Generative ai methods and systems for small molecule structure generation

Abstract

Disclosed herein is a method and system to generate 3D models of small molecules. The methods and systems are disclosed for an equivariant shape-based virtual screening operation that generates small molecule 3D structures that fit into and bind to a provided protein pocket. The model is configured to learn from existing 3D structures of small molecules in a data-driven manner using forward diffusion and backward diffusion processes to learn and represent the major characteristics of molecule 3D structures. Additional disclosure relates to the model that is further configured to learn from the 3D model of the protein pocket.

Description

GENERATIVE AI METHODS AND SYSTEMS FOR SMALL MOLECULE STRUCTURE GENERATION STATEMENT OF GOVERNMENT SUPPORT

[0001] This invention was made with government support under grant / contract no.2133650 awarded by the National Science Foundation. The government has certain rights in the invention. CROSS REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to, and the benefit of, U.S. Provisional Patent Application No.63 / 519,833, filed August 15, 2023, entitled, “Generative AI Methods and Systems for Small Molecule,” U.S. Provisional Patent Application No.63 / 520,439, filed August 18, 2023, entitled, “Generative AI Methods and Systems for Small Molecule Structure Generation,” and U.S. Provisional Patent Application No.63 / 651,734, filed May 24, 2024, entitled, “Generative AI Methods and Systems for Small Molecule Structure Generation”, each of which is incorporated by reference herein in its entirety. BACKGROUND

[0003] Generating novel molecular candidates is beneficial in drug discovery to find possible therapeutic solutions. Conventionally, the process is characterized by the use of knowledge and experience from medicinal chemists, which not only requires substantial resources but also spans expensive time frames.

[0004] Computational approaches to generate molecular candidates have been developed to accelerate the conventional paradigm, including molecular generative models that can operate on either molecule SMILES strings or molecular graphs.

[0005] Structured-based drug design, as one example of these molecular generative models, has been developed to generate molecules in the 3D space that fit the given protein pocket. SBDD relies on the availability of high-quality 3D structures of protein targets and assumes knowledge of binding sites, which could be lacking for many targets. Models for existing SBDD often oversimplify the interaction between ligands and proteins by ignoring the dynamicity of binding pockets.

[0006] Different from SBDD, ligand-based drug design (LBDD) focuses on the ligands known to interact with a protein target.

[0007] Shape-based virtual screening (SBVS) is a widely used technique in ligand-based drug design, grounded in the principle that molecules with similar characteristics are likely to exhibit similar biological effects. SBVS operates by searching molecules from a library that have 3D shapes similar to known binding molecules but with novel 2D chemical structures.

[0008] There is a benefit to improving generative AI models for small molecule generation. SUMMARY

[0009] Exemplary generative AI methods and systems are disclosed for an equivariant shape-based virtual screening operation that may generate small molecule 3D structures that may fit into and bind to a provided protein pocket. The generative AI model is configured to learn from existing 3D structures of small molecules in a data-driven manner using forward diffusion and backward diffusion processes to learn and represent the major characteristics of molecule 3D structures.

[0010] In some aspects, a method of generating a 3D model of a small molecule is disclosed. The method includes: generating a starting structure, wherein the starting structure is defined by atom positions and atom features; providing the starting structure to a trained conditional diffusion model; and generating, via the trained conditional diffusion model, the 3D model of a small molecule, wherein generating includes: removing variance from the atom position and atom feature data of the starting structure in a backwards diffusion process to generate the 3D model of the small molecule, wherein constraints, based on a latent embedding of a target ligand (Hs) (i.e. condition) that is equivariant to transformations, are applied during the backward diffusion process.

[0011] In some aspects, the latent embedding (Hs) of the target ligand is generated by: generating, using an autoencoder, the latent embedding of the target ligand from a point cloud derived from a molecular surface of the target ligand; and determining, by the autoencoder, a signed distance of a randomly sampled point from the point cloud of the target ligand, wherein the autoencoder includes an encoder having vector neurons and a decoder including multilayer perceptrons.

[0012] In some aspects, constraints are applied by: providing the latent embedding of the target ligand (Hs) and variance from the atom position and atom feature data to a geometric vector perceptron model (GVP, eq.28); determining, by a first module, shape-aware scalar embeddings and shape-aware vector embeddings of atoms using the latent embedding of the target ligand and the starting structure; determining, by a second module, bond-type weighting factors of each pair of atoms of the starting structure; determining, by the geometric vectorperceptron model, a scalar embedding and a vector embedding using the shape-aware scalar embeddings, the shape-aware vector embeddings, and the bond-type weighting factors; and estimating an atom type and position for each atom of the starting structure.

[0013] In other aspects, the constraints are applied by: determining, by a first multi-layer graph neural network including includes atom type attention layers, an atom type for each atom of the starting structure using the latent embedding of the target ligand; and determining, by a second multi-layer graph neural network including atom position attention layers, a position for each atom of the starting structure.

[0014] In yet other aspects, the constraints are additionally based on a second latent embedding of a pocket of interest (Hp) that is equivariant to transformations; wherein the second latent embedding of the pocket of interest (Hp) is generated using at least an autoencoder configured to generate the latent embedding of a set of residues and atoms of the pocket of interest by masking off randomly selected atoms; wherein the autoencoder includes an encoder including vector neurons; and wherein the latent embedding of the target ligand and the second latent embedding of the pocket of interest are modified (e.g., fine-tuned) relative to each other using a contrastive learning operation.

[0015] In still other aspects, the constraints are applied by: providing the latent embedding of the target ligand, the latent embedding of the pocket of interest and the starting structure to a molecule prediction model; determining, by a convolutional neural network (CNN), a geometric shift embedding and an atomic feature embedding using the latent embedding of the target ligand, the latent embedding of the pocket of interest and noisy data, wherein, at each layer of the CNN, geometric vector perceptrons are used; determining, by a first module, condition- aware geometric shift embeddings; determining, by a second module including, a condition- aware atomic feature embedding; repeating the determination of the geometric shift embedding and atomic feature embedding using the condition-aware geometric shift embedding and the condition-aware atomic feature embedding; and estimating an atom type and position for each atom of the starting structure.

[0016] In additional aspects, the constraints are applied by: determining a distance of an atom of the starting structure to one or more atoms of a pocket of interest; and based on a determination that the atom of the starting structure is within a pre-defined distance to the one or more atoms of the pocket of interest, moving the atom of the starting structure to a position away from an atom of the one or more atoms of the pocket of interest by a given distance (e.g. pocket guidance).

