Patent Publication Number: US-2019175744-A1

Title: Insulin-incretin conjugates

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims benefit of U.S. Provisional Application No. 62/310,145 filed Mar. 18, 2016, which is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     (1) Field of the Invention 
     The present invention relates to insulin-incretin conjugates comprising a peptide having agonist activity at the glucagon-like 1 (GLP-1) receptor, the glucagon (GCG) receptor, and/or the gastric inhibitory protein (GIP) receptor conjugated to an insulin molecule having agonist activity at the insulin receptor and use of the conjugates for treatment of metabolic diseases, for example, Type 2 diabetes. 
     (2) Description of Related Art 
     Insulin is an essential therapy for type 1 diabetes mellitus (T1DM) patients and many type 2 mellitus diabetics (T2DMs), prescribed to close to one third of U.S. patients among all anti-diabetic drug users in the past decade. The worldwide market for insulins is growing at a faster rate than all other anti-diabetic agents combined and is expected to reach US$32.24 billion by 2019. Type 2 diabetes mellitus (T2DM) in particular is a growing global public health problem. However, challenges of current insulin therapies, including narrow therapeutic index (TI) to hypoglycemia and body weight gain, limit their wider adoption and potential for patients to achieve ideal glycemic control, particularly for patients with T2DM. 
     Due to the progressive nature of diabetes, a combination(s) of two or more drugs acting on different pathophysiological processes is often necessary to achieve an early and sustained achievement of individualized glycemic targets. However, in choosing a therapy it is important that the treatment avoids hypoglycemia. Incretins are a relatively recent class of anti-diabetic drugs and have been shown to have efficacy with an acceptable safety profile. Attempts have been made to combine various incretins with a basal insulin for management of T2DM. Currently, exenatide/long acting exenatide and liraglutide have been co-administered with basal insulin like glargine and detemir, respectively. Currently, a fixed-dose or fixed-ratio combination of insulin degludec and liraglutide is under development. Fixed-dose or fixed-ratio combination or by co-administration may improve control of fasting and postprandial glucose. 
     Incretins are a group of gastrointestinal hormones that that are involved in a wide variety of physiological functions, including glucose homeostasis, insulin secretion, gastric emptying, and intestinal growth, as well as the regulation of food intake. Pre-proglucagon is a 158 amino acid precursor peptide that is processed in different tissues to form a number of different peptides. Incretins include a number of proglucagon-derived peptides, including glucagon (GCG), glucagon-like peptide-1 (GLP-1; amino acids 7-36 and amino acids 7-35, glucagon-like peptide-2 (GLP-2) and oxyntomodulin (OXM). 
     GCG is a 29-amino acid peptide that corresponds to amino acids 33 through 61 of pre-proglucagon, while GLP-1 is produced as a 37-amino acid peptide that corresponds to amino acids 72 through 108 of pre-proglucagon. GLP-1(7-36) C-terminal amide and GLP-1(7-37) acid are biologically potent forms of GLP-1 that demonstrate essentially equivalent activity at the GLP-1 receptor. 
     GCG is a life-saving medicine that is used in the acute treatment of severe hypoglycemia. Oxyntomodulin (OXM) has been reported to have pharmacological ability to suppress appetite and lower body weight. Clinical studies with GLP-1 receptor agonists or stabilized GLP-1 analogs have proven this family of peptides to be an effective treatment for T2DM. 
     Gastric inhibitory peptide or glucose-dependent insulinotropic peptide (GIP) is a member of the secretin family of hormones. GIP is derived from a 153-amino acid proprotein encoded by the GIP gene and circulates as a biologically active 42-amino acid peptide. The GIP gene is expressed in the small intestine as well as the salivary glands and is a weak inhibitor of gastric acid secretion. In addition to its inhibitory effects in the stomach, in the presence of glucose, GIP enhances insulin release by pancreatic beta islet cells when administered in physiological doses. GIP is believed to function as an enteric factor that stimulates the release of pancreatic insulin and that may play a physiological role in maintaining glucose homeostasis. 
     GCG-related peptide analogs and derivatives modified to have various degrees of activity at the GLP-1 receptor, the GIP receptor, and the GCG receptor have been disclosed in Published International Application Nos. WO2008/1010017, WO2009/155258, WO2011/075393, WO2012/177444, and WO2012/177443. Two independent and simultaneous papers reported the use of relatively balanced GLP-1 receptor/GCG receptor co-agonists as being of enhanced efficacy and safety relative to pure GLP1R agonists in the treatment of rodent obesity, with simultaneous improvement in glycemic control (Day et al., Nat. Chem. Biol. 5: 749-757 (2009); Pocai eta al., Diabetes 58: 2258-2266 (2009)). 
     While fixed-dose or fixed-ratio combination or by co-administration may lead to improved control over fasting and postprandial glucose, neither method is without limitations, e.g., pH solubility/stability incompatibility and/or limited ability to adjust the ratio between two molecules having different pharmacologies. 
     An improvement to simultaneous administration of insulin and an incretin to control T2DM was disclosed in WO2014158900, which disclosed conjugates formed between an insulin molecule and an incretin, including for example a GCG-related peptide, wherein the conjugate has agonist activity at both the insulin receptor and the corresponding incretin receptor(s). 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention provides insulin-incretin conjugates formed between an insulin molecule and an incretin, including for example a GCG-related peptide, wherein the conjugate has agonist activity at both the insulin receptor and the corresponding incretin receptor(s). The conjugation of a GCG-related peptide (e.g., a peptide having agonist activity at the GIP receptor, the GLP-1 receptor, the GCG receptor or combinations thereof) is anticipated to produce a beneficial therapeutic addition to the insulin molecule activity. 
     The present invention provides a compound comprising an insulin molecule having agonist activity at the insulin receptor conjugated via a non-peptide linking moiety to a peptide having agonist activity at the glucagon-like 1 (GLP-1) receptor, the glucagon (GCG) receptor, and/or the gastric inhibitory protein (GIP) receptor, wherein the non-peptide linking moiety comprises a 1,4-disubstituted 1, 2, 3-triazole. 
     In particular embodiments, the peptide comprises (a) a first linker arm having a proximal end linked to an amino acid of the peptide and a distal end linked to an azide group and the insulin molecule comprises a second linker arm having a proximal end linked to an amino acid of the insulin molecule and a distal end linked to an alkyne group, wherein the azide group and the alkyne group form the 1,4-disubstituted 1,2,3-triazole; or (b) a first linker arm having a proximal end linked to an amino acid of the peptide and a distal end linked to an alkyne group and the insulin molecule comprises a second linker arm having a proximal end linked to an amino acid of the insulin molecule and a distal end linked to an azide group, wherein the azide group and the alkyne group form the 1,4-disubstituted 1,2,3-triazole in either case. 
     In particular embodiments, the peptide comprises within its amino acid sequence (a) an azido-norleucine and the insulin molecule comprises a linker arm having a proximal end linked to the amino group of an amino acid of the insulin molecule and a distal end linked to an alkynyl group, wherein the azido group and the alkynyl group form the 1,4-disubstituted 1,2,3-triazole; or (b) an alkynyl-norleucine and the insulin molecule comprises a linker arm having a proximal end linked to the amino group of an amino acid of the insulin molecule and a distal end linked to an azido group, wherein the azido group and the alkynyl group form the 1,4-disubstituted 1,2,3-triazole; or (c) a propargyl-Glycine and the insulin molecule comprises a linker arm having a proximal end linked to the amino group of an amino acid of the insulin molecule and a distal end linked to an azido group, wherein the azido group and the alkynyl group form the 1,4-disubstituted 1,2,3-triazole. 
     In particular embodiments, the insulin molecule comprises within its amino acid sequence (a) an azido-norleucine and the peptide comprises a linker arm having a proximal end linked to the amino group of an amino acid of the peptide and a distal end linked to an alkynyl group, wherein the azido group and the alkynyl group form the 1,4-disubstituted 1,2,3-triazole; or (b) an alkynyl-norleucine and the peptide comprises a linker arm having a proximal end linked to the amino group of an amino acid of the peptide and a distal end linked to an azido group, wherein the azido group and the alkynyl group form the 1,4-disubstituted 1,2,3-triazole; or (c) a propargyl-Glycine and the insulin molecule comprises a linker arm having a proximal end linked to the amino group of an amino acid of the insulin molecule and a distal end linked to an azido group, wherein the azido group and the alkynyl group form the 1,4-disubstituted 1,2,3-triazole. 
     In particular embodiments, the insulin molecule comprises an A-chain peptide and a B-chain peptide. 
     In particular embodiments, the insulin molecule is a heterodimer molecule or a single-chain insulin molecule. 
     In particular embodiments, the insulin molecule is selected from the group consisting of human insulin, insulin lispro, insulin detemir, insulin glulisine, and insulin glargine. 
     In particular embodiments, the insulin molecule is conjugated to the peptide via the N-terminal amino acid of the A-chain peptide, the N-terminal amino acid of the B-chain peptide, or the amino acid at position 28 or 29 of the B-chain peptide. 
     In particular embodiments, the peptide is conjugated to the insulin molecule via an amino acid at position 20, 21, 24, 30, or 31 of the peptide. 
     In particular embodiments, the peptide is also conjugated to a fatty acid or fatty diacid. In further rembodiments, the fatty acid or fatty diacid is conjugated to the epsilon amine of a lysine residue at amino acid position 10 or 20 of the peptide. 
     In particular embodiments, the conjugate comprises the formula 
     
       
         
         
             
             
         
       
     
     wherein R 1  and R 2  independently comprise a C 1 -C 50  hydrocarbon chain or substituted hydrocarbon chain, a PEG n  wherein n is 1-50, a (PEG 2 ) n  wherein n is 1-50, a (PEG 2 ) n -(γGlu) p -C n  wherein each n is independently 1-50 and p is 1 or 2, a (PEG 2 ) n -C n  wherein each n is independently is 1-50, a (PEG) n (PEG) n  wherein each n is independently 1-50, a PEG n -(Lys-(γGlu) p -C n )—C n  wherein each n is independently 1-50 and p is 1 or 2, and a C 5 -Lys(γE-C n )-PEG n  wherein each n is independently 1-50, and wherein the bond between the linking moiety and the insulin molecule and the incretin peptide are indicated by the wavy lines with the proviso that if the bond adjacent to R 1  is to insulin then the bond adjacent to R 2  is to the incretin peptide or that if the bond adjacent to R 1  is to the incretin peptide then the bond adjacent to R 2  is to insulin. 
     In particular embodiments, the incretin peptide is a glucagon derived that comprises the amino acid sequence 
                            (SEQ ID NO: 1)           HSQGTFTSDYSKYLDERAAQDFVQWLLDT            
which further includes at least the following modifications: (i) a substitution of the amino acid at position 2 with an amino acid that renders the peptide resistant to cleavage and inactivation by dipeptidyl peptidase IV; (ii) a lipid moiety covalently linked to the peptide at a lysine residue substituted for the tyrosine residue at position 10 or the glutamine at position 20 of the peptide; (iii) an azide group or an alkyne group conjugated to an amino acid at position 20, 21, 24, 30, or 31; (iv) 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10 additional amino acid substitutions in addition to the substitution at position 2; and optionally, a protecting group that is joined to the C-terminal carboxy group and/or the N-terminal amino group. In embodiments in which the modified glucagon peptide has agonist activity at the GIP receptor, the Histidine at position 1 is substituted with Tyrosine, Phenylalanine, Tryptophan, or other amino acid with an aromatic group.
 
     In particular embodiments, the peptide comprises a substitution of the Ser at position 2 with Val, Ile, Asp, Glu, Met, Trp, Asn, D-Ala, D-Ser, a-methyl-Ser, a-methyl-D-Ser or a-aminoisobutyric acid (aib or U). In particular embodiments, the Ser is substituted with D-Ser or aib. These substitutions at position 2 render the peptide resistant to DPP-4 and active at the GLP-1 receptor. Peptides with a substitution are co-agonists of the GCG and the GLP-1 receptors. 
     In particular embodiments, the Gln at position 3 is substituted with Glu or Asp. These substitutions increase the selectivity of the peptide for the GLP-1 receptor over the GCG receptor. Such peptides have little or no activity at the GCG receptor. 
     In particular embodiments, the peptide includes a substitution of the Glu at position 16 with aib, Asn, Ser, or Ala. 
     In particular embodiments the His at position 1 is substituted with an amino acid with a large aromatic group, for example, Tyr, Phe, or Trp. When this substitution includes the substitution of the Ser at position 2 with aib or D-Ser, the substitution of the Lys at position 12 with Ile and substitution of the Glu at position 16 with aib, the peptide has agonist activity at the GCG, GLP-1 and GIP receptors. When the peptide further includes a substitution of the Gln at position 3 with Glu or Asp, the peptide has agonist activity at the GLP-1 and GIP receptors. 
     In particular embodiments, the compound comprises a peptide selected from the group consisting of peptides shown in Table 1,e.g., a group of peptides consisting of PEP1, PEP2, PEP3, PEP4, PEP5, PEP6, PEP7, PEP8, PEP9, PEP10, PEP11, PEP12, PEP13, PEP14, PEP15, PEP16, PEP17, PEP18, PEP19, PEP20, PEP21, PEP22, PEP23, PEP24, PEP25, PEP26, PEP27, PEP28, PEP29, PEP30, PEP31, PEP32, PEP33, PEP34, PEP35, PEP36, PEP37, PEP38, PEP39, PEP40, PEP41, PEP42, PEP43, PEP44, PEP45, PEP46, PEP47, PEP48, PEP49, PEP50, PEP51, PEP52, PEP53, PEP54, PEP55, PEP56, PEP57, PEP58, PEP59, PEP60, PEP61, PEP62, PEP63, PEP64, PEP65, PEP66, PEP67, PEP68, PEP69, PEP70, PEP71, PEP72, PEP73, PEP74, PEP75, PEP76, PEP77, PEP78, PEP79, PEP80, PEP81, PEP82, PEP83, PEP84, PEP85, PEP86, PEP87, PEP88, PEP89, PEP90, PEP91, PEP92, PEP93, PEP94, PEP95, PEP96, PEP97, PEP98, PEP99, PEP100, PEP101, PEP102, PEP103, PEP104, PEP105, PEP106, PEP107, PEP108, PEP109, PEP110, PEP111, PEP112, PEP113, PEP114, PEP115, PEP116, PEP117, PEP118, PEP119, PEP120, PEP121, PEP122, PEP123, PEP124, PEP125, PEP126, PEP127, PEP128, PEP129, PEP130, PEP131, and PEP132. 
     The present invention further provides a conjugate comprising an insulin analog selected from the group consisting of INS1, INS2, INS3, INS4, INS5, INS6, INS7, INS8, INS9, INS10, INS11, INS12, INS13, INS14, INS15, INS16, INS17, INS18, INS19, INS20, INS21, INS22, INS23, INS24, INS25, INS26, INS27, INS28, INS29, INS30, and INS31 conjugated to a peptide selected from the group consisting of PEP1, PEP2, PEP3, PEP4, PEP5, PEP6, PEP7, PEP8, PEP9, PEP10, PEP11, PEP12, PEP13, PEP14, PEP15, PEP16, PEP17, PEP18, PEP19, PEP20, PEP21, PEP22, PEP23, PEP24, PEP25, PEP26, PEP27, PEP28, PEP29, PEP30, PEP31, PEP32, PEP33, PEP34, PEP35, PEP36, PEP37, PEP38, PEP39, PEP40, PEP41, PEP42, PEP43, PEP44, PEP45, PEP46, PEP47, PEP48, PEP49, PEP50, PEP51, PEP52, PEP53, PEP54, PEP55, PEP56, PEP57, PEP58, PEP59, PEP60, PEP61, PEP62, PEP63, PEP64, PEP65, PEP66, PEP67, PEP68, PEP69, PEP70, PEP71, PEP72, PEP73, PEP74, PEP75, PEP76, PEP77, PEP78, PEP79, PEP80, PEP81, PEP82, PEP83, PEP84, PEP85, PEP86, PEP87, PEP88, PEP89, PEP90, PEP91, PEP92, PEP93, PEP94, PEP95, PEP96, PEP97, PEP98, PEP99, PEP100, PEP101, PEP102, PEP103, PEP104, PEP105, PEP106, PEP107, PEP108, PEP109, PEP110, PEP111, PEP112, PEP113, PEP114, PEP115, PEP116, PEP117, PEP118, PEP119, PEP120, PEP121, PEP122, PEP123, PEP124, PEP125, PEP126, PEP127, PEP128, PEP129, PEP130, PEP131, and PEP132. 
     The present invention further provides a conjugate selected from group of conjugates shown in Table 4, e.g., a conjugate selected from the group consisting of CON1, CON2, CON3, CON4, CON5, CON6, CON7, CON8, CON9, CON10, CON11, CON12, CON13, CON14, CON15, CON16, CON17, CON19, CON20, CON21, CON22, CON23, CON24, CON25, CON26, CON27, CON28, CON29, CON30, CON31, CON32, CON33, CON34, CON35, CON36, CON37, CON38, CON39, CON40, CON41, CON42, CON43, CON44, CON45, CON46, CON47, CON48, CON49, CON50, CON51, CON52, CON53, CON55, CON56, CON57, CON58, CON59, CON60, CON61, CON62, CON63, CON64, CON65, CON66, CON67, CON68, CON69, CON70, CON71, CON72, CON73, CON74, CON75, CON76, CON77, CON78, CON79, CON80, CON81, CON82, CON83, CON84, CON85, CON86, CON87, CON88, CON89, CON90, CON91, CON92, CON93, CON94, CON95, CON96, CON97, CON98, CON99, CON101, CON102, CON103, CON104, CON105, CON106, CON107, CON108, CON109, CON110, CON111, CON112, CON113, CON114, CON115, CON116, CON117, CON118, CON119, CON120, CON121, CON122, CON123, CON124, CON125, CON126, CON127, CON128, CON129, CON130, CON131, CON132, CON133, CON134, CON135, CON136, CON137, CON138, CON139, CON140, CON141, CON142, CON143, CON144, CON145, CON146, CON147, CON148, CON149, CON150, CON151, CON152, CON153, CON154, CON155, CON156, CON157, CON158, CON159, CON160, and CON161. 
     The present invention further provides pharmaceutical formulation comprising a compound of the above and a pharmaceutically acceptable carrier. 
     The present invention further provides for the use of a compound of the above in a treatment for a metabolic disease. 
     The present invention further provides for the use of a compound of the above for the manufacture of a medicament for the treatment of a metabolic disease. 
     The present invention further provides a method for treating a metabolic disease, comprising administering to an individual in need an effective amount of a compound of any one of the preceding claims to treat the metabolic disease. In particular embodiments, the metabolic disease is diabetes. 
     Definitions 
     The term “about” as used herein means greater or lesser than the value or range of values stated by 10 percent, but is not intended to designate any value or range of values to only this broader definition. Each value or range of values preceded by the term “about” is also intended to encompass the embodiment of the stated absolute value or range of values. 
     As used herein, the term “pharmaceutically acceptable carrier” includes any of the standard pharmaceutical carriers, such as a phosphate buffered saline solution, water, emulsions such as an oil/water or water/oil emulsion, and various types of wetting agents. The term also encompasses any of the agents approved by a regulatory agency of the U.S. Federal government or listed in the U.S. Pharmacopeia for use in animals, including humans. 
     As used herein the term “pharmaceutically acceptable salt” refers to salts of compounds that retain the biological activity of the parent compound, and which are not biologically or otherwise undesirable. Many of the compounds disclosed herein are capable of forming acid and/or base salts by virtue of the presence of amino and/or carboxyl groups or groups similar thereto. 
     Pharmaceutically acceptable base addition salts can be prepared from inorganic and organic bases. Salts derived from inorganic bases, include by way of example only, sodium, potassium, lithium, ammonium, calcium and magnesium salts. Salts derived from organic bases include, but are not limited to, salts of primary, secondary and tertiary amines. 
     As used herein, the term “treating” includes prophylaxis of the specific disorder or condition, or alleviation of the symptoms associated with a specific disorder or condition and/or preventing or eliminating said symptoms. For example, as used herein the term “treating diabetes” will refer in general to altering glucose blood levels in the direction of normal levels and may include increasing or decreasing blood glucose levels depending on a given situation. 
     As used herein an “effective” amount or a “therapeutically effective amount” of a glucagon peptide refers to a nontoxic but sufficient amount of the peptide to provide the desired effect or a meaningful patient benefit. For example one desired effect would be the prevention or treatment of hyperglycemia, e.g., as measured by a change in blood glucose level closer to normal, or inducing weight loss/preventing weight gain, e.g., as measured by reduction in body weight, or preventing or reducing an increase in body weight, or normalizing body fat distribution. The amount that is “effective” will vary from subject to subject, depending on the age and general condition of the individual, mode of administration, and the like. Thus, it is not always possible to specify an exact “effective amount.” However, an appropriate “effective” amount in any individual case may be determined by one of ordinary skill in the art using routine experimentation. 
     The term, “parenteral” means not through the alimentary canal but by some other route, e.g., subcutaneous, intramuscular, intraspinal, or intravenous. 
     As used herein, the term “peptide” encompasses a chain of 11 or more amino acids and typically less than 50 amino acids, wherein the amino acids are naturally occurring or coded or non-naturally occurring or non-coded amino acids. Non-naturally occurring amino acids refer to amino acids that do not naturally occur in vivo but which, nevertheless, can be incorporated into the peptide structures described herein. “Non-coded” as used herein refers to an amino acid that is not an L-isomer of any of the following 20 amino acids: Ala, Cys, Asp, Glu, Phe, Gly, His, Ile, Lys, Leu, Met, Asn, Pro, Gln, Arg, Ser, Thr, Val, Trp, Tyr. “Coded” as used herein refers to an amino acid that is an L-isomer of any of the following 20 amino acids: Ala, Cys, Asp, Glu, Phe, Gly, His, Ile, Lys, Leu, Met, Asn, Pro, Gln, Arg, Ser, Thr, Val, Trp, Tyr. In some embodiments, the peptides and variant peptides described herein are about the same length as SEQ ID NO: 1 (which is 29 amino acids in length), e.g. 25-35 amino acids in length. Exemplary lengths include 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, or 50 amino acids in length. The term further includes peptides wherein one or more amino acids is conjugated to a second molecule via a linker. 
     Amino acid “modification” refers to an insertion, deletion or substitution of one amino acid with another. In some embodiments, the amino acid substitution or replacement is a conservative amino acid substitution, e.g., a conservative substitution of the amino acid at one or more of positions 2, 5, 7, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 24, 27, 28 or 29. As used herein, the term “conservative amino acid substitution” is the replacement of one amino acid with another amino acid having similar properties, e.g., size, charge, hydrophobicity, hydrophilicity, and/or aromaticity, and includes exchanges within one of the following five groups: 
     I. Small aliphatic, nonpolar or slightly polar residues: 
     Ala, Ser, Thr, Pro, Gly; 
     II. Polar, negative-charged residues and their amides and esters:
 
Asp, Asn, Glu, Gln, cysteic acid and homocysteic acid;
 
III. Polar, positive-charged residues:
 
     His, Arg, Lys; Omithine (Orn) 
     IV. Large, aliphatic, nonpolar residues:
 
Met, Leu, Ile, Val, Cys, Norleucine (Nle), homocysteine
 
V. Large, aromatic residues:
 
Phe, Tyr, Trp, acetyl phenylalanine
 
     In some embodiments, the amino acid substitution is not a conservative amino acid substitution, e.g., is a non-conservative amino acid substitution. 
     As used herein the term “charged amino acid” or “charged residue” refers to an amino acid that comprises a side chain that is negative-charged (i.e., de-protonated) or positive-charged (i.e., protonated) in aqueous solution at physiological pH. For example negative-charged amino acids include aspartic acid, glutamic acid, cysteic acid, homocysteic acid, and homoglutamic acid, whereas positive-charged amino acids include arginine, lysine and histidine. Charged amino acids include the charged amino acids among the 20 coded amino acids, as well as atypical or non-naturally occurring or non-coded amino acids. 
     As used herein the term “acidic amino acid” refers to an amino acid that comprises a second acidic moiety (other than the carboxylic acid of the amino acid), including for example, a carboxylic acid or sulfonic acid group. 
     As used herein, the term “acylated amino acid” refers to an amino acid comprising an acyl group which is non-native to a naturally-occurring amino acid, regardless of the means by which it is produced (e.g. acylation prior to incorporating the amino acid into a peptide, or acylation after incorporation into a peptide). 
     As used herein the term “alkylated amino acid” refers to an amino acid comprising an alkyl group which is non-native to a naturally-occurring amino acid, regardless of the means by which it is produced. Accordingly, the acylated amino acids and alkylated amino acids of the present disclosures are non-coded amino acids. 
     As used herein, the term “selectivity” of a molecule for a first receptor relative to a second receptor refers to the following ratio: EC 50  of the molecule at the second receptor divided by the EC 50  of the molecule at the first receptor. For example, a molecule that has an EC50 of 1 nM at a first receptor and an EC 50  of 100 nM at a second receptor has 100-fold selectivity for the first receptor relative to the second receptor. 
     As used herein, “glucagon potency” or “potency compared to native glucagon” of a molecule refers to the inverse ratio of the EC 50  of the molecule at the glucagon receptor divided by the EC 50  of native glucagon at glucagon receptor. 
     As used herein, “GLP-1 potency” or “potency compared to native GLP-1” of a molecule refers to the inverse ratio of the EC 50  of the molecule at GLP-1 receptor divided by the EC 50  of native GLP-1 at GLP-1 receptor. 
     As used herein, “PEG” refers to a polyethylene glycol molecule and “PEG n ” refers to a polyethylene glycol molecule have n number of ethylene groups. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  shows a 3D schematic representation of an insulin-incretin conjugate in which a 1,4-disubstituted 1, 2, 3,-triazole linking moiety links the B1 amino acid to an Nle amino acid in an incretin peptide. 
         FIG. 1B  shows in the upper panel a schematic representation of a Cu(I)-catalyzed Azide-Alkyne Cycloaddition (CuAAC) process that may be used to construct the insulin-incretin conjugates disclosed herein and in the lower panel a Cu-free AAC process that may be used to construct insulin-incretin conjugates wherein one linker comprises a terminal azide and the other linker comprises a strained cyclooctyne. 
         FIG. 2A ,  FIG. 2B , and  FIG. 2C  show various exemplary insulin-incretin conjugates in which the Norleucine (Nle) amino acid of particular incretins is conjugated to the epsilon amino group of Lysine (Lys) at position B29 of the B-chain peptide. The “*” indicates that the incretin has the amino acid sequence and structure of the indicated incretin but wherein the azide group of the linker has formed a 1,2-disubstituted 1,2,3-triazole with the alkyne group on the insulin. 
         FIG. 3  shows various exemplary insulin-incretin conjugates in which the Nle amino acid of particular incretins is conjugated to the amino group of the Glycine (Gly) at position A1 of the A-chain peptide. The “*” indicates that the incretin has the amino acid sequence and structure of the indicated incretin but wherein the azide group of the linker has formed a 1,2-disubstituted 1,2,3-triazole with the alkyne group on the insulin. 
         FIG. 4A ,  FIG. 4B ,  FIG. 4C ,  FIG. 4D ,  FIG. 4E ,  FIG. 4F ,  FIG. 4G ,  FIG. 4H ,  FIG. 4I ,  FIG. 4J ,  FIG. 4K ,  FIG. 4L ,  FIG. 4M ,  FIG. 4N ,  FIG. 4O , and  FIG. 4P  show exemplary insulin-incretin conjugates in which the Nle amino acid of particular incretins is conjugated to the amino group of the Phenylalanine (Phe) at position B1 of the B-chain peptide. The “*” indicates that the incretin has the amino acid sequence and structure of the indicated incretin but wherein the azide group of the linker has formed a 1,2-disubstituted 1,2,3-triazole with the alkyne group on the insulin. 
         FIG. 5  shows an exemplary insulin-incretin conjugate in which the Nle amino acid of PEP74* is conjugated to the amino group of the Phe at position B1 of the B-chain peptide. The “*” indicates that the incretin has the amino acid sequence and structure of the indicated incretin but wherein the azide group of the linker has formed a 1,4,5-trisubstituted 1,2,3-triazole with the alkyne group on the insulin. 
         FIG. 6A ,  FIG. 6B ,  FIG. 6C , and  FIG. 6D  show exemplary insulin-incretin conjugates in which the epsilon amino group of Lys of the incretin is conjugated to the amino group of the Phe at position B1 of the B-chain peptide. The “*” indicates that the incretin has the amino acid sequence and structure of the indicated incretin but wherein the azide group of the linker has formed a 1,2-disubstituted 1,2,3-triazole with the alkyne group on the insulin. 
         FIG. 7  shows that the length of the linking moiety at B1 has an effect on the ratio of glucagon (GCG) activity to GLP-1 activity. 
         FIG. 8  shows that the length of the linking moiety at B29 has an effect on the activity of the insulin at the insulin receptor ratio of GCG activity to GLP-1 activity. 
         FIG. 9A ,  FIG. 9B ,  FIG. 9C ,  FIG. 9D ,  FIG. 9E ,  FIG. 9F ,  FIG. 9G ,  FIG. 9H ,  FIG. 9I ,  FIG. 9J ,  FIG. 9K , and  FIG. 9L  show exemplary insulin-incretin conjugates in which the Norleucine (Nle) amino acid of the incretin is conjugated to the amino group of the Phe at position B1 of the B-chain peptide. The “*” indicates that the incretin has the amino acid sequence and structure of the indicated incretin but wherein the azide group of the linker has formed a 1,2-disubstituted 1,2,3-triazole with the alkyne group on the insulin. 
         FIG. 10A ,  FIG. 10B ,  FIG. 10C ,  FIG. 10D ,  FIG. 10E ,  FIG. 10F , and  FIG. 10G  show exemplary insulin-incretin conjugates in which the epsilon amino group of Lys of the incretin is conjugated to the amino group of the Phenylalanine (Phe) at position B1 of the B-chain peptide. The “*” indicates that the incretin has the amino acid sequence and structure of the indicated incretin but wherein the azide group of the linker has formed a 1,2-disubstituted 1,2,3-triazole with the alkyne group on the insulin. 
         FIG. 11  shows exemplary insulin-incretin conjugates CON106 and CON107. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention provides insulin-incretin conjugates that are anticipated to impart a beneficial addition to insulin therapies for diabetes. For example, linking an incretin peptide having agonist activity at the GCG receptor to an insulin molecule may enhance targeting of the conjugate to the liver since the GCG receptor is predominately located in the liver. Targeting the conjugate to the liver may be desirable since the liver is primarily involved in glucose production not glucose utilization. Thus, targeting the liver may provide a safer approach to shutting off glucose production than would occur when the insulin contacts other tissues such as muscle or fat, where in addition to turning off glucose production it also stimulates glucose use leading to a higher risk of hypoglycemia. Also, there are GCG receptors present on the alpha cells of the pancreas. Delivering the conjugate to the alpha cells may suppress additional glucagon production or make the alpha cell more sensitive to hypoglycemia. It is also anticipated that the presence of GCG in the conjugates may serve as a buffer on the activity of the insulin to provide a more baseline activity and thus avoid spikes in blood glucose levels. Furthermore, whereas insulin stimulates lipogenesis in fat cells and weight gain, GCG increases lipolysis and energy expenditure and effects a decrease in weight gain, which may be beneficial in countering the weight gain that may occur during insulin therapies. 
     Similarly, it is anticipated that conjugates of insulin with other GCG-related peptides including the incretins GLP-1 and GIP and other related peptides having activity at the GLP-1 and/or GIP receptors may produce conjugates having beneficial properties. For example, GLP-1 receptor agonist-insulin conjugate may be targeted to the hypothalamus, to decrease appetite as well as reduce blood glucose. Alternatively or additionally, the GLP-1 receptor agonist-insulin conjugate may be targeted to the beta cells to drive anabolic response (increase islet beta cells production of insulin). 
     The incretin-insulin conjugates herein are also suitable for further structural enhancements that are envisioned to yield improved therapeutic index, through the use of prodrug chemistry; extended duration of action, by linkage of plasma proteins such as albumin, or other modifications, including pegylation and acylation; and enhanced physical stability, by glycosylation. The preparation of single chain insulin analogs using a C-peptide or peptide linker also provides a novel structural location for where many of these chemical modifications can be successfully deployed. The primary use of the conjugates disclosed herein would be in the treatment of insulin-dependent diabetes, including for example, T1DM, T2DM, and gestational diabetes. 
     Insulin-Incretin Conjugates 
     The insulin-incretin conjugate of the present invention comprises an insulin molecule having agonist activity at the insulin receptor conjugated via a non-peptide linking moiety to a peptide having incretin activity, wherein the non-peptide linking moiety comprises a 1,4-disubstituted 1, 2, 3-triazole and the incretin is a peptide having agonist activity at the glucagon-like 1 (GLP-1) receptor, the glucagon (GCG) receptor, the gastric inhibitory protein (GIP) receptor, or both the GLP-1 receptor and the GCG receptor or both the GLP-1 receptor and the GIP receptor.  FIG. 1A  provides a schematic representation of an insulin-incretin conjugate. 
     In specific embodiments, the insulin may have an EC 50  at the insulin receptor of about 20 nM or less, 10 nM or less, 5 nM or less, or between 1 to nM. In specific embodiments, the incretin may have an EC 50  at the GLP-1 receptor of about 10 nM or less, 5 nM or less, 1 nM or less, or between 0.01 nM and 1 nM. In specific embodiments, the incretin may have an EC 50  at the GIP receptor of about 10 nM or less, 5 nM or less, 1 nM or less, or between 0.01 nM and 1 nM. In specific embodiments, the incretin may have an EC 50  at the GCG1 receptor of about 10 nM or less, 5 nM or less, 1 nM or less, or between 0.01 nM and 1 nM. In specific embodiments, the incretin is a co-agonist in which the activity at the GLP-1 receptor and the GCG receptor are relatively balanced. 
     In particular embodiments, the insulin-incretin conjugate comprises (i) an insulin molecule having insulin activity and comprising an alkyne group conjugated to a peptide having incretin activity and comprising an azide group under conditions wherein the alkyne group and the azide group form a linking moiety comprising a 1,4-disubstituted 1, 2, 3-triazole or (ii) an insulin molecule comprising an azide group conjugated to an incretin peptide comprising an alkyne group under conditions wherein the azide group and the alkyne group form a 1,4-disubstituted 1, 2, 3-triazole. 
     In particular embodiments, the peptide comprises (i) a first linker arm having a proximal end linked to an amino acid of the peptide and a distal end linked to an azide group and the insulin molecule comprises a second linker arm having a proximal end linked to an amino acid of the insulin molecule and a distal end linked to an alkyne group; or (ii) the compound of claim  1 , wherein the peptide comprises a first linker arm having a proximal end linked to an amino acid of the peptide and a distal end linked to an alkyne group and the insulin molecule comprises a second linker arm having a proximal end linked to an amino acid of the insulin molecule and a distal end linked to an azide group; or (c) a propargyl-Glycine and the insulin molecule comprises a linker arm having a proximal end linked to the amino group of an amino acid of the insulin molecule and a distal end linked to an azido group, wherein the azido group and the alkynyl group form the 1,4-disubstituted 1,2,3-triazole. 
     In a particular embodiment, the insulin-incretin conjugate comprises an insulin molecule having agonist activity at the insulin receptor conjugated via a non-peptide linking moiety to a peptide having agonist activity at the glucagon-like 1 (GLP-1) receptor, the glucagon (GCG) receptor, or both the GLP-1 receptor and the GCG receptor, wherein the non-peptide linking moiety comprises a 1,4-disubstituted 1, 2, 3-triazole; or in a particular embodiment, the insulin-incretin conjugate comprises an insulin molecule having agonist activity at the insulin receptor conjugated via a non-peptide linking moiety to a peptide having agonist activity at the gastric inhibitory protein (GIP) receptor or both the GLP-1 receptor and the GIP receptor, wherein the non-peptide linking moiety comprises a 1,4-disubstituted 1, 2, 3-triazole. 
     In particular embodiments of the insulin-incretin conjugates herein, the insulin-incretin conjugate comprises (i) an insulin molecule comprising an alkyne group conjugated to an incretin peptide comprising an azide group under conditions wherein the alkyne group and the azide group form a linking moiety comprising a 1,4-disubstituted 1, 2, 3-triazole or (ii) an insulin molecule comprising an azide group conjugated to an incretin peptide comprising an alkyne group under conditions wherein the azide group and the alkyne group form a 1,4-disubstituted 1, 2, 3-triazole; or (iii) a propargyl-Glycine and the insulin molecule comprises a linker arm having a proximal end linked to the amino group of an amino acid of the insulin molecule and a distal end linked to an azido group, wherein the azido group and the alkynyl group form the 1,4-disubstituted 1,2,3-triazole. 
     In particular embodiments, the peptide comprises (a) a first linker arm having a proximal end linked to an amino acid of the peptide and a distal end linked to an azide group and the insulin molecule comprises a second linker arm having a proximal end linked to an amino acid of the insulin molecule and a distal end linked to an alkyne group; or (b) the compound of claim  1 , wherein the peptide comprises a first linker arm having a proximal end linked to an amino acid of the peptide and a distal end linked to an alkyne group and the insulin molecule comprises a second linker arm having a proximal end linked to an amino acid of the insulin molecule and a distal end linked to an azide group. 
     In particular embodiments, the linking moiety comprises the formula 
     
