Knowledge Guided Geometric Editing for Unsupervised Drug Design

1 INTRODUCTION . Finding a drug molecule that can cure specific diseases is a major and significant challenge in the field of medicine . Traditional drug design methods usually use a screening approach ( Bajorath , 2002 ) , such as molecular docking ( Ferreira et al. , 2015 ; Meng et al. , 2011 ) , to filter molecules from a large database , which can not generate novel molecules and heavily relies on expert experience for further modification . In recent years , the surge of deep learning has benefited the field of automatic drug design . Intuitively , automatic drug design can be modeled as a conditional generation problem , namely generating a ligand ( i.e. , drug molecular ) from a disease-related target ( usually a protein pocket ) . Currently , majority of the deep learning-based drug design methods express molecules as a SMILES ( Weininger , 1988 ) string ( 1D ) or a graph ( 2D ) , which encourages the application of sequence-based ( Gómez-Bombarelli et al. , 2018 ; Kang & Cho , 2018 ; Segler et al. , 2018 ) and graphbased ( Seff et al. , 2019 ; Liu et al. , 2018 ; Ma et al. , 2018 ; Simonovsky & Komodakis , 2018 ; Samanta et al. , 2019 ; De Cao & Kipf , 2018 ) models in drug design . However , deep neural networks that model molecules in 1D/2D formats requires massive experimental activity data to learn relations between low dimensional features and their activities against specific protein targets . This is not only expensive but also limits these models ’ application scope into proteins with rich activity data . For example , Jin et al . ( 2018b ) formulate the drug design problem as translating one molecule to another with better properties supervised with labeled molecular pair data . Similarly , Xie et al . ( 2021 ) and Jin et al . ( 2020 ) use activity predictors trained from target-specific activity data to guide property optimization via Markov chain Monte Carlo and reinforcement learning respectively . In fact , we can leverage physicochemical knowledge to estimate the bio-activities without any labeled data given 3D structural information . In general , a drug molecule exhibits its activity by forming a 3D complex with a disease-related target . The tighter they bind , the more effective is the drug . The tightness can be measured by the minimum binding energy between these two chemical compounds and we have plenty of existing molecular docking software to estimate this energy . However , the searching and optimization for the minimum energy is a computational expensive process , which makes it non-trivial to efficiently extract the knowledge in docking and apply it to automatic drug design . In this paper , we propose Gometric Editing under KnOwledge guidance ( GEKO ) to achieve unsupervised drug design . We utilize the knowledge from molecular docking , drug-likeness and synthesizability as these knowledge is broadly applicable for all targets and offers great resources for guid- ing drug design . Inspired by the knowledge form and a classical medicinal concept called structure activity relation ( Guha , 2013 ) 1 , we aim to learn the effects of incremental molecular modifications in a 3D molecular space . In more details , we carefully design a geometric molecular editing module to traverse the space by adding or deleting fragments and modeling the dihedral angles in between . Then a hierarchical message passing neural network is tailored to capture both atom and fragment level information . We train the network with self-generated data and use simulated annealing to generate molecules under the guidance of knowledge . With a large amount of self-generated data , the model is able to learn the fundamental knowledge for drug design more efficiently and eliminate the dependence on experimental labeled data . We compare our method with baseline models on 12 targets including those without sufficient experimental data for developing data-driven models . GEKO outperforms other methods on both the 3D molecular space exploration power and capability of generating highly active molecules . The generated 3D molecules show good shape complimentarity with the target surface , which indicates strong interactions between the binding partners . 2 RELATED WORKS . 