 2 C(O)O(C 1-3  alkyl), —C(O)NH 2 , —CH 2 NR y C(O)NH 2 , —(CH 2 ) 1-2 NR y C(O)O(C 1-2  alkyl), —(CR y R y ) 1-5 OC(O)CH 2 NR y R y , —CH 2 CH 2 S(O) 2 CH 3 , —CH 2 S(O) 2 (C 1-3  alkyl), —CH 2 S(O) 2 (phenyl), or NH(aminocyclohexyl); or 
         (ii) —(CH 2 ) 0-3 R z  or —(CH 2 ) 0-1 C(O)R z , wherein R z  is C 3-6  cycloalkyl, azetidinyl, oxetanyl, tetrahydrofuranyl, tetrahydropyranyl, piperidinyl, piperazinyl, pyrrolyl, pyrrolidinonyl, morpholinyl, pyrrolidinyl, phenyl, pyrazolyl, imidazolyl, pyridinyl, pyrimidinyl, dioxopyrimidinyl, benzo[d]imidazolyl, benzo[d]thiazolyl, 1,3-dioxolanyl, or 8-azabicyclo[3.2.1]octanyl, each substituted with zero to 4 substituents independently from F, —CN, —OH, —NR y R y , C 1-3  alkyl, C 1-3  fluoroalkyl, C 1-3  hydroxyalkyl, —CH(phenyl) 2 , —O(C 1-4  alkyl), —C(O)(C 1-4  alkyl), —C(O)(C 1-4  deuteroalkyl), —C(O)(C 1-5  hydroxyalkyl), —C(O)(C 1-3  fluoroalkyl), —C(O)(C 3-6 cycloalkyl), —C(O)O(C 1-3  alkyl), —C(O)NR y R y , —C(O)(phenyl), —C(O)(pyridinyl), —C(O)CH 2 (C 3-6  cycloalkyl), —C(O)O(C 1-4  alkyl), —NH(C 1-4  alkyl), —NH(C 1-3 fluoroalkyl), —NHC(O)CH 3 , —NHC(O)O(C 1-3  alkyl), —NHC(O)OC(CH 3 ) 3 , —S(O) 2 (C 1-3  alkyl), —OS(O) 2 (C 1-3  alkyl), methyl oxadiazolyl, and pyrimidinyl; 
         each R b  is independently selected from H, Cl, —CN, —NH 2 , and —C(O)NH 2 , wherein said heteroaryl is attached to the pyridinyl group by a nitrogen atom in said heteroaryl; and 
         each R y  is independently H or C 1-2  alkyl;
 
as defined and described in WO 2016/210034 and US 2018/0186799, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-hh-1, I-hh-2, I-hh-3, or I-hh-4 respectively: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         each X 1 , X 2  and X 3  are independently CR 2  or N; 
         A is O, S, S(O) or S(O) 2 ; 
         Z 1  is optionally substituted heteroaryl, optionally substituted heterocycloalkyl, optionally substituted aryl, optionally substituted cycloalkyl, optionally substituted (heterocycloalkyl)alkyl-, optionally substituted aralkyl-, optionally substituted heteroaralkyl-, optionally substituted (cycloalkyl)alkyl-, optionally substituted aryloxy-, optionally substituted heteroaryloxy-, optionally substituted heterocycloalkyloxy-, optionally substituted cycloalkyloxy-, optionally substituted aryl-NR′—, optionally substituted heteroaryl-NR′—, optionally substituted heterocycloalkyl-NR′—, optionally substituted cycloalkyl-NR′—, optionally substituted aryl-S—, optionally substituted heteroaryl-S—, optionally substituted heterocycloalkyl-S—, optionally substituted cycloalkyl-S—, optionally substituted (cycloalkyl)alkyl-NR′—, optionally substituted aralkyl-NR′—, optionally substituted (heterocycloalkyl)alkyl-NR′—, optionally substituted heteroaralkyl-NR′—, optionally substituted (cycloalkyl)alkyl-S—, optionally substituted aralkyl-S—, optionally substituted (heterocycloalkyl)alkyl-S—, optionally substituted heteroaralkyl-S—, optionally substituted (cycloalkyl)alkyl-O—, optionally substituted aralkyl-O—, optionally substituted (heterocycloalkyl)alkyl-O—, optionally substituted heteroaralkyl-O—; e.g., wherein each optional substituent independently represents an occurrence of R x ; 
         Z 2  is absent or optionally substituted cycloalkyl, optionally substituted aryl, optionally substituted heterocycloalkyl, optionally substituted heteroaryl, optionally substituted aryloxy-, optionally substituted heteroaryloxy-, optionally substituted cycloalkyloxy-, optionally substituted heterocycloalkyloxy-, optionally substituted (cycloalkyl)alkyl-, optionally substituted aralkyl-, optionally substituted (heterocycloalkyl)alkyl-, optionally substituted heteroaralkyl-, optionally substituted (cycloalkyl)alkyl-NR″—, optionally substituted aralkyl-NR″—, optionally substituted (heterocycloalkyl)alkyl-NR″—, optionally substituted heteroaralkyl-NR″—, optionally substituted (cycloalkyl)alkyl-O—, optionally substituted aralkyl-O—, optionally substituted (heterocycloalkyl)alkyl-O—, optionally substituted heteroaralkyl-O—, optionally substituted (cycloalkyl)alkyl-S—, optionally substituted aralkyl-S—, optionally substituted (heterocycloalkyl)alkyl-S— or optionally substituted heteroaralkyl-S—; e.g., wherein each optional substituent independently represents an occurrence of R y ; 
         Z 3  is optionally substituted cycloalkyl, optionally substituted aryl, optionally substituted heterocycloalkyl, optionally substituted heteroaryl, optionally substituted aryloxy-, optionally substituted heteroaryloxy-, optionally substituted cycloalkyloxy-, optionally substituted heterocycloalkyloxy-, optionally substituted (cycloalkyl)alkyl-, optionally substituted aralkyl-, optionally substituted (heterocycloalkyl)alkyl-, optionally substituted heteroaralkyl-, optionally substituted (cycloalkyl)-NR′″—, optionally substituted aryl-NR′″—, optionally substituted heteroaryl-NR′″—, optionally substituted heterocycloalkyl-NR′″—, optionally substituted aryl-S—, optionally substituted heteroaryl-S—, optionally substituted cycloalkyl-S—, optionally substituted heterocycloalkyl-S—, optionally substituted (cycloalkyl)alkyl-NR′″—, optionally substituted aralkyl-NR′″—, optionally substituted (heterocycloalkyl)alkyl-NR′″ optionally substituted heteroaralkyl-NR′″—, optionally substituted (cycloalkyl)alkyl-O—, optionally substituted aralkyl-O—, optionally substituted (heterocycloalkyl)alkyl-O—, optionally substituted heteroaralkyl-O—, optionally substituted (cycloalkyl)alkyl-S—, optionally substituted aralkyl-S—, optionally substituted (heterocycloalkyl)alkyl-S— or optionally substituted heteroaralkyl-S—; e.g., wherein each optional substituent independently represents an occurrence of R z ; 
         each R 2  is independently selected from hydrogen, alkyl, haloalkyl, halo, cyano, optionally substituted alkoxy, optionally substituted cycloalkyl, optionally substituted (cycloalkyl)alkyl-, optionally substituted cycloalkyloxy-, optionally substituted aryl, optionally substituted aralkyl-, optionally substituted heterocycloalkyl, optionally substituted heteroaryl, optionally substituted (heterocycloalkyl)alkyl-, optionally substituted heteroaralkyl-, —NR a R b , —O—R 3  and —S—R 3 ; e.g., wherein each optional substituent independently represents alkyl, alkoxy, halo, haloalkyl, hydroxy, hydroxyalkyl, —SH, —S(alkyl), cyano, amido, amino, carboxylate, glycinate, alaninate, oxo, aryl, cycloalkyl, heterocycloalkyl or heteroaryl; 
         each R′, R″ and R′″ is independently selected from hydrogen, alkyl, hydroxy, hydroxyalkyl, acyl and cycloalkyl; 
         each R x , R y  and R z  is independently selected from alkyl, alkenyl, alkynyl, halo, hydroxy, haloalkyl, hydroxyalkyl, aminoalkyl, alkoxy, —SH, —S(alkyl), cyano, amido, carboxylic acid, carboxylate, ester, thioester, alkoxycarbonyl, —C(O)NH(alkyl), oxo, cycloalkyl, cycloalkyloxy, (cycloalkyl)alkyl-, aryl, aralkyl-, heterocycloalkyl, heteroaryl, (heterocycloalkyl)alkyl-, heteroaralkyl-, —NR a R b , —O—R 4  or —S—R 4 ; optionally wherein the cycloalkyl, aryl, heterocycloalkyl, and heteroaryl are further substituted by one or more substituents selected from halo, haloalkyl, amino, hydroxy, alkyl, cyano, nitro, alkenyl, aminoalkyl, hydroxyalkyl and haloalkoxy; 
         each R a  and R b  is independently selected from hydrogen, alkyl, aminoalkyl, acyl, aminoacyl, halo, haloalkyl, hydroxy, haloalkoxy, hydroxyalkyl, nitro, cyano, cycloalkyl, heterocycloalkyl, aryl, heteroaryl, (cycloalkyl)alkyl-, (heterocycloalkyl)alkyl-, aralkyl-, and (heteroaryl)alkyl-; optionally wherein the cycloalkyl, heterocycloalkyl, aryl and heteroaryl are further substituted by one or more substituents selected from alkyl, halo, alkenyl, cyano, hydroxy, hydroxyalkyl, alkoxy, amino and nitro; or 
         R a  and R b  are taken together along with the atoms which they are attached to form a 3 to 8 membered optionally substituted ring; and 
         each R 3  and R 4  is independently selected from hydrogen, alkyl, aminoacyl, phosphate, phosphonate, alkylphosphate, alkoxycarbonyl, cycloalkyl, (cycloalkyl)alkyl-, aryl, heteroaryl, heterocycloalkyl, aralkyl-, heteroaralkyl and (heterocycloalkyl)alkyl-; as defined and described in WO 2017/009806 and US 2018/0208605, the entirety of each of which is herein incorporated by reference. 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-ii-1: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         X is CR or N; 
         A is O, S, SO 2 , SO, —NRC(O), —NRSO 2 , or N(R); or A is absent; 
         R 3  is —R, halogen, -haloalkyl, —OR, —SR, —CN, —NO 2 , —SO 2 R, —SOR, —C(O)R, —CO 2 R, —C(O)N(R) 2 , —NRC(O)R, —NRC(O)N(R) 2 , —NRSO 2 R, or —N(R) 2 ; or
       when A is —NRC(O), —NRSO 2 , or N(R); then R and R 3 , together with the atoms to which each is attached, may form a 3-7 membered heterocylic ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or a 5-6 membered monocyclic heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur; each of which is optionally substituted;   
     
         X′ is CR or N; 
         Ring Z is a 3-7 membered heterocylic ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or a 5-6 membered monocyclic heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur; each of which is optionally substituted; 
         R 1  is —R, halogen, -haloalkyl, —OR, —SR, —CN, —NO 2 , —SO 2 R, —SOR, —C(O)R, —CO 2 R, —C(O)N(R) 2 , —NRC(O)R, —NRC(O)N(R) 2 , —NRSO 2 R, or —N(R) 2 ; 
         R a  is absent, —R, halogen, -haloalkyl, —OR, —SR, —CN, —NO 2 , —SO 2 R, —SOR, —C(O)R, —CO 2 R, —C(O)N(R) 2 , —NRC(O)R, —NRC(O)N(R) 2 , —NRSO 2 R, or —N(R) 2 ; 
         Ring Y is an optionally substituted 5-6 membered monocyclic heteroaryl ring having 2-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         R 2  is —R, halogen, -haloalkyl, —OR, —SR, —CN, —NO 2 , —SO 2 R, —SOR, —C(O)R, —CO 2 R, —C(O)N(R) 2 , —NRC(O)R, —NRC(O)N(R) 2 , —NRSO 2 R, or —N(R) 2 ; 
         R b  is absent, —R, halogen, -haloalkyl, —OR, —SR, —CN, —NO 2 , —SO 2 R, —SOR, —C(O)R, —CO 2 R, —C(O)N(R) 2 , —NRC(O)R, —NRC(O)N(R) 2 , —NRSO 2 R, or —N(R) 2 ; 
         each R is independently hydrogen, C 1-6  aliphatic, C 3-10  aryl, a 3-8 membered saturated or partially unsaturated carbocyclic ring, a 3-7 membered heterocylic ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or a 5-6 membered monocyclic heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur; each of which is optionally substituted; or
       two R groups on the same atom are taken together with the atom to which they are attached to form a C 3-10  aryl, a 3-8 membered saturated or partially unsaturated carbocyclic ring, a 3-7 membered heterocylic ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or a 5-6 membered monocyclic heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur; each of which is optionally substituted;
 
as defined and described in WO 2016/081679 and US 2016/0145252, the entirety of each of which is herein incorporated by reference.
   
     
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-jj-1 or I-jj-2 respectively: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         X is NH or O; 
         b is 0 or 1; 
         n is 0, 1, 2, 3 or 4; 
         R 1  and R 2  are independently H, (C 1 -C 4 )alkyl and heterocyclyl, or R 1  and R 2  can be taken together with the nitrogen to which they are attached to form a monocyclic or bicyclic (fused, bridged or spirocyclic) heterocycle containing 3-8 carbon atoms optionally containing, in addition to the nitrogen, one or two additional heteroatoms selected from N, O and S, said alkyl and heterocycle are optionally substituted with one or more substituents selected from R a ; 
         R 3  is (C 1 -C 4 )alkyl wherein two adjacent alkyl groups can join together and form a bridged moiety of 3-6 carbon atoms; 
         R 4  is absent, halo or O b (C 1 -C 4 )alkyl; 
         R 5  is selected from C 1 -C 4  alkyl and C 2 -C 4  alkenyl which are optionally substituted with one or more substituents selected from R b ; 
         R 6  is absent, halo, or O(C 1 -C 4 )alkyl; 
         R a  is halo, oxo, OH, O b (C 1 -C 4 )alkyl, CF 3 , SO 2 (C 1 -C 4 )alkyl, or heterocyclyl, said heterocyclyl optionally substituted with one or more substituents independently selected from F, and (C 1 -C 4 )alkyl; and 
         R b  is independently selected from OH, halo, O b (C 1 -C 4 )alkyl, and CN;
 
as defined and described in WO 2016/053769 and US 2017/0247388, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-kk-1 or I-kk-2 respectively: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         B is CH, N or S; D is CH or N; E is CH or N; F is CH or N; G is CH or N; and J is C or N, wherein when B is S then D is CH, E is N, F is CH, G is N and J is C; 
         X is O, S, CH 2  or N; 
         m is 0 or 1; n is 0, 1 or 2; 
         Ring A is pyridinyl, pyrazolyl, thiophenyl, furanyl or phenyl; 
         R 1  is independently selected from (C 1 -C 4 )alkyl, pyrimidine, piperidine and phenyl, each optionally substituted with (C 1 -C 4 )alkyl, OH, halo, O(C 1 -C 4 )alkyl, methylpiperidine, S(O) 2 R c , C(O)N(R b ) 2 , or C(O)O(C 1 -C 4 )alkyl; 
         R 2  is absent or H and R 3  is independently selected from: (C 1 -C 4 )alkyl, pyranyl, cyclopentyl, cyclohexyl, cycloheptyl, thiopyranyl, pyrazolyl, piperidinyl, morpholinyl, piperazinyl each optionally substituted with one or more substituents independently selected from halo, OH, oxo, N(R b ) 2 , oxopyrrolidinyl, or morpholinyl, or R 2  and R 3  can be taken together with the nitrogen to which they are attached to form piperazine or morpholine, each optionally substituted with oxo; 
         R 4  is independently H or methyl; 
         R b  is independently selected from H and (C 1 -C 4 )alkyl; and 
         R c  is methyl;
 
as defined and described in WO 2016/144844 and US 2018/0051027, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-kk′-1 or I-kk′-2 respectively: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein each of the variables A, B, D, E, F, G, J, X, R 1 , R 2 , R 3  and n is as defined and described in WO 2016/144844 and US 2018/0051027, the entirety of each of which is herein incorporated by reference. Such IRAK4 inhibitors are well known to one of ordinary skill in the art and include those described in Smith et al.,  Bioorg. Med. Chem.,  2017, 27(12): 2721-2726 and Lim et al.,  ACS Med. Chem. Lett.,  2015, 6(6): 683-688. 
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-ll-1 or I-ll′-2 respectively: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         Ring A is aryl or heterocyclyl; 
         n is 0, 1, 2, 3 or 4; 
         R 1  is independently selected from: (C 1 -C 4 )alkyl, (C 3 -C 6 )cycloalkyl, heterocyclyl, CF 3 , CHF 2 , CN, halo, said alkyl, cycloalkyl and heterocyclyl optionally substituted with halo, OH, CH 3 , and OCH 3 ; 
         R 2  is H and R 3  is independently selected from: (C 1 -C 6 )alkyl, (C 3 -C 8 )cycloalkyl, and heterocyclyl each optionally substituted with one or more halo, OH, N(R b ) 2 , or morpholinyl, or R 2  and R 3  can be taken together with the nitrogen to which they are attached to form a heterocyclyl, said heterocyclyl optionally substituted with one or more substituents selected from R a ; 
         R a  is independently selected from (C 1 -C 4 )alkyl, (C 3 -C 6 )cycloalkyl, CF 3 , CHF 2 , OH, halo and NH 2 , said alkyl optionally substituted with (C 3 -C 6 )cycloalkyl and CF 3 ; and 
         R b  is independently selected from H and (C 1 -C 4 )alkyl;
 
as defined and described in WO 2016/144847 and US 2018/0051029, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-mm-1 or I-mm′-2 respectively: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         Ring A is aryl or heterocyclyl; 
         n is 0, 1, 2, 3 or 4; 
         R 1  is independently selected from: (C 1 -C 4 )alkyl, (C 3 -C 6 )cycloalkyl, heterocyclyl, CF 3 , CHF 2 , CN and halo, said alkyl, cycloalkyl and heterocyclyl optionally substituted with halo, OH, CH 3 , and OCH 3 ; 
         R 2  is H and R 3  is independently selected from: (C 1 -C 6 )alkyl, (C 3 -C 8 )cycloalkyl, and heterocyclyl each optionally substituted with one or more halo, OH, N(R b ) 2 , or morpholinyl, or R 2  and R 3  can be taken together with the nitrogen to which they are attached to form a heterocyclyl, said heterocyclyl optionally substituted with one or more substituents selected from R a ; 
         R a  is independently selected from (C 1 -C 4 )alkyl, (C 3 -C 6 )cycloalkyl, CF 3 , CHF 2 , OH, halo and NH 2 , said alkyl optionally substituted with (C 3 -C 6 )cycloalkyl or CF 3 ; and 
         R b  is independently selected from H and (C 1 -C 4 )alkyl;
 
as defined and described in WO 2016/144846 and US 2018/0051028, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-nn-1 or I-nn′-2 respectively: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         Ring A is aryl or heterocyclyl; 
         n is 0, 1, 2, 3 or 4; 
         R 1  is independently selected from: (C 1 -C 4 )alkyl, (C 3 -C 6 )cycloalkyl, heterocyclyl, CF 3 , CHF 2 , CN, halo, said alkyl, cycloalkyl and heterocyclyl optionally substituted with halo, OH, CH 3 , and OCH 3 ; 
         R 2  is H and R 3  is independently selected from: (C 1 -C 6 )alkyl, (C 3 -C 8 )cycloalkyl, and heterocyclyl each optionally substituted with one or more halo, OH, N(R b ) 2 , or morpholinyl, or R 2  and R 3  can be taken together with the nitrogen to which they are attached to form a heterocyclyl, said heterocyclyl optionally substituted with one or more substituents selected from R a ; 
         R a  is independently selected from (C 1 -C 4 )alkyl, (C 3 -C 6 )cycloalkyl, CF 3 , CHF 2 , OH, halo and NH 2 , said alkyl optionally substituted with (C 3 -C 6 )cycloalkyl and CF 3 ; and 
         R b  is independently selected from H and (C 1 -C 4 )alkyl;
 
as defined and described in WO 2016/144848 and US 2018/0051030, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-oo-1 or I-oo′-2 respectively: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         Ring A is aryl or heterocyclyl; 
         n is 0, 1, 2, 3 or 4; 
         R 1  is independently selected from: (C 1 -C 4 )alkyl, (C 3 -C 6 )cycloalkyl, heterocyclyl, CF 3 , CHF 2 , CN, halo, said alkyl, cycloalkyl and heterocyclyl optionally substituted with halo, OH, CH 3 , and OCH 3 ; 
         R 2  is H and R 3  is independently selected from: (C 1 -C 6 )alkyl, (C 3 -C 8 )cycloalkyl and heterocyclyl each optionally substituted with one or more halo, OH, N(R b ) 2 , or morpholinyl, or R 2  and R 3  can be taken together with the nitrogen to which they are attached to form a heterocyclyl, said heterocyclyl optionally substituted with one or more substituents selected from R a ; 
         R a  is independently selected from (C 1 -C 4 )alkyl, (C 3 -C 6 )cycloalkyl, CF 3 , CHF 2 , OH, halo and NH 2 , said alkyl optionally substituted with (C 3 -C 6 )cycloalkyl and CF 3 ; and 
         R b  is independently selected from H and (C 1 -C 4 )alkyl;
 
as defined and described in WO 2016/144849 and US 2018/0051035, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK1 and IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-pp-1: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         Ring A is a 3-7 membered saturated or partially unsaturated carbocyclic ring or a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         Ring B is 
       
    
     
       
         
         
             
             
         
       
         
         wherein   represents the portion of the ring fused to the pyrimidine ring and # is -L 2 (R 4 ) P —R X ; each R 1  and R 1′  is independently —R 2 , halogen, —CN, —NO 2 , —OR, —SR, —N(R) 2 , —S(O) 2 R, —S(O) 2 N(R) 2 , —S(O)R, —C(O)R, —C(O)OR, —C(O)N(R) 2 , —C(O)N(R)OR, —N(R)C(O)OR, —N(R)C(O)N(R) 2 , Cy, or —N(R)S(O) 2 R; or R 1  is selected from one of the following formulae: 
       
    
     
       
         
         
             
             
         
       
         
          or 
         two R 1  groups are taken together with their intervening atoms to form an optionally substituted 4-7 membered fused, spiro-fused, or bridged bicyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each Cy is independently an optionally substituted ring selected from a 3-7 membered saturated or partially unsaturated carbocyclic ring or a 4-10 membered saturated or partially unsaturated heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; each R is independently hydrogen, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or: 
         two R groups on the same nitrogen are taken together with their intervening atoms to form a 4-7 membered saturated, partially unsaturated, or heteroaryl ring having 0-3 heteroatoms, in addition to the nitrogen, independently selected from nitrogen, oxygen, or sulfur; 
         each R 2  is independently an optionally substituted group selected from C 1-6 aliphatic, phenyl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each R 4  is independently halogen, —CN, —NO 2 , —OR, —SR, —N(R) 2 , —S(O) 2 R, —S(O) 2 N(R) 2 , —S(O)R, —C(O)R, —C(O)OR, —C(O)N(R) 2 , —N(R)C(O)R, 
         —N(R)C(O)N(R) 2 , —C(O)N(R)OR, —N(R)C(O)OR, —N(R)S(O) 2 N(R) 2 , —N(R)S(O) 2 R, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         R x  is hydrogen, —R 2 , —CN, —NO 2 , halogen, —C(O)N(R) 2 , —C(O)OR, —C(O)R, —N(R) 2 , —NH[Ar], —OR, or —S(O) 2 N(R) 2 ; 
         R z  is hydrogen, —R 2 , —CN, —NO 2 , halogen, —C(O)N(R) 2 , —C(O)OR, —C(O)R, —N(R) 2 , —NH[Ar], —OR, or —S(O) 2 N(R) 2 ; 
         [Ar] is phenyl or a 5-6 membered heteroaromatic ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, wherein [Ar] is substituted by m instances of R 1 ; 
         L 1  is a covalent bond or a C 1-6  bivalent hydrocarbon chain wherein one or two methylene units of the chain are optionally and independently replaced by —N(R)—, —N(R)C(O)—, —C(O)N(R)—, —N(R)S(O) 2 —, —S(O) 2 N(R)—, —O—, —C(O)—, —OC(O)—, —C(O)O—, —S—, —S(O)— or —S(O) 2 —; 
         L 2  is a covalent bond or a C 1-6  bivalent hydrocarbon chain wherein one or two methylene units of the chain are optionally and independently replaced by —N(R)—, —N(R)C(O)—, —C(O)N(R)—, —N(R)S(O) 2 —, —S(O) 2 N(R)—, —O—, —C(O)—, —OC(O)—, —C(O)O—, —S—, —S(O)— or —S(O) 2 —; 
         m is 0-4; 
         n is 0-4; and 
         p is 0-2;
 
as defined and described in WO 2017/004133, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK1 and IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-qq-1: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         Y is N or C—R x ; 
         Ring A is a 3-7 membered saturated or partially unsaturated carbocyclic ring or a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each R 1  and is independently —R 2 , halogen, —CN, —NO 2 , —OR, —SR, —N(R) 2 , —S(O) 2 R, —S(O) 2 N(R) 2 , —S(O)R, —C(O)R, —C(O)OR, —C(O)N(R) 2 , —C(O)N(R)OR, —N(R)C(O)OR, —N(R)C(O)N(R) 2 , Cy, or —N(R)S(O) 2 R; or R 1  is selected from one of the following formulas: 
       
    
     
       
         
         
             
             
         
       
         
          or 
         two R 1  groups are taken together with their intervening atoms to form an optionally substituted 4-7 membered fused, spiro-fused, or bridged bicyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each Cy is independently an optionally substituted ring selected from a 3-7 membered saturated or partially unsaturated carbocyclic ring or a 4-10 membered saturated or partially unsaturated heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each R is independently hydrogen, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or: two R groups on the same nitrogen are taken together with their intervening atoms to form a 4-7 membered saturated, partially unsaturated, or heteroaryl ring having 0-3 heteroatoms, in addition to the nitrogen, independently selected from nitrogen, oxygen, or sulfur; 
         each R 2  is independently an optionally substituted group selected from C 1-6 aliphatic, phenyl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each of R x  and R y  is independently hydrogen, —R 2 , —CN, —NO 2 , halogen, —C(O)N(R) 2 , —C(O)OR, —C(O)R, —N(R) 2 , —H[Ar], —OR, or —S(O) 2 N(R) 2 ; or 
         R x  and R y  are taken together together with their intervening atoms to form a 4-7 membered partially unsaturated carbocyclic ring or a partially unsaturated heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
         R z  is hydrogen, —R 2 , —CN, —NO 2 , halogen, —C(O)N(R) 2 , —C(O)OR, —C(O)R, —N(R) 2 , —NH[Ar], —OR, or —S(O) 2 N(R) 2 ; 
         [Ar] is phenyl or a 5-6 membered heteroaromatic ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, wherein said [Ar] is substituted by m instances of R r ; 
         L 1  is a covalent bond or a C 1-6  bivalent hydrocarbon chain wherein one or two methylene units of the chain are optionally and independently replaced by —N(R)—, —N(R)C(O)—, —C(O)N(R)—, —N(R)S(O) 2 —, —S(O) 2 N(R)—, —O—, —C(O)—, —OC(O)—, —C(O)O—, —S—, —S(O)— or —S(O) 2 —; 
         m is 0-4; and 
         n is 0-4;
 
as defined and described in WO 2017/004134, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-rr-1, I-rr-2, or I-rr-3: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         R is aliphatic, heteroaliphatic, heteroaryl, aryl, halo, amide or CN; 
         R 1  is H, aliphatic or heteroaliphatic; 
         or R and R 1 , together with the atoms to which they are attached, form a heterocyclyl ring; 
         R 2  is H, aliphatic, heteroaliphatic, heterocycloaliphatic, aryl, amide, heterocyclyl or araliphatic; 
         each R 3  independently is H, aliphatic, halogen, heteroaliphatic, —O-aliphatic, heterocyclyl, aryl, araliphatic, —O-heterocyclyl, hydroxyl, nitro, cyano, carboxyl, carboxyl ester, acyl, amide, amino, sulfonyl, sulfonamide, sulfanyl, sulfinyl, haloalkyl, alkylphosphate, or alkylphosphonate; 
         y is from 1 to 6;
 
as defined and described in WO 2016/172560 and US 2016/0311839, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-ss-1: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
       
    
     
       
         
         
             
             
         
       
     
     
       
         
         
             
             
         
       
         
         A is 
         X is N or C—R 7 ; 
         R is hydrogen, R 1 , halogen, cyano, nitro, —OR 1 , —C(═O)—R 1 , —C(═O)O—R 1 , —C(═O)NR 11 —R 1 , —S(═O) 2 —R 1 , —NR 11 C(═O)—R 1 , —NR 11 C(═O)NR 11 R 11 , —NR 11 C(═O)O—R 1 , —NR 11 S(═O) 2 R 1  or —NR 11 R 11 ; 
         R 1  is C 1-6  alkyl substituted with 0-4 R 1a , C 1-6  haloalkyl, C 2-6  alkenyl substituted with 0-3 R 1a , C 2 -6 alkynyl substituted with 0-3 R 1a , C 3-10  cycloalkyl substituted with 0-3 R 1a , C 6-10  aryl substituted with 0-3 R 1a , a 5-10 membered heterocycle containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-3 R 1a , or a 5-10 membered heteroaryl containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-3 R 1a ; 
         R 1a  is hydrogen, ═O, F, Cl, Br, OCF 3 , CN, NO 2 , —(CH 2 ) r OR b , —(CH 2 ) r SR b , —(CH 2 ) r C(O)R b , —(CH 2 ) r C(O)OR b , —(CH 2 ) r OC(O)R b , —(CH 2 ) r NR 11 R 11 , —(CH 2 ) r C(O)NR 11 R 11 , —(CH 2 ) r NR b C(O)R c , —(CH 2 ) r NR b C(O)OR c , —NR b C(O)NR 11 R 11 , —S(O) p NR 11 R 11 , —NR b S(O) p R c , —S(O)R c , —S(O) 2 R c , C 1-6  alkyl substituted with 0-2 R a , C 1-6  haloalkyl, —(CH 2 ) r -3-14 membered carbocycle substituted with 0-3 R a , or —(CH 2 ) r -5-7 membered heterocycle or heteroaryl, each comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p  substituted with 0-3 R a ; 
         R 2  is C 6-11 ) aryl substituted with 0-4 R 2a , a 5-10 membered heterocycle containing 1-4 heteroatoms selected from N, O, and S, substituted with 1-4 R 2a , or a 5-10 membered heteroaryl containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-4 R 1a ; 
         R 2a  at each occurrence is independently selected from hydrogen, ═O, halo, OCF 3 , CN, NO 2 , —(CH 2 ) r OR b , —(CH 2 ) r SR b , —(CH 2 ) r C(O)R b , —(CH 2 ) r C(O)OR b , —(CH 2 ) r OC(O)R b , —(CH 2 ) r NR 11 R 11 , —(CH 2 ) r C(O)NR 11 R 11 , —(CH 2 ) r NR b C(O)R c , —(CH 2 ) r NR b C(O)OR c , —NR b C(O)NR 11 R 11 , —S(O) p NR 11 R 11 , —NR b S(O) p R c , —S(O)R c , —S(O) 2 R c , C 1-6  alkyl substituted with 0-2 R a , C 1-6  haloalkyl, —(CH 2 ) r -3-14 membered carbocycle substituted with 0-1 R a , or —(CH 2 ) r -5-7 membered heterocycle or heteroaryl, each comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p  substituted with 0-2 R a ; 
         R 3  is C 1-6  alkyl substituted with 0-3 R 3a , C 1-6  haloalkyl, C 2-6  alkenyl substituted with 0-3 R 3a , C 2 -6 alkynyl substituted with 0-3 R 1a , C 3-10  cycloalkyl substituted with 0-3 R 3a , C 6-10  aryl substituted with 0-3 R 3a , a 5-10 membered heterocyclyl containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-3 R 3a  or a 5-10 membered heteroaryl containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-3 R 1a ; 
         R 3a  is hydrogen, ═O, F, Cl, Br, OCF 3 , CN, NO 2 , —(CH 2 ) r OR b , —(CH 2 ) r SR b , —(CH 2 ) r C(O)R b , —(CH 2 ) r C(O)OR b , —(CH 2 ) r OC(O)R b , —(CH 2 ) r NR 11 R 11 , —(CH 2 ) r C(O)NR 11 R 11 , —(CH 2 ) r NR b C(O)R c , —(CH 2 ) r NR b C(O), —NR b C(O)NR 11 R 11 , —S(O) p NR 11 R 11 , —NR b S(O) p R c , —S(O)R c , —S(O) 2 R c , C 1-6  alkyl substituted with 0-2 R a , C 1-6 haloalkyl, —(CH 2 ) r -3-14 membered carbocycle substituted with 0-1 R a , or —(CH 2 ) r -5-7 membered heterocycle or heteroaryl, each comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p  substituted with 0-1 R a ; 
         R 4  and R 5  are independently selected from hydrogen, C 1-4  alkyl substituted with 0-1 R f , —(CH 2 )-phenyl substituted with 0-3 R d , and a —(CH 2 ) r -5-7 membered heterocycle comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p ; 
         R 6  and R 7  are independently at each occurrence is selected from hydrogen, ═O, F, Cl, Br, OCF 3 , —CN, NO 2 , —(CH 2 ) r OR b , —(CH 2 ) r SR b , —(CH 2 ) r C(O)R b , —(CH 2 ) r C(O)OR b , —(CH 2 ) r OC(O)R b , —(CH 2 ) r NR 11 R 11 , —(CH 2 ) r C(O)NR 11 R 11 , —(CH 2 ) r NR b C(O)R c , —(CH 2 ) r NR b C(O)OR c , —NR b C(O)NR 11 R 11 , —S(O) p NR 11 R 11 , —NR b S(O) p R c , —S(O) 2 R c , —S(O) 2 R c , C 1-6  alkyl substituted with 0-2 R a , C 1-6 haloalkyl, —(CH 2 ) r -3-14 membered carbocycle substituted with 0-3 R a , or —(CH 2 ) r -5-7 membered heterocycle or heteroaryl, each comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p  substituted with 0-3 R a , provided R 6  and Rare not both hydrogen; 
         R 11  at each occurrence is independently hydrogen, R e , C 1-4  alkyl substituted with 0-1 R f , CH 2 -phenyl substituted with 0-3 R d , or —(CH 2 ) r -5-7 membered heterocycle comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p  substituted with 0-3 R d ; or 
         R 11  and along with another R 11 , R 1 , or R 2  on the same nitrogen atom may join to form an optionally substituted heterocycle; 
         R a  is hydrogen, F, Cl, Br, OCF 3 , CF 3 , CHF 2 , CN, NO 2 , —(CH 2 ) r OR b , —(CH 2 ) r SR b , —(CH 2 ) r C(O)R b , —(CH 2 ) r C(O)OR b , —(CH 2 ) r OC(O)R b , —(CH 2 ) r NR 11 R 11 , —(CH 2 ) r C(O)NR 11 R 11 , —(CH 2 ) r NR b C(O)R c , —(CH 2 ) r NR b  C(O)OR c , —NR b C(O)NR 11 R 11 , —(O) p NR 11 R 11 , —NR b S(O) p R c , —S(O)R c , —S(O) 2 R c , C 1-6  alkyl substituted with 0-1 R f , C 1-6  haloalkyl, —(CH 2 ) r -3-14 membered carbocycle, or —(CH 2 ) r -5-7 membered heterocycle or heteroaryl, each comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p ; or two R a  on adjacent or the same carbon atom form a cyclic acetal of the formula —O—(CH 2 ) r —O—, or —O—CF 2 —O—, wherein n is selected from 1 or 2; 
         R b  is hydrogen, R e , C 1-6  alkyl substituted with 0-2 R d , C 1-6 haloalkyl, C 3-6  cycloalkyl substituted with 0-2 R d , or (CH 2 ) r -phenyl substituted with 0-3 R d ; 
         R c  is C 1-6  alkyl substituted with 0-1 R f , C 3-6  cycloalkyl, or (CH 2 ) r -phenyl substituted with 0-3 R f ; 
         R d  is hydrogen, F, Cl, Br, OCF 3 , CF 3 , CN, NO 2 , —OR e , —(CH 2 ) r C(O)R c , —NR e R e , —NR e C(O)OR c , C 1-6  alkyl, or (CH 2 ) r -phenyl substituted with 0-3 R f ; 
         R e  is selected from hydrogen, C 1-6  alkyl, C 3-6  cycloalkyl, and (CH 2 ) r -phenyl substituted with 0-3 R f ; 
         R f  is hydrogen, halo, NH 2 , OH, or O(C 1-6 alkyl); 
         p is 0, 1, or 2; 
         r is 0, 1, 2, 3, or 4; and 
         m is 0, 1, or 2;
 
as defined and described in WO 2013/106612 and US 2015/0011532, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-tt-1: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         A is a triazole optionally substituted by 0-2 R; 
         X is N or C—R 7 ; 
         R is hydrogen, R′, halogen, cyano, nitro, —OR 1 , —C(═O)—R 1 , —C(═O)O—R 1 , —C(═O)NR 11 —R 1 , —S(═O) 2 —R 1 , —NR 11 C(═O)—R′, —NR 11 C(═O)NR 11 R 11 , —NR 11 C(═O)O—R′, (═O) 2 R 1  or —NR 11 R 11 , 
         R 1  is C 1-6  alkyl substituted with 0-4 R 1a , C 1-6  haloalkyl, C 2-6  alkenyl substituted with 0-3 R 1a , C 2 -6 alkynyl substituted with 0-3 R 1a , C 3-10 cycloalkyl substituted with 0-3 R 1a , C 6-10  aryl substituted with 0-3 R 1a , a 5-10 membered heterocycle containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-3 R 1a , or a 5-10 membered heteroaryl containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-3 R 1a ; 
         R 1a  is hydrogen, ═O, F, Cl, Br, OCF 3 , CN, NO 2 , —(CH 2 ) r OR b , —(CH 2 ) r SR b , —(CH 2 ) r C(O)R b , —(CH 2 ) r C(O)OR b , —(CH 2 ) r OC(O)R b , —(CH 2 ) r NR 11 R 11 , —(CH 2 ) r C(O)NR 11 R 11 , —(CH 2 ) r NR b  C(O)R c , —(CH 2 ) r NR b C(O)—NR b C(O)NR 11 R 11 , —S(O) p NR 11 R 11 , —NR b S(O) p R c , —S(C)R c , —S(O) 2 R c , C 1-6  alkyl substituted with 0-2 R a , C 1-6  haloalkyl, —(CH 2 ) r -3-14 membered carbocycle substituted with 0-3 R a , or —(CH 2 ) r -5-7 membered heterocycle or heteroaryl, each comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p  substituted with 0-3 R a ; 
         R 2  is C 6-11 ) aryl substituted with 0-4 R 2a , a 5-10 membered heterocycle containing 1-4 heteroatoms selected from N, O, and S, substituted with 1-4 R 2a , or a 5-10 membered heteroaryl containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-4 R 2a ; 
         R 2a  at each occurrence is independently selected from hydrogen, ═O, halo, OCF 3 , CN, NO 2 , —(CH 2 ) r OR b , —(CH 2 ) r SR b , —(CH 2 ) r C(O)R b , —(CH 2 ) r C(O)OR b , —(CH 2 ) r OC(O)R b , —(CH 2 ) r NR 11 R 11 , —(CH 2 ) r C(O)NR 11 R 11 , —(CH 2 ) r NR b C(O)R c , —(CH 2 ) r NR b C(O)OR c , —NR b C(O)NR 11 R 11 , —S(O) p NR 11 R 11 , —NR b S(O) p R c , —S(O)R c , —S(O) 2 R c , C 1-6  alkyl substituted with 0-2 R a , C 1-6  haloalkyl, —(CH 2 ) r -3-14 membered carbocycle substituted with 0-1 R a , or —(CH 2 ) r -5-7 membered heterocycle or heteroaryl, each comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p  substituted with 0-2 R a ; 
         R 3  is C 1-6  alkyl substituted with 0-3 R 3a , C 1-6  haloalkyl, C 2-6  alkenyl substituted with 0-3 R 3a , C 2 -6 alkynyl substituted with 0-3 R 3a , C 3-10 cycloalkyl substituted with 0-3 R 3a , C 6-10  aryl substituted with 0-3 R 3a , a 5-10 membered heterocyclyl containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-3 R 3′  or a 5-10 membered heteroaryl containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-3 R 1a ; 
         R 3a  is hydrogen, ═O, F, Cl, Br, OCF 3 , CN, NO 2 , —(CH 2 ) r OR b , —(CH 2 ) r SR b , —(CH 2 ) r C(O)R b , —(CH 2 ) r C(O)OR b , —(CH 2 ) r OC(O)R b , —(CH 2 ) r NR 11 R 11 , —(CH 2 ) r C(O)NR 11 R 11 , —(CH 2 ) r NR b  C(O)R c , —(CH 2 ) r NR b C(O)OR c , —NR b C(O)NR 11 R 11 , S(O) p NR 11 R 11 , —NR b S(O) p R c , —S(O)R c , —S(O) 2 R c , C 1-6  alkyl substituted with 0-2 R a , C 1-6 haloalkyl, —(CH 2 ) r -3-14 membered carbocycle substituted with 0-1 R a , or —(CH 2 ) r -5-7 membered heterocycle or heteroaryl, each comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p  substituted with 0-1 R a ; 
         R 4  and R 5  are independently selected from hydrogen, C 1-4  alkyl substituted with 0-1 R f , —(CH 2 )-phenyl substituted with 0-3 R d , and a —(CH 2 ) r -5-7 membered heterocycle comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p ; 
         R 6  and R 7  are independently at each occurrence is selected from hydrogen, ═O, F, Cl, Br, OCF 3 , —CN, NO 2 , —(CH 2 ) r OR b , —(CH 2 ) r SR b , —(CH 2 ) r C(O)R b , —(CH 2 ) r C(O)OR b , —(CH 2 ) r OC(O)R b , —(CH 2 ) r NR 11 R 11 , —(CH 2 ) r C(O)NR 11 R 11 , —(CH 2 ) r NR b C(O)R c , —(CH 2 ) r NR b C(O)OR c , —NR b C(O)NR 11 R 11 , —S(O) p NR 11 R 11 , —NR b S(O) p R c , —S(O)R c , —S(O) 2 R c , C 1-6  alkyl substituted with 0-2 R a , C 1-6 haloalkyl, —(CH 2 ) r -3-14 membered carbocycle substituted with 0-3 R a , or —(CH 2 ) r -5-7 membered heterocycle or heteroaryl, each comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p  substituted with 0-3 R a , provided R 6  and R 7  are not both hydrogen; 
         R 11  at each occurrence is independently hydrogen, R e , C 1-4  alkyl substituted with 0-1 R f , CH 2 -phenyl substituted with 0-3 R d , or —(CH 2 ) r -5-7 membered heterocycle comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p  substituted with 0-3 R d ; or 
         R 11  and along with another R 11 , R 1 , or R 2  on the same nitrogen atom may join to form an optionally substituted heterocycle; 
         R a  is hydrogen, F, Cl, Br, OCF 3 , CF 3 , CHF 2 , CN, NO 2 , —(CH 2 ) r OR b , —(CH 2 ) r SR b , —(CH 2 ) r C(O)R b , —(CH 2 ) r C(O)OR b , —(CH 2 ) r OC(O)R b , —(CH 2 ) r NR 11 R 11 , —(CH 2 ) r C(O)NR 11 R 11 , —(CH 2 ) r NR b C(O)R c , —(CH 2 ) r NR b C(O)OR c , —NR b C(O)NR 11 R 11 , —S(O) p NR 11 R 11 , —NR b S(O) p R c , —S(O)R c , —S(O) 2 R c , C 1-6  alkyl substituted with 0-1 R f , C 1-6  haloalkyl, —(CH 2 ) r -3-14 membered carbocycle, or —(CH 2 ) r -5-7 membered heterocycle or heteroaryl, each comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p ; or two R a  on adjacent or the same carbon atom form a cyclic acetal of the formula —O—(CH 2 ) r —O—, or —O—CF 2 —O—, wherein n is selected from 1 or 2; 
         R b  is hydrogen, R e , C 1-6  alkyl substituted with 0-2 R d , C 1-6  haloalkyl, C 3-6  cycloalkyl substituted with 0-2 R d , or (CH 2 ) r -phenyl substituted with 0-3 R d ; 
         R c  is C 1-6  alkyl substituted with 0-1 R f , C 3-6  cycloalkyl, or (CH 2 ) r -phenyl substituted with 0-3 R f ; 
         R d  is hydrogen, F, Cl, Br, OCF 3 , CF 3 , CN, NO 2 , OR e —(CH 2 ) r C(O)R c , —NR e R e , —NR e C(O)OR c , C 1-6  alkyl, or (CH 2 ) r -phenyl substituted with 0-3 R f ; 
         R e  is selected from hydrogen, C 1-6  alkyl, C 3-6  cycloalkyl, and (CH 2 ) r -phenyl substituted with 0-3 
         R f ; 
         R f  is hydrogen, halo, NH 2 , OH, or O(C 1-6 alkyl); 
         p is 0, 1, or 2; 
         r is 0, 1, 2, 3, or 4; and 
         m is 0, 1, or 2;
 