       
         
         
             
             
         
       
     
     wherein R 1  and R 2  independently comprise a C 1 -C 50  hydrocarbon chain or substituted hydrocarbon chain, a PEG n  wherein n is 1-50, a (PEG 2 ) n  wherein n is 1-50, a (PEG 2 ) n -(γGlu) p -C n  wherein each n is independently 1-50 and p is 1 or 2, a (PEG 2 ) n -C n  wherein each n is independently is 1-50, a (PEG) n (PEG) n  wherein each n is independently 1-50, a PEG n -(Lys-(γGlu) p -C n )—C n  wherein each n is independently 1-50 and p is 1 or 2, and a C 5 -Lys(γE-C n )-PEG n  wherein each n is independently 1-50, and wherein the bond between the linking moiety and the insulin molecule and the incretin peptide are indicated by the wavy lines with the proviso that if the bond adjacent to R 1  is to insulin then the bond adjacent to R 2  is to the incretin peptide or that if the bond adjacent to R 1  is to the incretin peptide then the bond adjacent to R 2  is to insulin. 
     In particular aspects, the peptide optionally includes a protecting group covalently joined to the N-terminal amino group. A protecting group covalently joined to the N-terminal amino group of the peptide reduces the reactivity of the amino terminus under in vivo conditions. Amino protecting groups include —C 1-10  alkyl, —C 1-10  substituted alkyl, —C 2-10  alkenyl, —C 2-10  substituted alkenyl, aryl, —C 1-6  alkyl aryl, —C(O)—(CH 2 ) 1-6 —COOH, —C(O)—C 1-6  alkyl, —C(O)-aryl, —C(O)—O—C 1-6  alkyl, or —C(O)—O-aryl. In particular embodiments, the amino terminus protecting group is selected from the group consisting of acetyl, propyl, succinyl, benzyl, benzyloxycarbonyl, and t-butyloxycarbonyl. Deamination of the N-terminal amino acid is another modification that is contemplated for reducing the reactivity of the amino terminus under in vivo conditions. 
     In particular aspects, the peptide may be modified to have a protecting group covalently joined to the C-terminal carboxy group, which reduces the reactivity of the carboxy terminus under in vivo conditions. For example, carboxylic acid groups of the peptide, whether carboxyl-terminal or side chain, may be provided in the form of a salt of a pharmacologically-acceptable cation or esterified to form a C 1-6  ester, or converted to an amide of formula NRR 2  wherein R and R 2  are each independently H or C 1-6  alkyl, or combined to form a heterocyclic ring, such as a 5- or 6-membered ring. The carboxy terminus protecting group is preferably attached to the a-carbonyl group of the last amino acid. Carboxy terminus protecting groups include, but are not limited to, amide, methylamide, and ethylamide. Amino groups of the peptide, whether N-terminal or side chain, may be in the form of a pharmacologically-acceptable acid addition salt, such as the HCl, HBr, acetic, benzoic, toluene sulfonic, maleic, tartaric, and other organic salts, or may be modified to C 1-6  alkyl or dialkyl amino or further converted to an amide. 
     The present invention further provides a conjugate comprising the formula 
       A-LM-B 
     wherein A is human insulin molecule or human insulin analog molecule; B is an incretin peptide (e.g., glucagon, GLP-1, or GIP) or a glucagon peptide modified to have agonist activity at the GLP1 receptor, agonist activity at the GIP receptor, agonist the GLP1 and GCG receptors, or agonist activity at the GLP-1 and GIP receptors; LM is a linking moiety comprising a cyclic or acyclic bisamide, a heterocycle and a substituted heterocycle, a C 1 —C 50  hydrocarbon chain or substituted hydrocarbon chain, a PEG n  wherein n is 1-50, a (PEG 2 ) n  wherein n is 1-50, a (PEG 2 ) n -(γGlu) p -C n  wherein each n is independently 1-50 and p is 1 or 2, a (PEG 2 ) n -C n  wherein each n is independently is 1-50, a (PEG) n (PEG) n  wherein each n is independently 1-50, a PEG n -(Lys-(γGlu) p -C n )—C n  wherein each n is independently 1-50 and p is 1 or 2, or a C 5 -Lys(γE-C n )-PEG n  wherein each n is independently 1-50. 
     In particular embodiments, LM is selected from a straight or branched, saturated or unsaturated, optionally substituted C 1-30  hydrocarbon chain wherein one or more methylene units of Y are optionally and independently replaced by —O—, —S—, —N(R)—, —C(O)—, C(O)O—, OC(O)—, —N(R)C(O)—, —C(O)N(R)—, —S(O)—, —S(O) 2 —, —N(R)SO 2 —, SO 2 N(R)—, a heterocyclic group, an aryl group, or a heteroaryl group, wherein each occurrence of R is independently hydrogen, a suitable protecting group, an acyl moiety, arylalkyl moiety, aliphatic moiety, aryl moiety, heteroaryl moiety, or heteroaliphatic moiety. 
     In particular embodiments, the human insulin molecule or human insulin analog molecule may be a heterodimer comprising an A-chain peptide and a B-chain peptide connected by disulfide linkages characteristic of human insulin or a single-chain insulin molecule comprising the disulfide linkages characteristic of human insulin wherein the C-terminal amino acid of the B-chain is conjugated to the N-terminal amino acid of the A-chain peptide by a peptide or non-peptide linker. 
     In particular embodiments, the N-terminal amino acid of the A-chain peptide of the human insulin or human insulin analog molecule is conjugated via LM to an amino acid in the incretin peptide or modified glucagon peptide; or, the N-terminal amino acid of the B-chain peptide of the human insulin or human insulin analog molecule is conjugated via LM to an amino acid in the incretin peptide or modified glucagon peptide; or, the epsilon amino group of a Lysine in the human insulin or human insulin analog molecule is conjugated via LM to an amino acid in the incretin peptide or modified glucagon peptide. 
     In particular embodiments, the N-terminal amino acid of the A-chain peptide of the human insulin or human insulin analog molecule is conjugated via LM to a Lysine or Norleucine in the incretin peptide or modified glucagon peptide; or, the N-terminal amino acid of the B-chain peptide of the human insulin or human insulin analog molecule is conjugated via LM to a Lysine or Norleucine in the incretin peptide or modified glucagon peptide; or, the epsilon amino group of a Lysine in the human insulin or human insulin analog molecule is conjugated via LM to a Lysine or Norleucine in the incretin peptide or modified glucagon peptide. 
     Incretin 
     The incretin comprising the insulin-incretin conjugate may be any peptide having agonist activity at the glucagon-like 1 (GLP-1) receptor, the glucagon (GCG) receptor, the gastric inhibitory protein (GIP) receptor, or both the GLP-1 receptor and the GCG receptor or both the GLP-1 receptor and the GIP receptor. In particular embodiments, the incretin is a glucagon peptide modified to have agonist activity at the glucagon-like 1 (GLP-1) receptor, the glucagon (GCG) receptor, the gastric inhibitory protein (GIP) receptor, or both the GLP-1 receptor and the GCG receptor or both the GLP-1 receptor and the GIP receptor. 
     In particular embodiments, the peptide comprises a modified glucagon peptide comprising the amino acid sequence 
                            (SEQ ID NO: 1)           HSQGTFTSDYSKYLDERAAQDFVQWLLDT,            
which further includes at least the following modifications: (i) a substitution of the amino acid at position 2 with an amino acid that renders the peptide resistant to cleavage and inactivation by dipeptidyl peptidase IV; (ii) a lipid moiety covalently linked to the peptide at a lysine residue substituted for the tyrosine residue at position 10 or the glutamine at position 20 of the peptide; (iii) an azide group or an alkyne group conjugated to an amino acid at position 20, 21, 24, 30, or 31; (iv) 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10 additional amino acid substitutions in addition to the substitution at position 2; and optionally, a protecting group that is joined to the C-terminal carboxy group and/or the N-terminal amino group. In embodiments in which the modified glucagon peptide has agonist activity at the GIP receptor, the Histidine at position 1 is substituted Tyrosine, Phenylalanine, Tryptophan, or other amino acid with an aromatic group.
 
     In general, the peptide comprises a substitution of the Ser at position 2 with Val, Ile, Asp, Glu, Met, Trp, Asn, D-Ala, D-Ser, a-methyl-Ser, a-methyl-D-Ser or a-aminoisobutyric acid (aib or U). In particular embodiments, the Ser is substituted with D-Ser or aib. These substitutions at position 2 render the peptide resistant to DPP-4 and active at the GLP-1 receptor. Peptides with a substitution are co-agonists of the GCG and the GLP-1 receptors. 
     In particular embodiments, the Gln at position 3 is substituted with Glu or Asp. These substitutions increase the selectivity of the peptide for the GLP-1 receptor over the GCG receptor. Such peptides have little or no activity at the GCG receptor. 
     In particular embodiments, the peptide includes a substitution of the Glu at position 16 with aib, Asn, Ser, or Ala. 
     In particular embodiments the His at position 1 is substituted with an amino acid with a large aromatic group, for example, Tyr, Phe, or Trp. When this substitution includes the substitution of the Ser at position 2 with aib or D-Ser, the substitution of the Lys at position 12 with Ile and substitution of the Glu at position 16 with aib, the peptide has agonist activity at the GCG, GLP-1 and GIP receptors. When the peptide further includes a substitution of the Gln at position 3 with Glu or Asp, the peptide has agonist activity at the GLP-1 and GIP receptors. 
     In particular embodiments, the insulin molecule comprises an alkyne group and the peptide agonist activity is selective for the GLP-1 receptor and comprises the structure 
                            (SEQ ID NO: 2)           HX 2 X 3 GTFTSX9X 10 SX 12 YX 14 DX 16 X 17 X 18 AX 20 X 21 X 22 V                       X 24 X 25 X 26 X 27 X 28 X 29 X 30 X 31 ,            
wherein X 2  is amionisobutyric acid (Aib), Gly, D-Serine (s), alpha-methyl Serine (αMS), or alpha-methyl D-Serine (αMs);
 
     X 3  is Val, Glu or Asp; 
     X 9  is Asp or alpha-methyl Aspartic acid (αMD);
 
X 10  is Tyr or Lys conjugated to a lipid moiety;
 
     X 12  is Lysine, Leucine, or Serine; 
     X 14  is Leu of alpha-methyl Leucine (αML);
 
X 16  is Glutamic acid, Asparagine, Serine, Alanine, or Aib;
 
     X 17  is Arginine or Lysine; 
     X 18  is Alanine or Arginine; 
     X 20  is Glutamine or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal azide group or to a fatty acid or fatty diacid;
 
X 21  is Aspartic acid, αMD, Azidonorleucine (Norleucine conjugated via its epsilon carbon to an azide group (Nle(εN 3 ))), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal azide group;
 
     X 22  is Phe or αMF; 
     X 24  is Glutamine, Nle(εN 3 ), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal azide group;
 
X 25  is Tryptophan or alpha-methyl Tryptophan (αMW);
 
     X 26  is Leucine or αML; 
     X 27  is Methionine, Leucine, Methionine sulfoxide, or L-methionine sulphone (2);
 
X 28  is Aspartic acid, Alanine, Lysine, Asparagine, γGlu, Glutamine, or αMD;
 
     X 29  is Threonine or Glycine; 
     X 30  is Arginine, Lysine, or Nle(εN 3 ), or X 30  is absent; and
 
X 31  is Glycine, γGlu, Nle(εN 3 ), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal azide group, or X 31  is absent; and
 
     wherein the C-terminal amino acid optionally is amidated, and with the proviso that either X 10  is a Lysine residue conjugated via its epsilon amino acid to the lipid moiety and one of X 20 , X 21 , X 24 , X 30 , or X 31  comprises the azide group or X 20  is a Lysine residue conjugated via its epsilon amino acid to the lipid moiety and one of X 21 , X 24 , X 30 , or X 31  comprises the azide group. 
     In particular embodiments, the insulin molecule comprises an azide group and the peptide agonist activity is selective for the GLP-1 receptor and comprises the structure 
                            (SEQ ID NO: 3)           HX 2 X 3 GTFTSX9X 10 SX 12 YX 14 DX 16 X 17 X 18 AX 20 X 21 X 22 V-                       X 24 X 25 X 26 X 27 X 28 X 29 X 30 X 31 ,            
wherein X 2  is aminoisobutyric acid (Aib), D-Serine (s), or alpha-methyl Serine (αMS);
 
     X 3  is Val, Glu, or Asp; 
     X 9  is Asp or alpha-methyl Aspartic acid (αMD);
 
X 10  is Tyr or Lys conjugated to a lipid moiety;
 
     X 12  is Lysine, Leucine, or Serine; 
     X 14  is Leu of alpha-methyl Leucine (αML);
 
X 16  is Glutamic acid, Asparagine, Serine, Alanine, or Aib;
 
     X 17  is Arginine or Lysine; 
     X 18  is Alanine or Arginine; 
     X 20  is Glutamine or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal alkyne group or to a fatty acid or fatty diacid;
 
X 21  is Aspartic acid, αMD, Alkynylnorleucine (Norleucine conjugated via its epsilon carbon to an alkyne group (Nle(ε-alkyne))), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal alkyne group;
 
X 22  is Phe or alpha-methyl Phenylalanine (αMF);
 
X 24  is Glutamine, Nle(ε-alkyne), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal alkyne group;
 
X 25  is Tryptophan or alpha-methyl Tryptophan (αMW);
 
     X 26  is Leucine or αML; 
     X 27  is Methionine, Leucine, methionine sulfoxide, or L-methionine sulphone (2);
 
X 28  is Aspartic acid, Alanine, Lysine, Asparagine, γGlu, Glutamine, or αMD;
 
     X 29  is Threonine or Glycine; 
     X 30  is Arginine, Lysine, or Nle(ε-alkyne), or X 30  is absent; and
 
X 31  is Glycine, γGlu, Nle(ε-alkyne), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal alkyne group, or X 31  is absent; and
 
     wherein the C-terminal amino acid optionally is amidated, and with the proviso that either X 10  is a Lysine residue conjugated via its epsilon amino acid to the lipid moiety and one of X 20 , X 21 , X 24 , X 30 , or X 31  comprises the alkyne group or X 20  is a Lysine residue conjugated via its epsilon amino acid to the lipid moiety and one of X 21 , X 24 , X 30 , or X 31  comprises the alkyne group. 
     In particular embodiments, the insulin molecule comprises an alkyne group and the peptide has agonist activity at the GLP-1 and GCG receptors and comprises the structure 
                            (SEQ ID NO: 4)           HX 2 QGTFTSX9X 10 SX 12 YX 14 DX 16 X 17 X 18 AX 20 X 21 X 22 V-                       X 24 X 25 X 26 X 27 X 28 X 29 X 30 X 31 ,            
wherein X 2  is aminoisobutyric acid (Aib), D-Serine (s), or alpha-methyl Serine (αMS);
 
X 9  is Asp or alpha-methyl Aspartic acid (αMD);
 
X 10  is Tyr or Lys conjugated to a lipid moiety;
 
     X 12  is Lysine, Leucine, or Serine; 
     X 14  is Leu of alpha-methyl Leucine (αML);
 
X 16  is Glutamic acid, Asparagine, Serine, Alanine, or Aib;
 
     X 17  is Arginine or Lysine; 
     X 18  is Alanine or Arginine; 
     X 20  is Glutamine or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal azide group or to a fatty acid or fatty diacid;
 
X 21  is Aspartic acid, αMD, Azidonorleucine (Norleucine conjugated via its epsilon carbon to an azide group (Nle(εN 3 ))), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal azide group;
 
X 22  is Phe or alpha-methyl Phenylalanine (αMF);
 
X 24  is Glutamine, Nle(εN 3 ), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal azide group;
 
X 25  is Tryptophan or alpha-methyl Tryptophan (αMW);
 
     X 26  is Leucine or αML; 
     X 27  is Methionine, Leucine, methionine sulfoxide, or L-methionine sulphone (2);
 
X 28  is Aspartic acid, Alanine, Lysine, Asparagine, γGlu, Glutamine, or αMD;
 
     X 29  is Threonine or Glycine; 
     X 30  is Arginine, Lysine, or Nle(εN 3 ), or X 30  is absent; and
 
X 31  is Glycine, γGlu, Nle(εN 3 ), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal azide group, or X 31  is absent; and
 
     wherein the C-terminal amino acid optionally is amidated, and with the proviso that either X 10  is a Lysine residue conjugated via its epsilon amino acid to the lipid moiety and one of X 20 , X 21 , X 24 , X 30 , or X 31  comprises the azide group or X 20  is a Lysine residue conjugated via its epsilon amino acid to the lipid moiety and one of X 21 , X 24 , X 30 , or X 31  comprises the azide group. 
     In particular embodiments, the insulin molecule comprises an azide group and the peptide has agonist activity at the GLP-1 and GCG receptors and comprises the structure 
                            (SEQ ID NO: 5)           HX 2 QGTFTSX9X 10 SX 12 YX 14 DX 16 X 17 X 18 AX 20 X 21 X 22 V-                       X 24 X 25 X 26 X 27 X 28 X 29 X 30 X 31 ,            
wherein X 2  is aminoisobutyric acid (Aib), D-Serine (s), or alpha-methyl Serine (αMS);
 
X 9  is Asp or alpha-methyl Aspartic acid (αMD);
 
X 10  is Tyr or Lys conjugated to a lipid moiety;
 
     X 12  is Lysine, Leucine, or Serine; 
     X 14  is Leu of alpha-methyl Leucine (αML);
 
X 16  is Glutamic acid, Asparagine, Serine, Alanine, or Aib;
 
     X 17  is Arginine or Lysine; 
     X 18  is Alanine or Arginine; 
     X 20  is Glutamine or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal alkyne group or to a fatty acid or fatty diacid;
 
X 21  is Aspartic acid, αMD, Alkynylnorleucine (Norleucine conjugated via its epsilon carbon to an alkyne group (Nle(ε-alkyne))), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal alkyne group;
 
X 22  is Phe or alpha-methyl Phenylalanine (αMF);
 
X 24  is Glutamine, Nle(ε-alkyne), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal alkyne group;
 
X 25  is Tryptophan or alpha-methyl Tryptophan (αMW);
 
     X 26  is Leucine or αML; 
     X 27  is Methionine, Leucine, methionine sulfoxide, or L-methionine sulphone (2);
 
X 28  is Aspartic acid, Alanine, Lysine, Asparagine, γGlu, Glutamine, or αMD;
 
     X 29  is Threonine or Glycine; 
     X 30  is Arginine, Lysine, or Nle(ε-alkyne), or X 30  is absent; and
 
X 31  is Glycine, γGlu, Nle(ε-alkyne), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal alkyne group, or X 31  is absent; and
 
     wherein the C-terminal amino acid optionally is amidated, and with the proviso that either X 10  is a Lysine residue conjugated via its epsilon amino acid to the lipid moiety and one of X 20 , X 21 , X 24 , X 30 , or X 31  comprises the alkyne group or X 20  is a Lysine residue conjugated via its epsilon amino acid to the lipid moiety and one of X 21 , X 24 , X 30 , or X 31  comprises the alkyne group. 
     In particular embodiments, the insulin molecule comprises an alkyne group and the peptide has agonist activity predominantly at the GLP-1 receptor and GIP receptor and comprises the structure 
                            (SEQ ID NO: 6)           X 1 X 2 X 3 GTFTSX9X 10 SX 12 YX 14 DX 16 X 17 X 18 AX 20 X 21 X 22 V-                       X 24 X 25 X 26 X 27 X 28 X 29 X 30 X 31 ,            
wherein X 1  is Tyrosine, Phenylalanine, Tryptophan, or other amino acid with an aromatic group;
 
X 2  is amionisobutyric acid (Aib), Gly, D-Serine (s), or alpha-methyl Serine (αMS);
 
     X 3  is Val, Glu, or Asp; 
     X 9  is Asp or alpha-methyl Aspartic acid (αMD);
 
X 10  is Tyr or Lys conjugated to a lipid moiety;
 
     X 12  is Isoleucine, Lysine, Leucine, or Serine; 
     X 14  is Leu of alpha-methyl Leucine (αML);
 
X 16  is Glutamic acid, Asparagine, Serine, Alanine, or Aib;
 
     X 17  is Arginine or Lysine; 
     X 18  is Alanine or Arginine; 
     X 20  is Glutamine or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal azide group or to a fatty acid or fatty diacid;
 
X 21  is Aspartic acid, αMD, Azidonorleucine (Norleucine conjugated via its epsilon carbon to an azide group (Nle(εN 3 ))), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal azide group;
 
X 22  is Phe or alpha-methyl Phenylalanine (αMF),
 
X 24  is Glutamine, Nle(εN 3 ), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal azide group;
 
X 25  is Tryptophan or alpha-methyl Tryptophan (αMW);
 
     X 26  is Leucine or αML; 
     X 27  is Met, Leucine, methionine sulfoxide, or L-methionine sulphone (2);
 
X 28  is Aspartic acid, Alanine, Lysine, Asparagine, γGlu, Glutamine, or αMD;
 
     X 29  is Threonine or Glycine; 
     X 30  is Arginine, Lysine, or Nle(εN 3 ), or X 30  is absent; and
 
X 31  is Glycine, γGlu, Nle(εN 3 ), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal azide group, or X 31  is absent; and
 
     wherein the C-terminal amino acid optionally is amidated, and with the proviso that either X 10  is a Lysine residue conjugated via its epsilon amino acid to the lipid moiety and one of X 20 , X 21 , X 24 , X 30 , or X 31  comprises the azide group or X 20  is a Lysine residue conjugated via its epsilon amino acid to the lipid moiety and one of X 21 , X 24 , X 30 , or X 31  comprises the azide group. 
     In particular embodiments, the insulin molecule comprises an azide group and the peptide has agonist activity at the GLP-1 receptor and GIP receptor and comprises the structure 
                            (SEQ ID NO: 7)           X 1 X 2 X 3 GTFTSX9X 10 SX 12 YX 14 DX 16 X 17 X 18 AX 20 X 21 X 22 V-                       X 24 X 25 X 26 X 27 X 28 X 29 X 30 X 31 ,            
wherein X 1  is Tyrosine, Phenylalanine, Tryptophan, or other amino acid with an aromatic group;
 
X 2  is aminoisobutyric acid (Aib), D-Serine (s), or alpha-methyl Serine (αMS);
 
     X 3  is Val, Glu, or Asp; 
     X 9  is Asp or alpha-methyl Aspartic acid (αMD);
 
X 10  is Tyr or Lys conjugated to a lipid moiety;
 
     X 12  is Isoleucine, Lysine, Leucine, or Serine; 
     X 14  is Leu of alpha-methyl Leucine (αML);
 
X 16  is Glutamic acid, Asparagine, Serine, Alanine, or Aib;
 
     X 17  is Arginine or Lysine; 
     X 18  is Alanine or Arginine; 
     X 20  is Glutamine or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal alkyne group or to a fatty acid or fatty diacid;
 
X 21  is Aspartic acid, αMD, Alkynylnorleucine (Norleucine conjugated via its epsilon carbon to an alkyne group (Nle(ε-alkyne))), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal alkyne group;
 
X 22  is Phe or alpha-methyl Phenylalanine (αMF), X 24  is Glutamine, Nle(ε-alkyne), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal alkyne group;
 
X 25  is Tryptophan or alpha-methyl Tryptophan (αMW);
 
     X 26  is Leucine or αML; 
     X 27  is Methionine, Leucine, methionine sulfoxide, or L-methionine sulphone (2);
 
X 28  is Aspartic acid, Alanine, Lysine, Asparagine, γGlu, Glutamine, or αMD;
 
     X 29  is Threonine or Glycine; 
     X 30  is Arginine, Lysine, or Nle(ε-alkyne), or X 30  is absent; and
 
X 31  is Glycine, γGlu, Nle(ε-alkyne), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal alkyne group, or X 31  is absent; and
 
     wherein the C-terminal amino acid optionally is amidated, and with the proviso that either X 10  is a Lysine residue conjugated via its epsilon amino acid to the lipid moiety and one of X 20 , X 21 , X 24 , X 30 , or X 31  comprises the alkyne group or X 20  is a Lysine residue conjugated via its epsilon amino acid to the lipid moiety and one of X 21 , X 24 , X 30 , or X 31  comprises the alkyne group. 
     In particular embodiments, the insulin molecule comprises an alkyne group and the peptide has agonist activity at the GLP-1, GIP, and GCG receptors and comprises the structure 
                            (SEQ ID NO: 8)           X 1 X 2 QGTFTSX9X 10 SX 12 YX 14 DX 16 X 17 X 18 AX 20 X 21 X 22 V-                       X 24 X 25 X 26 X 27 X 28 X 29 X 30 X 31 ,            
wherein X 1  is Tyrosine, Phenylalanine, Tryptophan, or other amino acid with an aromatic group;
 
X 2  is amionisobutyric acid (Aib), Gly, D-Serine (s), or alpha-methyl Serine (αMS);
 
X 9  is Asp or alpha-methyl Aspartic acid (αMD);
 
X 10  is Tyr or Lys conjugated to a lipid moiety;
 
     X 12  is Isoleucine, Lysine, Leucine, or Serine; 
     X 14  is Leu of alpha-methyl Leucine (αML);
 
X 16  is Glutamic acid, Asparagine, Serine, Alanine, or Aib;
 
     X 17  is Arginine or Lysine; 
     X 18  is Alanine or Arginine; 
     X 20  is Glutamine or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal azide group or to a fatty acid or fatty diacid;
 
X 21  is Aspartic acid, αMD, Azidonorleucine (Norleucine conjugated via its epsilon carbon to an azide group (Nle(εN 3 ))), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal azide group;
 
X 22  is Phe or alpha-methyl Phenylalanine (αMF);
 
X 24  is Glutamine, Nle(εN 3 ), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal azide group;
 
X 25  is Tryptophan or alpha-methyl Tryptophan (αMW);
 
     X 26  is Leucine or αML; 
     X 27  is methionine, Leucine, methionine sulfoxide, or L-methionine sulphone (2);
 
X 28  is Aspartic acid, Alanine, Lysine, Asparagine, γGlu, Glutamine, or αMD;
 
     X 29  is Threonine or Glycine; 
     X 30  is Arginine, Lysine, or Nle(εN 3 ), or X 30  is absent; and
 
X 31  is Glycine, γGlu, Nle(εN 3 ), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal azide group, or X 31  is absent; and
 
     wherein the C-terminal amino acid optionally is amidated, and with the proviso that either X 10  is a Lysine residue conjugated via its epsilon amino acid to the lipid moiety and one of X 20 , X 21 , X 24 , X 30 , or X 31  comprises the azide group or X 20  is a Lysine residue conjugated via its epsilon amino acid to the lipid moiety and one of X 21 , X 24 , X 30 , or X 31  comprises the azide group. 
     In particular embodiments, the insulin molecule comprises an azide group and the peptide has agonist activity at the GLP-1, GIP, and GCG receptors and comprises the structure 
                            (SEQ ID NO: 9)           X 1 X 2 QGTFTSX9X 10 SX 12 YX 14 DX 16 X 17 X 18 AX 20 X 21 FV-                       X 24 X 25 X 26 X 27 X 28 X 29 X 30 X 31 ,            
wherein X 1  is Tyrosine, Phenylalanine, Tryptophan, or other amino acid with an aromatic group;
 
X 2  is aminoisobutyric acid (Aib), D-Serine (s), or alpha-methyl Serine (αMS);
 
X 9  is Asp or alpha-methyl Aspartic acid (αMD);
 
X 10  is Tyr or Lys conjugated to a lipid moiety;
 
     X 12  is Isoleucine, Lysine, Leucine, or Serine; 
     X 14  is Leu of alpha-methyl Leucine (αML);
 
X 16  is Glutamic acid, Asparagine, Serine, Alanine, or Aib;
 
     X 17  is Arginine or Lysine; 
     X 18  is Alanine or Arginine; 
     X 20  is Glutamine or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal alkyne group or to a fatty acid or fatty diacid;
 
X 21  is Aspartic acid, αMD, Alkynylnorleucine (Norleucine conjugated via its epsilon carbon to an alkyne group (Nle(ε-alkyne))), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal alkyne group;
 
X 22  is Phe or alpha-methyl Phenylalanine (αMF);
 
X 24  is Glutamine, Nle(ε-alkyne), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal alkyne group;
 
X 25  is Tryptophan or alpha-methyl Tryptophan (αMW);
 
     X 26  is Leucine or αML; 
     X 27  is methionine, Leucine, methionine sulfoxide, or L-methionine sulphone (2);
 
X 28  is Aspartic acid, Alanine, Lysine, Asparagine, γGlu, Glutamine, or αMD;
 
     X 29  is Threonine or Glycine; 
     X 30  is Arginine, Lysine, or Nle(ε-alkyne), or X 30  is absent; and
 
X 31  is Glycine, γGlu, Nle(ε-alkyne), or Lysine conjugated via its epsilon amino group to a non-peptide linker comprising a terminal alkyne group, or X 31  is absent; and
 
     wherein the C-terminal amino acid optionally is amidated, and with the proviso that either X 10  is a Lysine residue conjugated via its epsilon amino acid to the lipid moiety and one of X 20 , X 21 , X 24 , X 30 , or X 31  comprises the alkyne group or X 20  is a Lysine residue conjugated via its epsilon amino acid to the lipid moiety and one of X 21 , X 24 , X 30 , or X 31  comprises the alkyne group. 
     The lipid moiety may be a monocarboxylic acid comprising an aliphatic chain of 13 to 20 methylene groups (fatty acid) wherein one end of the molecule is the proximal end and the other end is the distal end and only one of the proximal end and the distal end has a carboxyl (COOH) group. The fatty acid may be represented by the structure HO 2 C(CH 2 ) n CH 3 , wherein n is 11, 12, 13, 14, 15, 16, 17, or 18. The fatty acid may have one of the following structures 
     
       
         
         
             
             
         
       
     
     The lipid moiety may be an α,ω-dicarboxylic acid comprising an aliphatic chain of 13 to 20 methylene groups (fatty diacid) wherein one end of the molecule is the proximal end and the other end is the distal end and wherein the proximal end and the distal end both have a carboxyl (COOH) group. The fatty diacid may be represented by the structure HO 2 C(CH 2 ) n CO 2 H, wherein n is 11, 12, 13, 14, 15, 16, 17, or 18. The fatty diacid may have one of the following structures 
     
       
         
         
             
             
         
       
     
     As a component of the peptide, the acid functionality at the proximal end of the fatty diacid is conjugated to the amino group of a linker in a C(O)—NH linkage and the acid functionality at the distal end of the fatty diacid is a free carboxyl group (COOH). The COOH group at the distal end helps confer a longer half-life to the peptide by its ability to non-covalently bind to serum albumin, a known carrier for fatty acids in serum. The COOH group enhances duration of action as it provides a better non-covalent interaction with serum albumin than peptides that have been acylated using a fatty acid, which bind serum albumin less efficiently and form a less stable non-covalent interaction with the serum albumin. 
     When the fatty acid or diacid is conjugated to a linking moiety or linker, it is subsequently referred to as a fatty acid component. The linker may be PEG 2  (8-amino-3,6-dioxaoctanoic acid) linked to Gamma-Glutamic acid (gamma-Glu, γGlu, or γE), which has the structure 
     