[0017] In still more aspects, the constraints are applied by: determining a distance of an atom of the starting structure to one or more atoms of the target ligand; and based on a determination that the atom of the starting structure is outside a pre-defined distance from the target ligand, moving the atom of the starting structure to a position closer to an atom of the one or more atoms of the target ligand a given distance, wherein the constrained starting structure forms a shape more similar to the target ligand (e.g. shape guidance).

[0018] In some aspects, the trained conditional diffusion model is trained by: receiving 3D models of known molecules; determining a shape latent embedding of each 3D model of known molecules, wherein a shape latent embedding is generated using at least an autoencoder configured to generate the latent embedding of the target ligand from a point cloud derived from a molecular surface of the target ligand; wherein the autoencoder includes an encoder having vector neurons; wherein the autoencoder includes a decoder including multilayer perceptrons, wherein the decoder determines a signed distance of a randomly sampled point from the point cloud of the target ligand; adding variance to atom position and atom feature data of the 3D models of known molecules in a forward diffusion process; removing variance from the atom position and atom feature data of the 3D models of known molecules in a backwards diffusion process, conditioned on the respective shape latent embeddings; comparing, using a loss function, a resulting atom position and atom feature data from the backwards diffusion process to the atom position and atom feature data of a respective 3D model of a known molecule; and adjusting weights of the backward diffusion process based on the comparison.

[0019] In some aspects, the small molecule includes a binding portion of an antibody- antigen, a binding portion of a protein, or a ligand.

[0020] In other aspects, a method to generate 3D models of small molecules is disclosed. The method includes: generating, via a trained conditional diffusion model, a 3D model of a small molecule conditioned on a shape latent embedding of a molecular shape of an input molecule to yield molecules with a similar shape to an input molecule, wherein the trained conditional diffusion model includes: a 3D shape autoencoder that embeds the molecular shape of the input molecule into a shape latent embedding, and wherein the shape latent embeddings are equivariant to transformations; and a backward diffusion process and employs the trained conditional diffusion model to generate atom features and atom positions to form the 3D model of a small molecule, guided by the shape latent embedding.

[0021] In some aspects, the 3D shape autoencoder is configured to learn latent embeddings of a molecular shape from a point cloud derived from a molecular surface of an input molecule, wherein an encoder of the 3D shape autoencoder includes vector neurons and is configured toproduce shape latent embeddings that are equivariant to transformations of the 3D model of a small molecule; and wherein the 3D shape autoencoder is trained to predict, via a decoder, if a randomly sampled point of the molecular shape is located within the point cloud or outside of the point cloud.

[0022] In some aspects, the backward diffusion process within the trained conditional diffusion model includes transformer-based layers to predict atom positions and atom types, wherein each layer includes an atom type attention layer and an atom position attention layer, wherein the atom type attention layer employs, at least, as inputs: atom type embeddings from previous layers, distances between atoms, neighboring atom type embeddings, and shape latent embeddings to generate an atom type output; and wherein the atom position attention layer employs, at least, as inputs, updated atom type embeddings, distance between atoms, relative position, neighboring atom type embeddings and shape latent embeddings to generate an atom position difference.

[0023] In some aspects, the backward diffusion process includes steps of: providing the shape latent embedding to a geometric vector perceptron model (GVP, eq.28); determining, by a first module, shape-aware scalar embeddings and shape-aware vector embeddings of atoms using the shape latent embedding; determining, by a second module, bond-type weighting factors of each pair of atoms of the 3D model of a small molecule; determining, by the geometric vector perceptron model, a scalar embedding and a vector embedding using the shape- aware scalar embeddings, the shape-aware vector embeddings, and the bond-type weighting factors; and estimating an atom type and an atom position of the 3D model of a small molecule.

[0024] In some aspects, the trained conditional diffusion model further includes: a pocket of interest autoencoder that embeds the molecular shape of a pocket of interest into a latent embedding of the pocket of interest (Hp), wherein the latent embedding of the pocket of interest (Hp) is generated in part using an autoencoder, wherein the pocket of interest autoencoder is configured to learn the latent embedding of a set of residues and atoms of the pocket of interest by masking off randomly selected atoms; wherein the autoencoder includes an encoder includes vector neurons, and wherein the encoder is configured to produce latent embeddings that are equivariant to transformations of the pocket of interest; and wherein the shape latent embedding and the latent embedding of the pocket of interest (Hp) are fine-tuned relative to each other using contrastive learning; and wherein the backward diffusion process is guided by the shape latent embedding and the latent embedding of the pocket of interest (Hp).

[0025] In some aspects, the backward diffusion process includes steps of: determining, by a convolutional neural network (CNN), a geometric shift embedding and an atomic featureembedding using the shape latent embedding, latent embedding of the pocket of interest (Hp), and wherein, at each layer of the CNN, geometric vector perceptrons are used; determining, by a first module, condition-aware geometric shift embeddings; determining, by a second module including, a condition-aware atomic feature embedding; repeating the determination of the geometric shift embedding and atomic feature embedding using the condition-aware geometric shift and condition-aware atomic feature embedding; and estimating an atom type and position for each atom of the 3D model of a small molecule.

[0026] In some aspects, the backward diffusion process further includes steps of: determining a distance of an atom of the 3D model of a small molecule to an atom of the pocket of interest; and wherein, based on a determination that the atom from the 3D model of a small molecule is too close to an atom of the pocket of interest, moving the atom from the input molecule away from the atom of the pocket of interest a given distance. (e.g. pocket guidance)

[0027] In some aspects, the backward diffusion process further includes steps of: determining a distance of an atom from the 3D model of a small molecule to an atom of the input molecule, wherein, based on a determination that the atom of the 3D model of a small molecule is too far from the input molecule, moving the atom of the 3D model of a small molecule closer to the atom of the input molecule a given distance; and wherein the atom positions of the 3D model of a small molecule form a shape more similar to the input molecule. (e.g. shape guidance)

[0028] In some aspects, a 3D model of a small molecule includes a binding portion of an antibody-antigen, a binding portion of a protein, or a ligand.