as defined and described in WO 2013/106614 and US 2015/0045347, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-uu-1: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         X is N or C—R 7 ; 
         R is R 1 , halogen, cyano, nitro, —O—R 1 , —C(═O)—R 1 , —C(═O)O—R 1 , —C(═O)NR 11 —R 1 , —S(═O) 2 —R 1 , —NR 11 C(═O)—R 1 , —NR 11 C(═O)NR 11 —R 1 , —NR 11 C(═O)O—R 1 , —NR 11 S(═O) 2 —R 1 , or —NR 11 —R 1 ; 
         R 1  is C 1-6  alkyl substituted with 0-4 R 1a , C 1-6  haloalkyl, C 2-6  alkenyl substituted with 0-3 R 1a , C 2 -6 alkynyl substituted with 0-3 R 1a , C 3-10 cycloalkyl substituted with 0-3 R 1a , C 6-10  aryl substituted with 0-3 R 1a , a 5-10 membered heterocycle containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-3 R 1a , a 5-10 membered heteroaryl containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-3 R 1a ; 
         R 1a  is hydrogen, ═O, F, Cl, Br, OCF 3 , CN, NO 2 , —(CH 2 ) r OR b , —(CH 2 ) r SR b , —(CH 2 ) r C(O)R b , —(CH 2 ) r C(O)OR b , —(CH 2 ) r OC(O)R b , —(CH 2 ) r C(O)NR 11 R 11 , —(CH 2 ) r NR b C(O)R c , —(CH 2 ) r NR b C(O)OR c , —NR b C(O)NR 11 R 11 , —S(O) p NR 11 R 11 , —NR b S(O) p R c , —S(O)R c , —S(O) 2 R c , C 1-6  alkyl substituted with 0-2 R a , C 1-6  haloalkyl, —(CH 2 ) r -3-14 membered carbocycle substituted with 0-3 R a , or —(CH 2 ) r -5-7 membered heterocycle comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p  substituted with 0-3 R a ; 
         R 2  is C 6-10  aryl substituted with 0-4 R 2a , a 5-10 membered heterocycle containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-4 R 2a , a 5-10 membered heteroaryl containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-4 R 2a ; 
         R 2a  at each occurrence is independently selected from hydrogen, ═O, halo, OCF 3 , CN, NO 2 , —(CH 2 ) r OR b , —(CH 2 ) r SR b , —(CH 2 ) r C(O)R b , —(CH 2 ) r C(O)OR b , —(CH 2 ) r OC(O)R b , —(CH 2 ) r NR 11 R 11 , —(CH 2 ) r C(O)NR 11 R 11 , —(CH 2 ) r NR b C(O)R c , —(CH 2 ) r NR b C(O)OR c , —NR b C(O)NR 11 R 11 , —X(O) p NR 11 R 11 , NR b S(O) p R c , —S(O)R c , —S(O) 2 R ◯ , C 1-6  alkyl substituted with 0-2 R a , C 1-6  haloalkyl, —(CH 2 ) r -3-14 membered carbocycle substituted with 0-1 R a , or —(CH 2 ) r -5-7 membered heterocycle or heteroaryl, each comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p  substituted with 0-2 R a ; 
         R 3  is C 1-6  alkyl substituted with 0-3 R 3a , C 1-6  haloalkyl, C 2-6  alkenyl substituted with 0-3 R 3a , C 2 -6 alkynyl substituted with 0-3 R 3a , C 3-10 cycloalkyl substituted with 0-3 R 3a , C 6-10  aryl substituted with 0-3 R 3a , a 5-10 membered heterocycle containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-3 R 3a , or a 5-10 membered heteroaryl containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-3 R 1a ; 
         R 3a  is hydrogen, ═O, F, Cl, Br, OCF 3 , CN, NO 2 , —(CH 2 ) r OR b , —(CH 2 ) r SR b , —(CH 2 ) r C(O)R b , —(CH 2 ) r C(O)OR b , —(CH 2 ) r OC(O)R b , —(CH 2 ) r NR 11 R 11 , (CH 2 ) r C(O)NR 11 R 11 , —(CH 2 ) r NR b C(O)R c , —(CH 2 ) r NR b C(O)OR c , —NR b C(O)NR 11 R 11 , S(O) p NR 11 R 11 , —NR b S(O) p R c , —S(O)R c , —S(O) 2 R c , C 1-6  alkyl substituted with 0-2 R a , C 1-6  haloalkyl, —(CH 2 ) r -3-14 membered carbocycle substituted with 0-1 R a , or —(CH 2 ) r -5-7 membered heterocycle or heteroaryl, each comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p  substituted with 0-1 R a ; 
         R 4  and R 5  are independently selected from hydrogen, C 1-4  alkyl substituted with 0-1 R f , —(CH 2 )-phenyl substituted with 0-3 R d , and a —(CH 2 ) r -5-7 membered heterocycle comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p ; 
         R 6  and R 7  are independently at each occurrence is selected from hydrogen, ═O, F, Cl, Br, OCF 3 , —CN, NO 2 , —(CH 2 ) r OR b , —(CH 2 ) r SR b , —(CH 2 ) r C(O)R b , —(CH 2 ) r C(O)OR b , —(CH 2 ) r OC(O)R b , —(CH 2 ) r NR 11 R 11 , —(CH 2 ) r C(O)NR 11 R 11 , —(CH 2 ) r NR b C(O)R c , —(CH 2 ) r NR b C(O)OR c , —NR b C(O)NR 11 R 11 , —S(O) p NR 11 R 11 , NR b S(O) p R c , —S(O)R c , —S(O) 2 R c , C 1-6  alkyl substituted with 0-2 R a , C 1-6  haloalkyl, —(CH 2 ) r -3-14 membered carbocycle substituted with 0-3 R a , or —(CH 2 ) r -5-7 membered heterocycle or heteroaryl, each comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p  substituted with 0-3 R a , provided R 6  and R 7  are not both hydrogen; 
         R 11  at each occurrence is independently R e , C 1-4  alkyl substituted with 0-1 R f , CH 2 -phenyl substituted with 0-3 R d , or —(CH 2 ) r -5-7 membered heterocycle or heteroaryl, each comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p  substituted with 0-3 R d ; 
         alternatively, R 11  and along with another R 11 , R 1 , or R 2  on the same nitrogen atom may join to form an optionally substituted azetidinyl, pyrrolidinyl, piperidinyl, morpholinyl, or 4-(C 1-6  alkyl)piperazinyl; 
         R a  is R d , F, Cl, Br, OCF 3 , CF 3 , CHF 2 , CN, NO 2 , —(CH 2 ) r OR b , —(CH 2 ) r SR b , —(CH 2 ) r C(O)R b , —(CH 2 ) r C(O)OR b , —(CH 2 ) r OC(O)R b , —(CH 2 ) r NR 11 R 11 , —(CH 2 ) r C(O)NR 11 R 11 , —(CH 2 ) r NR b  C(O)R c , —(CH 2 ) r NR b C(O)OR c , —NR b C(O)NR 11 R 11 , —S(O) p NR 11 R 11 , —NR b S(O) p R c , —S(O) 2 R c , —S(O) 2 R c , C 1-6  alkyl substituted with 0-1 R f , C 1-6  haloalkyl, —(CH 2 ) r -3-14 membered carbocycle, or —(CH 2 ) r -5-7 membered heterocycle comprising carbon atoms and 1-4 heteroatoms selected from N, O, and S(O) p ; alternatively two R a  on adjacent or the same carbon atom form a cyclic acetal of the formula —O—(CH 2 ) p —O—, or —O—CF 2 —O—, wherein n is selected from 1 or 2; 
         R b  is R c , C 1-6  alkyl substituted with 0-2 R d , C 1-6  haloalkyl, C 3-6 cycloalkyl substituted with 0-2 R d , or (CH 2 ) r -phenyl substituted with 0-3 R d ; 
         R c  is C 1-6  alkyl substituted with 0-1 R f , C 3-6  cycloalkyl, or (CH 2 ) r -phenyl substituted with 0-3 R f ; 
         R d  is hydrogen, F, Cl, Br, OCF 3 , CF 3 , CN, NO 2 , OR e —(CH 2 ) r C(O)R c , —NR e R e , —NR e C(O)OR c , C 1-6  alkyl, or (CH 2 ) r -phenyl substituted with 0-3 R f ; 
         R e  is selected from hydrogen, C 1-6  alkyl, C 3-6  cycloalkyl, and (CH 2 ) r -phenyl substituted with 0-3 
         R f ; 
         R f  is hydrogen, halo, NH 2 , OH, or O(C 1-6 alkyl); 
         p is 0, 1, or 2; 
         r is 0, 1, 2, 3, or 4; and 
         m is 0, 1, or 2;
 
as defined and described in WO 2013/106641 and US 2015/0018344, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-vv-1 or I-vv-2: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         R 1  is:
       (a) C 2-3  hydroxyalkyl substituted with zero to 4 R 1a  wherein R 1a  is independently selected from F, Cl, —OH, —CHF 2 , —CN, —CF 3 , —OCH 3 , and cyclopropyl;   (b) C 1-3  alkyl substituted with —O(C 1-3  alkyl) and zero to 4 R 1a  wherein R 1a  is independently selected from F, Cl, —OH, —CHF 2 , —CN, —CF 3 , and cyclopropyl;   (c) C 4-8  alkyl substituted with zero to 7 R 1a  wherein R 1a  is independently selected from F, Cl, —OH, —CHF 2 , —CF 3 , —CN—OCH 3 , cyclopropyl, and —OP(O)(OH) 2 ;   (d) —(CH 2 ) 2-4 NHC(O)(C 1-6  alkyl), —(CH 2 ) 2 CH(CH 3 )NHC(O)(C 1-6 alkyl), —(CH 2 ) 2 CH(CH 3 )NHC(O)(CH 2 ) 0-1 NH(C 1-6  alkyl), or —(CH 2 ) 2 CH(CH 3 )NHC(O)(CH 2 ) 0-1 N(C 1-4  alkyl) 2 ;   (e) cyclohexyl substituted with zero to 2 substituents independently selected from —OH, —OCH 3 , C 1-6  alkyl, C 1-6 hydroxyalkyl, —C(O)NH 2 , —C(O)NH(C 1-3  alkyl), —C(O)NH(C 1-6  hydroxyalkyl), —C(O)NH(C 3-6  cycloalkyl), —C(O)NH(C 3-6  fluoro cycloalkyl), —NHC(O)(C 1-3  alkyl), —NHC(O)O(C 1-3  alkyl), —NHS(O) 2 CH 3 , —S(O) 2 NH 2 , —S(O) 2 (C 1-3  alkyl), —S(C 1-3  alkyl), thiazolyl, methyl pyrazolyl, and C 1-3  alkyl substituted with —OH and cyclopropyl;   (f) —(CH 2 ) 2 (phenyl) wherein said phenyl is substituted with —C(O)NH 2 , —C(O)NH(C 1-3  alkyl), or —S(O) 2 NH 2 ; or   (g) piperidinyl substituted with —C(O)(C 1-3  alkyl);   
     
         R 2  is phenyl, pyridinyl, pyridazinyl, pyrimidinyl, pyrazolyl, thiazolyl, or triazolyl, each substituted with zero to 2 substituents independently selected from F, Cl, —OH, —CN, C 1-3  alkyl, —CH 2 C(O)OCH 3 , —O(C 1-3 alkyl), —NH 2 , —NH(C 1-3  alkyl), —NH(cyclopropyl), —C(O)NH 2 , —NHC(O)(C 1-3  alkyl), —NH(tetrahydropyranyl), hydroxypyrrolidinyl, ═O, —O(piperidinyl), and pyridinyl; and 
         R 3  is:
       (a) C 1-6  alkyl substituted with zero to 4 substituents independently selected from F, —OH, —CH 3 , —CF 3 , and C 3-6 cycloalkyl;   (b) C 3-6  cycloalkyl substituted with zero to 2 substituents independently selected from F, —OH, C 1-3  hydroxyalkyl, —CH 3 , —CF 2 H, —NH 2 , and —C(O)OCH 2 CH 3 ;   (c) oxetanyl, tetrahydropyranyl, or fluoro tetrahydropyranyl;   (d) phenyl substituted with zero to 2 substituents independently selected from —OH, —CN, —O(C 1-3  alkyl), C 1-3  hydroxyalkyl, —C(O)NH 2 , —S(O) 2 NH 2 , —NHS(O) 2 (C 1-3  alkyl), pyrazolyl, imidazolyl, and methyl tetrazolyl; or   
     
       
    
     
       
         
         
             
             
         
       
         
         
           
             (e) 
           
         
       
    
     
       
         
         
             
             
         
       
     
     as defined and described in WO 2014/074675 and US 2015/0284382, the entirety of each of which is herein incorporated by reference. 
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-xx-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         R 1  is an optionally substituted aromatic heterocyclic group or an optionally substituted C 6-14  aryl group; 
         R 2  is a hydrogen atom or a substituent; 
         R 3  and R 4  are independently a hydrogen atom or a substituent, or R 3  and R 4  in combination optionally form an optionally substituted ring; 
         R 5  and R 6  are independently a hydrogen atom or a substituent, or R 5  and R 6  in combination optionally form an optionally substituted ring; 
         X is CR 7 R 8 , NR 9 , 0 or S; 
         R 7  and R 8  are independently a hydrogen atom or a substituent, or Wand R 8  in combination optionally form an optionally substituted ring; and 
         R 9  is a hydrogen atom or a substituent;
 
as defined and described in WO 2015/068856 and US 2015/0133451, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein LBM is an E3 ubiquitin ligase (IAP) binding moiety 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-yy-1 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, and wherein the variable R is as defined and described in Ohoka, N. et al. (2017). In Vivo Knockdown of Pathogenic Proteins via Specific and Nongenetic Inhibitor of Apoptosis Protein (IAP)-dependent Protein Erasers (SNIPERs).  Journal of Biological Chemistry,  292(11), 4556-4570 the entirety of each of which is herein incorporated by reference. 
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-zz-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         R 1  denotes absent, A or Q-Het, 
         Z is 
       
    
     
       
         
         
             
             
         
       
         
         wherein 
         X denotes O, S or N, 
         Y denotes C or N, 
         T denotes C or N, or 
         Z denotes a pyridine or a pyridazine group, 
         R a  is absent, OR 3 , CF 3 , Hal, or NO 2 , 
         R b  is absent, A, or COHet, 
         R 2  denotes H, Het, Q-Het, Cyc, A or OA, 
         each Het is independently a 4-9 membered monocyclic ring or a fused, spiro or bridged bicyclic ring, which is saturated, unsaturated, or aromatic, which contains 1 to 3 heteroatoms independently selected from N, O, and S, and a group CO, SO or SO 2 , and wherein 1 or 2H atoms may be replaced by A, OA, COA, CN, Hal, NO 2 , OR 3 , SOA and/or SO 2 A, 
         Cyc denotes a 4-8 saturated carbocyclic ring optionally containing a group SO, SO 2 , or CO, and optionally substituted once or twice by a group selected from CO(NR 3 ) 2 , COHet, OR 3 , Het 1 , A, CH 2 Het 1 , NH 2 , NHCOA, OCH 2 Cyc 1 , SO 2 A and —SA(═NH)(═O), 
         each Q is independently a linear or branched alkylene, having 1 to 6 carbon atoms wherein 1-5H atoms may be replaced by a group independently selected from OR 3 , Hal, and N(R 3 ) 2 , and wherein 1 or 2 CH 2  groups may be replaced by a group independently selected from CO, SO, SO 2  and NR 3 , or Q denotes a 4-8-membered bivalent heterocyclic ring, which is saturated, unsaturated or aromatic and which contains 1 to 3 heteroatoms independently selected from N, O and S, 
         each A is independently a linear or branched alkyl having 1 to 10 carbon atoms wherein 1 to 7H atoms may be replaced by a group independently selected from —OR 3 , Hal, NHSO 2 A, SO 2 A, SOA, and N(R 3 ) 2 , and wherein 1, 2 or 3 non-adjacent —CH 2 — groups may be replaced by a group independently selected from —CO—, NR 3  and —O—, 
         each Hal is independently F, Cl, Br or I, 
         each R 3  is independently H or C 1 -C 6 -alkyl wherein 1H atom may be replaced by a group selected from OH, O—C 1 -C 6 -alkyl, and Hal, 
         each Het 1  is independently a five- or six membered saturated monocyclic heterocycle which contains 1-3 N- and/or O-atoms, which optionally is monosubstituted by A, 
         Cyc 1  denotes cycloalkyl with 3-7 atoms; as defined and described in WO 2014/008992 and US 2015/0141396, the entirety of each of which is herein incorporated by reference. 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-aaa-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         Ring A is a monocyclic heteroaryl; 
         R 1  is one to three optionally substituted with R 10  monocyclic or bicyclic heteroaryl; 
         R 2  is, —C(O)NH 2 , —C(O)NH—R 0 , —C(O)NH—R 00 —OH, —C(O)NH—R 00 —OR 0 , —C(O)N(R 0 ) 2 , —C(O)NH-cycloalkyl, —C(O)NH-heterocycloalkyl, —C(O)NH-(pyrazolyl optionally substituted with) R 0 ), —C(O)—R 0 , —C(O)-cycloalkyl, —S(O) 2 NH 2 , —S(O) 2 NH—R 0 , —S(O) 2 NH-cycloalkyl, —R 00 —OH, —R 00 —OR 0 , —R 00 -(morpholin-4-yl) phenyl, oxadiazolyl, or tetrazolyl optionally substituted with R 0 , wherein oxadiazolyl in R 2  is, R 0 , R 00 —OH or may be substituted with R ◯ —OR ◯ ; 
         R 3  is, H, R ◯ , halogeno-lower alkyl, cycloalkyl, heterocycloalkyl, phenyl, pyridyl, pyrimidinyl, pyrazinyl, —C(O)N(R 0 ) 2 , —R 00 -cycloalkyl, —R 00 -heterocycloalkyl, —R 00 -phenyl, —R 00 —OH or a —R 00 —OR 0 , wherein the cycloalkyl in R 3 , heterocycloalkyl, phenyl and pyridyl, R 0 , halogen, —C(O)OR 0 , —C(O)—R 0 , —OH, —OR 0 , —S(O) 2 —R 0 , —O-halogeno-lower alkyl, —OR 00 -(morpholin-4-yl), —R 00 —OH, —R 00 —OR 0 , morpholin-4-yl or, —R 00 -(morpholin-4-yl) may be substituted; 
         R 10  may be the same or different from each other, R 0 , halogen, halogeno-lower alkyl, cycloalkyl, —OR 0 , optionally substituted amino, —O-halogeno-lower alkyl, —R 00 —OH, —R 00 —OR 0  or —R 00 — is optionally amino substituted, 
         R 0  is the same or different from each other, lower alkyl, 
         R 00  are identical or different from each other, it is a lower alkylene;
 
as defined and described in WO 2011/043371, the entirety of which is herein incorporated by reference.
 
       
    
     In some embodiments, the compound of formula I-aaa-1 above is provided as a compound of formula I-aaa-2, I-aaa-3, or I-aaa-4: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein: 
         each of LBM, L, R 1 , R 2 , R 3 , and R m  is as defined above. 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-bbb-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         X is selected from O, S, and NH; 
         A is selected from aryl or heteroaryl; 
         R at each occurrence is independently selected from hydrogen, cyano, halo, hydroxy, —NO 2 , —NR 3 R 4 , optionally substituted alkyl, optionally substituted aryl, optionally substituted cycloalkyl, optionally substituted heterocycloalkyl or optionally substituted heteroaryl; wherein the optional substituent, in each occurrence, is independently selected from halo, alkyl, haloalkyl, cyano, —NR 5 R 6  or —COOR 7 ; 
         R 1  at each occurence is independently selected from hydrogen, halogen, alkyl, aryl, heterocycloalkyl, heterocycloalkylalkyl, heteroaryl, Y-arylalkyl or —Y-cycloalkyl; wherein cycloalkyl, aryl, heterocycloalkyl, heterocycloalkylalkyl, heteroaryl and arylalkyl can be optionally substituted with hydroxy, alkyl, haloalkyl, cyano or halo; 
         Y is selected from direct bond, O, —C(O)— or NR 7 ; 
         R 2  at each occurence is independently selected from hydrogen, carboxy, cyano, hydroxy, hydroxyalkyl, alkyl, aryl, heteroaryl, —SO 2 R 5  or oxo; 
         R 3  and R 4  are independently selected from hydrogen, hydroxyalkyl, aminoalkyl, optionally substituted alkyl, optionally substituted heterocyclyl, optionally substituted aryl; wherein the optional substituent, in each occurrence, is independently selected from halo, haloalkyl or —COOR 7 ; 
         R 5  and R 6  are independently selected from hydrogen, alkyl, COR 7  or —COOR 7 ; 
         R 7  at each occurrence is independently selected from hydrogen or alkyl; and 
         m, n and p are selected from 1, 2 or 3;
 
as defined and described in WO 2013/042137, the entirety of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-ccc-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         Ring Z 1  is an optionally substituted heteroaryl; 
         Ring Z 2  is an optionally substituted heterocycloalkyl, optionally substituted heteroaryl or a direct bond; 
         R 1  is alkyl, cyano, —NR a R b  or optionally substituted groups selected from cycloalkyl, aryl or heterocyclyl; wherein the substituent, at each occurrence, independently is alkyl, alkoxy, halogen, hydroxyl, hydroxyalkyl, amino, aminoalkyl, nitro, cyano, haloalkyl, haloalkoxy, —OCO—CH 2 —O-alkyl, —OP(O)(O-alkyl) 2  or —CH 2 —OP(O)(O-alkyl) 2 ; 
         R 2 , at each occurrence, independently is an optionally substituted group selected from alkyl or cycloalkyl; wherein the substituent, at each occurrence, is independently halogen, alkoxy, hydroxyl, hydroxyalkyl, haloalkyl or haloalkoxy; 
         R 3 , at each occurrence, independently is hydrogen, halogen, alkyl, haloalkyl, haloalkoxy, alkoxy, —NR a R b , hydroxyl or hydroxyalkyl; 
         R a  is hydrogen or alkyl; 
         R b  is hydrogen, alkyl, acyl, hydroxyalkyl, —SO 2 -alkyl or optionally substituted cycloalkyl; 
         m and n are independently 1 or 2;
 
as defined and described in WO 2015/104662 and US 2016/0326151, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-ddd-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         X 1  and X 3  independently are CH or N; X 2  is CR 2  or N; provided one and not more than one of X 1 , X 2  or X 3  is N; 
         A is O or S; 
         Y is —CH 2 — or O; 
         Ring Z is aryl or heterocyclyl; 
         R 1 , at each occurrence, is independently halo or optionally substituted heterocyclyl; wherein the substituent is alkyl, alkoxy, aminoalkyl, halo, hydroxyl, hydroxyalkyl or —NR a R b ; 
         R 2  is hydrogen, optionally substituted cycloalkyl, optionally substituted aryl, optionally substituted heterocyclyl or —NR a R b ; wherein the substituent is alkyl, amino, halo or hydroxyl; 
         R 3 , at each occurrence, is alkyl or hydroxyl; 
         R a  and R b  are independently hydrogen, alkyl, acyl or heterocyclyl; 
         m and n are independently 0, 1 or 2; 
         p is 0 or 1;
 
as defined and described in WO 2015/104688 and US 2016/0340366, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-eee-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         Z 1  is optionally substituted cycloalkyl, optionally substituted aryl, optionally substituted heterocyclyl or is absent; 
         Z 2  is optionally substituted cycloalkyl, aryl or heterocyclyl; 
         R 1  is hydrogen, optionally substituted alkyl, amino, halogen, cyano, optionally substituted cycloalkyl, optionally substituted aryl, optionally substituted heterocyclyl, optionally substituted arylalkyl or optionally substituted heterocyclylalkyl; 
         R 2  at each occurrence is hydrogen, halogen, amino, optionally substituted alkyl, optionally substituted cycloalkyl, optionally substituted aryl, optionally substituted heterocyclyl, optionally substituted arylalkyl or optionally substituted heterocyclylalkyl; 
         R 3  at each occurrence is hydroxy, halogen, optionally substituted alkyl, optionally substituted alkoxy, optionally substituted cycloalkyl or —NR a R b ; 
         R a  and R b , independently for each occurrence, are hydrogen, optionally substituted alkyl, optionally substituted acyl, optionally substituted cycloalkyl, optionally substituted aryl, optionally substituted heterocyclyl, optionally substituted arylalkyl or optionally substituted heterocyclylalkyl; 
         m at each occurrence, is 0, 1 or 2; and 
         n at each occurrence, is 0, 1, or 2;
 
as defined and described in WO 2015/193846 and US 2017/0152263, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-fff-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein R 0  represents hydrogen or C 1 -C 4 -alkyl, where the C 1 -C 4 -alkyl radical may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy and halogen; 
         R 1  represents hydrogen, halogen, cyano, C(═O)OH, C(═O)OR a , C(═O)NH 2 , C(═O)N(H)R a , C(═O)N(R a )R b , C(═O)R d , hydroxy or C 1 -C 6 -alkyl, where the C 1 -C 6 -alkyl radical is optionally mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)OH, C(═O)OR a , S(═O) 2 —C 1 -C 6 -alkyl, NH 2 , NHR a , N(R a )R b , C 1 -C 6 -alkoxy which is optionally mono- or polysubstituted by identical or different radicals from the group consisting of halogen, C 3 -C 8 -cycloalkoxy which is optionally mono- or polysubstituted by identical or different radicals from the group consisting of halogen, heterocycloalkyl which is optionally mono- or polysubstituted by identical or different radicals from the group consisting of R c ,
       or represents C 1 -C 6 -alkoxy, where the C 1 -C 6 -alkoxy radical may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)OH, C(═O)OR a , S(═O) 2 —C 1 -C 6 -alkyl, NH 2 , NHR a , N(R a )R b , C 3 -C 8 -cycloalkyl which is optionally mono- or polysubstituted by identical or different radicals from the group consisting of halogen, C 1 -C 6 -alkoxy which is optionally mono- or polysubstituted by identical or different radicals from the group consisting of halogen, C 3 -C 8 -cycloalkoxy which is optionally mono- or polysubstituted by identical or different radicals from the group consisting of halogen, heterocycloalkyl which is optionally mono- or polysubstituted by identical or different radicals from the group consisting of R c , aryl which is optionally mono- or polysubstituted by identical or different radicals from the group consisting of R c , or 5- or 6-membered heteroaryl which is optionally mono- or polysubstituted by identical or different radicals from the group consisting of R c ,   or represents C 3 -C 8 -cycloalkoxy or heterocycloalkoxy which may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano and C 1 -C 6 -alkyl,   or represents aryloxy or 5- or 6-membered heteroaryloxy in which aryloxy and 5- or 6-membered heteroaryloxy may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)OH, C(═O)OR a , C 1 -C 6 -alkyl and C 1 -C 6 -alkoxy,   or represents C 3 -C 8 -cycloalkyl or heterocycloalkyl which may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano and C 1 -C 6 -alkyl,   or represents C 2 -C 6 -alkenyl or C 2 -C 6 -alkynyl,   or represents aryl, 5- to 10-membered heteroaryl, aryl-C 1 -C 4 -alkyl or 5- or 6-membered heteroaryl-C 1 -C 4 -alkyl, where aryl and heteroaryl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of halogen, hydroxy, cyano, C(═O)OH, C(═O)OR a , C 1 -C 6 -alkyl, C 3 -C 8 -cycloalkyl and C 1 -C 6 -alkoxy;   
     
         R a  represents C 1 -C 6 -alkyl, C 3 -C 10 -cycloalkyl, heterocycloalkyl, aryl or heteroaryl, where alkyl, cycloalkyl, heterocycloalkyl, aryl and heteroaryl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of halogen, hydroxy, cyano, C 1 -C 3 -alkyl, C 1 -C 3 -alkoxy, heterocycloalkyl, —C(═O)O—C 1 -C 6 -alkyl and S(═O) 2 —C 1 -C 6 -alkyl; 
         R b  represents C 1 -C 6 -alkyl or C 3 -C 10 -cycloalkyl;
       or R a  and R b  together with the nitrogen atom form a 5- or 6-membered heterocycle which may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, and C 1 -C 6 -alkyl;   
     
         R c  represents hydroxy, halogen, cyano, C 1 -C 3 -alkyl or C 1 -C 3 -alkoxy; 
         R d  represents hydrogen, C 1 -C 6 -alkyl or C 3 -C 10 -cycloalkyl; 
         R 2  represents hydrogen, C 1 -C 6 -alkyl or C 3 -C 6 -cycloalkyl; 
         R 13  represents hydrogen or C 1 -C 6 -alkyl; 
         W represents 5-membered heteroaryl which contains one to three heteroatoms selected from the group consisting of N, O and S and may optionally be monosubstituted by R 3  and optionally be mono- or polysubstituted by identical or different radicals R 4  or 
         W represents pyridyl, pyrazinyl, pyridazinyl, 1,2,4-triazinyl or 1,3,5-triazinyl which may optionally be monosubstituted by R 3  and optionally be mono- or polysubstituted by identical or different radicals R 4 ; 
         R 3  represents hydrogen, halogen, cyano, C(═O)R a , NH 2 , NHR a , N(R a )R b , N(H)C(═O)R a  or C 1 -C 6 -alkyl,
       where C 1 -C 6 -alkyl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)R a , C(═O)OH, C(═O)OR a , S(═O) 2 —C 1 -C 6 -alkyl, NH 2 , NHR a , N(R a )R b , C 1 -C 6 -alkoxy, C 3 -C 8 -cycloalkoxy,   where C 1 -C 6 -alkoxy and C 3 -C 8 -cycloalkoxy may optionally be mono- or polysubstituted by identical or different halogen radicals;   or C 1 -C 6 -alkyl is optionally mono- or polysubstituted by identical or radicals from the group consisting of C 3 -C 6 -cycloalkyl and heterocycloalkyl,   where C 3 -C 6 -cycloalkyl and heterocycloalkyl may optionally be mono-, di- or trisubstituted by identical or different radicals from the group consisting of halogen, cyano, C 1 -C 3 -alkyl and C 1 -C 3 -alkoxy,   or C 1 -C 6 -alkyl is optionally mono- or polysubstituted by identical or different radicals from the group consisting of aryl and 5- or 6-membered heteroaryl,   where aryl and 5- or 6-membered heteroaryl may optionally be mono-, di- or trisubstituted by identical or different radicals from the group consisting of halogen, cyano, C 1 -C 3 -alkyl and C 1 -C 3 -alkoxy,   
     
         or R 3  represents C 1 -C 6 -alkoxy,
       where C 1 -C 6 -alkoxy may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)OR a , S(═O) 2 —C 1 -C 6 -alkyl, N(R a )R b , C 3 -C 8 -cycloalkyl, C 1 -C 4 -alkoxy, C 3 -C 8 -cycloalkoxy,   or represents C 3 -C 6 -cycloalkyl, heterocycloalkyl or C 5 -C 11 -spirocycloalkyl, where cycloalkyl, heterocycloalkyl and spirocycloalkyl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)R a , C(═O)OH, C(═O)OR a , C 1 -C 6 -alkyl and C 1 -C 4 -alkoxy; or represents aryl or 5- to 10-membered heteroaryl,   where aryl and heteroaryl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of halogen, hydroxy, cyano, C(═O)OR a , S(═O) 2 —C 1 -C 6 -alkyl, NO 2 , NH 2 , NHR a , N(R a )R b , N(H)C(═O)R a , C 3 -C 8 -cycloalkyl, C 1 -C 3 -alkoxy and C 1 -C 3 -alkyl, where   
     
         C 1 -C 3 -alkyl may optionally be mono- or polysubstituted by identical or different halogen radicals; 
         R 4  represents halogen, hydroxy, cyano or C 1 -C 6 -alkyl, where C 1 -C 6 -alkyl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of halogen, C 1 -C 6 -alkoxy, where C 1 -C 6 -alkoxy may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of halogen, C 2 -C 6 -alkenyl, C 2 -C 6 -alkynyl, C 3 -C 10 -cycloalkyl, 3- to 10-membered heterocycloalkyl and aryl, where aryl may optionally be mono- or polysubstituted by identical or different radicals R; 
         or R 4  represents aryl or heteroaryl which may optionally be mono- or polysubstituted by identical or different radicals R; 
         or R 4  represents C(═O)R a , C(═O)NH 2 , C(═O)N(H)R a , C(═O)N(R a )R b , C(═O)OR a , NH 2 , NHR a , N(R a )R b , N(H)C(═O)R a , N(R a )(═O)R a , N(H)C(═O)NH 2 , N(H)C(═O)NHR a , N(H)C(═O)N(R a )R b , N(R a )(═O)NH 2 , N(R a )(═O)NHR a , N(R))C(═O)N(R a )R b , N(H) C(═O) OR a , N(R a )(═O)OR a , NO 2 , N(H)S(═O)R a , N(R a )S(═O)R a , N(H)S(═O) 2 R a , N(R a )S(═O) 2 R a , N═S(═O)(R a )R b , OC(═O)R a , OC(═O)NH 2 , OC(═O)NHR a , OC(═O)N(R a )R b , SH, SR a , S(═O)R a , S(═O) 2 R a , S(═O) 2 NH 2 , S(═O) 2 NHR a , S(═O) 2 N(R a )R b  or S(═O)(═N—R a )R b ; 
         R represents halogen, cyano, C 1 -C 6 -alkyl, C 2 -C 6 -alkenyl, C 2 -C 6 -alkynyl, C 3 -C 10 -cycloalkyl, 3- to 10-membered heterocycloalkyl, aryl, heteroaryl, C(═O)R a , C(═O)NH 2 , C(═O)N(H)R a , C(═O)N(R a )R b , C(═O)OR a , NH 2 , NHR a , N(R a )R b , N(H)C(═O)R a , N(R a )C(═O)R a , N(H)C(═O)NH 2 , N(H)C(═O)NHR a , N(H)C(═O)N(R a )R b , N(R a )C(═O)NH 2 , N(R a )C(═O)NHR a , N(R a )C(═O)N(R a )R b , N(H)C(═O)OR a , N(R a )C(═O)OR a , NO 2 , N(H)S(═O)R a , N(R a )S(═O)R a , N(H)S(═O) 2 R a , N(R a )S(═O) 2 R a , N═S(═O)(R a )R b , OH, C 1 -C 6 -alkoxy, OC(═O)R a , OC(═O)NH 2 , OC(═O)NHR a , OC(═O)N(R a )R b , SH, S(═O)R a , S(═O) 2 R a , S(═O) 2 NH 2 , S(═O) 2 NHR a , S(═O) 2 N(R a )R b  or S(═O)(═NR a )R b ; 
         n represents 0 or 1; 
         Y represents a group selected from: 
       
    
     
       
         
         
             
             
         
       
         
         where * represents the point of attachment of the group to the remainder of the molecule; 
         R 5  represents hydrogen, C 1 -C 6 -alkyl or C 3 -C 10 -cycloalkyl, where
       C 1 -C 6 -alkyl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)OH, C(═O)OR a , S(═O) 2 —C 1 -C 6 -alkyl, N(R a )R b , C 1 -C 4 -alkoxy and C 3 -C 8 -cycloalkyl;   
     
         R 6  represents hydrogen or C 1 -C 6 -alkyl, where
       C 1 -C 6 -alkyl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C 3 -C 10 -cycloalkyl, C(═O)R a , C(═O)OH, C(═O)OR a , S(═O) 2 —C 1 -C 6 -alkyl, N(R a )R b , C 1 -C 4 -alkoxy and C 3 -C 8 -cycloalkoxy, or represents C 3 -C 10 -cycloalkyl, where   C 3 -C 10 -cycloalkyl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano and C 1 -C 6 -alkyl, where   C 1 -C 6 -alkyl may optionally be substituted by hydroxy, or represents heterocycloalkyl, where heterocycloalkyl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of halogen, cyano, C 1 -C 3 -alkyl and C 1 -C 3 -alkoxy, or represents aryl or 5- or 6-membered heteroaryl, where   aryl and 5- or 6-membered heteroaryl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of halogen, cyano, C 1 -C 3 -alkyl, C 1 -C 3 -alkoxy, S(═O) 2 NH 2 , S(═O) 2 NHR a  and S(═O) 2 N(R a )R b ;   
     
         R 7a  represents hydrogen, halogen, N(R a )R b , C 1 -C 6 -alkyl or C 3 -C 10 -cycloalkyl, where C 1 -C 6 -alkyl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)OH, C(═O)OR a , S(═O) 2 —C 1 -C 6 -alkyl, N(R a )R b , C 1 -C 4 -alkoxy, C 3 -C 8 -cycloalkyl and heterocycloalkyl; 
         R 7b  represents hydrogen, halogen or C 1 -C 6 -alkyl, where C 1 -C 6 -alkyl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)OH, C(═O)OR a , S(═O) 2 —C 1 -C 6 -alkyl, N(R a )R b , C 1 -C 4 -alkoxy, C 3 -C 8 -cycloalkyl and heterocycloalkyl; 
         or R 7a  and R 7b  together with the carbon atom form C 3 -C 6 -cycloalkyl which may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano and C 1 -C 6 -alkyl, or R 7a  and R 7b  together represent an oxo group; 
         R 7c  represents hydrogen, halogen, N(R a )R b , C 1 -C 6 -alkyl or C 3 -C 10 -cycloalkyl, where
       C 1 -C 6 -alkyl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)OH, C(═O)OR a , S(═O) 2 —C 1 -C 6 -alkyl, N(R a )R b , C 1 -C 4 -alkoxy, C 3 -C 8 -cycloalkyl and heterocycloalkyl;   
     
         R 7d  represents hydrogen, halogen or C 1 -C 6 -alkyl, where
       C 1 -C 6 -alkyl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)OH, C(═O)OR a , S(═O) 2 —C 1 -C 6 -alkyl, N(R a )R b , C 1 -C 4 -alkoxy, C 3 -C 8 -cycloalkyl and heterocycloalkyl;   
     
         or R 7c  and R 7d  together with the carbon atom form C 3 -C 6 -cycloalkyl which may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano and C 1 -C 6 -alkyl, 
         or R 7c  and 10 together represent an oxo group; 
         R 8a  represents hydrogen, halogen, N(R a )R b , C 1 -C 6 -alkyl or C 3 -C 10 -cycloalkyl, where
       C 1 -C 6 -alkyl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)OH, C(═O)OR a , S(═O) 2 —C 1 -C 6 -alkyl, N(R a )R b , C 1 -C 4 -alkoxy, C 3 -C 8 -cycloalkyl and heterocycloalkyl;   
     
         R 8b  represents hydrogen, halogen or C 1 -C 6 -alkyl, where
       C 1 -C 6 -alkyl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)OH, C(═O)OR a , S(═O) 2 —C 1 -C 6 -alkyl, N(R a )R b , C 1 -C 4 -alkoxy, C 3 -C 8 -cycloalkyl and heterocycloalkyl;   
     
         or R 8a  and R 8b  together with the carbon atom form C 3 -C 6 -cycloalkyl which may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano and C 1 -C 6 -alkyl, 
         or R 8c  represents hydrogen, halogen, N(R a )R b , C 1 -C 6 -alkyl or C 3 -C 10 -cycloalkyl, where
       C 1 -C 6 -alkyl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)OH, C(═O)OR a , S(═O) 2 —C 1 -C 6 -alkyl, N(R a )R b , C 1 -C 4 -alkoxy, C 3 -C 8 -cycloalkyl and heterocycloalkyl;   
     
         R 8d  represents hydrogen, halogen or C 1 -C 6 -alkyl, where
       C 1 -C 6 -alkyl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)OH, C(═O)OR a , S(═O) 2 —C 1 -C 6 -alkyl, N(R a )R b , C 1 -C 4 -alkoxy, C 3 -C 8 -cycloalkyl and heterocycloalkyl;   or R 8c  and R 8d  together with the carbon atom form C 3 -C 6 -cycloalkyl which may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano and C 1 -C 6 -alkyl,   
     
         or R 8c  and R 8d  together represent an oxo group; 
         represents 0, 1 or 2, 
         p represents 0, 1 or 2, 
         q represents 0, 1 or 2, 
         r represents 0, 1 or 2, 
         s represents 0, 1 or 2, 
         where o, p, q, r and s do not simultaneously represent 0; 
         Z represents a group selected from C(═O), CR 9 R 10 , —, S, S(═O) and S(═O) 2 ; 
         R 9  represents hydrogen or C 1 -C 6 -alkyl, 
         R 10  represents hydrogen, halogen, cyano, C(═O)R a , C(═O)OH, C(═O)OR a , C(═O)NH 2 , C(═O)N(H)R a , C(═O)N(R a )R b , N(H)C(═O)R a , N(R b )C(═O)R a , S(═O) 2 R a , hydroxy, N(R a )R b  and C 1 -C 6 -alkyl, where
       C 1 -C 6 -alkyl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)R a , C(═O)OH, C(═O)OR a , S(═O) 2 —C 1 -C 6 -alkyl, N(R a )R b , C 1 -C 4 -alkoxy and C 3 -C 8 -cycloalkoxy, or represents C 1 -C 6 -alkoxy, where   C 1 -C 6 -alkoxy may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)OH, C(═O)OR a , S(═O) 2 —   C 1 -C 6 -alkyl, N(R a )R b , C 3 —C g-cycloalkyl, C 1 -C 4 -alkoxy, C 3 -C 8 -cycloalkoxy, heterocycloalkyl, aryl and 5- or 6-membered heteroaryl, where   aryl and 5- or 6-membered heteroaryl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of halogen, cyano, C 1 -C 3 -alkyl and C 1 -C 3 -alkoxy, or represents aryloxy or 5- or 6-membered heteroaryloxy in which aryloxy and 5- or 6-membered heteroaryloxy may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)OH, C(═O)OR a , C 1 -C 3 -alkyl and C 1 -C 3 -alkoxy,   or represents C 3 -C 8 -cycloalkyl, C 3 -C 8 -cycloalkyl-C 1 -C 4 -alkyl, heterocycloalkyl or heterocycloalkyl-C 1 -C 4 -alkyl, which may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)R a , C(═O)OH, C(═O)OR a , C 1 -C 6 -alkyl and C 1 -C 6 -alkoxy, where   C 1 -C 6 -alkoxy may optionally be mono- or polysubstituted by identical or different halogen radicals or an oxo group;   or represents C 2 -C 6 -alkenyl or C 2 -C 6 -alkynyl,   or represents aryl, 5- to 10-membered heteroaryl, aryl-C 1 -C 4 -alkyl or 5- or 6-membered heteroaryl-C 1 -C 4 -alkyl, where   aryl and heteroaryl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of halogen, hydroxy, cyano, C(═O)OH, C(═O)OR a , NHR a , N(R a )R b , C 1 -C 3 -alkyl, C 3 -C 8 -cycloalkyl and C 1 -C 3 -alkoxy;   or R 9  and R 10  together with the carbon atom form C 3 -C 8 -cycloalkyl or a 4- to 6-membered heterocycle, where   the C 3 -C 8 -cycloalkyl radical or the 4- to 6-membered heterocycle may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C 1 -C 6 -alkyl, C(═O)R a  and an oxo group;   
     
         R 11  represents hydrogen, C(═O)R a , C(═O)OR a , C(═O)NH 2 , C(═O)N(H)R a , C(═O)N(R a )R b , S(═O) 2 R a , S(═O) 2 N(R a )R b  or C 1 -C 6 -alkyl, where
       C 1 -C 6 -alkyl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C(═O)R a , C(═O)OR a , C(═O)NH 2 , C(═O)N(H)R a , C(═O)N(R a )R b , S(═O) 2 —C 1 -C 6 -alkyl, N(R a )R b , C 3 -C 8 -cycloalkyl, C 1 -C 4 -alkoxy and C 3 -C 8 -cycloalkoxy, where   C 3 -C 8 -cycloalkyl, C 1 -C 4 -alkoxy and C 3 -C 8 -cycloalkoxy may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy and halogen;   or represents C 3 -C 8 -cycloalkyl, heterocycloalkyl or heterocycloalkyl-C 1 -C 4 -alkyl which may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of hydroxy, halogen, cyano, C 1 -C 6 -alkyl, C 1 -C 6 -alkoxy, where alkyl and alkoxy may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of halogen and an oxo group,   or represents C 2 -C 6 -alkenyl or C 2 -C 6 -alkynyl,   or represents aryl, 5- to 10-membered heteroaryl, aryl-C 1 -C 4 -alkyl or 5- or 6-membered heteroaryl-C 1 -C 4 -alkyl, where   aryl and heteroaryl may optionally be mono- or polysubstituted by identical or different radicals from the group consisting of halogen, hydroxy, cyano, C(═O)OH, C(═O)OR a , C 1 -C 3 -alkyl, C 3 -C 8 -cycloalkyl and C 1 -C 3 -alkoxy;
 
as defined and described in WO 2015/091426 and US 2016/0311833, the entirety of each of which is herein incorporated by reference.
   