       
         
         
             
             
         
       
     
     or the linker may be Gamma-Glutamic acid-gamma glutamic acid (gamma-Glu-gamma-Glu, or γGlu-γGlu, or γEγE), which has the structure 
     
       
         
         
             
             
         
       
     
     The structure of K(PEG 2 PEG 2 γE-fatty acid) wherein the linker is PEG 2 PEG 2 γE and the fatty acid component comprises C14, C16, C17, C18, C19, or C20 fatty acid is represented by 
     
       
         
         
             
             
         
       
     
     wherein n is 7, 9, 10, 11, 12, 13, or 14 respectively, and the wavy lines represent the bonds between adjacent amino acids in the peptide sequence. 
     The structure of K(γEγE-fatty acid) wherein the linker is γEγE and the fatty acid component comprises C14, C16, C17, C18, C19, or C20 fatty acid is represented by 
     
       
         
         
             
             
         
       
     
     wherein n is 7, 9, 10, 11, 12, 13, or 14, respectively, and the wavy lines represent the bonds between adjacent amino acids in the peptide sequence. 
     The structure of K(PEG 2 PEG 2 γE-fatty acid) wherein the linker is PEG 2 PEG 2 γE and the fatty acid component comprises C14, C16, C17, C18, C19, or C20 fatty diacid is represented by 
     
       
         
         
             
             
         
       
     
     wherein n is 7, 9, 10, 11, 12, 13, or 14 respectively, and the wavy lines represent the bonds between adjacent amino acids in the peptide sequence. 
     The structure of K(γEγE-fatty acid) wherein the linker is γEγE and the fatty acid component comprises C14, C16, C17, C18, C19, or C20 fatty diacid is represented by 
     
       
         
         
             
             
         
       
     
     wherein n is 7, 9, 10, 11, 12, 13, or 14, respectively, and the wavy lines represent the bonds between adjacent amino acids in the peptide sequence. 
     In particular aspects, the peptide may comprise a lysine residue at the C-terminus that is conjugated to a γE residue to provide a KyE at position 30 in the peptide, which is represented by 
     
       
         
         
             
             
         
       
     
     wherein the wavy lines represent the bonds between adjacent amino acids in the peptide sequence. 
     In a further embodiment, the insulin molecule comprises an alkyne group and the peptide has agonist activity at the GLP-1 and GCG receptors and comprises the structure 
                            (SEQ ID NO: 10)           HX 2 QGTFTSX9X 10 SX 12 YX 14 DX 16 X 17 X 18 AX 20 X 21 FV-                       X 24 X 25 X 26 X 27 X 28 X 29 X 30 X 31 ,            
wherein X 2  is aminoisobutyric acid (Aib), D-Serine (s), or alpha-methyl Serine (αMS);
 
X 9  is Serine or alpha-methyl Aspartic acid (αMD);
 
X 10  is Tyr or Lys conjugated to γGlu-γGlu-C 16 ;
 
     X 12  is Lysine, Leucine, or Serine; 
     X 14  is Leu of alpha-methyl Leucine (αML);
 
X 16  is Glutamic acid, Asparagine, Serine, Alanine, or Aib;
 
     X 17  is Arginine or Lysine; 
     X 18  is Alanine or Arginine; 
     X 20  is Glutamine or Lysine conjugated via its epsilon amine group to PEG 2 -C 5 N 3 , PEG 2 PEG 2 -C 5 N 3 , PEG 2 PEG 2 -γGlu-C 16 N 3 , PEG 2 PEG 2 -γGlu-C 18 —OH, or PEG 2 PEG 2 γE-C 20 —OH;
 
X 21  is Aspartic acid, alpha-methyl Phenylalanine (αMF), αMD, Azidonorleucine (Norleucine conjugated via its epsilon carbon to an azide group (Nle(εN 3 ))), or Lys conjugated via its epsilon amine group to PEG 2 -C 5 N 3 , PEG 2 PEG 2 -C 5 N 3 , or PEG 2 PEG 2 -γGlu-C 16 N 3 ;
 
X 24  is Glutamine, Nle(εN 3 ), or Lysine conjugated to PEG 2 PEG 2 -γGlu-C 16 N 3 ;
 
X 25  is Tryptophan or alpha-methyl Tryptophan (αMW);
 
     X 26  is Leucine or αML; 
     X 27  is Leucine or L-methionine sulphone (2);
 
X 28  is Aspartic acid, Alanine, Lysine, Asparagine, γGlu, Glutamine, or αMD;
 
     X 29  is Threonine or Glycine; 
     X 30  is Arginine, Lysine, or Nle(εN 3 ), or X 30  is absent; and
 
X 31  is Glycine, γGlu, Nle(εN 3 ), or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 N 3 , PEG 2 -C 5 N 3  or PEG 2 PEG 2 -C 5 N 3 , or X 31  is absent; and
 
     wherein the C-terminal amino acid optionally is amidated, and with the proviso that either X 10  is a Lysine residue conjugated via its epsilon amino group to a γGlu-γGlu-C 16  and one of X 20 , X 21 , X 24 , X 30 , or X 31  comprises the azide or N 3  group or X 20  is a Lysine residue conjugated via its epsilon amino group to the PEG 2 PEG 2 -γGlu-C 18 —OH or the PEG 2 PEG 2 γE-C 20 —OH and one of X 21 , X 24 , X 30 , or X 31  comprises the azide or N 3  group. 
     In a further embodiment, the insulin molecule comprises an alkyne group and the peptide has agonist activity at the GLP-1 and GCG receptors and comprises the structure 
                            (SEQ ID NO: 11)           HX 2 QGTFTSX9X 10 SX 12 YX 14 DX 16 X 17 X 18 AX 20 X 21 FV-                       X 24 X 25 X 26 X 27 X 28 X 29 X 30 X 31 ,            
wherein X 2  is aminoisobutyric acid (Aib), D-Serine (s), or alpha-methyl Serine (αMS);
 
X 9  is Serine or alpha-methyl Aspartic acid (αMD);
 
X 10  is Tyr or Lys conjugated to γGlu-γGlu-C 16 ;
 
     X 12  is Lysine, Leucine, or Serine; 
     X 14  is Leu of alpha-methyl Leucine (αML);
 
X 16  is Glutamic acid, Asparagine, Serine, Alanine, or Aib;
 
     X 17  is Arginine or Lysine; 
     X 18  is Alanine or Arginine; 
     X 20  is Glutamine or Lysine conjugated via its epsilon amine group to PEG 2 -C 5 N 3 , PEG 2 PEG 2 -C 5 -alkyne, PEG 2 PEG 2 -γGlu-C 16 -alkyne, PEG 2 PEG 2 -γGlu-C 18 —OH, or PEG 2 PEG 2 γE-C 20 —OH;
 
X 21  is Aspartic acid, alpha-methyl Phenylalanine (αMF), αMD, Alkynylnorleucine (Norleucine conjugated via its epsilon carbon to an alkyne group (Nle(ε-alkyne))), or Lys conjugated via its epsilon amine group to PEG 2 -C 5 -alkyne, PEG 2 PEG 2 -C 5 -alkyne, or PEG 2 PEG 2 -γGlu-C 16 -alkyne;
 
X 24  is Glutamine, Nle(ε-alkyne), or Lysine conjugated to PEG 2 PEG 2 -γGlu-C 16 -alkyne;
 
X 25  is Tryptophan or alpha-methyl Tryptophan (αMW);
 
     X 26  is Leucine or αML; 
     X 27  is Leucine or L-methionine sulphone (2);
 
X 28  is Aspartic acid, Alanine, Lysine, Asparagine, γGlu, Glutamine, or αMD;
 
     X 29  is Threonine or Glycine; 
     X 30  is Arginine, Lysine, or Nle(ε-alkyne), or X 30  is absent; and
 
X 31  is Glycine, γGlu, Nle(ε-alkyne), or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 -alkyne, PEG 2 -C 5 -alkyne, PEG 2 PEG 2 -C 5 -alkyne, or X 31  is absent; and wherein the C-terminal amino acid optionally is amidated, and with the proviso that either X 10  is a Lysine residue conjugated via its epsilon amino group to a γGlu-γGlu-C 16  and one of X 20 , X 21 , X 24 , X 30 , or X 31  comprises the -alkyne or X 20  is a Lysine residue conjugated via its epsilon amino group to the PEG 2 PEG 2 -γGlu-C 18 —OH or the PEG 2 PEG 2 YE-C 20 —OH and one of X 21 , X 24 , X 30 , or X 31  comprises the -alkyne.
 
     In a further embodiment, the insulin molecule comprises an alkyne group and the peptide has agonist activity selective for the GLP-1 receptor and comprises the structure 
                            (SEQ ID NO: 12)           HX 2 X 3 GTFTSX9X 10 SX 12 YX 14 DX 16 X 17 X 18 AX 20 X 21 FV-                       X 24 X 25 X 26 X 27 X 28 X 29 X 30 X 31 ,            
wherein X 2  is aminoisobutyric acid (Aib), D-Serine (s), or alpha-methyl Serine (αMS);
 
     X 3  is Glu or Asp; 
     X 9  is Serine or alpha-methyl Aspartic acid (αMD);
 
X 10  is Tyr or Lys conjugated to γGlu-γGlu-C 16 ;
 
     X 12  is Lysine, Leucine, or Serine; 
     X 14  is Leu of alpha-methyl Leucine (αML);
 
X 16  is Glutamic acid, Asparagine, Serine, Alanine, or Aib;
 
     X 17  is Arginine or Lysine; 
     X 18  is Alanine or Arginine; 
     X 20  is Glutamine or Lysine conjugated via its epsilon amine group to PEG 2 -C 5 N 3 , PEG 2 PEG 2 -C 5 N 3 , PEG 2 PEG 2 -γGlu-C 16 N 3 , PEG 2 PEG 2 -γGlu-C 18 —OH, or PEG 2 PEG 2 γE-C 20 —OH;
 
X 21  is Aspartic acid, alpha-methyl Phenylalanine (αMF), αMD, Azidonorleucine (Norleucine conjugated via its epsilon carbon to an azide group (Nle(εN 3 ))), or Lys conjugated via its epsilon amine group to PEG 2 -C 5 N 3 , PEG 2 PEG 2 -C 5 N 3 , or PEG 2 PEG 2 -γGlu-C 16 N 3 ;
 
X 24  is Glutamine, Nle(εN 3 ), or Lysine conjugated to PEG 2 PEG 2 -γGlu-C 16 N 3 ;
 
X 25  is Tryptophan or alpha-methyl Tryptophan (αMW);
 
     X 26  is Leucine or αML; 
     X 27  is Leucine or L-methionine sulphone (2);
 
X 28  is Aspartic acid, Alanine, Lysine, Asparagine, γGlu, Glutamine, or αMD;
 
     X 29  is Threonine or Glycine; 
     X 30  is Arginine, Lysine, or Nle(εN 3 ), or X 30  is absent; and
 
X 31  is Glycine, γGlu, Nle(εN 3 ), or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 N 3 , PEG 2 -C 5 N 3  or PEG 2 PEG 2 -C 5 N 3 , or X 31  is absent; and
 
     wherein the C-terminal amino acid optionally is amidated, and with the proviso that either X 10  is a Lysine residue conjugated via its epsilon amino group to a γGlu-γGlu-C 16  and one of X 20 , X 21 , X 24 , X 30 , or X 31  comprises the azide or N 3  group or X 20  is a Lysine residue conjugated via its epsilon amino group to the PEG 2 PEG 2 -γGlu-C 18 —OH or the PEG 2 PEG 2 γE-C 20 —OH and one of X 21 , X 24 , X 30 , or X 31  comprises the azide or N 3  group. 
     In a further embodiment, the insulin molecule comprises an alkyne group and the peptide has agonist activity selective for the GLP-1 receptor and comprises the structure 
                            (SEQ ID NO: 13)           HX 2 X 3 GTFTSX9X 10 SX 12 YX 14 DX 16 X 17 X 18 AX 20 X 21 FV-                       X 24 X 25 X 26 X 27 X 28 X 29 X 30 X 31 ,            
wherein X 2  is aminoisobutyric acid (Aib), D-Serine (s), or alpha-methyl Serine (αMS);
 
     X 3  is Glu or Asp; 
     X 9  is Serine or alpha-methyl Aspartic acid (αMD);
 
X 10  is Tyr or Lys conjugated to γGlu-γGlu-C 16 ;
 
     X 12  is Lysine, Leucine, or Serine; 
     X 14  is Leu of alpha-methyl Leucine (αML);
 
X 16  is Glutamic acid, Asparagine, Serine, Alanine, or Aib;
 
     X 17  is Arginine or Lysine; 
     X 18  is Alanine or Arginine; 
     X 20  is Glutamine or Lysine conjugated via its epsilon amine group to PEG 2 -C 5 N 3 , PEG 2 PEG 2 -C 5 -alkyne, PEG 2 PEG 2 -γGlu-C 16 -alkyne, PEG 2 PEG 2 -γGlu-C 18 —OH, or PEG 2 PEG 2 γE-C 20 —OH;
 
X 21  is Aspartic acid, alpha-methyl Phenylalanine (αMF), αMD, Alkynylnorleucine (Norleucine conjugated via its epsilon carbon to an alkyne group (Nle(ε-alkyne))), or Lys conjugated via its epsilon amine group to PEG 2 -C 5 -alkyne, PEG 2 PEG 2 -C 5 -alkyne, or PEG 2 PEG 2 -γGlu-C 16 -alkyne;
 
X 24  is Glutamine, Nle(ε-alkyne), or Lysine conjugated to PEG 2 PEG 2 -γGlu-C 16 -alkyne;
 
X 25  is Tryptophan or alpha-methyl Tryptophan (αMW);
 
     X 26  is Leucine or αML; 
     X 27  is Leucine or L-methionine sulphone (2);
 
X 28  is Aspartic acid, Alanine, Lysine, Asparagine, γGlu, Glutamine, or αMD;
 
     X 29  is Threonine or Glycine; 
     X 30  is Arginine, Lysine, or Nle(ε-alkyne), or X 30  is absent; and
 
X 31  is Glycine, γGlu, Nle(ε-alkyne), or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 -alkyne, PEG 2 -C 5 -alkyne, PEG 2 PEG 2 -C 5 -alkyne, or X 31  is absent; and wherein the C-terminal amino acid optionally is amidated, and with the proviso that either X 10  is a Lysine residue conjugated via its epsilon amino group to a γGlu-γGlu-C 16  and one of X 20 , X 21 , X 24 , X 30 , or X 31  comprises the -alkyne or X 20  is a Lysine residue conjugated via its epsilon amino group to the PEG 2 PEG 2 -γGlu-C 18 —OH or the PEG 2 PEG 2 γE-C 20 —OH and one of X 21 , X 24 , X 30 , or X 31  comprises the -alkyne.
 
     In a further embodiment, the insulin molecule comprises an alkyne group and the peptide has agonist activity at the GLP-1 and GIP receptors and comprises the structure 
                            (SEQ ID NO: 14)           X 1 X 2 X 3 GTFTSX9X 10 SX 12 YX 14 DX 16 X 17 X 18 AX 20 X 21 FV-                       X 24 X 25 X 26 X 27 X 28 X 29 X 30 X 31 ,            
wherein X 1  is Tyrosine, Phenylalanine, Tryptophan, or other amino acid with an aromatic group;
 
X 2  is aminoisobutyric acid (Aib), D-Serine (s), or alpha-methyl Serine (αMS);
 
     X 3  is Glu or Asp; 
     X 9  is Serine or alpha-methyl Aspartic acid (αMD);
 
X 10  is Tyr or Lys conjugated to γGlu-γGlu-C 16 ;
 
     X 12  is Isoleucine, Lysine, Leucine, or Serine; 
     X 14  is Leu of alpha-methyl Leucine (αML);
 
X 16  is Glutamic acid, Asparagine, Serine, Alanine, or Aib;
 
     X 17  is Arginine or Lysine; 
     X 18  is Alanine or Arginine; 
     X 20  is Glutamine or Lysine conjugated via its epsilon amine group to PEG 2 -C 5 N 3 , PEG 2 PEG 2 -C 5 N 3 , PEG 2 PEG 2 -γGlu-C 16 N 3 , PEG 2 PEG 2 -γGlu-C 18 —OH, or PEG 2 PEG 2 γE-C 20 —OH;
 
X 21  is Aspartic acid, alpha-methyl Phenylalanine (αMF), αMD, Azidonorleucine (Norleucine conjugated via its epsilon carbon to an azide group (Nle(εN 3 ))), or Lys conjugated via its epsilon amine group to PEG 2 -C 5 N 3 , PEG 2 PEG 2 -C 5 N 3 , or PEG 2 PEG 2 -γGlu-C 16 N 3 ;
 
X 24  is Glutamine, Nle(εN 3 ), or Lysine conjugated to PEG 2 PEG 2 -γGlu-C 16 N 3 ;
 
X 25  is Tryptophan or alpha-methyl Tryptophan (αMW);
 
     X 26  is Leucine or αML; 
     X 27  is Leucine or L-methionine sulphone (2);
 
X 28  is Aspartic acid, Alanine, Lysine, Asparagine, γGlu, Glutamine, or αMD;
 
     X 29  is Threonine or Glycine; 
     X 30  is Arginine, Lysine, or Nle(εN 3 ), or X 30  is absent; and
 
X 31  is Glycine, γGlu, Nle(εN 3 ), or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 N 3 , PEG 2 -C 5 N 3  or PEG 2 PEG 2 -C 5 N 3 , or X 31  is absent; and
 
     wherein the C-terminal amino acid optionally is amidated, and with the proviso that either X 10  is a Lysine residue conjugated via its epsilon amino group to a γGlu-γGlu-C 16  and one of X 20 , X 21 , X 24 , X 30 , or X 31  comprises the azide or N 3  group or X 20  is a Lysine residue conjugated via its epsilon amino group to the PEG 2 PEG 2 -γGlu-C 18 —OH or the PEG 2 PEG 2 γE-C 20 —OH and one of X 21 , X 24 , X 30 , or X 31  comprises the azide or N 3  group. 
     In a further embodiment, the insulin molecule comprises an alkyne group and the peptide has agonist activity at the GLP-1 and GIP receptors and comprises the structure 
                            (SEQ ID NO: 15)           X 1 X 2 X 3 GTFTSX 9 X 10 SX 12 YX 14 DX 16 X 17 X 18 AX 20 X 21 FV-           X 24 X 25 X 26 X 27 X 28 X 29 X 30 X 31 ,            
wherein X 1  is Tyrosine, Phenylalanine, Tryptophan, or other amino acid with an aromatic group;
 
X 2  is aminoisobutyric acid (Aib), D-Serine (s), or alpha-methyl Serine (αMS);
 
     X 3  is Glu or Asp; 
     X 9  is Serine or alpha-methyl Aspartic acid (αMD);
 
X 10  is Tyr or Lys conjugated to γGlu-γGlu-C 16 ;
 
     X 12  is Isoleucine, Lysine, Leucine, or Serine; 
     X 14  is Leu of alpha-methyl Leucine (αML);
 
X 16  is Glutamic acid, Asparagine, Serine, Alanine, or Aib;
 
     X 17  is Arginine or Lysine; 
     X 18  is Alanine or Arginine; 
     X 20  is Glutamine or Lysine conjugated via its epsilon amine group to PEG 2 -C 5 N 3 , PEG 2 PEG 2 -C 5 -alkyne, PEG 2 PEG 2 -γGlu-C 16 -alkyne, PEG 2 PEG 2 -γGlu-C 18 —OH, or PEG 2 PEG 2 γE-C 20 —OH;
 
X 21  is Aspartic acid, alpha-methyl Phenylalanine (αMF), αMD, Alkynylnorleucine (Norleucine conjugated via its epsilon carbon to an alkyne group (Nle(ε-alkyne))), or Lys conjugated via its epsilon amine group to PEG 2 -C 5 -alkyne, PEG 2 PEG 2 -C 5 -alkyne, or PEG 2 PEG 2 -γGlu-C 16 -alkyne;
 
X 24  is Glutamine, Nle(ε-alkyne), or Lysine conjugated to PEG 2 PEG 2 -γGlu-C 16 -alkyne;
 
X 25  is Tryptophan or alpha-methyl Tryptophan (αMW);
 
     X 26  is Leucine or αML; 
     X 27  is Leucine or L-methionine sulphone (2);
 
X 28  is Aspartic acid, Alanine, Lysine, Asparagine, γGlu, Glutamine, or αMD;
 
     X 29  is Threonine or Glycine; 
     X 30  is Arginine, Lysine, or Nle(ε-alkyne), or X 30  is absent; and
 
X 31  is Glycine, γGlu, Nle(ε-alkyne), or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 -alkyne, PEG 2 -C 5 -alkyne, PEG 2 PEG 2 -C 5 -alkyne, or X 31  is absent; and wherein the C-terminal amino acid optionally is amidated, and with the proviso that either X 10  is a Lysine residue conjugated via its epsilon amino group to a γGlu-γGlu-C 16  and one of X 20 , X 21 , X 24 , X 30 , or X 31  comprises the -alkyne or X 20  is a Lysine residue conjugated via its epsilon amino group to the PEG 2 PEG 2 -γGlu-C 18 —OH or the PEG 2 PEG 2 γE-C 20 —OH and one of X 21 , X 24 , X 30 , or X 31  comprises the -alkyne.
 
     In a further embodiment, the insulin molecule comprises an alkyne group and the peptide has agonist activity at the GLP-1, GIP, and GCG receptors and comprises the structure 
                            (SEQ ID NO: 16)           X 1 X 2 QGTFTSX 9 X 10 SX 12 YX 14 DX 16 X 17 X 18 AX 20 X 21 FV-           X 24 X 25 X 26 X 27 X 28 X 29 X 30 X 31 ,            
wherein X 1  is Tyrosine, Phenylalanine, Tryptophan, or other amino acid with an aromatic group;
 
X 2  is aminoisobutyric acid (Aib), D-Serine (s), or alpha-methyl Serine (αMS);
 
X 9  is Serine or alpha-methyl Aspartic acid (αMD);
 
X 10  is Tyr or Lys conjugated to γGlu-γGlu-C 16 ;
 
     X 12  is Isoleucine, Lysine, Leucine, or Serine; 
     X 14  is Leu of alpha-methyl Leucine (αML);
 
X 16  is Glutamic acid, Asparagine, Serine, Alanine, or Aib;
 
     X 17  is Arginine or Lysine; 
     X 18  is Alanine or Arginine; 
     X 20  is Glutamine or Lysine conjugated via its epsilon amine group to PEG 2 -C 5 N 3 , PEG 2 PEG 2 -C 5 N 3 , PEG 2 PEG 2 -γGlu-C 16 N 3 , PEG 2 PEG 2 -γGlu-C 18 —OH, or PEG 2 PEG 2 γE-C 20 —OH;
 
X 21  is Aspartic acid, alpha-methyl Phenylalanine (αMF), αMD, Azidonorleucine (Norleucine conjugated via its epsilon carbon to an azide group (Nle(εN 3 ))), or Lys conjugated via its epsilon amine group to PEG 2 -C 5 N 3 , PEG 2 PEG 2 -C 5 N 3 , or PEG 2 PEG 2 -γGlu-C 16 N 3 ;
 
X 24  is Glutamine, Nle(εN 3 ), or Lysine conjugated to PEG 2 PEG 2 -γGlu-C 16 N 3 ;
 
X 25  is Tryptophan or alpha-methyl Tryptophan (αMW);
 
     X 26  is Leucine or αML; 
     X 27  is Leucine or L-methionine sulphone (2);
 
X 28  is Aspartic acid, Alanine, Lysine, Asparagine, γGlu, Glutamine, or αMD;
 
     X 29  is Threonine or Glycine; 
     X 30  is Arginine, Lysine, or Nle(εN 3 ), or X 30  is absent; and
 
X 31  is Glycine, γGlu, Nle(εN 3 ), or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 N 3 , PEG 2 -C 5 N 3  or PEG 2 PEG 2 -C 5 N 3 , or X 31  is absent; and
 
     wherein the C-terminal amino acid optionally is amidated, and with the proviso that either X 10  is a Lysine residue conjugated via its epsilon amino group to a γGlu-γGlu-C 16  and one of X 20 , X 21 , X 24 , X 30 , or X 31  comprises the azide or N 3  group or X 20  is a Lysine residue conjugated via its epsilon amino group to the PEG 2 PEG 2 -γGlu-C 18 —OH or the PEG 2 PEG 2 γE-C 20 —OH and one of X 21 , X 24 , X 30 , or X 31  comprises the azide or N 3  group. 
     In a further embodiment, the insulin molecule comprises an alkyne group and the peptide has agonist activity at the GLP-1, GIP, and GCG receptors and comprises the structure 
                            (SEQ ID NO: 17)           X 1 X 2 QGTFTSX 9 X 10 SX 12 YX 14 DX 16 X 17 X 18 AX 20 X 21 FV-           X 24 X 25 X 26 X 27 X 28 X 29 X 30 X 31 ,            
wherein X 1  is Tyrosine, Phenylalanine, Tryptophan, or other amino acid with an aromatic group;
 
X 2  is aminoisobutyric acid (Aib), D-Serine (s), or alpha-methyl Serine (αMS);
 
X 9  is Serine or alpha-methyl Aspartic acid (αMD);
 
X 10  is Tyr or Lys conjugated to γGlu-γGlu-C 16 ;
 
     X 12  is Isoleucine, Lysine, Leucine, or Serine; 
     X 14  is Leu of alpha-methyl Leucine (αML);
 
X 16  is Glutamic acid, Asparagine, Serine, Alanine, or Aib;
 
     X 17  is Arginine or Lysine; 
     X 18  is Alanine or Arginine; 
     X 20  is Glutamine or Lysine conjugated via its epsilon amine group to PEG 2 -C 5 N 3 , PEG 2 PEG 2 -C 5 -alkyne, PEG 2 PEG 2 -γGlu-C 16 -alkyne, PEG 2 PEG 2 -γGlu-C 18 —OH, or PEG 2 PEG 2 γE-C 20 —OH;
 
X 21  is Aspartic acid, alpha-methyl Phenylalanine (αMF), αMD, Alkynylnorleucine (Norleucine conjugated via its epsilon carbon to an alkyne group (Nle(ε-alkyne))), or Lys conjugated via its epsilon amine group to PEG 2 -C 5 -alkyne, PEG 2 PEG 2 -C 5 -alkyne, or PEG 2 PEG 2 -γGlu-C 16 -alkyne;
 
X 24  is Glutamine, Nle(ε-alkyne), or Lysine conjugated to PEG 2 PEG 2 -γGlu-C 16 -alkyne;
 
X 25  is Tryptophan or alpha-methyl Tryptophan (αMW);
 
     X 26  is Leucine or αML; 
     X 27  is Leucine or L-methionine sulphone (2);
 
X 28  is Aspartic acid, Alanine, Lysine, Asparagine, γGlu, Glutamine, or αMD;
 
     X 29  is Threonine or Glycine; 
     X 30  is Arginine, Lysine, or Nle(ε-alkyne), or X 30  is absent; and
 
X 31  is Glycine, γGlu, Nle(ε-alkyne), or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 -alkyne, PEG 2 -C 5 -alkyne, PEG 2 PEG 2 -C 5 -alkyne, or X 31  is absent; and wherein the C-terminal amino acid optionally is amidated, and with the proviso that either X 10  is a Lysine residue conjugated via its epsilon amino group to a γGlu-γGlu-C 16  and one of X 20 , X 21 , X 24 , X 30 , or X 31  comprises the -alkyne or X 20  is a Lysine residue conjugated via its epsilon amino group to the PEG 2 PEG 2 -γGlu-C 18 —OH or the PEG 2 PEG 2 γE-C 20 —OH and one of X 21 , X 24 , X 30 , or X 31  comprises the -alkyne.
 
     In particular embodiments, the peptide is a GLP-1 analog having the amino acid sequence 
                            (SEQ ID NO: 18)           HGEGTFTSDX 10 SSYLEEQAAX 20 x 21 FIAWLVX 28 GGGX 20 ,            
wherein X 10  is Valine, Nle(ε-N 3 ), or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 —N 3 , PEG 2 -C 5 —N 3 , or PEG 2 PEG 2 -C 5 —N 3 ;
 
X 20  is Lysine, Nle(ε-N 3 ), or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 —N 3 , PEG 2 -C 5 —N 3 , or PEG 2 PEG 2 -C 5 —N 3 ;
 
X 21  is glutamic acid, Nle(ε-N 3 ), or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 —N 3 , PEG 2 -C 5 —N 3 , or PEG 2 PEG 2 -C 5 —N 3 ;
 
X 28  is Lysine, Nle(ε-N 3 ), or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 —N 3 , PEG 2 -C 5 —N 3 , or PEG 2 PEG 2 -C 5 —N 3 ;
 
X 29  Nle(ε-N 3 ), or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 —N 3 , PEG 2 -C 5 —N 3 , PEG 2 PEG 2 -C 5 —N 3  or absent;
 
     with the proviso that only one of X 10 , X 20 , X 21 , or X 28 , or X 29  is Nle(ε-N 3 ) or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 —N 3 , PEG 2 -C 5 —N 3 , PEG 2 PEG 2 -C 5 —N 3 . 
     The peptide may be a GLP-1 analog, for example a GLP(7-37) molecule and analogs thereof comprising 1, 2, 3, 4, 5, or 6 amino acid substitutions or deletions. 
     In particular embodiments, the peptide is aGLP-1 analog having the amino acid sequence 
                            (SEQ ID NO: 19)           HGEGTFTSDX 10 SSYLEEQAAX 20 x 21 FIAWLVX 28 GGGX 20 ,            
wherein X 10  is Valine, Nle(ε-alkyne), or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 -alkyne, PEG 2 -C 5 -alkyne, or PEG 2 PEG 2 -C 5 -alkyne;
 
X 20  is Lysine, Nle(ε-N 3 ), or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 -alkyne, PEG 2 -C 5 -alkyne, or PEG 2 PEG 2 -C 5 -alkyne;
 
X 21  is glutamic acid, Nle(ε-alkyne), or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 -alkyne, PEG 2 -C 5 -alkyne, or PEG 2 PEG 2 -C 5 -alkyne;
 
X 28  is Lysine, Nle(ε-alkyne), or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 -alkyne, PEG 2 -C 5 -alkyne, or PEG 2 PEG 2 -C 5 -alkyne;
 
X 29  Nle(ε-alkyne), or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 -alkyne, PEG 2 -C 5 -alkyne, PEG 2 PEG 2 -C 5 -alkyne or absent;
 
     with the proviso that only one of X 10 , X 20 , X 21 , or X 28 , or X 29  is Nle(ε-N 3 ) or Lysine conjugated via its epsilon amine group to PEG 2 PEG 2 -γGlu-C 16 -alkyne, PEG 2 -C 5 -alkyne, PEG 2 PEG 2 -C 5 -alkyne. 
     Table 1 shows exemplary peptides comprising an azide group that may be conjugated to an insulin molecule comprising an alkyne group under conditions suitable for the azide group and the alkyne group to form a 1,4-disubstituted 1, 2, 3-triazole. 
     