[0029] In some aspects, a method of training a diffusion model for prediction of 3D models of small molecules is disclosed. The method includes: receiving 3D models of known molecules; determining a shape latent embedding of each 3D model of known molecules; adding variance to atom position and atom feature data of the 3D models of known molecules in a forward diffusion process; removing variance from the atom position and atom feature data of the 3D models of known molecules in a backwards diffusion process, conditioned on the respective shape latent embeddings; comparing, using a loss function, a resulting atom position and atom feature data from the backwards diffusion process to the atom position and atom feature data of a respective 3D model of a known molecule; and adjusting weights of the backward diffusion process based on the comparison.

[0030] In some aspects, the conditional diffusion model includes a 3D shape autoencoder that embeds a molecular shape of a respective 3D model of a known molecule into a latent embedding, and wherein the shape latent embedding is equivariant to transformations; whereinthe 3D shape autoencoder is configured to learn latent embeddings of a molecular shape from a point cloud derived from a molecular surface of the respective 3D model of a known molecule; and wherein an encoder of the 3D shape autoencoder includes vector neurons and is configured to produce shape latent embeddings that are equivariant to transformations of 3D molecules; wherein the 3D shape autoencoder is trained to predict, via a decoder, if a randomly sampled point within the respective 3D model of a known molecule is located within the point cloud or outside of the point cloud.

[0031] In some aspects, the conditional diffusion model includes transformer-based layers to predict atom positions and atom types, wherein each layer includes an atom type attention layer and an atom position attention layer, wherein the atom type attention layer employs, at least, as inputs: atom type embeddings from previous layers, distances between atoms, neighboring atom type embeddings, and shape latent embeddings to generate an atom type output; and wherein the atom position attention layer employs, at least, as inputs, updated atom type embeddings, distance between atoms, relative position, neighboring atom type embeddings and shape latent embeddings to generate an atom position difference.

[0032] In some aspects, the backward diffusion process includes steps of: providing the shape latent embedding to a geometric vector perceptron model (GVP, eq.25); determining, by a first module, shape-aware scalar embeddings and shape-aware vector embeddings of atoms using the shape latent embedding; determining, by a second module, bond-type weighting factors of each pair of atoms; determining, by the geometric vector perceptron model, a scalar embedding and a vector embedding using the shape-aware scalar embeddings, the shape-aware vector embeddings, and the bond-type weighting factors; and estimating an atom type and an atom position.

[0033] In some aspects, the conditional diffusion model further includes: a 3D pocket of interest autoencoder that embeds a molecular shape of a pocket of interest into a latent embedding of the pocket of interest (Hp), wherein the latent embedding of the pocket of interest (Hp) is generated in part using an autoencoder, wherein the 3D pocket of interest autoencoder is configured to learn the latent embedding of residuals and atoms of the pocket of interest by masking off randomly selected atoms; wherein the autoencoder includes an encoder includes vector neurons, and wherein the encoder is configured to produce latent embeddings that are equivariant to transformations of the 3D pocket of interest; and wherein the shape latent embedding and the pocket of interest latent embedding are fine-tuned relative to each other using contrastive learning; and wherein the backward diffusion process is conditioned on the shape latent embedding and the pocket of interest latent embedding.

[0034] In some aspects, the conditional diffusion model further includes steps of: determining, by a convolutional neural network (CNN), a geometric shift embedding and an atomic feature embedding using the shape latent embedding, the pocket of interest latent embedding, and a set of noisy atomic data, wherein, at each layer of the CNN, geometric vector perceptrons are used; determining, by a first module, condition-aware geometric shift embeddings using; determining, by a second module including, a condition-aware atomic feature embedding; repeating the determination of the geometric shift embedding and atomic feature embedding using the condition-aware geometric shift and condition-aware atomic feature embedding; and estimating an atom type and position for each atom.

[0035] In some aspects, the techniques described herein relate to a system having a processor and memory having instructions to execute the methods are stored thereon.

[0036] In some aspects, the techniques described herein relate to a non-transitory computer readable medium having instructions to execute the methods are stored thereon. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figs.1A-1B show example operational flow charts of the exemplary generative AI method to generate three-dimensional molecules.

[0038] Figs.2A-2B show example schematic architecture generative AI method for three- dimensional molecules.

[0039] Fig.3A shows an exemplary DiffSMol method comprising shape embedding (SE), shape-conditioned molecule diffusion model (DIFF), pocket guidance (PG), shape-conditioned molecule prediction (SMP), and shape guidance (SG).

[0040] Fig.3B shows the shape embedding process in the exemplary DiffSMol method.

[0041] Fig.3C shows the shape-conditioned molecule diffusion model (DIFF) in the exemplary DiffSMol method.

[0042] Fig.3D shows the shape-conditioned molecule prediction (SMP) process in the exemplary DiffSMol method.

[0043] Fig.3E shows the pocket guidance (PG) process in the exemplary DiffSMol method.

[0044] Fig.3F shows the shape guidance (SG) process in the exemplary DiffSMol method.

[0045] Figs.4A – 4C show algorithms implementing the exemplary DiffSMol method.

[0046] Figs.5A – 5D show heatmaps of similarities calculated from molecules generated by the exemplary DiffSMol method and a SQUID method.

[0047] Figs.6A – 6D show generated three-dimensional (3D) molecules from virtual screening (VS) method, SQUID method, and DiffSMol method.

[0048] Figs.7A – 7C show surface representation of a generated molecule NL-001 for cyclin-dependent kinase 6 (CDK6) target.

[0049] Figs.8A – 8C show surface representation of a generated molecule NL-002 for cyclin-dependent kinase 6 (CDK6) target.

[0050] Figs.9A – 9C show surface representation of a generated molecule NL-003 for neprilysin (NEP) target.

[0051] Fig.10A shows comparison on absorption, distribution, metabolism, excretion, and toxicity (ADMET) profiles among generated molecules (e.g., NL-001, NL-002) and approved drugs targeting CDK6 (e.g., Abemaciclib, Palbociclib, Ribociclib).

[0052] Fig.10B shows comparison on absorption, distribution, metabolism, excretion, and toxicity (ADMET) profiles between generated molecule NL-003 and approved drugs targeting NEP (e.g., Donepezil, Galantamine, Rivastigmine).

[0053] Fig.11 shows an exemplary mDiffSMol method comprising an equivariant condition representation pre-training module and a condition diffusion-based molecule generation module.

[0054] Figs.12A – 12C show example generated molecules generated from mDiffSMol method and SQUID method.

[0055] Fig.13 shows an exemplary ShapeMol method comprising shape embedding (SE) and shape-conditioned molecule diffusion model (DIFF).

[0056] Figs.14A – 14D show example 3D molecules generated from virtual screening, SQUID, and ShapeMol methods.