     
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-ggg-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         Ring A is phenylene or 5- to 6-membered heteroarylene containing 1-3 heteroatoms chosen from O, S, and N, wherein ring A is optionally substituted with lower alkyl that is further optionally substituted, 
         Ring B is phenylene, 5- to 6-membered heterocycloalkylene containing 1-3 heteroatoms chosen from O, S, and N, or 5- to 6-membered heteroarylene containing 1-3 heteroatoms chosen from O, S, and N, wherein ring B is optionally substituted with lower alkyl that is further optionally substituted, 
         R 3  is chosen from hydrogen, lower alkyl optionally substituted with alkoxy, amino, N-(alkyl)amino, N,N-(dialkyl)amino, or phenyl, heterocycloalkyl, and heteroaryl, 
         wherein phenyl, heterocycloalkyl, and heteroaryl are optionally substituted with one or two groups independently chosen from lower alkyl and wherein alkoxy is optionally substituted with tri(alkyl)silyl, 
         R 4  is chosen from heteroarylene and arylene, each of which is optionally substituted, or R 4  and R 3  taken together with the nitrogen to which they are bound, form an optionally substituted 3- to 7-membered heterocycloalkyl ring, or R 4  is an alkylene chain having 1-3 carbon atoms that is optionally substituted with one or two groups independently chosen from lower alkyl and cycloalkyl, each of which groups is optionally substituted with hydroxyl or alkoxy, or R 4  is absent, 
         R 5  is chosen from C(O)NR 51 , NR 52 , and O or R 5  is absent, provided that if R 4  is absent, then R 5  is ab sent, 
         R 6  is an alkylene or alkenylene chain having one or two double bonds, 
         wherein the alkylene or alkenylene chain has 2 to 10 carbon atoms, 
         wherein the alkylene or alkenylene chain is optionally substituted with one or two groups independently chosen from lower alkyl and cycloalkyl, each of which groups is optionally substituted with hydroxyl or alkoxy, and 
         further wherein one or two of the carbon atoms in the alkylene chain is optionally replaced by an O, S, SO, SO 2 , or NR 61 , and 
         wherein two of the carbon atoms in the alkylene chain, are optionally connected by a two or three carbon atom alkylene chain to form a 5- to 7-membered ring. 
         R 7  is chosen from NR 71  and O or R 7  is absent, 
         R 51  is chosen from hydrogen and lower alkyl, 
         R 52  is chosen from hydrogen, lower alkyl, and —C(O)OR 81 , 
         R 61  is chosen from hydrogen, lower alkyl, and —C(O)OR 81 , 
         R 71  is chosen from hydrogen, lower alkyl, and —C(O)OR 81 , and 
         R 81  is lower alkyl;
 
as defined and described in WO 2014/143672 and US 2016/0002265, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-hhh-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein HET is a heteroaryl selected from pyrazolyl, indolyl, pyrrolo[2,3-b]pyridinyl, pyrrolo[2,3-d]pyrimidinyl, pyrazolo[3,4-b]pyridinyl, pyrazolo[3,4-d]pyrimidinyl, 2,3-dihydro-1H-pyrrolo[2,3-b]pyridinyl, imidazo[4,5-b]pyridinyl, and purinyl, wherein said heteroaryl is substituted with R a  and R b ; 
         R a  is H, F, Cl, Br, —CN, —OH, C 1-4  alkyl, C 1-4  fluoroalkyl, C 1-4 hydroxyalkyl, C 1-4  alkoxy, —NH 2 , —NH(C 1-4  alkyl), —N(C 1-4  alkyl) 2 , —NH(C 1-4  hydroxyalkyl), —NH(C 1-4  fluoroalkyl), —NH(C 1-6  hydroxy-fluoroalkyl), —C(O)NH 2 , —CH 2 NHC(O)(C 1-6  alkyl), —CH 2 NHC(O)(C 1-6 hydroxyalkyl), —CH 2 NHC(O)NH(C 1-6  alkyl), —CH 2 NHC(O)NHCH 2 (phenyl), —CH 2 NHC(O)N(C 1-4  alkyl) 2 , —CH 2 NHC(O)O(C 1-4  alkyl), —CH 2 NHC(O)(C 3-6  cycloalkyl), —CH 2 NHC(O)(tetrahydrofuranyl), —CH 2 NHC(O)CH 2 (C 3-6  cycloalkyl), —CH 2 NHC(O)CH 2 (tetrahydropyranyl), —CH 2 NHC(O)CH 2 (phenyl), —NHC(O)(C 1-4  alkyl), pyrrolidinyl, hydroxypyrrolidinyl, or pyridazinyl; 
         R b  is H or —NH 2 ; 
         R 1  is:
       (i) C 1-6  alkyl, C 1-6  fluoroalkyl, C 1-6  hydroxyalkyl, C 1-8  hydroxy-fluoroalkyl, —(C 1-6  alkylenyl)O(C 1-4  alkyl), —(C 1-6  alkyl enyl)O(C 1-4 fluoroalkyl), —(C 1-6  fluoroalkyl enyl)O(C 1-4  alkyl), —(C 1-6 fluoroalkyl enyl)O(C 1-4  deuteroalkyl), (C 1-6  fluoroalkylenyl)O(C 1-4 fluoroalkyl), —(C 1-4  fluoroalkylenyl)C(C 3-6  cycloalkyl) 2 (OH), —(C 1-4  alkyl enyl)NHC(O)(C 1-4  alkyl enyl)OC(O)(C 1-3  alkyl), —(C 1-6  alkylenyl)NHS(O) 2 (C 1-4  alkyl), —(C 1-6  alkylenyl)P(O)(C 1-4  alkoxy) 2 , —(C 1-6  fluoroalkylenyl)NH(C 1-4  alkyl), —(C 1-6  alkylenyl)C(O)NH(C 1-4  alkyl), —(C 1-6  fluoroalkyl enyl)C(O)NH(C 1-4  alkyl), —(C 1-6 fluoroalkyl enyl)C(O)NH(C 1-4  hydroxyalkyl), or —(C 1-6 fluoroalkylenyl)OP(O)(OH) 2 ;   (ii) —(C 1-3  alkylenyl)R x , —(C 1-3  fluoroalkylenyl)R x , —(C 1-3 alkylenyl)C(O)R x , —(C 1-3  alkyl enyl)C(O)NHR x , —(C 1-3 fluoroalkylenyl)C(O)R x , or CH 2 CF=(tetrahydropyranyl), wherein R x  is a cyclic group selected from C 3-6  cycloalkyl, tetrazolyl, 1,1-dioxidotetrahydrothiophenyl, 1,1-dioxidothiomorpholinyl, oxadiazolyl, piperidinyl, piperazinyl, pyrrolidinyl, oxetanyl, tetrahydrofuranyl, tetrahydropyranyl, pyridinyl, imidazolyl, morpholinyl, phenyl, and triazinyl, wherein each cyclic group is substituted with zero to 3 substituents independently selected from F, —OH, —CH 3 , —C(CH 2 ) 2 OH, —OCH 3 , —C(O)CH 2 CN, —S(O) 2 CH 3 , —S(O) 2 NH 2 , —NHC(O)CH 3 , —N(S(O) 2 CH 3 ) 2 , —CH 2 CH 2 (acetamidophenyl), —CH 2 CH 2 (methoxyphenyl), —CH 2 CH 2 (sulfamoylphenyl), oxetanyl, benzyl, and morpholinyl;   (iii) C 3-6  cycloalkyl or C 4-6  cycloalkenyl, each substituted with zero to 3 substituents independently selected from F, —OH, —CN, C 1-3  alkyl, C 1-3  alkoxy, —S(C 1-3  alkyl), —NO 2 , —S(O) 2 (C 1-3  C 1-4 hydroxyalkyl, —C(C 1-3  alkyl)(OH)(C 3-6  cycloalkyl), —CH 2 C(O)NH(C 1-3  alkyl), —NHC(O)(C 1-3  alkyl), —NHC(O)(C 1-4 hydroxyalkyl), —C(O)NH(C 1-3  alkyl), —C(O)NH(C 1-3  deuteroalkyl), —C(O)NH(C 3-6  cycloalkyl), —NHC(O)O(C 1-3  alkyl), —NHS(O) 2 (C 1-3 alkyl), pyridinyl, imidazolyl, pyrazolyl, methylimidazolyl, methylpyrazolyl, and thiazolyl;   (iv) tetrahydropyranyl, piperidinyl, pyrazolyl, phenyl, pyridinyl, or pyrimidinyl, each substituted with zero to 1 substituent selected from —OH, C 1-3  alkyl, C 1-3  fluoroalkyl, C 1-4  hydroxyalkyl, C 1-3  alkoxy, —C(O)(C 1-4  alkyl), —S(O) 2  (C 1-4  alkyl), —S(O) 2 NH(C 1-4  alkyl), —NH(C 1-3  alkyl), —N(C 1-3  alkyl) 2 , —O(C 1-3  alkylenyl)N(C 1-3  alkyl) 2 , —CH 2 (morpholinyl), azetidinyl, oxetanyl, tetrahydropyranyl, morpholinyl, piperazinyl, piperidinyl, methylpiperazinyl, methoxypiperidinyl, pyridinyl, pyrimidinyl, methyl sulfonyl azetidinyl, and C(O)(methyl sulfonyl azetidinyl); or   (v) pyrrolo[2,3-c]pyridinyl, bicyclo[2.2.1]heptan-1-ol, tetrahydrobenzo[d]thiazol-2-amine, or 1,3-diazaspiro[4.5]decane-2,4-dione; and   
     
         R 2  is:
       (i) C 1-7  alkyl or C 2-6  alkenyl, each substituted with zero to three substituents independently selected from F, —OH, and —CN; —(C 1-4  alkylenyl)O(C 1-4  alkyl), —(C 1-4  alkylenyl)O(C 1-4  fluoroalkyl), —(C 1-6  alkyl enyl)NH 2 , —(C 1-6  alkylenyl)S(O) 2 (C 1-3  alkyl), —(C 1-6  fluoroalkylenyl)NH(C 1-3  alkyl), or —(C 1-6  alkyl enyl)NHC(O)(C 1-4 fluoroalkyl);   (ii) —(C 1-4  alkyl enyl)R y  wherein R y  is C 3-6  cycloalkyl, azetidinyl, oxetanyl, oxazolyl, pyridinyl, tetrahydropyranyl, or morpholinyl, each substituted with zero to 2 substituents independently selected from F, —OH, and C 1-3  alkyl;   (iii) C 3-6  cycloalkyl, azetidinyl, oxetanyl, furanyl, tetrahydrofuranyl, pyrrolidinyl, piperidinyl, or tetrahydropyranyl, each substituted with zero to 3 substituents independently selected from F, —OH, C 1-3  alkyl, C 1-3  hydroxyalkyl, —C(O)(C 1-3  alkyl), —C(O)(C 1-3  fluoroalkyl), —C(O)(C 1-3  cyanoalkyl), —C(O)O(C 1-3  alkyl), —C(O)NH 2 , —C(O)NH(C 1-3  alkyl), —C(O)(difluorophenyl), —NH 2 , —NH(C 1-3  alkyl), —NH(C 1-3  fluoroalkyl), —NH(oxetanyl), —NHC(O)(C 1-3  alkyl), —NHC(O)(C 1-3  fluoroalkyl), —NHC(O)(C 3-6  cycloalkyl), —NHC(O)(fluorophenyl), —S(O) 2 (C 1-3  alkyl), imidazolyl, phenyl, pyrimidinyl, fluoropyrimidinyl, chloropyrimidinyl, and methoxypyrimidinyl;   (iv) adamantanyl, hydroxyadamantanyl, benzo[d]imidazolyl, benzo[d]oxazolyl, benzo[d]triazolyl, benzothiazolyl, bicyclo[1.1.1]pentanyl, or hydroxy-bicyclo[2.2.1]heptanyl; or   (v) phenyl, pyrazolyl, thiazolyl, thiadiazolyl, or indazolyl, each substituted with 0 to 2 substituents independently selected from F, Cl, —OH, —CN, C 1-4  alkyl, C 1-4  hydroxyalkyl, C 1-4  fluoroalkyl, C 1-4 cyanoalkyl, C 1-3  alkoxy, C 3-6  cycloalkyl, —(C 1-3  alkylenyl)O(C 1-3 alkyl), —(C 1-3  alkylenyl)O(C 1-3 fluoroalkyl), —C(O)NH 2 , —C(O)NH(C 1-3  alkyl), —NHC(O)(C 1-3  alkyl), —NHC(O)S(O) 2 (C 1-3 alkyl), —S(O) 2 NH 2 , —S(O) 2 (C 1-3  alkyl), pyrazolyl, methyl pyrazolyl, imidazolyl, triazolyl, methyl tetrazolyl, ethyl tetrazolyl, phenyl, pyrimidinyl, fluoropyrimidinyl, and tetrahydropyranyl;
 
as defined and described in WO 2015/103453 and US 2015/0191464, the entirety of each of which is herein incorporated by reference.
   
     
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-iii-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein   is a single or double bond; 
         W is selected from CH, CH—CH, O, S, NR 6 , and CO; 
         Y is N or CR 9 ; 
         Z is N or C, and Z is N if W is CH and Y is CR 9 ; 
         R 4  is selected from hydrogen, halogen, OR 6 , CN, NR 7 R 8 , CH 2 OR 6 , an optionally substituted aryl, an optionally substituted heteroaryl, an optionally substituted non-aromatic ring, an optionally substituted carbocycle, an optionally substituted C 1 -C 6  alkyl, an optionally substituted C 1 -C 6  haloalkyl, an optionally substituted C 1 -C 6 heteroalkyl, an optionally substituted C 1 -C 6  alkenyl, an optionally substituted C 1 -C 6  alkynyl, CO 2 R 6 , SO 3 R 6 , SO 2 R 6  and SO 2 NR 7 R 8 ; 
         R 5  is selected from hydrogen, halogen, OR 6 , an optionally substituted C 1 -C 6  alkyl, an optionally substituted C 1 -C 6  haloalkyl, an optionally substituted C 1 -C 6  heteroalkyl, an optionally substituted C 1 -C 6 haloheteroalkyl, an optionally substituted C 1 -C 6  alkenyl, and an optionally substituted C 1 -C 6  alkynyl; 
         or R 4  and R 5  are linked to form an optionally substituted non-aromatic ring; 
         each R 6  is independently selected from an optionally substituted aryl, an optionally substituted heteroaryl, and an optionally substituted non-aromatic ring, each optionally fused with a substituted aryl or a substituted heteroaryl, hydrogen, an optionally substituted C 1 -C 10 alkyl, an optionally substituted C 1 -C 10  haloalkyl, and an optionally substituted C 1 -C 10 heteroalkyl; 
         each R 7  and R 8  is independently selected from an optionally substituted aryl, an optionally substituted heteroaryl, an optionally substituted non-aromatic ring, each optionally fused with a substituted aryl or a substituted heteroaryl, hydrogen, an optionally substituted C 1 -C 10 alkyl, an optionally substituted C 1 -C 10  haloalkyl, an optionally substituted C 1 -C 10 alkenyl, an optionally substituted C 1 -C 10  alkynyl, and an optionally substituted C 1 -C 10 heteroalkyl, or Wand R 8  are linked to form an optionally substituted non-aromatic ring; 
         R 9  is selected from hydrogen, halogen, OR 6 , CN, NR 7 R 8 , CH 2 OR 6 , an optionally substituted aryl, an optionally substituted heteroaryl, an optionally substituted non-aromatic ring, an optionally substituted C 1 -C 6  alkyl, an optionally substituted C 1 -C 6  haloalkyl, an optionally substituted C 1 -C 6  heteroalkyl, an optionally substituted C 1 -C 6  alkenyl, an optionally substituted C 1 -C 6  alkynyl, CO 2 R 6 , SO 3 R 6 , and SO 2 NR 7 R 8 ; 
         A is an optionally substituted aryl or an optionally substituted heteroaryl group; 
         each optionally substituted group is either unsubstituted or substituted with one or more groups independently selected from alkyl, heteroalkyl, alkenyl, alkynyl, haloalkyl, heterohaloalkyl, aryl, arylalkyl, heteroaryl, non-aromatic ring, hydroxy, alkoxy, aryloxy, mercapto, alkylthio, arylthio, cyano, halo, carbonyl, thiocarbonyl, O-carbamyl, N-carbamyl, O-thiocarbamyl, N-thiocarbamyl, C-amido, N-amido, S-sulfonamido, N-sulfonamido, C-carboxy, O-carboxy, isocyanato, thiocyanato, isothiocyanato, nitro, silyl, trihalomethanesulfonyl, ═O, ═S, amino, and protected derivatives of amino groups;
 
as defined and described in WO 2012/068546 and US 2014/0155379, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-iii-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         Q denotes Ar or Het; 
         E denotes —(CH 2 ) m CO—, —(CH 2 ) m SO 2 , —(CH 2 ) q —, —(CH 2 ) m NHCO—, or a single bond; 
         R 1  denotes H, OH, NH—C 1 -C 6 -alkyl, OC 1 -C 6 -alkyl, C 1 -C 6 -alkyl, C 2 -C 6 -alkenyl, C 2 -C 6 -alkynyl, Cyc, Hal, Het 1 , O-Het 1 , CO-Het 1 , NH-Het 1 , CO—Ar 1 , O—Ar 1 , Ar 1 , NH—Ar 1 , —(CH 2 ) q Het 1 , —CONH—(CH 2 ) q Het 1 , —CONH-Het 1 , —(CH 2 ) q O—Het 1 , —(CH 2 ) q OAr 1 , —(CH 2 ) q Ar 1 , —CONH(CH 2 ) q Ar 1 , —CONH—Ar 1 , —CONHC 3 -C 6 -cycloalkyl, —(CH 2 ) q Hal, —(CH 2 ) q Cyc, CF 3 , —(CH 2 ) s NH(CH 2 ) q -Het 1 , —(CH 2 ) s NH(CH 2 ) q —Ar 1 , wherein NH—C 1 -C 6 -alkyl, OC 1 -C 6 -alkyl, C 1 -C 6 -alkyl, C 2 -C 6 -alkenyl, C 2 -C 6 -alkynyl, C 3 -C 6 -cycloalkyl may be substituted by 1 to 3 groups independently selected from OC 1 -C 3 -alkyl, OH, CONH 2 , NH 2 ; 
         R 2  denotes H, C 1 -C 6 -alkyl, C 2 -C 6 -alkenyl, C 2 -C 6 -alkynyl, Hal, CF 3 , preferably H; 
         R 3  denotes Het 1 , Ar 1 , NR a R b  COOH, —(CH 2 ) q Het 1 , —(CH 2 ) q Ar 1 , —(CH 2 ) q NR a R b , —(CH 2 ) q COOH, or C 1 -C 6 -alkyl wherein 1 to 3 hydrogen atoms may be independently replaced by OH or CF 3 ; 
         R 4  denotes H, C 1 -C 6 -alkyl, C 2 -C 6 -alkenyl, Hal; 
         R a  denotes H, linear, branched or cyclic C 1 -C 6 -alkyl; 
         R b  denotes H, Het b , Ar b , —CO-Het b , —CO—Ar b , a C 3 -C 8 -cycloalkyl or a linear or branched alkyl having 1 to 6 carbon atoms, wherein 1 to 3 hydrogen atoms may be replaced by Het b , Ar b , NH 2 , N(C 1 -C 6 -alkyl) 2 , NH(C 1 -C 6 -alkyl), N(C 1 -C 6 -alkyl)(C 3 -C 8 -cycloalkyl), NH(C 3 -C 8 -cycloalkyl), O(C 1 -C 6 -alkyl), CN, OH, CF 3 , Hal; 
         n is 0, 1, 2, 3 or 4; 
         m is 0, 1, 2, 3 or 4; 
         q is 1, 2, or 3; 
         s is 0, 1, 2 or 3; 
         Hal denotes Cl, Br, I, F, preferably Cl or F; 
         Ar denotes a divalent monocyclic or fused bicyclic arylen group having 6 to 14 carbon atoms, which may be further substituted with 1 to 4 substitutents selected from Hal, C 1 -C 6 -alkyl, —(CH 2 ) m OC 1 -C 6 -alkyl, CN, OH, NO 2 , CF 3 , —(CH 2 ) m COOH, —(CH 2 ) m COOC 1 -C 6 -alkyl; 
         Het denotes a divalent monocyclic or fused bicyclic unsaturated, saturated or aromatic heterocyclic group having 1 to 5 heteroatom independently selected from N, O, S and/or a group C═O, which may be further substituted with 1 to 4 substituent selected from Hal, C 1 -C 6 -alkyl, —(CH 2 ) m OC 1 -C 6 -alkyl, CN, OH, NO 2 , CF 3 , —(CH 2 ) m COOH, —(CH 2 ) m COOC 1 -C 6 -alkyl; 
         Ar 1  denotes a monocyclic or bicyclic, aromatic carbocyclic ring having 6 to 14 carbon atoms, which is unsubstituted or monosubstituted, disubstituted or trisubstituted by Hal, —CF 3 , —OCF 3 , —NO 2 , —CN, perfluoroalkyl, Hal, —CF 3 , —OCF 3 , —NO 2 , —CN, perfluoroalkyl, linear or branched C 1 -C 6 -alkyl, cycloalkyl, —OH, —OC 1 -C 6 -alkyl, —COC 1 -C 6 -alkyl, —NH 2 , —COH, —COOH, —CONH 2 , a group R b  such as —CH 2 O(C 1 -C 6 -alkyl), —SO 2 NR a R b  or SO 2 (C 1 -C 6 alkyl); 
         Het 1  denotes a monocyclic or bicyclic (fused, bridged or spiro) saturated, unsaturated or aromatic heterocyclic ring having 1 to 4 heteroatom independently selected from N, O, S and/or a CO group, which is unsubstituted or monosubstituted, disubstituted or trisubstituted by Hal, —CF 3 , —OCF 3 , —NO 2 , —CN, perfluoroalkyl, linear or branched C 1 -C 6 -alkyl, C 3 -C 8 -cycloalkyl, —OH, —OC 1 -C 6 -alkyl, —NH 2 , —N(C 1 -C 6 -alkyl) 2 , —COH, —COOH, —CONH 2 , —COC 1 -C 6 -alkyl, —NHCO(C 3 -C 6 cycloalkyl), a group R b SO 2 NR a R b  or SO 2 (C 1 -C 6 alkyl); 
         Het b  denotes a monocyclic or bicyclic (fused or spiro) saturated, unsaturated or aromatic heterocyclic ring having 1 to 4 heteroatom independently selected from N, O, S and/or a CO group, which is unsubstituted or monosubstituted, disubstituted or trisubstituted by Hal, —CF 3 , —OCF 3 , —NO 2 , —CN, perfluoroalkyl, —OH, —OC 1 -C 6 -alkyl, —NH 2 , —COH, —COOH, —CONH 2 , or by a linear or branched C 1 -C 6 -alkyl wherein 1 to 3 hydrogen atoms may be replaced by NH 2 , N(C 1 -C 6 -alkyl) 2 , NH(C 1 -C 6 -alkyl), N(C 1 -C 6 -alkyl)(C 3 -C 8 -cycloalkyl), NH(C 3 -C 8 -cycloalkyl), O(C 1 -C 6 -alkyl), CN, OH, CF 3 , Hal, C 3 -C 8 -cycloalkyl, or by a 4 to 8-membered heterocyclic ring containing an heteroatom selected from O, S and N; 
         Ar b  denotes a monocyclic or bicyclic, aromatic carbocyclic ring having 6 to 14 carbon atoms, which is unsubstituted or monosubstituted, disubstituted or trisubstituted by Hal, —CF 3 , —OCF 3 , —NO 2 , —CN, perfluoroalkyl, Hal, —CF 3 , —OCF 3 , —NO 2 , —CN, perfluoroalkyl, —OH, —OC 1 -C 6 -alkyl, —NH 2 , —COH, —COOH, —CONH 2 , or by a linear or branched C 1 -C 6 -alkyl wherein 1 to 3 hydrogen atoms may be replaced by NH 2 , N(C 1 -C 6 -alkyl) 2 , NH(C 1 -C 6 -alkyl), N(C 1 -C 6 -alkyl)(C 3 -C 8 -cyclalkyl), NH(C 3 -C 8 -cycloalkyl), O(C 1 -C 6 -alkyl), CN, OH, CF 3 , Hal, C 3 -C 8 -cycloalkyl, or by a 4 to 8-membered heterocyclic ring containing an heteroatom selected from O, S and N; 
         Cyc denotes a saturated or unsaturated carbocyclic ring having 3 to 8 carbon atoms, preferrably 5 or 6 carbon atoms, wherein 1 to 5H atoms are replaced by Hal, —CF 3 , —OCF 3 , —NO 2 , —CN, perfluoroalkyl, Hal, —CF 3 , —OCF 3 , —NO 2 , —CN, perfluoroalkyl, linear or branched C 1 -C 6 -alkyl, cycloalkyl, —OH, —COC 1 -C 6 -alkyl, —NH 2 , —COH, —COOH, —CONH 2 , a group R b  such as —CH 2 O(C 1 -C 6 -alkyl), —SO 2 NR a R b  or SO 2 (C 1 -C 6 alkyl); or
 
as defined and described in WO 2012/084704 and US 2013/0274241, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-kkk-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         R 1  is aryl, heteroaryl, heterocyclyl or (C 1-6  alkyl)R 6 , wherein said aryl, heteroaryl, and heterocyclyl groups are optionally substituted with one or two substituents selected from the group consisting of halo, cyano, R 4 , C 3-8  cycloalkyl, C 1-3  aminoalkyl, C 1-3 hydroxyalkyl, NR 4 R 5 , NR 4 COR 6 , NR 4 SO 2 R 6 , SO 2 NR 4 R 5 , CONR 4 R 5  and CONR 4 R 5 ; 
         R 2  is aryl, heteroaryl, C 3-8  cycloalkyl, heterocyclyl or (C 1-6  alkyl)R 6 , wherein said aryl, heteroaryl, cycloalkyl and heterocyclyl groups are optionally substituted with one or two substituents selected from the group consisting of halo, cyano, oxo, hydroxyl, imino, hydroxyimino, R 4 , OR 4 , O(C 3-8  cycloalkyl), (C═O)OR 4 , SO m R 6 , SO m R 4 , NR 4 R 5 , SO 2 NR 4 R 5  and NR 4 SO 2 R 6 ; 
         R 3  is halo, cyano, oxo, hydroxyl, imino, hydroxyimino, R 4 , OR 4 , C 3-8 cycloalkyl, SO m R 6 , SO m R 4 NR 4 R 5  or (C═O)NR 4 R 5 , NR 4 (CO)R 6 , SO m NR 4 R 5  and NR 4 SO 2 R 6 ; 
         R 4  is hydrogen or C 1-6  alkyl, wherein said alkyl is optionally substituted with one to three halo or hydroxyl; 
         R 5  is hydrogen or C 1-6  alkyl, wherein said alkyl is optionally substituted with halo or hydroxyl; 
         R 6  is aryl, heteroaryl, C 3-8  cycloalkyl or heterocyclyl; 
         m is an integer from zero to two;
 
as defined and described in WO 2012/129258 and US 2014/0194404, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-lll-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         X is —N═ or —CH═; 
         Y is selected from the group consisting of —NR 2 —, —CH 2 —, —CHR— and —O—, such that when Y is —CHR—, R and R 3  together with the carbon to which they are attached optionally form a 4- to 6-membered cycloalkyl, cycloalkenyl or heterocyclic ring, wherein the 4- to 6-membered cycloalkyl, cycloalkenyl, or heterocyclic ring is optionally substituted with one to three substituents independently selected from the group consisting of C 1-4  alkyl, C 3-6  cycloalkyl, phenyl, CF 3 , heterocyclyl, halogen, —COOR 8 , —NHR 8 , —SR 8 , —OR 8 , —SO 2 R 8 , —COR 8 , —NHCOR 8 , and —CONHR 8 ; or when Y is —NR 2 —, R 2  and R 3  together with the nitrogen to which they are attached optionally form a 4- to 6-membered heterocyclic ring, wherein the 4- to 6-membered heterocyclic ring is optionally substituted with one to three substituents independently selected from the group consisting of C 1-4  alkyl, C 3-6  cycloalkyl, phenyl, CF 3 , heterocyclyl, halogen, —COOR 8 , —NHR 8 , SR 8 , —OR 8 , —SO 2 R 8 , —COR 8 , —NHCOR 8 , and —CONHR 8 ; 
         R 1  is selected from the group consisting of hydrogen, C 1-10  alkyl, C 3-8 cycloalkyl, aryl, heterocyclyl, halogen, —COOR 7 , —NHR 7 , —SR 7 , —OR 7 , —SO 2 R 7 , —COR 7 , —NHCOR 7 , and CONHR 7 ; wherein said alkyl, cycloalkyl, aryl and heterocyclyl are optionally substituted with one to three substituents independently selected from the group consisting of C 1-4  alkyl, C 3-6  cycloalkyl, CN, phenyl, CF 3 , heterocyclyl, halogen, —COOR 8 , —NHR 8 , —SR 8 , —OR 8 , —SO 2 R 8 , —COR 8 , —NHCOR 8 , and —CONHR S , wherein said —NHR 8  is optionally substituted with —N(C 1-4 alkyl)NH 2  or —N(C 3-6  cycloalkyl)NH 2 ; 
         R 2  is selected from the group consisting of hydrogen, C 1-10  alkyl, and C 3-8  cycloalkyl; 
         R 3  is selected from the group consisting of hydrogen, C 1-10  alkyl, C 3-8 cycloalkyl, aryl, heterocyclyl, and —COOR 7 ; wherein said alkyl, cycloalkyl, aryl and heterocyclyl are optionally substituted with one to three substituents independently selected from the group consisting of C 1-4  alkyl, C 3-6  cycloalkyl, phenyl, CF 3 , heterocyclyl, halogen, —COOR 8 , —NHR 8 , —SR 8 , —OR 8 , —SO 2 R 8 , —COR 8 , —NHCOR 8 , and —CONHR 8 ; 
         R 6  is selected from the group consisting of C 1-10  alkyl, C 3-8  cycloalkyl, aryl, heterocyclyl, —COOR 7 , —SO 2 R 7 , and —COR 7 ; wherein said alkyl, cycloalkyl, aryl and heterocyclyl are optionally substituted with one to three substituents independently selected from the group consisting of C 1-4  alkyl, C 3-6  cycloalkyl, phenyl, CF 3 , heterocyclyl, halogen, —COOR 8 , —NHR 8 , —OR 8 , —SO 2 R 8 , —COR 8 , —NHCOR 8 , and —CONHR 8 ; 
         R 7  is selected from the group consisting of hydrogen, C 1-10  alkyl, C 3-8 cycloalkyl, aryl, and heteroaryl; wherein said alkyl, cycloalkyl, aryl and heterocyclyl are optionally substituted with one to three substituents independently selected from the group consisting of 4 alkyl, C 3-6  cycloalkyl, phenyl, CF 3 , heterocyclyl, halogen, —COOR 8 , —NHR 8 , —OR 8 , —SO 2 R 8 , —COR 8 , —NHCOR 8 , and —CONHR 8 ; and 
         R 8  is selected from the group consisting of hydrogen, C 1-6  alkyl and C 3-6  cycloalkyl;
 
as defined and described in WO 2013/066729 and US 2014/0329799, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-mmm-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         X is independently CH or N; 
         Y is H or methyl; 
         a is 0 or 1; b is 0 or 1; m is 0, 1 or 2; n is 0, 1, 2, 3 or 4; 
         Ring A is (C 3 -C 8 )cycloalkenyl, aryl or heterocycle optionally substituted with one to three substituents independently selected from R 1 ; 
         R 1  is selected from: H, oxo, (C═O) a O b (C 1 -C 10 )alkyl, (C═O) a O b -aryl, (C═O) a O b (C 2 -C 10 )alkenyl, (C═O) a O b (C 2 -C 10 )alkynyl, CO 2 H, halo, OH, O b (C 1 -C 6 )fluoroalkyl, (C═O) a NR 5 R 6 , CN, (C═O) a O b (C 3 -C 8 )cycloalkyl, S(O) m NR5R 6 , SH, S(O) m —(C 1 -C 10 )alkyl and (C═O) a O b -heterocyclyl, said alkyl, aryl, alkenyl, alkynyl, cycloalkyl, and heterocyclyl are optionally substituted with one or more substituents selected from R a ; 
         R 2  and R 3  are independently selected from: H, (C═O) a O b C 1 -C 10  alkyl, (C═O) a O b aryl, C 2 -C 10  alkenyl, C 2 -C 10  alkynyl, (C═O) a O b  heterocyclyl, CO 2 H, CN, O b C 1 -C 6 fluoroalkyl, O a (C═O) b NR 5 R 6 , CHO, (N═O)R 5 R 6 , S(O) m NR 5 R 6 , SH, S(O) m —(C 1 -C 10 )alkyl, (C═O) a O b C 3 -C 8  cycloalkyl, optionally substituted with one or more substituents selected from R 1 ; or R 2  and R 3  can be taken together with the nitrogen to which they are attached to form a monocyclic or bicyclic heterocycle with 3-7 members in each ring and optionally containing, in addition to the nitrogen, one or two additional heteroatoms selected from N, O and S, said monocyclic or bicyclic heterocycle optionally substituted with one or more substituents selected from R 1 ; 
         R 4  is independently selected from: (C 1 -C 6 )alkyl, OH, methoxy, CF 3  and F, said alkyl optionally substituted with OH; 
         R 5  and R 6  are independently selected from H, (C═O) a O b (C 1 -C 10 )alkyl, (C═O) a O b -aryl, (C═O) a O b (C 2 -C 10 )alkenyl, (C═O) a O b (C 2 -C 10 )alkynyl, CO 2 H, O b (C 1 -C 6 )fluoroalkyl, (C═O) a N(R a ) 2 , CN, (C═O) a O b (C 3 -C 8 )cycloalkyl, S(O) m N(R a ) 2 , SH, S(O) m —(C 1 -C 10 )alkyl and (C═O) a O b -heterocyclyl, said alkyl, aryl, alkenyl, alkynyl, cycloalkyl, and heterocyclyl are optionally substituted with one or more substituents selected from R a ; 
         R a  is independently selected from R b , OH, (C 1 -C 6 )alkoxy, halogen, cyclopropyl, CO 2 H, CN, O a (C═O) b (C 1 -C 6 )alkyl, oxo, and N(R b ) 2 ; and 
         R b  is independently selected from H and (C 1 -C 6 )alkyl;
 
as defined and described in WO 2014/058685 and US 2015/0299224, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-nnn-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         X is CH or N; 
         a is 0 or 1; b is 0 or 1; m is 0, 1 or 2; 
         Ring A is (C 3 -C 8 )cycloalkyl, (C 3 -C 8 )cycloalkenyl, aryl or heterocycle optionally substituted with one to three substituents independently selected from R 1 ; 
         R 1  is selected from: H, oxo, (C═O) a O b (C 1 -C 10 )alkyl, (C═O) a O b -aryl, (C═O) a O b (C 2 -C 10 )alkenyl, (C═O) a O b (C 2 -C 10 )alkynyl, CO 2 H, halo, OH, O b (C 1 -C 6 )fluoroalkyl, (C═O) a NR 5 R 6 , CN, (C═O) a O b (C 3 -C 8 )cycloalkyl, S(O) m NR 5 R 6 , SH, S(O) m —(C 1 -C 10 )alkyl and (C═O) a O b -heterocyclyl, said alkyl, aryl, alkenyl, alkynyl, cycloalkyl, and heterocyclyl are optionally substituted with one or more substituents selected from R a ; 
         R 2  and R 3  are independently selected from: H, (C═O) a O b C 1 -C 10  alkyl, (C═O) a O b aryl, C 2 -C 10 alkenyl, C 2 -C 10 alkynyl, (C═O) a O b  heterocyclyl, CO 2 H, CN, O b C 1 -C 6  fluoroalkyl, O a (C═O) b NR 5 R 6 , CHO, (N═O)R 5 R 6 , S(O) m NR 5 R 6 , SH, S(O) m —(C 1 -C 10 )alkyl, (C═O) a O b C 3 -C 8  cycloalkyl, optionally substituted with one or more substituents selected from R 1 ; or R 2  and R 3  can be taken together with the nitrogen to which they are attached to form a monocyclic or bicyclic heterocycle with 3-7 members in each ring and optionally containing, in addition to the nitrogen, one or two additional heteroatoms selected from N, O and S, said monocyclic or bicyclic heterocycle optionally substituted with one or more substituents selected from R 1 ; 
         R 4  is selected from: (C 1 -C 6 )alkyl and (C 3 -C 6 )cycloalkyl, optionally substituted with R a ; 
         R 5  and R 6  are independently selected from: H, oxo, (C═O) a O b (C 1 -C 10 )alkyl, (C═O) a O b -aryl, (C═O) a O b (C 2 -C 10 )alkenyl, (C═O) a O b (C 2 -C 10 )alkynyl, CO 2 H, O b (C 1 -C 6 )fluoroalkyl, (C═O) a N(R a ) 2 , CN, (C═O) a O b (C 3 -C 8 )cycloalkyl, S(O) m N(R a ) 2 , SH, S(O) m —(C 1 -C 10 )alkyl and (C═O) a O b -heterocyclyl, said alkyl, aryl, alkenyl, alkynyl, cycloalkyl, and heterocyclyl are optionally substituted with one or more substituents selected from R a ; 
         R a  is independently selected from R b , OH, (C 1 -C 6 )alkoxy, halogen, cyclopropyl, CO 2 H, CN, O a (C═O) b (C 1 -C 6 )alkyl, oxo, and N(R b ) 2 ; and 
         R b  is independently selected from H and (C 1 -C 6 )alkyl;
 
as defined and described in WO 2014/058691 and US 2015/0274708, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-nnn′-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein each of the variables R 3 , R 4 , X, and Ring A is as defined and described in WO 2014/058691, the entirety of each of which is herein incorporated by reference. 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-ooo-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         Z denotes a group 
       
    
     
       
         
         
             
             
         
       
         
          wherein 
         X is CH or N; 
         Y is CH or N; 
         Ra, Rc, R1 denote each independently H, Hal or Al; 
         Rb is H or alkyl; 
         Al is branched or linear alkyl having 1 to 12 C-atoms, wherein one or more, such as 1 to 7, H atoms may be replaced by Hal, ORb, COORb, CN or N(Rb) 2  and wherein one or more, preferably 1 to 5 CH 2 -groups may be replaced by O, CO, NRb or S, SO, SO 2 , 1,2-, 1,3- or 1,4-phenylen, —CH═CH— or —C≡C—; and 
         Hal denotes F, Cl, Br, I;
 
as defined and described in WO 2014/121931 and US 2015/0376167, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-ppp-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         R1, R3 denote each, independently of one another H, (CH 2 ) p CON(R 5 ) 2 , OA, Hal, COOH, COOA, (CH 2 ) p NHCOA, (CH 2 ) p Het1, (CH 2 ) p NR 2 R 5 , or OH; 
         R2 denotes H or linear or branched alkyl with 1, 2 or 3 C atoms, wherein one or two H atoms of the alkyl group are optionally replaced by OR6, NR 5 R 6 , NHCOR5, CONR5R 6 ; 
         R4 denotes H or A; 
         R5 denotes H or linear or branched alkyl with 1, 2 or 3 C atoms; 
         R6 denotes H or linear or branched alkyl with 1, 2 or 3 C atoms; 
         Z is absent or denotes Ar-diyl or Het-diyl; 
         L denotes (CH 2 ), wherein one or two CH 2  groups are optionally replaced by 0 and/or a CH═CH— group, and/or wherein one or two H atoms are optionally replaced by OR2, NR2R5 or Het1; 
         Ar-diyl denotes 1,2-, 1,3- or 1,4-phenylen optionally substituted with from 1 to 5 groups independently selected from the group consisting of Hal, CN, —CF 3 , —OCF 3 , OH, O-A, SO 2 -A, COOH, COOA, —CO-A, O-phenyl, SO 2 -phenyl, SO 2 —CF 3 , Het2 and A; 
         Het-diyl denotes an unsaturated, saturated or aromatic 5- or 6-membered heterocycle comprising 1 to 2 N, O and/or S atoms, which are optionally unsubstituted or mono-, di- or trisubstituted by Hal, CN, —CF 3 , —OCF 3 , O-A, SO 2 -A, COOH, COOA, —CO-A, O-phenyl, SO 2 -phenyl, SO 2 —CF 3 , Het2 and/or A; 
         A denotes an unbranched or branched alkyl comprising 1 to 10 C atoms, in which 1 to 5H atoms are optionally replaced by F and/or in which one or two non-adjacent CH 2  groups are optionally replaced by 0; 
         Het1 denotes morpholinyl, piperidinyl or pyrrolidinyl; 
         Het2 denotes morpholinyl, piperidinyl or pyrrolidinyl; 
         Hal denotes F, Cl, Br, I; 
         n denotes 1, 2, 3, 4, 5 or 6; 
         p denotes 0, 1 or 2;
 
as defined and described in WO 2014/121942 and US 2015/0376206, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK1 and/or IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-qqq-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein Ring A is a 3-7 membered saturated or partially unsaturated carbocyclic ring or a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         n is 0-4; 
         each R 1  is independently —R, halogen, —CN, —NO 2 , —OR, —CH 2 OR, —SR, —N(R) 2 , —SO 2 R, —SO 2 N(R) 2 , —SOR, —C(O)R, —CO I R, —C(O)N(R) 2 , —C(O)N(R)—OR, —NRC(O)R, —NRC(O)N(R) 2 , Cy, or —NRSO 2 R; or R 1  is selected from one of the following formulas: 
       
    
     
       
         
         
             
             
         
       
         
         or two R 1  groups are taken together with their intervening atoms to form an optionally substituted 4-7 membered fused, spiro-fused, or bridged bicyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each Cy is an optionally substituted ring selected from a 3-7 membered saturated or partially unsaturated carbocyclic ring or a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each R is independently hydrogen or an optionally substituted group selected from C 1-6  aliphatic, aryl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or: two R groups on the same nitrogen are taken together with their intervening atoms to form a 4-7 membered saturated, partially unsaturated, or heteroaryl ring having 0-3 heteroatoms, in addition to the nitrogen, independently selected from nitrogen, oxygen, or sulfur; 
         R z  is —R, —CN, —NO 2 , halogen, —C(O)N(R) 2 , —C(O)OR, —C(O)R, —N(R) 2 , —OR, or SO 2 N(R) 2 ; 
         Ring B is an unsubstituted 4-8 membered partially unsaturated carbocyclic fused ring; and 
         L is a C 1-6  bivalent hydrocarbon chain wherein one or two methylene units of the chain are optionally and independently replaced by —NR—, —N(R)C(O)—, —C(O)N(R)—, —N(R)SO 2 —, —SO 2 N(R)—, —O—, —C(O)—, —OC(O)—, —C(O)O—, —S—, —SO— or —SO 2 —;
 
as defined and described in WO 2012/097013 and US 2012/0283238, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK1 and/or IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-rrr-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         Ring A is a 3-7 membered saturated or partially unsaturated carbocyclic ring or a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         n is 0-4; 
         each R 1  is independently —R, halogen, —CN, —NO 2 , —OR, —CH 2 OR, —SR, —N(R) 2 , —SO 2 R, —SO 2 N(R) 2 , —SOR, —C(O)R, —CO 2 R, —C(O)N(R) 2 , —C(O)N(R)—OR, —NRC(O)OR, —NRC(O)N(R) 2 , Cy, or —NRSO 2 R; or R 1  is selected from one of the following formulas: 
       
    
     
       
         
         
             
             
         
       
         
         or two R 1  groups are taken together with their intervening atoms to form an optionally substituted 4-7 membered fused, spiro-fused, or bridged bicyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each Cy is an optionally substituted ring selected from a 3-7 membered saturated or partially unsaturated carbocyclic ring or a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each R is independently hydrogen, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or: 
         two R groups on the same nitrogen are taken together with their intervening atoms to form a 4-7 membered saturated, partially unsaturated, or heteroaryl ring having 0-3 heteroatoms, in addition to the nitrogen, independently selected from nitrogen, oxygen, or sulfur; 
         Ring B is a cyclopento or cyclohexo fused ring; 
         m is 1-2; 
         p is 0-2; 
         W is N; 
         R z  is R, CN, NO 2 , halogen, —C(O)N(R) 2 , —C(O)OR, —C(O)R, —N(R)C(O)OR, —NRC(O)N(R) 2 , —OR, or —SO 2 N(R) 2 ; 
         L 1  is a covalent bond or a C 1-6  bivalent hydrocarbon chain wherein one or two methylene units of the chain are optionally and independently replaced by —NR—, —N(R)C(O)—, —C(O)N(R)—, —N(R)SO 2 —, —SO 2 N(R)—, —O—, —C(O)—, —OC(O)—, —C(O)O—, —S—, —SO— or —SO 2 —; 
         each L 2  is independently a covalent bond or a C 1-6  bivalent hydrocarbon chain wherein one or two methylene units of the chain are optionally and independently replaced by —NR—, —N(R)C(O)—, —C(O)N(R)—, —N(R)SO 2 —, —SO 2 N(R)—, —O—, —C(O)—, —OC(O)—, —C(O)O—, —S—, —SO— or —SO 2 —; 
         each R 4  is independently halogen, —CN, —NO 2 , —OR, —SR, —N(R) 2 , —SO 2 R, —SO 2 N(R) 2 , —SOR, —C(O)R, —CO 2 R, —C(O)N(R) 2 , —NRC(O)R, —NRC(O)N(R) 2 , —C(O)N(R)OR, —N(R)C(O)OR, —N(R)S(O) 2 N(R) 2 , —NRSO 2 R, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or: 
         two -L 2 (R 4 ) p —R 4  groups are taken together with their intervening atoms to form an optionally substituted 4-7 membered fused, spiro-fused, or bridged bicyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur;
 
as defined and described in WO 2013/106535 and US 2013/0231328, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK1 and/or IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-sss-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein Ring A is a 3-7 membered saturated or partially unsaturated carbocyclic ring or a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
         n is 0-4; 
         each R 1  is independently —R, halogen, —CN, —NO 2 , —OR, —CH 2 OR, —SR, —N(R) 2 , —S(O) 2 R, —S(O) 2 N(R) 2 , —SOR, —C(O)R, —CO 2 R, —C(O)N(R) 2 , —C(O)N(R)—OR, —N(R)C(O)R, —N(R)C(O)OR, —N(R)C(O)N(R) 2 , Cy, or —N(R)S(O) 2 R, or R 1  is selected from one of the following formulas: 
       
    
     
       
         
         
             
             
         
       
         
         or two R 1  groups are taken together with their intervening atoms to form an optionally substituted 4-7 membered fused, spiro-fused, or bridged bicyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
         each Cy is an optionally substituted ring selected from a 3-7 membered saturated or partially unsaturated carbocyclic ring or a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
         each R is independently hydrogen, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or: 
         two R groups on the same nitrogen are taken together with their intervening atoms to form a 4-7 membered saturated, partially unsaturated, or heteroaryl ring having 0-3 heteroatoms, in addition to the nitrogen, independently selected from nitrogen, oxygen, and sulfur; 
         Ring B is selected from a benzo fused ring and a 5-6 membered heteroaromatic fused ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; wherein said Ring B may be optionally substituted by one or more oxo, thiono, or imino groups; 
         m is 0-4; 
         p is 0-2; 
         W is N or —C(R 3 ); 
         R z  is R, CN, NO 2 , halogen, —C(O)N(R) 2 , —C(O)OR, —C(O)R, —N(R) 2 , —N(R)C(O)OR, —N(R)C(O)N(R) 2 , —OR, or —S(O) 2 N(R) 2 ; 
         R 3  is hydrogen, halogen, —CN, C 1-4  aliphatic, C 1-4  haloaliphatic, —OR, —C(O)R, or 
       
    
     C(O)N(R) 2 ;
     L 1  is a covalent bond or a C 1-6  bivalent hydrocarbon chain wherein one or two methylene units of the chain are optionally and independently replaced by —N(R)—, —N(R)C(O)—, —C(O)N(R)—, —N(R)S(O) 2 —, —S(O) 2 N(R)—, —O—, —C(O)—, —OC(O)—, —C(O)O—, —S—, —S(O)— or —S(O) 2 ;   each L 2  is independently a covalent bond or a C 1-6  bivalent hydrocarbon chain wherein one or two methylene units of the chain are optionally and independently replaced by —N(R)—, —N(R)C(O)—, —C(O)N(R)—, —N(R)S(O) 2 —, —S(O) 2 N(R)—, —O—, —C(O)—, —OC(O)—, —C(O)O—, —S—, —S(O)— or —S(O) 2 —; and   each R 4  is independently halogen, —CN, —NO 2 , —OR, —SR, —N(R) 2 , —S(O) 2 R, —S(O) 2 N(R) 2 , —S(O)R, —C(O)R, —CO 2 R, —C(O)N(R) 2 , —N(R)C(O)R, —N(R)C(O)N(R) 2 , —C(O)N(R) OR, —N(R)C(O)OR, —N(R)S(O) 2 N(R) 2 , —N(R)S(O) 2 R, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or   two -L 2 (R 4 ) p —R 4  groups are taken together with their intervening atoms to form an optionally substituted 4-7 membered fused, or bridged bicyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur;
 
as defined and described in WO 2014/011902 and US 2014/0018343, the entirety of each of which is herein incorporated by reference.
   