       
         
           
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                 SEQ 
                   
               
               
                   
                 ID 
                   
               
               
                 Peptide 
                 NO: 
                 Sequence 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 PEP1 
                 35 
                 HsQGTFTSD-K(γEγEC 16 )SKYLDERAAQ-Nle(ϵN 3 )FVQWLLDT-NH 2   
               
               
                 PEP2 
                 36 
                 HUQGTFTSD-K(γEγEC 16 )SKYLDERAAQDFV-Nle(ϵN 3 )WLLDGRG-NH 2   
               
               
                 PEP3 
                 37 
                 HUQGTFTSD-K(γEγEC 16 )SKYLDURAAQDFV-Nle(ϵN 3 )WL2KGRG-NH 2   
               
               
                 PEP4 
                 38 
                 HsQGTFTSD-K(γEγEC 16 )-SLYLDURAAQDFV-Nle(ϵN 3 )WLLNT-K(γE)- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP5 
                 39 
                 HsQGTFTSD-K(γEγEC 16 )-SLYLDURAAQDFVQWLLNT-Nle(ϵN 3 )-KγE- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP6 
                 40 
                 HUQGTFTSD-K(γEγEC 16 )SKYLDURRAQDFVQWLLDT-Nle(ϵN 3 )γE- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP7 
                 41 
                 HsQGTGTSD-K(γEγEC 16 )SKYLDURAAQDFV-Nle(ϵN 3 )-WLLDT-NH 2   
               
               
                 PEP8 
                 42 
                 HsQGTFTSD-K(γEγEC 16 )SSYLDURAAQDFVQWLLNT-Nle(ϵN 3 )-γE- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP9 
                 43 
                 HsQGTFTSD-K(γEγEC 16 )SSYLDURAAQDFV-Nle(ϵN 3 )-WLLNTKγE- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP10 
                 44 
                 HUQGTFTSD-K(γEγEC 16 )SKYLDURAAQDFV-Nle(ϵN 3 )-WL2DT-NH 2   
               
               
                 PEP11 
                 45 
                 HsQGTFTSD-K(γEγEC 16 )SKYLDERAAQDFV-Nle(ϵN 3 )-WLLγET-NH 2   
               
               
                 PEP12 
                 46 
                 HsQGTFTSD-K(γEγEC 16 )SKYLDNKRAQDFV-Nle(ϵN 3 )-WLLQT-NH 2   
               
               
                 PEP13 
                 47 
                 HsQGTFTSD-K(γEγEC 16 )SKYLDSRRAHDFV-Nle(ϵN 3 )-WLLNT-NH 2   
               
               
                 PEP14 
                 48 
                 HsQGTFTSD-K(γEγEC 16 )SKYLDERAAQDFV-K(PEG 2 -C 5 N 3 )WLLDT- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP15 
                 49 
                 HsQGTFTSD-K(γEγEC 16 )SKYLDERAAQDFV-K(PEG 2 PEG 2 -C 5 N 3 )- 
               
               
                   
                   
                 WLLDT-NH 2   
               
               
                 PEP16 
                 50 
                 HsQGTFTSD-K(γEγEC 16 )SKYLDERAA-K(PEG 2 -C 5 N 3 )-DFVQWLLDT- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP17 
                 51 
                 HsQGTFTSD-K(γEγEC 16 )SKYLDERAA-K(PEG 2 PEG 2 -C 5 N 3 )- 
               
               
                   
                   
                 DFVQWLLDT-NH 2   
               
               
                 PEP18 
                 52 
                 HUQGTFTSDYSKYLDURAAQDFVQWLLDTK-Nle(ϵN 3 )-NH 2   
               
               
                 PEP19 
                 53 
                 HUQGTFTSD-K(γEγEC 16 )SKYLDURAAQDFVQWLLDTK-Nle(ϵN 3 )-NH 2   
               
               
                 PEP20 
                 54 
                 HUQGTFTSD-K(γEγEC 16 )SKYLDURAAQDFVQWLLDTK-K(PEG 2 - 
               
               
                   
                   
                 C 5 N 3 )—NH2 
               
               
                 PEP21 
                 55 
                 HUQGTFTSD-K(γEγEC 16 )SKYLDURAAQDFVQWLLDTK- 
               
               
                   
                   
                 K(PEG 2 PEG 2 -C 5 N 3 )—NH 2   
               
               
                 PEP22 
                 56 
                 HUQGTFTSD-K(γEγEC 16 )SKYLDURAAQDFV-Nle(ϵN 3 )-WLLDTKγE- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP23 
                 57 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQNLe(ϵN 3 )FVQWL2DT-NH 2   
               
               
                 PEP24 
                 58 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQNle(ϵN 3 )FVQWL2 αMD T-NH 2   
               
               
                 PEP25 
                 59 
                 HsQGTFTSDYSKYLDERAAQDFV-K(PEG 2 PEG 2 γE-C 16 N 3 )-WLLDT- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP26 
                 60 
                 HsQGTFTSDYSKYLDERAA-K(PEG 2 PEG 2 γE-C 16 N 3 )-DFVQ 
               
               
                   
                   
                 WLLDT-NH 2   
               
               
                 PEP27 
                 61 
                 HsQGTFTSDYSKYLDERAAQ-K(PEG 2 PEG 2 γE-C 16 N 3 )-FVQWLLDT- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP28 
                 62 
                 HUQGTFTSDYSKYLDURAAQDFVQWLLDTK-K(PEG 2 PEG 2 γE-C 16 N 3 )- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP29 
                 63 
                 HsQGTFTSDK(PEG 2 PEG 2 γEC 18 - 
               
               
                   
                   
                 OH)SKYLDERAAQDFVNle(ϵN 3 )WLLDT-NH 2   
               
               
                 PEP30 
                 64 
                 HUQGTFTSDYSKYLDARAAK(PEG 2 PEG 2 γEC18- 
               
               
                   
                   
                 OH)DFVNle(ϵN 3 )WL2DT-NH 2   
               
               
                 PEP31 
                 65 
                 HUQGTFTSDYSKYLDARAAK(PEG 2 PEG 2 γEC20- 
               
               
                   
                   
                 OH)DFVNle(ϵN 3 )WL2DT-NH 2   
               
               
                 PEP32 
                 66 
                 HsQGTFTS αMDK (γEγEC 16 )SKYLeuDERAAQDFVNle(ϵN 3 )WL2DT-NH 2   
               
               
                 PEP33 
                 67 
                 HsQGTFTSDK(γEγEC 16 )SKY αML DERAAQDFVNle(ϵN 3 )WL2DT-NH 2   
               
               
                 PEP34 
                 68 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQ αMD FVNle(ϵN 3 )WL2DT-NH 2   
               
               
                 PEP35 
                 69 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQD αMF VNle(ϵN 3 )WL2DT-NH 2   
               
               
                 PEP36 
                 70 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVNle(ϵN 3 ) αMW L2DT-NH 2   
               
               
                 PEP37 
                 71 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVNle(ϵN 3 )W αML 2DT-NH 2   
               
               
                 PEP38 
                 72 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVNle(ϵN 3 )WL2 αMD T-NH 2   
               
               
                 PEP39 
                 73 
                 H αMS QGTFTSDK(γEγEC 16 )SKYLDURAAQDFV-Nle(ϵN 3 )-WLLATKγE- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP40 
                 74 
                 H αMs QGTFTSDK(γEγEC 16 )SKYLDURAAQDFV-Nle(ϵN 3 )-WLLATKγE- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP41 
                 75 
                 H αMS QGTFTSDK(γEγEC 16 )SKYLDARAAQDFV-Nle(ϵN 3 )-WLLDT-NH 2   
               
               
                 PEP42 
                 76 
                 H αMs QGTFTSDK(γEγEC 16 )SKYLDARAAQDFV-Nle(ϵN 3 )-WLLDT-NH 2   
               
               
                 PEP43 
                 77 
                 H αMs VGTFTSDK(γEγEC 16 )SKYLDURAAQDFV-Nle(ϵN 3 )-WL2DT-NH 2   
               
               
                 PEP44 
                 78 
                 HUQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVNle(ϵN 3 )WL2DGRG-NH 2   
               
               
                 PEP45 
                 79 
                 HUQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVNle(ϵN 3 )WL2 αMD GRG- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP46 
                 80 
                 HUQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVQWLLDTNle(ϵN 3 )γE-NH 2   
               
               
                 PEP47 
                 81 
                 HUQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVQWL2DTNle(ϵN 3 )γE-NH 2   
               
               
                 PEP48 
                 82 
                 HUQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVQWL2 αMD TNle(ϵN 3 )γE- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP49 
                 83 
                 HUQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVNle(ϵN 3 )WL 2αMD T-NH 2   
               
               
                 PEP50 
                 84 
                 HsEGTFTSDK(γEγEC 16 )SKYLDERAAQDFVNle(ϵN 3 )WLLDT-NH 2   
               
               
                 PEP51 
                 85 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVK(PEG 2 PEG 2 - 
               
               
                   
                   
                 C 5 N 3 )WL2DT-NH 2   
               
               
                 PEP52 
                 86 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVK(PEG 2 PEG 2 - 
               
               
                   
                   
                 C 5 N 3 )WL2 αMD T-NH 2   
               
               
                 PEP53 
                 87 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVK(PEG 2 -C 10 N 3 )WLLDT- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP54 
                 88 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVK(PEG 2 -C 16 N 3 )WLLDT- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP55 
                 89 
                 HUQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVK(PEG 2 -C 5 N 3 )WL2DT- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP56 
                 90 
                 HUQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVK(PEG 2 PEG 2 - 
               
               
                   
                   
                 C 5 N 3 )WL2DT-NH 2   
               
               
                 PEP57 
                 91 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAK(PEG 2 PEG 2 γE- 
               
               
                   
                   
                 C 10 N 3 )DFVQWLLDT-NH 2   
               
               
                 PEP58 
                 92 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAK(PEG 2 PEG 2 γE- 
               
               
                   
                   
                 C 16 N 3 )DFVQWLLDT-NH 2   
               
               
                 PEP59 
                 93 
                 HsQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVQWLLDTKNle(ϵN 3 )-NH 2   
               
               
                 PEP60 
                 94 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVQWLLDTKNle(ϵN 3 )-NH 2   
               
               
                 PEP61 
                 95 
                 HsQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVQWLLDTKK(PEG 2 PEG 2 - 
               
               
                   
                   
                 C 5 N 3 )NH 2   
               
               
                 PEP62 
                 96 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVQWLLDTKK(PEG 2 PEG 2 - 
               
               
                   
                   
                 C 5 N 3 )NH 2   
               
               
                 PEP63 
                 97 
                 HsQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVNle(ϵN 3 )WLLDTKγE-NH 2   
               
               
                 PEP64 
                 98 
                 HUQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVK(PEG 2 - 
               
               
                   
                   
                 C 5 N 3 )WLLDTKγE-NH 2   
               
               
                 PEP65 
                 99 
                 HUQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVK(PEG 2 PEG 2 - 
               
               
                   
                   
                 C5N 3 )WLLDTKγE-NH 2   
               
               
                 PEP66 
                 100 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQK(PEG 2 PEG 2 γEC 16 N 3 )FVQWL 
               
               
                   
                   
                 LDT-NH 2   
               
               
                 PEP67 
                 101 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVK(PEG 2 PEG 2 γEC 16 N 3 )WL 
               
               
                   
                   
                 LDT-NH 2   
               
               
                 PEP68 
                 102 
                 HUQGTFTSDKSKYLDURAAQDFVNle(ϵN 3 )WLMNTKQ-COOH 
               
               
                 PEP69 
                 103 
                 HsQGTFTSDKSKYLDERAAQDFVNle(ϵN 3 )WLLDT-NH 2   
               
               
                 PEP70 
                 104 
                 HUQGTFTSDKSKYLDERAANle(ϵN 3 )DFVQWLLDT-NH 2   
               
               
                 PEP71 
                 105 
                 HsQGTFTSDKSKYLDERAANle(ϵN 3 )DFVQWLLDT-NH 2   
               
               
                 PEP72 
                 106 
                 HUQGTFTSDKSKYLDURAAQDFVQWLMNTKQ Nle(ϵN 3 )-NH 2   
               
               
                 PEP73 
                 107 
                 HsQGTFTSDKSKYLDERAAQDFVQWLLDT Nle(ϵN 3 )-NH 2   
               
               
                 PEP74 
                 108 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVNle(ϵN 3 )WLLDT-NH 2   
               
               
                 PEP75 
                 109 
                 HsEGTFTSDK(γEγEC16)SKYLDERAAQDFVNle(ϵN 3 )WLLDT-NH 2   
               
               
                 PEP76 
                 110 
                 HUQGTFTSDK(γEC16)SKYLDERAAQDFVNle(ϵN 3 )WLLDGGPSSGAPPP 
               
               
                   
                   
                 S-NH 2   
               
               
                 PEP77 
                 111 
                 HGEGTFTSDLSKQMEEEAVRLFINle(ϵN 3 )WLKNGGPSSGAPPPS-NH 2   
               
               
                 PEP78 
                 112 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVKWLLDT-NH 2   
               
               
                 PEP79 
                 113 
                 HsQGTFTSDK(γEγEC 16 )SKY αML DERAAQDFVNle(ϵN 3 )WL2DT-NH 2   
               
               
                 PEP80 
                 114 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVNle(ϵN 3 ) αMW L2DT-NH 2   
               
               
                 PEP81 
                 115 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVNle(ϵN 3 )WL2 αMD T-NH 2   
               
               
                 PEP82 
                 116 
                 H αMS QGTFTSDK(γEγEC 16 )SKYLDURAAQDFV-Nle(ϵN 3 )WLLATKγE- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP83 
                 117 
                 H αMs QGTFTSDK(γEγEC 16 )SKYLDURAAQDFVNle(ϵN 3 )WLLATKγE- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP84 
                 118 
                 H αMsV GTFTSDK(γEγEC 16 )SKYLDURAAQDFVNle(ϵN 3 )WL2DT-NH 2   
               
               
                 PEP85 
                 119 
                 H αMs QGTFTSDK(γEγEC 16 )SKYLDARAAQDFVNle(ϵN 3 )WLLDT-NH 2   
               
               
                 PEP86 
                 120 
                 H αMS QGTFTSDK(γEγEC 16 )SKYLDARAAQDFVNle(ϵN 3 )WLLDT-NH 2   
               
               
                 PEP87 
                 121 
                 HsEGTFTSDK(γEγEC 16 )SKYLDERAAQDFVNle(ϵN 3 )WLLDT-NH 2   
               
               
                 PEP88 
                 122 
                 HsQGTFTSD-K(γEγEC 16 )SKYLDERAAQNle(ϵN 3 )FVQWL2DT-NH 2   
               
               
                 PEP89 
                 123 
                 HsQGTFTSD-K(γEγEC 16 )SKYLDERAAQNle(ϵN 3 )FVQWL2αMDT-NH 2   
               
               
                 PEP90 
                 124 
                 HUQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVQWL2αMDTNle(ϵN 3 )γE- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP91 
                 125 
                 HUQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVNle(ϵN 3 )WL2 αMD T-NH 2   
               
               
                 PEP92 
                 126 
                 HUQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVNle(ϵN 3 )WL2DGRG-NH 2   
               
               
                 PEP93 
                 127 
                 HUQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVQWLLDTNle(ϵN 3 )γE-NH 2   
               
               
                 PEP94 
                 128 
                 HUQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVQWL2DTNle(ϵN 3 )γE-NH 2   
               
               
                 PEP95 
                 129 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVK(PEG 2 PEG 2 - 
               
               
                   
                   
                 C 5 N 3 )WL2DT-NH 2   
               
               
                 PEP96 
                 130 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVK(PEG 2 PEG 2 - 
               
               
                   
                   
                 C 5 N 3 )WL2 αMD T-NH 2   
               
               
                 PEP97 
                 131 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVK(PEG 2 -C 10 N 3 )WLLDT- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP98 
                 132 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVK(PEG 2 -C 16 N 3 )WLLDT- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP99 
                 133 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAK(PEG 2 PEG 2 γE- 
               
               
                   
                   
                 C 10 N 3 )DFVQWLLDT-NH 2   
               
               
                 PEP100 
                 134 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAK(PEG 2 PEG 2 γE- 
               
               
                   
                   
                 C 16 N 3 )DFVQWLLDT-NH 2   
               
               
                 PEP101 
                 135 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVpraWLLDT-NH 2   
               
               
                 PEP102 
                 136 
                 HsQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVQWLLDTKNle(ϵN 3 )-NH 2   
               
               
                 PEP103 
                 137 
                 HsQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVQWLLDTKK(PEG 2 PEG 2 - 
               
               
                   
                   
                 C 5 N 3 )-NH 2   
               
               
                 PEP104 
                 138 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQK(PEG 2 PEG 2 γEC 16 N 3 )FVQWL 
               
               
                   
                   
                 LDT-NH 2   
               
               
                 PEP105 
                 139 
                 HUQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVK(PEG 2 PEG 2 - 
               
               
                   
                   
                 C 5 N 3 )WL2DT-NH 2   
               
               
                 PEP106 
                 140 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVQWLLDTKNle(ϵN 3 )-CONH 2   
               
               
                 PEP107 
                 141 
                 HsQGTFTSDK(γEγEC6)SKYLDERAAQDFVK(PEG 2 PEG 2γ EC 16 N 3 )WL 
               
               
                   
                   
                 LDT-NH 2   
               
               
                 PEP108 
                 142 
                 HUQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVK(PEG 2 -C 5 N 3 )WL2DT- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP109 
                 143 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVQWLLDTKK(PEG 2 PEG 2 - 
               
               
                   
                   
                 C 5 N 3 )CONH 2   
               
               
                 PEP110 
                 144 
                 HsQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVNle(ϵN 3 )WLLDTKγE-NH 2   
               
               
                 PEP111 
                 145 
                 HUQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVK(PEG 2 PEG 2 - 
               
               
                   
                   
                 C 5 N 3 )WLLDTKγE-NH2 
               
               
                 PEP112 
                 146 
                 HUQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVK(PEG 2 - 
               
               
                   
                   
                 C 5 N 3 )WLLDTKγE-NH 2   
               
               
                 PEP113 
                 147 
                 HsQGTFTSDK(γEγEC 16 )SKYLDSRAAQDFVNle(ϵN 3 )WLLDT-NH 2   
               
               
                 PEP114 
                 148 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVNle(ϵN 3 )WLLγET-NH 2   
               
               
                 PEP115 
                 149 
                 HsQGTFTSDK(γEγEC 16 )SKYLDNKRAQDFVNle(ϵN 3 )WLMQT-NH 2   
               
               
                 PEP116 
                 150 
                 HUQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVNle(ϵN 3 )WL2γEt-NH 2   
               
               
                 PEP117 
                 151 
                 HUQGTFVSDK(γEγEC 16 )SKYLDURAAQDFVNle(ϵN 3 )WL2ET-NH 2   
               
               
                 PEP118 
                 152 
                 HUQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVNle(ϵN 3 )WLLdTKγE-NH 2   
               
               
                 PEP119 
                 153 
                 HUQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVNle(ϵN 3 ) αMW L2DT-NH 2   
               
               
                 PEP120 
                 154 
                 HUQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVNle(ϵN 3 )WL2 αMD T-NH 2   
               
               
                 PEP121 
                 155 
                 HUQGTFTSDK(γEyEC 16 )SKYLDURAAQDFVNle(ϵN 3 ) αMW L2DT-NH 2   
               
               
                 PEP122 
                 156 
                 HUQGTFTSDK(γEγEC 16 )SKYLDURAAQDFVNle(ϵN 3 )WL2 αMD T-NH 2   
               
               
                 PEP123 
                 157 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVQWL2 αMD TKNle(ϵN 3 )- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP124 
                 158 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVQ αMW L2DTKNle(ϵN 3 )- 
               
               
                   
                   
                 NH 2   
               
               
                 PEP125 
                 159 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVQ αMW L2DTKK 
               
               
                   
                   
                 (PEG 2 PEG 2 C 5 N 3 )—NH 2   
               
               
                 PEP126 
                 160 
                 HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVQWL2 αMD TKK(PEG2PET2 
               
               
                   
                   
                 C 5 N 3 )—NH 2   
               
               
                 PEP127 
                 161 
                 HUQGTFTSDYSKYLDARAAK(PEG 2 PEG 2 γEC 18 OH)DFVQWL2DTKNle 
               
               
                   
                   
                 (ϵN3)-NH 2   
               
               
                 PEP128 
                 162 
                 HsQGTFTSDK(PEG 2 PEG 2 γEC 18 OH)SKYLDERAAQDFVQWLLDTKNle 
               
               
                   
                   
                 (ϵN 3 )—NH 2   
               
               
                 PEP129 
                 163 
                 HUQGTFTSDYSKYLDARAAK(PEG 2 PEG 2 γEC 18 OH)CFVNle(ϵN 3 )WL2 α   
               
               
                   
                   
                   MD T-NH 2   
               
               
                 PEP130 
                 164 
                 HUQGTFTSDYSKYLDARAAK(PEG 2 PEG 2 γEC 18 OH)DFVK 
               
               
                   
                   
                 (PEG 2 PEG 2 C 16 N 3 )WL2 αMD T-NH 2   
               
               
                 PEP131 
                 165 
                 HUQGTFTS αMD K(γEγEC 16 )SKYLDERAAQDFVNle(ϵN 3 )WL2DT-NH 2   
               
               
                 PEP132 
                 166 
                 HUQGTFTS αMD K(γEγEC 16 )SKYLDERAAQDFVK(PEG 2 PEG 2 C 16 N 3 ) 
               
               
                   
                   
                 WL2DT-NH 2   
               
               
                   
               
               
                 Table legend: 
               
               
                 U = aminoisobutyric acid; 
               
               
                 γE = γ-glutamic acid; 
               
               
                 2 = L-methionine sulphone; 
               
               
                 αMD = alpha-Methyl-L-Aspartic acid; 
               
               
                 αML = alpha-Methyl-L-leucine; 
               
               
                 αMF = alpha-Methyl-L-phenylalanine; 
               
               
                 αMW = alpha-Methyl-L-tryptophan; 
               
               
                 s = D-serine; 
               
               
                 αMS = alpha-Methyl-L-Serine; 
               
               
                 αMs = alpha-Methyl-D-serine; 
               
               
                 Nle(ϵN 3 ) = ϵ-azidonorleucine; 
               
               
                 PEG 2  = 8-amino-3,6-dioxaoctanoic acid; 
               
               
                 C 5 N 3  = 5-azido pentinoic acid; 
               
               
                 C 10 N 3  = 10-azido-decanoic acid; 
               
               
                 C 16 N 3  = 16-azido-hexadecanoic acid; 
               
               
                 C 18 -OH = -CO—(CH 2 ) 16 —COOH; 
               
               
                 C 20 -OH = -CO—(C 2 ) 18 —COOH; 
               
               
                 NH 2  = C-terminal amide; 
               
               
                 pra = propargyl glycine 
               
               
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
            
           
         
       
     
     The peptide disclosed herein may have anywhere from at least about 1% (including at least about 1.5%, 2%, 5%, 7%, 10%, 20%, 30%, 40%, 50%, 60%, 75%, 100%, 125%, 150%, 175%) to about 200 % or higher activity at the GLP-1 receptor relative to native GLP-1 and anywhere from 5 at least about 1% (including about 1.5%, 2%, 5%, 7%, 10%, 20%, 30%, 40%, 50%, 60%, 75%, 100%, 125%, 150%, 175%, 200%, 250%, 300%, 350%, 400%, 450%) to about 500% or higher activity at the glucagon receptor relative to native glucagon. In some embodiments, the peptides described herein exhibit no more than about 100%, 1000%, 10,000%, 100,000%, or 1,000,000% of the activity of native glucagon at the glucagon receptor. In some embodiments, the peptides described herein exhibit no more than about 100%, 1000%, 10,000%, 100,000%, or 1,000,000% of the activity of native GLP-1 at the GLP-1 receptor. In exemplary embodiments, a peptide may exhibit at least 10% of the activity of native glucagon at the glucagon receptor and at least 50% of the activity of native GLP-1 at the GLP-1 receptor, or at least 40% of the activity of native glucagon at the glucagon receptor and at least 40% of the activity of native GLP-1 at the GLP-1 receptor, or at least 60% of the activity of native glucagon at the glucagon receptor and at least 60% of the activity of native GLP-1 at the GLP-1 receptor. 
     Selectivity of a peptide for the glucagon receptor versus the GLP-1 receptor can be described as the relative ratio of glucagon/GLP-1 activity (the peptide analog&#39;s activity at the glucagon receptor relative to native glucagon, divided by the peptide&#39;s activity at the GLP-1 receptor relative to native GLP-1). For example, a peptide that exhibits 60% of the activity of native glucagon at the glucagon receptor and 60% of the activity of native GLP-1 at the GLP-1 receptor has a 1:1 ratio of glucagon/GLP-1 activity. Exemplary ratios of glucagon/GLP-1 activity include about 1:1, 1.5:1, 2:1, 3:1, 4:1, 5:1, 6:1, 7:1, 8:1, 9:1 or 10:1, or about 1:10, 1:9, 1:8, 1:7, 1:6, 1:5, 1:4, 1:3, 1:2, or 1:1.5. As an example, a glucagon/GLP-1 activity ratio of 10:1 indicates a 10-fold selectivity for the glucagon receptor versus the GLP-1 receptor. Similarly, a GLP-1/glucagon activity ratio of 10:1 indicates a 10-fold selectivity for the GLP-1 receptor versus the glucagon receptor. 
     Insulin Molecules 
     The insulin molecule comprising the conjugates disclosed herein encompasses all salt and non-salt forms of the insulin molecule. It will be appreciated that the salt form may be anionic or cationic depending on the insulin molecule. The term “insulin” or “an insulin molecule” is intended to encompass both wild-type insulin and modified forms of insulin as long as they are bioactive (i.e., capable of causing a detectable reduction in glucose when administered in vivo). Wild-type insulin includes insulin from any species whether in purified, synthetic or recombinant form (e.g., human insulin, porcine insulin, bovine insulin, rabbit insulin, sheep insulin, etc.). A number of these are available commercially, e.g., from Sigma-Aldrich (St. Louis, Mo.). A variety of modified forms of insulin are known in the art (e.g. see Crotty and Reynolds,  Pediatr. Emerg. Care.  23:903-905, 2007 and Gerich,  Am. J Med.  113:308-16, 2002 and references cited therein). Modified forms of insulin (insulin analogs) may be chemically modified (e.g., by addition of a chemical moiety such as a PEG group or a fatty acyl chain as described below) and/or mutated (i.e., by addition, deletion or substitution of one or more amino acids). 
     In particular embodiments, an insulin molecule comprising the conjugate may be wild-type human recombinant insulin or may differ from a wild-type insulin by 1-10 (e.g., 1-9, 1-8, 1-7, 1-6, 1-5, 1-4, 1-3, 1-2, 2-9, 2-8, 2-7, 2-6, 2-5, 2-4, 2-3, 3-9, 3-8, 3-7, 3-6, 3-5, 3- 4, 4-9, 4-8, 4-7, 4-6, 4-5, 5-9, 5-8, 5-7, 5-6, 6-9, 6-8, 6-7, 7-9, 7-8, 8-9, 9, 8, 7, 6, 5, 4, 3, 2 or 1) amino acid substitutions, additions and/or deletions. In particular embodiments, an insulin molecule of the present disclosure will differ from wild-type insulin by amino acid substitutions only. In particular embodiments, an insulin molecule of the present disclosure will differ from wild-type insulin by amino acid additions only. In particular embodiments, an insulin molecule of the present disclosure will differ from wild-type insulin by both amino acid substitutions and additions. In particular embodiments, an insulin molecule of the present disclosure will differ from a wild-type insulin by both amino acid substitutions and deletions. 
     In particular embodiments, amino acid substitutions may be made on the basis of similarity in polarity, charge, solubility, hydrophobicity, hydrophilicity, and/or the amphipathic nature of the residues involved. In particular embodiments, a substitution may be conservative, that is, one amino acid is replaced with one of similar shape and charge. Conservative substitutions are well known in the art and typically include substitutions within the following groups: glycine, alanine; valine, isoleucine, leucine; aspartic acid, glutamic acid; asparagine, glutamine; serine, threonine; lysine, arginine; and tyrosine, phenylalanine. In particular embodiments, the hydrophobic index of amino acids may be considered in choosing suitable mutations. The importance of the hydrophobic amino acid index in conferring interactive biological function on a peptide is generally understood in the art. Alternatively, the substitution of like amino acids can be made effectively on the basis of hydrophilicity. The importance of hydrophilicity in conferring interactive biological function of a peptide or peptide is generally understood in the art. The use of the hydrophobic index or hydrophilicity in designing peptides is further discussed in U.S. Pat. No. 5,691,198. 
     The wild-type sequence of recombinant human insulin (A-chain and B-chain) is shown in Table 2 below. In various embodiments, an insulin molecule of the present disclosure is mutated at the B28 and/or B29 positions of the B-peptide sequence. For example, insulin lispro (HUMALOG®) is a rapid acting insulin mutant in which the penultimate lysine and proline residues on the C-terminal end of the B-peptide have been reversed (Lys B28 Pro B29 -human insulin) (SEQ ID NO:22). This modification blocks the formation of insulin multimers. Insulin aspart (NOVOLOG®) is another rapid acting insulin mutant in which proline at position B28 has been substituted with aspartic acid (Asp B28 -human insulin) (SEQ ID NO:23). This mutant also prevents the formation of multimers. In some embodiments, mutation at positions B28 and/or B29 is accompanied by one or more mutations elsewhere in the insulin peptide. For example, insulin glulisine (APIDRA®) is yet another rapid acting insulin mutant in which aspartic acid at position B3 has been replaced by a lysine residue and lysine at position B29 has been replaced with a glutamic acid residue (Lys B3 Glu B29 -human insulin) (SEQ ID NO:24). 
     
       
         
           
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 SEQ ID 
                   
                   
               
               
                 NO: 
                 Description 
                 Sequence 
               
               
                   
               
             
            
               
                 20 
                 Human insulin A chain 
                 GIVEQCCTSICSLYQLENYCN 
               
               
                   
               
               
                 21 
                 Human insulin B chain 
                 FVNQHLCGSHLVEALYLVCGERGFFYTPKT 
               
               
                   
               
               
                 22 
                 Insulin lispro B chain 
                 FVNQHLCGSHLVEALYLVCGERGFFYTKPT 
               
               
                   
               
               
                 23 
                 Insulin aspart B chain 
                 FVNQHLCGSHLVEALYLVCGERGFFYTDKT 
               
               
                   
               
               
                 24 
                 Insulin glusiline B chain 
                 FVKQHLCGSHLVEALYLVCGERGFFYTPET 
               
               
                   
               
               
                 25 
                 Insulin glargine A chain 
                 GIVEQCCTSICSLYQLENYCG 
               
               
                   
               
               
                 26 
                 Insulin glargine B chain 
                 FVNQHLCGSHLVEALYLVCGERGFFYTPKTR 
               
               
                   
                   
                 R 
               
               
                   
               
            
           
         
       
     
     In various embodiments, the insulin molecule comprising the conjugate may have an isoelectric point that is shifted relative to human insulin. In some embodiments, the shift in isoelectric point is achieved by adding one or more arginine residues to the N-terminus of the insulin A-peptide and/or the C-terminus of the insulin B-peptide. Examples of such insulin peptides include Arg A0 -human insulin, Arg B31 Arg B32 -human insulin, Gly A21 Arg B31 Arg B32 -human insulin, Arg A0 Arg B31 Arg B32 -human insulin, and Arg A0 Gly A21 Arg B31 Arg B32 -human insulin. By way of further example, insulin glargine (LANTUS®) is an exemplary long acting insulin mutant in which Asp A21  has been replaced by glycine (SEQ ID NO:25), and two arginine residues have been added to the C-terminus of the B-peptide (SEQ ID NO:26). The effect of these changes is to shift the isoelectric point, producing a solution that is completely soluble at pH 4. Thus, in some embodiments, an insulin molecule of the present disclosure comprises an A-peptide sequence wherein A21 is Gly and B-peptide sequence wherein B31 and B32 are Arg-Arg. It is to be understood that the present disclosure encompasses all single and multiple combinations of these mutations and any other mutations that are described herein (e.g., Gly A21 -human insulin, Gly A2 1Arg B3 -human insulin, Arg B31 Arg B32 -human insulin, Arg B3 1-human insulin). 
     In various embodiments, the insulin molecule comprising the conjugate may be truncated. For example, in particular embodiments, a B-peptide sequence of an insulin peptide of the present disclosure is missing B1, B2, B3, B26, B27, B28, B29 and/or B30. In particular embodiments, combinations of residues are missing from the B-peptide sequence of an insulin peptide of the present disclosure. For example, the B-peptide sequence may be missing residues B(1-2), B(1-3), B(29-30), B(28-30), B(27-30) and/or B(26-30). In some embodiments, these deletions and/or truncations apply to any of the aforementioned insulin molecules (e.g., without limitation to produce des(B30)-insulin lispro, des(B30)-insulin aspart, des(B30)-insulin glulisine, des(B30)-insulin glargine, etc.). 
     In some embodiments, the insulin molecule may comprise additional amino acid residues on the N- or C-terminus of the A or B-peptide sequences. In some embodiments, one or more amino acid residues are located at positions A0, A21, B0 and/or B31. In some embodiments, one or more amino acid residues are located at position A0. In some embodiments, one or more amino acid residues are located at position A21. In some embodiments, one or more amino acid residues are located at position B0. In some embodiments, one or more amino acid residues are located at position B31. In particular embodiments, an insulin molecule does not include any additional amino acid residues at positions A0, A21, B0 or B31. 
     In particular embodiments, the insulin molecule comprising the conjugate may be mutated such that one or more amidated amino acids are replaced with acidic forms. For example, asparagine may be replaced with aspartic acid or glutamic acid. Likewise, glutamine may be replaced with aspartic acid or glutamic acid. In particular, Asn A18 , Asn A21 , or Asn B3 , or any combination of those residues, may be replaced by aspartic acid or glutamic acid. Gln A15  or Gln B4 , or both, may be replaced by aspartic acid or glutamic acid. In particular embodiments, an insulin molecule has aspartic acid at position A21 or aspartic acid at position B3, or both. 
     One skilled in the art will recognize that it is possible to mutate yet other amino acids in the insulin molecule while retaining biological activity. For example, without limitation, the following modifications are also widely accepted in the art: replacement of the histidine residue of position B10 with aspartic acid (His B10 →Asp B10 ); replacement of the phenylalanine residue at position B1 with aspartic acid (Phe B1 →Asp B1 ); replacement of the threonine residue at position B30 with alanine (Thr B30 →Ala B30 ); replacement of the tyrosine residue at position B26 with alanine (Tyr B26 →Ala B26 ); and replacement of the serine residue at position B9 with aspartic acid (Ser B9 →Asp B9 ). 
     In various embodiments, the insulin molecule comprising the conjugate may have a protracted profile of action. Thus, in particular embodiments, an insulin molecule of the present disclosure may be acylated with a fatty acid. That is, an amide bond is formed between an amino group on the insulin molecule and the carboxylic acid group of the fatty acid. The amino group may be the alpha-amino group of an N-terminal amino acid of the insulin molecule, or may be the epsilon-amino group of a lysine residue of the insulin molecule. An insulin molecule of the present disclosure may be acylated at one or more of the three amino groups that are present in wild-type human insulin or may be acylated on lysine residue that has been introduced into the wild-type human insulin sequence. In particular embodiments, an insulin molecule may be acylated at position B1. In particular embodiments, an insulin molecule may be acylated at position B29. In particular embodiments, the fatty acid is selected from myristic acid (C 14 ), pentadecylic acid (C 15 ), palmitic acid (C 16 ), heptadecylic acid (C 17 ) and stearic acid (C 18 ). For example, insulin detemir (LEVEMIR®) is a long acting insulin mutant in which Thr B30  has been deleted, and a C 14  fatty acid chain (myristic acid) has been attached to Lys B29 . 
     In some embodiments, the N-terminus of the A-peptide, the N-terminus of the B-peptide, the epsilon-amino group of Lys at position B29 or any other available amino group in an insulin molecule of the present disclosure is covalently linked to a fatty acid moiety of general formula: 
     
       
         
         
             
             
         