[0057] Various objects, aspects, features, and advantages of the disclosure will become more apparent and better understood by referring to the detailed description taken in conjunction with the accompanying drawings, in which like reference characters identify corresponding elements throughout. In the drawings, like reference numbers generally indicate identical, functionally similar, and / or structurally similar elements. DETAILED DESCRIPTION

[0058] Referring generally to the figures, generative artificial intelligence methods for small molecule structure generation are shown, according to various implementations.

[0059] Exemplary generative AI methods and systems are disclosed for an equivariant shape-based virtual screening operation that generates small molecule 3D structures that fit into and bind to a provided protein pocket. The generative AI model is configured to learn from existing 3D structures of small molecules in a data-driven manner using forward diffusion andbackward diffusion processes to learn and represent the major characteristics of molecule 3D structures.

[0001] Referring now to Fig.1A, a method of training a conditional diffusion model 100 is shown. The method includes steps of: receive 3D model of known molecules 102; generate a shape latent embedding of each 3D model of known molecules 104 In some aspects, the shape latent embedding is generated using at least an autoencoder configured to generate the latent embedding of the target ligand from a point cloud derived from a molecular surface of the target ligand. The autoencoder comprises an encoder having vector neurons and a decoder comprising multilayer perceptrons. The decoder determines a signed distance of a randomly sampled point from the point cloud of the target ligand.

[0002] The method 100 further includes the steps of: add variance to atom position and atom feature data of the 3D models of known molecules in a forward diffusion process 106; remove variance from the atom position and atom feature data of the 3D models of known molecules in a backwards diffusion process, conditioned on the respective shape latent embeddings 108; generate a 3D model of a respective known molecules 110; compare, using a loss function, a resulting atom position and atom feature data from the backwards diffusion process to the atom position and atom feature data of a respective 3D model of a known molecule 112; and adjusting weights of the backward diffusion process based on the comparison 114.

[0003] Referring now to Fig.1B, a method 101 of generating a 3D model of a small molecule is shown. The method includes steps of: receive a 3D model of a target ligand and a pocket of interest 120; generate a latent embedding of the target ligand 122; generate a starting structure 124, wherein the starting structure is defined by atom positions and atom features; provide the starting structure to a trained conditional diffusion model 126. Using the trained conditional diffusion model, the 3D model of a small molecule is generated by the steps of:, remove variance from the atom position and atom feature data of the starting structure in a backwards diffusion, conditioned on the latent embedding 128; apply constraints to the starting structure 130; and generate the 3D model of a small molecule for the pocket of interest 132. In some aspects, constraints, based on a latent embedding of a target ligand (Hs) (i.e. condition) are equivariant to transformations.

[0060] Referring now to Fig.2A, the method 100 is carried out using the system 200 as shown. 3D models of known molecules 205 are provided to a shape embedding module 210 to generate respective shape latent embeddings 215 of respective 3D models of known molecules. The shape latent embeddings are used in the shape-conditioned molecule prediction module 230.Separately, a respective 3D model of a known molecule ( ^^^^0, ^^^^0) 260 is used in the diffusion module, forward diffusion 220, which adds variance to the respective 3D model of a known molecule to produce noisy data, (xT, vT) 265. The noisy data (xT, vT) 265 is used in a diffusion module with backward diffusion processes 225. The shape-conditioned molecule prediction module 230 is applied to the diffusion module 225 during the backward diffusion process. The output of the diffusion module and shape-conditioned molecule prediction module is a generated 3D model of a respective known molecule 270. The generated 3D model of arespective known molecu 270 is compared to the 3D model of the known molecule260 in a loss function.

[0061] Referring now to Fig.2B, the method 101 is carried out using the system 201 as shown. A target ligand and / or pocket if interest 206 is shared to a shape embedding (SE) module 210, which is configured to generate latent embeddings 215, for example the latent embedding of the target ligand (Hs) and / or the latent embedding of the pocket of interest (Hp). A shape-conditioned molecule prediction module 230 utilizes the latent embeddings (Hs / Hp) 215 and optionally constraints are applied in a pocket guidance module 240, which is informed by the 3D model of the pocket of interest, and / or a shape guidance module 250, which is informed by the 3D model of the target ligand. A generated starting structure (xT, vT) 265 is used in a trained diffusion module 225 with backward diffusion processes. The shape-conditioned molecule prediction module 230 is applied to the diffusion module 225 during the backward diffusion process. The output of the diffusion module and shape-conditioned molecule prediction module is a 3D model of a small molecu270.

[0062] Other exemplary systems are shown in Fig.3A, which is further described Example 1; Fig.11, which is further described in Example 2; and Fig.13, which is further described in Example 3.

[0063] In some aspects, the latent embedding of the target ligand (Hs) is generated at the SE module 210 using at least an autoencoder configured to generate the latent embedding of the target ligand from a point cloud derived from a molecular surface of the target ligand. In some aspects, the autoencoder includes an encoder having vector neurons. In some aspects, the autoencoder includes a decoder including multilayer perceptrons, wherein the decoder determines a signed distance of a randomly sampled point from the point cloud of the target ligand.

[0064] In some aspects, the constraints are additionally based on a second latent embedding of the pocket of interest (Hp) that is equivariant to transformations. In some aspects, the second latent embedding of the pocket of interest (Hp) is generated at the SE module 210 using at leastan autoencoder configured to generate the latent embedding of the residuals and atoms of the pocket of interest by masking off randomly selected atoms. In some aspects, the autoencoder includes an encoder including vector neurons.

[0065] In some aspects, the latent embedding of the target molecule and the latent embedding of the pocket of interest are fine-tuned relative to each other using contrastive learning at the SE module 210.

[0066] In some aspects, applying constraints 108 includes providing the latent embedding of the target ligand (Hs) and the noisy data (xi,vi) to a geometric vector perceptron model; determining, by a first module, shape-aware scalar embeddings and shape-aware vector embeddings of atoms using the latent embedding of the target ligand and the noisy data; determining, by a second module, bond-type weighting factors of each pair of atoms; determining, by the geometric vector perceptron model, a scalar embedding and a vector embedding using the shape-aware scalar embeddings, the shape-aware vector embeddings, and the bond-type weighting factors; and estimating an atom type and position for each atom.

[0067] In some aspects, applying constraints 108 include determining, by a first multi-layer graph neural network including includes atom type attention layers, an atom type for each atom using the noisy data and latent embedding; determining, by a second multi-layer graph neural network including atom position attention layers, position for each atom.

