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: This paper proposes a method to optimize the multiple properties of a molecule. They first define rigid fragment library as a building block, which is used to generate a new molecule through geometric editing. They represent a molecule using HMPNN and the whole model is trained using the weighted maximum likelihood estimation. The proposed model is compared with some baselines on several multi-objective optimization tasks and shows good performance.