     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK1 and/or IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-ttt-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein Ring A is a 3-7 membered saturated or partially unsaturated carbocyclic ring or a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
         n is 0-4; 
         each R 1  is independently —R, halogen, —CN, —NO 2 , —OR, —CH 2 OR, —SR, —N(R) 2 , —S(O) 2 R, —S(O) 2 N(R) 2 , —S(O)R, —C(O)R, —C(O)OR, —C(O)N(R) 2 , —C(O)N(R)—OR, —N(R)C(O)R, —N(R)C(O)OR, —N(R)C(O)N(R) 2 , Cy, or —N(R)S(O) 2 R; or R 1  is selected from one of the following formulas: 
       
    
     
       
         
         
             
             
         
       
         
         two R 1  groups are taken together with their intervening atoms to form an optionally substituted 4-7 membered fused, spiro-fused, or bridged bicyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
         each Cy is an optionally substituted ring selected from a 3-7 membered saturated or partially unsaturated carbocyclic ring or a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
         each R is independently hydrogen, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or: 
         two R groups on the same nitrogen are taken together with their intervening atoms to form a 4-7 membered saturated, partially unsaturated, or heteroaryl ring having 0-3 heteroatoms, in addition to the nitrogen, independently selected from nitrogen, oxygen, and sulfur; 
         Ring B is selected from a 4-8 membered partially unsaturated carbocyclic fused ring and a 4-7 membered partially unsaturated heterocyclic fused ring having 1-2 heteroatoms selected from nitrogen, oxygen, and sulfur; wherein said Ring B may be optionally substituted by one or more oxo, thiono, or imino groups; 
         m is 0-4; 
         p is 0-2; 
         R z  is —R, —CN, —NO 2 , halogen, —C(O)N(R) 2 , —C(O)OR, —C(O)R, —N(R) 2 , —N(R)C(O)OR, —N(R)C(O)N(R) 2 , —OR, or —S(O) 2 N(R) 2 ; 
         R 3  is hydrogen, halogen, —CN, C 1-4  aliphatic, C 1-4  haloaliphatic, —OR, —C(O)R, or C(O)N(R) 2 ; 
         L 1  is a covalent bond or a C 1-6  bivalent hydrocarbon chain wherein one or two methylene units of the chain are optionally and independently replaced by —N(R)—, —N(R)C(O)—, —C(O)N(R)—, —N(R)S(O) 2 —, —S(O) 2 N(R)—, —O—, —C(O)—, —OC(O)—, —C(O)O—, —S—, —S(O)— or —S(O) 2 ; 
         each L 2  is independently a covalent bond or a C 1-6  bivalent hydrocarbon chain wherein one or two methylene units of the chain are optionally and independently replaced by —N(R)—, —N(R)C(O)—, —C(O)N(R)—, —N(R)S(O) 2 —, —S(O) 2 N(R)—, —O—, —C(O)—, —OC(O)—, —C(O)O—, —S—, —S(O)— or —S(O) 2 —; and 
         each R 4  is independently halogen, —CN, —NO 2 , —OR, —SR, —N(R) 2 , —S(O) 2 R, —S(O) 2 N(R) 2 , —S(O)R, —C(O)R, —C(O)OR, —C(O)N(R) 2 , —N(R)C(O)R, —N(R)C(O)N(R) 2 , —C(O)N(R) OR, —N(R)C(O)OR, —N(R)S(O) 2 N(R) 2 , —N(R)S(O) 2 R, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or 
         two -L 2 (R 4 ) p —R 4  groups are taken together with their intervening atoms to form an optionally substituted 4-7 membered fused, spiro-fused, or bridged bicyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur;
 
as defined and described in WO 2014/011906 and US 2014/0018357, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK1 and/or IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-uuu-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         Ring A is a 3-7 membered saturated or partially unsaturated carbocyclic ring or a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
         n is 0-4; 
         each R 1  is independently —R, halogen, —CN, —NO 2 , —OR, —CH 2 OR, —SR, —N(R) 2 , —S(O) 2 R, —S(O) 2 N(R) 2 , —S(O)R, —C(O)R, —C(O)OR, —C(O)N(R) 2 , —C(O)N(R)—OR, —N(R)C(O)R, —N(R)C(O)OR, —N(R)C(O)N(R) 2 , Cy, or —N(R)S(O) 2 R; or R 1  is selected from one of the following formulas: 
       
    
     
       
         
         
             
             
         
       
     
     or two R 1  groups are taken together with their intervening atoms to form an optionally substituted 4-7 membered fused, spiro-fused, or bridged bicyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur;
     each Cy is an optionally substituted ring selected from a 3-7 membered saturated or partially unsaturated carbocyclic ring or a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur;   each R is independently hydrogen, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or:   two R groups on the same nitrogen are taken together with their intervening atoms to form a 4-7 membered saturated, partially unsaturated, or heteroaryl ring having 0-3 heteroatoms, in addition to the nitrogen, independently selected from nitrogen, oxygen, and sulfur;   each of R x  and R y  is independently —R, halogen, —CN, —NO 2 , —OR, —SR, —N(R) 2 , —S(O) 2 R, —S(O) 2 N(R) 2 , —S(O)R, —C(O)R, —C(O)OR, —C(O)N(R) 2 , —N(R)C(O)R, —N(R)C(O)N(R) 2 , or —N(R)S(O) 2 R, or:   R x  and R y  are taken together with their intervening atoms to form Ring B substituted with m occurrences of   

     
       
         
         
             
             
         
       
         
         Ring B is selected from a benzo fused ring, a 4-8 membered partially unsaturated carbocyclic fused ring, a 4-8 membered partially unsaturated heterocyclic fused ring having one or two heteroatoms independently selected from nitrogen oxygen and sulfur, and a 5-6 membered heteroaromatic fused ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; wherein said Ring B may be optionally substituted by one or more oxo, thiono, or imino groups; 
         m is 0-4; 
         p is 0-2; 
         Q is —O— or —N(R) 
         W is N or —C(R 3 )—; 
         R z  is —R, —CN, —NO 2 , halogen, —C(O)N(R) 2 , —C(O)OR, —C(O)R, —N(R) 2 , —N(R)C(O)OR, —N(R)C(O)N(R) 2 , —OR, or —S(O) 2 N(R) 2 ; 
         R 3  is hydrogen, halogen, —CN, C 1-4  aliphatic, C 1-4  haloaliphatic, —OR, —C(O)R, or —C(O)N(R) 2 ; 
         L 1  is a covalent bond or a C 1-6  bivalent hydrocarbon chain wherein one or two methylene units of the chain are optionally and independently replaced by —N(R)—, —N(R)C(O)—, —C(O)N(R)—, —N(R)S(O) 2 —, —S(O) 2 N(R)—, —O—, —C(O)—, —OC(O)—, —C(O)O—, —S—, —S(O)— or —S(O) 2 ; 
         each L 2  is independently a covalent bond or a C 1-6  bivalent hydrocarbon chain wherein one or two methylene units of the chain are optionally and independently replaced by —N(R)—, —N(R)C(O)—, —C(O)N(R)—, —N(R)S(O) 2 —, —S(O) 2 N(R)—, —O—, —C(O)—, —OC(O)—, —C(O)O—, —S—, —S(O)— or —S(O) 2 —; and 
         each R 4  is independently halogen, —CN, —NO 2 , —OR, —SR, —N(R) 2 , —S(O) 2 R, —S(O) 2 N(R) 2 , —S(O)R, —C(O)R, —C(O)OR, —C(O)N(R) 2 , —N(R)C(O)R, —N(R)C(O)N(R) 2 , —C(O)N(R) OR, —N(R)C(O)OR, —N(R)S(O) 2 N(R) 2 , —N(R) S(O) 2 R, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or 
         two -L 2 (R 4 ) p —R 4  groups are taken together with their intervening atoms to form an optionally substituted 4-7 membered fused, spiro, or bridged bicyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur;
 
as defined and described in WO 2014/011911 and US 2014/0018361, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK1 and/or IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-vvv-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         Q is CH, C—CN, or N; 
         X is C-L 2 (R 4 ) p —R x  and Y is N; or 
         X is N and Y is C—R x ; 
         Ring A is a 3-7 membered saturated or partially unsaturated carbocyclic ring or a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each R 1  and R 1′  is independently —R 2 , halogen, —CN, —NO 2 , —OR, —SR, —N(R) 2 , —S(O) 2 R, —S(O) 2 N(R) 2 , —S(O)R, —C(O)R, —C(O)OR, —C(O)N(R) 2 , —C(O)N(R)OR, —N(R)C(O)OR, —N(R)C(O)N(R) 2 , Cy, or —N(R)S(O) 2 R; or R 1  is selected from one of the following formulas: 
       
    
     
       
         
         
             
             
         
       
         
         or two R 1  groups are taken together with their intervening atoms to form an optionally substituted 4-7 membered fused, spiro-fused, or bridged bicyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each Cy is an optionally substituted ring selected from a 3-7 membered saturated or partially unsaturated carbocyclic ring or a 4-10 membered saturated or partially unsaturated heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each R is independently hydrogen, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or: 
         two R groups on the same nitrogen are taken together with their intervening atoms to form a 4-7 membered saturated, partially unsaturated, or heteroaryl ring having 0-3 heteroatoms, in addition to the nitrogen, independently selected from nitrogen, oxygen, or sulfur; 
         each R 2  is independently an optionally substituted group selected from C 1-6  aliphatic, phenyl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each R 4  is independently halogen, —CN, —NO 2 , —OR, —SR, —N(R) 2 , —S(O) 2 R, —S(O) 2 N(R) 2 , —S(O)R, —C(O)R, —C(O)OR, —C(O)N(R) 2 , —N(R)C(O)R, —N(R)C(O)N(R) 2 , —C(O)N(R)OR, —N(R)C(O)OR, —N(R)S(O) 2 N(R) 2 , —N(R)S(O) 2 R, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         R x  is hydrogen, —R 2 , —CN, —NO 2 , halogen, —C(O)N(R) 2 , —C(O)OR, —C(O)R, —N(R) 2 , —NH[Ar], —OR, or —S(O) 2 N(R) 2 ; 
         R z  is hydrogen, —R 2 , —CN, —NO 2 , halogen, —C(O)N(R) 2 , —C(O)OR, —C(O)R, —N(R) 2 , —NH[Ar], —OR, or —S(O) 2 N(R) 2 ; 
         [Ar] is a phenyl or heteroaromatic ring substituted by m instances of R 1′ ; 
         L 1  is a covalent bond or a C 1-6  bivalent hydrocarbon chain wherein one or two methylene units of the chain are optionally and independently replaced by —N(R)—, —N(R)C(O)—, —C(O)N(R)—, —N(R)S(O) 2 —, —S(O) 2 N(R)—, —O—, —C(O)—, —OC(O)—, —C(O)O—, —S—, —S(O)— or —S(O) 2 ; 
         L 2  is a covalent bond or a C 1-6  bivalent hydrocarbon chain wherein one or two methylene units of the chain are optionally and independently replaced by —N(R)—, —N(R)C(O)—, —C(O)N(R)—, —N(R)S(O) 2 —, —S(O) 2 N(R)—, —O—, —C(O)—, —OC(O)—, —C(O)O—, —S—, —S(O)— or —S(O) 2 ; 
         m is 0-4; 
         n is 0-4; and 
         p is 0-2;
 
as defined and described in WO 2015/048281 and US 2015/0094305, the entirety of each of which is herein incorporated by reference.
 
       
    
     In some embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-vvv′-1: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein 
         L and LBM are as defined above and described in embodiments herein; 
         each A, B, C, D, E, F, G, H, X 1 , X 2 , and X 3  are independently a carbon atom, a nitrogen atom, an oxygen atom, or a sulfur atom; and 
         each R 1 , R 2 , R 3 , and R 4  are independently hydrogen or a substituted group selected from C 1-6  aliphatic, phenyl, a 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or:
       R 1  and R 2  and R 3  and R 4  are each optionally taken together with their intervening atoms to form a 4-7 membered saturated, partially unsaturated, or heteroaryl ring having 0-3 heteroatoms, independently selected from nitrogen, oxygen, and sulfur.   
     
       
    
     Such IRAK4 inhibitors are well known to one of ordinary skill in the art and include those described in Scott et al.,  J. Med. Chem.,  2017, 60(24): 10071-10091 and Degorce et al.,  Bioorg. Med. Chem.,  2018, 26(4): 913-924. 
     In certain embodiments, the present invention provides a compound of Formula I or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-vvv′-2, I-vvv′-3, I-vvv′-4, I-vvv′-5, I-vvv′-6, I-vvv′-7, I-vvv′-8, I-vvv′-9, I-vvv′-10, I-vvv′-11, I-vvv′-12, I-vvv′-13, I-vvv′-14, I-vvv′-15, I-vvv′-16, I-vvv′-17, I-vvv′-18, I-vvv′-19, I-vvv′-20, I-vvv′-21, I-vvv′-22, I-vvv′-23, I-vvv′-24, I-vvv′-25, I-vvv′-26, I-vvv′-27, I-vvv′-28, I-vvv′-29, I-vvv′-30, I-vvv′-31, I-vvv′-32, I-vvv′-33, I-vvv′-34, I-vvv′-35, I-vvv′-36, I-vvv′-37, I-vvv′-38, and I-vvv′-39: 
     
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein 
         L and LBM are as defined above and described in embodiments herein; 
         each X 1 , X 2 , and X 3  are independently a carbon atom, a nitrogen atom, an oxygen atom, or a sulfur atom; and 
         each R 1 , R 2 , R 3 , and R 4  are independently hydrogen or a substituted group selected from C 1-6  aliphatic, phenyl, a 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or:
       R 1  and R 2  or R 3  and R 4  are optionally taken together with their intervening atoms to form a 4-7 membered saturated, partially unsaturated, or heteroaryl ring having 0-3 heteroatoms, independently selected from nitrogen, oxygen, and sulfur.   
     
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK1 and/or IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-www-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         Q is ═N— or ═CH—; 
         Ring A is a 3-7 membered saturated or partially unsaturated carbocyclic ring or a 4-7 membered saturated or partially unsaturated heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each R 1  is independently —R 2 , halogen, —CN, —NO 2 , —OR, —SR, —NR 2 , —S(O) 2 R, —S(O) 2 NR 2 , —S(O)R, —C(O)R, —C(O)OR, —C(O)NR 2 , —C(O)N(R)OR, —N(R)C(O)OR, —N(R)C(O)NR 2 , Cy, or —N(R)S(O) 2 R; or R 1  is selected from one of the following formulas: 
       
    
     
       
         
         
             
             
         
       
         
         or two R 1  groups are taken together with their intervening atoms to form an optionally substituted 4-7 membered fused, spiro-fused, or bridged bicyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each Cy is independently an optionally substituted ring selected from a 3-7 membered saturated or partially unsaturated carbocyclic ring or a 4-10 membered saturated or partially unsaturated heterocyclic ring having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each R is independently hydrogen, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or: 
         two R groups on the same nitrogen are taken together with their intervening atoms to form a 4-7 membered saturated, partially unsaturated, or heteroaryl ring having 0-3 heteroatoms, in addition to the nitrogen, independently selected from nitrogen, oxygen, or sulfur; 
         each R 2  is independently an optionally substituted group selected from C 1-6  aliphatic, phenyl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each of R 5  and R 6  is independently hydrogen or -L 2 (R 4 ) p —R x ; or 
         R 5  and R 6  are taken together with their intervening atoms to form a 4-7 membered partially unsaturated, or aromatic ring having 0-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; 
         each R 4  is independently halogen, —CN, —NO 2 , —OR, —SR, —NR 2 , —S(O) 2 R, —S(O) 2 NR 2 , —S(O)R, —C(O)R, —C(O)OR, —C(O)NR 2 , —N(R)C(O)R, —N(R)C(O)NR 2 , —C(O)N(R)OR, —N(R)C(O)OR, —N(R)S(O) 2 NR 2 , —N(R)S(O) 2 R, or an optionally substituted group selected from C 1-6  aliphatic, phenyl, 4-7 membered saturated or partially unsaturated heterocyclic having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
         R x  is hydrogen, —R 2 , —CN, —NO 2 , halogen, —C(O)NR 2 , —C(O)OR, —C(O)R, —NR 2 , —NH[Ar], —OR, or —S(O) 2 NR 2 ; 
         R z  is hydrogen, —R 2 , —CN, —NO 2 , halogen, —C(O)NR 2 , —C(O)OR, —C(O)R, —NR 2 , —NH[Ar], —OR, or —S(O) 2 NR 2 ; 
         [Ar] is an optionally substituted phenyl or an optionally substituted 5-6 membered heteroaryl ring having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; 
         L 1  is a covalent bond or a C 1-6  bivalent hydrocarbon chain wherein one or two methylene units of the chain are optionally and independently replaced by —N(R)—, —N(R)C(O)—, —C(O)N(R)—, —N(R)S(O) 2 —, —S(O) 2 N(R)—, —O—, —C(O)—, —OC(O)—, —C(O)O—, —S—, —S(O)— or —S(O) 2 —; 
         L 2  is a covalent bond or a C 1-6  bivalent hydrocarbon chain wherein one or two methylene units of the chain are optionally and independently replaced by —N(R)—, —N(R)C(O)—, —C(O)N(R)—, —N(R)S(O) 2 —, —S(O) 2 N(R)—, —O—, —C(O)—, —OC(O)—, —C(O)O—, —S—, —S(O)— or —S(O) 2 —; 
         m is 0-4; 
         n is 0-4; and 
         p is 0-2;
 
as defined and described in WO 2015/164374 and US 2015/0329498, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-xxx-1 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         X and X′ are each independently CR 8 , N or —N + —O − ; Y is independently N, —N + —O −  or CR 8′ ; provided that at least one of X, X′ or Y is neither N nor —N+—O −  and that no more than one of X, X′ or Y is —N + —O − ; 
         R 1  is C 1 -C 6 alkyl; C 2 -C 6 alkenyl; C 2 -C 6 alkynyl; —(CR 3a R 3b ) m -(3- to 7-membered cycloalkyl); (CR 3a R 3b ) m -(3- to 7-membered heterocycloalkyl) having one to three heteroatoms; (CR 3a R 3b ) m -(5- to 10-membered heteroaryl), having one to three heteroatoms; or (CR 3a R 3b ) m —C 6 -C 12 aryl; wherein said alkyl, alkenyl, alkynyl, cycloalkyl, heterocycloalkyl, heteroaryl or aryl is optionally substituted with one to five halogen, deuterium, —OR 5 , —SR 5 , —NR 11a R 11b  cyano, C 1 -C 6 alkyl, C 3 -C 6 cycloalkyl or —C 1 -C 6  alkoxy; 
         R 2  is —(CR 3a R 3b ) m -(3- to 10-membered cycloalkyl); —(CR 3a R 3b ) m -(3- to 10-membered heterocycloalkyl) having one to three heteroatoms; —(CR 3a R 3b ) m -(5- to 10 membered heteroaryl) having one to three heteroatoms; or —(CR 3a R 3b ) m —C 6 -C 12 aryl; wherein said cycloalkyl, heterocycloalkyl, heteroaryl or aryl is optionally substituted with one to five R 4 ; and wherein, if the heteroatom on said heterocycloalkyl and heteroaryl is N, said N is 
         optionally substituted with R 4′ ; or R 2  is C 1 -C 6 alkyl, wherein said alkyl is optionally substituted with NH 2 , OH or cyano; 
         R 3a  and R 3b  for each occurrence are independently hydrogen or C 1 -C 3 alkyl; 
         R 4  for each occurrence is independently a bond, deuterium halogen, cyano, C 1 -C 6 alkyl, C 2 -C 6 alkenyl, oxo, —OR 5 , —SR 5 , —S(O)R 9 , —S(O) 2 R 9 , —NR 11a R 11b , —C(O)R 10 , —(CR 3a R 3b ) n -(3-to 7-membered cycloalkyl), —(CR 3a R 3b ) n -(4- to 10-membered heterocycloalkyl), having one to three heteroatoms, —(CR 3a R 3b ) n -(5- to 10 membered heteroaryl), having one to three heteroatoms, or —(CR 3a R 3b ) n —C 6 -C 12 aryl wherein said alkyl, cycloalkyl, heterocycloalkyl, heteroaryl or aryl is each optionally and independently substituted with one to five deuterium, halogen, OR 5 , —SR 5 , —NR 11a R 11b , cyano, C 1 -C 6 alkyl, C 3 -C 6 cycloalkyl or —C 1 -C 6 alkoxy; or two R 4  taken together with the respective carbons to which each are bonded form a 3- to 6-membered cycloalkyl or 4- to 6-membered heterocycloalkyl, wherein said cycloalkyl or heterocycloalkyl is optionally substituted with one to three halogen, deuterium, —OR 5 , —SR 5 , —NR 11a R 11b , cyano or C 1 -C 6 alkyl or C 1 -C 6 alkoxy, wherein the alkyl or alkoxy is optionally substituted with halogen, deuterium, —OR 5 , —SR 5 , NR 11a R 11b  or cyano; and wherein, if a heteroatom on said heterocycloalkyl is N, said N is optionally substituted with R 4′ ; 
         R 4′  is independently C 1 -C 6 alkyl, C 2 -C 6 alkenyl, —C(O)R 10 , —S(O) 2 R 9 , —(CR 3a R 3b ) n -(3-to 7-membered cycloalkyl), —(CR 3a R 3b ) n -(4- to 10-membered heterocycloalkyl) or C(O)(CH 2 ) t CN; wherein said alkyl, alkenyl, cycloalkyl, or heterocycloalkyl is each optionally and independently substituted with one to five deuterium, halogen, OH, cyano or C 1 -C 6 alkoxy; or R 4  and R 4′  taken together with the respective atoms to which each are bonded form a 3- to 6-membered cycloalkyl or 4- to 6-membered heterocycloalkyl, wherein said cycloalkyl or heterocycloalkyl is optionally substituted with one to three halogen, deuterium, —OR 5 , —SR 5 , —NR 11a R 11b  cyano, C 1 -C 6 alkyl or C 1 -C 6 alkoxy, wherein the alkyl or alkoxy is optionally substituted with halogen, deuterium, —OR 5 , —SR 5 , —NR 11a R 11b , or cyano; 
         R 5  is independently hydrogen or C 1 -C 6 alkyl, wherein said alkyl is optionally substituted with halogen, deuterium, C 1 -C 6 alkoxy, C 1 -C 6 alkylthiolyl, —NR 11a R 11b , cyano, C 1 -C 6 alkyl or C 3 -C 6 cycloalkyl; or two R 5  taken together with the oxygen atoms to which they are bonded form a 5- or 6-membered heterocycloalkyl; 
         R 6  is —C(O)NHR 7 , CO 2 R 7  or cyano; 
         R 7  is hydrogen or C 1 -C 6 alkyl; 
         each R 8  is independently hydrogen, halogen, cyano, —OR 5 , —SR 5 , —NR 11a R 11b , C 6 alkyl, C 3 -C 6 cycloalkyl, 3- to 10-membered heterocycloalkyl or 5- to 6-membered heteroaryl or aryl, wherein said alkyl, cycloalkyl, heterocycloalkyl, heteroaryl or aryl is optionally substituted with one to three halogen, —NR 11a R 11b , OR 5 , —SR 5 , cyano, C 1 -C 3  alkyl, —C(O)R 10  or oxo; 
         R 8′  is hydrogen, deuterium, halogen, cyano, —OR 5 , —SR 5  or NR 11a R 11b ; 
         R 9  is —(CR 3a R 3b ) p —(C 1 -C 3 alkyl), —(CR 3a R 3b ) p -(4- to 6-membered cycloalkyl), —(CR 3a R 3b ) p -(4- to 6-membered heterocycloalkyl) or —(CR 3a R 3b ) p —(C 5 -C 9 aryl), wherein said alkyl, cycloalkyl, heterocycloalkyl or aryl are each optionally substituted with fluoro or C 1 -C 3  alkyl; 
         R 10  is C 1 -C 6 alkyl, wherein said alkyl is optionally substituted with deuterium, halogen, OH, C 1 -C 6 alkoxy or cyano; 
         R 11a  and R 11b  are each independently hydrogen or C 1 -C 6 alkyl, wherein said alkyl is optionally substituted with deuterium, C 1 -C 6 alkoxy or cyano; and if C 2 -C 6 alkyl, said alkyl is optionally substituted with deuterium, C 1 -C 6 alkoxy, cyano, halogen or OH; 
         m is independently 0, 1, 2 or 3; 
         n is independently 0, 1, 2 or 3; 
         p is independently 0 or 1; and 
         t is 1, 2 or 3;
 
as defined and described in WO 2015/150995 and US 2015/0284405, the entirety of each of which is herein incorporated by reference.
 
       
    
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 inhibitor 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-yyy-1 or I-yyy-2: 
     
       
         
         
             
             
         
       
         
         or a pharmaceutically acceptable salt thereof, wherein L and LBM are as defined above and described in embodiments herein, and wherein: 
         X is N or CH 
         m is 1 or 2; 
         Ar is optionally substituted aryl or optionally substituted heteroaryl; 
         R 1  is hydrogen, C 1-6  alkyl, C 1-6  alkoxy, hydroxyl, hydroxy-C 1-6  alkyl, C 1-6  alkyl-amino, amino-C 1-6 alkyl, amino-C 1-6  alkyl-amino, hydroxy-C 1-6  alkylamino, C 3-6  cycloalkylamino, amino-C 3-6 cycloalkylamino, amino-C 3-6  heterocycloalkylamino, aminocarbonyl, halo, hydroxy-C 1-6 alkyl, or hydroxy-C 1-6  alkoxy; and 
         R 2  is hydrogen or C 1-6 alkyl;
 
as defined and described in WO 2012/007375 and US 2012/0015962, the entirety of each of which is herein incorporated by reference.
 
       
    
     As defined above and described herein, IRAK is an IRAK binding moiety capable of binding to one or more of IRAK-1, -2, -3, or -4. 
     In some embodiments, IRAK is an IRAK binding moiety capable of binding to IRAK-1. In some embodiments, IRAK is an IRAK binding moiety capable of binding to IRAK-2. In some embodiments, IRAK is an IRAK binding moiety capable of binding to IRAK-3. In some embodiments, IRAK is an IRAK binding moiety capable of binding to IRAK-4. 
     In some embodiments, IRAK is selected from a moiety recited in Aurigene Discovery Tech. Ltd. Presentation:  Novel IRAK -4  Inhibitors exhibit highly potent anti proliferative activity in DLBCL cell lines with activation MYD 88  L 264 P mutation , such as, for example: AU-5850, AU-2807, AU-6686, and AU-5792, wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, IRAK is selected from a moiety recited in Scott, J. S. et al.  Discovery and Optimization of Pyrrolopyrimidine Inhibitors of Interleukin -1  Receptor Associated Kinase  4 ( IRAK 4)  for the Treatment of Mutant MYD 88  Diffuse Large B - cell Lymphoma . J. Med. Chem. Manuscript, Nov. 29, 2017, 10.1021/acs.jmedchem.7b01290 such as, for example: 
     
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, IRAK is selected from a moiety recited in Powers, J. P. et al.,  Discovery and initial SAR of inhibitors of interleukin -1  receptor - associated kinase -4, Bioorg. Med Chem Lett. (2006) 16(11): 2842-45, such as, for example: 
     
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, IRAK is selected from a moiety recited in Wang, et al.,  Crystal Structure of IRAK -4  Kinase in Complex with Inhibitors: Serine/Threonine Kinase with Tyrosine as a Gatekeeper , Structure, 2006, 14(12): 1835-44, such as, for example: 
     
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, IRAK is selected from a moiety recited in Wang, Z. et al.,  Discovery of potent, selective, and orally bioavailable inhibitors of interleukin -1  receptor - associated kinase  4, Bioorg. Med. Chem Lett., 2015, 25(23): 5546-50, such as, for example: 
     
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, IRAK is selected from a moiety recited in Chaudhary, D. et al.,  Recent Advances in the Discovery of Small Molecule Inhibitors of Interleukin -1  Receptor - Associated Kinase  4 ( IRAK 4)  as a Therapeutic Target for Inflammation and Oncology Disorders , J. Med Chem., 2015, 58(1): 96-110, such as, for example: 
     
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, IRAK is selected from a moiety recited in Zhang, D. et al.,  Constitutive IRAK 4  Activation Underlies Poor Prognosis and Chemoresistance in Pancreatic Ductal Adenocarcinoma , Clin. Can. Res., 2017, 23(7): 1748-59, such as, for example: 
     
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, IRAK is selected from a moiety recited in Cushing, L. et al.,  IRAK 4  kinase controls Toll - like receptor induced inflammation through the transcription factor IRF 5  in primary human monocytes , J. Bio. Chem., 2017, 292(45): 18689-698, such as, for example: 
     
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, IRAK is selected from a moiety recited in Li, N. et al.,  Targeting interleukin -1  receptor - associated kinase for human hepatocellular carcinoma , J. Ex. Clin. Can. Res., 2016, 35(1): 140-50, such as, for example: 
     
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, IRAK is selected from a moiety recited in Dudhgaonkar, S. et al.,  Selective IRAK 4  Inhibition Attenuates Disease in Murine Lupus Models and Demonstrates Steroid Sparing Activity , J. of Immun., 2017, 198(3): 1308-19, such as, for example: 
     BMS-986126 
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, IRAK is selected from a moiety recited in Wang, Z. et al.,  IRAK -4  Inhibitors for Inflammation , Cur. Top. Med. Chem., 2009, 9(8): 724-37, such as, for example: 
     
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, IRAK is selected from a moiety recited in Kelly, P. N. et al.,  Selective interleukin -1  receptor - associated kinase  4  inhibitors for the treatment of autoimmune disorders and lymphoid malignancy , J. Exp. Med., 2015, 212(13): 2189-201, such as, for example: 
     
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, IRAK is selected from a moiety recited in Dunne, A. et al.,  IRAK 1  and IRAK 4  Promote Phosphorylation, Ubiquitation, and Degradation of MyD 88  Adaptor - like  ( Mal ), J. Bio. Chem., 2010, 285(24): 18276-82, such as, for example: 
     
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, IRAK is selected from a moiety recited in Kuppers, R.,  IRAK inhibition to shut down TLR signaling in autoimmunity and MyD 88- dependent lymphomas , J. Exp. Med, 2015, 212(13): 2184, such as, for example: 
     
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, IRAK is selected from a moiety recited in Chiang, E. Y. et al.,  Immune Complex - Mediated Cell Activation from Systemic Lupus Erythematosus and Rheumatoid Arthritis Patients Elaborate Different Requirements for IRAK 1/4  Kinase Activity across human Cell Types , J. Immunol., 2011, 186(2): 1279-88, such as, for example: 
     
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, IRAK is selected from a moiety recited in Lee, K. L. et al.,  Discovery of Clinical Candidate  1-{[2 S, 3 S, 4 S )-3- ethyl -4- fluoro -5- oxopyrrolidin -2- yl ] methoxy }-7- methoxyisoquinoine -6- carboxamide  ( PF -06650833),  a Potent, Selective Inhibitor of Interleukin -1  Receptor Associated Kinase  4 9 IRAK 4),  by Fragment - Based Drug Design , J. Med. Chem., 2017, 60(13): 5521-42, such as, for example: 
     
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, IRAK is selected from a moiety recited in Kondo, M. et al.,  Renoprotective effects of novel interleukin -1  receptor - associated kinase  4  inhibitor AS 2444697  through anti - inflammatory action in  5/6  nephrectomized rats , Naunyn-Schmiedeberg&#39;s Arch Pharmacol., 2014, 387(10): 909-19, such as, for example: 
     
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, IRAK is selected from a moiety recited in Song, K. W. et al.,  The Kinase activities of interleukin -1  receptor associated kinase  ( IRAK )-1  and  4  are redundant in the control of inflammatory cytokine expression in human cells , Mol. Immunol., 2009, 46(7): 1458-66, such as, for example: RO0884, RO1679, or RO6245, wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, IRAK is selected from a moiety recited in Vollmer, S. et al.,  The mechanism of activation of IRAK 1  and IRAK 4  by interleukin -1  and Toll - like receptor agonists , Biochem. J., 2017, 474(12): 2027-38, such as, for example: IRAK-IN-1A, JNK-IN-7, and JNK-IN-8, wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, an IRAK ligand is selected from moiety recited in McElroy, W. T., et al.,  Potent and Selective Amidopyrazole Inhibitors of IRAK 4  That Are Efficacious in a Rodent Model of Inflammation , Med. Chem. Lett., 2015, 6(6): 677-82, such as, for example: 
     
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, an IRAK ligand is selected from moiety recited in Seganish, W. M., et al.,  Discovery and Structure Enabled Synthesis of  2, 6- diaminopyrimidine -4- one IRAK 4  Inhibitors , Med. Chem. Lett., 2015, 6(8): 942-47, such as, for example: 
     
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, an IRAK ligand is selected from moiety recited in Seganish, W. M., et al.,  Initial optimization and series evolution of diaminopyrimidine inhibitors of interleukin -1  receptor associated kinase  4, Bioorg. Med. Chem. Lett., 2015, 25(16): 3203-207, such as, for example: 
     
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, an 
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some IRAK ligand is selected from moiety recited in McElroy, W. T., et al.,  Discovery and hit - to - lead optimization of  2, 6- diaminopyrimidine Inhibitors of interleukin -1  receptor - associated kinase  4, Bioorg. Med. Chem. Lett., 2015, 25(9): 1836-41, such as, for example: 
     
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In some embodiments, an IRAK ligand is selected from moiety recited in Tumey, L. N., et al.,  Identification and optimization of indolo [2,3- c ] quinoline inhibitors of IRAK 4, Bioorg. Med. Chem. Lett., 2014, 24(9): 2066-72, such as, for example: 
     
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
       
         
         
             
             
         
       
     
     wherein 
     
       
         
         
             
             
         
       
     
     is attached to a modifiable carbon, oxygen, nitrogen or sulfur atom. 
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 binding moiety 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-zzz: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, and wherein X, Y, R 1 , R 2 , and R 3  are as defined and described in WO 2018/209012, the entirety of which is herein incorporated by reference. 
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 binding moiety 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-aaaa: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, and wherein R 1 , R 2 , R 3 , R 4 , R 5 , R 6 , and R 7  are as defined and described in US 2018/0230157, the entirety of which is herein incorporated by reference. 
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK1 and/or IRAK4 binding moiety 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-bbbb: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, and wherein Ring A1, Ring B, Ring C, L 1A , R 1 , R 2 , R 3 , R 4 , n, and p are as defined and described in WO 2018/098367, the entirety of which is herein incorporated by reference. 
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 binding moiety 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-cccc: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, and wherein R 1 , R 2 , R 3 , R 4 , R 5  and R 6  are as defined and described in WO 2018/052058, the entirety of which is herein incorporated by reference. 
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK1 and/or IRAK4 binding moiety 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-dddd: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, and wherein Ring A, Ring B, R 2 , and R 3  are as defined and described in US 2017/0369476, the entirety of which is herein incorporated by reference. 
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 binding moiety 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-eeee: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, and wherein R 1 , R 2 , R 3 , and R 4  are as defined and described in WO 2017/207385, the entirety of which is herein incorporated by reference. 
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 binding moiety 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-ffff: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, and wherein Ring A, X, Y, L 1 , Cy 1 , Cy 2 , R 1  R 8 , R 9 , k, m, and n are as defined and described in WO 2017/205766, the entirety of which is herein incorporated by reference. 
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 binding moiety 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-gggg: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, and wherein Ring A, L 1 , Cy 1 , Cy 2 , R 1  R 8 , R 9 , m, and n are as defined and described in WO 2017/205762, the entirety of which is herein incorporated by reference. 
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 binding moiety 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-hhhh: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, and wherein Ring A, R 1 , R 3 , R 4 , R 5 , and R 16  are as defined and described in WO 2017/108723, the entirety of which is herein incorporated by reference. 
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK1 and/or IRAK4 binding moiety 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-iiii: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, and wherein Ring X, Z, R 1 , R 2 , R 3 , R 4 , R a  and p are as defined and described in WO 2017/049068, the entirety of which is herein incorporated by reference. 
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 binding moiety 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-jjjj: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, and wherein X, X′, Y, Y′, z, R 2 , R 3 , R 4a , R 4b , R 5a , R 5b  and R 6  are as defined and described in WO 2017/033093, the entirety of which is herein incorporated by reference. 
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK4 binding moiety 
     
       
         
         
             
             
         
       
     
     thereby forming a compound of formula I-kkkk: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and described in embodiments herein, and wherein X, X′, Y, Y′, z, R 1 , R 2 , R 3 , R 4a , R 4b , R 5a , R 5b  and R 6  are as defined and described in WO 2017/033093, the entirety of which is herein incorporated by reference. 
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK-4 binding moiety thereby forming a compound of formula I-llll: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and DIM are as defined above and described in embodiments herein, and wherein each of the variables R 1 , R 2 , and R 3  is as described and defined in WO 2017/148902 and US 2019/071432, the entirety of each of which is herein incorporated by reference. 
     In certain embodiments, the present invention provides a compound of formula I, I′, or II, wherein IRAK is an IRAK-4 binding moiety thereby forming a compound of formula I-mmmm: 
     
       
         
         
             
             
         
       
     
     or a pharmaceutically acceptable salt thereof, wherein L and DIM are as defined above and described in embodiments herein, and wherein each of the variables R 1 , R 2 , and R 3  is as described and defined in WO 2017/108744, the entirety of each of which is herein incorporated by reference. 
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is 
     
       
         
         
             
             
         
       
     
     In some embodiments, IRAK is selected from those depicted in Table 1, below. 
     Linker (L) 
     As defined above and described herein, L is a bivalent moiety that connects IRAK to LBM. 
     In some embodiments, L is a bivalent moiety that connects IRAK to LBM. 
     In some embodiments, L is a covalent bond or a bivalent, saturated or unsaturated, straight or branched C 1-50  hydrocarbon chain, wherein 0-6 methylene units of L are independently replaced by —C(D)(H)—, —C(D) 2 -, —CRF—, —CF 2 —, -Cy-, —O—, —N(R)—, —Si(R) 2 —, —Si(OH)(R)—, —Si(OH) 2 —, —P(O)(OR)—, —P(O)(R)—, —P(O)(NR 2 )—, —S—, —OC(O)—, —C(O)O—, —C(O)—, —S(O)—, —S(O) 2 —, —N(R)S(O) 2 —, —S(O) 2 N(R)—, —N(R)C(O)—, —C(O)N(R)—, —OC(O)N(R)—, —N(R)C(O)O—, 
     
       
         
         
             
             
         
       
     
     wherein:
     each -Cy- is independently an optionally substituted bivalent ring selected from phenylenyl, an 8-10 membered bicyclic arylenyl, a 4-7 membered saturated or partially unsaturated carbocyclylenyl, a 4-11 membered saturated or partially unsaturated spiro carbocyclylenyl, an 8-10 membered bicyclic saturated or partially unsaturated carbocyclylenyl, a 4-7 membered saturated or partially unsaturated heterocyclylenyl having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, a 4-11 membered saturated or partially unsaturated spiro heterocyclylenyl having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, an 8-10 membered bicyclic saturated or partially unsaturated heterocyclylenyl having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, a 5-6 membered heteroarylenyl having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or an 8-10 membered bicyclic heteroarylenyl having 1-5 heteroatoms independently selected from nitrogen, oxygen, or sulfur; and   each p is independently 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10   

     In some embodiments, each -Cy- is independently an optionally substituted bivalent phenylenyl. In some embodiments, each -Cy- is independently an optionally substituted 8-10 membered bicyclic arylenyl. In some embodiments, each -Cy- is independently an optionally substituted 4-7 membered saturated or partially unsaturated carbocyclylenyl. In some embodiments, each -Cy- is independently an optionally substituted 4-11 membered saturated or partially unsaturated spiro carbocyclylenyl. In some embodiments, each -Cy- is independently an optionally substituted 8-10 membered bicyclic saturated or partially unsaturated carbocyclylenyl. In some embodiments, each -Cy- is independently an optionally substituted 4-7 membered saturated or partially unsaturated heterocyclylenyl having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, each -Cy- is independently an optionally substituted 4-11 membered saturated or partially unsaturated spiro heterocyclylenyl having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, each -Cy- is independently an optionally substituted 8-10 membered bicyclic saturated or partially unsaturated heterocyclylenyl having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, each -Cy- is independently an optionally substituted 5-6 membered heteroarylenyl having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, each -Cy- is independently an optionally substituted 8-10 membered bicyclic heteroarylenyl having 1-5 heteroatoms independently selected from nitrogen, oxygen, or sulfur. 
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is 
     
       
         
         
             
             
         
       
     
     In some embodiments, -Cy- is selected from those depicted in Table 1, below. 
     In some embodiments, L is selected from those depicted in Table 1, below. 
     In some embodiments, r is 0. In some embodiments, r is 1. In some embodiments, r is 2. In some embodiments, r is 3. In some embodiments, r is 4. In some embodiments, r is 5. In some embodiments, r is 6. In some embodiments, r is 7. In some embodiments, r is 8. In some embodiments, r is 9. In some embodiments, r is 10. 
     In some embodiments, r is selected from those depicted in Table 1, below. 
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
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     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is 
     
       
         
         
             
             
         
       
     
     In some embodiments, L is selected from those depicted in Table 1, below. 
     Without limitation, the point of attachment of L to IRAK and LBM can be, for example when L is 
     
       
         
         
             
             
         
       
     
     either 
     
       
         
         
             
             
         
       
     
     In some embodiments, a provided compound or pharmaceutically acceptable salt thereof, is selected from those wherein LBM is 
     
       
         
         
             
             
         
       
     
     IRAK is selected from any of those in Table A below, and L is selected from any of those in Table B below. 
     In some embodiments, a provided compound or pharmaceutically acceptable salt thereof, is selected from those wherein LBM is 
     
       
         
         
             
             
         
       
     
     IRAK is selected from any of those in Table A below, and L is selected from any of those in Table B below. 
     In some embodiments, a provided compound or pharmaceutically acceptable salt thereof, is selected from those wherein LBM is 
     
       
         
         
             
             
         
       
     
     IRAK is selected from any of those in Table A below, and L is selected from any of those in Table B below. 
     In some embodiments, a provided compound or pharmaceutically acceptable salt thereof, is selected from those wherein LBM is 
     
       
         
         
             
             
         
       
     
     IRAK is selected from any of those in Table A below, and L is selected from any of those in Table B below. 
     In some embodiments, a provided compound or pharmaceutically acceptable salt thereof, is selected from those wherein UBM is 
     
       
         
         
             
             
         
       
     
     TBM is selected from but not limited to any of those in Table A below, and L is selected from any of those in Table B below. 
     In some embodiments, a provided compound or pharmaceutically acceptable salt thereof, is selected from those wherein UBM is 
     
       
         
         
             
             
         
       
     
     TBM is selected from but not limited to any of those in Table A below, and L is selected from any of those in Table B below. 
     In some embodiments, a provided compound or pharmaceutically acceptable salt thereof, is selected from those wherein UBM is 
     
       
         
         
             
             
         
       
     
     TBM is selected from but not limited to any of those in Table A below, and L is selected from any of those in Table B below. 
     In some embodiments, a provided compound or pharmaceutically acceptable salt thereof, is selected from those wherein UBM is 
     
       
         
         
             
             
         
       
     
     TBM is selected from but not limited to any of those in Table A below, and L is selected from any of those in Table B below. 
     In some embodiments, a provided compound or pharmaceutically acceptable salt thereof, is selected from those wherein UBM is 
     
       
         
         
             
             
         
       
     
     TBM is selected from but not limited to any of those in Table A below, and L is selected from any of those in Table B below. 
     In some embodiments, a provided compound or pharmaceutically acceptable salt thereof, is selected from those wherein UBM is 
     
       
         
         
             
             
         
       
     
     TBM is selected from but not limited to any of those in Table A below, and L is selected from any of those in Table B below. 
     In some embodiments, a provided compound or pharmaceutically acceptable salt thereof, is selected from those wherein UBM is 
     
       
         
         
             
             
         
       
     
     TBM is selected from but not limited to any of those in Table A below, and L is selected from any of those in Table B below. 
     In some embodiments, a provided compound or pharmaceutically acceptable salt thereof, is selected from those wherein UBM is 
     
       
         
         
             
             
         
       
     
     TBM is selected from but not limited to any of those in Table A below, and L is selected from any of those in Table B below. 
     
       
         
           
               
             
               
                 TABLE A 
               
               
                   
               
               
                 Exemplified IRAK binders (IRAK) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (a) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (b) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (c) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (d) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (e) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (f) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (g) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (h) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (i) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (j) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (k) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (l) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (m) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (n) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (o) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (p) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (q) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (r) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (s) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (t) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (u) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (v) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (w) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (x) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (y) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (z) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (aa) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (bb) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (cc) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (dd) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (ee) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (ff) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (gg) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (hh) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (ii) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (jj) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (kk) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (ll) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (mm) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (nn) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (oo) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (pp) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (qq) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (rr) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (ss) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (tt) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (uu) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (vv) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (ww) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (xx) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (yy) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (zz) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (aaa) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (bbb) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (ccc) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (ddd) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (eee) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (fff) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (ggg) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (hhh) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (iii) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (jjj) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (kkk) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (lll) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (mmm) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (nnn) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (ooo) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (ppp) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (qqq) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (rrr) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (sss) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (ttt) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (uuu) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (vvv) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (www) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (xxx) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (yyy) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (zzz) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (aaaa) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (bbbb) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (cccc) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (dddd) 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE B 
               
               
                   
               
               
                 Exemplified Linkers (L) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (1) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (2) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (3) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (4) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (5) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (6) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (7) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (8) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (9) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (10) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (11) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (12) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (13) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (14) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (15) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (16) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (17) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (18) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (19) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (20) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (21) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (22) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (23) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (24) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (25) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (26) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (27) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (28) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (29) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (30) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (31) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (32) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (33) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (34) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (35) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (36) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (37) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (38) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (39) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (40) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (41) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (42) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (43) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (44) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (45) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (46) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (47) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (49) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (50) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (51) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (52) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (53) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (54) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (55) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (56) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (57) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (58) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (59) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (60) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (61) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (62) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (63) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (64) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (65) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (66) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (67) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (68) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (69) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (70) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (71) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (72) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (73) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (74) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (75) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (76) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (77) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (78) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (79) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (80) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (81) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (82) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (83) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (84) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (85) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (86) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (87) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (88) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (89) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (90) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (91) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (92) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (93) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (94) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (95) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (96) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (97) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (98) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (99) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (100) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (101) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (102) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (103) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (104) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (105) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (106) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (107) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (108) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (109) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (110) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (111) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (112) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (113) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (114) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (115) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (116) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (117) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
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                 (589) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (590) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (591) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (592) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (593) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (594) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (595) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (596) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (597) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (598) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (599) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (600) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (601) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (602) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (603) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (604) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (605) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (606) 
               
               
                   
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
                 (607) 
               
               
                   
               
            
           
         
       
     
     In some embodiments, the present invention provides a compound having an LBM binding moiety described and disclosed herein, an IRAK set forth in Table A above, and a linker set forth in Table B above, or a pharmaceutically acceptable salt thereof 
     Exemplary compounds of the invention are set forth in Table 1, below. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Exemplary Compounds 
               
            
           
           
               
               
            
               
                 I-# 
                 Structure 
               
               
                   
               
               
                 I-1 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-2 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-3 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-4 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-5 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-6 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-7 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-8 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-9 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-10 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-11 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-12 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-13 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-14 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-15 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-16 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-17 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-18 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-19 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-20 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-21 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-22 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-23 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-24 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-25 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-26 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-27 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-28 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-29 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-30 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-31 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-32 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-33 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-34 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-35 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-36 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-37 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-38 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-39 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-40 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-41 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-42 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-43 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-44 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-45 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-46 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-47 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-48 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-49 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-50 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-51 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-52 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-53 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-54 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-55 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-56 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-57 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-58 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-59 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-60 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-61 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-62 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-63 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-64 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-65 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-66 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-67 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-68 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-69 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-70 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-71 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-72 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-73 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-74 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-75 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-76 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-77 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-78 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-79 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-80 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-81 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-82 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-83 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-84 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-85 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-86 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-87 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-88 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-89 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 I-90 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     In some embodiments, the present invention provides a compound set forth in Table 1, above, or a pharmaceutically acceptable salt thereof. 
     4. General Methods of Providing the Present Compounds 
     The compounds of this invention may be prepared or isolated in general by synthetic and/or semi-synthetic methods known to those skilled in the art for analogous compounds and by methods described in detail in the Examples, herein. 
     In the Schemes below, where a particular protecting group, leaving group, or transformation condition is depicted, one of ordinary skill in the art will appreciate that other protecting groups, leaving groups, and transformation conditions are also suitable and are contemplated. Such groups and transformations are described in detail in  March&#39;s Advanced Organic Chemistry: Reactions, Mechanisms, and Structure , M. B. Smith and J. March, 5 th  Edition, John Wiley &amp; Sons, 2001,  Comprehensive Organic Transformations , R. C. Larock, 2 nd  Edition, John Wiley &amp; Sons, 1999, and  Protecting Groups in Organic Synthesis , T. W. Greene and P. G. M. Wuts, 3 rd  edition, John Wiley &amp; Sons, 1999, the entirety of each of which is hereby incorporated herein by reference. 
     As used herein, the phrase “oxygen protecting group” includes, for example, carbonyl protecting groups, hydroxyl protecting groups, etc. Hydroxyl protecting groups are well known in the art and include those described in detail in  Protecting Groups in Organic Synthesis , T. W. Greene and P. G. M. Wuts, 3 rd  edition, John Wiley &amp; Sons, 1999, the entirety of which is incorporated herein by reference. Examples of suitable hydroxyl protecting groups include, but are not limited to, esters, allyl ethers, ethers, silyl ethers, alkyl ethers, arylalkyl ethers, and alkoxyalkyl ethers. Examples of such esters include formates, acetates, carbonates, and sulfonates. Specific examples include formate, benzoyl formate, chloroacetate, trifluoroacetate, methoxyacetate, triphenylmethoxyacetate, p-chlorophenoxyacetate, 3-phenylpropionate, 4-oxopentanoate, 4,4-(ethylenedithio)pentanoate, pivaloate (trimethylacetyl), crotonate, 4-methoxy-crotonate, benzoate, p-benylbenzoate, 2,4,6-trimethylbenzoate, carbonates such as methyl, 9-fluorenylmethyl, ethyl, 2,2,2-trichloroethyl, 2-(trimethylsilyl)ethyl, 2-(phenyl sulfonyl)ethyl, vinyl, allyl, and p-nitrobenzyl. Examples of such silyl ethers include trimethylsilyl, triethylsilyl, t-butyldimethylsilyl, t-butyldiphenylsilyl, triisopropylsilyl, and other trialkylsilyl ethers. Alkyl ethers include methyl, benzyl, p-methoxybenzyl, 3,4-dimethoxybenzyl, trityl, t-butyl, allyl, and allyloxycarbonyl ethers or derivatives. Alkoxyalkyl ethers include acetals such as methoxymethyl, methylthiomethyl, (2-methoxyethoxy)methyl, benzyloxymethyl, b eta-(trimethylsilyl)ethoxymethyl, and tetrahydropyranyl ethers. Examples of arylalkyl ethers include benzyl, p-methoxybenzyl (MPM), 3,4-dimethoxybenzyl, O-nitrobenzyl, p-nitrobenzyl, p-halobenzyl, 2,6-dichlorobenzyl, p-cyanobenzyl, and 2- and 4-picolyl. 
     Amino protecting groups are well known in the art and include those described in detail in Protecting Groups in Organic Synthesis, T. W. Greene and P. G. M. Wuts, 3 rd  edition, John Wiley &amp; Sons, 1999, the entirety of which is incorporated herein by reference. Suitable amino protecting groups include, but are not limited to, aralkylamines, carbamates, cyclic imides, allyl amines, amides, and the like. Examples of such groups include t-butyloxycarbonyl (BOC), ethyloxycarbonyl, methyl oxycarbonyl, trichloroethyloxycarbonyl, allyloxycarbonyl (Alloc), benzyloxocarbonyl (CBZ), allyl, phthalimide, benzyl (Bn), fluorenylmethylcarbonyl (Fmoc), formyl, acetyl, chloroacetyl, dichloroacetyl, trichloroacetyl, phenylacetyl, trifluoroacetyl, benzoyl, and the like. 
     In certain embodiments, compounds of the present invention are generally prepared according to Scheme 1 set forth below: 
     
       
         
         
             
             
         
       
     
     As depicted in Scheme 1, above, amine A-1 is coupled to acid A-2 using the coupling agent HATU in the presence of the base DIPEA in DMF to form a provided compound with a linker comprising an amide bond. The squiggly bond,  , represents the portion of the linker between IRAK and the terminal amino group of A-1 or the portion of the linker between LBM and the terminal carboxyl group of A-2, respectively. Additionally, an amide bond can be formed using coupling reagents known in the art such as, but not limited to DCC, DIC, EDC, HBTU, HCTU, PyAOP, PyBrOP, BOP, BOP—Cl, DEPBT, T3P, TATU, TBTU, TNTU, TOTU, TPTU, TSTU, or TDBTU. 
     In certain embodiments, compounds of the present invention are generally prepared according to Scheme 2 set forth below: 
     
       
         
         
             
             
         
       
     
     As depicted in Scheme 2, above, amine A-1 is coupled to acid A-2 using the coupling agent PyBOP in the presence of the base DIPEA in DMF to form a provided compound with a linker comprising an amide bond. The squiggly bond,  , represents the portion of the linker between IRAK and the terminal amino group of A-1 or the portion of the linker between LBM and the terminal carboxyl group of A-2, respectively. Additionally, an amide bond can be formed using coupling reagents known in the art such as, but not limited to DCC, DIC, EDC, HBTU, HCTU, PyAOP, PyBrOP, BOP, BOP—Cl, DEPBT, T3P, TATU, TBTU, TNTU, TOTU, TPTU, TSTU, or TDBTU. 
     In certain embodiments, compounds of the present invention are generally prepared according to Scheme 3 set forth below: 
     
       
         
         
             
             
         
       
     
     As depicted in Scheme 3, above, acid A-3 is coupled to amine A-4 using the coupling agent HATU in the presence of the base DIPEA in DMF to form a provided compound with a linker comprising an amide bond. The squiggly bond,  , represents the portion of the linker between IRAK and the terminal carboxyl group of A-3 or the portion of the linker between LBM and the terminal amino group of A-4, respectively. Additionally, an amide bond can be formed using coupling reagents known in the art such as, but not limited to DCC, DIC, EDC, HBTU, HCTU, PyAOP, PyBrOP, BOP, BOP—Cl, DEPBT, T3P, TATU, TBTU, TNTU, TOTU, TPTU, TSTU, or TDBTU. 
     In certain embodiments, compounds of the present invention are generally prepared according to Scheme 4 set forth below: 
     
       
         
         
             
             
         
       
     
     As depicted in Scheme 4, above, acid A-3 is coupled to amine A-4 using the coupling agent PyBOP in the presence of the base DIPEA in DMF to form a provided compound with a linker comprising an amide bond. The squiggly bond,  , represents the portion of the linker between IRAK and the terminal carboxyl group of A-3 or the portion of the linker between LBM and the terminal amino group of A-4, respectively. Additionally, an amide bond can be formed using coupling reagents known in the art such as, but not limited to DCC, DIC, EDC, HBTU, HCTU, PyAOP, PyBrOP, BOP, BOP—Cl, DEPBT, T3P, TATU, TBTU, TNTU, TOTU, TPTU, TSTU, or TDBTU. 
     In certain embodiments, compounds of the present invention are generally prepared according to Scheme 5 set forth below: 
     
       
         
         
             
             
         
       
     
     As depicted in Scheme 5, above, an S N Ar displacement of fluoride A-6 by amine A-5 is effected in the presence of the base DIPEA in DMF to form a provided compound with a linker comprising a secondary amine. The squiggly bond,  , represents the portion of the linker between IRAK and the terminal amino group of A-5. 
     In certain embodiments, compounds of the present invention are generally prepared according to Scheme 6 set forth below: 
     
       
         
         
             
             
         
       
     
     As depicted in Scheme 6, above, an S N Ar displacement of fluoride A-7 by amine A-8 is effected in the presence of the base DIPEA in DMF to form a provided compound with a linker comprising a secondary amine. The squiggly bond,  , represents the portion of the linker between LBM and the terminal amino group of A-8. 
     