[0068] In some aspects, applying constraints 108 include providing the latent embedding of the target molecule, the latent embedding of the pocket of interest and noisy data to a molecule prediction model; determining, by a convolutional neural network (CNN), a geometric shift embedding and an atomic feature embedding using the latent embedding of the target molecule, the latent embedding of the pocket of interest and noisy data, wherein, at each layer of the CNN, geometric vector perceptrons are used; determining, by a first module, condition-aware geometric shift embeddings; determining, by a second module including, a condition-aware atomic feature embedding; repeating the determination of the geometric shift embedding and atomic feature embedding using the condition-aware geometric shift and condition-aware atomic feature embedding, and estimating an atom type and position for each atom.

[0069] In some aspects, applying constraints 108 include determining a distance of an atom from the noisy data to one or more atoms of the pocket of interest, and based on a determination that the atom from the noisy data is within a pre-defined distance to the one or more atoms of the pocket of interest, adjusting position the atom from the noisy data to a position away from an atom of the one or more atoms of the pocket of interest by a given distance (e.g. pocket guidance).

[0070] In some aspects, applying constraints 108 include determining a distance of an atom from the noisy data to one or more atoms of the target ligand; and wherein, based on a determination that the atom from the noisy data is outside a pre-defined distance from the target ligand, adjusting position of the atom from the noisy data to a position closer to an atom of the one or more atoms of the target ligand a given distance; wherein the noisy data form a shape more similar to the target molecule. (e.g. shape guidance).

[0071] The convolutional neural network (CNN) is a type of deep neural network that has been applied, for example, to image analysis applications. Unlike traditional neural networks, each layer in a CNN has a plurality of nodes arranged in three dimensions (width, height, depth). CNNs can include different types of layers, e.g., convolutional, pooling, and fully-connected (also referred to herein as “dense”) layers. A convolutional layer includes a set of filters and performs the bulk of the computations. A pooling layer is optionally inserted between convolutional layers to reduce the computational power and / or control overfitting (e.g., by downsampling). A fully-connected layer includes neurons, where each neuron is connected to all of the neurons in the previous layer. The layers are stacked similarly to traditional neural networks. Graph convolutional neural networks (GCNNs) are CNNs that have been adapted to work on structured datasets such as graphs.

[0072] In some aspects, the generated small molecule includes a binding portion of an antibody-antigen, a binding portion of a protein, or a ligand. In some aspects the small molecule can fit, or have a portion that can fit, in the pocket of interest.

[0073] In another exemplary aspect, a method to generate 3D models of small molecules is disclosed. The method includes generating, via a trained conditional diffusion model, 3D molecules conditioned on a shape latent embedding of a molecular shape of an input molecule to yield molecules with a similar shape to an input molecule, wherein the trained conditional diffusion model includes a 3D shape autoencoder that embeds the molecular shape of the input molecule into a latent embedding, and wherein the shape latent embeddings are equivariant to transformations.

[0074] In some aspects, the 3D shape autoencoder is configured to learn latent embeddings of a molecular shape from a point cloud derived from a molecular surface of an input molecule. In some aspects, an encoder of the 3D shape autoencoder includes vector neurons and is configured to produce shape latent embeddings that are equivariant to transformations of 3D molecules. In some aspects, the 3D shape autoencoder is trained to predict, via a decoder, if a randomly sampled point within the space is located within the point cloud or outside of the point cloud.

[0075] In some aspects, the conditional diffusion model includes a forward noising process and a backward denoising process and employs the denoising model to generate atom features and atom positions to form the 3D molecules, guided by the shape latent embedding.

[0076] In some aspects, the denoising model within the conditional diffusion model includes transformer-based layers to predict atom positions and atom types, wherein each layer includes an atom type attention layer and an atom position attention layer; wherein the atom type attention layer employs, at least, as inputs: atom type embeddings from previous layers, distances between atoms, neighboring atom type embeddings, and shape latent embeddings to generate an atom type output; and wherein the atom position attention layer employs, at least, as inputs, updated atom type embeddings, distance between atoms, relative position, neighboring atom type embeddings and shape latent embeddings to generate an atom position difference.

[0077] In some aspects, the backward denoising process includes steps of: providing the shape latent embedding to a geometric vector perceptron model; determining, by a first module, shape-aware scalar embeddings and shape-aware vector embeddings of atoms using the shape latent embedding; determining, by a second module, bond-type weighting factors of each pair of atoms; determining, by the geometric vector perceptron model, a scalar embedding and a vector embedding using the shape-aware scalar embeddings, the shape-aware vector embeddings, and the bond-type weighting factors; and estimating an atom type and an atom position.

[0078] In some aspects, the trained conditional diffusion model further includes a 3D pocket of interest autoencoder that embeds the molecular shape of the pocket of interest into a latent embedding of the pocket of interest (Hp). In some aspects, the techniques described herein relate to a method, wherein the latent embedding (Hp) of the pocket of interest is generated in part using an autoencoder, wherein the 3D pocket of interest autoencoder is configured to learn the latent embedding of residuals and atoms of the pocket of interest by masking off randomly selected atoms. In some aspects, the autoencoder includes an encoder includes vector neurons, and wherein the encoder is configured to produce latent embeddings that are equivariant to transformations of the 3D pocket of interest. In some aspects, the shape latent embedding and the pocket of interest latent embedding are fine-tuned relative to each other using contrastive learning.

[0079] In some aspects, the conditional diffusion model includes a forward noising process and a backward denoising process and employs the denoising model to generate atom features and atom positions to form the 3D molecules, guided by the shape latent embedding and the pocket of interest latent embedding. In some aspects, the backward denoising process includes steps of: determining, by a convolutional neural network (CEGCNN), a geometric shiftembedding and an atomic feature embedding using the shape latent embedding, the pocket of interest latent embedding, and a set of noisy atomic data, wherein, at each layer of the CNN, geometric vector perceptrons are used; determining, by a first module, condition-aware geometric shift embeddings using ; determining, by a second module including, a condition- aware atomic feature embedding; repeating the determination of the geometric shift embedding and atomic feature embedding using the condition-aware geometric shift and condition-aware atomic feature embedding, and estimating an atom type and position for each atom.