       
     
     wherein R F  is hydrogen or a C 1-30  alkyl group. In some embodiments, R F  is a C 1-20  alkyl group, a C 3-19  alkyl group, a C 5-18  alkyl group, a C 6-17  alkyl group, a C 8-16  alkyl group, a C 10-15  alkyl group, or a C 12-14  alkyl group. In particular embodiments, the insulin molecule is conjugated to the moiety at the A1 position. In particular embodiments, the insulin molecule is conjugated to the moiety at the B1 position. In particular embodiments, the insulin molecule is conjugated to the moiety at the epsilon-amino group of Lys at position B29. In particular embodiments, position B28 of the insulin molecule is Lys and the epsilon-amino group of Lys B28  is conjugated to the fatty acid moiety. In particular embodiments, position B3 of the insulin molecule is Lys and the epsilon-amino group of Lys B3  is conjugated to the fatty acid moiety. In some embodiments, the fatty acid chain is 8-20 carbons long. In some embodiments, the fatty acid is octanoic acid (C8), nonanoic acid (C9), decanoic acid (C10), undecanoic acid (C11), dodecanoic acid (C12), or tridecanoic acid (C13). In particular embodiments, the fatty acid is myristic acid (C14), pentadecanoic acid (C15), palmitic acid (C16), heptadecanoic acid (C17), stearic acid (C18), nonadecanoic acid (C19), or arachidic acid (C20). 
     In various embodiments, the insulin molecule comprising the conjugate may have the three wild-type disulfide bridges (i.e., one between position 7 of the A-chain peptide and position 7 of the B-chain peptide, a second between position 20 of the A-chain peptide and position 19 of the B-chain peptide, and a third between positions 6 and 11 of the A-chain peptide). In particular embodiments, an insulin molecule is mutated such that the site of mutation is used as a conjugation point, and conjugation at the mutated site reduces binding to the insulin receptor (e.g., Lys A3 ). In particular other embodiments, conjugation at an existing wild-type amino acid or terminus reduces binding to the insulin receptor (e.g., Gly A1 ). In some embodiments, an insulin molecule is conjugated at position A4, A5, A8, A9, or B30. In particular embodiments, the conjugation at position A4, A5, A8, A9, or B30 takes place via a wild-type amino acid side chain (e.g., Glu A4 ). In particular other embodiments, an insulin molecule is mutated at position A4, A5, A8, A9, or B30 to provide a site for conjugation (e.g., Lys A4 , Lys A5 , Lys A8 , Lys A9 , or Lys B30 ). 
     In particular embodiments, the insulin molecule comprising the conjugate may have an A chain sequence comprising a sequence of GIVEQCCX 1 SICSLYQLENYCX 2  (SEQ ID NO: 27); and a B chain sequence comprising a sequence of X 3 LCGX 4 X 5 LVEALYLVCG ERGFF (SEQ ID NO: 28) or X 8 VNQX 3 LCGX 4 X 5 LVEALYLVCGERGFFYTX 6  X 7 (SEQ ID NO: 29) wherein 
     X 1  is selected from the group consisting of threonine and histidine; 
     X 2  is asparagine or glycine; 
     X 3  is selected from the group consisting of histidine and threonine; 
     X 4  is selected from the group consisting of alanine, glycine and serine; 
     X 5  is selected from the group consisting of histidine, aspartic acid, glutamic acid, homocysteic acid and cysteic acid; 
     X 6  is aspartate-lysine dipeptide, a lysine-proline dipeptide, or a proline-lysine dipeptide; 
     X 7  is threonine, alanine, or a threonine-arginine-arginine tripeptide; and 
     X 8  is selected from the group consisting of phenylalanine and desamino-phenylalanine. In particular embodiments, the insulin is conjugated to an alkyne-C 2 -C 16  acyl, alkyne-PEG n  wherein n is 1-50, or alkyne-(PEG 2 ) n  wherein n is 1-20 or the one Lysine is conjugated to an azide-C 2 -C 16  acyl, azide-PEG n  wherein n is 1-50, or azide-(PEG 2 ) n  wherein n is 1-20 with the proviso that one of R1, R2, or R3 is alkyne —C 2 -C 16  acyl, azide-PEG n  wherein n is 1-50, or azide-(PEG 2 ) n  wherein n is 1-20. 
     In particular embodiments, the A-chain may have the amino acid sequence set forth in SEQ ID NO:20 or SEQ ID NO:25 and the B-chain may have the amino acid sequence set forth in SEQ ID NO:21, SEQ ID NO:22, SEQ ID NO:23, or SEQ ID NO:24. In particular embodiments, the A-chain may have the amino acid sequence set forth in SEQ ID NO:25 and the B-chain may have the amino acid sequence set forth in SEQ ID NO:26. In particular embodiments, the insulin analog is a desB30 insulin analog, a des B29-B30 insulin analog, a des B28-B30 insulin analog, a des B27-B30 insulin analog or a des B26-B30 insulin analog. 
     In any one of the above embodiments, at least one amino group of the insulin molecule is conjugated to a linker comprising a terminal azide group or alkyne group. The amino group may be at the A1 position, the B1 position, or an epsilon amino group of a lysine residue on the A chain or the B chain. In particular embodiments, the lysine residue is at the B29 position of the B chain. In particular embodiments, the lysine residue is at the B28 position of the B chain, for example, insulin lispro has a lysine at the B28 position. In particular embodiments, the lysine residue is at the B3 position of the B chain, for example, insulin glulisine has a lysine at the B3 position. In particular embodiments, the epsilon amine of the lysine residue is converted to an azide group, which provides a norleucine with an epsilon azide group. 
     In particular embodiments, the insulin molecule comprising the conjugate has an A chain peptide sequence comprising a sequence of X 1 I X 2 E X 3 CCX 4  X 5  X 6 CS X 7  X 8  X 9 LE X 10 YC X 11 X 12  (SEQ ID NO:30); and a B chain peptide sequence comprising a sequence of X 13 VX 14 X 15 HLCGSHLVEALX 16 X 17 VCGERGFX 18 YTX 19 X 20 X 21 X 22 X 23 X 24 X 25 X 26  (SEQ ID NO:31) wherein 
     X 1  is glycine (G) or lysine (K); 
     X 2  is valine (V), glycine (G), or lysine (K); 
     X 3  is glutamine (Q) or lysine (K); 
     X 4  is threonine (T) or histidine (H); 
     X 5  is serine (S) or lysine (K); 
     X 6  is isoleucine (I) or lysine; 
     X 7  is leucine (L) or lysine (K); 
     X 8  is tyrosine (Y) or lysine (K); 
     X 9  is glutamine (Q) or lysine (K); 
     X 10  is asparagine (N) or lysine (K); 
     X 11  is asparagine (N) or glycine (G); 
     X 12  is arginine (R), lysine (K) or absent; 
     X 13  is phenylalanine (F) or lysine (K); 
     X 14  is asparagine (N) or lysine (K); 
     X 15  is glutamine (Q) or lysine (K); 
     X 16  is tyrosine (Y) or lysine (K); 
     X 17  is leucine (L) or lysine (K); 
     X 18  is phenylalanine (F) or lysine (K); 
     X 19  is proline (P) or lysine (K); 
     X 20  is lysine (K) or proline (P); 
     X 21  is threonine (T) or absent; 
     X 22  is arginine (R) if X 21  is threonine (T), or absent; 
     X 23  is proline (P) if X 22  is arginine (R), or absent; 
     X 24  is arginine (R) if X 23  is proline (P), or absent; 
     X 25  is proline (P) if X 24  is arginine (R), or absent; and 
     X 26  is arginine (R) if X 25  is proline (P), or absent, 
     With the proviso that at least one of X 1 , X 2 , X 3 , X 5 , X 6 , X 7 , X 8 , X 9 , X 10 , X 12 , X 13 , X 14 , X 15 , X 16 , X 17 , X 18 , X 19 , or X 20  is a lysine (K) wherein when X 20  is a lysine (K) then X 21  is absent or if X 21  is present then at least one of X 1 , X 2 , X 3 , X 4 , X 5 , X 6 , X 7 , X 8 , X 9 , X 10 , X 11 , X 12 , X 13 , X 14 , X 15 , X 16 , X 17  is lysine (K), or X 4  is histidine (H), or X 11  is glycine (G); or at least one of X 12  or X 22  is present. In particular aspects, if X 1 , X 2 , X 3 , X 5 , X 6 , X 7 , X 8 , X 9 , X 10 , X 12 , X 13 , X 14 , X 15 , X 16 , X 17 , X 18 , or X 19  is a lysine (K) then X 20  is not a lysine (K); and with the proviso that at least one Lysine (K) is conjugated to a linker having a terminal alkyne or azide group or the epsilon amine of at least one lysine residue is converted to an azide group, which provides a norleucine with an epsilon azide group. 
     In particular embodiments, the insulin molecule comprising the conjugate may be a desB30 human insulin analog, which may comprise an A chain peptide sequence comprising a sequence of X 1 I X 2 E X 3 CCX 4  X 5  X 6 CS X 7  X 8  X 9 LE X 10 YC X 11 X 12  (SEQ ID NO:30); and a B chain peptide sequence comprising a sequence of X 13 VX 14 X 15 HLCGSHLVEALX 16 X 17 VCGERGFX 18 YTX 19 X 20  (SEQ ID NO:32) wherein 
     X 1  is glycine (G) or lysine (K); 
     X 2  is valine (V), glycine (G), or lysine (K); 
     X 3  is glutamine (Q) or lysine (K); 
     X 4  is threonine (T) or histidine (H); 
     X 5  is serine (S) or lysine (K); 
     X 6  is isoleucine (I) or lysine; 
     X 7  is leucine (L) or lysine (K); 
     X 8  is tyrosine (Y) or lysine (K); 
     X 9  is glutamine (Q) or lysine (K); 
     X 10  is asparagine (N) or lysine (K); 
     X 11  is asparagine (N) or glycine (G); 
     X 12  is arginine (R), lysine (K) or absent; 
     X 13  is phenylalanine (F) or lysine (K); 
     X 14  is asparagine (N) or lysine (K); 
     X 15  is glutamine (Q) or lysine (K); 
     X 16  is tyrosine (Y) or lysine (K); 
     X 17  is leucine (L) or lysine (K); 
     X 18  is phenylalanine (F) or lysine (K); 
     X 19  is proline (P) or lysine (K); 
     X 20  is lysine (K) or proline (P); 
     With the proviso that at least one of X 1 , X 2 , X 3 , X 5 , X 6 , X 7 , X 8 , X 9 , X 10 , X 12 , X 13 , X 14 , X 15 , X 16 , X 17 , X 18 , X 19 , or X 20  is a lysine (K); and with the proviso that at least one Lysine (K) is conjugated to a linker having a terminal alkyne or azide group or the epsilon amine of at least one lysine residue is converted to an azide group, which provides a norleucine with an epsilon azide group. 
     In particular embodiments, the insulin molecule comprising the conjugate may comprise an A chain peptide sequence comprising a sequence of X 1 I X 2 E X 3 CCX 4  X 5  X 6 CS X 7  X 8  X 9 LE X 10 YC X 11 X 12  (SEQ ID NO:30); and a B chain peptide sequence comprising a sequence of X 13 VX 14 X 15 HLCGSHLVEALX 16 X 17 VCGERGFX 18 YTX 19 X 20 TRPRPR (SEQ ID NO:33) wherein 
     X 1  is glycine (G) or lysine (K); 
     X 2  is valine (V), glycine (G), or lysine (K); 
     X 3  is glutamine (Q) or lysine (K); 
     X 4  is threonine (T) or histidine (H); 
     X 5  is serine (S) or lysine (K); 
     X 6  is isoleucine (I) or lysine; 
     X 7  is leucine (L) or lysine (K); 
     X 8  is tyrosine (Y) or lysine (K); 
     X 9  is glutamine (Q) or lysine (K); 
     X 10  is asparagine (N) or lysine (K); 
     X 11  is asparagine (N) or glycine (G); 
     X 12  is arginine (R), lysine (K) or absent; 
     X 13  is phenylalanine (F) or lysine (K); 
     X 14  is asparagine (N) or lysine (K); 
     X 15  is glutamine (Q) or lysine (K); 
     X 16  is tyrosine (Y) or lysine (K); 
     X 17  is leucine (L) or lysine (K); 
     X 18  is phenylalanine (F) or lysine (K); 
     X 19  is proline (P) or lysine (K); 
     X 20  is lysine (K) or proline (P); 
     with the proviso that at least one of X 1 , X 2 , X 3 , X 5 , X 6 , X 7 , X 8 , X 9 , X 10 , X 12 , X 13 , X 14 , X 15 , X 16 , X 17 , X 18 , X 19 , or X 20  is a lysine (K); and with the proviso that at least one Lysine (K) is conjugated to a linker having a terminal alkyne or azide group or the epsilon amine of at least one lysine residue is converted to an azide group, which provides a norleucine with an epsilon azide group. 
     In particular embodiments, the insulin molecule comprising the conjugate may have an A chain peptide sequence comprising a sequence of X 1 I X 2 E X 3 CCX 4  X 5  X 6 CS X 7  X 8  X 9 LE X 10 YC X 11 X 12  (SEQ ID NO: 30); and a B chain peptide sequence comprising a sequence of X 13 VX 14 X 15 HLCGSHLVEALX 16 X 17 VCGERGFX 18 YTX 19 X 20 TRPR (SEQ ID NO: 34) wherein 
     X 1  is glycine (G) or lysine (K); 
     X 2  is valine (V), glycine (G), or lysine (K); 
     X 3  is glutamine (Q) or lysine (K); 
     X 4  is threonine (T) or histidine (H); 
     X 5  is serine (S) or lysine (K); 
     X 6  is isoleucine (I) or lysine; 
     X 7  is leucine (L) or lysine (K); 
     X 8  is tyrosine (Y) or lysine (K); 
     X 9  is glutamine (Q) or lysine (K); 
     X 10  is asparagine (N) or lysine (K); 
     X 11  is asparagine (N) or glycine (G); 
     X 12  is arginine (R), lysine (K) or absent; 
     X 13  is phenylalanine (F) or lysine (K); 
     X 14  is asparagine (N) or lysine (K); 
     X 15  is glutamine (Q) or lysine (K); 
     X 16  is tyrosine (Y) or lysine (K); 
     X 17  is leucine (L) or lysine (K); 
     X 18  is phenylalanine (F) or lysine (K); 
     X 19  is proline (P) or lysine (K); 
     X 20  is lysine (K) or proline (P); 
     with the proviso that at least one of X 1 , X 2 , X 3 , X 5 , X 6 , X 7 , X 8 , X 9 , X 10 , X 12 , X 13 , X 14 , X 15 , X 16 , X 17 , X 18 , X 19 , or X 20  is a lysine (K); and with the proviso that at least one Lysine (K) is conjugated to a linker having a terminal alkyne or azide group or the epsilon amine of at least one lysine residue is converted to an azide group, which provides a norleucine with an epsilon azide group. 
     The following structure represents human insulin (e.g., recombinant human insulin (RHI)) or any insulin analog disclosed herein 
     
       
         
         
             
             
         
       
     
     wherein the insulin is a heterodimer in which the cysteine residues a positions 6 and 11 of the A chain are linked in a disulfide bond, the cysteine residues at position 7 of the A chain and position 7 of the B chain are linked in a disulfide bond, and the cysteine residues at position 20 of the A chain and 19 of the B chain are linked in a disulfide bond and wherein A1 is the amino acid at position 1 of the A chain peptide, B1 is the amino acid at position 1 of the B chain peptide, and K is a lysine, which may be in any position in the insulin or insulin analog. In particular embodiments, the lysine is at position B29, B28, or B3. In particular embodiments, the lysine is at position B29 and is represented by the structure 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the lysine is at position B28 and is represented by the structure. 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the lysine is at position B3 and is represented by the structure 
     
       
         
         
             
             
         
       
     
     Unless otherwise indicated, the term “insulin” is used to indicate the insulin is a human insulin in which the A chain has amino acid sequence GIVEQCCTSICSLYQLENYCN (SEQ ID NO:20) and the B chain has amino acid sequence FVNQHLCGSHLVEALYLVCGERGFFYTPKT (SEQ ID NO:21). 
     The following structure represents a single-chain insulin analog (SCI) in which the C-terminal amino acid of the B chain is covalently linked the N-terminal amino acid of the A chain by a non-peptide linker or a peptide linker comprising three to 35 amino acids 
     
       
         
         
             
             
         
       
     
     wherein the cysteine residues a positions 6 and 11 of the A chain are linked in a disulfide bond, the cysteine residues at position 7 of the A chain and position 7 of the B chain are linked in a disulfide bond, and the cysteine residues at position 20 of the A chain and 19 of the B chain are linked in a disulfide bond and wherein B1 is the amino acid at position 1 of the B chain peptide and K is a lysine, which may be in any position in the insulin or insulin analog. In particular embodiments, the lysine is at position B29, B28, or B3. In particular embodiments, the lysine is at position B29 and is represented by the structure 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the lysine is at position B28 and is represented by the structure 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the lysine is at position B3 and is represented by the structure 
     
       
         
         
             
             
         
       
     
     Unless otherwise indicated, the term “SCI” is used to indicate the single-chain insulin an A chain having an amino acid sequence GIVEQCCTSICSLYQLENYCN (SEQ ID NO:20) and a B chain having the amino acid sequence FVNQHLCGSHLVEALYLVCGERGFFYTPKT (SEQ ID NO:21). 
     Single-chain insulins and analogs thereof have been disclosed in U.S. Pat. No. 8,940,860, which is incorporated herein by reference in its entirety and U.S. Publications US 20150374795 and US 20150299285, which are incorporated herein by reference in their entirety. 
     Linkers 
     The linker conjugated to the insulin or the insulin may be any non-peptide linker comprising a terminal azide group or a terminal alkyne group with the proviso that when the incretin is conjugated to a linker comprising an azide group then the insulin is conjugated to a linker comprising an alkyne group and when the incretin is conjugated to a linker comprising an azide group then the insulin is conjugated to a linker comprising an alkyne group. 
     The non-peptide linker may comprise a C 1 -C 50  hydrocarbon chain or substituted hydrocarbon chain, a PEG n  wherein n is 1-50, a (PEG 2 ) n  wherein n is 1-50, a (PEG 2 ) n -(γGlu) p -C n  wherein each n is independently 1-50 and p is 1 or 2, a (PEG 2 ) n -C n  wherein each n is independently is 1-50, a (PEG) n (PEG) n  wherein each n is independently 1-50, a (PEG) n (PEG) n (PEG) n  wherein each n is independently 1-50a PEG n -(Lys-(γGlu) p -C n )—C n  wherein each n is independently 1-50 and p is 1 or 2, and a C 5 -Lys(γE-C n )-PEG n  wherein each n is independently 1-50. 
     In particular embodiments, the linker may be a propargyl-polyethylene glycol (PEG) linker having the general formula 
     
       
         
         
             
             
         
       
     
     wherein n is 0-50 and the wavy line indicates the bond between the linker and an amino group on the insulin molecule or analog or an amino group on the incretin peptide. In particular embodiments n is 1-25. In particular embodiments, the linker may be selected from the group 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the linker may be a propargyl-C 5 -(polyethylene glycol 2) n  ((PEG 2 ) n ) linker having the general formula 
     
       
         
         
             
             
         
       
     
     wherein n is 1-50 and the wavy line indicates the bond between the linker and an amino group on the insulin molecule or analog or an amino group on the incretin peptide. In particular embodiments n is 1-5. In particular embodiments, the linker may be selected from the group 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the linker may be a propargyl-C 5 -Lys(γE-C n )-PEG n  linker having the general formula 
     
       
         
         
             
             
         
       
     
     wherein each n is independently 1-50 and the wavy line indicates the bond between the linker and an amino group on the insulin molecule or analog or an amino group on the incretin peptide. In particular embodiments, the linker has the formula 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the linker may be a propargyl-(PEG n )(PEG n ) linker having the general formula 
     
       
         
         
             
             
         
       
     
     wherein each n is independently 0-50 and the wavy line indicates the bond between the linker and an amino group on the insulin molecule or analog or an amino group on the incretin peptide. In particular embodiments, the linker is selected from 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the linker may be an propargyl-(PEG n )(PEG n )(PEG n ) linker having the general formula 
     
       
         
         
             
             
         
       
     
     wherein each n is independently 0-50 and the wavy line indicates the bond between the linker and an amino group on the insulin molecule or analog or an amino group on the incretin peptide. In particular embodiments, the linker may be 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the linker may be a propargyl-C n  having the general formula 
     
       
         
         
             
             
         
       
     
     wherein n is 1-50 and the wavy line indicates the bond between the linker and an amino group on the insulin molecule or analog or an amino group on the incretin peptide. In particular embodiments, the linker is 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the linker may be a BCN-PEG 4 (endo) linker having the general formula 
     
       
         
         
             
             
         
       
     
     wherein n is 1-50 and the wavy line indicates the bond between the linker and an amino group on the insulin molecule or analog or an amino group on the incretin peptide. In particular embodiments, the linker is 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the linker may be a propargyl-phenylacetate linker having the general formula 
     
       
         
         
             
             
         
       
     
     wherein the wavy line indicates the bond between the linker and an amino group on the insulin molecule or analog or an amino group on the incretin peptide. In particular embodiments, the linker is selected from 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the linker may be an azido-polyethylene glycol (PEG) linker having the general formula 
     
       
         
         
             
             
         
       
     
     wherein n is 0-50 and the wavy line indicates the bond between the linker and an amino group on the insulin molecule or analog or an amino group on the incretin peptide. In particular embodiments n is 1-25. In particular embodiments, the linker may be selected from the group 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the linker may be an azido-C 5 -Lys(γE-C n )-PEG n  linker having the general formula 
     
       
         
         
             
             
         
       
     
     wherein each n is independently 1-50 and the wavy line indicates the bond between the linker and an amino group on the insulin molecule or analog or an amino group on the incretin peptide. In particular embodiments, the linker has the formula 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the linker may be an azido-(PEG n )(PEG n ) linker having the general formula 
     
       
         
         
             
             
         
       
     
     wherein each n is independently 0-50 and the wavy line indicates the bond between the linker and an amino group on the insulin molecule or analog or an amino group on the incretin peptide. In particular embodiments, the linker is selected from 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the linker may be an azido-(PEG n )(PEG n )(PEG n ) linker having the general formula 
     
       
         
         
             
             
         
       
     
     wherein each n is independently 0-50 and the wavy line indicates the bond between the linker and an amino group on the insulin molecule or analog or an amino group on the incretin peptide. In particular embodiments, the linker may be 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the linker may be an azido-C n  having the general formula 
     
       
         
         
             
             
         
       
     
     wherein n is 1-50 and the wavy line indicates the bond between the linker and an amino group on the insulin molecule or analog or an amino group on the incretin peptide. In particular embodiments, the linker is 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the linker may be an azido-phenylacetate linker having the general formula 
     
       
         
         
             
             
         
       
     
     wherein the wavy line indicates the bond between the linker and an amino group on the insulin molecule or analog or an amino group on the incretin peptide. In particular embodiments, the linker is selected from 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the linker may be an azido-C n -(PEG 2 ) n  linker having the general formula 
     
       
         
         
             
             
         
       
     
     wherein each n is independently 1-10 and the wavy line indicates the bond between the linker and an amino group on the insulin molecule or analog or an amino group on the incretin peptide. 
     In particular embodiments, C n  is C 5  and the linker may be selected from the group 
     
       
         
         
             
             
         
       
     
     In particular embodiments, C n  is C 10  and the linker may be selected from the group 
     
       
         
         
             
             
         
       
     
     In particular embodiments, C n  is C 16  and the linker may be selected from the group 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the linker may be an azido-C n -γE-(PEG 2 ) n -linker having the general formula 
     
       
         
         
             
             
         
       
     
     wherein each n is independently 1-10 and the wavy line indicates the bond between the linker and an amino group on the insulin molecule or analog or an amino group on the incretin peptide. In particular embodiments, C n  is C 16  and the linker may be selected from the group 
     
       
         
         
             
             
         
       
     
     In particular embodiments, C n  is C 10  and the linker may be selected from the group 
     
       
         
         
             
             
         
       
     
     In particular embodiments, the linker may be azido-norleucine having the structure 
     
       
         
         
             
             
         
       
     
     wherein the wavy lines indicate the bonds between the azido-norleucine and adjacent amino acids in either the insulin molecule or the incretin peptide. 
     In particular embodiments, the linking moiety conjugating the insulin molecule to the incretin peptide comprises the formula 
     
       
         
         
             
             
         
       
     
     wherein R 1  and R 2  independently comprise a C 1 -C 50  hydrocarbon chain or substituted hydrocarbon chain, a PEG n  wherein n is 1-50, a (PEG 2 ) n  wherein n is 1-50, a (PEG 2 ) n -(γGlu) p -C n  wherein each n is independently 1-50 and p is 1 or 2, a (PEG 2 ) n -C n  wherein each n is independently is 1-50, a (PEG) n (PEG) n  wherein each n is independently 1-50, a PEG n -(Lys-(γGlu) p -C n )—C n  wherein each n is independently 1-50 and p is 1 or 2, and a C 5 -Lys(γE-C)-PEG n  wherein each n is independently 1-50, and wherein the bond between the linking moiety and the insulin molecule and the incretin peptide are indicated by the wavy lines with the proviso that if the bond adjacent to R 1  is to insulin then the bond adjacent to R 2  is to the incretin peptide or that if the bond adjacent to R 1  is to the incretin peptide then the bond adjacent to R 2  is to insulin. 
     Exemplary linking moieties are shown in Table 3. For structures 1-25, the wavy line on the left indicates the bond between alpha and beta carbons of Norleucine (Nle) or Lysine (Lys or K) and the wavy line on the right indicates the bond between the CO and an amino group of an amino acid. For 26, the wavy line on the left is a bound between an amino acid having an alkyne group and the wavy line on the right is a bound between an amino acid having an azide group. 
     
       
         
           
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                 # 
                 Name 
                 Structure 
               
               
                   
               
             
            
               
                  1 
                 Nle(ϵN 3 ) x C 5   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                  2 
                 Nle(ϵN 3  x PEG 3   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                  3 
                 Nle(ϵN 3 ) x PEG 4   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                  4 
                 Nle(ϵN 3 ) x PEG 5   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                  5 
                 Nle(ϵN 3 ) x PEG 6   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                  6 
                 Nle(ϵN 3 ) x PEG 8   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                  7 
                 Nle(ϵN 3 ) x PEG 10   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                  8 
                 Nle(ϵN 3 ) x PEG 13   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                  9 
                 Nle(ϵN 3 ) x PEG 14   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 10 
                 Nle(ϵN 3 ) x PEG 25   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 11 
                 Nle(ϵN 3 ) x (PEG 2 )C 5   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 12 
                 Nle(ϵN 3 ) x (PEG 2 ) 3 C 5   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 13 
                 Nle(ϵN 3 ) x (PEG 24 )(PEG 4 ) 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 14 
                 Nle(ϵN 3 ) x (PEG 36 )(PEG 4 ) 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 15 
                 Nle(ϵN 3 ) x PEG 12 (LysγE- C 16 )C 5   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 16 
                 Nle(ϵN 3 ) x BCN 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 17 
                 Lys(PEG 2 )C 5 N 3  x C 5 ) 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 18 
                 Lys(PEG 2 )(PEG 2 ) C 5 N 3  x C 5 ) 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 19 
                 Lys(PEG 2 ) 2 γEC 16 N 3  x C 5 ) 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 20 
                 Nle(ϵN 3 ) x (PEG 36 ) 2 (PEG 5 ) 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 21 
                 Nle(ϵN 3 ) x propargyl-C5- Lys(γE-C 16 )- PEG 24   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 22 
                 Nle(ϵN 3 ) x propargyl-C5- Lys(γE-C 12 )- PEG 12   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 23 
                 Nle(ϵN 3 ) x propargyl-C5- Lys(γE-C 16 )- PEG 4   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 24 
                 Nle(ϵN 3 ) x propargyl-C5- Lys(γE-C 18 —OH)- PEG 4   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 25 
                 C8 hydrocarbon linker 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 26 
                 pra x azide 
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
            
           
         
       
     