       
         
         
             
             
         
       
     
     As depicted in Scheme 7, above, reductive amination of the mixture of aldehyde A-9 and amine A-10 is effected in the presence of NaHB(OAc) 3  and KOAc in DMF/THF to form a provided compound with a linker comprising a secondary amine. The squiggly bond,  , represents the portion of the linker between LBM and the terminal amino group of A-8. 
     One of skill in the art will appreciate that various functional groups present in compounds of the invention such as aliphatic groups, alcohols, carboxylic acids, esters, amides, aldehydes, halogens and nitriles can be interconverted by techniques well known in the art including, but not limited to reduction, oxidation, esterification, hydrolysis, partial oxidation, partial reduction, halogenation, dehydration, partial hydration, and hydration. “March&#39;s Advanced Organic Chemistry”, 5 th  Ed.: Smith, M. B. and March, J., John Wiley &amp; Sons, New York: 2001, the entirety of which is incorporated herein by reference. Such interconversions may require one or more of the aforementioned techniques, and certain methods for synthesizing compounds of the invention are described below in the Exemplification. 
     5. Uses, Formulation and Administration 
     Pharmaceutically Acceptable Compositions 
     According to another embodiment, the invention provides a composition comprising a compound of this invention or a pharmaceutically acceptable derivative thereof and a pharmaceutically acceptable carrier, adjuvant, or vehicle. The amount of compound in compositions of this invention is such that is effective to measurably degrade and/or inhibit an IRAK protein kinase, or a mutant thereof, in a biological sample or in a patient. In certain embodiments, the amount of compound in compositions of this invention is such that is effective to measurably degrade and/or inhibit an IRAK protein kinase, or a mutant thereof, in a biological sample or in a patient. In certain embodiments, a composition of this invention is formulated for administration to a patient in need of such composition. In some embodiments, a composition of this invention is formulated for oral administration to a patient. 
     The term “patient”, as used herein, means an animal, preferably a mammal, and most preferably a human. 
     The term “pharmaceutically acceptable carrier, adjuvant, or vehicle” refers to a non-toxic carrier, adjuvant, or vehicle that does not destroy the pharmacological activity of the compound with which it is formulated. Pharmaceutically acceptable carriers, adjuvants or vehicles that may be used in the compositions of this invention include, but are not limited to, ion exchangers, alumina, aluminum stearate, lecithin, serum proteins, such as human serum albumin, buffer substances such as phosphates, glycine, sorbic acid, potassium sorbate, partial glyceride mixtures of saturated vegetable fatty acids, water, salts or electrolytes, such as protamine sulfate, disodium hydrogen phosphate, potassium hydrogen phosphate, sodium chloride, zinc salts, colloidal silica, magnesium trisilicate, polyvinyl pyrrolidone, cellulose-based substances, polyethylene glycol, sodium carboxymethylcellulose, polyacrylates, waxes, polyethylene-polyoxypropylene-block polymers, polyethylene glycol and wool fat. 
     A “pharmaceutically acceptable derivative” means any non-toxic salt, ester, salt of an ester or other derivative of a compound of this invention that, upon administration to a recipient, is capable of providing, either directly or indirectly, a compound of this invention or an inhibitorily or degratorily active metabolite or residue thereof. 
     As used herein, the term “inhibitorily active metabolite or residue thereof” means that a metabolite or residue thereof is also an inhibitor of an IRAK protein kinase, or a mutant thereof. 
     As used herein, the term “degratorily active metabolite or residue thereof” means that a metabolite or residue thereof is also a degrader of an IRAK protein kinase, or a mutant thereof. 
     Compositions of the present invention may be administered orally, parenterally, by inhalation spray, topically, rectally, nasally, buccally, vaginally or via an implanted reservoir. The term “parenteral” as used herein includes subcutaneous, intravenous, intramuscular, intra-articular, intra-synovial, intrasternal, intrathecal, intrahepatic, intralesional and intracranial injection or infusion techniques. Preferably, the compositions are administered orally, intraperitoneally or intravenously. Sterile injectable forms of the compositions of this invention may be aqueous or oleaginous suspension. These suspensions may be formulated according to techniques known in the art using suitable dispersing or wetting agents and suspending agents. The sterile injectable preparation may also be a sterile injectable solution or suspension in a non-toxic parenterally acceptable diluent or solvent, for example as a solution in 1,3-butanediol. Among the acceptable vehicles and solvents that may be employed are water, Ringer&#39;s solution and isotonic sodium chloride solution. In addition, sterile, fixed oils are conventionally employed as a solvent or suspending medium. 
     For this purpose, any bland fixed oil may be employed including synthetic mono- or di-glycerides. Fatty acids, such as oleic acid and its glyceride derivatives are useful in the preparation of injectables, as are natural pharmaceutically-acceptable oils, such as olive oil or castor oil, especially in their polyoxyethylated versions. These oil solutions or suspensions may also contain a long-chain alcohol diluent or dispersant, such as carboxymethyl cellulose or similar dispersing agents that are commonly used in the formulation of pharmaceutically acceptable dosage forms including emulsions and suspensions. Other commonly used surfactants, such as Tweens, Spans and other emulsifying agents or bioavailability enhancers which are commonly used in the manufacture of pharmaceutically acceptable solid, liquid, or other dosage forms may also be used for the purposes of formulation. 
     Pharmaceutically acceptable compositions of this invention may be orally administered in any orally acceptable dosage form including, but not limited to, capsules, tablets, aqueous suspensions or solutions. In the case of tablets for oral use, carriers commonly used include lactose and corn starch. Lubricating agents, such as magnesium stearate, are also typically added. For oral administration in a capsule form, useful diluents include lactose and dried cornstarch. When aqueous suspensions are required for oral use, the active ingredient is combined with emulsifying and suspending agents. If desired, certain sweetening, flavoring or coloring agents may also be added. 
     Alternatively, pharmaceutically acceptable compositions of this invention may be administered in the form of suppositories for rectal administration. These can be prepared by mixing the agent with a suitable non-irritating excipient that is solid at room temperature but liquid at rectal temperature and therefore will melt in the rectum to release the drug. Such materials include cocoa butter, beeswax and polyethylene glycols. 
     Pharmaceutically acceptable compositions of this invention may also be administered topically, especially when the target of treatment includes areas or organs readily accessible by topical application, including diseases of the eye, the skin, or the lower intestinal tract. Suitable topical formulations are readily prepared for each of these areas or organs. 
     Topical application for the lower intestinal tract can be effected in a rectal suppository formulation (see above) or in a suitable enema formulation. Topically-transdermal patches may also be used. 
     For topical applications, provided pharmaceutically acceptable compositions may be formulated in a suitable ointment containing the active component suspended or dissolved in one or more carriers. Carriers for topical administration of compounds of this invention include, but are not limited to, mineral oil, liquid petrolatum, white petrolatum, propylene glycol, polyoxyethylene, polyoxypropylene compound, emulsifying wax and water. Alternatively, provided pharmaceutically acceptable compositions can be formulated in a suitable lotion or cream containing the active components suspended or dissolved in one or more pharmaceutically acceptable carriers. Suitable carriers include, but are not limited to, mineral oil, sorbitan monostearate, polysorbate 60, cetyl esters wax, cetearyl alcohol, 2-octyldodecanol, benzyl alcohol and water. 
     For ophthalmic use, provided pharmaceutically acceptable compositions may be formulated as micronized suspensions in isotonic, pH adjusted sterile saline, or, preferably, as solutions in isotonic, pH adjusted sterile saline, either with or without a preservative such as benzylalkonium chloride. Alternatively, for ophthalmic uses, the pharmaceutically acceptable compositions may be formulated in an ointment such as petrolatum. 
     Pharmaceutically acceptable compositions of this invention may also be administered by nasal aerosol or inhalation. Such compositions are prepared according to techniques well-known in the art of pharmaceutical formulation and may be prepared as solutions in saline, employing benzyl alcohol or other suitable preservatives, absorption promoters to enhance bioavailability, fluorocarbons, and/or other conventional solubilizing or dispersing agents. 
     Most preferably, pharmaceutically acceptable compositions of this invention are formulated for oral administration. Such formulations may be administered with or without food. In some embodiments, pharmaceutically acceptable compositions of this invention are administered without food. In other embodiments, pharmaceutically acceptable compositions of this invention are administered with food. 
     The amount of compounds of the present invention that may be combined with the carrier materials to produce a composition in a single dosage form will vary depending upon the host treated, the particular mode of administration. Preferably, provided compositions should be formulated so that a dosage of between 0.01-100 mg/kg body weight/day of the compound can be administered to a patient receiving these compositions. 
     It should also be understood that a specific dosage and treatment regimen for any particular patient will depend upon a variety of factors, including the activity of the specific compound employed, the age, body weight, general health, sex, diet, time of administration, rate of excretion, drug combination, and the judgment of the treating physician and the severity of the particular disease being treated. The amount of a compound of the present invention in the composition will also depend upon the particular compound in the composition. 
     Uses of Compounds and Pharmaceutically Acceptable Compositions 
     Compounds and compositions described herein are generally useful for the degradation and/or inhibition of kinase activity of one or more enzymes. 
     Examples of kinases that are degraded and/or inhibited by the compounds and compositions described herein and against which the methods described herein are useful include those of the interleukin-1 receptor-associated kinase (IRAK) family of kinases, the members of which include IRAK-1, IRAK-2, and IRAK-4, or a mutant thereof. Li et al., “IRAK-4: A novel member of the IRAK family with the properties of an IRAK-kinase,”  PNAS  2002, 99(8), 5567-5572, Flannery et al., “The interleukin-1 receptor-associated kinases: Critical regulators of innate immune signaling”  Biochem Pharm  2010, 80(12), 1981-1991 incorporated by reference in its entirety. 
     The activity of a compound utilized in this invention as a degrader and/or inhibitor of IRAK-1, IRAK-2, and/or IRAK-4, or a mutant thereof, may be assayed in vitro, in vivo or in a cell line. In vitro assays include assays that determine inhibition of either the phosphorylation activity and/or the subsequent functional consequences, or ATPase activity of activated IRAK-1, IRAK-2, and/or IRAK-4, or a mutant thereof. Alternate in vitro assays quantitate the ability of the inhibitor to bind to IRAK-1, IRAK-2 and/or IRAK-4. Inhibitor binding may be measured by radiolabeling the inhibitor prior to binding, isolating the inhibitor/IRAK-1, inhibitor/IRAK-2, or inhibitor/IRAK-4 complex and determining the amount of radiolabel bound. Alternatively, inhibitor binding may be determined by running a competition experiment where new inhibitors are incubated with IRAK-1, IRAK-2, and/or IRAK-4 bound to known radioligands. Representative in vitro and in vivo assays useful in assaying an IRAK-4 inhibitor include those described and disclosed in, e.g., Kim et al., “A critical role for IRAK4 kinase activity in Toll-like receptor-mediated innate immunity,”  J. Exp. Med.  2007 204(5), 1025-1036; Lebakken et al., “A Fluorescence Lifetime Based Binding Assay to Characterize Kinase Inhibitors,”  J. Biomol. Screen.  2007, 12(6), 828-841; Maschera et al., “Overexpression of an enzymatically inactive interleukin-1-receptor-associated kinase activates nuclear factor-κB,”  Biochem. J.  1999, 339, 227-231; Song et al., “The kinase activities of interleukin-e receptor associated kinase (IRAK)-1 and 4 are redundant in the control of inflammatory cytokine expression in human cells,”  Mol. Immunol.  2009, 46, 1458-1466, each of, the entirety of each of which is herein incorporated by reference. Detailed conditions for assaying a compound utilized in this invention as a degrader and/or inhibitor of IRAK-1, IRAK-2, and/or IRAK-4, or a mutant thereof, are set forth in the Examples below. 
     The best characterized member of the IRAK family is the serine/threonine kinase IRAK-4. IRAK-4 is implicated in signaling innate immune responses from Toll-like receptors (TLRs) and Toll/IL-1 receptors (TIRs). 
     Innate immunity detects pathogens through the recognition of pathogen-associated molecular patterns by TLRs, when then links to the adaptive immune response. TLRs recognize conserved structures of both microbes and endogenous molecules. TLRs which recognize bacterial and fungal components are located on the cell surface, whereas TLRs which recognize viral or microbial nucleic acids are localized to intracellular membranes such as endosomes and phagosomes. Cell surface TLRs can be targeted by small molecules and antibodies, whereas intracellular TLRs require targeting with oligonucleotides. 
     TLRs mediate the innate immune response by upregulating the expression of inflammatory genes in multiple target cells. See, e.g., Sen et al., “Transcriptional signaling by double-stranded RNA: role of TLR3 ,” Cytokine  &amp;  Growth Factor Rev.  2005, 16, 1-14, incorporated by reference in its entirety. While TLR-mediated inflammatory response is critical for innate immunity and host defense against infections, uncontrolled inflammation is detrimental to the host leading to sepsis and chronic inflammatory diseases, such as chronic arthritis, atherosclerosis, multiple sclerosis, cancers, autoimmune disorders such as rheumatoid arthritis, lupus, asthma, psoriasis, and inflammatory bowel diseases. 
     Upon binding of a ligand, most TLRs recruit the adaptor molecule MyD88 through the TIR domain, mediating the MyD88-dependent pathway. MyD88 then recruits IRAK-4, which engages with the nuclear factor-κB (NF-κB), mitogen-activated protein (MAP) kinase and interferon-regulatory factor cascades and leads to the induction of pro-inflammatory cytokines. The activation of NF-κB results in the induction of inflammatory cytokines and chemokines, such as TNF-α, IL-1α, IL-6 and IL-8. The kinase activity of IRAK-4 has been shown to play a critical role in the TLR-mediated immune and inflammatory responses. IRAK4 is a key mediator of the innate immune response orchestrated by interleukin-1 receptor (IL-1R), interleukin-18 receptor (IL-18R), IL-33 receptor (IL-33R), and Toll-like receptors (TLRs). Inactivation of IRAK-1 and/or IRAK-4 activity has been shown to result in diminished production of cytokines and chemokines in response to stimulation of IL-1 and TLR ligands. See, e.g., Picard et al., “Clinical features and outcome of patients with IRAK-4 and MyD88 deficiency,”  Medicine  ( Baltimore ), 2010, 89(6), 043-25; Li, “IRAK4 in TLR/IL-1R signaling: Possible clinical applications,”  Eur. J. Immunology  2008, 38:614-618; Cohen et al., “Targeting protein kinases for the development of anti-inflammatory drugs,”  Curr. Opin. Cell Bio.  2009, 21:317-324; Flannery et al., “The interleukin-1 receptor-associated kinases: Critical regulators of innate immune signalling,”  Biochem. Pharm.  2010, 80(12), 1981-1991; Gottipati et al., “IRAK1: A critical signaling mediator of innate immunity,”  Cellular Signaling  2008, 20, 269-276; Kim et al., “A critical role for IRAK4 kinase activity in Toll-like receptor-mediated innate immunity,”  J. Exp. Med.  2007 204(5), 1025-1036; Koziczak-Holbro et al., “IRAK-4 Kinase Activity Is Required for Interleukin-1 (IL-1) Receptor- and Toll-like Receptor 7-mediated Signaling and Gene Expression,”  J. Biol. Chem.  2007, 282(18), 13552-13560; Kubo-Murai et al., “IRAK-4-dependent Degradation of IRAK-1 is a Negative Feedback Signal for TLR-mediated NF-κB Activation,”  J. Biochem.  2008, 143, 295-302; Maschera et al., “Overexpression of an enzymatically inactive interleukin-1-receptor-associated kinase activates nuclear factor-κB,”  Biochem. J.  1999, 339, 227-231; Lin et al., “Helical assembly in the MyD88-IRAK4-IRAK2 complex in TLR/IL-1R signalling,”  Nature  2010, 465(17), 885-891; Suzuki et al., “IRAK-4 as the central TIR signaling mediator in innate immunity,”  TRENDS in Immunol.  2002, 23(10), 503-506; Suzuki et al., “Severe impairment of interleukin-1 and Toll-like receptor signalling in mice lacking IRAK-4 ,” Nature  2002, 416, 750-754; Swantek et al., “IL-1 Receptor-Associated Kinase Modulates Host Responsiveness to Endotoxin,”  J. Immunol.  2000, 164, 4301-4306; Hennessy, E., et al., “Targeting Toll-like receptors: emerging therapeutics?”  Nature Reviews , vol. 9, pp: 293-307 (2010); Dinarello, C. “Interleukin-18 and the Pathogenesis of Inflammatory Diseases,”  Seminars in Nephrology , vol. 27, no. 1, pp: 98-114 (2007), each of, the entirety of each of which is herein incorporated by reference. In fact, knockdown mice that express a catalytically inactive mutant IRAK-4 protein are completely resistant to septic shock and show impaired IL-1 activity. Moreover, these mice are resistant to joint and bone inflammation/destruction in an arthritis model, suggesting that IRAK-4 may be targeted to treat chronic inflammation. Further, while IRAK-4 appears to be vital for childhood immunity against some pyogenic bacteria, it has been shown to play a redundant role in protective immunity to most infections in adults, as demonstrated by one study in which patients older than 14 lacking IRAK-4 activity exhibited no invasive infections. Cohen et al., “Targeting protein kinases for the development of anti-inflammatory drugs,”  Curr. Opin. Cell Bio.  2009, 21:317-324; Ku et al., “Selective predisposition to bacterial infections in IRAK-4-deficient children: IRAK-4-dependent TLRs are otherwise redundant in protective immunity,”  J. Exp. Med.  2007, 204(10), 2407-2422; Picard et al., “Inherited human IRAK-4 deficiency: an update,”  Immunol. Res.  2007, 38, 347-352; Song et al., “The kinase activities of interleukin-e receptor associated kinase (IRAK)-1 and 4 are redundant in the control of inflammatory cytokine expression in human cells,”  Mol. Immunol.  2009, 46, 1458-1466; Rokosz, L. et al., “Kinase inhibitors as drugs for chronic inflammatory and immunological diseases: progress and challenges,”  Expert Opinions on Therapeutic Targets,  12(7), pp: 883-903 (2008); Gearing, A. “Targeting toll-like receptors for drug development: a summary of commercial approaches,”  Immunology and Cell Biology,  85, pp: 490-494 (2007); Dinarello, C. “IL-1: Discoveries, controversies and future directions,”  European Journal of Immunology,  40, pp: 595-653 (2010), each of, the entirety of each of which is herein incorporated by reference. Because TLR activation triggers IRAK-4 kinase activity, IRAK-4 inhibition presents an attractive target for treating the underlying causes of inflammation in countless diseases. 
     Representative IRAK-4 inhibitors include those described and disclosed in e.g., Buckley et al.,  Bioorg. Med. Chem. Lett.  2008, 18, 3211-3214; Buckley et al.,  Bioorg. Med. Chem. Lett.  2008, 18, 3291-3295; Buckley et al.,  Bioorg. Med. Chem. Lett.  2008, 18, 3656-3660; Powers et al., “Discovery and initial SAR of inhibitors of interleukin-1 receptor-associated kinase-4 ,” Bioorg. Med. Chem. Lett.  2006, 16, 2842-2845; Wng et al., “IRAK-4 Inhibitors for Inflammation,”  Curr. Topics in Med. Chem.  2009, 9, 724-737, each of, the entirety of each of which is herein incorporated by reference. 
     As used herein, the terms “treatment,” “treat,” and “treating” refer to reversing, alleviating, delaying the onset of, or inhibiting the progress of a disease or disorder, or one or more symptoms thereof, as described herein. In some embodiments, treatment may be administered after one or more symptoms have developed. In other embodiments, treatment may be administered in the absence of symptoms. For example, treatment may be administered to a susceptible individual prior to the onset of symptoms (e.g., in light of a history of symptoms and/or in light of genetic or other susceptibility factors). Treatment may also be continued after symptoms have resolved, for example to prevent or delay their recurrence. 
     Provided compounds are degraders and/or inhibitors of one of more of IRAK-1, IRAK-2, and/or IRAK-4 and are therefore useful for treating one or more disorders associated with activity of one or more of IRAK-1, IRAK-2, and/or IRAK-4. Thus, in certain embodiments, the present invention provides a method for treating a IRAK-1-mediated, a IRAK-2-mediated, and/or a IRAK-4-mediated disorder comprising the step of administering to a patient in need thereof a compound of the present invention, or pharmaceutically acceptable composition thereof. 
     As used herein, the terms “IRAK-1-mediated”, “IRAK-2-mediated”, and/or “IRAK-4-mediated” disorders, diseases, and/or conditions as used herein means any disease or other deleterious condition in which one or more of IRAK-1, IRAK-2, and/or IRAK-4, or a mutant thereof, are known to play a role. Accordingly, another embodiment of the present invention relates to treating or lessening the severity of one or more diseases in which one or more of IRAK-1, IRAK-2, and/or IRAK-4, or a mutant thereof, are known to play a role. 
     In some embodiments, the present invention provides a method for treating one or more disorders, diseases, and/or conditions wherein the disorder, disease, or condition is a cancer, a neurodegenative disorder, a viral disease, an autoimmune disease, an inflammatory disorder, a hereditary disorder, a hormone-related disease, a metabolic disorder, conditions associated with organ transplantation, immunodeficiency disorders, a destructive bone disorder, a proliferative disorder, an infectious disease, a condition associated with cell death, thrombin-induced platelet aggregation, liver disease, pathologic immune conditions involving T cell activation, a cardiovascular disorder, or a CNS disorder. 
     Diseases and conditions treatable according to the methods of this invention include, but are not limited to, cancer (see, e.g., Ngo, V. et al., “Oncogenically active MYD88 mutations in human lymphoma,”  Nature , vol. 000, pp: 1-7 (2010); Lust, J. et al., “Induction of a Chronic Disease State in patients With Smoldering of Indolent Multiple Myeloma by Targeting Interleukin 1β-Induced Interleukin 6 Production and the Myeloma Proliferative Component,”  Mayo Clinic Proceedings,  84(2), pp: 114-122 (2009)), diabetes, cardiovascular disease, viral disease, autoimmune diseases such as lupus (see, e.g., Dinarello, C. “Interleukin-18 and the Pathogenesis of Inflammatory Diseases,”  Seminars in Nephrology , vol. 27, no. 1, pp: 98-114 (2007); Cohen et al., “Targeting protein kinases for the development of anti-inflammatory drugs,”  Curr. Opin. Cell Bio.  2009, 21:317-324) and rheumatoid arthritis (see, e.g., Geyer, M. et al., “Actual status of antiinterleukin-1 therapies in rheumatic diseases,”  Current Opinion in Rheumatology,  22, pp: 246-251 (2010)), autoinflammatory syndromes (see, e.g., Hoffman, H. et al., “Efficacy and Safety of Rilonacept (Interleukin-1 Trap) in Patients with Cryopyrin-Associated Periodic Syndromes,”  Arthritis  &amp;  Rheumatism , vol. 58, no. 8, pp: 2443-2452 (2008)), atherosclerosis, psoriasis, allergic disorders, inflammatory bowel disease (see, e.g., Cario, E. “Therapeutic Impact of Toll-like Receptors on Inflammatory Bowel Diseases: A Multiple-edged Sword,”  Inflamm. Bowel Dis.,  14, pp: 411-421 (2008)), inflammation (see, e.g., Dinarello, C. “Interleukin 1 and interleukin 18 as mediators of inflammation and the aging process,” The American  Journal of Clinical Nutrition,  83, pp: 447S-455S (2006)), acute and chronic gout and gouty arthritis (see, e.g., Terkeltaub, R. “Update on gout: new therapeutic strategies and options,” Nature, vol. 6, pp: 30-38 (2010); Weaver, A. “Epidemiology of gout,”  Cleveland Clinic Journal of Medicine , vol. 75, suppl. 5, pp: S9-512 (2008); Dalbeth, N. et al., “Hyperuricaemia and gout: state of the art and future perspectives,”  Annals of Rheumatic Diseases,  69, pp: 1738-1743 (2010); Martinon, F. et al., “Gout-associated uric acid crystals activate the NALP3 inflammasome,”  Nature , vol. 440, pp: 237-241 (2006); So, A. et al., “A pilot study of IL-1 inhibition by anakinra in acute gout,”  Arthritis Research  &amp;  Therapy , vol. 9, no. 2, pp: 1-6 (2007); Terkeltaub, R. et al., “The interleukin 1 inhibitor rilonacept in treatment of chronic gouty arthritis: results of a placebo-controlled, monosequence crossover, non-randomised, single-blind pilot study,”  Annals of Rheumatic Diseases,  68, pp: 1613-1617 (2009); Tones, R. et al., “Hyperalgesia, synovitis and multiple biomarkers of inflammation are suppressed by interleukin 1 inhibition in a novel animal model of gouty arthritis,”  Annals of Rheumatic Diseases,  68, pp: 1602-1608 (2009)), neurological disorders, metabolic syndrome (see, e.g., Troseid, M. “The role of interleukin-18 in the metabolic syndrome,”  Cardiovascular Diabetology,  9:11, pp: 1-8 (2010)), immunodeficiency disorders such as AIDS and HIV (see, e.g., Iannello, A. et al., “Role of Interleukin-18 in the Development and Pathogenesis of AIDS,”  AIDS Reviews,  11, pp: 115-125 (2009)), destructive bone disorders (see, e.g., Hennessy, E., et al., “Targeting Toll-like receptors: emerging therapeutics?”  Nature Reviews , vol. 9, pp: 293-307 (2010)), osteoarthritis, proliferative disorders, Waldenström&#39;s Macroglobulinemia (see, e.g., Treon, et al., “Whole genome sequencing reveals a widely expressed mutation (MYD88 L265P) with oncogenic activity in Waldenström&#39;s Macroglobulinemia” 53 rd  ASH Annual Meeting; Xu, et al., “A somatic variant in MYD88 (L256P) revealed by whole genome sequencing differentiates lymphoplasmacytic lymphoma from marginal zone lymphomas” 53 rd  ASH Annual Meeting; Yang et al., “Disruption of MYD88 pathway signaling leads to loss of constitutive IRAK1, NK-kB and JAK/STAT signaling and induces apoptosis of cells expressing the MYD88 L265P mutation in Waldenström&#39;s Macroglobulinemia” 53 rd  ASH Annual Meeting; Iriyama et al., “Clinical significance of genetic mutations of CD79B, CARD11, MYD88, and EZH2 genes in diffuse large B-cell lymphoma patients” 53 rd  ASH Annual Meeting; infectious diseases, conditions associated with cell death, pathologic immune conditions involving T cell activation, and CNS disorders in a patient. In one embodiment, a human patient is treated with a compound of the current invention and a pharmaceutically acceptable carrier, adjuvant, or vehicle, wherein said compound is present in an amount to measurably degrade and/or inhibit IRAK-1 only, IRAK-2-only, IRAK-4-only and/or IRAK1 and IRAK4 kinase activity. 
     Compounds of the current invention are useful in the treatment of a proliferative disease selected from a benign or malignant tumor, solid tumor, carcinoma of the brain, kidney, liver, adrenal gland, bladder, breast, stomach, gastric tumors, ovaries, colon, rectum, prostate, pancreas, lung, vagina, cervix, testis, genitourinary tract, esophagus, larynx, skin, bone or thyroid, sarcoma, glioblastomas, neuroblastomas, multiple myeloma, gastrointestinal cancer, especially colon carcinoma or colorectal adenoma, a tumor of the neck and head, an epidermal hyperproliferation, psoriasis, prostate hyperplasia, a neoplasia, a neoplasia of epithelial character, adenoma, adenocarcinoma, keratoacanthoma, epidermoid carcinoma, large cell carcinoma, non-small-cell lung carcinoma, lymphomas, Hodgkins and Non-Hodgkins, a mammary carcinoma, follicular carcinoma, undifferentiated carcinoma, papillary carcinoma, seminoma, melanoma, an IL-1 driven disorder, an MyD88 driven disorder, Smoldering of indolent multiple myeloma, or hematological malignancies (including leukemia, diffuse large B-cell lymphoma (DLBCL), ABC DLBCL, chronic lymphocytic leukemia (CLL), chronic lymphocytic lymphoma, primary effusion lymphoma, Burkitt lymphoma/leukemia, acute lymphocytic leukemia, B-cell prolymphocytic leukemia, lymphoplasmacytic lymphoma, Waldenström&#39;s macroglobulinemia (WM), splenic marginal zone lymphoma, multiple myeloma, plasmacytoma, intravascular large B-cell lymphoma). 
     In some embodiments the proliferative disease which can be treated according to the methods of this invention is an MyD88 driven disorder. In some embodiments, the MyD88 driven disorder which can be treated according to the methods of this invention is selected from ABC DLBCL, Waldenström&#39;s macroglobulinemia, Hodgkin&#39;s lymphoma, primary cutaneous T-cell lymphoma and chronic lymphocytic leukemia. 
     In some embodiments the proliferative disease which can be treated according to the methods of this invention is an IL-1 driven disorder. In some embodiments the IL-1 driven disorder is Smoldering of indolent multiple myeloma. 
     Compounds according to the invention are useful in the treatment of inflammatory or obstructive airways diseases, resulting, for example, in reduction of tissue damage, airways inflammation, bronchial hyperreactivity, remodeling or disease progression. Inflammatory or obstructive airways diseases to which the present invention is applicable include asthma of whatever type or genesis including both intrinsic (non-allergic) asthma and extrinsic (allergic) asthma, mild asthma, moderate asthma, severe asthma, bronchitic asthma, exercise-induced asthma, occupational asthma and asthma induced following bacterial infection. Treatment of asthma is also to be understood as embracing treatment of subjects, e.g. of less than 4 or 5 years of age, exhibiting wheezing symptoms and diagnosed or diagnosable as “wheezy infants”, an established patient category of major medical concern and now often identified as incipient or early-phase asthmatics. 
     Compounds according to the invention are useful in the treatment of heteroimmune diseases. Examples of such heteroimmune diseases include, but are not limited to, graft versus host disease, transplantation, transfusion, anaphylaxis, allergies (e.g., allergies to plant pollens, latex, drugs, foods, insect poisons, animal hair, animal dander, dust mites, or cockroach calyx), type I hypersensitivity, allergic conjunctivitis, allergic rhinitis, and atopic dermatitis. 
     Prophylactic efficacy in the treatment of asthma will be evidenced by reduced frequency or severity of symptomatic attack, e.g. of acute asthmatic or bronchoconstrictor attack, improvement in lung function or improved airways hyperreactivity. It may further be evidenced by reduced requirement for other, symptomatic therapy, such as therapy for or intended to restrict or abort symptomatic attack when it occurs, for example antiinflammatory or bronchodilatory. Prophylactic benefit in asthma may in particular be apparent in subjects prone to “morning dipping”. “Morning dipping” is a recognized asthmatic syndrome, common to a substantial percentage of asthmatics and characterized by asthma attack, e.g. between the hours of about 4 to 6 am, i.e. at a time normally substantially distant form any previously administered symptomatic asthma therapy. 
     Compounds of the current invention can be used for other inflammatory or obstructive airways diseases and conditions to which the present invention is applicable and include acute lung injury (ALI), adult/acute respiratory distress syndrome (ARDS), chronic obstructive pulmonary, airways or lung disease (COPD, COAD or COLD), including chronic bronchitis or dyspnea associated therewith, emphysema, as well as exacerbation of airways hyperreactivity consequent to other drug therapy, in particular other inhaled drug therapy. The invention is also applicable to the treatment of bronchitis of whatever type or genesis including, but not limited to, acute, arachidic, catarrhal, croupus, chronic or phthinoid bronchitis. Further inflammatory or obstructive airways diseases to which the present invention is applicable include pneumoconiosis (an inflammatory, commonly occupational, disease of the lungs, frequently accompanied by airways obstruction, whether chronic or acute, and occasioned by repeated inhalation of dusts) of whatever type or genesis, including, for example, aluminosis, anthracosis, asbestosis, chalicosis, ptilosis, siderosis, silicosis, tabacosis and byssinosis. 
     With regard to their anti-inflammatory activity, in particular in relation to inhibition of eosinophil activation, compounds of the invention are also useful in the treatment of eosinophil related disorders, e.g. eosinophilia, in particular eosinophil related disorders of the airways (e.g. involving morbid eosinophilic infiltration of pulmonary tissues) including hypereosinophilia as it effects the airways and/or lungs as well as, for example, eosinophil-related disorders of the airways consequential or concomitant to Loffler&#39;s syndrome, eosinophilic pneumonia, parasitic (in particular metazoan) infestation (including tropical eosinophilia), bronchopulmonary aspergillosis, polyarteritis nodosa (including Churg-Strauss syndrome), eosinophilic granuloma and eosinophil-related disorders affecting the airways occasioned by drug-reaction. 
     Compounds of the invention are also useful in the treatment of inflammatory or allergic conditions of the skin, for example psoriasis, contact dermatitis, atopic dermatitis, alopecia areata, erythema multiforma, dermatitis herpetiformis, scleroderma, vitiligo, hypersensitivity angiitis, urticaria, bullous pemphigoid, lupus erythematosus, systemic lupus erythematosus, pemphigus vulgaris, pemphigus foliaceus, paraneoplastic pemphigus, epidermolysis bullosa acquisita, acne vulgaris, and other inflammatory or allergic conditions of the skin. 
     Compounds of the invention may also be used for the treatment of other diseases or conditions, such as diseases or conditions having an inflammatory component, for example, treatment of diseases and conditions of the eye such as ocular allergy, conjunctivitis, keratoconjunctivitis sicca, and vernal conjunctivitis, diseases affecting the nose including allergic rhinitis, and inflammatory disease in which autoimmune reactions are implicated or having an autoimmune component or etiology, including autoimmune hematological disorders (e.g. hemolytic anemia, aplastic anemia, pure red cell anemia and idiopathic thrombocytopenia), systemic lupus erythematosus, rheumatoid arthritis, polychondritis, scleroderma, Wegener granulamatosis, dermatomyositis, chronic active hepatitis, myasthenia gravis, Steven-Johnson syndrome, idiopathic sprue, autoimmune inflammatory bowel disease (e.g. ulcerative colitis and Crohn&#39;s disease), irritable bowel syndrome, celiac disease, periodontitis, hyaline membrane disease, kidney disease, glomerular disease, alcoholic liver disease, multiple sclerosis, endocrine opthalmopathy, Grave&#39;s disease, sarcoidosis, alveolitis, chronic hypersensitivity pneumonitis, multiple sclerosis, primary biliary cirrhosis, uveitis (anterior and posterior), Sjogren&#39;s syndrome, keratoconjunctivitis sicca and vernal keratoconjunctivitis, interstitial lung fibrosis, psoriatic arthritis, systemic juvenile idiopathic arthritis, cryopyrin-associated periodic syndrome, nephritis, vasculitis, diverticulitis, interstitial cystitis, glomerulonephritis (with and without nephrotic syndrome, e.g. including idiopathic nephrotic syndrome or minal change nephropathy), chronic granulomatous disease, endometriosis, leptospiriosis renal disease, glaucoma, retinal disease, ageing, headache, pain, complex regional pain syndrome, cardiac hypertrophy, musclewasting, catabolic disorders, obesity, fetal growth retardation, hyperchlolesterolemia, heart disease, chronic heart failure, mesothelioma, anhidrotic ecodermal dysplasia, Behcet&#39;s disease, incontinentia pigmenti, Paget&#39;s disease, pancreatitis, hereditary periodic fever syndrome, asthma (allergic and non-allergic, mild, moderate, severe, bronchitic, and exercise-induced), acute lung injury, acute respiratory distress syndrome, eosinophilia, hypersensitivities, anaphylaxis, nasal sinusitis, ocular allergy, silica induced diseases, COPD (reduction of damage, airways inflammation, bronchial hyperreactivity, remodeling or disease progression), pulmonary disease, cystic fibrosis, acid-induced lung injury, pulmonary hypertension, polyneuropathy, cataracts, muscle inflammation in conjunction with systemic sclerosis, inclusion body myositis, myasthenia gravis, thyroiditis, Addison&#39;s disease, lichen planus, Type 1 diabetes, or Type 2 diabetes, appendicitis, atopic dermatitis, asthma, allergy, blepharitis, bronchiolitis, bronchitis, bursitis, cervicitis, cholangitis, cholecystitis, chronic graft rejection, colitis, conjunctivitis, Crohn&#39;s disease, cystitis, dacryoadenitis, dermatitis, dermatomyositis, encephalitis, endocarditis, endometritis, enteritis, enterocolitis, epicondylitis, epididymitis, fasciitis, fibrositis, gastritis, gastroenteritis, Henoch-Schonlein purpura, hepatitis, hidradenitis suppurativa, immunoglobulin A nephropathy, interstitial lung disease, laryngitis, mastitis, meningitis, myelitis myocarditis, myositis, nephritis, oophoritis, orchitis, osteitis, otitis, pancreatitis, parotitis, pericarditis, peritonitis, pharyngitis, pleuritis, phlebitis, pneumonitis, pneumonia, polymyositis, proctitis, prostatitis, pyelonephritis, rhinitis, salpingitis, sinusitis, stomatitis, synovitis, tendonitis, tonsillitis, ulcerative colitis, uveitis, vaginitis, vasculitis, or vulvitis. 
     In some embodiments the inflammatory disease which can be treated according to the methods of this invention is an disease of the skin. In some embodiments, the inflammatory disease of the skin is selected from contact dermatitits, atompic dermatitis, alopecia areata, erythema multiforma, dermatitis herpetiformis, scleroderma, vitiligo, hypersensitivity angiitis, urticaria, bullous pemphigoid, pemphigus vulgaris, pemphigus foliaceus, paraneoplastic pemphigus, epidermolysis bullosa acquisita, and other inflammatory or allergic conditions of the skin. 
     In some embodiments the inflammatory disease which can be treated according to the methods of this invention is selected from acute and chronic gout, chronic gouty arthritis, psoriasis, psoriatic arthritis, rheumatoid arthritis, Juvenile rheumatoid arthritis, Systemic jubenile idiopathic arthritis (SJIA), Cryopyrin Associated Periodic Syndrome (CAPS), and osteoarthritis. 
     In some embodiments the inflammatory disease which can be treated according to the methods of this invention is a TH17 mediated disease. In some embodiments the TH17 mediated disease is selected from Systemic lupus erythematosus, Multiple sclerosis, and inflammatory bowel disease (including Crohn&#39;s disease or ulcerative colitis). 
     In some embodiments the inflammatory disease which can be treated according to the methods of this invention is selected from Sjogren&#39;s syndrome, allergic disorders, osteoarthritis, conditions of the eye such as ocular allergy, conjunctivitis, keratoconjunctivitis sicca and vernal conjunctivitis, and diseases affecting the nose such as allergic rhinitis. 
     Cardiovascular diseases which can be treated according to the methods of this invention include, but are not limited to, restenosis, cardiomegaly, atherosclerosis, myocardial infarction, ischemic stroke, congestive heart failure, angina pectoris, reocclusion after angioplasty, restenosis after angioplasty, reocclusion after aortocoronary bypass, restenosis after aortocoronary bypass, stroke, transitory ischemia, a peripheral arterial occlusive disorder, pulmonary embolism, and deep venous thrombosis. 
     In some embodiments, the neurodegenerative disease which can be treated according to the methods of this invention include, but are not limited to, Alzheimer&#39;s disease, Parkinson&#39;s disease, amyotrophic lateral sclerosis, Huntington&#39;s disease, cerebral ischemia, and neurodegenerative disease caused by traumatic injury, glutamate neurotoxicity, hypoxia, epilepsy, treatment of diabetes, metabolic syndrome, obesity, organ transplantation and graft versus host disease. 
     The loss of IRAK4 function results in decreased Aβ levels in an in vivo murine model of Alzheimer&#39;s disease and was associated with diminished microgliosis and astrogliosis in aged mice. Analysis of microglia isolated from the adult mouse brain revealed an altered pattern of gene expression associated with changes in microglial phenotype that were associated with expression of IRF transcription factors that govern microglial phenotype. Further, loss of IRAK4 function also promoted amyloid clearance mechanisms, including elevated expression of insulin-degrading enzyme. Finally, blocking IRAK function restored olfactory behavior (Cameron et al. “Loss of Interleukin Receptor-Associated Kinase 4 Signaling Suppresses Amyloid Pathology and Alters Microglial Phenotype in a Mouse Model of Alzheimer&#39;s Disease” Journal of Neuroscience (2012) 32(43), 15112-15123. 
     In some embodiments the invention provides a method of treating, preventing or lessening the severity of Alzheimer&#39;s disease comprising administering to a patient in need thereof a provided compound or a pharmaceutically acceptable salt or composition thereof. 
     In some embodiments the invention provides a method of treating a disease or condition commonly occurring in connection with transplantation. In some embodiments, the disease or condition commonly occurring in connection with transplantation is selected from organ transplantation, organ transplant rejection, and graft versus host disease. 
     In some embodiments the invention provides a method of treating a metabolic disease. In some embodiments the metabolic disease is selected from Type 1 diabetes, Type 2 diabetes, metabolic syndrome, and obesity. 
     In some embodiments the invention provides a method of treating a viral disease. In some embodiments, the viral infection is HIV infection. 
     Furthermore, the invention provides the use of a compound according to the definitions herein, or a pharmaceutically acceptable salt, or a hydrate or solvate thereof for the preparation of a medicament for the treatment of a proliferative disease, an inflammatory disease, an obstructive respiratory disease, a cardiovascular disease, a metabolic disease, a neurological disease, a neurodegenerative disease, a viral disease, or a disorder commonly occurring in connection with transplantation. 
     Combination Therapies 
     Depending upon the particular condition, or disease, to be treated, additional therapeutic agents, which are normally administered to treat that condition, may be administered in combination with compounds and compositions of this invention. As used herein, additional therapeutic agents that are normally administered to treat a particular disease, or condition, are known as “appropriate for the disease, or condition, being treated.” 
     In certain embodiments, a provided combination, or composition thereof, is administered in combination with another therapeutic agent. 
     In some embodiments, the present invention provides a method of treating a disclosed disease or condition comprising administering to a patient in need thereof an effective amount of a compound disclosed herein or a pharmaceutically acceptable salt thereof and co-administering simultaneously or sequentially an effective amount of one or more additional therapeutic agents, such as those described herein. In some embodiments, the method includes co-administering one additional therapeutic agent. In some embodiments, the method includes co-administering two additional therapeutic agents. In some embodiments, the combination of the disclosed compound and the additional therapeutic agent or agents acts synergistically. 
     Examples of agents the combinations of this invention may also be combined with include, without limitation: treatments for Alzheimer&#39;s Disease such as Aricept® and Excelon®; treatments for HIV such as ritonavir; treatments for Parkinson&#39;s Disease such as L-DOPA/carbidopa, entacapone, ropinrole, pramipexole, bromocriptine, pergolide, trihexephendyl, and amantadine; agents for treating Multiple Sclerosis (MS) such as beta interferon (e.g., Avonex® and Rebif®), Copaxone®, and mitoxantrone; treatments for asthma such as albuterol and Singulair®; agents for treating schizophrenia such as zyprexa, risperdal, seroquel, and haloperidol; anti-inflammatory agents such as corticosteroids, TNF blockers, IL-1 RA, azathioprine, cyclophosphamide, and sulfasalazine; immunomodulatory and immunosuppressive agents such as cyclosporin, tacrolimus, rapamycin, mycophenolate mofetil, interferons, corticosteroids, cyclophophamide, azathioprine, and sulfasalazine; neurotrophic factors such as acetylcholinesterase inhibitors, MAO inhibitors, interferons, anti-convulsants, ion channel blockers, riluzole, and anti-Parkinsonian agents; agents for treating cardiovascular disease such as beta-blockers, ACE inhibitors, diuretics, nitrates, calcium channel blockers, and statins; agents for treating liver disease such as corticosteroids, cholestyramine, interferons, and anti-viral agents; agents for treating blood disorders such as corticosteroids, anti-leukemic agents, and growth factors; agents that prolong or improve pharmacokinetics such as cytochrome P450 inhibitors (i.e., inhibitors of metabolic breakdown) and CYP3A4 inhibitors (e.g., ketokenozole and ritonavir), and agents for treating immunodeficiency disorders such as gamma globulin. 
     In certain embodiments, combination therapies of the present invention, or a pharmaceutically acceptable composition thereof, are administered in combination with a monoclonal antibody or an siRNA therapeutic. 
     Those additional agents may be administered separately from a provided combination therapy, as part of a multiple dosage regimen. Alternatively, those agents may be part of a single dosage form, mixed together with a compound of this invention in a single composition. If administered as part of a multiple dosage regime, the two active agents may be submitted simultaneously, sequentially or within a period of time from one another normally within five hours from one another. 
     As used herein, the term “combination,” “combined,” and related terms refers to the simultaneous or sequential administration of therapeutic agents in accordance with this invention. For example, a combination of the present invention may be administered with another therapeutic agent simultaneously or sequentially in separate unit dosage forms or together in a single unit dosage form. 
     The amount of additional therapeutic agent present in the compositions of this invention will be no more than the amount that would normally be administered in a composition comprising that therapeutic agent as the only active agent. Preferably the amount of additional therapeutic agent in the presently disclosed compositions will range from about 50% to 100% of the amount normally present in a composition comprising that agent as the only therapeutically active agent. 
     One or more other therapeutic agent may be administered separately from a compound or composition of the invention, as part of a multiple dosage regimen. Alternatively, one or more other therapeutic agents agents may be part of a single dosage form, mixed together with a compound of this invention in a single composition. If administered as a multiple dosage regime, one or more other therapeutic agent and a compound or composition of the invention may be administered simultaneously, sequentially or within a period of time from one another, for example within 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 18, 20, 21, 22, 23, or 24 hours from one another. In some embodiments, one or more other therapeutic agent and a compound or composition of the invention are administered as a multiple dosage regimen within greater than 24 hours apart. 
     In one embodiment, the present invention provides a composition comprising a provided compound and one or more additional therapeutic agents. The therapeutic agent may be administered together with a provided compound, or may be administered prior to or following administration of a provided compound. Suitable therapeutic agents are described in further detail below. In certain embodiments, a provided compound may be administered up to 5 minutes, 10 minutes, 15 minutes, 30 minutes, 1 hour, 2 hours, 3 hours, 4 hours, 5, hours, 6 hours, 7 hours, 8 hours, 9 hours, 10 hours, 11 hours, 12 hours, 13 hours, 14 hours, 15 hours, 16 hours, 17 hours, or 18 hours before the therapeutic agent. In other embodiments, a provided compound may be administered up to 5 minutes, 10 minutes, 15 minutes, 30 minutes, 1 hour, 2 hours, 3 hours, 4 hours, 5, hours, 6 hours, 7 hours, 8 hours, 9 hours, 10 hours, 11 hours, 12 hours, 13 hours, 14 hours, 15 hours, 16 hours, 17 hours, or 18 hours following the therapeutic agent. 
     In another embodiment, the present invention provides a method of treating an inflammatory disease, disorder or condition by administering to a patient in need thereof a provided compound and one or more additional therapeutic agents. Such additional therapeutic agents may be small molecules or recombinant biologic agents and include, for example, acetaminophen, non-steroidal anti-inflammatory drugs (NSAIDS) such as aspirin, ibuprofen, naproxen, etodolac (Lodine®) and celecoxib, colchicine (Colcrys®), corticosteroids such as prednisone, prednisolone, methylprednisolone, hydrocortisone, and the like, probenecid, allopurinol, febuxostat (Uloric®), sulfasalazine (Azulfidine®), antimalarials such as hydroxychloroquine (Plaquenil®) and chloroquine (Aralen®), methotrexate (Rheumatrex®), gold salts such as gold thioglucose (Solganal®), gold thiomalate (Myochrysine®) and auranofin (Ridaura®), D-penicillamine (Depen® or Cuprimine®), azathioprine (Imuran®), cyclophosphamide (Cytoxan®), chlorambucil (Leukeran®), cyclosporine (Sandimmune®), leflunomide (Arava®) and “anti-TNF” agents such as etanercept (Enbrel®), infliximab (Remicade®), golimumab (Simponi®), certolizumab pegol (Cimzia®) and adalimumab (Humira®), “anti-IL-1” agents such as anakinra (Kineret®) and rilonacept (Arcalyst®), canakinumab (Ilaris®), anti-Jak inhibitors such as tofacitinib, antibodies such as rituximab (Rituxan®), “anti-T-cell” agents such as abatacept (Orencia®), “anti-IL-6” agents such as tocilizumab (Actemra®), diclofenac, cortisone, hyaluronic acid (Synvisc® or Hyalgan®), monoclonal antibodies such as tanezumab, anticoagulants such as heparin (Calcinparine® or Liquaemin®) and warfarin (Coumadin®), antidiarrheals such as diphenoxylate (Lomotil®) and loperamide (Imodium®), bile acid binding agents such as cholestyramine, alosetron (Lotronex®), lubiprostone (Amitiza®), laxatives such as Milk of Magnesia, polyethylene glycol (MiraLax®), Dulcolax®, Correctol® and Senokot®, anticholinergics or antispasmodics such as dicyclomine (Bentyl®), Singulair®, beta-2 agonists such as albuterol (Ventolin® HFA, Proventil® HFA), levalbuterol (Xopenex®), metaproterenol (Alupent®), pirbuterol acetate (Maxair®), terbutaline sulfate (Brethaire®), salmeterol xinafoate (Serevent®) and formoterol (Foradil®), anticholinergic agents such as ipratropium bromide (Atrovent®) and tiotropium (Spiriva®), inhaled corticosteroids such as beclomethasone dipropionate (Beclovent®, Qvar®, and Vanceril®), triamcinolone acetonide (Azmacort®), mometasone (Asthmanex®), budesonide (Pulmocort®), and flunisolide (Aerobid®), Afviar®, Symbicort®, Dulera®, cromolyn sodium (Intal®), methylxanthines such as theophylline (Theo-Dur®, Theolair®, Slo-bid®, Uniphyl®, Theo-24®) and aminophylline, IgE antibodies such as omalizumab (Xolair®), nucleoside reverse transcriptase inhibitors such as zidovudine (Retrovir®), abacavir (Ziagen®), abacavir/lamivudine (Epzicom®), abacavir/lamivudine/zidovudine (Trizivir®), didanosine (Videx®), emtricitabine (Emtriva®), lamivudine (Epivir®), lamivudine/zidovudine (Combivir®), stavudine (Zerit®), and zalcitabine (Hivid®), non-nucleoside reverse transcriptase inhibitors such as delavirdine (Rescriptor®), efavirenz (Sustiva®), nevairapine (Viramune®) and etravirine (Intelence®), nucleotide reverse transcriptase inhibitors such as tenofovir (Viread®), protease inhibitors such as amprenavir (Agenerase®), atazanavir (Reyataz®), darunavir (Prezista®), fosamprenavir (Lexiva®), indinavir (Crixivan®), lopinavir and ritonavir (Kaletra®), nelfinavir (Viracept®), ritonavir (Norvir®), saquinavir (Fortovase® or Invirase®), and tipranavir (Aptivus®), entry inhibitors such as enfuvirtide (Fuzeon®) and maraviroc (Selzentry®), integrase inhibitors such as raltegravir (Isentress®), doxorubicin (Hydrodaunorubicin®), vincristine (Oncovin®), bortezomib (Velcade®), and dexamethasone (Decadron®) in combination with lenalidomide (Revlimid g), or any combination(s) thereof. 
     In another embodiment, the present invention provides a method of treating gout comprising administering to a patient in need thereof a provided compound and one or more additional therapeutic agents selected from non-steroidal anti-inflammatory drugs (NSAIDS) such as aspirin, ibuprofen, naproxen, etodolac (Lodine®) and celecoxib, colchicine (Colcrys®), corticosteroids such as prednisone, prednisolone, methylprednisolone, hydrocortisone, and the like, probenecid, allopurinol and febuxostat (Uloric®). 
     In another embodiment, the present invention provides a method of treating rheumatoid arthritis comprising administering to a patient in need thereof a provided compound and one or more additional therapeutic agents selected from non-steroidal anti-inflammatory drugs (NSAIDS) such as aspirin, ibuprofen, naproxen, etodolac (Lodine®) and celecoxib, corticosteroids such as prednisone, prednisolone, methylprednisolone, hydrocortisone, and the like, sulfasalazine (Azulfidine®), antimalarials such as hydroxychloroquine (Plaquenil®) and chloroquine (Aralen®), methotrexate (Rheumatrex®), gold salts such as gold thioglucose (Solganal®), gold thiomalate (Myochrysine®) and auranofin (Ridaura®), D-penicillamine (Depen® or Cuprimine®), azathioprine (Imuran®), cyclophosphamide (Cytoxan®), chlorambucil (Leukeran®), cyclosporine (Sandimmune®), leflunomide (Arava®) and “anti-TNF” agents such as etanercept (Enbrel®), infliximab (Remicade®), golimumab (Simponi®), certolizumab pegol (Cimzia®) and adalimumab (Humira®), “anti-IL-1” agents such as anakinra (Kineret®) and rilonacept (Arcalyst®), antibodies such as rituximab (Rituxan®), “anti-T-cell” agents such as abatacept (Orencia®) and “anti-IL-6” agents such as tocilizumab (Actemra®). 
     In some embodiments, the present invention provides a method of treating osteoarthritis comprising administering to a patient in need thereof a provided compound and one or more additional therapeutic agents selected from acetaminophen, non-steroidal anti-inflammatory drugs (NSAIDS) such as aspirin, ibuprofen, naproxen, etodolac (Lodine®) and celecoxib, diclofenac, cortisone, hyaluronic acid (Synvisc® or Hyalgan®) and monoclonal antibodies such as tanezumab. 
     In some embodiments, the present invention provides a method of treating lupus comprising administering to a patient in need thereof a provided compound and one or more additional therapeutic agents selected from acetaminophen, non-steroidal anti-inflammatory drugs (NSAIDS) such as aspirin, ibuprofen, naproxen, etodolac (Lodine®) and celecoxib, corticosteroids such as prednisone, prednisolone, methylprednisolone, hydrocortisone, and the like, antimalarials such as hydroxychloroquine (Plaquenil®) and chloroquine (Aralen®), cyclophosphamide (Cytoxan®), methotrexate (Rheumatrex®), azathioprine (Imuran®) and anticoagulants such as heparin (Calcinparine® or Liquaemin®) and warfarin (Coumadin®). 
     In some embodiments, the present invention provides a method of treating inflammatory bowel disease comprising administering to a patient in need thereof a provided compound and one or more additional therapeutic agents selected from mesalamine (Asacol®) sulfasalazine (Azulfidine®), antidiarrheals such as diphenoxylate (Lomotil®) and loperamide (Imodium®), bile acid binding agents such as cholestyramine, alosetron (Lotronex®), lubiprostone (Amitiza®), laxatives such as Milk of Magnesia, polyethylene glycol (MiraLax®), Dulcolax®, Correctol® and Senokot® and anticholinergics or antispasmodics such as dicyclomine (Bentyl®), anti-TNF therapies, steroids, and antibiotics such as Flagyl or ciprofloxacin. 
     In some embodiments, the present invention provides a method of treating asthma comprising administering to a patient in need thereof a provided compound and one or more additional therapeutic agents selected from Singulair®, beta-2 agonists such as albuterol (Ventolin® HFA, Proventil® HFA), levalbuterol (Xopenex®), metaproterenol (Alupent®), pirbuterol acetate (Maxair®), terbutaline sulfate (Brethaire®), salmeterol xinafoate (Serevent®) and formoterol (Foradil®), anticholinergic agents such as ipratropium bromide (Atrovent®) and tiotropium (Spiriva®), inhaled corticosteroids such as prednisone, prednisolone, beclomethasone dipropionate (Beclovent®, Qvar®, and Vanceril®), triamcinolone acetonide (Azmacort®), mometasone (Asthmanex®), budesonide (Pulmocort®), flunisolide (Aerobid®), Afviar®, Symbicort®, and Dulera®, cromolyn sodium (Intal®), methylxanthines such as theophylline (Theo-Dur®, Theolair®, Slo-bid®, Uniphyl®, Theo-24®) and aminophylline, and IgE antibodies such as omalizumab (Xolair®). 