[0080] In some aspects, the backward denoising process further includes steps of: determining a distance of an atom from the noisy atomic data to an atom of the pocket of interest; and wherein, based on a determination that the atom from the noisy atomic data is too close to an atom of the pocket of interest, moving the atom from the noisy atomic data away from the atom of the pocket of interest a given distance. (e.g. pocket guidance)

[0081] In some aspects, the backward denoising process further includes steps of: determining a distance of an atom from the noisy atomic data to an atom of the input molecule; wherein, based on a determination that the atom from the noisy atomic data is too far from the input molecule, moving the atom from the noisy atomic data closer to the atom of the target ligand a given distance; wherein the atom positions of the noisy data form a shape more similar to the input molecule. (e.g. shape guidance). THEORY

[0082] The exemplary generative AI methods and systems employ a plurality of properties that includes a plurality of representations and notations.

[0083] Specifically, a molecule, M, represents a set of atoms M = {a1, a2,…, a|M||ai = (xi, vi)}, where |M| is the number of atoms in M; ai is the i-th atom in M; xi ∈ R3represents the position of aiin 3D space; and vi∈Kis the one-hot atom feature vector of aiindicating the atom type and its aromaticity. The Euclidean distance between each pair of atoms aiand ajas dij∈ R, and the type of the bond in between as a one-hot vector bij∈ R4, in which the four dimensions of bijrepresent the absence of a bond, a single bond, a double bond, and an aromatic bond, respectively. Bonds between atoms may be determined by the atom types and the atomic distances among atoms

[0027] .

[0084] 3D surface shapes of a molecule M are represented as a point cloud (P) constructed by sampling points over the molecular surface. To generate a point cloud, a molecule surface mesh may be generated using the algorithm from the Open Drug Discovery Toolkit

[0046] . Points on the mesh surface may be uniformly sampled with probability proportional to the face area.This may be completed by using, for example, the algorithm from PyTorch3D

[0047] . The point cloud may be then centralized by setting the center of its points to zero.

[0085] The set P = {z1, z2, · · · z|P||zj= (zj)} represents the point cloud, where |P| is the number of points in P; zjis the j-th point; and zj∈ R3represents the position of zjin 3D space. The latent embedding P is represented by Hswhere dp is the dimension of the latent embedding. The symbol o represents the distance of a point randomly sampled in 3D space to the molecule surface, referred to as a signed distance, with a positive (negative) sign indicating the point is inside (outside) the surface. For convenience, Table 1 summarizes example representations and notations used in the exemplary generative AI methods and systems. Table 1. Notations

[0086] Equivariance and Invariance properties: Equivariance refers to the property of a function f(x) that any translation and rotation transformation from the special Euclidean group (e.g., SE(3)

[0056] ) applied to a geometric object x ∈ R3is mirrored in the output of f(x), accordingly. This property ensures f(x) to learn a consistent representation of an object’s geometric information, regardless of its orientation or location in 3D space. Formally, given any translation transformation t ∈ R3and rotation transformation R ∈ R3×3(RTR = I, f(x) is equivariant with respect to these transformations if it satisfies Equation 1:

[0087] Invariance refers to the property of a function that its output f(x) remains constant under any translation and rotation transformations of the input x. This property enables f(x) toaccurately capture the inherent features (e.g., atom features for 3D molecules) that are invariant of its orientation or position in 3D space. Formally, f(x) is invariant under any translation t and rotation R if it satisfies Equation 2:

[0088] Point cloud construction module:

[0089] In exemplary embodiments, the method includes a point cloud construction module. In the point cloud construction module, molecular surface shapes are represented using point clouds (P). P serves as input to a shape embedding encoder (i.e., SE-enc), from which shape latent embeddings are derived. To generate P, a molecular surface mesh is initially generated using the algorithm from the Open Drug Discovery Toolkit [35’’]. Following this, points on the mesh surface are uniformly sampled with probability proportional to the face area, using the algorithm from PyTorch3D [33’’]. The point cloud P is then centralized by setting the center of its points to zero.

[0090] Query point sampling module:

[0091] In exemplary embodiments, the method includes a query point sampling module. In the query point sampling module, signed distances of query points zq to molecule surface shape P are used to optimize SE. In particular, how to sample these points zqin 3D space is disclosed. Prior to shape embedding, a bounding box around the molecular surface shape is determined using the maximum and minimum (x, y, z)-axis coordinates for points in our point cloud P, denoted as (xmin, ymin, zmin) and (xmax, ymax, zmax). The bounding box is slightly extended by defining its corners as (xmin − 1, ymin − 1, zmin − 1) and (xmax + 1, ymax + 1, zmax + 1). For sampling |Z| query points, an even distribution of points inside and outside the molecule surface shape is needed. When a bounding box is defined around the molecular surface shape, there may be a lot of empty spaces within the box that the molecule does not occupy due to its complex and irregular shape. This may lead to that fewer points within the molecule surface shape that may be sampled within the box. Therefore, the sampling may be started by randomly sampling 3,000 points within the bounding box to ensure that there are sufficient points within the surface, then using an algorithm from Trimesh [1] based on the molecule surface mesh to determine whether each point lies within the molecular surface. If there are nw points found within the surface, n = min(nw, k / 2) points from these points may be selected, and the remaining k − n points from those outside the surface may be randomly chosen. For each query point, its signed distance to the molecule surface is determined by its closest distance to points in P with a sign indicating whether it is inside the surface.

[0092] Equivariant shape embedding (SE):

[0093] In exemplary embodiments, the method includes a shape embedding module. A shape embedding (SE) module is pre-trained to generate surface shape embeddings Hs. Fig.3B shows a shape embedding module employing an encoder SE-enc to map P to the equivariant latent embedding Hsand a decoder SE-dec to optimize Hsby recovering the signed distances [19’’] of sampled query points in 3D space to the molecule surface based on Hs. Hsis used to guide the diffusion process later.

[0094] Shape encoder (SE-enc): As shown in Fig.3B, SE-enc generates equivariant shape embeddings Hsfrom the 3D surface shape P of molecules, such that Hsis equivariant to both translation and rotation of P. That is, any translation and rotation applied to P is reflected in Hsaccordingly. To ensure translation equivariance, SE-enc shifts the center of each P to zero to eliminate all translations. To ensure rotation equivariance, SE-enc leverages Vector Neurons (VNs) [5’’] and Dynamic Graph Convolutional Neural Networks (DGCNNs) [24’’] as shown in Equation 3: ^^^^^

[0095] In Equation 3, VN-DGCNN(·) is a VN-based DGCNN network to generate equivariant embedding ^^^^^^^^∈ ^^^^^^^^ ^^^^×3for each point z in P; ands ^^^^ ^^^^×3^^^^j H ∈ ^^^^ is the embedding of P generated via a mean-pooling over the embeddings of all the points. Note that VN-DGCNN(·) generates a matrix as the embedding of each point (i.e., ^^^^^^^^^^^^) to guarantee the equivariance.