       FIG. 2A ,  FIG. 2B , and  FIG. 2C  show various exemplary insulin-incretin conjugates in which the Norleucine (Nle) amino acid of particular incretins is conjugated to the epsilon amino group of Lysine (Lys) at position B29 of the B-chain peptide. 
       FIG. 3  shows various exemplary insulin-incretin conjugates in which the Nle amino acid of particular incretins is conjugated to the amino group of the Glycine (Gly) at position A1 of the A-chain peptide. 
       FIG. 4A ,  FIG. 4B ,  FIG. 4C ,  FIG. 4D ,  FIG. 4E ,  FIG. 4F ,  FIG. 4G ,  FIG. 4H ,  FIG. 4I ,  FIG. 4J ,  FIG. 4K ,  FIG. 4L ,  FIG. 4M ,  FIG. 4N ,  FIG. 4O , and  FIG. 4P  show exemplary insulin-incretin conjugates in which the Nle amino acid of particular incretins is conjugated to the amino group of the Phenylalanine (Phe) at position B1 of the B-chain peptide. 
       FIG. 5  shows an exemplary insulin-incretin conjugate in which the Nle amino acid of PEP74* is conjugated to the amino group of the Phe at position B1 of the B-chain peptide. 
       FIG. 6A ,  FIG. 6B ,  FIG. 6C , and  FIG. 6D  show exemplary insulin-incretin conjugates in which the epsilon amino group of Lys of the incretin is conjugated to the amino group of the Phe at position B1 of the B-chain peptide. 
       FIG. 9A ,  FIG. 9B ,  FIG. 9C ,  FIG. 9D ,  FIG. 9E ,  FIG. 9F ,  FIG. 9G ,  FIG. 9H ,  FIG. 9I ,  FIG. 9J ,  FIG. 9K , and  FIG. 9L , which show exemplary insulin-incretin conjugates in which the Norleucine (Nle) amino acid of the incretin is conjugated to the amino group of the Phe at position B1 of the B-chain peptide. 
       FIG. 10A ,  FIG. 10B ,  FIG. 10C ,  FIG. 10D ,  FIG. 10E ,  FIG. 10F , and  FIG. 10G , which show exemplary insulin-incretin conjugates in which the epsilon amino group of Lys of the incretin is conjugated to the amino group of the Phenylalanine (Phe) at position B1 of the B-chain peptide. 
       FIG. 11 , which shows exemplary insulin-incretin conjugates CON106 and CON107. 
     Pharmaceutical Compositions 
     Further provided are pharmaceutical compositions comprising a therapeutically effective amount of one or more of the peptides disclosed herein for the treatment of a metabolic disorder in an individual. Such disorders include, but are not limited to, obesity, metabolic syndrome or syndrome X, type II diabetes, complications of diabetes such as retinopathy, hypertension, dyslipidemias, cardiovascular disease, gallstones, osteoarthritis, and certain forms of cancers. The obesity-related disorders herein are associated with, caused by, or result from obesity. 
     “Obesity” is a condition in which there is an excess of body fat. The operational definition of obesity is based on the Body Mass Index (BMI), calculated as body weight per height in meters squared (kg/m2). “Obesity” refers to a condition whereby an otherwise healthy subject has a Body Mass Index (BMI) greater than or equal to 30 kg/m2, or a condition whereby a subject with at least one co-morbidity has a BMI greater than or equal to 27 kg/m2. An “obese subject” is an otherwise healthy subject with a Body Mass Index (BMI) greater than or equal to 30 kg/m2 or a subject with at least one co-morbidity with a BMI greater than or equal to 27 kg/m2. A “subject at risk for obesity” is an otherwise healthy subject with a BMI of 25 kg/m2 to less than 30 kg/m2 or a subject with at least one co-morbidity with a BMI of 25 kg/m2 to less than 27 kg/m2. 
     The increased risks associated with obesity occur at a lower Body Mass Index (BMI) in Asians. In Asian countries, including Japan, “obesity” refers to a condition whereby a subject with at least one obesity-induced or obesity-related co-morbidity that requires weight reduction or that would be improved by weight reduction, has a BMI greater than or equal to 25 kg/m2. In Asian countries, including Japan, an “obese subject” refers to a subject with at least one obesity-induced or obesity-related co-morbidity that requires weight reduction or that would be improved by weight reduction, with a BMI greater than or equal to 25 kg/m2. In Asian countries, a “subject at risk of obesity” is a subject with a BMI of greater than 23 kg/m2 to less than 25 kg/m2. 
     As used herein, the term “obesity” is meant to encompass all of the above definitions of obesity. 
     Obesity-induced or obesity-related co-morbidities include, but are not limited to, diabetes, non-insulin dependent diabetes mellitus—type 2, impaired glucose tolerance, impaired fasting glucose, insulin resistance syndrome, dyslipidemia, hypertension, hyperuricacidemia, gout, coronary artery disease, myocardial infarction, angina pectoris, sleep apnea syndrome, Pickwickian syndrome, non-alcoholic fatty liver disease (NAFLD), non-alcoholic steatohepatitis (NASH), fatty liver; cerebral infarction, cerebral thrombosis, transient ischemic attack, orthopedic disorders, arthritis deformans, lumbodynia, emmeniopathy, and infertility. In particular, co-morbidities include: hypertension, hyperlipidemia, dyslipidemia, glucose intolerance, cardiovascular disease, sleep apnea, diabetes mellitus, and other obesity-related conditions. 
     “Treatment” (of obesity and obesity-related disorders) refers to the administration of the compounds of the present invention to reduce or maintain the body weight of an obese subject. One outcome of treatment may be reducing the body weight of an obese subject relative to that subject&#39;s body weight immediately before the administration of the compounds of the present invention. Another outcome of treatment may be preventing body weight regain of body weight previously lost as a result of diet, exercise, or pharmacotherapy. Another outcome of treatment may be decreasing the occurrence of and/or the severity of obesity-related diseases. The treatment may suitably result in a reduction in food or calorie intake by the subject, including a reduction in total food intake, or a reduction of intake of specific components of the diet such as carbohydrates or fats; and/or the inhibition of nutrient absorption; and/or the inhibition of the reduction of metabolic rate; and in weight reduction in patients in need thereof. The treatment may also result in an alteration of metabolic rate, such as an increase in metabolic rate, rather than or in addition to an inhibition of the reduction of metabolic rate; and/or in minimization of the metabolic resistance that normally results from weight loss. 
     “Prevention” (of obesity and obesity-related disorders) refers to the administration of the compounds of the present invention to reduce or maintain the body weight of a subject at risk of obesity. One outcome of prevention may be reducing the body weight of a subject at risk of obesity relative to that subject&#39;s body weight immediately before the administration of the compounds of the present invention. Another outcome of prevention may be preventing body weight regain of body weight previously lost as a result of diet, exercise, or pharmacotherapy. Another outcome of prevention may be preventing obesity from occurring if the treatment is administered prior to the onset of obesity in a subject at risk of obesity. Another outcome of prevention may be decreasing the occurrence and/or severity of obesity-related disorders if the treatment is administered prior to the onset of obesity in a subject at risk of obesity. Moreover, if treatment is commenced in already obese subjects, such treatment may prevent the occurrence, progression or severity of obesity-related disorders, such as, but not limited to, arteriosclerosis, Type II diabetes, polycystic ovarian disease, cardiovascular diseases, osteoarthritis, dermatological disorders, hypertension, insulin resistance, hypercholesterolemia, hypertriglyceridemia, and cholelithiasis. 
     The obesity-related disorders herein are associated with, caused by, or result from obesity. Examples of obesity-related disorders include overeating and bulimia, hypertension, diabetes, elevated plasma insulin concentrations and insulin resistance, dyslipidemias, hyperlipidemia, endometrial, breast, prostate and colon cancer, osteoarthritis, obstructive sleep apnea, cholelithiasis, gallstones, heart disease, abnormal heart rhythms and arrythmias, myocardial infarction, congestive heart failure, coronary heart disease, sudden death, stroke, polycystic ovarian disease, craniopharyngioma, the Prader-Willi Syndrome, Frohlich&#39;s syndrome, GH-deficient subjects, normal variant short stature, Turner&#39;s syndrome, and other pathological conditions showing reduced metabolic activity or a decrease in resting energy expenditure as a percentage of total fat-free mass, e.g, children with acute lymphoblastic leukemia. Further examples of obesity-related disorders are metabolic syndrome, also known as syndrome X, insulin resistance syndrome, sexual and reproductive dysfunction, such as infertility, hypogonadism in males and hirsutism in females, gastrointestinal motility disorders, such as obesity-related gastro-esophageal reflux, respiratory disorders, such as obesity-hypoventilation syndrome (Pickwickian syndrome), cardiovascular disorders, inflammation, such as systemic inflammation of the vasculature, arteriosclerosis, hypercholesterolemia, hyperuricaemia, lower back pain, gallbladder disease, gout, and kidney cancer. The compounds of the present invention are also useful for reducing the risk of secondary outcomes of obesity, such as reducing the risk of left ventricular hypertrophy. 
     The term “diabetes,” as used herein, includes both insulin-dependent diabetes mellitus (IDDM, also known as type I diabetes) and non-insulin-dependent diabetes mellitus (NIDDM, also known as Type II diabetes). Type I diabetes, or insulin-dependent diabetes, is the result of an absolute deficiency of insulin, the hormone which regulates glucose utilization. Type II diabetes, or insulin-independent diabetes (i.e., non-insulin-dependent diabetes mellitus), often occurs in the face of normal, or even elevated levels of insulin and appears to be the result of the inability of tissues to respond appropriately to insulin. Most of the Type II diabetics are also obese. The compounds of the present invention are useful for treating both Type I and Type II diabetes. The compounds are especially effective for treating Type II diabetes. The compounds of the present invention are also useful for treating and/or preventing gestational diabetes mellitus. 
     U.S. Pat. No. 6,852,690, which is incorporated herein in its entirety, discloses methods for enhancing metabolism of nutrients comprising administering to a non-diabetic patient a formulation comprising a nutritively effective amount of one or more nutrients or any combination thereof and one or more insulinotropic peptides. The peptides disclosed herein are insulinotropic and can be administered to patients with a disturbed glucose metabolism such as insulin resistance but no overt diabetes, as well as patients who for any reason cannot receive nutrition through the alimentary canal. Such patients include surgery patients, comatose patients, patients in shock, patients with gastrointestinal disease, patients with digestive hormone disease, and the like. In particular, obese patients, atherosclerotic patients, vascular disease patients, patients with gestational diabetes, patients with liver disease such as liver cirrhosis, patients with acromegaly, patients with glucorticoid excess such as cortisol treatment or Cushings disease, patients with activated counterregulatory hormones such as would occur after trauma, accidents and surgery and the like, patients with hypertriglyceridemia and patients with chronic pancreatitis can be readily and suitably nourished according to the invention without subjecting the patient to hypo- or hyperglycemia. In particular, the administration to such a patient aims to provide a therapy to as rapidly as possible deliver the nutritional and caloric requirements to the patient while maintaining his plasma glucose below the so-called renal threshold of about 160 to 180 milligrams per deciliter of glucose in the blood. Although normal patients not having glucose levels just below the renal threshold can also be treated according to the invention as described above, patients with disturbed glucose metabolism such as hyperglycemic patients whose plasma glucose level is just above the renal threshold also find the therapy suitable for their condition. In particular, such patients who have a degree of hyperglycemia below the renal threshold at intermittent intervals can receive a combination treatment of nutrients plus insulinotropic peptides according to any of the following regimens. Normal patients not suffering from such hyperglycemia can also be treated using the peptides disclosed herein. 
     The peptides disclosed herein may be used in a pharmaceutical composition when combined with a pharmaceutically acceptable carrier. Such compositions comprise a therapeutically-effective amount of one or more of the peptides disclosed herein and a pharmaceutically acceptable carrier. Such a composition may also be comprised of (in addition to the peptides disclosed herein and a carrier) diluents, fillers, salts, buffers, stabilizers, solubilizers, and other materials well known in the art. Compositions comprising the peptides disclosed herein can be administered, if desired, in the form of salts provided the salts are pharmaceutically acceptable. Salts may be prepared using standard procedures known to those skilled in the art of synthetic organic chemistry. 
     The term “individual” is meant to include humans and companion or domesticated animals such as dogs, cats, horses, and the like. Therefore, the compositions comprising a compound as disclosed herein are also useful for treating or preventing obesity and obesity-related disorders in cats and dogs. As such, the term “mammal” includes companion animals such as cats and dogs. 
     The term “pharmaceutically acceptable salts” refers to salts prepared from pharmaceutically acceptable non-toxic bases or acids including inorganic or organic bases and inorganic or organic acids. Salts derived from inorganic bases include aluminum, ammonium, calcium, copper, ferric, ferrous, lithium, magnesium, manganic salts, manganous, potassium, sodium, zinc, and the like. Particularly preferred are the ammonium, calcium, magnesium, potassium, and sodium salts. Salts derived from pharmaceutically acceptable organic non-toxic bases include salts of primary, secondary, and tertiary amines, substituted amines including naturally occurring substituted amines, cyclic amines, and basic ion exchange resins, such as arginine, betaine, caffeine, choline, N,N′-dibenzylethylenediamine, diethylamine, 2-diethylaminoethanol, 2-dimethylaminoethanol, ethanolamine, ethylenediamine, N-ethyl-morpholine, N-ethylpiperidine, glucamine, glucosamine, histidine, hydrabamine, isopropylamine, lysine, methylglucamine, morpholine, piperazine, piperidine, polyamine resins, procaine, purines, theobromine, triethylamine, trimethylamine, tripropylamine, tromethamine, and the like. The term “pharmaceutically acceptable salt” further includes all acceptable salts such as acetate, lactobionate, benzenesulfonate, laurate, benzoate, malate, bicarbonate, maleate, bisulfate, mandelate, bitartrate, mesylate, borate, methylbromide, bromide, methylnitrate, calcium edetate, methylsulfate, camsylate, mucate, carbonate, napsylate, chloride, nitrate, clavulanate, N-methylglucamine, citrate, ammonium salt, dihydrochloride, oleate, edetate, oxalate, edisylate, pamoate (embonate), estolate, palmitate, esylate, pantothenate, fumarate, phosphate/diphosphate, gluceptate, polygalacturonate, gluconate, salicylate, glutamate, stearate, glycollylarsanilate, sulfate, hexylresorcinate, subacetate, hydrabamine, succinate, hydrobromide, tannate, hydrochloride, tartrate, hydroxynaphthoate, teoclate, iodide, tosylate, isothionate, triethiodide, lactate, panoate, valerate, and the like which can be used as a dosage form for modifying the solubility or hydrolysis characteristics or can be used in sustained release or pro-drug formulations. It will be understood that, as used herein, references to the OXM analogs disclosed herein are meant to also include the pharmaceutically acceptable salts. 
     The following examples are intended to promote a further understanding of the present invention. 
     Example 1 
     A general procedure for synthesizing the peptides shown in Table 1 may be performed as follows. 
     The peptides may be synthesized by solid phase synthesis using Fmoc/t-Bu chemistry on a peptide multisynthesizer Symphony (Protein Technologies Inc.) on a 150 mol scale, using either a Rink-amide PEG-PS resin (Champion, Biosearch Technologies, loading 0.28 mmol/g) or a Rink-amide PS resin (Chemlmpex loading 0.47 mmol/g). 
     All the amino acids are dissolved at a 0.3 M concentration in DMF. The amino acids are activated with equimolar amounts of HATU (O-(7-azabenzotriazol-1-yl)-N,N,N′,N′-tetramethyluronium hexafluorophosphate) solution 0.3 M in DMF, and a 2-fold molar excess of DIEA (N,N-diisopropylethylamine), solution 2M in NMP. The acylation reactions are performed in general for 1 hour with a 5-fold excess of activated amino acid over the resin free amino groups with double 45 minutes acylation reactions performed from His 1  to Thr 7 , from D 15  to U 16  and from F 22  to V 23 . 
     The side chain protecting groups may be: tert-butyl for Glu, Ser, D-Ser, Thr and Tyr; trityl for Asn, Gln and His; tert-butoxy-carbonyl for Lys, Trp; and, 2,2,4,6,7-pentamethyldihydrobenzofuran-5-sulfonyl for Arg; His may be introduced as Boc-His(Trt)-OH at the end of the sequence assembly. Amino acid 2 (L-methionine-sulphone) may be introduced by acylation of Fmoc-L-methionine-sulphone-COOH; Nle(εN 3 ) (ε-azidonorleucine) was introduced by acylation of Fmoc-E-azidonorleucine-COOH. 
     The lysine that may be used for linker-lipid derivatization, may be incorporated with a Dde [1-(4,4-dimethyl-2,6-dioxocyclohex-1-ylidene)ethyl] protecting group or Alloc (allyloxycarbonyl) protecting group on the side chain amino group. For those sequences comprising an alpha methyl amino acid and the corresponding following residue, the incorporation may be performed by manual coupling with HOAt (Hydroxybenzoazatriazole) and DIC (N,N′-diisopropylcarbodiimide). 
     At the end of the assembly, the Dde protecting group of Lys(Dde) is removed by treatment with 2% hydrazine in DMF and the Alloc protecting group of Lys(Alloc) is removed by treatment with Pd(PPh 3 ) 4  and PhSiH 3 . The side chains of Lys are derivatized with different linkers and fatty acids by incorporation of Fmoc-Glu-OtBu (γ-glutamic acid), Fmoc-PEG 2  [8-(9-Fluorenylmethyloxycarbonyl-amino)-3,6-dioxaoctanoic acid], the lipid diacids (Octadecanedioic acid; Eicosanedioic acid) and Azido acids (C 5 N 3 =5-azido pentinoic acid; C 10 N 3 =10-azido-decanoic acid; C 16 N 3 =16-azido-hexadecanoic acid) using HOAt and DIC as activators. 
     At the end of the synthesis, the dry peptide-resins are individually treated with 25 mL of the cleavage mixture, 88% TFA, 5% phenol, 2% triisopropylsilane and 5% water for 1.5 hours at room temperature. Each resin is then filtered and then added to cold methyl-t-butyl ether in order to precipitate the peptide. After centrifugation, the peptide pellets are washed with fresh cold methyl-t-butyl ether to remove the organic scavengers. The process may be repeated twice. Final pellets are dried, resuspended in H 2 O, 20% acetonitrile, and lyophilized. 
     The crude peptides (140 mg in 3 mL of DMSO) are purified by reverse-phase HPLC using preparative Waters Deltapak C 4  (40×200 mm, 15 μm, 3001) and using as eluents (A) 0.1% TFA in water and (B) 0.1% TFA in acetonitrile. 
     Analytical HPLC may be performed on an Acquity UPLC Waters Chromatograph with a BEH300 C 4  Acquity Waters column 2.1×100 mm, 1.7 μm, at 45° C., using H 2 O, 0.1% TFA (A) and CH 3 CN, 0.1% TFA (B) as solvents. The peptides may be characterized by electrospray mass spectrometry on an Acquity SQ Detector. 
     Example 2 
     Synthesis of Linker 16-Azido Esadecanoic Acid May be Performed as Follows 
     
       
         
         
             
             
         
       
     
     To a solution of 16-bromo hexadecanoic acid in DMF, sodium azide (2 eq) is added. After 12 hours at 85 C°, the reaction mixture is cooled to room temperature. DCM is added and the organic phase is washed with HCl 0.1N, brine and dried over Na 2 SO 4 . The solvents are removed under reduced pressure and 16-azido hexadecanoic acid is obtained.  1 H NMR (400 MHz, CDCl 3 -d 6 , 300K) δ 12.35 (s, 1H), 3.30-3.22 (m, 2H), 2.40-2.32 (m, 2H), 1.69-1.56 (m, 4H), 1.4-1.2 (m, 20H). 
     Example 3 
     Synthesis of Linker Propargyl-PEG 25 -Acid May be as Follows 
     
       
         
         
             
             
         
       
     
     Step 1: 
     To a suspension of sodium hydride, 60% dispersion in mineral oil (18 mg, 0.450 mmol) in THF (1 mL) cooled in an ice bath is added a solution of hydroxy-PEG 24 -t-butyl ester (250 mg, 0.208 mmol) in Tetrahydrofuran (THF) (1.5 mL). The reaction mixture is stirred for 15 minutes and propargyl bromide, 80% in toluene (26.9 μl, 0.249 mmol) is added. The ice bath is removed and the reaction is allowed to warm to room temperature (RT) and stirred overnight. The reaction is quenched with water (50 μL), diluted with EtOAc, dried over sodium sulfate, filtered and concentrated to give the crude product propargyl-PEG 25 -t-butyl ester. 
     Step 2: 
     TFA (1 mL, 12.98 mmol) is added to the crude propargyl-PEG 25 -t-butyl ester and the reaction is stirred at RT for one hour. The volatiles are evaporated and the residue is purified by mass-directed RP-HPLC (ACN/water with 0.1% ammonium hydroxide as modifier) to give propargyl-PEG 25 -acid. MS: 1186 (M+1). 
     Example 4 
     Synthesis of Linker 2-(2-(2-(Pent-4-ynamido)ethoxy)ethoxy)acetic acid (Propargyl-C 5 -PEG 2 -acid) May be as Follows 
     
       
         
         
             
             
         
       
     
     To a solution of 2-(2-(2-aminoethoxy)ethoxy)acetic acid (1.0 g, 6.13 mmol) and 2,5-dioxopyrrolidin-1-yl pent-4-ynoate (1.2 g, 6.13 mmol) in dimethylformamide (DMF) (10 mL) is added N,N-diisopropylethylamine (DIPEA) (1.28 ml, 7.35 mmol) at RT. The mixture is stirred at RT overnight. The reaction is quenched with water and lyophilized to dryness. The residue is purified by mass-directed RP-HPLC (ACN/water with 0.1% TFA as modifier) to give 2-(2-(2-(pent-4-ynamido)ethoxy)ethoxy)acetic acid. MS: 266 (M+23). 
     Example 5 
     Synthesis of Linker 10,19,28-Trioxo-3,6,12,15,21,24-hexaoxa-9,18,27-triazadotriacont-31-ynoic acid (Propargyl-C 5 -(PEG 2 ) 3 -acid) 
     
       
         
         
             
             
         
       
     
     Step 1: 
     In a 20 mL vial is added 2-(2-(2-(pent-4-ynamido)ethoxy)ethoxy)acetic acid (500 mg, 2.055 mmol) and DMSO (2 mL). TSTU (dimethylamino-(2,5-dioxopyrrolidin-1-yl)oxymethylidene]-dimethylazanium; tetrafluoroborate; 681 mg, 2.261 mmol) and triethylamine (573 μl, 4.11 mmol) are added. The mixture is stirred at RT for two hours. The freshly prepared N-Hydroxysuccinimide (NHS) ester is then added to a solution of 2-(2-aminoethoxy)ethoxy)acetic acid (419 mg, 2.57 mmol) and triethylamine (2.86 ml, 20.55 mmol) in DMSO (1 mL). The reaction is stirred at RT for 48 hours and triethylamine is removed under reduced pressure. Two drops of trifluoroacetate (TFA) are added to neutralize the reaction. The mixture is filtered through a syringe filter. The residue is purified by mass-directed RP-HPLC (ACN/water with 0.1% TFA as modifier) to give 10,19-dioxo-3,6,12,15-tetraoxa-9,18-diazatricos-22-ynoic acid. 
     Step 2: 
     In a 20 ml vial is added 10,19-dioxo-3,6,12,15-tetraoxa-9,18-diazatricos-22-ynoic acid (132 mg, 0.340 mmol) and DMSO (1 mL). TSTU (113 mg, 0.374 mmol) and triethylamine (95 μl, 0.680 mmol) are added. The mixture is stirred at RT for two hours. The freshly prepared NHS ester is then added to a solution of 2-(2-(2-aminoethoxy)ethoxy)acetic acid (111 mg, 0.680 mmol) and triethylamine (474 μl, 3.40 mmol) in DMSO (1 mL). The reaction is quenched with TFA aqueous solution to slightly acidic. Water is added and the mixture is lyophilized to dryness. The residue purified by mass-directed RP-HPLC (ACN/water with 0.1% TFA as modifier) to give 10,19,28-trioxo-3,6,12,15,21,24-hexaoxa-9,18,27-triazadotriacont-31-ynoic acid. MS: 534 (M+1). 
     Example 6 
     Synthesis of Linker Propargyl-C 5 -Lys(γE- t BuC 16 )-PEG 12 -acid 
     
       
         
         
             
             
         
       
     
     Step 1: 
     To a mixture of L-Glu-O t Bu (580 mg, 2.85 mmol) and NaHCO 3  (527 mg, 6.28 mmol) in water (10 mL) and THF (5 ml) at RT is added a solution of 2,5-dioxopyrrolidin-1-yl palmitate (1.01 g, 2.85 mmol) in THF (10 ml). The reaction mixture is stirred at RT overnight. THF is evaporated under reduced pressure. The reaction mixture is neutralized with 1N HCl (7 mL), diluted with water, extracted with EtOAc, washed with brine, dried over sodium sulfate, filtered and concentrated to give the crude product (S)-5-(tert-butoxy)-5-oxo-4-palmitamidopentanoic acid. 
     Step 2: 
     To a mixture of H-Lys(Boc)-OH (600 mg, 2.436 mmol) and NaHCO 3  (450 mg, 5.36 mmol) in water (10 mL) and THF (5 mL) at RT is added a solution of 2,5-dioxopyrrolidin-1-yl pent-4-ynoate (475 mg, 2.436 mmol) in THF (10 mL). The reaction mixture is stirred at RT overnight. THF is evaporated under reduced pressure. The reaction mixture is neutralized with 1N HCl (7 mL), diluted with water, extracted with EtOAc, washed with brine, dried over sodium sulfate, filtered and concentrated to give the product (S)-6-((tert-butoxycarbonyl)amino)-2-(pent-4-ynamido)hexanoic acid as light yellow oil. TFA (3 mL, 38.9 mmol) is added to the crude (S)-6-((tert-butoxycarbonyl)amino)-2-(pent-4-ynamido)hexanoic acid (0.795 g, 2.436 mmol) at room temperature and the reaction mixture is stirred for one hour. TFA is evaporated under reduced pressure and the residue is quenched with water and lyophilized to give the product (S)-6-amino-2-(pent-4-ynamido)hexanoic acid, 2TFA. 
     Step 3: 
     In a 20 mL vial is added (S)-5-(tert-butoxy)-5-oxo-4-palmitamidopentanoic acid (500 mg, 1.13 mmol) and DMSO (1 mL). TSTU (375 mg, 1.245 mmol) and triethylamine (316 μl, 2.264 mmol) are added. The mixture is stirred at RT for two hours. The freshly prepared NHS ester is then added to a solution of (S)-6-amino-2-(pent-4-ynamido)hexanoic acid, 2TFA (643 mg, 1.415 mmol) and triethylamine (1.58 mL, 11.32 mmol) in DMSO (1 mL). The reaction mixture is stirred at RT overnight. The reaction is diluted with water, acidified with 1N HCl, extracted with EtOAc, washed with water and brine, dried over sodium sulfate, filtered and concentrated. The residue is purified by mass-directed RP-HPLC (ACN/water with 0.1% TFA as modifier) to give N 6 —((S)-5-(tert-butoxy)-5-oxo-4-palmitamidopentanoyl)-N 2 -(pent-4-ynoyl)-L-lysine. 
     Step 4: 
     In a 20 mL vial is added N 6 —((S)-5-(tert-butoxy)-5-oxo-4-palmitamidopentanoyl)-N 2 -(pent-4-ynoyl)-L-lysine (100 mg, 0.154 mmol) and DMSO (0.8 mL). TSTU (51 mg, 0.169 mmol) and triethylamine (43 μl, 0.308 mmol) is added. The mixture is stirred at RT for two hours. The freshly prepared NHS ester is then added to a solution of amino-PEG 12 -acid (124 mg, 0.192 mmol) and triethylamine (214 μl, 1.539 mmol) in DMSO (0.5 mL). The reaction is stirred at RT overnight. The reaction is diluted with water and lyophilized to dryness. The residue is purified by mass-directed RP-HPLC (ACN/water with 0.1% TFA as modifier) to give propargyl-C 5 -Lys(γE- t Bu 16 )-PEG 12 -acid. MS: 1250 (M+1). 
     Example 7 
     Synthesis of Propargyl-(PEG 4 )(PEG 24 )-acid 
     
       
         
         
             
             
         
       
     
     Amino-PEG 24 -acid (100 mg, 0.087 mmol) and NaHCO 3  (16.12 mg, 0.192 mmol) are suspended in water (2 mL) and THF (1 ml) at room temperature. To the mixture is added a solution of propargyl-PEG 4 -NHS (32.7 mg, 0.092 mmol) in THF (2 mL). The reaction is stirred at RT overnight. The reaction is neutralized by 0.1 M HCl (2 mL) and lyophilized to dryness. The residue is purified by mass-directed RP-HPLC (ACN/water with 0.1% TFA as modifier) to give propargyl-(PEG 4 )(PEG 24 )-acid. MS: 695 (M+2)/2. 
     Example 8 
     Synthesis of Propargyl-(PEG 4 )(PEG 36 )-acid 
     
       
         
         
             
             
         
       
     
     Amino-PEG 36 -acid (100 mg, 0.060 mmol) and NaHCO 3  (11.03 mg, 0.131 mmol) are suspended in water (2 mL) and THF (1 mL) at room temperature. To the mixture is added a solution of propargyl-PEG 4 -NHS (22.4 mg, 0.063 mmol) in THF (2 mL). The reaction is stirred at RT overnight. The reaction is neutralized by 0.1 M HCl (2 mL) and lyophilized to dryness. The residue is purified by mass-directed RP-HPLC (ACN/water with 0.1% TFA as modifier) to give propargyl-(PEG 4 )(PEG 36 )-acid. MS: 640 (M+3)/3. 
     Example 9 
     Synthesis of Propargyl-(PEG 5 (PEG 36 ) 2 -acid 
     
       
         
         
             
             
         
       
     
     Step 1: 
     Amino-PEG 36 -acid (1.04 g, 0.623 mmol) and NaHCO 3  (115 mg, 1.37 mmol) are suspended in water (20 mL) and THF (10 mL) at room temperature. To the mixture is added a solution of propargyl-PEG 5 -NHS (262 mg, 0.65 mmol) in THF (20 mL). The reaction is stirred at RT overnight. The reaction is neutralized by 0.1 M HCl (20 mL) and lyophilized to dryness. The residue is purified by mass-directed RP-HPLC (ACN/water with 0.1% TFA as modifier) to give propargyl-(PEG 5 )(PEG 36 )-acid as white solids. 
     Step 2: 
     In a 20 ml vial was added propargyl-(PEG 5 )(PEG 36 )-acid (100 mg, 0.051 mmol) and DMSO (0.8 mL). TSTU (16.88 mg, 0.056 mmol) and triethylamine (14.21 L, 0.102 mmol) was added. The mixture was stirred at RT for two hours. The freshly prepared NHS ester is then added to a solution of amino-PEG 36 -acid (107 mg, 0.064 mmol) and triethylamine (71.1 μL, 0.510 mmol) in DMSO (0.5 mL). The reaction is stirred at RT overnight. The reaction is diluted with water and lyophilized to dryness. The residue is purified by mass-directed RP-HPLC (ACN/water with 0.1% TFA as modifier) to give proparyl-(PEG 5 )(PEG 36 ) 2 -acid as white solids. MS: 517.85 (M+7)/7. 
     Example 10 
     Synthesis of N αA1 N εB29  bis-Boc RHI 
     
       
         
         
             
             
         
       
     
     RHI (10 g) is dissolved in DMSO (200 mL) at RT the mixture is stirred at RT until homogeneous. To the solution is added 2,2,6,6-tetramethylpiperidine (5.8 mL) followed slow addition of a solution of tert-butyl (2,5-dioxopyrrolidin-1-yl) carbonate (Boc-OSu, 0.8 g) in DMSO (10 mL). The reaction is agitated for four hours and the mixture is transferred to IPAc (1 L) over 20 minutes. The slurry is centrifuged for two hours and the solid is filtered, washed with IPAc (20 ml×3) and dried under vacuum to give N αA1 N εB29  bis-Boc RHI. 
     Example 11 
     Synthesis of N αA1 -propargyl-C 5  RHI (INS1) 
     
       
         
         
             
             
         
       
     
     Insulin (655 mg, 0.113 mmol) is first dissolved in pH 2.5 water (12 mL) and then adjusted to pH 8.5 with 1N NaOH. A stock solution of 2,5-dioxopyrrolidin-1-yl pent-4-ynoate (35 mg, 0.174 mmol) in DMSO (200 μL) is added in four portions to the above insulin solution over one hour. The pH is maintained at 8.0-8.5. The reaction is quenched with ethanolamine (17 μL) after five hours and adjusted to pH 7.0. The reaction mixture is first purified by IEC HPLC with the following conditions: PolySULFOETHYL ATM column, 250×21.0 mm, 5 um, 1000 Å, eluent (A: 1 L ACN, 3 L H 2 O, 4 ml H 3 PO 4 ; B: 1 L ACN, 2.6 L H 2 O, 400 ml 5M NaCl, 4 ml H 3 PO 4 ), FR=15 mL/minute, wavelength 210 nm, B % from 10% to 40%. The major fractions are concentrated down to 15 mL by 8×10K Amicon centrifuge tube. The concentrated crude is further purified by RP-HPLC, using the separation condition (28-33%) 0.05% TFA in ACN/H 2 O on Kromasil 100-10-C 8  from AkzoNobel, 100 A and 10 uM 50×250 mm column; FR=85 ml/min, ramp 25 minutes, wavelength=210 nm. The desired fractions are collected and lyophilized to N αA1 -propargyl-C 5  RHI. 
     Example 12 
     Synthesis of N αB1 -propargyl-C 5  RHI (INS2) 
     
       
         
         
             
             
         
       
     
     Step 1: 
     RHI (2.74 g, 0.472 mmol) is dissolved in DMSO (50 mL) and the mixture is stirred at RT until homogeneous (about 45 minutes). To the solution is added 1,1,3,3-tetramethylguanidine (0.19 mL, 1.179 mmol) and followed by slow addition of a solution of Boc-OSu (0.216 g, 1.005 mmol) DMSO (2.1 mL, plus 0.4 mL wash) over 30 minutes. The reaction is further stirred for 1.5 hours for N αA1 N εB29  bis-Boc RHI to be formed. To the reaction mixture is added a solution of 2,5-dioxopyrrolidin-1-yl pent-4-ynoate in DMSO (1 mL) using a syringe pump over 30 minutes. After stirring for two hours, the reaction mixture is dropwise added to a stirred 275 mL of IPAc to precipitate the product. The white solids are filtered, washed with IPAc and dried under N 2  and vacuum for one hour. 
     Step 2: 
     TFA (15 mL, 195 mmol) is added to the above crude material (3 g, 0.493 mmol) and the reaction is stirred and sonicated until solids fully dissolved (about 30 minutes). The reaction mixture is dropwise added to water (75 mL) and the precipitated solids are filtered and dried under N 2  and vacuum. The crude material is purified using RP-HPLC to give the N αB1 -propargyl-C 5  RHI. 
     Example 13 
     Synthesis of N αB1 -propargyl-PEG 4  RHI (INS3) 
     
       
         
         
             
             
         
       
     
     Step 1: 
     To a solution of N αA1 N εB29  bis-Boc RHI (317 mg, 0.053 mmol) in DMSO (2 mLl) is added Et 3 N (37 μL, 0.264 mmol) and followed by slow addition of alkyne-PEG 4 -NHS (2,5-dioxopyrrolidin-1-yl 4,7,10,13-tetraoxahexadec-15-ynoate, 37.7 mg, 0.106 mmol) in DMSO (800 μL) via syringe pump over one hour. The reaction mixture is stirred at RT overnight. The reaction mixture is dropwise added to stirred isopropyl acetate (IPAc, 50 mL) to precipitate the product. The white precipitate is collected by filtration and dried under nitrogen gas and vacuum for one hour to give the crude product N αA1 N εB29  bis-Boc, N αB1 -propargyl-PEG 4  RHI. 
     Step 2: 
     TFA (1.5 mL, 19.47 mmol) is added to the crude N αA1 N εB29  bis-Boc, N αB1 -PEG 4 -alkyne RHI. The reaction is stirred and sonicated at RT until solids fully dissolved (about 30 minutes). The reaction mixture is dropwise added to tert-butyl methyl ether (TBME, 20 mL) and solids precipitated out. The reaction is filtered, washed with TBME and IPAc. The white solid is dried under nitrogen gas and vacuum for one hour to give crude product as white solids. The solids are dissolved in water (15 mL). It is purified by RP-HPLC column using the separation condition (28-35%) 0.05% TFA in AcCN/H 2 O on Kromasil 100-10-C 8  from AkzoNobel, 100 A and 10 μM 50×250 mm column; FR=85 mL/minute, ramp 25 minutes, wavelength=210 nm. The fractions are collected and lyophilized to give N αB1 -propargyl-PEG 4 -RHI. 
     INS4-INS6 shown below may be prepared using the methodology herein and the general procedure described for INS3. 
     
       
         
           
               
               
               
             
               
                   
               
             
            
               
                   
                 INS 4 
                 N aB1 -propargyl-PEG 3  RHI 
               
               
                   
               
               
                   
                   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                   
                 INS 5 
                 N aB1 -propargyl-PEG 5  RHI 
               
               
                   
               
               
                   
                   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                   
                 INS 6 
                 N aB1 -BCN-PEG 4 (endo)RHI 
               
               
                   
               
               
                   
                   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     Example 14 
     Synthesis of N αB1 -propargyl-PEG 6  RHI (INS7) 
     
       
         
         
             
             
         
       
     
     In a small vial, propargyl-PEG 6 -acid (4,7,10,13,16,19-hexaoxadocos-21-yn-1-oic acid, 11.6 mg, 0.033 mmol) is dissolved in DMSO (500 μL). To the solution is added TSTU (O—(N-Succinimidyl)-N,N,N′,N′-tetramethyluronium tetrafluoroborate, 10.0 mg, 0.033 mmol) and Et 3 N (4.6 μl, 0.033 mmol). The mixture is stirred at RT for two hours to give the crude propargyl-PEG 6 -NHS. The freshly made propargyl-PEG 6 -NHS solution is added to a solution of N αA1 N εB29  bis-Boc RHI (100 mg, 0.017 mmol) and Et 3 N (12 μL, 0.086 mmol) in DMSO (1 mL) via syringe pump over 30 minutes. The reaction mixture is stirred at RT for two hours. The reaction mixture is dropwise added to a stirred IPAc (20 mL) to precipitate the product. The white precipitate is collected by filtration and dried under nitrogen gas and vacuum for one hour to give the crude product N αA1 N εB29  bis-Boc, N αB1 -propargyl-PEG 6  RHI. 
     TFA (0.5 ml, 6.49 mmol) is added to the crude N αA1 N εB29  bis-Boc, N αB1- PEG 6 -alkyne RHI. The reaction is stirred and sonicated at RT until solids fully dissolved (about 30 minutes). The reaction mixture is dropwise added to tert-butyl methyl ether (TBME, 10 mL) and solids precipitated out. The reaction is filtered, washed with TBME and IPAc. The white solid is dried under nitrogen gas and vacuum for one hour to give crude product as white solids. The solids are dissolved in water (8 mL). It is purified by RP-HPLC column using the separation condition (28-35%) 0.05% TFA in AcCN/H 2 O on Kromasil 100-10-C8 from AkzoNobel, 100 A and 10 μM 50×250 mm column; FR=85 mL/minute, ramp 25 minutes, wavelength=210 nm. The fractions are collected and lyophilized to give the N αB1 -propargyl PEG 6  RHI. 
     INS 8-INS15 shown below may be prepared using the methodology herein and the general procedure described for INS7. 
     