     In some embodiments, the present invention provides a method of treating COPD comprising administering to a patient in need thereof a provided compound and one or more additional therapeutic agents selected from beta-2 agonists such as albuterol (Ventolin® HFA, Proventil® HFA), levalbuterol (Xopenex®), metaproterenol (Alupent®), pirbuterol acetate (Maxair®), terbutaline sulfate (Brethaire®), salmeterol xinafoate (Serevent®) and formoterol (Foradil®), anticholinergic agents such as ipratropium bromide (Atrovent®) and tiotropium (Spiriva®), methylxanthines such as theophylline (Theo-Dur®, Theolair®, Slo-bid®, Uniphyl®, Theo-24®) and aminophylline, inhaled corticosteroids such as prednisone, prednisolone, beclomethasone dipropionate (Beclovent®, Qvar®, and Vanceril®), triamcinolone acetonide (Azmacort®), mometasone (Asthmanex®), budesonide (Pulmocort®), flunisolide (Aerobid®), Afviar®, Symbicort®, and Dulera®, 
     In some embodiments, the present invention provides a method of treating HIV comprising administering to a patient in need thereof a provided compound and one or more additional therapeutic agents selected from nucleoside reverse transcriptase inhibitors such as zidovudine (Retrovir®), abacavir (Ziagen®), ab acavir/lamivudine (Epzicom®), abacavir/lamivudine/zidovudine (Trizivir®), didanosine (Videx®), emtricitabine (Emtriva®), lamivudine (Epivir®), lamivudine/zidovudine (Combivir®), stavudine (Zerit®), and zalcitabine (Hivid®), non-nucleoside reverse transcriptase inhibitors such as delavirdine (Rescriptor®), efavirenz (Sustiva®), nevairapine (Viramune®) and etravirine (Intelence®), nucleotide reverse transcriptase inhibitors such as tenofovir (Viread®), protease inhibitors such as amprenavir (Agenerase®), atazanavir (Reyataz®), darunavir (Prezista®), fosamprenavir (Lexiva®), indinavir (Crixivan®), lopinavir and ritonavir (Kaletra®), nelfinavir (Viracept®), ritonavir (Norvir®), saquinavir (Fortovase® or Invirase®), and tipranavir (Aptivus®), entry inhibitors such as enfuvirtide (Fuzeon®) and maraviroc (Selzentry®), integrase inhibitors such as raltegravir (Isentress®), and combinations thereof. 
     In another embodiment, the present invention provides a method of treating a hematological malignancy comprising administering to a patient in need thereof a provided compound and one or more additional therapeutic agents selected from rituximab (Rituxan®), cyclophosphamide (Cytoxan®), doxorubicin (Hydrodaunorubicin®), vincristine (Oncovin®), prednisone, a hedgehog signaling inhibitor, a BTK inhibitor, a JAK/pan-JAK inhibitor, a TYK2 inhibitor, a PI3K inhibitor, a SYK inhibitor, and combinations thereof. 
     In another embodiment, the present invention provides a method of treating a solid tumor comprising administering to a patient in need thereof a provided compound and one or more additional therapeutic agents selected from rituximab (Rituxan®), cyclophosphamide (Cytoxan®), doxorubicin (Hydrodaunorubicin®), vincristine (Oncovin®), prednisone, a hedgehog signaling inhibitor, a BTK inhibitor, a JAK/pan-JAK inhibitor, a TYK2 inhibitor, a PI3K inhibitor, a SYK inhibitor, and combinations thereof. 
     In another embodiment, the present invention provides a method of treating a hematological malignancy comprising administering to a patient in need thereof a provided compound and a Hedgehog (Hh) signaling pathway inhibitor. In some embodiments, the hematological malignancy is DLBCL (Ramirez et al “Defining causative factors contributing in the activation of hedgehog signaling in diffuse large B-cell lymphoma” Leuk. Res. (2012), published online July 17, and incorporated herein by reference in its entirety). 
     In another embodiment, the present invention provides a method of treating diffuse large B-cell lymphoma (DLBCL) comprising administering to a patient in need thereof a provided compound and one or more additional therapeutic agents selected from rituximab (Rituxan®), cyclophosphami de (Cytoxan®), doxorubicin (Hydrodaunorubicin®), vincristine (Oncovin®), prednisone, a hedgehog signaling inhibitor, and combinations thereof. 
     In another embodiment, the present invention provides a method of treating multiple myeloma comprising administering to a patient in need thereof a provided compound and one or more additional therapeutic agents selected from bortezomib (Velcade®), and dexamethasone (Decadron®), a hedgehog signaling inhibitor, a BTK inhibitor, a JAK/pan-JAK inhibitor, a TYK2 inhibitor, a PI3K inhibitor, a SYK inhibitor in combination with lenalidomide (Revlimid®). 
     In another embodiment, the present invention provides a method of treating Waldenström&#39;s macroglobulinemia comprising administering to a patient in need thereof a provided compound and one or more additional therapeutic agents selected from chlorambucil (Leukeran®), cyclophosphamide (Cytoxan®, Neosar®), fludarabine (Fludara®), cladribine (Leustatin®), rituximab (Rituxan®), a hedgehog signaling inhibitor, a BTK inhibitor, a JAK/pan-JAK inhibitor, a TYK2 inhibitor, a PI3K inhibitor, and a SYK inhibitor. 
     In some embodiments, one or more other therapeutic agent is an antagonist of the hedgehog pathway. Approved hedgehog pathway inhibitors which may be used in the present invention include sonidegib (Odomzo®, Sun Pharmaceuticals); and vismodegib (Erivedge®, Genentech), both for treatment of basal cell carcinoma. 
     In some embodiments, one or more other therapeutic agent is a Poly ADP ribose polymerase (PARP) inhibitor. In some embodiments, a PARP inhibitor is selected from olaparib (Lynparza®, AstraZeneca); rucaparib (Rubraca®, Clovis Oncology); niraparib (Zejula®, Tesaro); talazoparib (MDV3800/BMN 673/LT00673, Medivation/Pfizer/Biomarin); veliparib (ABT-888, AbbVie); and BGB-290 (BeiGene, Inc.). 
     In some embodiments, one or more other therapeutic agent is a histone deacetylase (HDAC) inhibitor. In some embodiments, an HDAC inhibitor is selected from vorinostat (Zolinza®, Merck); romidepsin (Istodax®, Celgene); panobinostat (Farydak®, Novartis); belinostat (Beleodaq®, Spectrum Pharmaceuticals); entinostat (SNDX-275, Syndax Pharmaceuticals) (NCT00866333); and chidamide (Epidaza®, HBI-8000, Chipscreen Biosciences, China). 
     In some embodiments, one or more other therapeutic agent is a CDK inhibitor, such as a CDK4/CDK6 inhibitor. In some embodiments, a CDK 4/6 inhibitor is selected from palbociclib (Ibrance®, Pfizer); ribociclib (Kisqali®, Novartis); abemaciclib (Ly2835219, Eli Lilly); and trilaciclib (G1T28, G1 Therapeutics). 
     In some embodiments, one or more other therapeutic agent is a folic acid inhibitor. Approved folic acid inhibitors useful in the present invention include pemetrexed (Alimta®, Eli Lilly). 
     In some embodiments, one or more other therapeutic agent is a CC chemokine receptor 4 (CCR4) inhibitor. CCR4 inhibitors being studied that may be useful in the present invention include mogamulizumab (Poteligeo®, Kyowa Hakko Kirin, Japan). 
     In some embodiments, one or more other therapeutic agent is an isocitrate dehydrogenase (IDH) inhibitor. IDH inhibitors being studied which may be used in the present invention include AG120 (Celgene; NCT02677922); AG221 (Celgene, NCT02677922; NCT02577406); BAY1436032 (Bayer, NCT02746081); IDH305 (Novartis, NCT02987010). 
     In some embodiments, one or more other therapeutic agent is an arginase inhibitor. Arginase inhibitors being studied which may be used in the present invention include AEB1102 (pegylated recombinant arginase, Aeglea Biotherapeutics), which is being studied in Phase 1 clinical trials for acute myeloid leukemia and myelodysplastic syndrome (NCT02732184) and solid tumors (NCT02561234); and CB-1158 (Calithera Biosciences). 
     In some embodiments, one or more other therapeutic agent is a glutaminase inhibitor. Glutaminase inhibitors being studied which may be used in the present invention include CB-839 (Calithera Biosciences). 
     In some embodiments, one or more other therapeutic agent is an antibody that binds to tumor antigens, that is, proteins expressed on the cell surface of tumor cells. Approved antibodies that bind to tumor antigens which may be used in the present invention include rituximab (Rituxan®, Genentech/BiogenIdec); ofatumumab (anti-CD20, Arzerra®, GlaxoSmithKline); obinutuzumab (anti-CD20, Gazyva®, Genentech), ibritumomab (anti-CD20 and Yttrium-90, Zevalin®, Spectrum Pharmaceuticals); daratumumab (anti-CD38, Darzalex®, Janssen Biotech), dinutuximab (anti-glycolipid GD2, Unituxin®, United Therapeutics); trastuzumab (anti-HER2, Herceptin®, Genentech); ado-trastuzumab emtansine (anti-HER2, fused to emtansine, Kadcyla®, Genentech); and pertuzumab (anti-HER2, Perjeta®, Genentech); and brentuximab vedotin (anti-CD30-drug conjugate, Adcetrisg, Seattle Genetics). 
     In some embodiments, one or more other therapeutic agent is a topoisomerase inhibitor. Approved topoisomerase inhibitors useful in the present invention include irinotecan (Onivyde®, Merrimack Pharmaceuticals); topotecan (Hycamtin®, GlaxoSmithKline). Topoisomerase inhibitors being studied which may be used in the present invention include pixantrone (Pixuvri®, CTI Biopharma). 
     In some embodiments, one or more other therapeutic agent is an inhibitor of anti-apoptotic proteins, such as BCL-2. Approved anti-apoptotics which may be used in the present invention include venetoclax (Venclexta®, AbbVie/Genentech); and blinatumomab (Blincyto®, Amgen). Other therapeutic agents targeting apoptotic proteins which have undergone clinical testing and may be used in the present invention include navitoclax (ABT-263, Abbott), a BCL-2 inhibitor (NCT02079740). 
     In some embodiments, one or more other therapeutic agent is an androgen receptor inhibitor. Approved androgen receptor inhibitors useful in the present invention include enzalutamide (Xtandi®, Astellas/Medivation); approved inhibitors of androgen synthesis include abiraterone (Zytiga®, Centocor/Ortho); approved antagonist of gonadotropin-releasing hormone (GnRH) receptor (degaralix, Firmagon®, Ferring Pharmaceuticals). 
     In some embodiments, one or more other therapeutic agent is a selective estrogen receptor modulator (SERM), which interferes with the synthesis or activity of estrogens. Approved SERMs useful in the present invention include raloxifene (Evista®, Eli Lilly). 
     In some embodiments, one or more other therapeutic agent is an inhibitor of bone resorption. An approved therapeutic which inhibits bone resorption is Denosumab (Xgeva®, Amgen), an antibody that binds to RANKL, prevents binding to its receptor RANK, found on the surface of osteoclasts, their precursors, and osteoclast-like giant cells, which mediates bone pathology in solid tumors with osseous metastases. Other approved therapeutics that inhibit bone resorption include bisphosphonates, such as zoledronic acid (Zometa®, Novartis). 
     In some embodiments, one or more other therapeutic agent is an inhibitor of interaction between the two primary p53 suppressor proteins, MDMX and MDM2. Inhibitors of p53 suppression proteins being studied which may be used in the present invention include ALRN-6924 (Aileron), a stapled peptide that equipotently binds to and disrupts the interaction of MDMX and MDM2 with p53. ALRN-6924 is currently being evaluated in clinical trials for the treatment of AML, advanced myelodysplastic syndrome (MDS) and peripheral T-cell lymphoma (PTCL) (NCT02909972; NCT02264613). 
     In some embodiments, one or more other therapeutic agent is an inhibitor of transforming growth factor-beta (TGF-beta or TGFβ). Inhibitors of TGF-beta proteins being studied which may be used in the present invention include NIS793 (Novartis), an anti-TGF-beta antibody being tested in the clinic for treatment of various cancers, including breast, lung, hepatocellular, colorectal, pancreatic, prostate and renal cancer (NCT 02947165). In some embodiments, the inhibitor of TGF-beta proteins is fresolimumab (GC1008; Sanofi-Genzyme), which is being studied for melanoma (NCT00923169); renal cell carcinoma (NCT00356460); and non-small cell lung cancer (NCT02581787). Additionally, in some embodiments, the additional therapeutic agent is a TGF-beta trap, such as described in Connolly et al. (2012)  Int&#39;l J. Biological Sciences  8:964-978. One therapeutic compound currently in clinical trials for treatment of solid tumors is M7824 (Merck KgaA—formerly MSB0011459X), which is a bispecific, anti-PD-L1/TGFβ trap compound (NCT02699515); and (NCT02517398). M7824 is comprised of a fully human IgG1 antibody against PD-L1 fused to the extracellular domain of human TGF-beta receptor II, which functions as a TGFβ “trap.” 
     In some embodiments, one or more other therapeutic agent is selected from glembatumumab vedotin-monomethyl auristatin E (MMAE) (Celldex), an anti-glycoprotein NMB (gpNMB) antibody (CR011) linked to the cytotoxic MMAE. gpNMB is a protein overexpressed by multiple tumor types associated with cancer cells&#39; ability to metastasize. 
     In some embodiments, one or more other therapeutic agent is an antiproliferative compound. Such antiproliferative compounds include, but are not limited to aromatase inhibitors; antiestrogens; topoisomerase I inhibitors; topoisomerase II inhibitors; microtubule active compounds; alkylating compounds; histone deacetylase inhibitors; compounds which induce cell differentiation processes; cyclooxygenase inhibitors; MMP inhibitors; mTOR inhibitors; antineoplastic antimetabolites; platin compounds; compounds targeting/decreasing a protein or lipid kinase activity and further anti-angiogenic compounds; compounds which target, decrease or inhibit the activity of a protein or lipid phosphatase; gonadorelin agonists; anti-androgens; methionine aminopeptidase inhibitors; matrix metalloproteinase inhibitors; bisphosphonates; biological response modifiers; antiproliferative antibodies; heparanase inhibitors; inhibitors of Ras oncogenic isoforms; telomerase inhibitors; proteasome inhibitors; compounds used in the treatment of hematologic malignancies; compounds which target, decrease or inhibit the activity of Flt-3; Hsp90 inhibitors such as 17-AAG (17-allylaminogeldanamycin, NSC330507), 17-DMAG (17-dimethylaminoethylamino-17-demethoxy-geldanamycin, NSC707545), IPI-504, CNF1010, CNF2024, CNF1010 from Conforma Therapeutics; temozolomide (Temodal®)); kinesin spindle protein inhibitors, such as SB715992 or SB743921 from GlaxoSmithKline, or pentamidine/chlorpromazine from CombinatoRx; MEK inhibitors such as ARRY142886 from Array BioPharma, AZd 6 244 from AstraZeneca, PD181461 from Pfizer and leucovorin. 
     In some embodiments, the present invention provides a method of treating Alzheimer&#39;s disease comprising administering to a patient in need thereof a provided compound and one or more additional therapeutic agents selected from donepezil (Aricept®), rivastigmine (Excelon), galantamine (Razadyne®), tacrine (Cognex®), and memantine (Namenda). 
     In some embodiments, one or more other therapeutic agent is a taxane compound, which causes disruption of microtubules, which are essential for cell division. In some embodiments, a taxane compound is selected from paclitaxel (Taxol®, Bristol-Myers Squibb), docetaxel (Taxotere®, Sanofi-Aventis; Docefrez®, Sun Pharmaceutical), albumin-bound paclitaxel (Abraxane®; Abraxis/Celgene), cabazitaxel (Jevtana®, Sanofi-Aventis), and SID530 (SK Chemicals, Co.) (NCT00931008). 
     In some embodiments, one or more other therapeutic agent is a nucleoside inhibitor, or a therapeutic agent that interferes with normal DNA synthesis, protein synthesis, cell replication, or will otherwise inhibit rapidly proliferating cells. 
     In some embodiments, a nucleoside inhibitor is selected from trabectedin (guanidine alkylating agent, Yondeli OD, Janssen Oncology), mechlorethamine (alkylating agent, Valchlor®, Aktelion Pharmaceuticals); vincristine (Oncovin®, Eli Lilly; Vincasar®, Teva Pharmaceuticals; Marqibo®, Talon Therapeutics); temozolomide (prodrug to alkylating agent 5-(3-methyltriazen-1-yl)-imidazole-4-carboxamide (MTIC) Temodar®, Merck); cytarabine injection (ara-C, antimetabolic cytidine analog, Pfizer); lomustine (alkylating agent, CeeNU®, Bristol-Myers Squibb; Gleostine®, NextSource Biotechnology); azacitidine (pyrimidine nucleoside analog of cytidine, Vidaza®, Celgene); omacetaxine mepesuccinate (cephalotaxine ester) (protein synthesis inhibitor, Synribo®; Teva Pharmaceuticals); asparaginase  Envinia chrysanthemi  (enzyme for depletion of asparagine, Elspar®, Lundbeck; Erwinaze®, EUSA Pharma); eribulin mesylate (microtubule inhibitor, tubulin-based antimitotic, Halaven®, Eisai); cabazitaxel (microtubule inhibitor, tubulin-based antimitotic, Jevtana®, Sanofi-Aventis); capacetrine (thymidylate synthase inhibitor, Xeloda®, Genentech); bendamustine (bifunctional mechlorethamine derivative, believed to form interstrand DNA cross-links, Treanda®, Cephalon/Teva); ixabepilone (semi-synthetic analog of epothilone B, microtubule inhibitor, tubulin-based antimitotic, Ixempra®, Bristol-Myers Squibb); nelarabine (prodrug of deoxyguanosine analog, nucleoside metabolic inhibitor, Arranon®, Novartis); clorafabine (prodrug of ribonucleotide reductase inhibitor, competitive inhibitor of deoxycytidine, Clolar®, Sanofi-Aventis); and trifluridine and tipiracil (thymidine-based nucleoside analog and thymidine phosphorylase inhibitor, Lonsurf®, Taiho Oncology). 
     In some embodiments, one or more other therapeutic agent is a kinase inhibitor or VEGF-R antagonist. Approved VEGF inhibitors and kinase inhibitors useful in the present invention include: bevacizumab (Avastin®, Genentech/Roche) an anti-VEGF monoclonal antibody; ramucirumab (Cyramza®, Eli Lilly), an anti-VEGFR-2 antibody and ziv-aflibercept, also known as VEGF Trap (Zaltrap®; Regeneron/Sanofi). VEGFR inhibitors, such as regorafenib (Stivarga®, Bayer); vandetanib (Caprelsa®, AstraZeneca); axitinib (Inlyta®, Pfizer); and lenvatinib (Lenvima®, Eisai); Raf inhibitors, such as sorafenib (Nexavar®, Bayer AG and Onyx); dabrafenib (Tafinlar®, Novartis); and vemurafenib (Zelboraf®, Genentech/Roche); MEK inhibitors, such as cobimetanib (Cotellic®, Exelexis/Genentech/Roche); trametinib (Mekinist®, Novartis); Bcr-Abl tyrosine kinase inhibitors, such as imatinib (Gleevec®, Novartis); nilotinib (Tasigna®, Novartis); dasatinib (Sprycel Bri stolMyers Squibb); bosutinib (Bosulif®, Pfizer); and ponatinib (Inclusig®, Ariad Pharmaceuticals); Her2 and EGFR inhibitors, such as gefitinib (Iressa®, AstraZeneca); erlotinib (Tarceeva®, Genentech/Roche/Astellas); lapatinib (Tykerb®, Novartis); afatinib (Gilotrif®, Boehringer Ingelheim); osimertinib (targeting activated EGFR, Tagrisso AstraZeneca); and brigatinib (Alunbrig®, Ariad Pharmaceuticals); c-Met and VEGFR2 inhibitors, such as cabozanitib (Cometriq®, Exelexis); and multikinase inhibitors, such as sunitinib (Sutent®, Pfizer); pazopanib (Votrient®, Novartis); ALK inhibitors, such as crizotinib (Xalkori®, Pfizer); ceritinib (Zykadia®, Novartis); and alectinib (Alecenza®, Genentech/Roche); Bruton&#39;s tyrosine kinase inhibitors, such as ibrutinib (Imbruvica®, Pharmacyclics/Janssen); and Flt3 receptor inhibitors, such as midostaurin (Rydapt®, Novartis). 
     Other kinase inhibitors and VEGF-R antagonists that are in development and may be used in the present invention include tivozanib (Aveo Pharmaecuticals); vatalanib (Bayer/Novartis); lucitanib (Clovis Oncology); dovitinib (TKI258, Novartis); Chiauanib (Chipscreen Biosciences); CEP-11981 (Cephalon); linifanib (Abbott Laboratories); neratinib (HKI-272, Puma Biotechnology); radotinib (Supect®, IY5511, Il-Yang Pharmaceuticals, S. Korea); ruxolitinib (Jakafi®, Incyte Corporation); PTC299 (PTC Therapeutics); CP-547,632 (Pfizer); foretinib (Exelexis, GlaxoSmithKline); quizartinib (Daiichi Sankyo) and motesanib (Amgen/Takeda). 
     In another embodiment, the present invention provides a method of treating organ transplant rejection or graft vs. host disease comprising administering to a patient in need thereof a provided compound and one or more additional therapeutic agents selected from a steroid, cyclosporin, FK506, rapamycin, a hedgehog signaling inhibitor, a BTK inhibitor, a JAK/pan-JAK inhibitor, a TYK2 inhibitor, a PI3K inhibitor, and a SYK inhibitor. 
     In another embodiment, the present invention provides a method of treating or lessening the severity of a disease comprising administering to a patient in need thereof a provided compound and a BTK inhibitor, wherein the disease is selected from inflammatory bowel disease, arthritis, systemic lupus erythematosus (SLE), vasculitis, idiopathic thrombocytopenic purpura (ITP), rheumatoid arthritis, psoriatic arthritis, osteoarthritis, Still&#39;s disease, juvenile arthritis, diabetes, myasthenia gravis, Hashimoto&#39;s thyroiditis, Ord&#39;s thyroiditis, Graves&#39; disease, autoimmune thyroiditis, Sjogren&#39;s syndrome, multiple sclerosis, systemic sclerosis, Lyme neuroborreliosis, Guillain-Barre syndrome, acute disseminated encephalomyelitis, Addison&#39;s disease, opsoclonus-myoclonus syndrome, ankylosing spondylosis, antiphospholipid antibody syndrome, aplastic anemia, autoimmune hepatitis, autoimmune gastritis, pernicious anemia, celiac disease, Goodpasture&#39;s syndrome, idiopathic thrombocytopenic purpura, optic neuritis, scleroderma, primary biliary cirrhosis, Reiter&#39;s syndrome, Takayasu&#39;s arteritis, temporal arteritis, warm autoimmune hemolytic anemia, Wegener&#39;s granulomatosis, psoriasis, alopecia universalis, Behcet&#39;s disease, chronic fatigue, dysautonomia, membranous glomerulonephropathy, endometriosis, interstitial cystitis, pemphigus vulgaris, bullous pemphigoid, neuromyotonia, scleroderma, vulvodynia, a hyperproliferative disease, rejection of transplanted organs or tissues, Acquired Immunodeficiency Syndrome (AIDS, also known as HIV), type 1 diabetes, graft versus host disease, transplantation, transfusion, anaphylaxis, allergies (e.g., allergies to plant pollens, latex, drugs, foods, insect poisons, animal hair, animal dander, dust mites, or cockroach calyx), type I hypersensitivity, allergic conjunctivitis, allergic rhinitis, and atopic dermatitis, asthma, appendicitis, atopic dermatitis, asthma, allergy, blepharitis, bronchiolitis, bronchitis, bursitis, cervicitis, cholangitis, cholecystitis, chronic graft rejection, colitis, conjunctivitis, Crohn&#39;s disease, cystitis, dacryoadenitis, dermatitis, dermatomyositis, encephalitis, endocarditis, endometritis, enteritis, enterocolitis, epicondylitis, epididymitis, fasciitis, fibrositis, gastritis, gastroenteritis, Henoch-Schonlein purpura, hepatitis, hidradenitis suppurativa, immunoglobulin A nephropathy, interstitial lung disease, laryngitis, mastitis, meningitis, myelitis myocarditis, myositis, nephritis, oophoritis, orchitis, osteitis, otitis, pancreatitis, parotitis, pericarditis, peritonitis, pharyngitis, pleuritis, phlebitis, pneumonitis, pneumonia, polymyositis, proctitis, prostatitis, pyelonephritis, rhinitis, salpingitis, sinusitis, stomatitis, synovitis, tendonitis, tonsillitis, ulcerative colitis, uveitis, vaginitis, vasculitis, or vulvitis, B-cell proliferative disorder, e.g., diffuse large B cell lymphoma, follicular lymphoma, chronic lymphocytic lymphoma, chronic lymphocytic leukemia, acute lymphocytic leukemia, B-cell prolymphocytic leukemia, lymphoplasmacytic lymphoma/Waldenstrom macroglobulinemia, splenic marginal zone lymphoma, multiple myeloma (also known as plasma cell myeloma), non-Hodgkin&#39;s lymphoma, Hodgkin&#39;s lymphoma, plasmacytoma, extranodal marginal zone B cell lymphoma, nodal marginal zone B cell lymphoma, mantle cell lymphoma, mediastinal (thymic) large B cell lymphoma, intravascular large B cell lymphoma, primary effusion lymphoma, Burkitt lymphoma/leukemia, or lymphomatoid granulomatosis, breast cancer, prostate cancer, or cancer of the mast cells (e.g., mastocytoma, mast cell leukemia, mast cell sarcoma, systemic mastocytosis), bone cancer, colorectal cancer, pancreatic cancer, diseases of the bone and joints including, without limitation, rheumatoid arthritis, seronegative spondyloarthropathies (including ankylosing spondylitis, psoriatic arthritis and Reiter&#39;s disease), Behcet&#39;s disease, Sjogren&#39;s syndrome, systemic sclerosis, osteoporosis, bone cancer, bone metastasis, a thromboembolic disorder, (e.g., myocardial infarct, angina pectoris, reocclusion after angioplasty, restenosis after angioplasty, reocclusion after aortocoronary bypass, restenosis after aortocoronary bypass, stroke, transitory ischemia, a peripheral arterial occlusive disorder, pulmonary embolism, deep venous thrombosis), inflammatory pelvic disease, urethritis, skin sunburn, sinusitis, pneumonitis, encephalitis, meningitis, myocarditis, nephritis, osteomyelitis, myositis, hepatitis, gastritis, enteritis, dermatitis, gingivitis, appendicitis, pancreatitis, cholocystitus, agammaglobulinemia, psoriasis, allergy, Crohn&#39;s disease, irritable bowel syndrome, ulcerative colitis, Sjogren&#39;s disease, tissue graft rejection, hyperacute rejection of transplanted organs, asthma, allergic rhinitis, chronic obstructive pulmonary disease (COPD), autoimmune polyglandular disease (also known as autoimmune polyglandular syndrome), autoimmune alopecia, pernicious anemia, glomerulonephritis, dermatomyositis, multiple sclerosis, scleroderma, vasculitis, autoimmune hemolytic and thrombocytopenic states, Goodpasture&#39;s syndrome, atherosclerosis, Addison&#39;s disease, Parkinson&#39;s disease, Alzheimer&#39;s disease, diabetes, septic shock, systemic lupus erythematosus (SLE), rheumatoid arthritis, psoriatic arthritis, juvenile arthritis, osteoarthritis, chronic idiopathic thrombocytopenic purpura, Waldenstrom macroglobulinemia, myasthenia gravis, Hashimoto&#39;s thyroiditis, atopic dermatitis, degenerative joint disease, vitiligo, autoimmune hypopituitarism, Guillain-Barre syndrome, Behcet&#39;s disease, scleraderma, mycosis fungoides, acute inflammatory responses (such as acute respiratory distress syndrome and ischemia/reperfusion injury), and Graves&#39; disease. 
     In another embodiment, the present invention provides a method of treating or lessening the severity of a disease comprising administering to a patient in need thereof a provided compound and a PI3K inhibitor, wherein the disease is selected from a cancer, a neurodegenative disorder, an angiogenic disorder, a viral disease, an autoimmune disease, an inflammatory disorder, a hormone-related disease, conditions associated with organ transplantation, immunodeficiency disorders, a destructive bone disorder, a proliferative disorder, an infectious disease, a condition associated with cell death, thrombin-induced platelet aggregation, chronic myelogenous leukemia (CML), chronic lymphocytic leukemia (CLL), liver disease, pathologic immune conditions involving T cell activation, a cardiovascular disorder, and a CNS disorder. 
     In another embodiment, the present invention provides a method of treating or lessening the severity of a disease comprising administering to a patient in need thereof a provided compound and a PI3K inhibitor, wherein the disease is selected from benign or malignant tumor, carcinoma or solid tumor of the brain, kidney (e.g., renal cell carcinoma (RCC)), liver, adrenal gland, bladder, breast, stomach, gastric tumors, ovaries, colon, rectum, prostate, pancreas, lung, vagina, endometrium, cervix, testis, genitourinary tract, esophagus, larynx, skin, bone or thyroid, sarcoma, glioblastomas, neuroblastomas, multiple myeloma or gastrointestinal cancer, especially colon carcinoma or colorectal adenoma or a tumor of the neck and head, an epidermal hyperproliferation, psoriasis, prostate hyperplasia, a neoplasia, a neoplasia of epithelial character, adenoma, adenocarcinoma, keratoacanthoma, epidermoid carcinoma, large cell carcinoma, non-small-cell lung carcinoma, lymphomas, (including, for example, non-Hodgkin&#39;s Lymphoma (NHL) and Hodgkin&#39;s lymphoma (also termed Hodgkin&#39;s or Hodgkin&#39;s disease)), a mammary carcinoma, follicular carcinoma, undifferentiated carcinoma, papillary carcinoma, seminoma, melanoma, or a leukemia, diseases include Cowden syndrome, Lhermitte-Dudos disease and Bannayan-Zonana syndrome, or diseases in which the PI3K/PKB pathway is aberrantly activated, asthma of whatever type or genesis including both intrinsic (non-allergic) asthma and extrinsic (allergic) asthma, mild asthma, moderate asthma, severe asthma, bronchitic asthma, exercise-induced asthma, occupational asthma and asthma induced following bacterial infection, acute lung injury (ALI), adult/acute respiratory distress syndrome (ARDS), chronic obstructive pulmonary, airways or lung disease (COPD, COAD or COLD), including chronic bronchitis or dyspnea associated therewith, emphysema, as well as exacerbation of airways hyperreactivity consequent to other drug therapy, in particular other inhaled drug therapy, bronchitis of whatever type or genesis including, but not limited to, acute, arachidic, catarrhal, croupus, chronic or phthinoid bronchitis, pneumoconiosis (an inflammatory, commonly occupational, disease of the lungs, frequently accompanied by airways obstruction, whether chronic or acute, and occasioned by repeated inhalation of dusts) of whatever type or genesis, including, for example, aluminosis, anthracosis, asbestosis, chalicosis, ptilosis, siderosis, silicosis, tabacosis and byssinosis, Loffler&#39;s syndrome, eosinophilic, pneumonia, parasitic (in particular metazoan) infestation (including tropical eosinophilia), bronchopulmonary aspergillosis, polyarteritis nodosa (including Churg-Strauss syndrome), eosinophilic granuloma and eosinophil-related disorders affecting the airways occasioned by drug-reaction, psoriasis, contact dermatitis, atopic dermatitis, alopecia areata, erythema multiforma, dermatitis herpetiformis, scleroderma, vitiligo, hypersensitivity angiitis, urticaria, bullous pemphigoid, lupus erythematosus, pemphisus, epidermolysis bullosa acquisita, conjunctivitis, keratoconjunctivitis sicca, and vernal conjunctivitis, diseases affecting the nose including allergic rhinitis, and inflammatory disease in which autoimmune reactions are implicated or having an autoimmune component or etiology, including autoimmune hematological disorders (e.g. hemolytic anemia, aplastic anemia, pure red cell anemia and idiopathic thrombocytopenia), systemic lupus erythematosus, rheumatoid arthritis, polychondritis, sclerodoma, Wegener granulamatosis, dermatomyositis, chronic active hepatitis, myasthenia gravis, Steven-Johnson syndrome, idiopathic sprue, autoimmune inflammatory bowel disease (e.g. ulcerative colitis and Crohn&#39;s disease), endocrine opthalmopathy, Grave&#39;s disease, sarcoidosis, alveolitis, chronic hypersensitivity pneumonitis, multiple sclerosis, primary biliary cirrhosis, uveitis (anterior and posterior), keratoconjunctivitis sicca and vernal keratoconjunctivitis, interstitial lung fibrosis, psoriatic arthritis and glomerulonephritis (with and without nephrotic syndrome, e.g. including idiopathic nephrotic syndrome or minal change nephropathy, restenosis, cardiomegaly, atherosclerosis, myocardial infarction, ischemic stroke and congestive heart failure, Alzheimer&#39;s disease, Parkinson&#39;s disease, amyotrophic lateral sclerosis, Huntington&#39;s disease, and cerebral ischemia, and neurodegenerative disease caused by traumatic injury, glutamate neurotoxicity and hypoxia. 
     In some embodiments, one or more other therapeutic agent is a phosphatidylinositol 3 kinase (PI3K) inhibitor. In some embodiments, a PI3K inhibitor is selected from idelalisib (Zydelig®, Gilead), alpelisib (BYL719, Novartis), taselisib (GDC-0032, Genentech/Roche); pictilisib (GDC-0941, Genentech/Roche); copanlisib (BAY806946, Bayer); duvelisib (formerly IPI-145, Infinity Pharmaceuticals); PQR309 (Piqur Therapeutics, Switzerland); and TGR1202 (formerly RP5230, TG Therapeutics). 
     The compounds and compositions, according to the method of the present invention, may be administered using any amount and any route of administration effective for treating or lessening the severity of a cancer, an autoimmune disorder, a proliferative disorder, an inflammatory disorder, a neurodegenerative or neurological disorder, schizophrenia, a bone-related disorder, liver disease, or a cardiac disorder. The exact amount required will vary from subject to subject, depending on the species, age, and general condition of the subject, the severity of the infection, the particular agent, its mode of administration, and the like. Compounds of the invention are preferably formulated in dosage unit form for ease of administration and uniformity of dosage. The expression “dosage unit form” as used herein refers to a physically discrete unit of agent appropriate for the patient to be treated. It will be understood, however, that the total daily usage of the compounds and compositions of the present invention will be decided by the attending physician within the scope of sound medical judgment. The specific effective dose level for any particular patient or organism will depend upon a variety of factors including the disorder being treated and the severity of the disorder; the activity of the specific compound employed; the specific composition employed; the age, body weight, general health, sex and diet of the patient; the time of administration, route of administration, and rate of excretion of the specific compound employed; the duration of the treatment; drugs used in combination or coincidental with the specific compound employed, and like factors well known in the medical arts. 
     Pharmaceutically acceptable compositions of this invention can be administered to humans and other animals orally, rectally, parenterally, intracisternally, intravaginally, intraperitoneally, topically (as by powders, ointments, or drops), bucally, as an oral or nasal spray, or the like, depending on the severity of the infection being treated. In certain embodiments, the compounds of the invention may be administered orally or parenterally at dosage levels of about 0.01 mg/kg to about 50 mg/kg and preferably from about 1 mg/kg to about 25 mg/kg, of subject body weight per day, one or more times a day, to obtain the desired therapeutic effect. 
     Liquid dosage forms for oral administration include, but are not limited to, pharmaceutically acceptable emulsions, microemulsions, solutions, suspensions, syrups and elixirs. In addition to the active compounds, the liquid dosage forms may contain inert diluents commonly used in the art such as, for example, water or other solvents, solubilizing agents and emulsifiers such as ethyl alcohol, isopropyl alcohol, ethyl carbonate, ethyl acetate, benzyl alcohol, benzyl benzoate, propylene glycol, 1,3-butylene glycol, dimethylformamide, oils (in particular, cottonseed, groundnut, corn, germ, olive, castor, and sesame oils), glycerol, tetrahydrofurfuryl alcohol, polyethylene glycols and fatty acid esters of sorbitan, and mixtures thereof. Besides inert diluents, the oral compositions can also include adjuvants such as wetting agents, emulsifying and suspending agents, sweetening, flavoring, and perfuming agents. 
     Injectable preparations, for example, sterile injectable aqueous or oleaginous suspensions may be formulated according to the known art using suitable dispersing or wetting agents and suspending agents. The sterile injectable preparation may also be a sterile injectable solution, suspension or emulsion in a nontoxic parenterally acceptable diluent or solvent, for example, as a solution in 1,3-butanediol. Among the acceptable vehicles and solvents that may be employed are water, Ringer&#39;s solution, U.S.P. and isotonic sodium chloride solution. In addition, sterile, fixed oils are conventionally employed as a solvent or suspending medium. For this purpose any bland fixed oil can be employed including synthetic mono- or diglycerides. In addition, fatty acids such as oleic acid are used in the preparation of injectables. 
     Injectable formulations can be sterilized, for example, by filtration through a bacterial-retaining filter, or by incorporating sterilizing agents in the form of sterile solid compositions which can be dissolved or dispersed in sterile water or other sterile injectable medium prior to use. 
     In order to prolong the effect of a compound of the present invention, it is often desirable to slow the absorption of the compound from subcutaneous or intramuscular injection. This may be accomplished by the use of a liquid suspension of crystalline or amorphous material with poor water solubility. The rate of absorption of the compound then depends upon its rate of dissolution that, in turn, may depend upon crystal size and crystalline form. Alternatively, delayed absorption of a parenterally administered compound form is accomplished by dissolving or suspending the compound in an oil vehicle. Injectable depot forms are made by forming microencapsule matrices of the compound in biodegradable polymers such as polylactide-polyglycolide. Depending upon the ratio of compound to polymer and the nature of the particular polymer employed, the rate of compound release can be controlled. Examples of other biodegradable polymers include poly(orthoesters) and poly(anhydrides). Depot injectable formulations are also prepared by entrapping the compound in liposomes or microemulsions that are compatible with body tissues. 
     Compositions for rectal or vaginal administration are preferably suppositories which can be prepared by mixing the compounds of this invention with suitable non-irritating excipients or carriers such as cocoa butter, polyethylene glycol or a suppository wax which are solid at ambient temperature but liquid at body temperature and therefore melt in the rectum or vaginal cavity and release the active compound. 
     Solid dosage forms for oral administration include capsules, tablets, pills, powders, and granules. In such solid dosage forms, the active compound is mixed with at least one inert, pharmaceutically acceptable excipient or carrier such as sodium citrate or dicalcium phosphate and/or a) fillers or extenders such as starches, lactose, sucrose, glucose, mannitol, and silicic acid, b) binders such as, for example, carboxymethylcellulose, alginates, gelatin, polyvinylpyrrolidinone, sucrose, and acacia, c) humectants such as glycerol, d) disintegrating agents such as agar-agar, calcium carbonate, potato or tapioca starch, alginic acid, certain silicates, and sodium carbonate, e) solution retarding agents such as paraffin, f) absorption accelerators such as quaternary ammonium compounds, g) wetting agents such as, for example, cetyl alcohol and glycerol monostearate, h) absorbents such as kaolin and bentonite clay, and i) lubricants such as talc, calcium stearate, magnesium stearate, solid polyethylene glycols, sodium lauryl sulfate, and mixtures thereof. In the case of capsules, tablets and pills, the dosage form may also comprise buffering agents. 
     Solid compositions of a similar type may also be employed as fillers in soft and hard-filled gelatin capsules using such excipients as lactose or milk sugar as well as high molecular weight polyethylene glycols and the like. The solid dosage forms of tablets, dragees, capsules, pills, and granules can be prepared with coatings and shells such as enteric coatings and other coatings well known in the pharmaceutical formulating art. They may optionally contain opacifying agents and can also be of a composition that they release the active ingredient(s) only, or preferentially, in a certain part of the intestinal tract, optionally, in a delayed manner. Examples of embedding compositions that can be used include polymeric substances and waxes. Solid compositions of a similar type may also be employed as fillers in soft and hard-filled gelatin capsules using such excipients as lactose or milk sugar as well as high molecular weight polethylene glycols and the like. 
     The active compounds can also be in micro-encapsulated form with one or more excipients as noted above. The solid dosage forms of tablets, dragees, capsules, pills, and granules can be prepared with coatings and shells such as enteric coatings, release controlling coatings and other coatings well known in the pharmaceutical formulating art. In such solid dosage forms the active compound may be admixed with at least one inert diluent such as sucrose, lactose or starch. Such dosage forms may also comprise, as is normal practice, additional substances other than inert diluents, e.g., tableting lubricants and other tableting aids such a magnesium stearate and microcrystalline cellulose. In the case of capsules, tablets and pills, the dosage forms may also comprise buffering agents. They may optionally contain opacifying agents and can also be of a composition that they release the active ingredient(s) only, or preferentially, in a certain part of the intestinal tract, optionally, in a delayed manner. Examples of embedding compositions that can be used include polymeric substances and waxes. 
     Dosage forms for topical or transdermal administration of a compound of this invention include ointments, pastes, creams, lotions, gels, powders, solutions, sprays, inhalants or patches. The active component is admixed under sterile conditions with a pharmaceutically acceptable carrier and any needed preservatives or buffers as may be required. Ophthalmic formulation, ear drops, and eye drops are also contemplated as being within the scope of this invention. Additionally, the present invention contemplates the use of transdermal patches, which have the added advantage of providing controlled delivery of a compound to the body. Such dosage forms can be made by dissolving or dispensing the compound in the proper medium. Absorption enhancers can also be used to increase the flux of the compound across the skin. The rate can be controlled by either providing a rate controlling membrane or by dispersing the compound in a polymer matrix or gel. 
     According to one embodiment, the invention relates to a method of inhibiting protein kinase activity or degrading a protein kinase in a biological sample comprising the step of contacting said biological sample with a compound of this invention, or a composition comprising said compound. 
     According to another embodiment, the invention relates to a method of inhibiting or degrading IRAK-1, IRAK-2, and/or IRAK-4, or a mutant thereof, activity in a biological sample comprising the step of contacting said biological sample with a compound of this invention, or a composition comprising said compound. 
     The term “biological sample”, as used herein, includes, without limitation, cell cultures or extracts thereof biopsied material obtained from a mammal or extracts thereof; and blood, saliva, urine, feces, semen, tears, or other body fluids or extracts thereof. 
     Inhibition and/or degradation of a protein kinase, or a protein kinase selected from IRAK-1, IRAK-2, and/or IRAK-4, or a mutant thereof, activity in a biological sample is useful for a variety of purposes that are known to one of skill in the art. Examples of such purposes include, but are not limited to, blood transfusion, organ-transplantation, biological specimen storage, and biological assays. 
     Another embodiment of the present invention relates to a method of degrading a protein kinase and/or inhibiting protein kinase activity in a patient comprising the step of administering to said patient a compound of the present invention, or a composition comprising said compound. 
     According to another embodiment, the invention relates to a method of degrading and/or inhibiting one or more of IRAK-1, IRAK-2, and/or IRAK-4, or a mutant thereof, activity in a patient comprising the step of administering to said patient a compound of the present invention, or a composition comprising said compound. In other embodiments, the present invention provides a method for treating a disorder mediated by one or more of IRAK-1, IRAK-2, and/or IRAK-4, or a mutant thereof, in a patient in need thereof, comprising the step of administering to said patient a compound according to the present invention or pharmaceutically acceptable composition thereof. Such disorders are described in detail herein. 
     Depending upon the particular condition, or disease, to be treated, additional therapeutic agents that are normally administered to treat that condition, may also be present in the compositions of this invention. As used herein, additional therapeutic agents that are normally administered to treat a particular disease, or condition, are known as “appropriate for the disease, or condition, being treated.” 
     A compound of the current invention may also be used to advantage in combination with other antiproliferative compounds. Such antiproliferative compounds include, but are not limited to aromatase inhibitors; antiestrogens; topoisomerase I inhibitors; topoisomerase II inhibitors; microtubule active compounds; alkylating compounds; histone deacetylase inhibitors; compounds which induce cell differentiation processes; cyclooxygenase inhibitors; MMP inhibitors; mTOR inhibitors; antineoplastic antimetabolites; platin compounds; compounds targeting/decreasing a protein or lipid kinase activity and further anti-angiogenic compounds; compounds which target, decrease or inhibit the activity of a protein or lipid phosphatase; gonadorelin agonists; anti-androgens; methionine aminopeptidase inhibitors; matrix metalloproteinase inhibitors; bisphosphonates; biological response modifiers; antiproliferative antibodies; heparanase inhibitors; inhibitors of Ras oncogenic isoforms; telomerase inhibitors; proteasome inhibitors; compounds used in the treatment of hematologic malignancies; compounds which target, decrease or inhibit the activity of Flt-3; Hsp90 inhibitors such as 17-AAG (17-allylaminogeldanamycin, NSC330507), 17-DMAG (17-dimethylaminoethylamino-17-demethoxy-geldanamycin, NSC707545), IPI-504, CNF1010, CNF2024, CNF1010 from Conforma Therapeutics; temozolomide (Temodal®); kinesin spindle protein inhibitors, such as SB715992 or SB743921 from GlaxoSmithKline, or pentamidine/chlorpromazine from CombinatoRx; MEK inhibitors such as ARRY142886 from Array BioPharma, AZD6244 from AstraZeneca, PD181461 from Pfizer and leucovorin. 
     The term “aromatase inhibitor” as used herein relates to a compound which inhibits estrogen production, for instance, the conversion of the substrates androstenedione and testosterone to estrone and estradiol, respectively. The term includes, but is not limited to steroids, especially atamestane, exemestane and formestane and, in particular, non-steroids, especially aminoglutethimide, roglethimide, pyridoglutethimide, trilostane, testolactone, ketokonazole, vorozole, fadrozole, anastrozole and letrozole. Exemestane is marketed under the trade name Aromasin™. Formestane is marketed under the trade name Lentaron™. Fadrozole is marketed under the trade name Afema™. Anastrozole is marketed under the trade name Arimidex™ Letrozole is marketed under the trade names Femara™ or Femar™. Aminoglutethimide is marketed under the trade name Orimeten™. A combination of the invention comprising a chemotherapeutic agent which is an aromatase inhibitor is particularly useful for the treatment of hormone receptor positive tumors, such as breast tumors. 
     In some embodiments, one or more other therapeutic agent is an mTOR inhibitor, which inhibits cell proliferation, angiogenesis and glucose uptake. In some embodiments, an mTOR inhibitor is everolimus (Afinitor®, Novartis); temsirolimus (Torisel (ID, Pfizer); and sirolimus (Rapamune®, Pfizer). 
     In some embodiments, one or more other therapeutic agent is an aromatase inhibitor. In some embodiments, an aromatase inhibitor is selected from exemestane (Aromasin®, Pfizer); anastazole (Arimidex®, AstraZeneca) and letrozole (Femora®, Novartis). 
     The term “antiestrogen” as used herein relates to a compound which antagonizes the effect of estrogens at the estrogen receptor level. The term includes, but is not limited to tamoxifen, fulvestrant, raloxifene and raloxifene hydrochloride. Tamoxifen is marketed under the trade name Nolvadex™. Raloxifene hydrochloride is marketed under the trade name Evista™. Fulvestrant can be administered under the trade name Faslodex™. A combination of the invention comprising a chemotherapeutic agent which is an antiestrogen is particularly useful for the treatment of estrogen receptor positive tumors, such as breast tumors. 
     The term “anti-androgen” as used herein relates to any substance which is capable of inhibiting the biological effects of androgenic hormones and includes, but is not limited to, bicalutamide (Casodex™). The term “gonadorelin agonist” as used herein includes, but is not limited to abarelix, goserelin and goserelin acetate. Goserelin can be administered under the trade name Zoladex™. 
     The term “topoisomerase I inhibitor” as used herein includes, but is not limited to topotecan, gimatecan, irinotecan, camptothecian and its analogues, 9-nitrocamptothecin and the macromolecular camptothecin conjugate PNU-166148. Irinotecan can be administered, e.g. in the form as it is marketed, e.g. under the trademark Camptosar™. Topotecan is marketed under the trade name Hycamptin™. 
     The term “topoisomerase II inhibitor” as used herein includes, but is not limited to the anthracyclines such as doxorubicin (including liposomal formulation, such as Caelyx™) daunorubicin, epirubicin, idarubicin and nemorubicin, the anthraquinones mitoxantrone and losoxantrone, and the podophillotoxines etoposide and teniposide. Etoposide is marketed under the trade name Etopophos™. Teniposide is marketed under the trade name VM 26-Bristol Doxorubicin is marketed under the trade name Acriblastin™ or Adriamycin™. Epirubicin is marketed under the trade name Farmorubicin™. Idarubicin is marketed. under the trade name Zavedos™. Mitoxantrone is marketed under the trade name Novantron. 
     The term “microtubule active agent” relates to microtubule stabilizing, microtubule destabilizing compounds and microtublin polymerization inhibitors including, but not limited to taxanes, such as paclitaxel and docetaxel; vinca alkaloids, such as vinblastine or vinblastine sulfate, vincristine or vincristine sulfate, and vinorelbine; discodermolides; cochicine and epothilones and derivatives thereof. Paclitaxel is marketed under the trade name Taxol™. Docetaxel is marketed under the trade name Taxotere™. Vinblastine sulfate is marketed under the trade name Vinblastin R.P™. Vincristine sulfate is marketed under the trade name Farmistin™. 
     The term “alkylating agent” as used herein includes, but is not limited to, cyclophosphamide, ifosfamide, melphalan or nitrosourea (BCNU or Gliadel). Cyclophosphamide is marketed under the trade name Cyclostin™. Ifosfamide is marketed under the trade name Holoxan™. 
     The term “histone deacetylase inhibitors” or “HDAC inhibitors” relates to compounds which inhibit the histone deacetylase and which possess antiproliferative activity. This includes, but is not limited to, suberoylanilide hydroxamic acid (SAHA). 
     The term “antineoplastic antimetabolite” includes, but is not limited to, 5-fluorouracil or 5-FU, capecitabine, gemcitabine, DNA demethylating compounds, such as 5-azacytidine and decitabine, methotrexate and edatrexate, and folic acid antagonists such as pemetrexed. Capecitabine is marketed under the trade name Xeloda™. Gemcitabine is marketed under the trade name Gemzar™. 
     The term “platin compound” as used herein includes, but is not limited to, carboplatin, cis-platin, cisplatinum and oxaliplatin. Carboplatin can be administered, e.g., in the form as it is marketed, e.g. under the trademark Carboplat™. Oxaliplatin can be administered, e.g., in the form as it is marketed, e.g. under the trademark Eloxatin™. 
     The term “Bcl-2 inhibitor” as used herein includes, but is not limited to compounds having inhibitory activity against B-cell lymphoma 2 protein (Bcl-2), including but not limited to ABT-199, ABT-731, ABT-737, apogossypol, Ascenta&#39;s pan-Bcl-2 inhibitors, curcumin (and analogs thereof), dual Bcl-2/Bcl-xL inhibitors (Infinity Pharmaceuticals/Novartis Pharmaceuticals), Genasense (G3139), HA14-1 (and analogs thereof; see WO2008118802), navitoclax (and analogs thereof, see U.S. Pat. No. 7,390,799), NH-1 (Shenayng Pharmaceutical University), obatoclax (and analogs thereof, see WO2004106328), S-001 (Gloria Pharmaceuticals), TW series compounds (Univ. of Michigan), and venetoclax. In some embodiments the Bcl-2 inhibitor is a small molecule therapeutic. In some embodiments the Bcl-2 inhibitor is a peptidomimetic. 
     The term “compounds targeting/decreasing a protein or lipid kinase activity; or a protein or lipid phosphatase activity; or further anti-angiogenic compounds” as used herein includes, but is not limited to, protein tyrosine kinase and/or serine and/or threonine kinase inhibitors or lipid kinase inhibitors, such as a) compounds targeting, decreasing or inhibiting the activity of the platelet-derived growth factor-receptors (PDGFR), such as compounds which target, decrease or inhibit the activity of PDGFR, especially compounds which inhibit the PDGF receptor, such as an N-phenyl-2-pyrimidine-amine derivative, such as imatinib, SU101, SU6668 and GFB-111; b) compounds targeting, decreasing or inhibiting the activity of the fibroblast growth factor-receptors (FGFR); c) compounds targeting, decreasing or inhibiting the activity of the insulin-like growth factor receptor I (IGF-IR), such as compounds which target, decrease or inhibit the activity of IGF-IR, especially compounds which inhibit the kinase activity of IGF-I receptor, or antibodies that target the extracellular domain of IGF-I receptor or its growth factors; d) compounds targeting, decreasing or inhibiting the activity of the Trk receptor tyrosine kinase family, or ephrin B4 inhibitors; e) compounds targeting, decreasing or inhibiting the activity of the AxI receptor tyrosine kinase family; f) compounds targeting, decreasing or inhibiting the activity of the Ret receptor tyrosine kinase; g) compounds targeting, decreasing or inhibiting the activity of the Kit/SCFR receptor tyrosine kinase, such as imatinib; h) compounds targeting, decreasing or inhibiting the activity of the C-kit receptor tyrosine kinases, which are part of the PDGFR family, such as compounds which target, decrease or inhibit the activity of the c-Kit receptor tyrosine kinase family, especially compounds which inhibit the c-Kit receptor, such as imatinib; i) compounds targeting, decreasing or inhibiting the activity of members of the c-Abl family, their gene-fusion products (e.g. BCR-Abl kinase) and mutants, such as compounds which target decrease or inhibit the activity of c-Abl family members and their gene fusion products, such as an N-phenyl-2-pyrimidine-amine derivative, such as imatinib or nilotinib (AMN107); PD180970; AG957; NSC 680410; PD173955 from ParkeDavis; or dasatinib (BMS-354825); j) compounds targeting, decreasing or inhibiting the activity of members of the protein kinase C (PKC) and Raf family of serine/threonine kinases, members of the MEK, SRC, JAK/pan-JAK, FAK, PDK1, PKB/Akt, Ras/MAPK, PI3K, SYK, TYK2, BTK and TEC family, and/or members of the cyclin-dependent kinase family (CDK) including staurosporine derivatives, such as midostaurin; examples of further compounds include UCN-01, safingol, BAY 43-9006, Bryostatin 1, Perifosine; llmofosine; RO 318220 and RO 320432; GO 6976; lsis 3521; LY333531/LY379196; isochinoline compounds; FTIs; PD184352 or QAN697 (a P13K inhibitor) or AT7519 (CDK inhibitor); k) compounds targeting, decreasing or inhibiting the activity of protein-tyrosine kinase inhibitors, such as compounds which target, decrease or inhibit the activity of protein-tyrosine kinase inhibitors include imatinib mesylate (Gleevec™) or tyrphostin such as Tyrphostin A23/RG-50810; AG 99; Tyrphostin AG 213; Tyrphostin AG 1748; Tyrphostin AG 490; Tyrphostin B44; Tyrphostin B44 (+) enantiomer; Tyrphostin AG 555; AG 494; Tyrphostin AG 556, AG957 and adaphostin (4-{[(2,5-dihydroxyphenyl)methyl]amino}-benzoic acid adamantyl ester; NSC 680410, adaphostin); 1) compounds targeting, decreasing or inhibiting the activity of the epidermal growth factor family of receptor tyrosine kinases (EGFR 1  ErbB2, ErbB3, ErbB4 as homo- or heterodimers) and their mutants, such as compounds which target, decrease or inhibit the activity of the epidermal growth factor receptor family are especially compounds, proteins or antibodies which inhibit members of the EGF receptor tyrosine kinase family, such as EGF receptor, ErbB2, ErbB3 and ErbB4 or bind to EGF or EGF related ligands, CP 358774, ZD 1839, ZM 105180; trastuzumab (Herceptin™) cetuximab (Erbitux™), Iressa, Tarceva, OSI-774, Cl-1033, EKB-569, GW-2016, E1.1, E2.4, E2.5, E6.2, E6.4, E2.11, E6.3 or E7.6.3, and 7H-pyrrolo-[2,3-d]pyrimidine derivatives; m) compounds targeting, decreasing or inhibiting the activity of the c-Met receptor, such as compounds which target, decrease or inhibit the activity of c-Met, especially compounds which inhibit the kinase activity of c-Met receptor, or antibodies that target the extracellular domain of c-Met or bind to HGF, n) compounds targeting, decreasing or inhibiting the kinase activity of one or more JAK family members (JAK1/JAK2/JAK3/TYK2 and/or pan-JAK), including but not limited to PRT-062070, SB-1578, baricitinib, pacritinib, momelotinib, VX-509, AZD-1480, TG-101348, tofacitinib, and ruxolitinib; o) compounds targeting, decreasing or inhibiting the kinase activity of PI3 kinase (PI3K) including but not limited to ATU-027, SF-1126, DS-7423, PBI-05204, GSK-2126458, ZSTK-474, buparlisib, pictrelisib, PF-4691502, BYL-719, dactolisib, XL-147, XL-765, and idelalisib; and; and q) compounds targeting, decreasing or inhibiting the signaling effects of hedgehog protein (Hh) or smoothened receptor (SMO) pathways, including but not limited to cyclopamine, vismodegib, itraconazole, erismodegib, and IPI-926 (saridegib). 
     Compounds which target, decrease or inhibit the activity of a protein or lipid phosphatase are e.g. inhibitors of phosphatase 1, phosphatase 2A, or CDC25, such as okadaic acid or a derivative thereof. 
     In some embodiments, one or more other therapeutic agent is a growth factor antagonist, such as an antagonist of platelet-derived growth factor (PDGF), or epidermal growth factor (EGF) or its receptor (EGFR). Approved PDGF antagonists which may be used in the present invention include olaratumab (Lartruvo®; Eli Lilly). Approved EGFR antagonists which may be used in the present invention include cetuximab (Erbitux®, Eli Lilly); necitumumab (Portrazza®, Eli Lilly), panitumumab (Vectibix®, Amgen); and osimertinib (targeting activated EGFR, Tagrisso®, AstraZeneca). 
     The term “PI3K inhibitor” as used herein includes, but is not limited to compounds having inhibitory activity against one or more enzymes in the phosphatidylinositol-3-kinase family, including, but not limited to PI3Kα, PI3Kγ, PI3Kδ, PI3Kβ, PI3K-C2α, PI3K-C2β, PI3K-C2γ, Vps34, p110-α, p110-β, p110-γ, p110-δ, p85-α, p85-β, p55-γ, p150, p101, and p87. Examples of PI3K inhibitors useful in this invention include but are not limited to ATU-027, SF-1126, DS-7423, PBI-05204, GSK-2126458, ZSTK-474, buparlisib, pictrelisib, PF-4691502, BYL-719, dactolisib, XL-147, XL-765, and idelalisib. 