3D Drug Design Generating 3D molecules is a relatively new area in AI powered drug discovery due to its intrinsic difficulty . Within this field , 3D drug design is a non-trivial task which requires the model to generate new 3D molecules geometrically constrained by the target binding site and also achieve multiple optimized drug-like properties . Comparing to molecular generation in 1D/2D representation , the additional dimension significantly increases the explorable molecular space . Regardless of its significance , limited efforts have been made in this field . Masuda et al . ( 2020 ) use a variational autoencoder ( VAE ) to learn the 3D molecular distribution conditioned on a target structure using CrossDocked2020 ( Francoeur et al. , 2020 ) , a 3D ligand-target complex database . Due to the limited amount of experimental measured complex data , many 3D complexes in this dataset are generated using molecular docking . Despite of the large amount of training data , the model still suffers from poor binding affinities of the generated molecules compared to an experimental reference . However , our approach , guided by structural knowledge , can successfully generate molecules with high binding affinity while keeping many other drug-related properties . 3D Conformation Prediction Within the scope of 3D molecular generation , 3D conformation prediction is a better studied field comparing to 3D drug design . This task is defined as predicting the 3D structure of a molecule with a given 2D molecular graph , which defines the number of atoms and the connectivity between atoms . These methods can largely be divided into two groups by the way they formulate the 3D generation problem . The first class aims to directly generate the atomic positions or the inter-atomic distance matrix ( Mansimov et al. , 2019 ; Simm & Hernandez-Lobato , 2020 ; Xu et al. , 2021 ; Shi et al. , 2021 ) . Methods in this class demonstrate initial success on relative small molecules , such as those in GEOM-QM9 dataset ( Axelrod & Gomez-Bombarelli , 2020 ) . However , their performances drop significantly when the molecular size increases , more specifically on drug-like molecules . The other class predicts the flexible dihedral angles which is the major cause of conformational flexibility in 3D molecules ( Gogineni et al. , 2020 ; Ganea et al. , 2021 ) . Modeling dihedral angles shows a more stable performance when the number of rotatable bonds increases ( Ganea et al. , 2021 ) . Unlike predicting the distance metrics , which tends to overparameterize the degree of freedoms in the molecules , dihedral angles represent the molecular flexibility more straight forward . This kind of approach has been widely used in even larger molecular conformation prediction , namely the proteins . In this work , we integrate this idea into our 3D geometric editing procedure . 1D and 2D Drug Design Deep learning methods have been applied to facilitate drug design mainly on the 1D and 2D representations . Drug design is essentially an optimization task , and previously deep models have used various approaches to optimize the properties , such as Bayesian optimization in a latent space ( Gómez-Bombarelli et al. , 2018 ; Jin et al. , 2018a ; Winter et al. , 2019 ) , reinforcement learning ( De Cao & Kipf , 2018 ; Popova et al. , 2018 ; You et al. , 2018 ; Popova et al. , 2019 ; Shi et al. , 1The structure of the drug influences its biological activity . Grasping this relation is the fundamental approach for modifying molecular structure and achieving higher drug activities . 2020 ) , evolutionary and genetic algorithms ( Ahn et al. , 2020 ; Jensen , 2019 ; Devi et al. , 2015 ; Nigam et al. , 2020 ; A Nicolaou et al. , 2012 ) and etc . More recently , sampling based approach has been used in molecular generation ( Fu et al. , 2021 ; Xie et al. , 2021 ) . Among them , MARS ( Xie et al. , 2021 ) has demonstrated state-of-the-art performance in multi-objective optimization via adaptive Markov chain Monte Carlo sampling . Although this model learns from self-generated data , it still relies on a data-driven predictor for biological activity optimization , which limits it application scope . In addition , directly transferring low dimensional drug design methods to 3D generation is not trivial , as the 3D molecular space is much more complex due to the rotation of dihedral angles . 3 THE PROPOSED METHOD . In this section , we address the procedure of GEKO . We first introduce the physical and chemical knowledge used for drug design and the need of 3D geometric editing . Then we describe how to model the automatic drug design as a geometric editing process and its parameterization . Finally , we show how to guide the editing process with these knowledge . 