       
         
           
               
               
             
               
                   
               
             
            
               
                 INS 8 
                 N aB1 -propargyl-PEG 8  RHI 
               
               
                   
               
               
                   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 INS 9 
                 N aB1 -propargyl-PEG 10  RHI 
               
               
                   
               
               
                   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 INS 10 
                 N aB1 -propargyl-PEG 13  RHI 
               
               
                   
               
               
                   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 INS 11 
                 N aB1 -propargyl-PEG 14  RHI 
               
               
                   
               
               
                   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 INS 12 
                 N aB1 -proopargyl-PEG 25  RHI 
               
               
                   
               
               
                   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 INS 13 
                 N aB1 -propargyl-PEG 2 -C 5  RHI 
               
               
                   
               
               
                   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 INS 14 
                 N aB1 -propargyl-C5-(PEG 2 ) 3  RHI 
               
               
                   
               
               
                   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 INS 15 
                 N aB1 -propargyl-C5-Lys(γE-C 16 )-PEG 12 -RHI 
               
               
                   
               
               
                   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     Example 15 
     Synthesis of N εB29 -propargyl-C 5  RHI (INS16) 
     
       
         
         
             
             
         
       
     
     General Method: In an appropriate sized container, RHI is dissolved, with gentle stirring, at room temperature in a mixed solvent: 2:3 v/v 0.1 M Na 2 CO 3 :AcCN. After the mixture cleared, the pH is adjusted to the value of 10.5-10.8 using alkaline solution, e.g., 0.1 N NaOH. In a separate vial, 2,5-dioxopyrrolidin-1-yl pent-4-ynoate is dissolved in an organic solvent, e.g., DMSO, at room temperature. Aliquots of the solution of the activated ester is added over a period of time to the solution containing insulin until UPLC chromatogram showed that most of the unmodified insulin had been reacted and that a substantial portion of the reaction mixture had been converted into B29-conjugated insulin. The reaction is quenched by the addition of an amine nucleophile, e.g., 2-aminoethanol. The reaction solution is stirred at room temperature for 30 minutes. The resulting solution is carefully diluted with cold H 2 O (20×) at 0° C. and its pH is adjusted to a final pH of 2.5 using 1 N HCl (and 0.1 N NaOH if needed). The solution is first concentrated by ultrafiltration, either through a tangential flow filtration (TFF) system or using Amicon Ultra-15 Centrifugal Units, with 1K, 3K or 10K MWCO membrane. The concentrated solution may be first subjected to ion exchange chromatography (PolySULFOETHYL A column, PolyLC Inc., 250×21 mm, 5 m, 1000 Å; Buffer A: 0.1% (v/v)H 3 PO 4 /25% AcCN; Buffer B: 0.1% (v/v)H 3 PO 4 /25% AcCN/0.5 M NaCl). Fractions containing B29-conjugate with desired purity are combined and concentrated using TFF system or Amicon Ultra-15. The resulting solution is then further purified by reverse phase HPLC (Waters C4 250×50 mm column, 10 m, 1000 Å column or Kromasil C8 250×50 mm, 10 am, 100 Å column; Buffer A: 0.05-0.1% TFA in water; Buffer B: 0.05-0.1% TFA in AcCN). Fractions containing the title conjugate are combined and freeze-dried or buffer exchanged using TFF system and/or Amicon Ultra-15 to give the N εB29 -propargyl-C 5  RHI. MS: 1472.56 (M+4)/4. 
     Example 16 
     Synthesis of N εB29 -propargyl-PEG 4  RHI (INS17) 
     
       
         
         
             
             
         
       
     
     In a 20 mL vial, RHI (200 mg, 0.034 mmol) is dissolved in DMSO (1 mL) and aged at RT until homogeneous. 1,1,3,3-tetramethylguanidine (86 μl, 0.689 mmol) is added and followed by slow addition of alkyne-PEG 4 -NHS (2,5-dioxopyrrolidin-1-yl 4,7,10,13-tetraoxahexadec-15-ynoate, 13.5 mg, 0.038 mmol) solution in DMSO (0.5 ml) via syringe pump over 30 min. The reaction is stirred at RT for one hour. The mixture is added dropwise to a mixed solvent IPAc/TBME(20 mL, 4:1) to precipitate out the product. HOAc (200 μl, 3.49 mmol) is added. The solids are filtered and dried under nitrogen gas and vacuum for 30 minutes. The solids are dissolved in 15 mL mix solvent (80% water, 20% ACN, pH=3.0), adjusted pH to 3. The residue is purified by RP-HPLC column, using the separation condition (28-35%) 0.05% TFA in AcCN/H 2 O on Kromasil 100-10-C 8  from AkzoNobel, 100 A and 10 μM 50×250 mm column; FR=85 mL/minute, ramp 25 minutes, wavelength=210 nm. The fractions are collected and lyophilized to give N εB29 -propargyl-PEG 4  RHI. 
     Example 17 
     N εB29 -Propargyl-PEG 4  Insulin Glargine (INS18) 
     
       
         
         
             
             
         
       
     
     N εB29 -propargyl-PEG 4  insulin glargine may be prepared using the methodology herein and the general procedure described for INS16. 
     Example 18 
     Synthesis of N εB29 -propargyl-PEG 13  RHI (INS19) 
     
       
         
         
             
             
         
       
     
     In a small vial, propargyl-PEG 13 -acid (4,7,10,13,16,19,22,25,28,31,34,37,40-tridecaoxatritetracont-42-ynoic acid, 24.9 mg, 0.038 mmol) is dissolved in DMSO (500 μL). 
     To the solution is added TSTU (11.4 mg, 0.038 mmol) and Et 3 N (7.2 μl, 0.052 mmol). The mixture is stirred at RT for two hours. The freshly made propargyl-PEG 6 -NHS solution is added to a solution of RHI (200 mg, 0.034 mmol) and 1,1,3,3-tetramethylguanidine (0.086 ml, 0.689 mmol) in DMSO two mL via syringe pump over 60 minutes. The reaction mixture is stirred at RT for 30 minutes. The reaction is quenched with 2-aminoethanol (10.4 μl, 0.172 mmol) for 10 minutes. The reaction mixture is dropwise added to a stirred 20 mL of IPAc/TBME (4:1) to precipitate the product. The solids are filtered, washed with IPAc, and dried under nitrogen gas and vacuum for one hour. The residue is purified by RP-HPLC (ACN/water with 0.1% TFA as modifier) to give N εB29 -propargyl-PEG 13  RHI. 
     INS20-INS21 shown below may be prepared using the methodology herein and the general procedure described for INS19. 
     
       
         
           
               
               
             
               
                   
               
             
            
               
                 INS 20 
                 N ϵB29 -propargyl-(PEG 4 )-(PEG 24 ) RHI 
               
               
                   
               
               
                   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 INS 21 
                 N ϵB29 -propargyl-(PEG 4 )-(PEG 36 ) RHI 
               
               
                   
               
               
                   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 INS 25 
                 N ϵB29 -propargyl-(PEG 5 )-(PEG 36 ) 2  RHI 
               
               
                   
               
               
                   
                 
                   
                     
                     
                         
                         
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     Example 19 
     Synthesis of N αB1 -propargyl-C 5  N εB29 C 14  RHI (INS22) 
     
       
         
         
             
             
         
       
     
     Step 1: N εB29 C 14  RHI (2.74 g, 0.472 mmol) is dissolved in DMSO (50 mL) and the mixture is stirred at RT until homogeneous (about 45 minutes). To the solution is added 1,1,3,3-tetramethylguanidine (0.19 mL, 1.179 mmol) and followed by slow addition of a solution of Boc-OSu (0.216 g, 1.005 mmol) DMSO (2.1 mL, plus 0.4 mL wash) over 30 minutes. The reaction is further stirred for 1.5 hours for N αA1  Boc RHI to be formed. To the reaction mixture is added a solution of 2,5-dioxopyrrolidin-1-yl pent-4-ynoate in DMSO (1 mL) using a syringe pump over 30 minutes. After stirring for two hours, the reaction mixture is dropwise added to a stirred 275 mL of IPAc to precipitate the product. The white solids are filtered, washed with IPAc and dried under N 2  and vacuum for one hour. 
     Step 2: 
     TFA (15 mL, 195 mmol) is added to the above crude material (3 g, 0.493 mmol) and the reaction is stirred and sonicated until solids fully dissolved (about 30 minutes). The reaction mixture is dropwise added to water (75 mL) and the precipitated solids are filtered and dried under N 2  and vacuum. The crude material is purified using RP-HPLC to give the N αB1 -propargyl-C 5  N εB29 C 14  RHI. 
     Example 20 
     Synthesis of N αB1 -propargyl-C 5  N εB29 γE-C 16  RHI (INS23) 
     
       
         
         
             
             
         
       
     
     Step 1: 
     N εB29 γE-C 16  RHI (2.74 g, 0.472 mmol) is dissolved in DMSO (50 mL) and the mixture is stirred at RT until homogeneous (about 45 minutes). To the solution is added 1,1,3,3-tetramethylguanidine (0.19 mL, 1.179 mmol) and followed by slow addition of a solution of Boc-OSu (0.216 g, 1.005 mmol) DMSO (2.1 mL, plus 0.4 mL wash) over 30 minutes. The reaction is further stirred for 1.5 hours for N αA1  Boc RHI to be formed. To the reaction mixture is added a solution of 2,5-dioxopyrrolidin-1-yl pent-4-ynoate in DMSO (1 mL) using a syringe pump over 30 minutes. After stirring for two hours, the reaction mixture is dropwise added to a stirred 275 mL of IPAc to precipitate the product. The white solids are filtered, washed with IPAc and dried under N 2  and vacuum for one hour. 
     Step 2: 
     TFA (15 mL, 195 mmol) is added to the above crude material (3 g, 0.493 mmol) and the reaction is stirred and sonicated until solids fully dissolved (about 30 minutes). The reaction mixture is dropwise added to water (75 mL) and the precipitated solids are filtered and dried under N 2  and vacuum. The crude material is purified using RP-HPLC to give the N αB1 -propargyl-C 5  N εB29 γE-C 16  RHI. 
     Example 21 
     Synthesis of N αB1 -propargyl-PEG 13  N εB29 γE-C 16  RHI (INS24) 
     
       
         
         
             
             
         
       
     
     Step 1: 
     N εB29 γE-C 16  RHI (2.74 g, 0.472 mmol) is dissolved in DMSO (50 mL) and the mixture is stirred at RT until homogeneous (about 45 minutes). To the solution is added 1,1,3,3-tetramethylguanidine (0.19 mL, 1.179 mmol) and followed by slow addition of a solution of Boc-OSu (0.216 g, 1.005 mmol) DMSO (2.1 mL, plus 0.4 mL wash) over 30 minutes. The reaction is further stirred for 1.5 hours for N αA1  Boc RHI to be formed. To the reaction mixture is added a solution of 2,5-dioxopyrrolidin-1-yl pent-4-ynoate in DMSO (1 mL) using a syringe pump over 30 minutes. After stirring for two hours, the reaction mixture is dropwise added to a stirred 275 mL of IPAc to precipitate the product. The white solids are filtered, washed with IPAc and dried under N 2  and vacuum for one hour. 
     Step 2: 
     TFA (15 mL, 195 mmol) is added to the above crude material (3 g, 0.493 mmol) and the reaction is stirred and sonicated until solids fully dissolved (about 30 minutes). The reaction mixture is dropwise added to water (75 mL) and the precipitated solids are filtered and dried under N 2  and vacuum. The crude material is purified using RP-HPLC to give the N αB1 -propargyl-PEG 13  N εB29 γE-C 16  RHI. 
     Example 21 
     General procedure A for insulin-incretin conjugate preparation (with TBTA ligand) using copper(I) catalyzed Azide-Alkyne Cycloaddition (CuAAC) (schematically shown in  FIG. 1B ): 
     A 10 mM Cu(II)-TBTA in 55% DMSO stock solution is prepared as follows: CuSO 4 .5H 2 O (50 mg) is dissolved in water (10 mL) and Tris[(1-benzyl-1H-1,2,3-triazol-4-yl)methyl]amine (TBTA, 116 mg) is dissolved in DMSO (11 mL). The two solutions are then mixed slowly at 0° C. 
     In a 20 mL vial, incretin peptide comprising an azido group (11 mg, 2.79 μmol) is dissolved in a pre-mixed solvent DMSO/H 2 O (5 mL, 2:3). In another 50 mL centrifuge tube insulin intermediate comprising an alkyne group, e.g. N αB1 -propargyl-PEG 4  RHI, (17.4 mg, 2.87 μmol) is dissolved in a pre-mixed solvent DMSO/H 2 O (5 ml, 2:3), and then 2 M triethylammonium acetate buffer solution (pH 7.0, 1.2 mL) is added. The above two solutions are mixed on a vortex and degassed by gently bubbling nitrogen gas. To the reaction mixture is added freshly prepared 5 mM ascorbic acid solution (1.2 ml) and the mixture vortexed. The solution is degassed by bubbling N 2  for one minute. A stock solution of 10 mM Cu(II)-TBTA in 55% DMSO (0.6 mL) is added and the mixture is flushed with N 2  for two minutes. The mixture is shaken slowly overnight. The reaction mixture is diluted with 50 mL mixed solvent (80% water, 20% ACN pH=3.0) and the pH is adjusted to 3.0. The solution is concentrated using 3K Amicon centrifuge tube to final total volume 15 mL. The residue is purified by RP-HPLC, using the separation condition (31-46%) 0.05% TFA in ACN/H 2 O on Kromasil 100-10-C 8  from AkzoNobel, 100 A and 10 μM 50×250 mm column; FR=85 mL/minute, ramp 25 minutes, wavelength=210 nm. The desired fractions are collected and lyophilized to give the insulin-incretin conjugate wherein the azido and akynyl groups have formed a 1,4-distributed 1,2,3-triazole. MS: 1993 (M+5)/5. 
     Example 22 
     General procedure B for CuAAC conjugate preparation (without TBTA ligand): insulin intermediate comprising an alkyne group, e.g. N εB29 -propargyl-(PEG 4 )-(PEG 24 ) RHI, (33 mg, 4.60 μmol) and incretin peptide comprising an azido group (23.9 mg, 5.52 μmol) are dissolved in DMSO (3.3 mL). Under nitrogen flow, to the above solution in a water bath is added dropwise a stock solution of CuSO 4 .5H 2 O in water (1.23 mL, 0.014 mmol, 2.8 mg/ml). Subsequently, a freshly prepared solution of sodium ascorbate in water (0.969 mL, 0.018 mmol, 3.76 mg/mL) is added dropwise. The reaction is stirred at RT for two hours, quenched with a mixed solvent (10 mL, 80% water, 20% ACN, pH=3.0) and pH is adjusted to 3.0. The reaction solution is purified by RP-HPLC column, using the separation condition (32-47%) 0.05% TFA in ACN/H 2 O on Kromasil 100-10-C 8  from AkzoNobel, 100 A and 10 μM 50×250 mm column; FR=85 mL/minute, ramp 25 minutes, wavelength=210 nm. The desired fractions are collected and lyophilized to give the insulin-incretin conjugate wherein the azido and akynyl groups have formed a 1,4-disubstituted 1,2,3-triazole. MS: 1849 (M+6)/6. 
     Example 23 
     Preparation of N αB1 -BCN-PEG 4  (endo) RHI-incretin peptide conjugate using Copper-free click chemistry. 
     Insulin intermediate, e.g., N αB1 -BCN-PEG 4  (endo), (17 mg, 2.73 μmol) is dissolved in water (3 mL) to give a clear solution. To the solution is added 0.5 mL pH 7 buffer (2 M triethylammonium acetate buffer, pH=7.0: 2.78 mL Et 3 N mixed with 1.14 ml acetic acid, water is added to 10 mL, and the pH is adjusted to 7.0). Incretin peptide comprising an azido group (14.8 mg, 3.41 μmol) is dissolved in a mixed solvent (3 mL, water/ACN 3:2). The two solutions are mixed together and stirred at RT for six hours. The solution is adjusted pH with 1.0 N HCl until the solution turns clear (total volume 8 mL). The reaction solution is purified by RP-HPLC column, using the separation condition (31-47%) 0.05% TFA in AcCN/H 2 O on Kromasil 100-10-C8 from AkzoNobel, 100 A and 10 μM 50×250 mm column; FR=85 mL/minute, ramp 25 minutes, wavelength=210 nm. Fractions are collected and lyophilized to give the product. MS: 1691 (M+6)/6. 
     Example 24 
     Table 4 shows various insulin-incretin conjugates (“CON”) that have been synthesized according to methods disclosed herein. Each conjugate was synthesized from a particular peptide having a linker with a terminal azido group and a particular insulin having a linker with a terminal alkynal group to produce the conjugate in which the insulin and peptide are linked via the azido and alkynal groups in a 1,4 disubstituted 1,2,3-triazol linkage, except for CON23 which is linked via a 1,4,5 disubstituted 1,2,3-triazol. 
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Conjugate 
               
            
           
           
               
               
               
            
               
                   
                 Components 
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Name 
                 Peptide 
                 Insulin 
               
               
                   
                   
               
               
                   
                 CON1 
                 PEP68 
                 INS16 
               
               
                   
                 CON2 
                 PEP68 
                 INS2 
               
               
                   
                 CON3 
                 PEP68 
                 INS1 
               
               
                   
                 CON4 
                 PEP69 
                 INS2 
               
               
                   
                 CON5 
                 PEP69 
                 INS16 
               
               
                   
                 CON6 
                 PEP69 
                 INS1 
               
               
                   
                 CON7 
                 PEP70 
                 INS16 
               
               
                   
                 CON8 
                 PEP70 
                 INS1 
               
               
                   
                 CON9 
                 PEP70 
                 INS2 
               
               
                   
                 CON10 
                 PEP71 
                 INS16 
               
               
                   
                 CON11 
                 PEP71 
                 INS2 
               
               
                   
                 CON12 
                 PEP71 
                 INS1 
               
               
                   
                 CON13 
                 PEP72 
                 INS2 
               
               
                   
                 CON14 
                 PEP73 
                 INS2 
               
               
                   
                 CON15 
                 PEP73 
                 INS16 
               
               
                   
                 CON16 
                 PEP74 
                 INS2 
               
               
                   
                 CON17 
                 PEP74 
                 INS16 
               
               
                   
                 CON19 
                 PEP69 
                 INS3 
               
               
                   
                 CON20 
                 PEP69 
                 INS10 
               
               
                   
                 CON21 
                 PEP74 
                 INS3 
               
               
                   
                 CON22 
                 PEP74 
                 INS10 
               
               
                   
                 CON23 
                 PEP74 
                 INS6 
               
               
                   
                 CON24 
                 PEP74 
                 INS4 
               
               
                   
                 CON25 
                 PEP74 
                 INS5 
               
               
                   
                 CON26 
                 PEP74 
                 INS13 
               
               
                   
                 CON27 
                 PEP74 
                 INS7 
               
               
                   
                 CON28 
                 PEP1 
                 INS2 
               
               
                   
                 CON29 
                 PEP2 
                 INS2 
               
               
                   
                 CON30 
                 PEP3 
                 INS2 
               
               
                   
                 CON31 
                 PEP4 
                 INS2 
               
               
                   
                 CON32 
                 PEP5 
                 INS2 
               
               
                   
                 CON33 
                 PEP6 
                 INS2 
               
               
                   
                 CON34 
                 PEP7 
                 INS2 
               
               
                   
                 CON35 
                 PEP8 
                 INS2 
               
               
                   
                 CON36 
                 PEP9 
                 INS2 
               
               
                   
                 CON37 
                 PEP10 
                 INS2 
               
               
                   
                 CON38 
                 PEP11 
                 INS2 
               
               
                   
                 CON39 
                 PEP12 
                 INS2 
               
               
                   
                 CON40 
                 PEP13 
                 INS2 
               
               
                   
                 CON41 
                 PEP14 
                 INS2 
               
               
                   
                 CON42 
                 PEP15 
                 INS2 
               
               
                   
                 CON43 
                 PEP16 
                 INS2 
               
               
                   
                 CON44 
                 PEP17 
                 INS2 
               
               
                   
                 CON45 
                 PEP18 
                 INS2 
               
               
                   
                 CON46 
                 PEP19 
                 INS2 
               
               
                   
                 CON47 
                 PEP20 
                 INS2 
               
               
                   
                 CON48 
                 PEP21 
                 INS2 
               
               
                   
                 CON49 
                 PEP22 
                 INS2 
               
               
                   
                 CON50 
                 PEP25 
                 INS2 
               
               
                   
                 CON51 
                 PEP26 
                 INS2 
               
               
                   
                 CON52 
                 PEP27 
                 INS2 
               
               
                   
                 CON53 
                 PEP28 
                 INS2 
               
               
                   
                 CON55 
                 PEP74 
                 INS8 
               
               
                   
                 CON56 
                 PEP74 
                 INS9 
               
               
                   
                 CON57 
                 PEP74 
                 INS11 
               
               
                   
                 CON58 
                 PEP69 
                 INS22 
               
               
                   
                 CON59 
                 PEP69 
                 INS23 
               
               
                   
                 CON60 
                 PEP74 
                 INS24 
               
               
                   
                 CON61 
                 PEP74 
                 INS19 
               
               
                   
                 CON62 
                 PEP74 
                 INS12 
               
               
                   
                 CON63 
                 PEP10 
                 INS3 
               
               
                   
                 CON64 
                 PEP74 
                 INS18 
               
               
                   
                 CON65 
                 PEP74 
                 INS17 
               
               
                   
                 CON66 
                 PEP74 
                 INS14 
               
               
                   
                 CON67 
                 PEP69 
                 INS15 
               
               
                   
                 CON68 
                 PEP74 
                 INS15 
               
               
                   
                 CON69 
                 PEP74 
                 INS25 
               
               
                   
                 CON70 
                 PEP74 
                 INS20 
               
               
                   
                 CON71 
                 PEP29 
                 INS2 
               
               
                   
                 CON72 
                 PEP30 
                 INS2 
               
               
                   
                 CON73 
                 PEP31 
                 INS2 
               
               
                   
                 CON74 
                 PEP32 
                 INS2 
               
               
                   
                 CON75 
                 PEP34 
                 INS2 
               
               
                   
                 CON76 
                 PEP35 
                 INS2 
               
               
                   
                 CON77 
                 PEP37 
                 INS2 
               
               
                   
                 CON78 
                 PEP74 
                 INS21 
               
               
                   
                 CON79 
                 PEP74 
                 INS1 
               
               
                   
                 CON80 
                 PEP1 
                 INS3 
               
               
                   
                 CON81 
                 PEP6 
                 INS3 
               
               
                   
                 CON82 
                 PEP29 
                 INS3 
               
               
                   
                 CON83 
                 PEP33 
                 INS2 
               
               
                   
                 CON84 
                 PEP36 
                 INS2 
               
               
                   
                 CON85 
                 PEP38 
                 INS2 
               
               
                   
                 CON86 
                 PEP39 
                 INS2 
               
               
                   
                 CON87 
                 PEP40 
                 INS2 
               
               
                   
                 CON88 
                 PEP43 
                 INS2 
               
               
                   
                 CON89 
                 PEP41 
                 INS2 
               
               
                   
                 CON90 
                 PEP42 
                 INS2 
               
               
                   
                 CON91 
                 PEP75 
                 INS2 
               
               
                   
                 CON92 
                 PEP74 
                 INS25 
               
               
                   
                 CON93 
                 PEP1 
                 INS3 
               
               
                   
                 CON94 
                 PEP6 
                 INS3 
               
               
                   
                 CON95 
                 PEP74 
                 INS25 
               
               
                   
                 CON96 
                 PEP74 
                 INS26 
               
               
                   
                 CON97 
                 PEP74 
                 INS27 
               
               
                   
                 CON98 
                 PEP74 
                 INS28 
               
               
                   
                 CON99 
                 PEP74 
                 INS29 
               
               
                   
                 CON100 
                 PEP74 
                 INS30 
               
               
                   
                 CON101 
                 PEP74 
                 INS31 
               
               
                   
                 CON102 
                 PEP76 
                 INS2 
               
               
                   
                 CON103 
                 PEP77 
                 INS2 
               
               
                   
                 CON104 
                 PEP74 
                 INS19 
               
               
                   
                 CON105 
                 PEP36 
                 INS19 
               
               
                   
                 CON106 
                 PEP78 
                 INS0 
               
               
                   
                 CON107 
                 PEP101 
                 INS32 
               
               
                   
                 CON108 
                 PEP79 
                 INS32 
               
               
                   
                 CON109 
                 PEP80 
                 INS32 
               
               
                   
                 CON110 
                 PEP81 
                 INS32 
               
               
                   
                 CON111 
                 PEP82 
                 INS32 
               
               
                   
                 CON112 
                 PEP83 
                 INS32 
               
               
                   
                 CON113 
                 PEP84 
                 INS32 
               
               
                   
                 CON114 
                 PEP85 
                 INS32 
               
               
                   
                 CON115 
                 PEP86 
                 INS32 
               
               
                   
                 CON116 
                 PEP87 
                 INS32 
               
               
                   
                 CON117 
                 PEP88 
                 INS32 
               
               
                   
                 CON118 
                 PEP89 
                 INS32 
               
               
                   
                 CON119 
                 PEP90 
                 INS32 
               
               
                   
                 CON120 
                 PEP91 
                 INS32 
               
               
                   
                 CON121 
                 PEP92 
                 INS32 
               
               
                   
                 CON122 
                 PEP93 
                 INS32 
               
               
                   
                 CON123 
                 PEP94 
                 INS32 
               
               
                   
                 CON124 
                 PEP95 
                 INS32 
               
               
                   
                 CON125 
                 PEP96 
                 INS32 
               
               
                   
                 CON126 
                 PEP97 
                 INS32 
               
               
                   
                 CON127 
                 PEP98 
                 INS32 
               
               
                   
                 CON128 
                 PEP99 
                 INS32 
               
               
                   
                 CON129 
                 PEP100 
                 INS32 
               
               
                   
                 CON130 
                 PEP101 
                 INS32 
               
               
                   
                 CON131 
                 PEP102 
                 INS32 
               
               
                   
                 CON132 
                 PEP103 
                 INS32 
               
               
                   
                 CON133 
                 PEP104 
                 INS32 
               
               
                   
                 CON134 
                 PEP105 
                 INS32 
               
               
                   
                 CON135 
                 PEP106 
                 INS32 
               
               
                   
                 CON136 
                 PEP107 
                 INS32 
               
               
                   
                 CON137 
                 PEP108 
                 INS32 
               
               
                   
                 CON138 
                 PEP109 
                 INS32 
               
               
                   
                 CON139 
                 PEP110 
                 INS32 
               
               
                   
                 CON140 
                 PEP111 
                 INS32 
               
               
                   
                 CON141 
                 PEP112 
                 INS32 
               
               
                   
                 CON142 
                 PEP113 
                 INS32 
               
               
                   
                 CON143 
                 PEP114 
                 INS32 
               
               
                   
                 CON144 
                 PEP115 
                 INS32 
               
               
                   
                 CON145 
                 PEP116 
                 INS32 
               
               
                   
                 CON146 
                 PEP117 
                 INS32 
               
               
                   
                 CON147 
                 PEP118 
                 INS32 
               
               
                   
                 CON148 
                 PEP119 
                 INS32 
               
               
                   
                 CON149 
                 PEP120 
                 INS32 
               
               
                   
                 CON150 
                 PEP121 
                 INS32 
               
               
                   
                 CON151 
                 PEP122 
                 INS32 
               
               
                   
                 CON152 
                 PEP123 
                 INS32 
               
               
                   
                 CON153 
                 PEP124 
                 INS32 
               
               
                   
                 CON154 
                 PEP125 
                 INS32 
               
               
                   
                 CON155 
                 PEP126 
                 INS32 
               
               
                   
                 CON156 
                 PEP127 
                 INS32 
               
               
                   
                 CON157 
                 PEP128 
                 INS32 
               
               
                   
                 CON158 
                 PEP129 
                 INS32 
               
               
                   
                 CON159 
                 PEP130 
                 INS32 
               
               
                   
                 CON160 
                 PEP131 
                 INS32 
               
               
                   
                 CON161 
                 PEP132 
                 INS32 
               
               
                   
                   
               
            
           
         
       
     
     The conjugates are shown in  FIG. 2A ,  FIG. 2B , and  FIG. 2C  which show various exemplary insulin-incretin conjugates in which the Norleucine (Nle) amino acid of particular incretins is conjugated to the epsilon amino group of Lysine (Lys) at position B29 of the B-chain peptide;  FIG. 3 , which shows various exemplary insulin-incretin conjugates in which the Nle amino acid of particular incretins is conjugated to the amino group of the Glycine (Gly) at position A1 of the A-chain peptide;  FIG. 4A ,  FIG. 4B ,  FIG. 4C ,  FIG. 4D ,  FIG. 4E ,  FIG. 4F ,  FIG. 4G ,  FIG. 4H ,  FIG. 4I ,  FIG. 4J ,  FIG. 4K ,  FIG. 4L ,  FIG. 4M ,  FIG. 4N ,  FIG. 4O , and  FIG. 4P , which show exemplary insulin-incretin conjugates in which the Nle amino acid of particular incretins is conjugated to the amino group of the Phenylalanine (Phe) at position B1 of the B-chain peptide;  FIG. 5 , which shows an exemplary insulin-incretin conjugate in which the Nle amino acid of PEP74* is conjugated to the amino group of the Phe at position B1 of the B-chain peptide;  FIG. 6A ,  FIG. 6B ,  FIG. 6C , and  FIG. 6D  show exemplary insulin-incretin conjugates in which the epsilon amino group of Lys of the incretin is conjugated to the amino group of the Phe at position B1 of the B-chain peptide;  FIG. 9A ,  FIG. 9B ,  FIG. 9C ,  FIG. 9D ,  FIG. 9E ,  FIG. 9F ,  FIG. 9G ,  FIG. 9H ,  FIG. 9I ,  FIG. 9J ,  FIG. 9K , and  FIG. 9L , which show exemplary insulin-incretin conjugates in which the Norleucine (Nle) amino acid of the incretin is conjugated to the amino group of the Phe at position B1 of the B-chain peptide;  FIG. 10A ,  FIG. 10B ,  FIG. 10C ,  FIG. 10D ,  FIG. 10E ,  FIG. 10F , and  FIG. 10G , which show exemplary insulin-incretin conjugates in which the epsilon amino group of Lys of the incretin is conjugated to the amino group of the Phenylalanine (Phe) at position B1 of the B-chain peptide; and  FIG. 11 , which shows exemplary insulin-incretin conjugates CON106 and CON107. The “*” shown for various peptides indicates that the incretin has the amino acid sequence and structure of the indicated incretin but wherein the azide group of the linker has formed a 1,2-disubstituted 1,2,3-triazole with the alkyne group on the insulin. 
     Example 25 
     Activity of the incretin peptides or the conjugates at the Glucagon receptor (GCGR) and GLP-1 receptor (GLP1R) may be measured in a cAMP activity assay as follows. 
     Peptides are dissolved in 100% DMSO and serially diluted to generate 10 point titrations. The peptide solutions are then transferred into 384-well assay plates (150 nL/well). Assay ready frozen cells expressing human GLP1R or human GCGR are suspended in growth media consisting of DMEM medium (GIBCO), 10% FBS (GIBCO), 1×NEAA(GIBCO), 1×P/S (GIBCO), 10 μg/mL Blasticidin (GIBCO) and 200 μg/mL Hygromycin (GIBCO). Cells are then diluted in assay buffer consisting of PBS (GIBCO), 7.5% BSA (Perkin Elmer), 100 μM RO 20-1724 (Sigma), with or without 20% human serum (MP Biomedical). The cell suspensions (15 μL) are then added to the assay plates containing the peptide solutions (30,000 cells/well for human GCGR; 10,000 cells/well for human GLP1R). The cells are incubated for one hour at room temperature in the dark. 
     Production of cAMP may be determined using HitHunterr cAMPXS kits (DiscoverX) following the manufacturer&#39;s protocol. The plates are incubated for overnight at room temperature in the dark. Luminescence may be measured using an EnVision Multilabel plate reader (Perkin Elmer). Native GLP-1 and Glucagon (Bachem) may be used as control peptides. EC 50  values may be calculated using uses a 4 parameter logistic fit based on the Levenberg-Marquardt algorithm. The results for several of the peptides are shown in Table 5. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 5 
               
               
                   
               
               
                 Peptide 
                 Azide 
                 hGCGR_EC 50   
                 hGLP1R EC 50   
                 GCGR/GLP1R 
               
               
                 Name 
                 position 
                 (nM) 
                 (nM) 
                 ratio 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 PEP1 
                 21 
                 0.01 
                 0.03 
                 0.5 
               
               
                 PEP2 
                 24 
                 0.11 
                 0.03 
                 3.7 
               
               
                 PEP3 
                 24 
                 0.07 
                 0.02 
                 4.6 
               
               
                 PEP4 
                 24 
                 0.41 
                 0.48 
                 0.9 
               
               
                 PEP5 
                 30 
                 0.24 
                 1.04 
                 0.2 
               
               
                 PEP6 
                 30 
                 0.07 
                 0.17 
                 0.4 
               
               
                 PEP7 
                 24 
                 0.06 
                 0.38 
                 0.2 
               
               
                 PEP8 
                 30 
                 0.77 
                 0.31 
                 2.5 
               
               
                 PEP9 
                 24 
                 0.45 
                 0.15 
                 3.1 
               
               
                 PEP10 
                 24 
                 0.02 
                 0.03 
                 0.7 
               
               
                 PEP11 
                 24 
                 0.03 
                 0.06 
                 0.4 
               
               
                 PEP12 
                 24 
                 0.02 
                 0.07 
                 0.3 
               
               
                 PEP13 
                 24 
                 0.04 
                 0.10 
                 0.4 
               
               
                 PEP14 
                 24 
                 0.05 
                 0.07 
                 0.8 
               
               
                 PEP15 
                 24 
                 0.02 
                 0.03 
                 0.7 
               
               
                 PEP16 
                 21 
                 0.05 
                 0.06 
                 0.8 
               
               
                 PEP17 
                 21 
                 0.06 
                 0.05 
                 1.2 
               
               
                 PEP18 
                 31 
                 0.21 
                 0.03 
                 6.7 
               
               
                 PEP19 
                 31 
                 0.47 
                 0.34 
                 1.4 
               
               
                 PEP20 
                 31 
                 0.10 
                 0.05 
                 2.0 
               
               
                 PEP21 
                 31 
                 0.08 
                 0.07 
                 1.1 
               
               
                 PEP22 
                 24 
                 0.13 
                 0.07 
                 1.9 
               
               
                 PEP25 
                 24 
                 0.04 
                 0.05 
                 0.8 
               
               
                 PEP26 
                 20 
                 0.12 
                 0.12 
                 1.0 
               
               
                 PEP27 
                 21 
                 0.39 
                 0.06 
                 6.5 
               
               
                 PEP28 
                 31 
                 0.17 
                 0.16 
                 1.1 
               
               
                 PEP29 
                 24 
                 3.26 
                 3.28 
                 1.0 
               
               
                 PEP30 
                 24 
                 2.27 
                 0.50 
                 4.5 
               
               
                 PEP31 
                 24 
                 4.24 
                 1.38 
                 3.1 
               
               
                 PEP32 
                 24 
                 0.06 
                 0.04 
                 1.5 
               
               
                 PEP34 
                 24 
                 0.05 
                 0.05 
                 1.0 
               
               
                 PEP35 
                 24 
                 0.05 
                 0.05 
                 1.0 
               
               
                 PEP37 
                 24 
                 0.06 
                 0.04 
                 1.5 
               
               
                 PEP68 
                 24 
                 2.7 
                 0.07 
                 38.6 
               
               
                 PEP69 
                 24 
                 0.31 
                 0.16 
                 1.9 
               
               
                 PEP70 
                 20 
                 3.47 
                 0.04 
                 86.8 
               
               
                 PEP71 
                 20 
                 0.12 
                 0.06 
                 2.0 
               
               
                 PEP72 
                 32 
                 3.90 
                 0.04 
                 97.5 
               
               
                 PEP73 
                 30 
                 4.57 
                 7.58 
                 0.6 
               
               
                 PEP74 
                 24 
                 0.02 
                 0.05 
                 0.4 
               
               
                 PEP75 
                 24 
                 &gt;5 
                 0.07 
                 &gt;72 
               