     The term “BTK inhibitor” as used herein includes, but is not limited to compounds having inhibitory activity against Bruton&#39;s Tyrosine Kinase (BTK), including, but not limited to AVL-292 and ibrutinib. 
     The term “SYK inhibitor” as used herein includes, but is not limited to compounds having inhibitory activity against spleen tyrosine kinase (SYK), including but not limited to PRT-062070, R-343, R-333, Excellair, PRT-062607, and fostamatinib 
     Further examples of BTK inhibitory compounds, and conditions treatable by such compounds in combination with compounds of this invention can be found in WO2008039218 and WO2011090760, the entirety of which are incorporated herein by reference. 
     Further examples of SYK inhibitory compounds, and conditions treatable by such compounds in combination with compounds of this invention can be found in WO2003063794, WO2005007623, and WO2006078846, the entirety of which are incorporated herein by reference. 
     Further examples of PI3K inhibitory compounds, and conditions treatable by such compounds in combination with compounds of this invention can be found in WO2004019973, WO2004089925, WO2007016176, U.S. Pat. No. 8,138,347, WO2002088112, WO2007084786, WO2007129161, WO2006122806, WO2005113554, and WO2007044729 the entirety of which are incorporated herein by reference. 
     Further examples of JAK inhibitory compounds, and conditions treatable by such compounds in combination with compounds of this invention can be found in WO2009114512, WO2008109943, WO2007053452, WO2000142246, and WO2007070514, the entirety of which are incorporated herein by reference. 
     Further anti-angiogenic compounds include compounds having another mechanism for their activity, e.g. unrelated to protein or lipid kinase inhibition e.g. thalidomide (Thalomid™) and TNP-470. 
     Examples of proteasome inhibitors useful for use in combination with compounds of the invention include, but are not limited to bortezomib, disulfiram, epigallocatechin-3-gallate (EGCG), salinosporamide A, carfilzomib, ONX-0912, CEP-18770, and MLN9708. 
     Compounds which target, decrease or inhibit the activity of a protein or lipid phosphatase are e.g. inhibitors of phosphatase 1, phosphatase 2A, or CDC25, such as okadaic acid or a derivative thereof. 
     Compounds which induce cell differentiation processes include, but are not limited to, retinoic acid, α- γ- or δ-tocopherol or α- γ- or δ-tocotrienol. 
     The term cyclooxygenase inhibitor as used herein includes, but is not limited to, Cox-2 inhibitors, 5-alkyl substituted 2-arylaminophenylacetic acid and derivatives, such as celecoxib (Celebrex™), rofecoxib (Vioxx™), etoricoxib, valdecoxib or a 5-alkyl-2- arylaminophenylacetic acid, such as 5-methyl-2-(2′-chloro-6′-fluoroanilino)phenyl acetic acid, lumiracoxib. 
     The term “bisphosphonates” as used herein includes, but is not limited to, etridonic, clodronic, tiludronic, pamidronic, alendronic, ibandronic, risedronic and zoledronic acid. Etridonic acid is marketed under the trade name Didronel™. Clodronic acid is marketed under the trade name Bonefos™. Tiludronic acid is marketed under the trade name Skelid™. Pamidronic acid is marketed under the trade name Aredia™. Alendronic acid is marketed under the trade name Fosamax™. Ibandronic acid is marketed under the trade name Bondranat™. Risedronic acid is marketed under the trade name Actonel™. Zoledronic acid is marketed under the trade name Zometa™. The term “mTOR inhibitors” relates to compounds which inhibit the mammalian target of rapamycin (mTOR) and which possess antiproliferative activity such as sirolimus (Rapamune®), everolimus (Certican™), CCI-779 and ABT578. 
     The term “heparanase inhibitor” as used herein refers to compounds which target, decrease or inhibit heparin sulfate degradation. The term includes, but is not limited to, PI-88. The term “biological response modifier” as used herein refers to a lymphokine or interferons. 
     The term “inhibitor of Ras oncogenic isoforms”, such as H-Ras, K-Ras, or N-Ras, as used herein refers to compounds which target, decrease or inhibit the oncogenic activity of Ras; for example, a “farnesyl transferase inhibitor” such as L-744832, DK8G557 or R115777 (Zarnestra™). The term “telomerase inhibitor” as used herein refers to compounds which target, decrease or inhibit the activity of telomerase. Compounds which target, decrease or inhibit the activity of telomerase are especially compounds which inhibit the telomerase receptor, such as telomestatin. 
     The term “methionine aminopeptidase inhibitor” as used herein refers to compounds which target, decrease or inhibit the activity of methionine aminopeptidase. Compounds which target, decrease or inhibit the activity of methionine aminopeptidase include, but are not limited to, bengamide or a derivative thereof. 
     The term “proteasome inhibitor” as used herein refers to compounds which target, decrease or inhibit the activity of the proteasome. Compounds which target, decrease or inhibit the activity of the proteasome include, but are not limited to, Bortezomib (Velcade™)); carfilzomib (Kyprolis®, Amgen); and ixazomib (Ninlaro®, Takeda), and MLN 341. 
     The term “matrix metalloproteinase inhibitor” or (“MMP” inhibitor) as used herein includes, but is not limited to, collagen peptidomimetic and nonpeptidomimetic inhibitors, tetracycline derivatives, e.g. hydroxamate peptidomimetic inhibitor batimastat and its orally bioavailable analogue marimastat (BB-2516), prinomastat (AG3340), metastat (NSC 683551) BMS-279251, BAY 12-9566, TAA211, MMI270B or AAJ996. 
     The term “compounds used in the treatment of hematologic malignancies” as used herein includes, but is not limited to, FMS-like tyrosine kinase inhibitors, which are compounds targeting, decreasing or inhibiting the activity of FMS-like tyrosine kinase receptors (Flt-3R); interferon, 1-β-D-arabinofuransylcytosine (ara-c) and bisulfan; and ALK inhibitors, which are compounds which target, decrease or inhibit anaplastic lymphoma kinase. 
     Compounds which target, decrease or inhibit the activity of FMS-like tyrosine kinase receptors (Flt-3R) are especially compounds, proteins or antibodies which inhibit members of the Flt-3R receptor kinase family, such as PKC412, midostaurin, a staurosporine derivative, SU11248 and MLN518. 
     The term “HSP90 inhibitors” as used herein includes, but is not limited to, compounds targeting, decreasing or inhibiting the intrinsic ATPase activity of HSP90; degrading, targeting, decreasing or inhibiting the HSP90 client proteins via the ubiquitin proteosome pathway. Compounds targeting, decreasing or inhibiting the intrinsic ATPase activity of HSP90 are especially compounds, proteins or antibodies which inhibit the ATPase activity of HSP90, such as 17-allylamino,17-demethoxygeldanamycin (17AAG), a geldanamycin derivative; other geldanamycin related compounds; radicicol and HDAC inhibitors. 
     The term “antiproliferative antibodies” as used herein includes, but is not limited to, trastuzumab (Herceptin™), Trastuzumab-DM1, erbitux, bevacizumab (Avastin™), rituximab (Rituxan), PRO64553 (anti-CD40) and 2C4 Antibody. By antibodies is meant intact monoclonal antibodies, polyclonal antibodies, multispecific antibodies formed from at least 2 intact antibodies, and antibodies fragments so long as they exhibit the desired biological activity. 
     For the treatment of acute myeloid leukemia (AML), compounds of the current invention can be used in combination with standard leukemia therapies, especially in combination with therapies used for the treatment of AML. In particular, compounds of the current invention can be administered in combination with, for example, farnesyl transferase inhibitors and/or other drugs useful for the treatment of AML, such as Daunorubicin, Adriamycin, Ara-C, VP-16, Teniposide, Mitoxantrone, Idarubicin, Carboplatinum and PKC412. 
     Other anti-leukemic compounds include, for example, Ara-C, a pyrimidine analog, which is the 2′-alpha-hydroxy ribose (arabinoside) derivative of deoxycytidine. Also included is the purine analog of hypoxanthine, 6-mercaptopurine (6-MP) and fludarabine phosphate. Compounds which target, decrease or inhibit activity of histone deacetylase (HDAC) inhibitors such as sodium butyrate and suberoylanilide hydroxamic acid (SAHA) inhibit the activity of the enzymes known as histone deacetylases. Specific HDAC inhibitors include MS275, SAHA, FK228 (formerly FR901228), Trichostatin A and compounds disclosed in U.S. Pat. No. 6,552,065 including, but not limited to, N-hydroxy-3[4-[[[2-(2-methyl-1H-indol-3-yl)-ethyl]-amino]methyl]phenyl]-2E-2-propenamide, or a pharmaceutically acceptable salt thereof and N-hydroxy-3-[4-[(2-hydroxyethyl){2-(1H-indol-3-yl)ethyl]-amino]methyl]phenyl]-2E-2- propenamide, or a pharmaceutically acceptable salt thereof, especially the lactate salt. Somatostatin receptor antagonists as used herein refer to compounds which target, treat or inhibit the somatostatin receptor such as octreotide, and SOM230. Tumor cell damaging approaches refer to approaches such as ionizing radiation. The term “ionizing radiation” referred to above and hereinafter means ionizing radiation that occurs as either electromagnetic rays (such as X-rays and gamma rays) or particles (such as alpha and beta particles). Ionizing radiation is provided in, but not limited to, radiation therapy and is known in the art. See Hellman, Principles of Radiation Therapy, Cancer, in Principles and Practice of Oncology, Devita et al., Eds., 4 th  Edition, Vol. 1, pp. 248-275 (1993). 
     Also included are EDG binders and ribonucleotide reductase inhibitors. The term “EDG binders” as used herein refers to a class of immunosuppressants that modulates lymphocyte recirculation, such as FTY720. The term “ribonucleotide reductase inhibitors” refers to pyrimidine or purine nucleoside analogs including, but not limited to, fludarabine and/or cytosine arabinoside (ara-C), 6-thioguanine, 5-fluorouracil, cladribine, 6-mercaptopurine (especially in combination with ara-C against ALL) and/or pentostatin. Ribonucleotide reductase inhibitors are especially hydroxyurea or 2-hydroxy-1H-isoindole-1,3-dione derivatives. 
     Also included are in particular those compounds, proteins or monoclonal antibodies of VEGF such as 1-(4-chloroanilino)-4-(4-pyridylmethyl)phthalazine or a pharmaceutically acceptable salt thereof, 1-(4-chloroanilino)-4-(4-pyridylmethyl)phthalazine succinate; Angiostatin™; Endostatin™; anthranilic acid amides; ZD4190; ZD6474; SU5416; SU6668; bevacizumab; or anti-VEGF antibodies or anti-VEGF receptor antibodies, such as rhuMAb and RHUFab, VEGF aptamer such as Macugon; FLT-4 inhibitors, FLT-3 inhibitors, VEGFR-2 IgGI antibody, Angiozyme (RPI 4610) and B evacizumab (Avastin™). 
     Photodynamic therapy as used herein refers to therapy which uses certain chemicals known as photosensitizing compounds to treat or prevent cancers. Examples of photodynamic therapy include treatment with compounds, such as Visudyne™ and porfimer sodium. 
     Angiostatic steroids as used herein refers to compounds which block or inhibit angiogenesis, such as, e.g., anecortave, triamcinolone, hydrocortisone, 11-α-epihydrocotisol, cortexolone, 17α-hydroxyprogesterone, corticosterone, desoxycorticosterone, testosterone, estrone and dexamethasone. 
     Implants containing corticosteroids refers to compounds, such as fluocinolone and dexamethasone. 
     Other chemotherapeutic compounds include, but are not limited to, plant alkaloids, hormonal compounds and antagonists; biological response modifiers, preferably lymphokines or interferons; antisense oligonucleotides or oligonucleotide derivatives; shRNA or siRNA; or miscellaneous compounds or compounds with other or unknown mechanism of action. 
     The compounds of the invention are also useful as co-therapeutic compounds for use in combination with other drug substances such as anti-inflammatory, bronchodilatory or antihistamine drug substances, particularly in the treatment of obstructive or inflammatory airways diseases such as those mentioned hereinbefore, for example as potentiators of therapeutic activity of such drugs or as a means of reducing required dosaging or potential side effects of such drugs. A compound of the invention may be mixed with the other drug substance in a fixed pharmaceutical composition or it may be administered separately, before, simultaneously with or after the other drug substance. Accordingly the invention includes a combination of a compound of the invention as hereinbefore described with an anti-inflammatory, bronchodilatory, antihistamine or anti-tussive drug substance, said compound of the invention and said drug substance being in the same or different pharmaceutical composition. 
     Suitable anti-inflammatory drugs include steroids, in particular glucocorticosteroids such as budesonide, beclamethasone dipropionate, fluticasone propionate, ciclesonide or mometasone furoate; non-steroidal glucocorticoid receptor agonists; LTB4 antagonists such LY293111, CGS025019C, CP-195543, SC-53228, BILL 284, ONO 4057, SB 209247; LTD4 antagonists such as montelukast and zafirlukast; PDE4 inhibitors such cilomilast (Ariflo® GlaxoSmithKline), Roflumilast (Byk Gulden), V-11294A (Napp), BAY19-8004 (Bayer), SCH-351591 (Schering-Plough), Arofylline (Almirall Prodesfarma), PD189659/PD168787 (Parke-Davis), AWD-12-281 (Asta Medica), CDC-801 (Celgene), SeICID™ CC-10004 (Celgene), VM554/UM565 (Vernalis), T-440 (Tanabe), KW-4490 (Kyowa Hakko Kogyo); A2a agonists; A2b antagonists; and beta-2 adrenoceptor agonists such as albuterol (salbutamol), metaproterenol, terbutaline, salmeterol fenoterol, procaterol, and especially, formoterol and pharmaceutically acceptable salts thereof. Suitable bronchodilatory drugs include anticholinergic or antimuscarinic compounds, in particular ipratropium bromide, oxitropium bromide, tiotropium salts and CHF 4226 (Chiesi), and glycopyrrolate. 
     Suitable antihistamine drug substances include cetirizine hydrochloride, acetaminophen, clemastine fumarate, promethazine, loratidine, desloratidine, diphenhydramine and fexofenadine hydrochloride, activastine, astemizole, azelastine, ebastine, epinastine, mizolastine and tefenadine. 
     Other useful combinations of compounds of the invention with anti-inflammatory drugs are those with antagonists of chemokine receptors, e.g. CCR-1, CCR-2, CCR-3, CCR-4, CCR-5, CCR-6, CCR-7, CCR-8, CCR-9 and CCR10, CXCR1, CXCR2, CXCR3, CXCR4, CXCR5, particularly CCR-5 antagonists such as Schering-Plough antagonists SC-351125, SCH-55700 and SCH-D, and Takeda antagonists such as N-[[4-[[[6,7-dihydro-2-(4-methylphenyl)-5H-benzo-cyclohepten-8-yl]carbonyl]amino]phenyl]-methyl]tetrahydro-N,N-dimethyl-2H-pyran-4-aminium chloride (TAK-770). 
     The structure of the active compounds identified by code numbers, generic or trade names may be taken from the actual edition of the standard compendium “The Merck Index” or from databases, e.g. Patents International (e.g. IMS World Publications). 
     A compound of the current invention may also be used in combination with known therapeutic processes, for example, the administration of hormones or radiation. In certain embodiments, a provided compound is used as a radiosensitizer, especially for the treatment of tumors which exhibit poor sensitivity to radiotherapy. 
     A compound of the current invention can be administered alone or in combination with one or more other therapeutic compounds, possible combination therapy taking the form of fixed combinations or the administration of a compound of the invention and one or more other therapeutic compounds being staggered or given independently of one another, or the combined administration of fixed combinations and one or more other therapeutic compounds. A compound of the current invention can besides or in addition be administered especially for tumor therapy in combination with chemotherapy, radiotherapy, immunotherapy, phototherapy, surgical intervention, or a combination of these. Long-term therapy is equally possible as is adjuvant therapy in the context of other treatment strategies, as described above. Other possible treatments are therapy to maintain the patient&#39;s status after tumor regression, or even chemopreventive therapy, for example in patients at risk. 
     Those additional agents may be administered separately from an inventive compound-containing composition, as part of a multiple dosage regimen. Alternatively, those agents may be part of a single dosage form, mixed together with a compound of this invention in a single composition. If administered as part of a multiple dosage regime, the two active agents may be submitted simultaneously, sequentially or within a period of time from one another normally within five hours from one another. 
     As used herein, the term “combination,” “combined,” and related terms refers to the simultaneous or sequential administration of therapeutic agents in accordance with this invention. For example, a compound of the present invention may be administered with another therapeutic agent simultaneously or sequentially in separate unit dosage forms or together in a single unit dosage form. Accordingly, the present invention provides a single unit dosage form comprising a compound of the current invention, an additional therapeutic agent, and a pharmaceutically acceptable carrier, adjuvant, or vehicle. 
     The amount of both an inventive compound and additional therapeutic agent (in those compositions which comprise an additional therapeutic agent as described above) that may be combined with the carrier materials to produce a single dosage form will vary depending upon the host treated and the particular mode of administration. Preferably, compositions of this invention should be formulated so that a dosage of between 0.01-100 mg/kg body weight/day of an inventive compound can be administered. 
     In those compositions which comprise an additional therapeutic agent, that additional therapeutic agent and the compound of this invention may act synergistically. Therefore, the amount of additional therapeutic agent in such compositions will be less than that required in a monotherapy utilizing only that therapeutic agent. In such compositions a dosage of between 0.01-1,000 μg/kg body weight/day of the additional therapeutic agent can be administered. 
     The amount of one or more other therapeutic agent present in the compositions of this invention may be no more than the amount that would normally be administered in a composition comprising that therapeutic agent as the only active agent. Preferably the amount of one or more other therapeutic agent in the presently disclosed compositions will range from about 50% to 100% of the amount normally present in a composition comprising that agent as the only therapeutically active agent. In some embodiments, one or more other therapeutic agent is administered at a dosage of about 50%, about 55%, about 60%, about 65%, about 70%, about 75%, about 80%, about 85%, about 90%, or about 95% of the amount normally administered for that agent. As used herein, the phrase “normally administered” means the amount an FDA approved therapeutic agent is approved for dosing per the FDA label insert. 
     The compounds of this invention, or pharmaceutical compositions thereof, may also be incorporated into compositions for coating an implantable medical device, such as prostheses, artificial valves, vascular grafts, stents and catheters. Vascular stents, for example, have been used to overcome restenosis (re-narrowing of the vessel wall after injury). However, patients using stents or other implantable devices risk clot formation or platelet activation. These unwanted effects may be prevented or mitigated by pre-coating the device with a pharmaceutically acceptable composition comprising a kinase inhibitor. Implantable devices coated with a compound of this invention are another embodiment of the present invention. 
     Exemplary Immuno-Oncology Agents 
     In some embodiments, one or more other therapeutic agent is an immuno-oncology agent. As used herein, the term “an immuno-oncology agent” refers to an agent which is effective to enhance, stimulate, and/or up-regulate immune responses in a subject. In some embodiments, the administration of an immuno-oncology agent with a compound of the invention has a synergic effect in treating a cancer. 
     An immuno-oncology agent can be, for example, a small molecule drug, an antibody, or a biologic or small molecule. Examples of biologic immuno-oncology agents include, but are not limited to, cancer vaccines, antibodies, and cytokines. In some embodiments, an antibody is a monoclonal antibody. In some embodiments, a monoclonal antibody is humanized or human. 
     In some embodiments, an immuno-oncology agent is (i) an agonist of a stimulatory (including a co-stimulatory) receptor or (ii) an antagonist of an inhibitory (including a co-inhibitory) signal on T cells, both of which result in amplifying antigen-specific T cell responses. 
     Certain of the stimulatory and inhibitory molecules are members of the immunoglobulin super family (IgSF). One important family of membrane-bound ligands that bind to co-stimulatory or co-inhibitory receptors is the B7 family, which includes B7-1, B7-2, B7-H1 (PD-L1), B7-DC (PD-L2), B7-H2 (ICOS-L), B7-H3, B7-H4, B7-H5 (VISTA), and B7-H6. Another family of membrane bound ligands that bind to co-stimulatory or co-inhibitory receptors is the TNF family of molecules that bind to cognate TNF receptor family members, which includes CD40 and CD40L, OX-40, OX-40L, CD70, CD27L, CD30, CD30L, 4-1BBL, CD137 (4-1BB), TRAIL/Apo2-L, TRAILR1/DR4, TRAILR2/DR5, TRAILR3, TRAILR4, OPG, RANK, RANKL, TWEAKR/Fn14, TWEAK, BAFFR, EDAR, XEDAR, TACI, APRIL, BCMA, LTβR, LIGHT, DcR3, HVEM, VEGUTL1A, TRAMP/DR3, EDAR, EDA1, XEDAR, EDA2, TNFR1, Lymphotoxin α/TNFβ, TNFR2, TNFα, LTβR, Lymphotoxin α1β2, FAS, FASL, RELT, DR6, TROY, NGFR. 
     In some embodiments, an immuno-oncology agent is a cytokine that inhibits T cell activation (e.g., IL-6, IL-10, TGF-β, VEGF, and other immunosuppressive cytokines) or a cytokine that stimulates T cell activation, for stimulating an immune response. 
     In some embodiments, a combination of a compound of the invention and an immuno-oncology agent can stimulate T cell responses. In some embodiments, an immuno-oncology agent is: (i) an antagonist of a protein that inhibits T cell activation (e.g., immune checkpoint inhibitors) such as CTLA-4, PD-1, PD-L1, PD-L2, LAG-3, TIM-3, Galectin 9, CEACAM-1, BTLA, CD69, Galectin-1, TIGIT, CD113, GPR56, VISTA, 2B4, CD48, GARP, PD1H, LAIR1, TIM-1, and TIM-4; or (ii) an agonist of a protein that stimulates T cell activation such as B7-1, B7-2, CD28, 4-1BB (CD137), 4-1BBL, ICOS, ICOS-L, OX40, OX40L, GITR, GITRL, CD70, CD27, CD40, DR3 and CD28H. 
     In some embodiments, an immuno-oncology agent is an antagonist of inhibitory receptors on NK cells or an agonists of activating receptors on NK cells. In some embodiments, an immuno-oncology agent is an antagonists of KIR, such as lirilumab. 
     In some embodiments, an immuno-oncology agent is an agent that inhibits or depletes macrophages or monocytes, including but not limited to CSF-1R antagonists such as CSF-1R antagonist antibodies including RG7155 (WO11/70024, WO11/107553, WO11/131407, WO13/87699, WO13/119716, WO13/132044) or FPA-008 (WO11/140249; WO13169264; WO14/036357). 
     In some embodiments, an immuno-oncology agent is selected from agonistic agents that ligate positive costimulatory receptors, blocking agents that attenuate signaling through inhibitory receptors, antagonists, and one or more agents that increase systemically the frequency of anti-tumor T cells, agents that overcome distinct immune suppressive pathways within the tumor microenvironment (e.g., block inhibitory receptor engagement (e.g., PD-L1/PD-1 interactions), deplete or inhibit Tregs (e.g., using an anti-CD25 monoclonal antibody (e.g., daclizumab) or by ex vivo anti-CD25 bead depletion), inhibit metabolic enzymes such as IDO, or reverse/prevent T cell energy or exhaustion) and agents that trigger innate immune activation and/or inflammation at tumor sites. 
     In some embodiments, an immuno-oncology agent is a CTLA-4 antagonist. In some embodiments, a CTLA-4 antagonist is an antagonistic CTLA-4 antibody. In some embodiments, an antagonistic CTLA-4 antibody is YERVOY (ipilimumab) or tremelimumab. 
     In some embodiments, an immuno-oncology agent is a PD-1 antagonist. In some embodiments, a PD-1 antagonist is administered by infusion. In some embodiments, an immuno-oncology agent is an antibody or an antigen-binding portion thereof that binds specifically to a Programmed Death-1 (PD-1) receptor and inhibits PD-1 activity. In some embodiments, a PD-1 antagonist is an antagonistic PD-1 antibody. In some embodiments, an antagonistic PD-1 antibody is OPDIVO (nivolumab), KEYTRUDA (pembrolizumab), or MEDI-0680 (AMP-514; WO2012/145493). In some embodiments, an immuno-oncology agent may be pidilizumab (CT-011). In some embodiments, an immuno-oncology agent is a recombinant protein composed of the extracellular domain of PD-L2 (B7-DC) fused to the Fc portion of IgG1, called AMP-224. 
     In some embodiments, an immuno-oncology agent is a PD-L1 antagonist. In some embodiments, a PD-L1 antagonist is an antagonistic PD-L1 antibody. In some embodiments, a PD-L1 antibody is MPDL3280A (RG7446; WO2010/077634), durvalumab (MEDI4736), BMS-936559 (WO2007/005874), and MSB0010718C (WO2013/79174). 
     In some embodiments, an immuno-oncology agent is a LAG-3 antagonist. In some embodiments, a LAG-3 antagonist is an antagonistic LAG-3 antibody. In some embodiments, a LAG3 antibody is BMS-986016 (WO10/19570, WO14/08218), or IMP-731 or IMP-321 (WO08/132601, WO009/44273). 
     In some embodiments, an immuno-oncology agent is a CD137 (4-1BB) agonist. In some embodiments, a CD137 (4-1BB) agonist is an agonistic CD137 antibody. In some embodiments, a CD137 antibody is urelumab or PF-05082566 (WO12/32433). 
     In some embodiments, an immuno-oncology agent is a GITR agonist. In some embodiments, a GITR agonist is an agonistic GITR antibody. In some embodiments, a GITR antibody is BMS-986153, BMS-986156, TRx-518 (WO006/105021, WO009/009116), or MK-4166 (WO11/028683). 
     In some embodiments, an immuno-oncology agent is an indoleamine (2,3)-dioxygenase (IDO) antagonist. In some embodiments, an IDO antagonist is selected from epacadostat (INCB024360, Incyte); indoximod (NLG-8189, NewLink Genetics Corporation); capmanitib (INC280, Novartis); GDC-0919 (Genentech/Roche); PF-06840003 (Pfizer); BMS:F001287 (Bristol-Myers Squibb); Phy906/KD108 (Phytoceutica); an enzyme that breaks down kynurenine (Kynase, Kyn Therapeutics); and NLG-919 (WO09/73620, WO009/1156652, WO11/56652, WO12/142237). 
     In some embodiments, an immuno-oncology agent is an OX40 agonist. In some embodiments, an OX40 agonist is an agonistic OX40 antibody. In some embodiments, an OX40 antibody is MEDI-6383 or MEDI-6469. 
     In some embodiments, an immuno-oncology agent is an OX40L antagonist. In some embodiments, an OX40L antagonist is an antagonistic OX40 antibody. In some embodiments, an OX40L antagonist is RG-7888 (WO06/029879). 
     In some embodiments, an immuno-oncology agent is a CD40 agonist. In some embodiments, a CD40 agonist is an agonistic CD40 antibody. In some embodiments, an immuno-oncology agent is a CD40 antagonist. In some embodiments, a CD40 antagonist is an antagonistic CD40 antibody. In some embodiments, a CD40 antibody is lucatumumab or dacetuzumab. 
     In some embodiments, an immuno-oncology agent is a CD27 agonist. In some embodiments, a CD27 agonist is an agonistic CD27 antibody. In some embodiments, a CD27 antibody is varlilumab. 
     In some embodiments, an immuno-oncology agent is MGA271 (to B7H3) (WO11/109400). 
     In some embodiments, an immuno-oncology agent is abagovomab, adecatumumab, afutuzumab, alemtuzumab, anatumomab mafenatox, apolizumab, atezolimab, avelumab, blinatumomab, BMS-936559, catumaxomab, durvalumab, epacadostat, epratuzumab, indoximod, inotuzumab ozogamicin, intelumumab, ipilimumab, isatuximab, lambrolizumab, MED14736, MPDL3280A, nivolumab, obinutuzumab, ocaratuzumab, ofatumumab, olatatumab, pembrolizumab, pidilizumab, rituximab, ticilimumab, samalizumab, or tremelimumab. 
     In some embodiments, an immuno-oncology agent is an immunostimulatory agent. For example, antibodies blocking the PD-1 and PD-L1 inhibitory axis can unleash activated tumor-reactive T cells and have been shown in clinical trials to induce durable anti-tumor responses in increasing numbers of tumor histologies, including some tumor types that conventionally have not been considered immunotherapy sensitive. See, e.g., Okazaki, T. et al. (2013) Nat. Immunol. 14, 1212-1218; Zou et al. (2016) Sci. Transl. Med. 8. The anti-PD-1 antibody nivolumab (Opdivo®, Bristol-Myers Squibb, also known as ONO-4538, MDX1106 and BMS-936558), has shown potential to improve the overall survival in patients with RCC who had experienced disease progression during or after prior anti-angiogenic therapy. 
     In some embodiments, the immunomodulatory therapeutic specifically induces apoptosis of tumor cells. Approved immunomodulatory therapeutics which may be used in the present invention include pomalidomide (Pomalyst®, Celgene); lenalidomide (Revlimid®, Celgene); ingenol mebutate (Picato®, LEO Pharma). 
     In some embodiments, an immuno-oncology agent is a cancer vaccine. In some embodiments, the cancer vaccine is selected from sipuleucel-T (Provenge®, Dendreon/Valeant Pharmaceuticals), which has been approved for treatment of asymptomatic, or minimally symptomatic metastatic castrate-resistant (hormone-refractory) prostate cancer; and talimogene laherparepvec (Imlygic®, BioVex/Amgen, previously known as T-VEC), a genetically modified oncolytic viral therapy approved for treatment of unresectable cutaneous, subcutaneous and nodal lesions in melanoma. In some embodiments, an immuno-oncology agent is selected from an oncolytic viral therapy such as pexastimogene devacirepvec (PexaVec/JX-594, SillaJen/formerly Jennerex Biotherapeutics), a thymidine kinase- (TK-) deficient vaccinia virus engineered to express GM-CSF, for hepatocellular carcinoma (NCT02562755) and melanoma (NCT00429312); pelareorep (Reolysin®, Oncolytics Biotech), a variant of respiratory enteric orphan virus (reovirus) which does not replicate in cells that are not RAS-activated, in numerous cancers, including colorectal cancer (NCT01622543); prostate cancer (NCT01619813); head and neck squamous cell cancer (NCT01166542); pancreatic adenocarcinoma (NCT00998322); and non-small cell lung cancer (NSCLC) (NCT 00861627); enadenotucirev (NG-348, PsiOxus, formerly known as ColoAd1), an adenovirus engineered to express a full length CD80 and an antibody fragment specific for the T-cell receptor CD3 protein, in ovarian cancer (NCT02028117); metastatic or advanced epithelial tumors such as in colorectal cancer, bladder cancer, head and neck squamous cell carcinoma and salivary gland cancer (NCT02636036); ONCOS-102 (Targovax/formerly Oncos), an adenovirus engineered to express GM-CSF, in melanoma (NCT03003676); and peritoneal disease, colorectal cancer or ovarian cancer (NCT02963831); GL-ONC1 (GLV-1h68/GLV-1h153, Genelux GmbH), vaccinia viruses engineered to express beta-galactosidase (beta-gal)/beta-glucoronidase or beta-gal/human sodium iodide symporter (hNIS), respectively, were studied in peritoneal carcinomatosis (NCT01443260); fallopian tube cancer, ovarian cancer (NCT 02759588); or CG0070 (Cold Genesys), an adenovirus engineered to express GM-CSF, in bladder cancer (NCT02365818). 
     In some embodiments, an immuno-oncology agent is selected from JX-929 (SillaJen/formerly Jennerex Biotherapeutics), a TK- and vaccinia growth factor-deficient vaccinia virus engineered to express cytosine deaminase, which is able to convert the prodrug 5-fluorocytosine to the cytotoxic drug 5-fluorouracil; TG01 and TG02 (Targovax/formerly Oncos), peptide-based immunotherapy agents targeted for difficult-to-treat RAS mutations; and TILT-123 (TILT Biotherapeutics), an engineered adenovirus designated: Ad5/3-E2F-delta24-hTNFα-IRES-hIL20; and VSV-GP (ViraTherapeutics) a vesicular stomatitis virus (VSV) engineered to express the glycoprotein (GP) of lymphocytic choriomeningitis virus (LCMV), which can be further engineered to express antigens designed to raise an antigen-specific CD8 +  T cell response. 
     In some embodiments, an immuno-oncology agent is a T-cell engineered to express a chimeric antigen receptor, or CAR. The T-cells engineered to express such chimeric antigen receptor are referred to as a CAR-T cells. 
     CARs have been constructed that consist of binding domains, which may be derived from natural ligands, single chain variable fragments (scFv) derived from monoclonal antibodies specific for cell-surface antigens, fused to endodomains that are the functional end of the T-cell receptor (TCR), such as the CD3-zeta signaling domain from TCRs, which is capable of generating an activation signal in T lymphocytes. Upon antigen binding, such CARs link to endogenous signaling pathways in the effector cell and generate activating signals similar to those initiated by the TCR complex. 
     For example, in some embodiments the CAR-T cell is one of those described in U.S. Pat. No. 8,906,682 (June; hereby incorporated by reference in its entirety), which discloses CAR-T cells engineered to comprise an extracellular domain having an antigen binding domain (such as a domain that binds to CD19), fused to an intracellular signaling domain of the T cell antigen receptor complex zeta chain (such as CD3 zeta). When expressed in the T cell, the CAR is able to redirect antigen recognition based on the antigen binding specificity. In the case of CD19, the antigen is expressed on malignant B cells. Over 200 clinical trials are currently in progress employing CAR-T in a wide range of indications. [https://clinicaltrials.gov/ct2/results?term=chimeric+antigen+receptors&amp;pg=1]. 
     In some embodiments, an immunostimulatory agent is an activator of retinoic acid receptor-related orphan receptor γ (RORγt). RORγt is a transcription factor with key roles in the differentiation and maintenance of Type 17 effector subsets of CD4+(Th17) and CD8+(Tc17) T cells, as well as the differentiation of IL-17 expressing innate immune cell subpopulations such as NK cells. In some embodiments, an activator of RORγt is LYC-55716 (Lycera), which is currently being evaluated in clinical trials for the treatment of solid tumors (NCT02929862). 
     In some embodiments, an immunostimulatory agent is an agonist or activator of a toll-like receptor (TLR). Suitable activators of TLRs include an agonist or activator of TLR9 such as SD-101 (Dynavax). SD-101 is an immunostimulatory CpG which is being studied for B-cell, follicular and other lymphomas (NCT02254772). Agonists or activators of TLR8 which may be used in the present invention include motolimod (VTX-2337, VentiRx Pharmaceuticals) which is being studied for squamous cell cancer of the head and neck (NCT02124850) and ovarian cancer (NCT02431559). 
     Other immuno-oncology agents that may be used in the present invention include urelumab (BMS-663513, Bristol-Myers Squibb), an anti-CD137 monoclonal antibody; varlilumab (CDX-1127, Celldex Therapeutics), an anti-CD27 monoclonal antibody; BMS-986178 (Bristol-Myers Squibb), an anti-OX40 monoclonal antibody; lirilumab (IPH2102/BMS-986015, Innate Pharma, Bristol-Myers Squibb), an anti-KIR monoclonal antibody; monalizumab (IPH2201, Innate Pharma, AstraZeneca) an anti-NKG2A monoclonal antibody; andecaliximab (GS-5745, Gilead Sciences), an anti-MMP9 antibody; MK-4166 (Merck &amp; Co.), an anti-GITR monoclonal antibody. 
     In some embodiments, an immunostimulatory agent is selected from elotuzumab, mifamurtide, an agonist or activator of a toll-like receptor, and an activator of RORγt. 
     In some embodiments, an immunostimulatory therapeutic is recombinant human interleukin 15 (rhIL-15). rhIL-15 has been tested in the clinic as a therapy for melanoma and renal cell carcinoma (NCT01021059 and NCT01369888) and leukemias (NCT02689453). In some embodiments, an immunostimulatory agent is recombinant human interleukin 12 (rhIL-12). In some embodiments, an IL-15 based immunotherapeutic is heterodimeric IL-15 (hetIL-15, Novartis/Admune), a fusion complex composed of a synthetic form of endogenous IL-15 complexed to the soluble IL-15 binding protein IL-15 receptor alpha chain (IL15:sIL-15RA), which has been tested in Phase 1 clinical trials for melanoma, renal cell carcinoma, non-small cell lung cancer and head and neck squamous cell carcinoma (NCT02452268). In some embodiments, a recombinant human interleukin 12 (rhIL-12) is NM-IL-12 (Neumedicines, Inc.), NCT02544724, or NCT02542124. 
     In some embodiments, an immuno-oncology agent is selected from those descripted in Jerry L. Adams ET. AL., “Big opportunities for small molecules in immuno-oncology,” Cancer Therapy 2015, Vol. 14, pages 603-622, the content of which is incorporated herein by reference in its entirety. In some embodiment, an immuno-oncology agent is selected from the examples described in Table 1 of Jerry L. Adams ET. AL. In some embodiments, an immuno-oncology agent is a small molecule targeting an immuno-oncology target selected from those listed in Table 2 of Jerry L. Adams ET. AL. In some embodiments, an immuno-oncology agent is a small molecule agent selected from those listed in Table 2 of Jerry L. Adams ET. AL. 
     In some embodiments, an immuno-oncology agent is selected from the small molecule immuno-oncology agents described in Peter L. Toogood, “Small molecule immuno-oncology therapeutic agents,” Bioorganic &amp; Medicinal Chemistry Letters 2018, Vol. 28, pages 319-329, the content of which is incorporated herein by reference in its entirety. In some embodiments, an immuno-oncology agent is an agent targeting the pathways as described in Peter L. Toogood. 
     In some embodiments, an immuno-oncology agent is selected from those described in Sandra L. Ross et al., “Bispecific T cell engager (BiTE®) antibody constructs can mediate bystander tumor cell killing”, PLoS ONE 12(8): e0183390, the content of which is incorporated herein by reference in its entirety. In some embodiments, an immuno-oncology agent is a bispecific T cell engager (BiTE®) antibody construct. In some embodiments, a bispecific T cell engager (BiTE®) antibody construct is a CD19/CD3 bispecific antibody construct. In some embodiments, a bispecific T cell engager (BiTE®) antibody construct is an EGFR/CD3 bispecific antibody construct. In some embodiments, a bispecific T cell engager (BiTE®) antibody construct activates T cells. In some embodiments, a bispecific T cell engager (BiTE®) antibody construct activates T cells, which release cytokines inducing upregulation of intercellular adhesion molecule 1 (ICAM-1) and FAS on bystander cells. In some embodiments, a bispecific T cell engager (BiTE®) antibody construct activates T cells which result in induced bystander cell lysis. In some embodiments, the bystander cells are in solid tumors. In some embodiments, the bystander cells being lysed are in proximity to the BiTE®-activated T cells. In some embodiment, the bystander cells comprises tumor-associated antigen (TAA) negative cancer cells. In some embodiment, the bystander cells comprise EGFR-negative cancer cells. In some embodiments, an immuno-oncology agent is an antibody which blocks the PD-L1/PD1 axis and/or CTLA4. In some embodiments, an immuno-oncology agent is an ex-vivo expanded tumor-infiltrating T cell. In some embodiments, an immuno-oncology agent is a bispecific antibody construct or chimeric antigen receptors (CARs) that directly connect T cells with tumor-associated surface antigens (TAAs). 
     Exemplary Immune Checkpoint Inhibitors 
     In some embodiments, an immuno-oncology agent is an immune checkpoint inhibitor as described herein. 
     The term “checkpoint inhibitor” as used herein relates to agents useful in preventing cancer cells from avoiding the immune system of the patient. One of the major mechanisms of anti-tumor immunity subversion is known as “T-cell exhaustion,” which results from chronic exposure to antigens that has led to up-regulation of inhibitory receptors. These inhibitory receptors serve as immune checkpoints in order to prevent uncontrolled immune reactions. 
     PD-1 and co-inhibitory receptors such as cytotoxic T-lymphocyte antigen 4 (CTLA-4, B and T Lymphocyte Attenuator (BTLA; CD272), T cell Immunoglobulin and Mucin domain-3 (Tim-3), Lymphocyte Activation Gene-3 (Lag-3; CD223), and others are often referred to as a checkpoint regulators. They act as molecular “gatekeepers” that allow extracellular information to dictate whether cell cycle progression and other intracellular signaling processes should proceed. 
     In some embodiments, an immune checkpoint inhibitor is an antibody to PD-1. PD-1 binds to the programmed cell death 1 receptor (PD-1) to prevent the receptor from binding to the inhibitory ligand PDL-1, thus overriding the ability of tumors to suppress the host anti-tumor immune response. 
     In one aspect, the checkpoint inhibitor is a biologic therapeutic or a small molecule. In another aspect, the checkpoint inhibitor is a monoclonal antibody, a humanized antibody, a fully human antibody, a fusion protein or a combination thereof. In a further aspect, the checkpoint inhibitor inhibits a checkpoint protein selected from CTLA-4, PDL1, PDL2, PD1, B7-H3, B7-H4, BTLA, HVEM, TIM3, GALS, LAG3, VISTA, KIR, 2B4, CD160, CGEN-15049, CHK 1, CHK2, A2aR, B-7 family ligands or a combination thereof. In an additional aspect, the checkpoint inhibitor interacts with a ligand of a checkpoint protein selected from CTLA-4, PDL1, PDL2, PD1, B7-H3, B7-H4, BTLA, HVEM, TIM3, GAL9, LAG3, VISTA, KIR, 2B4, CD160, CGEN-15049, CHK 1, CHK2, A2aR, B-7 family ligands or a combination thereof. In an aspect, the checkpoint inhibitor is an immunostimulatory agent, a T cell growth factor, an interleukin, an antibody, a vaccine or a combination thereof. In a further aspect, the interleukin is IL-7 or IL-15. In a specific aspect, the interleukin is glycosylated IL-7. In an additional aspect, the vaccine is a dendritic cell (DC) vaccine. 
     Checkpoint inhibitors include any agent that blocks or inhibits in a statistically significant manner, the inhibitory pathways of the immune system. Such inhibitors may include small molecule inhibitors or may include antibodies, or antigen binding fragments thereof, that bind to and block or inhibit immune checkpoint receptors or antibodies that bind to and block or inhibit immune checkpoint receptor ligands. Illustrative checkpoint molecules that may be targeted for blocking or inhibition include, but are not limited to, CTLA-4, PDL1, PDL2, PD1, B7-H3, B7-H4, BTLA, HVEM, GAL9, LAG3, TIM3, VISTA, KIR, 2B4 (belongs to the CD2 family of molecules and is expressed on all NK, γδ, and memory CD8 +  (αβ) T cells), CD160 (also referred to as BY55), CGEN-15049, CHK 1 and CHK2 kinases, A2aR, and various B-7 family ligands. B7 family ligands include, but are not limited to, B7- 1, B7-2, B7-DC, B7-H1, B7-H2, B7-H3, B7-H4, B7-H5, B7-H6 and B7-H7. Checkpoint inhibitors include antibodies, or antigen binding fragments thereof, other binding proteins, biologic therapeutics, or small molecules, that bind to and block or inhibit the activity of one or more of CTLA-4, PDL1, PDL2, PD1, BTLA, HVEM, TIM3, GAL9, LAG3, VISTA, KIR, 2B4, CD 160 and CGEN-15049. Illustrative immune checkpoint inhibitors include Tremelimumab (CTLA-4 blocking antibody), anti-OX40, PD-L1 monoclonal Antibody (Anti-B7-H1; MEDI4736), MK-3475 (PD-1 blocker), Nivolumab (anti-PD1 antibody), CT-011 (anti-PD1 antibody), BY55 monoclonal antibody, AMP224 (anti-PDL1 antibody), BMS-936559 (anti-PDL1 antibody), MPLDL3280A (anti-PDL1 antibody), MSB0010718C (anti-PDL1 antibody), and ipilimumab (anti-CTLA-4 checkpoint inhibitor). Checkpoint protein ligands include, but are not limited to PD-L1, PD-L2, B7-H3, B7-H4, CD28, CD86 and TIM-3. 
     In certain embodiments, the immune checkpoint inhibitor is selected from a PD-1 antagonist, a PD-L1 antagonist, and a CTLA-4 antagonist. In some embodiments, the checkpoint inhibitor is selected from the group consisting of nivolumab (Opdivo®), ipilimumab (Yervoy®), and pembrolizumab (Keytruda®). In some embodiments, the checkpoint inhibitor is selected from nivolumab (anti-PD-1 antibody, Opdivo®, Bristol-Myers Squibb); pembrolizumab (anti-PD-1 antibody, Keytruda®, Merck); ipilimumab (anti-CTLA-4 antibody, Yervoy®, Bristol-Myers Squibb); durvalumab (anti-PD-L1 antibody, Imfinzi®, AstraZeneca); and atezolizumab (anti-PD-L1 antibody, Tecentriq®, Genentech). 
     In some embodiments, the checkpoint inhibitor is selected from the group consisting of lambrolizumab (MK-3475), nivolumab (BMS-936558), pidilizumab (CT-011), AMP-224, MDX-1105, MEDI4736, MPDL3280A, BMS-936559, ipilimumab, lirlumab, IPH2101, pembrolizumab (Keytruda®), and tremelimumab. 
     In some embodiments, an immune checkpoint inhibitor is REGN2810 (Regeneron), an anti-PD-1 antibody tested in patients with basal cell carcinoma (NCT03132636); NSCLC (NCT03088540); cutaneous squamous cell carcinoma (NCT02760498); lymphoma (NCT02651662); and melanoma (NCT03002376); pidilizumab (CureTech), also known as CT-011, an antibody that binds to PD-1, in clinical trials for diffuse large B-cell lymphoma and multiple myeloma; avelumab (Bavencio®, Pfizer/Merck KGaA), also known as MSB0010718C), a fully human IgG1 anti-PD-L1 antibody, in clinical trials for non-small cell lung cancer, Merkel cell carcinoma, mesothelioma, solid tumors, renal cancer, ovarian cancer, bladder cancer, head and neck cancer, and gastric cancer; or PDR001 (Novartis), an inhibitory antibody that binds to PD-1, in clinical trials for non-small cell lung cancer, melanoma, triple negative breast cancer and advanced or metastatic solid tumors. Tremelimumab (CP-675,206; Astrazeneca) is a fully human monoclonal antibody against CTLA-4 that has been in studied in clinical trials for a number of indications, including: mesothelioma, colorectal cancer, kidney cancer, breast cancer, lung cancer and non-small cell lung cancer, pancreatic ductal adenocarcinoma, pancreatic cancer, germ cell cancer, squamous cell cancer of the head and neck, hepatocellular carcinoma, prostate cancer, endometrial cancer, metastatic cancer in the liver, liver cancer, large B-cell lymphoma, ovarian cancer, cervical cancer, metastatic anaplastic thyroid cancer, urothelial cancer, fallopian tube cancer, multiple myeloma, bladder cancer, soft tissue sarcoma, and melanoma. AGEN-1884 (Agenus) is an anti-CTLA4 antibody that is being studied in Phase 1 clinical trials for advanced solid tumors (NCT02694822). 
     In some embodiments, a checkpoint inhibitor is an inhibitor of T-cell immunoglobulin mucin containing protein-3 (TIM-3). TIM-3 inhibitors that may be used in the present invention include TSR-022, LY3321367 and MBG453. TSR-022 (Tesaro) is an anti-TIM-3 antibody which is being studied in solid tumors (NCT02817633). LY3321367 (Eli Lilly) is an anti-TIM-3 antibody which is being studied in solid tumors (NCT03099109). MBG453 (Novartis) is an anti-TIM-3 antibody which is being studied in advanced malignancies (NCT02608268). 
     In some embodiments, a checkpoint inhibitor is an inhibitor of T cell immunoreceptor with Ig and ITIM domains, or TIGIT, an immune receptor on certain T cells and NK cells. TIGIT inhibitors that may be used in the present invention include BMS-986207 (Bristol-Myers Squibb), an anti-TIGIT monoclonal antibody (NCT02913313); OMP-313M32 (Oncomed); and anti-TIGIT monoclonal antibody (NCT03119428). 
     In some embodiments, a checkpoint inhibitor is an inhibitor of Lymphocyte Activation Gene-3 (LAG-3). LAG-3 inhibitors that may be used in the present invention include BMS-986016 and REGN3767 and IMP321. BMS-986016 (Bristol-Myers Squibb), an anti-LAG-3 antibody, is being studied in glioblastoma and gliosarcoma (NCT02658981). REGN3767 (Regeneron), is also an anti-LAG-3 antibody, and is being studied in malignancies (NCT03005782). IMP321 (Immutep S.A.) is an LAG-3-Ig fusion protein, being studied in melanoma (NCT02676869); adenocarcinoma (NCT02614833); and metastatic breast cancer (NCT00349934). 
     Checkpoint inhibitors that may be used in the present invention include OX40 agonists. OX40 agonists that are being studied in clinical trials include PF-04518600/PF-8600 (Pfizer), an agonistic anti-OX40 antibody, in metastatic kidney cancer (NCT03092856) and advanced cancers and neoplasms (NCT02554812; NCT05082566); GSK3174998 (Merck), an agonistic anti-OX40 antibody, in Phase 1 cancer trials (NCT02528357); MEDI0562 (Medimmune/AstraZeneca), an agonistic anti-OX40 antibody, in advanced solid tumors (NCT02318394 and NCT02705482); MEDI6469, an agonistic anti-OX40 antibody (Medimmune/AstraZeneca), in patients with colorectal cancer (NCT02559024), breast cancer (NCT01862900), head and neck cancer (NCT02274155) and metastatic prostate cancer (NCT01303705); and BMS-986178 (Bristol-Myers Squibb) an agonistic anti-OX40 antibody, in advanced cancers (NCT02737475). 
     Checkpoint inhibitors that may be used in the present invention include CD137 (also called 4-1BB) agonists. CD137 agonists that are being studied in clinical trials include utomilumab (PF-05082566, Pfizer) an agonistic anti-CD137 antibody, in diffuse large B-cell lymphoma (NCT02951156) and in advanced cancers and neoplasms (NCT02554812 and NCT05082566); urelumab (BMS-663513, Bristol-Myers Squibb), an agonistic anti-CD137 antibody, in melanoma and skin cancer (NCT02652455) and glioblastoma and gliosarcoma (NC T02658981). 
     Checkpoint inhibitors that may be used in the present invention include CD27 agonists. CD27 agonists that are being studied in clinical trials include varlilumab (CDX-1127, Celldex Therapeutics) an agonistic anti-CD27 antibody, in squamous cell head and neck cancer, ovarian carcinoma, colorectal cancer, renal cell cancer, and glioblastoma (NCT02335918); lymphomas (NCT01460134); and glioma and astrocytoma (NCT02924038). 
     Checkpoint inhibitors that may be used in the present invention include glucocorticoid-induced tumor necrosis factor receptor (GITR) agonists. GITR agonists that are being studied in clinical trials include TRX518 (Leap Therapeutics), an agonistic anti-GITR antibody, in malignant melanoma and other malignant solid tumors (NCT01239134 and NCT02628574); GWN323 (Novartis), an agonistic anti-GITR antibody, in solid tumors and lymphoma (NCT 02740270); INCAGN01876 (Incyte/Agenus), an agonistic anti-GITR antibody, in advanced cancers (NCT02697591 and NCT03126110); MK-4166 (Merck), an agonistic anti-GITR antibody, in solid tumors (NCT02132754) and MEDI1873 (Medimmune/AstraZeneca), an agonistic hexameric GITR-ligand molecule with a human IgG1 Fc domain, in advanced solid tumors (NCT02583165). 
     Checkpoint inhibitors that may be used in the present invention include inducible T-cell co-stimulator (ICOS, also known as CD278) agonists. ICOS agonists that are being studied in clinical trials include MEDI-570 (Medimmune), an agonistic anti-ICOS antibody, in lymphomas (NCT02520791); GSK3359609 (Merck), an agonistic anti-ICOS antibody, in Phase 1 (NCT02723955); JTX-2011 (Jounce Therapeutics), an agonistic anti-ICOS antibody, in Phase 1 (NCT02904226). 
     Checkpoint inhibitors that may be used in the present invention include killer IgG-like receptor (KIR) inhibitors. KIR inhibitors that are being studied in clinical trials include lirilumab (IPH2102/BMS-986015, Innate Pharma/Bristol-Myers Squibb), an anti-KIR antibody, in leukemias (NCT01687387, NCT02399917, NCT02481297, NCT02599649), multiple myeloma (NCT02252263), and lymphoma (NCT01592370); IPH2101 (1-7F9, Innate Pharma) in myeloma (NCT01222286 and NCT01217203); and IPH4102 (Innate Pharma), an anti-KIR antibody that binds to three domains of the long cytoplasmic tail (KIR3DL2), in lymphoma (NCT02593045). 
     Checkpoint inhibitors that may be used in the present invention include CD47 inhibitors of interaction between CD47 and signal regulatory protein alpha (SIRPa). CD47/SIRPa inhibitors that are being studied in clinical trials include ALX-148 (Alexo Therapeutics), an antagonistic variant of (SIRPa) that binds to CD47 and prevents CD47/SIRPa-mediated signaling, in phase 1 (NCT03013218); TTI-621 (SIRPa-Fc, Trillium Therapeutics), a soluble recombinant fusion protein created by linking the N-terminal CD47-binding domain of SIRPa with the Fc domain of human IgG1, acts by binding human CD47, and preventing it from delivering its “do not eat” signal to macrophages, is in clinical trials in Phase 1 (NCT02890368 and NCT02663518); CC-90002 (Celgene), an anti-CD47 antibody, in leukemias (NCT02641002); and Hu5F9-G4 (Forty Seven, Inc.), in colorectal neoplasms and solid tumors (NCT02953782), acute myeloid leukemia (NCT02678338) and lymphoma (NCT02953509). 
     Checkpoint inhibitors that may be used in the present invention include CD73 inhibitors. CD73 inhibitors that are being studied in clinical trials include MEDI9447 (Medimmune), an anti-CD73 antibody, in solid tumors (NCT02503774); and BMS-986179 (Bristol-Myers Squibb), an anti-CD73 antibody, in solid tumors (NCT02754141). 
     Checkpoint inhibitors that may be used in the present invention include agonists of stimulator of interferon genes protein (STING, also known as transmembrane protein 173, or TMEM173). Agonists of STING that are being studied in clinical trials include MK-1454 (Merck), an agonistic synthetic cyclic dinucleotide, in lymphoma (NCT03010176); and ADU-S100 (MIW815, Aduro Biotech/Novartis), an agonistic synthetic cyclic dinucleotide, in Phase 1 (NCT02675439 and NCT03172936). 
     Checkpoint inhibitors that may be used in the present invention include CSF1R inhibitors. CSF1R inhibitors that are being studied in clinical trials include pexidartinib (PLX3397, Plexxikon), a CSF1R small molecule inhibitor, in colorectal cancer, pancreatic cancer, metastatic and advanced cancers (NCT02777710) and melanoma, non-small cell lung cancer, squamous cell head and neck cancer, gastrointestinal stromal tumor (GIST) and ovarian cancer (NCT02452424); and IMC-054 (LY3022855, Lilly), an anti-CSF-1R antibody, in pancreatic cancer (NCT03153410), melanoma (NCT03101254), and solid tumors (NCT02718911); and BLZ945 (4-[2((1R,2R)—2-hydroxycyclohexylamino)-benzothiazol-6-yloxyl]-pyridine-2-carboxylic acid methylamide, Novartis), an orally available inhibitor of CSF1R, in advanced solid tumors (NCT02829723). 
     Checkpoint inhibitors that may be used in the present invention include NKG2A receptor inhibitors. NKG2A receptor inhibitors that are being studied in clinical trials include monalizumab (IPH2201, Innate Pharma), an anti-NKG2A antibody, in head and neck neoplasms (NCT02643550) and chronic lymphocytic leukemia (NCT02557516). 
     In some embodiments, the immune checkpoint inhibitor is selected from nivolumab, pembrolizumab, ipilimumab, avelumab, durvalumab, atezolizumab, or pidilizumab. 
     EXEMPLIFICATION 
     Abbreviations 
     Ac: acetyl 
     AcOH: acetic acid 
     ACN: acetonitrile 
     Ad: adamantly 
     AIBN: 2,2′-azo bisisobutyronitrile 
     Anhyd: anhydrous 
     Aq: aqueous 
     B 2 Pin 2 : bis(pinacolato)diboron-4,4,4′,4′,5,5,5′,5′-octamethyl-2,2′-bi(1,3,2-dioxaborolane) 
     BINAP: 2,2′-bis(diphenylphosphino)-1,1′-binaphthyl 
     BH 3 : Borane 
     Bn: benzyl 
     Boc: tert-butoxycarbonyl 
     Boc 2 O: di-tert-butyl dicarbonate 
     BPO: benzoyl peroxide 
       n BuOH: n-butanol 
     CDI: carbonyldiimidazole 
     COD: cyclooctadiene 
     d: days 
     DABCO: 1,4-diazobicyclo[2.2.2]octane 
     DAST: diethylaminosulfur trifluoride 
     dba: dibenzylideneacetone 
     DBU: 1,8-diazobicyclo[5.4.0]undec-7-ene 
     DCE: 1,2-dichloroethane 
     DCM: dichloromethane 
     DEA: diethylamine 
     DHP: dihydropyran 
     DIBAL-H: diisobutylaluminum hydride 
     DIPA: diisopropylamine 
     DIPEA or DIEA: N,N-diisopropylethylamine 
     DMA: N,N-dimethylacetamide 
     DME: 1,2-dimethoxyethane 
     DMAP: 4-dimethylaminopyridine 
     DMF: N,N-dimethylformamide 
     DMP: Dess-Martin periodinane 
     DMSO-dimethyl sulfoxide 
     DPPA: diphenylphosphoryl azide 
     dppf: 1,1′-bis(diphenylphosphino)ferrocene 
     EDC or EDCI: 1-(3-dimethylaminopropyl)-3-ethylcarbodiimide hydrochloride 
     ee: enantiomeric excess 
     ESI: electrospray ionization 
     EA: ethyl acetate 
     EtOAc: ethyl acetate 
     EtOH: ethanol 
     FA: formic acid 
     h or hrs: hours 
     HATU: N,N,N′,N′-tetramethyl-O-(7-azabenzotriazol-1-yl)uronium hexafluorophosphate 
     HCl: hydrochloric acid 
     HPLC: high performance liquid chromatography 
     HOAc: acetic acid 
     IBX: 2-iodoxybenzoic acid 
     IPA: isopropyl alcohol 
     KHMDS: potassium hexamethyldisilazide 
     K 2 CO 3 : potassium carbonate 
     LAH: lithium aluminum hydride 
     LDA: lithium diisopropylamide 
     m-CPBA: meta-chloroperbenzoic acid 
     M: molar 
     MeCN: acetonitrile 
     MeOH: methanol 
     Me 2 S: dimethyl sulfide 
     MeONa: sodium methylate 
     Met iodomethane 
     min: minutes 
     mL: milliliters 
     mM: millimolar 
     mmol: millimoles 
     MPa: mega pascal 
     MOMCl: methyl chloromethyl ether 
     MsCl: methanesulfonyl chloride 
     MTBE: methyl tert-butyl ether 
     nBuLi: n-butyllithium 
     NaNO 2 : sodium nitrite 
     NaOH: sodium hydroxide 
     Na 2 SO 4 : sodium sulfate 
     NBS: N-bromosuccinimide 
     NCS: N-chlorosuccinimide 
     NFSI: N-Fluorobenzenesulfonimide 
     NMO: N-methylmorpholine N-oxide 
     NMP: N-methylpyrrolidine 
     NMR: Nuclear Magnetic Resonance 
     ° C.: degrees Celsius 
     Pd/C: Palladium on Carbon
         Pd(OAc) 2 : Palladium Acetate   PBS: phosphate buffered saline   PE: petroleum ether   POCl 3 : phosphorus oxychloride   PPh 3 : triphenylphosphine   PyBOP: (Benzotriazol-1-yloxy)tripyrrolidinophosphonium hexafluorophosphate   Rel: relative   R.T. or rt: room temperature   sat: saturated   SEMCl: chloromethyl-2-trimethylsilylethyl ether   SFC: supercritical fluid chromatography   SOCl 2 : sulfur dichloride   tBuOK: potassium tert-butoxide   TBAB: tetrabutylammonium bromide   TBAI: tetrabutylammonium iodide   TEA: triethylamine   Tf: trifluoromethanesulfonate   TfAA, TFMSA or Tf 2 O: trifluoromethanesulfonic anhydride   TFA: trifluoracetic acid   TIPS: triisopropylsilyl   THF: tetrahydrofuran   THP: tetrahydropyran   TLC: thin layer chromatography   TMEDA: tetramethylethylenediamine   pTSA: para-toluenesulfonic acid   wt: weight   Xantphos: 4,5-bis(diphenylphosphino)-9,9-dimethylxanthene       