3.1 INTEGRATING PHYSICOCHEMICAL KNOWLEDGE IN MOLECULAR GENERATION . We formulate drug design as a generative process with the objective of finding molecules possessing strong bio-activity with respect to the target protein , together with a sufficient level of drug-likeness and synthetic accessibility . The bio-activity largely depends on the tightness of formed target-ligand complex , which can be measured by the minimum binding energy between two chemical compounds . In particular , GEKO proposes to use Autodock Vina ( Trott & Olson , 2010 ; Eberhardt et al. , 2021 ) ( or Vina for short ) , one of the state-of-the-art molecular docking softwares , to estimate this energy . Drug-likeness is measured by QED ( Bickerton et al. , 2012 ) , which combines molecular weight , number of hydrogen bond donors , molecular surface area and many other drug-like properties . Synthetic accessibility is quantified by SAscore ( Ertl & Schuffenhauer , 2009 ) based on the fragment composition and molecular complexity2 . Combining three metrics , we then have the objective function for molecule x : J ( x ) = VINAmin ( x ) + α log QED ( x ) + β log SASCORE ( x ) . ( 1 ) Though QED and SAscore can be efficiently computed with the 2D structure of molecule , we need extra design to make Vina feasible to use . Specifically , Vina estimates the minimum binding energy by a stochastical global search in 3D conformational space together with local energy optimization ( the calculated energy as Vinadock ) , which is time-consuming and can not provide enough estimations in a reasonable amount of time . In fact , we can get rid of the global search of Vina , which makes it 100x faster , by directly generating in 3D molecular space . The model can learn to generate desired 3D poses so that local energy minimization ( the calculated energy as Vinamin ) is adequate for energy estimation . Details will be addressed in the following subsections . 3.2 TRAVERSING THE 3D MOLECULAR SPACE BY GEOMETRIC EDITING . A molecule ’ s 3D structure can be represented as a composition of rigid 3D fragments linked by bonds with flexible dihedral angles . These angles are formed between two intersecting planes , and in chemistry it is defined using four consecutive atoms and related to the rotation of one bond as shown in Figure 1 top left . They are the major cause of conformational flexibility in 3D molecular structures . Inspired by this , we propose to first construct a rigid fragment library , and then edit molecules by either selecting a fragment in the library to add and determining the dihedral angle between the added fragment and the original molecule , or selecting a rigid fragment in the molecule to delete . 2Note that we re-scale the SAscore to [ 0 , 1 ] . Rigid Fragment Library Single bond rotation is the major cause of dihedral angle changes , as single bond is less constrained and has lower rotational energy barrier comparing to double bonds and bonds in ring structures . Therefore , we construct a rigid fragment library by breaking single bonds in 2D molecules from the ChEMBL database ( Gaulton et al. , 2017 ) , which is a manually curated database of bioactive molecules with drug-like properties . As shown in Figure 1 top right , the broken bond for generating fragments are labeled as an editable site for molecular construction and a hydrogen atom is added to maintain the original valency3 . The same 2D fragment with different editable sites are merged as one member in the library and the editable sites are combined . The 3D conformation of the resulted fragments are generated using RDKit ( Landrum , 2021 ) . As rotational flexibility is constrained inside fragment , each 2D fragment only corresponds to one or a few valid 3D conformations and each conformation is considered as a separate member in the fragment library . Using rigid fragments as building blocks can enhance the validity of generated molecular structures and largely reduce the space of possible conformations by taking advantage of existing knowledge . Operations of Geometric Editing GEKO places an initial seed molecule within a target binding site , and builds 3D molecular structures by adding or deleting rigid fragments iteratively as shown in Figure 1 bottom panel . In order to achieve adding and deleting operations separately , the editable sites are categorized as addable sites , which correspond to the editable sites with hydrogen atoms attached , and deletable sites which correspond to the the ones with non-hydrogen atoms attached . In adding operations , the model firstly selects an addable bond in the original molecule . Then it chooses a 3D fragment from the fragment library and an addable bond in the fragment to attach to the original molecule . Lastly , it decides the