[0096] Shape decoder (SE-dec): In Fig.3B, to optimize Hs, SE learns a decoder SE-dec to predict the signed distance of a query point zq sampled from 3D space using Multi-layer Perceptrons (MLPs) (i.e., query point sampling) as shown in Equation 4: ^

[0097] In Equation s the predicted signed distance of zq, with positive and negative values indicating zq is inside or outside the surface shape s, respectively; [·, ·] represents the concatenation operation; ^·, ·^ is the dot-product operatos the squared Euclidean norm of the position ois an invariant VN network

[0058] that converts the equivariant shape embeddininto an invariant shape embeddin Intuitively, SE-dec predicts the signed distance between the query point and 3D surface by jointly considering the interaction between the point and surface the distance of the query pointo the origin, and the molecule surface shape (VN-Inv(·)). All these three terms areinvariant to any rotation transformations, as they are calculated from the dot-product operation^·, ·^. This operation is invariant to any rotations as ^Rz, Rz^ = zTRTRz = zTz = ^z, z^. Note that VN-Inv(·) comprises invariant dot-product operations and specifically designed invariant activations to learn invariant embeddings

[0058] . The predicted signed distance ^^�^^^^^^is later used to calculate the loss for the optimization of Hs.

[0098] SE pre-training: SE is pre-trained by minimizing the squared-errors loss between the predicted and the ground-truth signed distances of query points as shown in Equation 5:)

[0099] In Equation 5, Z is the set of sampled query points and ^^^^^^^^is the ground-truth signed distance of query point zq. By pretraining SE, ShapeMol learns Hsthat will be used as the condition in the following 3D molecule generation.

[0100] In some embodiments, the shape embedding module includes a new customized self- supervised equivariant encoder-decoder module for ligands and for pockets, respectively, to learn their expressive embeddings. To ensure high-quality learning, the two modules are fine- tuned together via a new joint contrastive process, after their independent pre-training.

[0101] Ligand embedding module (LE): As shown in Fig.11, a ligand shape will be represented by a cloud of points sampled over its molecular surface, which is feasible due to the small size of ligands. A dynamic graph convolutional neural network [34’] with vector neurons (VNs) [35’] is developed as an LE encoder to learn a ligand embedding matrix Hlfrom the point cloud. The VNs guarantees equivariance of Hlonce the center of point clouds is shifted to zero to ensure translation equivariance. An LE decoder is designed to measure how Hlmay recover the point cloud surface and thus, LE minimizes the distance between the ground-truth and recovered surfaces to optimize Hl, a type of self-supervision. The LE module is innovative since there is no prior work in molecule generation that employs point clouds to acquire equivalent representations of molecule shapes.

[0102] Pocket embedding module (PE): As shown in Fig.11, the SE module employs a new transformer-based PE encoder to encode all atoms of pocket residuals into an equivariant pocket representation matrix Hp, after a portion of atoms is randomly masked off in the pockets. The atom features used in the PE encoder will include their physicochemical properties and positions in 3D. During decoding, Hpis used to recover the masked-off atoms. Thus, PE is pre-trained by minimizing the difference between the predicted and masked-off atoms (i.e., self-supervision). An integration of residual-level details (e.g., polarity, hydrophobicity) into PE, through hierarchical encoding over residuals and atoms, is also developed. Hlis equivariant, achieved through VNs. Meanwhile, Hpencodes very rich information in the binding pockets.

[0103] LE and PE joint contrastive fine-tuning process: LE and PE are first pre-trained separately, capitalizing on abundant molecule and pocket data with known or estimated shapes, respectively. To further enhance their training quality, a joint contrastive fine-tuning strategy is developed using ligand-pocket binding complex data. As shown in Fig.11, the joint fine-tuning process not only refines ligand and pocket representations towards their binding modes but also facilitates seamless knowledge transfer between LE and PE, because they encode complementary information. The fine-tuning process leverages contrastive learning and maximize the difference of binding feasibilities between ligand-pocket binding and non-binding pairs. An invariant way to measure the binding feasibilities using Hland Hpis developed to avoid the complexity of super-positioning pocket shapes over ligand shapes in predicting binding. The joint contrastive fine-tuning strategy enhances the SE module.

[0104] Diffusion-based molecule generation module (DIFF):

[0105] In exemplary embodiments, the method includes a diffusion-based molecule generation module (DIFF). Fig.3C shows DIFF employing forward diffusion process (DIFF- forward), and backward generating process (DIFF-backward) to generate a 3D molecule structure (i.e., atom coordinates and features) conditioned on a given 3D surface shape that is represented by the shape latent embedding Hs(shown in Eq.3). Following the denoising diffusion probabilistic models [10’’], DIFF includes a forward diffusion process based on a Markov chain, denoted as DIFF-forward, which gradually adds noises step by step to the atom positions and features {(xi, vi)} in the training molecules. The noisy atom positions and features at step t are represented as {(xi,t, vi,t)} (t = 1,…,T), and the molecules without any noise are represented as {(xi,0, vi,0)}. At the final step T, {(xi,T, vi,T)} are completely unstructured and resemble a simple distribution like a Normal distribution N(0, I) or a uniform categorical distribution C(1 / K), in which I and 1 denotes the identity matrix and identity vector, respectively.

[0106] During training, DIFF is learned to reverse the forward diffusion process via another Markov chain, referred to as the backward generative process and denoted as DIFF-backward, to remove the noises in the noisy molecules. During inference, DIFF first samples noisy atom positions and features at step T from simple distributions and then generates a 3D molecule structure by removing the noises in the noisy molecules step by step until t reaches 1.

[0107] Variance scheduling: The variance schedul f atom coordinates using a sigmoidchedule is defined in Equation 6:)

[0108] In Equation 6, wi(i=1,2, or 3) and s are hyperparameters; T is the maximum step. w1was set to 6, w2 was set to 1.e-7, and w3 was set to 0.01.