     General Synthetic Methods 
     The following examples are intended to illustrate the invention and are not to be construed as being limitations thereon. Temperatures are given in degrees centigrade. If not mentioned otherwise, all evaporations are performed under reduced pressure, preferably between about 15 mm Hg and 100 mm Hg (=20-133 mbar). The structure of final products, intermediates and starting materials is confirmed by standard analytical methods, e.g., microanalysis and spectroscopic characteristics, e.g., MS, IR, NMR. Abbreviations used are those conventional in the art. 
     All starting materials, building blocks, reagents, acids, bases, dehydrating agents, solvents, and catalysts utilized to synthesis the compounds of the present invention are either commercially available or can be produced by organic synthesis methods known to one of ordinary skill in the art (Houben-Weyl 4th Ed. 1952, Methods of Organic Synthesis, Thieme, Volume 21). Further, the compounds of the present invention can be produced by organic synthesis methods known to one of ordinary skill in the art as shown in the following examples. 
     All reactions are carried out under nitrogen or argon unless otherwise stated. 
     Proton NMR NMR) is conducted in deuterated solvent. In certain compounds disclosed herein, one or more 41 shifts overlap with residual proteo solvent signals; these signals have not been reported in the experimental provided hereinafter. 
     
       
         
           
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Analytical instruments 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 LCMS 
                 Shimadzu UFLC MS: LCMS-2020 
               
               
                   
                 Agilent Technologies 1200 series MS: Agilent  
               
               
                   
                 Technologies 6110 
               
               
                   
                 Agilent Technologies 1200 series MS: LC/MSD VL 
               
               
                 NMR 
                 BRUKERAVANCE III/400; Frequency (MHz) 400.13;  
               
               
                   
                 Nucleus: 1H; Number of Transients: 8 
               
               
                 Prep-HPLC 
                 Gilson GX-281 systems: instruments GX-A, GX-B,  
               
               
                   
                 GX-C, GX-D, GX-E, GX-F, GX-G and GX-H 
               
               
                 GCMS 
                 SHIMADZU GCMS-QP2010 Ultra 
               
               
                 Analytical 
                 Agilent Technologies 1290 Infinity 
               
               
                 cSFC 
                   
               
               
                 Prep-cSFC 
                 Waters SFC Prep 80 
               
               
                   
               
            
           
         
       
     
     For acidic LCMS data: 
     LCMS is recorded on an Agilent 1200 Series LC/MSD or Shimadzu LCMS2020 equipped with electro-spray ionization and quadruple MS detector [ES+ve to give MH + ] and equipped with Chromolith Flash RP-18e 25*2.0 mm, eluting with 0.0375 vol % TFA in water (solvent A) and 0.01875 vol % TFA in acetonitrile (solvent B). Other LCMS is recorded on an Agilent 1290 Infinity RRLC attached with Agilent 6120 Mass detector. The column used is BEH C 18  50*2.1 mm, 1.7 micron. Column flow is 0.55 ml/min and mobile phase are used (A) 2 mM Ammonium Acetate in 0.1% Formic Acid in Water and (B) 0.1% Formic Acid in Acetonitrile. 
     For Basic LCMS Data: 
     LCMS is recorded on an Agilent 1200 Series LC/MSD or Shimadzu LCMS 2020 equipped with electro-spray ionization and quadruple MS detector [ES+ve to give MH + ] and equipped with Xbridge C18, 2.1×50 mm columns packed with 5 mm C18-coated silica or Kinetex EVO C18 2.1×30 mm columns packed with 5 mm C18-coated silica, eluting with 0.05 vol % NH 3 .H 2 O in water (solvent A) and acetonitrile (solvent B). 
     HPLC Analytical Method: 
     HPLC is carried out on X Bridge C18 150*4.6 mm, 5 micron. Column flow is 1.0 ml/min and mobile phase are used (A) 0.1% Ammonia in water and (B) 0.1% Ammonia in Acetonitrile. 
     Prep HPLC Analytical Method: 
     The compound is purified on Shimadzu LC-20AP and UV detector. The column used is X-BRIDGE C18 (250*19)mm, 5μ. Column flow is 16.0 ml/min. Mobile phase are used (A) 0.1% Formic Acid in Water and (B) Acetonitrile Basic method used (A) 5 mM ammonium bicarbonate and 0.1% NH 3  in Water and (B) Acetonitrile or (A) 0.1% Ammonium Hydroxide in Water and (B) Acetonitrile. The UV spectra are recorded at 202 nm &amp; 254 nm. 
     NMR Method: 
     The 1H NMR spectra are recorded on a Bruker Ultra Shield Advance 400 MHz/5 mm Probe (BBFO). The chemical shifts are reported in part-per-million. 
     As depicted in the Examples below, in certain exemplary embodiments, compounds are prepared according to the following general procedures. It will be appreciated that, although the general methods depict the synthesis of certain compounds of the present invention, the following general methods, and other methods known to one of ordinary skill in the art, can be applied to all compounds and subclasses and species of each of these compounds, as described herein. 
     Example 1: OCI-LY-10 DC 50    
     A MSD assay is run to determine the concentration of compound required to degrade 50% of protein (DC 50 ). 
     MSD Assay DC 50  Protocol 
     Day 1 
     Compounds are reconstituted to 10 mM in stock solutions. The stock solutions are diluted to 5 mM and 45 μL of each dilution is transferred to a 384 pp-plate. A3 fold, 8-point serial dilution is performed by transferring 15 μL of compound into 30 μL DMSO using Janus. 
     20 nL of each compounds are added into each well of a 96-well plate (Corning3799). 
     OCI-Ly10 cells are seeded into the 96-well plate at 3.0*10e 5  cells/100 μL/well. 
     The cell plate is shaken at 720 rpm for 5 min and incubated for 4 hr. 
     The 100 μL of cells are transferred into the 96-PCR plate and spun down at high speed for 5 mins. 
     The supernatant is discarded and 100 μL of RIPA lysis buffer with proteinase inhibitors is added per well. The plate is then sealed and shaken at 600 rpm and 4° C. for about 20 min. 
     The plate is then spun down at high speed (about 3200 g) for 30 min and then frozen in a −80° C. fridge. 
     A bare MSD plate (L15XA-3) is coated with 2 μg/mL of capture antibody (mouse Anti-IRAK4 antibody [2H9], ab119942) in PBS to 40 μL/well and incubated overnight at 4° C. 
     Day 2 
     The MSD coated plate is washed 3× (150 μL/well) with 1×TBST (CST #99975). 
     The MSD plate is then blocked with 150 μL of blocking buffer [3% Blocker A (MSD, R93BA-4) in TBST]/well and shaken for 1 hr at RT and 600 rpm. 
     The MSD plate is washed 3× (150 μL/well) with 1×TBST. The sample RIPA lysates are then added to the MSD plate (50 μL/well) and shaken for 1 hr at RT and 600 rpm. 
     The MSD plate is washed 3× (150 μL/well) with 1×TBST and the primary detection antibody (Rabbit Anti-IRAK4 antibody [Y279], ab32511) is added to a final concentration of 1 μg/ml with 25 μL/well. The plate is then shaken for 1 hr at RT and 600 rpm. 
     The MSD plate is washed 3× (150 μL/well) with 1×TBST and the secondary detection antibody, SULFO-TAG anti-species antibody (Anti Rabbit Antibody (R32AB-5) MSD, R32AB-1) is added to a volume of 25 μL/well at a final concentration of 1 μg/ml. The plate is then shaken for 1 hr at RT and 600 rpm. 
     The MSD plate is then washed 3× (150 μL/well) with 1×TBST. 
     1×MSD reading buffer is then added (150 μL/well) and the plate is diluted with 4× water. (MSD, R92TC-2) 
     The MSD instrument is then read. 
     Data Analysis 
     The remaining activity is calculated following the formula below: 
     
       
         
           
             
               Relative 
               ⁢ 
                   
               Level 
               ⁢ 
                   
               of 
               ⁢ 
                   
               IRAK 
               ⁢ 
               4 
               ⁢ 
               
                 ( 
                 % 
                 ) 
               
             
             = 
             
               100 
               ⁢ 
               % 
               × 
               
                 
                   
                     MSD 
                     ⁢ 
                         
                     
                       Signal 
                       Sample 
                     
                   
                   - 
                   
                     MSD 
                     ⁢ 
                         
                     
                       Signal 
                       NC 
                     
                   
                 
                 
                   
                     MSD 
                     ⁢ 
                         
                     
                       Signal 
                       PC 
                     
                   
                   - 
                   
                     MSD 
                     ⁢ 
                         
                     
                       Signal 
                       NC 
                     
                   
                 
               
             
           
         
       
     
     Calculate 
     The DC 50  is calculated by fitting the Curve using Xlfit (v5.3.1.3), equation 201: 
         Y =Bottom+(Top−Bottom)/(1+10{circumflex over ( )}((Log  IC 50− X )*HillSlope))
 
     OCI-LY-10 DC 50  results. The letter codes for IRAK4 DC 50  indicate the concentration of compound required to degrade 50% of protein: A (&lt;0.05 μM), B (0.05-0.1 μM), C (0.1-0.5 μM), D (0.5-1.0 μM), and E (&gt;1.0 μM). 
     
       
         
           
               
             
               
                 TABLE 3 
               
               
                   
               
             
            
               
                 OCI-LY-10% IRAK4 DC50 Results 
               
            
           
           
               
               
               
            
               
                   
                   
                 OCI-LY10 
               
               
                   
                 Compound Name 
                 IRAK4 DC 50  (μM) 
               
               
                   
                   
               
            
           
         
       
     
     Example 2: OCI-LY-10 EC 50    
     A CTG cell viability assay using OCI-LY-10 cells is run to determine compound-mediated cell viability (EC 50 ). 
     Cell Viability Protocol 
     Compound-mediated viability effect on OCI-LY10 is quantitatively determined using the CellTiter-Glo® Luminescent Cell Viability Assay kit from Promega (Catalog number G7570) following manufacturer&#39;s recommended procedures. Briefly, OCI-LY10 cells are seeded into 384 well plates (Grenier Bio-One, Catalog number 781080) with a density of 10,000 cells per well. Compounds are then added to the assay plate with final top concentration of 10 μM and 1:3 dilution series with total of 9 doses. The final DMSO concentration is normalized to 0.2%. The assay plates are incubated at 37° C. for 4 days under 5% CO 2 . Then the assay plate is equilibrated at room temperature for 10 minutes. To determine cell viability, 30 μL CellTiter Glo reagent is added to each well and the assay plate is centrifuged at 1000 rpm for 30 second, incubated at room temperature for 10 min, and analyzed by detecting the luminescence using a multimode plate reader (EnVision 2105, PerkinElmer). The data is then analyzed by software Prism 7.0 from GraphPad and the dose response curves are fit using a three-parameter logistic equation to calculate EC 50 . 
     OCI-LY-10 EC50 results. The letter codes for IRAK4 EC50 indicate the concentration of compound required to affect 50% of cells: A (&lt;0.05 μM), B (0.05-0.1 μM), C (0.1-0.5 μM), D (0.5-1.0 μM), and E (&gt;1.0 μM). 
     
       
         
           
               
             
               
                 TABLE 4 
               
               
                   
               
             
            
               
                 OCI-LY-10 IRAK4 EC5o Results 
               
            
           
           
               
               
               
            
               
                   
                   
                 OCI-LY10 
               
               
                   
                 Compound Name 
                 IRAK4 EC 50  (μM) 
               
               
                   
                   
               
            
           
         
       
     
     All of the U.S. patents, U.S. patent application publications, U.S. patent applications, foreign patents, foreign patent applications, and non-patent publications referred to in this specification are incorporated herein by reference in their entireties. 
     While we have described a number of embodiments of this invention, it is apparent that our basic examples may be altered to provide other embodiments that utilize the compounds and methods of this invention. Therefore, it will be appreciated that the scope of this invention is to be defined by the appended claims rather than by the specific embodiments that have been represented by way of example.