dihedral angle between the two connected components . The hydrogen atoms in the selected addable bonds are removed resulting in two partial bonds , which are then connected and rotated to the predicted dihedral angle . In deleting operations , the model chooses an deletable bond to break . A hydrogen atom is added to the broken bond to maintain the correct valency . Parameterization with Hierarchical MPNNs To better model the fragment-based molecular structure , we propose to use hierarchical message passing neural networks ( HMPNNs ) to predict the probability distributions of editing operations mentioned above . HMPNN is a two-level message passing neural network ( Gilmer et al. , 2017 ) that captures the interactions of both atoms and fragments . It takes a molecule x as input , which is represented as a graph g = ( A , f node , f edge ) with A as the adjacency matrix , f node and f edge as feature vectors . We pass the graph and feature vectors through the first MPNN to obtain atom-level representations : hnodeu = MPNN1 ( g ) u ∈ Rd ( 2 ) 3If a fragment only contains one atom , it is fused with its connecting fragment . where hnodeu is the hidden representation of node u . Note that atoms separated by rotatable single bonds are considered as belonging to different fragments . We then regard each fragment as a single node , which induces a new fragment-level adjacency matrix A′ , and obtain the fragment embedding znode by aggregating features of atoms that belong to it using mean pooling . We preserve those edges between fragments with feature vectors zedge initialized by fragment embeddings . znodei = MEANPOOLu∈Vi ( h node u ) ∈ Rd ( 3 ) zedgej , k = A1 · CONCAT ( z node j , z node k ) + b1 ∈ Rd ( 4 ) where Vi is the set of atoms in fragment i . The new graph g′ = ( A′ , znode , zedge ) is then passed to another MPNN to obtain fragment-level representations . onodei = MPNN2 ( g ′ ) i ∈ Rd ( 5 ) oedgej , k = A2 · CONCAT ( o node j , o node k ) + b2 ∈ Rd ( 6 ) With HMPNN as a representation extractor , we can predict the editing operations mentioned before . Let xskel be the skeleton molecule to be edited . The edge to edit is determined as follows : hnode , onode , oedge = HMPNN1 ( xskel ) ( 7 ) scorej , k = MLP1 ( o edge j , k ) ∈ R ( 8 ) padd ( r|xskel ) = softmax ( { scorej , k } ( j , k ) ∈Ea ) ( 9 ) pdelete ( r|xskel ) = softmax ( { scorej , k } ( j , k ) ∈Ed ) ( 10 ) where Ea and Ed are disjoint sets of editable edges on xskel for addition and deletion respectively . During generation , we sample a directed edge r = ( uskel , vskel ) from 12padd + 1 2pdelete . For deletion , we just replace the deleted fragment on uskel side with a hydrogen . For addition , we predict the fragment xfrag to add also on uskel side : scorexfrag = MLP2 ( o edge r ) xfrag ∈ R ( 11 ) pfragment ( xfrag|xskel , r ) = softmax ( { scorexfrag } xfrag∈H ) ( 12 ) where H is the rigid library . Then we sample a fragment xfrag from pfragment . The attachable bond on the fragment is then determined jointly by xskel and xfrag : hfrag-node , ofrag-node , ofrag-edge = HMPNN2 ( xfrag ) ( 13 ) ōnode = MEANPOOL ( onode ) ( 14 ) scorefragj , k = MLP3 ( CONCAT ( ō node , ofrag-edgej , k ) ) ∈ R ( 15 ) pattach ( a|xskel , r , xfrag ) = softmax ( { scorej , k } ( j , k ) ∈Efraga ) ( 16 ) whereEfraga is the set of attachable bonds on fragment xfrag . Then we sample a bond a = ( ufrag , vfrag ) to attach . Finally , we gather the features of four atoms , vskel , wskel , vfrag , wfrag , around the new bond4and determine the dihedral angle : hangle = CONCAT ( hnodevskel , h node wskel , h frag-node vfrag , h frag-node wfrag ) ( 17 ) scoreangleα = MLP4 ( h angle ) α ∈ R ( 18 ) pangle ( α|xskel , r , xfrag , a ) = softmax ( { scoreangleα } α∈A ) ( 19 ) and sample an angle α from pangle . We then concatenate the skeleton molecule and fragment molecule together by this dihedral angle α .

Summary: The paper proposes a method that designs molecules by combining fragments along "editable" (single) bonds. The method uses two graph neural networks (on atoms and on fragments) to learn to pick editable bonds. The method also uses simulated annealing to guide the combination of fragments (and possibly their dihedral angles) to optimize a weighted score that the authors have found helps their training. The model is able to propose reasonable molecules in 3D conformations within a ligand pocket using a docking score for guidance. The authors perform an ablation study that shows that even without the deep neural network for selecting the editable bonds, their sampling methodology performs rather well.