               
                   
               
            
           
         
       
     
     Example 26 
     The conjugate binding or affinity to the insulin receptor may be performed using the following Insulin Receptor Binding Assays. 
     Two competition binding assays may be utilized to determine affinity for the human insulin receptor type B (IR(B)) against the endogenous ligand, insulin, labeled with 125[I]. 
     Method 1 IR binding assay is a whole cell binding method using CHO cells overexpressing human IR(B). The cells are grown in F12 media containing 10% FBS and antibiotics (G418, Penicillin/Strepavidin), plated at 40,000 cells/well in a 96-well tissue culture plate for at least eight hours. The cells are then serum starved by switching to DMEM media containing 1% BSA (insulin-free) overnight. The cells are washed twice with chilled DMEM media containing 1% BSA (insulin-free) followed by the addition of conjugate at appropriate concentration in 90 μL of the same media. The cells are incubated on ice for 60 minutes. The  125 [I]-insulin (10 μL) is added at 0.015 nM final concentration and incubated on ice for four hours. The cells are then gently washed three times with chilled media and lysed with 30 μL of Cell Signaling lysis buffer (cat #9803) with shaking for 10 minutes at room temperature. The lysate is added to scintillation liquid and counted to determine 125 [I]-insulin binding to IR and the titration effects of the conjugate on this interaction. 
     Method 2 IR binding assay is run in a scintillation proximity assay (SPA) in 384-well format using cell membranes prepared from CHO cells overexpressing human IR(B) grown in F12 media containing 10% FBS and antibiotics (G418, Penicillin/Strepavidin). Cell membranes are prepared in 50 mM Tris buffer, pH 7.8 containing 5 mM MgCl 2 . The assay buffer contains 50 mM Tris buffer, pH 7.5, 150 mM NaCl, 1 mM CaCl 2 , 5 mM MgCl 2 , 0.1% BSA and protease inhibitors (Complete-Mini-Roche). Cell membranes are added to WGA PVT PEI SPA beads (5 mg/mL final concentration) followed by addition of conjugate at appropriate concentrations. After 5-15 min incubation at room temperature,  125 [I]-insulin is added at 0.015 nM final concentration for a final total volume of 50 μL. The mixture is then incubated with shaking at room temperature for 1 to 12 hours followed by scintillation counting to determine  125 [I]-insulin binding to IR and the titration effects of conjugate on this interaction. 
     Example 27 
     Conjugate agonist activity at the insulin receptor may be performed using the following Insulin Receptor Phosphorylation Assays. 
     Insulin receptor activation can be assessed by measuring phosphorylation of the Akt protein, a key step in the insulin receptor signaling cascade. CHO cell lines overexpressing either human, minipig or dog IR are utilized in an HTRF sandwich ELISA assay kit (Cisbio “Phospho-AKT(Ser473) and Phospho-AKT(Thr308) Cellular Assay Kits”). Cells are grown in F12 media supplemented with 10% FBS, 400 ug/ml G418 and 10 mM HEPES. Prior to assay, the cells are incubated in serum free media for 2 to 4 hours. Alternatively, the cells may be frozen and aliquoted ahead of time in media containing 20% DMSO and used in the assay upon thawing, spin down and re-suspension. 
     Cells are plated at 10,000 cells per well in 20 ul of the serum free F12 media in 384-well plates. Humulin and glargine controls were run on each plate of test compounds. The titrated compounds are added to the cells (2 μL per well, final concentrations=1000 nM titrated down to 0.512 pM in 1:5 fold dilutions) and incubated at 37° C. for 30 minutes. The cells are lysed with 8 μL of the prepared lysis buffer provided in the CisBio kit and incubated at 25° C. for one hour. The diluted antibody reagents (anti-AKT-d2 and anti-pAKT-Eu3/cryptate) are prepared according to the kit instructions and then 10 μL is added to each well of cell lysate followed by incubation at 25° C. for 3.5 to 5 hours. The plate may be read by in an Envision plate reader (Excitation=320 nm; Emission=665 nm) to determine the IR pAkt agonist activity with regard to both potency and maximum response for each compound. Alternatively, the compounds may be tested in the same manner in the presence of 1.6 nM of Humulin to determine how each compound was able to compete against the full agonist activity of insulin. 
     Example 28 
     Table 6 shows the incretin and insulin agonist activity of the various insulin incretin conjugates disclosed herein. Table 7 shows the incretin agonist activity or insulin agonist activity of several control molecules. Control molecule PEP76 has the amino acid sequence HsQGTFTSDK(γEγEC 16 )SKYLDERAAQDFVQWLLDT-NH 2  (SEQ ID NO:110) and corresponds to the amino acid sequence of PEP74 except that PEP76 has the amino acid Gln (Q) at position 24 instead of Nle(εN 3 ) as in PEP74. 
     
       
         
           
               
               
               
               
             
               
                 TABLE 6 
               
             
            
               
                   
               
               
                   
                 Incretin Receptor Assay 
                   
                   
               
               
                   
                 (cAMP) EC 50   
                   
                   
               
               
                   
                 (nM) 
                 Insulin Receptor 
                 Insulin Receptor 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 Ratio 
                 Binding Assay EC 50   
                 pAK Assay EC 50   
               
               
                   
                 GCGR 
                 GLP1R 
                 GCGR/ 
                 (nM) 
                 (nM) 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Conjugate 
                 (Human) 
                 (Human) 
                 GLP1R 
                 Human 
                 Minipig 
                 Human 
                 Minipig 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 CON1 
                 20 
                 1.42 
                 14.1 
                 1445 
                 2500 
                 4.325 
                 3.276 
               
               
                 CON2 
                 20 
                 3.35 
                 6.0 
                 2.347 
                 4.339 
                 0.185 
                 0.352 
               
               
                 CON3 
                 20 
                 4.93 
                 4.1 
                 2500 
                 2500 
                 24.6 
                 27.98 
               
               
                 CON4 
                 2.82 
                 6.1 
                 0.5 
                 1.1 
                 6 
                 0.206 
                 0.35 
               
               
                 CON5 
                 5 
                 5 
                 1.0 
                 22.5 
                 41.9 
                 0.9 
                 0.74 
               
               
                 CON6 
                 1.55 
                 3.67 
                 0.4 
                 61.13 
                 191.7 
                 4.353 
                 3.276 
               
               
                 CON7 
                 20 
                 2.72 
                 7.4 
                 372.5 
                 2500 
                 9.6 
                 3.276 
               
               
                 CON8 
                 20 
                 5 
                 4.0 
                 2500 
                 2500 
                 21.1 
                 21.3 
               
               
                 CON9 
                 20 
                 5 
                 4.0 
                 3.964 
                 7.5 
                 0.312 
                 0.63 
               
               
                 CON10 
                 2.56 
                 2.39 
                 1.1 
                 142.7 
                 451 
                 13.17 
                 13.86 
               
               
                 CON11 
                 3.34 
                 5 
                 0.7 
                 3.21 
                 8.988 
                 0.292 
                 0.673 
               
               
                 CON12 
                 5 
                 5 
                 1.0 
                 233.6 
                 234.6 
                 9.97 
                 6.22 
               
               
                 CON13 
                 20 
                 5 
                 4.0 
                 15.11 
                 24.36 
                 0.26 
                 0.65 
               
               
                 CON14 
                 20 
                 20 
                 1.0 
                 1.89 
                 3.43 
                 0.02 
                 0.07 
               
               
                 CON15 
                 20 
                 20 
                 1.0 
                 25.59 
                 13.71 
                 0.53 
                 0.37 
               
               
                 CON16 
                 0.06 
                 0.17 
                 0.4 
                 19.53 
                 13.67 
                 0.37 
                 0.63 
               
               
                 CON17 
                 0.1 
                 0.06 
                 1.7 
                 149.9 
                 169.9 
                 33 
                 16.2 
               
               
                 CON19 
                 5 
                 20 
                 0.3 
                 0.77 
                 2.15 
                 0.05 
                 0.13 
               
               
                 CON20 
                 5 
                 5 
                 1.0 
                 2.76 
                 3.93 
                 0.05 
                 0.09 
               
               
                 CON21 
                 0.09 
                 0.08 
                 1.1 
                 12.68 
                 26.58 
                 0.49 
                 0.96 
               
               
                 CON22 
                 0.06 
                 0.04 
                 1.5 
                 12 
                 29.84 
                 0.11 
                 0.19 
               
               
                 CON23 
                 0.12 
                 0.13 
                 0.9 
                 10.28 
                 23.59 
                 0.08 
                 0.18 
               
               
                 CON24 
                 0.07 
                 0.09 
                 0.8 
                 7.61 
                 16.76 
                 0.4 
                 0.75 
               
               
                 CON25 
                 0.1 
                 0.1 
                 1.0 
                 20.26 
                 28.66 
                 0.08 
                 0.19 
               
               
                 CON26 
                 0.08 
                 0.18 
                 0.4 
                   
                   
                 0.3 
                 0.83 
               
               
                 CON27 
                 0.08 
                 0.11 
                 0.7 
                   
                   
                 0.07 
                 0.27 
               
               
                 CON28 
                 0.32 
                 0.23 
                 1.4 
                   
                   
                 0.25 
                 0.74 
               
               
                 CON29 
                 1.47 
                 0.06 
                 24.5 
                   
                   
                 0.61 
                 0.95 
               
               
                 CON30 
                 2.89 
                 0.07 
                 41.3 
                   
                   
                 5.29 
                 17.24 
               
               
                 CON31 
                 2.02 
                 4.42 
                 0.5 
                   
                   
                 0.62 
                 2.04 
               
               
                 CON32 
                 1.2 
                 6.05 
                 0.2 
                   
                   
                 0.41 
                 2.54 
               
               
                 CON33 
                 0.25 
                 0.42 
                 0.6 
                   
                   
                 0.21 
                 0.97 
               
               
                 CON34 
                 0.42 
                 1.32 
                 0.3 
                   
                   
                 0.72 
                 1.65 
               
               
                 CON35 
                 2.2 
                 1.88 
                 1.2 
                   
                   
                 0.33 
                 1.35 
               
               
                 CON36 
                 16.47 
                 3.08 
                 5.3 
                   
                   
                 0.12 
                 0.35 
               
               
                 CON37 
                 0.34 
                 0.08 
                 4.3 
                   
                   
                 0.14 
                 0.5 
               
               
                 CON38 
                 0.34 
                 3.32 
                 0.1 
                   
                   
                 0.63 
                 2.22 
               
               
                 CON39 
                 0.08 
                 0.34 
                 0.2 
                   
                   
                 2.02 
                 4.55 
               
               
                 CON40 
                 0.13 
                 0.38 
                 0.3 
                   
                   
                 6.82 
                 12.58 
               
               
                 CON41 
                 0.18 
                 0.13 
                 1.4 
                   
                   
                 0.58 
                 1.28 
               
               
                 CON42 
                 0.11 
                 0.08 
                 1.4 
                   
                   
                 0.15 
                 0.32 
               
               
                 CON43 
                 0.31 
                 0.11 
                 2.8 
                   
                   
                 0.72 
                 1.71 
               
               
                 CON44 
                 0.21 
                 0.1 
                 2.1 
                   
                   
                 0.79 
                 1.81 
               
               
                 CON45 
                 2.42 
                 0.44 
                 5.5 
                   
                   
                 0.69 
                 1.49 
               
               
                 CON46 
                 0.76 
                 0.08 
                 9.5 
                   
                   
                 0.18 
                 0.53 
               
               
                 CON47 
                 0.72 
                 0.07 
                 10.3 
                   
                   
                 0.49 
                 1.25 
               
               
                 CON48 
                 0.53 
                 0.05 
                 10.6 
                   
                   
                 0.33 
                 0.66 
               
               
                 CON49 
                 0.65 
                 0.11 
                 5.9 
                   
                   
                 0.47 
                 0.72 
               
               
                 CON50 
                 0.53 
                 2.57 
                 0.2 
                   
                   
                 0.08 
                 0.2 
               
               
                 CON51 
                 1.42 
                 2.83 
                 0.5 
                   
                   
                 0.11 
                 0.3 
               
               
                 CON52 
                 0.43 
                 2.08 
                 0.2 
                   
                   
                 0.15 
                 0.42 
               
               
                 CON53 
                 4.95 
                 1.74 
                 2.8 
                   
                   
                 0.94 
                 2.84 
               
               
                 CON55 
                 0.16 
                 0.13 
                 1.2 
                   
                   
                 0.59 
                 1.42 
               
               
                 CON56 
                 0.12 
                 0.05 
                 2.4 
                   
                   
                 0.33 
                 0.59 
               
               
                 CON57 
                 0.23 
                 0.09 
                 2.6 
                   
                   
                 0.29 
                 0.5 
               
               
                 CON58 
                 19.8 
                 19.8 
                 1.0 
                   
                   
                 1.51 
                 2.82 
               
               
                 CON59 
                 19.8 
                 19.8 
                 1.0 
                   
                   
                 3.18 
                 4.49 
               
               
                 CON60 
                 1.23 
                 1.08 
                 1.2 
                   
                   
                 43.03 
                 1000 
               
               
                 CON61 
                 0.25 
                 0.1 
                 2.5 
                   
                   
                 6.47 
                 6.32 
               
               
                 CON62 
                 0.06 
                 0.02 
                 3.0 
                   
                   
                 0.25 
                 0.63 
               
               
                 CON63 
                 0.16 
                 0.05 
                 3.2 
                   
                   
                 0.05 
                 0.28 
               
               
                 CON64 
                 0.26 
                 0.16 
                 1.6 
                   
                   
                 9.8 
                 7.46 
               
               
                 CON65 
                 0.23 
                 0.08 
                 2.9 
                   
                   
                 1000 
                 1000 
               
               
                 CON66 
                 0.24 
                 0.1 
                 2.4 
                   
                   
                 0.17 
                 0.3 
               
               
                 CON67 
                 4.95 
                 4.95 
                 1.0 
                   
                   
                 0.18 
                 0.29 
               
               
                 CON68 
                 0.15 
                 0.09 
                 1.7 
                   
                   
                 2.43 
                 4.5 
               
               
                 CON69 
                 0.22 
                 0.17 
                 1.3 
                   
                   
                 1000 
                 117.8 
               
               
                 CON70 
                 0.0585 
                 0.035 
                 1.7 
                   
                   
                 3.28 
                 3.28 
               
               
                 CON71 
                 19.8 
                 19.8 
                 1.0 
                   
                   
                 15.01 
                 22.47 
               
               
                 CON72 
                 19.8 
                 11.95 
                 1.7 
                   
                   
                 47.6 
                 15.75 
               
               
                 CON73 
                 19.8 
                 8.69 
                 2.3 
                   
                   
                 14.6 
                 10.02 
               
               
                 CON74 
                 0.75 
                 1.53 
                 0.5 
                   
                   
                 0.27 
                 0.28 
               
               
                 CON75 
                 0.39 
                 2.32 
                 0.2 
                   
                   
                 0.96 
                 1.53 
               
               
                 CON76 
                 0.15 
                 3.05 
                 0.0 
                   
                   
                 0.55 
                 1.05 
               
               
                 CON77 
                 0.46 
                 2.17 
                 0.2 
                   
                   
                 1.27 
                 1.01 
               
               
                 CON78 
                 0.18 
                 0.11 
                 1.6 
                   
                   
                 1.65 
                 1.27 
               
               
                 CON79 
                 0.13 
                 0.14 
                 0.9 
                   
                   
                 51.23 
                 27.5 
               
               
                 CON80 
                 0.24 
                 0.25 
                 1.0 
                   
                   
                 0.25 
                 0.69 
               
               
                 CON81 
                 0.22 
                 0.46 
                 0.5 
                   
                   
                 0.21 
                 0.58 
               
               
                 CON82 
                 19.8 
                 19.8 
                 1.0 
                   
                   
                 5.13 
                 9.73 
               
               
                 CON83 
                 0.57 
                 0.86 
                 0.7 
                   
                   
                 6.1 
                 4.5 
               
               
                 CON84 
                 0.16 
                 0.3 
                 0.5 
                   
                   
                 0.05 
                 0.09 
               
               
                 CON85 
                 0.08 
                 0.68 
                 0.1 
                   
                   
                 0.07 
                 0.19 
               
               
                 CON86 
                 2.55 
                 0.26 
                 9.8 
                   
                   
                 0.71 
                 1.55 
               
               
                 CON87 
                 0.51 
                 1.73 
                 0.3 
                   
                   
                 0.51 
                 1.19 
               
               
                 CON88 
                 0.37 
                 2.13 
                 0.2 
                   
                   
                 0.61 
                 1.21 
               
               
                 CON89 
                 0.55 
                 0.15 
                 3.7 
                   
                   
                 0.27 
                 0.61 
               
               
                 CON90 
                 0.31 
                 0.19 
                 1.6 
                   
                   
                 0.14 
                 0.4 
               
               
                 CON91 
                 19.8 
                 0.21 
                 94.3 
                   
                   
                 0.15 
                 0.38 
               
               
                 CON92 
                 0.18 
                 0.18 
                 1.01 
                   
                   
                 0.23 
                   
               
               
                 CON93 
                 0.22 
                 0.46 
                 0.48 
                   
                   
                 0.205 
                   
               
               
                 CON94 
                 0.56 
                 15.24 
                 0.036 
                   
                   
                 2.94 
                   
               
               
                 CON95 
                 0.94 
                 2.62 
                 0.36 
                   
                   
                 1.4 
                   
               
               
                 CON96 
                 1.21 
                 2.78 
                 0.43 
                   
                   
                 8.67 
                   
               
               
                 CON97 
                 2.51 
                 4.04 
                 0.62 
                   
                   
                 4.86 
                   
               
               
                 CON98 
                 0.63 
                 1.11 
                 0.56 
                   
                   
                 17.29 
                   
               
               
                 CON99 
                 0.08 
                 0.16 
                 0.48 
                   
                   
                 0.96 
                   
               
               
                 CON101 
                 19.8 
                 1.19 
                 8.0916.5 
                   
                   
                 0.48 
                   
               
               
                 CON102 
                 1.81 
                 0.22 
                 7.74 
                   
                   
                 0.569 
                   
               
               
                 CON103 
                 19.8 
                 0.31 
                 62.79 
                   
                   
                 0.073 
                   
               
               
                 CON104 
                 0.08 
                 0.56 
                 0.14 
                   
                   
                 2.57 
                   
               
               
                 CON105 
                 0.18 
                 1.62 
                 0.11 
                   
                   
                 13.92 
                   
               
               
                 CON106 
                 0.21 
                 1.17 
                 0.17 
                   
                   
                 2.16 
                   
               
               
                 CON107 
                 0.08 
                 6.02 
                 0.013 
                   
                   
                 0.47 
                   
               
               
                 CON108 
                 0.57 
                 8.62 
                 0.066 
                   
                   
                 6.102 
                   
               
               
                 CON109 
                 0.16 
                 0.30 
                 0.53 
                   
                   
                 0.046 
                   
               
               
                 CON110 
                 0.09 
                 0.68 
                 0.13 
                   
                   
                 0.070 
                   
               
               
                 CON111 
                 2.55 
                 0.26 
                 9.7 
                   
                   
                 0.70 
                   
               
               
                 CON112 
                 0.51 
                 1.73 
                 0.29 
                   
                   
                 0.51 
                   
               
               
                 CON113 
                 0.37 
                 2.126 
                 0.17 
                   
                   
                 0.61 
                   
               
               
                 CON114 
                 0.31 
                 0.19 
                 1.63 
                   
                   
                 0.13 
                   
               
               
                 CON115 
                 0.55 
                 0.15 
                 3.55 
                   
                   
                 0.27 
                   
               
               
                 CON116 
                 19.8 
                 0.20 
                 96.39 
                   
                   
                 0.15 
                   
               
               
                 CON117 
                 0.17 
                 0.28 
                 0.60 
                   
                   
                 0.16 
                   
               
               
                 CON118 
                 0.22 
                 0.37 
                 0.59 
                   
                   
                 0.36 
                   
               
               
                 CON119 
                 0.68 
                 0.26 
                 2.72 
                   
                   
                 0.45 
                   
               
               
                 CON120 
                 0.16 
                 0.079 
                 1.42 
                   
                   
                 0.37 
                   
               
               
                 CON121 
                 2.5 
                 0.28 
                 9.0 
                   
                   
                 1.48 
                   
               
               
                 CON122 
                 2.42 
                 0.46 
                 5.28 
                   
                   
                 0.92 
                   
               
               
                 CON123 
                 14.07 
                 1.1 
                 12.72 
                   
                   
                 0.44 
                   
               
               
                 CON124 
                 0.22 
                 6.18 
                 0.035 
                   
                   
                 0.3454 
                   
               
               
                 CON125 
                 1.71 
                 1.15 
                 1.48 
                   
                   
                 0.28 
                   
               
               
                 CON126 
                 0.56 
                 0.59 
                 0.93 
                   
                   
                 0.438 
                   
               
               
                 CON127 
                 1.27 
                 19.8 
                 0.064 
                   
                   
                 0.93 
                   
               
               
                 CON128 
                 0.15 
                 0.20 
                 0.72 
                   
                   
                 0.197 
                   
               
               
                 CON129 
                 1.54 
                 1.75 
                 0.878 
                   
                   
                 1.44 
                   
               
               
                 CON130 
                 0.21 
                 19.8 
                 0.01 
                   
                   
                 0.137 
                   
               
               
                 CON131 
                 0.22 
                 1.73 
                 0.128 
                   
                   
                 0.51 
                   
               
               
                 CON132 
                 1.19 
                 1.66 
                 0.72 
                   
                   
                 0.36 
                   
               
               
                 CON133 
                 0.64 
                 0.47 
                 1.37 
                   
                   
                 0.42 
                   
               
               
                 CON134 
                 0.25 
                 0.05 
                 4.54 
                   
                   
                 0.25 
                   
               
               
                 CON135 
                 0.48 
                 0.71 
                 0.66 
                   
                   
                 0.14 
                   
               
               
                 CON136 
                 0.7 
                 0.50 
                 1.39 
                   
                   
                 2.09 
                   
               
               
                 CON137 
                 1.04 
                 0.16 
                 6.62 
                   
                   
                 0.063 
                   
               
               
                 CON138 
                 0.95 
                 0.72 
                 1.32 
                   
                   
                 0.12 
                   
               
               
                 CON139 
                 0.2 
                 19.8 
                 0.01 
                   
                   
                 0.47 
                   
               
               
                 CON140 
                 0.34 
                 0.21 
                 1.61 
                   
                   
                 0.066 
                   
               
               
                 CON141 
                 0.96 
                 0.72 
                 4.57 
                   
                   
                 0.12 
                   
               
               
                 CON142 
                 0.68 
                 0.74 
                 0.91 
                   
                   
                 0.730 
                   
               
               
                 CON143 
                 0.33 
                 2.77 
                 0.11 
                   
                   
                 1.04 
                   
               
               
                 CON144 
                 0.04 
                 1.95 
                 0.02 
                   
                   
                 27.9 
                   
               
               
                 CON145 
                 0.43 
                 0.20 
                 2.15 
                   
                   
                 0.10 
                   
               
               
                 CON146 
                 0.42 
                 4.95 
                 0.08 
                   
                   
                 0.20 
                   
               
               
                 CON147 
                 0.3555 
                 0.59 
                 0.59 
                   
                   
                 0.63 
                   
               
               
                 CON148 
                 0.29 
                 0.05 
                 5.8 
                   
                   
                 0.42 
                   
               
               
                 CON149 
                 0.22 
                 0.07 
                 3.14 
                   
                   
                 0.6 
                   
               
               
                 CON150 
                 0.17 
                 0.09 
                 1.88 
                   
                   
                 1.36 
                   
               
               
                 CON151 
                 0.27 
                 0.16 
                 1.68 
                   
                   
                 0.6 
                   
               
               
                 CON152 
                 0.37 
                 2.89 
                 0.13 
                   
                   
                 0.15 
                   
               
               
                 CON153 
                 3.47 
                 2.68 
                 1.29 
                   
                   
                 0.18 
                   
               
               
                 CON154 
                 1.73 
                 0.46 
                 2.82 
                   
                   
                 0.3 
                   
               
               
                 CON155 
                 0.32 
                 1.58 
                 0.20 
                   
                   
                 0.14 
                   
               
               
                 CON156 
                 &gt;20 
                 &gt;20 
                   
                   
                   
                 17.39 
                   
               
               
                 CON157 
                 &gt;20 
                 &gt;20 
                   
                   
                   
                 9.45 
                   
               
               
                 CON158 
                 &gt;5 
                 &gt;5 
                   
                   
                   
                 9.45 
                   
               
               
                 CON159 
                 &gt;20 
                 &gt;5 
                   
                   
                   
                 8.52 
                   
               
               
                 CON160 
                 1.87 
                 0.05 
                 37.4 
                   
                   
                 1.12 
                   
               
               
                 CON161 
                 5.99 
                 0.12 
                 49.9 
                   
                   
                 1.22 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                   
                 Incretin Receptor Assay 
                 Insulin  
                 Insulin  
               
               
                   
                 (cAMP) EC50 
                 Receptor 
                 Receptor 
               
               
                   
                 (nM) 
                 Binding  
                 pAK  
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 GCGR 
                 GLP1R 
                 Ratio 
                 Assay EC50 
                 Assay EC50 
               
               
                   
                 (Hu- 
                 (Hu- 
                 GCGR/ 
                 (nM) 
                 (nM) 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 man) 
                 man) 
                 GLP1R 
                 Human 
                 Minipig 
                 Human 
                 Minipig 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 PEP76 
                 0.009 
                 0.007 
                 1.3 
                   
                   
                   
                   
               
               
                 PEP74 
                 0.02  
                 0.05  
                 0.4 
                   
                   
                   
                   
               
               
                 RHI 
                   
                   
                   
                 0.35 
                 0.59 
                 0.01 
                 0.02 
               
               
                 IG 
                   
                   
                   
                 0.57 
                 0.77 
                 0.01 
                 0.01 
               
               
                 IL 
                   
                   
                   
                   
                   
                 0.51 
                 0.5 
               
               
                 ID 
                   
                   
                   
                 9.03 
                 8.46 
                 0.48 
                 0.35 
               
               
                   
               
               
                 RHI = Recombinant human insulin 
               
               
                 IG = Insulin glargine 
               
               
                 IL = Insulin levemir 
               
               
                 ID = Insulin degludec 
               
            
           
         
       
     
       FIG. 7  shows that the length of the linking moiety at B1 has an effect on the ratio of glucagon (GCG) activity to GLP-1 activity. 
       FIG. 8  shows that the length of the linking moiety at B29 has an effect on the activity of the insulin at the insulin receptor ratio of GCG activity to GLP-1 activity. 
     Example 29 
     The following compounds were prepared following the procedure as disclosed in Example 6 in the provisional filing. 
     
       
         
         
             
             
         
       
     
     Example 30 
     The insulin analogs shown below were prepared using the procedure described for INS7 (Example 14) 
     1. N αB1 -propargyl-C 5 -Lys(γE-C 16 )-PEG 24 -RHI (INS25) 
     
       
         
         
             
             
         
       
     
     2. N αB1 -propargyl-C 5 -Lys(γE-C 12 )-PEG 12 -RHI (INS26) 
     
       
         
         
             
             
         
       
     
     3. N αB1 -propargyl-C 5 -Lys(γE-C 16 )-PEG 4 -RHI (INS27) 
     
       
         
         
             
             
         
       
     
     4. N αB1 -propargyl-C 5 -Lys(γE-C 18 —OH)-PEG 12 -RHI (INS28) 
     
       
         
         
             
             
         
       
     
     Example 31 
     Synthesis of N εB28 -propargyl-PEG 4  Lispro (INS29) 
     
       
         
         
             
             
         
       
     
     was as follows. 
     In a 20 mL vial, insulin Lispro (100 mg, 0.017 mmol) is dissolved in DMSO (1 mL) and aged at RT until homogeneous. 1,1,3,3-tetramethylguanidine (43 μl, 0.35 mmol) is added and followed by slow addition of alkyne-PEG 4 -NHS (2,5-dioxopyrrolidin-1-yl 4,7,10,13-tetraoxahexadec-15-ynoate, 6.8 mg, 0.019 mmol) solution in DMSO (0.5 mL) via syringe pump over 30 min. The reaction is stirred at RT for one hour. The mixture is added dropwise to IPAc (20 mL) to precipitate out the product. The solids are filtered and dried under nitrogen gas and vacuum for 30 minutes. The solids are dissolved in 15 mL mix solvent (80% water, 20% ACN, pH=3.0), adjusted pH to 3. The residue is purified by RP-HPLC column, using the separation condition (28-35%) 0.05% TFA in AcCN/H 2 O on Kromasil 100-10-C 8  from AkzoNobel, 100 A and 10 μM 50×250 mm column; FR=85 mL/minute, ramp 25 minutes, wavelength=210 nm. The fractions are collected and lyophilized to give N F B28-propargyl-PEG 4  Lispro. 
     Example 32 
     Synthesis of N εB1 -propargyl-PEG 4  Lispro (INS30) 
     
       
         
         
             
             
         
       
     
     followed the procedure disclosed for INS3 (Example 13). 
     Example 33 
     Synthesis of N εB29 -propargyl-PEG 4  Aspart (INS31) 
     
       
         
         
             
             
         
       
     
     followed the procedure disclosed for INS17 (Example 16). 
     Example 34 
     Synthesis of CON106 in which a C 8  hydrocarbon linker links the lysine at position 24 of PEP78 to the B1 amino group of RHI (INS0) was as follows. 
     
       
         
         
             
             
         
       
     
     Step 1: Synthesis of PEP78 with Dde protecting groups at the N-terminus amino group and the lysine at position 12 followed the general procedure set out in Example 1. 
     Step 2: To a solution of bis(2,5-dioxopyrrolidin-1-yl) octanedioate (35.0 mg, 0.095 mmol) and TEA (0.026 ml, 0.190 mmol) in DMSO (2 ml) was added Pep7290-Dde (20 mg, 4.75 μmol) in DMSO (1 ml) via syringe pump over 1 h. The reaction was quenched after 2 h with 2 ml mixed solvent (ACN/water 20:80, pH 3) and adjusted to pH 2.5. The residue is purified by RP-HPLC, using the separation condition (50-70%) 0.05% TFA in ACN/H 2 O on Kromasil 100-10-C 8  from AkzoNobel, 100 A and 10 μM 50×250 mm column; FR=85 mL/minute, ramp 25 minutes, wavelength=210 nm. The desired fractions are collected and lyophilized to give the desired product. m/z 1489.5 [M+3]/3. 
     Step 3: A1,B29-bis-Boc RHI (34.4 mg, 5.73 μmol) was dissolved in DMF 0.5 ml in a 10 ml vail, to the solution was added Et 3 N (4 μl, 0.029 mmol). The product from step 1 (12.8 mg, 2.87 μmol) in DMSO (400 μl and rinsed with 200 μl) was added over 30 min. 
     The reaction mixture was stirred at rt overnight and used in the next step without purification. m/z: 1727.4 [M+6]/6. 
     Step 4: To the DMSO solution of crude product in step 3 was added 6 μl of hydrazine in DMF(36% in DMF). After stirring for one hour, the reaction mixture is dropwise added to a stirred 10 mL of IPAc to precipitate the product. The white solids are filtered, washed with IPAc and dried under N 2  and vacuum for one hour. m/z: 1672.2 [M+6]/6. 
     Step 5: TFA (0.5 mL, 6.5 mmol) is added to the above crude material (28.8 mg, 2.87 μmol) and the reaction is stirred and sonicated until solids fully dissolved (about 30 minutes). The reaction mixture is dropwise added to IPAc (10 mL) and the precipitated solids are filtered and dried under N 2  and vacuum. The crude material is purified by RP-HPLC, using the separation condition (32-46%) 0.05% TFA in ACN/H 2 O on Kromasil 100-10-C 8  from AkzoNobel, 100 A and 10 μM 50×250 mm column; FR=85 mL/minute, ramp 25 minutes, wavelength=210 nm. The desired fractions are collected and lyophilized to give the hydrocarbon linked conjugate CON106. m/z: 1966.4 [M+5]/5. 
     Example 35 
     Synthesis of B1 Azido RHI (INS32) was as Follows 
     
       
         
         
             
             
         
       
     
     A1,B29-Bis Boc Insulin (100 mg, 0.017 mmol), sodium bicarbonate (5.6 mg, 0.067 mmol), copper(II) sulfate (0.53 mg, 3.33 μmol) was dissolved in water (0.8 mL) and MeOH (0.2 mL) was added 1H-imidazole-1-sulfonyl azide hydrochloride (5.6 mg, 0.027 mmol), maintained pH 8-9 by adding aq. sat. NaHCO 3  solution and stirred at room temperature overnight. Lyophilized the crude material and added TFA (2 mL, 0.017 mmol) for deprotection to give INS32 in which the N-terminal amino group has been converted to an azido group. 
     INS32 was conjugated to PEP101 following procedures disclosed herein to produce CON107 having the structure 
     
       
         
         
             
             
         
       
     
     While the present invention is described herein with reference to illustrated embodiments, it should be understood that the invention is not limited hereto. Those having ordinary skill in the art and access to the teachings herein will recognize additional modifications and embodiments within the scope thereof. Therefore, the present invention is limited only by the claims attached herein.