[0109] For atom types, a cosine β schedule

[0014] was used for ^^^^^^^^^^^^as shown in Equation 7: ^^^^)

[0110] Forward diffusion process (i.e., DIFF-forward):As shown in Fig.3C, at step t ∈ [1, T], a small Gaussian noise and a small categorical noise are added to the continuous atom positions and discrete atom features {(xi,t−1, vi,t−1)}, respectively [8’’]. When no ambiguity arises, subscript i in the notations is eliminated and {(xi,t−1, vi,t−1)} becomes (xt−1, vt−1) for brevity. The noise levels of the Gaussian and categorical noises are determined by two predefined variance schedules, whereand^^are selected to be sufficiently small to ensure the smoothness of DIFF-forward. Formally, for atom positions, the probability of xt sampled given xt−1, denoted as q(xt|xt−1), is defined as shown in Equation 8: ^)

[0111] In Equation 8, N(·) is a Gaussian distribution of xt with mean andcovariance ^^ For atom features, the probability of vtacross K classes given vt−1is defined as shown in Equation 9: ^)

[0112] In Equation 9, C is a categorical distribution of vtderived by noising vt−1with a uniform noise across K classes.

[0113] Since the above distributions form Markov chains, the probability of any xt or vt may be derived from x0or v0as shown in Equation 10 and Equation 11, respectively: ) ^(Eq. 11)

[0114] Note that and are monotonically decreasing from 1 to 0 over t = [1, T]. As t →1, and are close to 1, leading to that xt or vt approximates x0 or v0. Conversely, as t → T,� and are close to 0, leading to that q(xT|x0) resembles N(0, I) and q(vT|v0) resembles C(1 / K).

[0115] Using Bayes theorem, the ground-truth Normal posterior of atom positions p(xt−1|xt, x0) may be calculated in a closed form

[0060] as shown in Equation 12: )

[0116] Similarly, the ground-truth categorical posterior of atom features p(vt−1|vt, v0) may be calculated

[0061] as in Equation 13: )

[0117] In the Equation 13,denotes the likelihood of k-th class across K classes indenotes the element-wise product operation;is calculated using vt and 0 and normalized intoso as to represent probabilities.

[0118] Backward generative process (DIFF-backward): As shown in Fig.3C, DIFF learns to reverse DIFF-forward by denoising from (xt, vt) to (xt−1, vt−1) at t ∈ [1, T], conditioned on the shape latent embedding Hs. The probabilities of (xt−1, vt−1) denoised from (xt, vt) are estimated by the approximates of the ground-truth posteriors p(xt−1|xt, x0) in Equation 12 and p(vt−1|vt, v0) in Equation 13. Given that (x0, v0) is unknown in the generative process, a shape-conditioned molecule prediction (SMP) module, which is a graph neural network (GNN) with multiple layers and is denoted as is employed to predict the atom position and feature (x0, v0) at time step t asshown in Equation 14:)

[0119] In Equation 14^and� are the predictions of x0and v0based on the informationat t (i.e., xt, vtand Hs).

[0120] With ^^�^^0, ^^^^, the probability of xt−1 denoised from xt, denoted as p(xt−1 | xt), may be estimated by the approximated posterior pΘ(xt−1 | xt, x�0,t)

[0060] as shown in Equation 15: ^)

[0121] In the Equation 15, Θ is the learnable parameter is an estimate of µ(xt,x ) by replacing x with its estimate in Equation 12. Similarly, with ^^�^^ , the probability ofvt−1 denoised from vt, denoted as p(vt−1 | vt), may be estimated by the approximated posterior as shown in Equation 16:)

[0122] In Equation 16, is an estimate of c(vt, v0) by replacing v0with its estimate^^�^^0, ^^^^in Equation 13.

[0123] DIFF Model Training: In some embodiments, the diffusion-based molecule generation module (DIFF) minimizes the atom position loss and the atom feature loss.

[0124] DIFF measures the squared errors (i.e., atom position loss) between the predicted positionsfrom the prediction module SMP as shown in Equation 14 and the ground-truth positions (e.g., x0) of atoms in molecules. Given a particular step t, the atom position loss is calculated as shown in Equation 17: ^^(Eq.17)

[0125] In the Equation 17,is a weight at step t and is calculated by clipping the signal-to- noise ratiowith a threshold δ > 0. Note that because� decreases monotonically as t increases from 1 to T as shown Equation 10,decreases monotonically over t as well until it is clipped. Thus imposes lower weights on the loss when the noise level in xt is higher (i.e., t close to T). This encourages the model training to focus more on accurately recovering molecule structures when there are sufficient signals in the data, rather than being potentially confused by major noises in the data.

[0126] DIFF also minimizes the Kullback-Leiber (KL) divergence (i.e., atom feature loss)

[0062] between the ground-truth posterior p(vt−1|vt, v0) in Equation 13 and its approximate in Equation 16 for discrete atom features to optimize DIFF

[0061] . Particularly, theKL divergence at t for a given molecule M is calculated as shown in Equation 18: ^(Eq.18)

[0127] In Equation 18, ^^ is a categorical distribution of vt-1in Equation 13; is an estimate of ^^^ in Equation 16.

[0128] The overall loss function, i.e., the sum of all the three loses, is shown in Equation 19:

[0129] In some embodiments, in addition to atom position loss and atom feature loss, DIFF also minimizes the classification errors (i.e., bond type loss) between the predicted bond types (eji) and the ground-truth types bijof bonds in molecules. At step t, for each l-th layer of SMP, DIFF predicts the bond types (eij,t,l) to understand the relations among atoms. Given a particular step t, the error on bond type prediction, i.e., bond type loss, at the l-th layer is calculated as shown in Equation 20:

[0130] In the Equation 20, N(xi,t) denotes the k-nearest neighbors of atom aiin position xi,t; H(·) denotes the cross-entropy loss. The bond type loss across different layers is then aggregated as shown in Equation 21:

[0131] In the Equation 21,is the weight at step t used in Equation 17; L is the number of layers in SMP. Same with the Equation 17, thein Equation 21 is used to encourage the model training to focus more on accurately predicting bond types when the data provides sufficient signals, rather than being confused by major noises in the data. Note that in Equation 21, different weights are used on the last layer (i.e., l=L) and all the other layers

[0063] . It is contemplated that this design benefits the generation performance.

[0132] In some embodiments, when DIFF computes bond type loss, the overall loss function, i.e., the sum of all the three loses, is defined as in Equation 22:

[0133] In Equation 22, M is the set of all the molecules in training; T is the set of timesteps;and are two hyper-parameters to balanceand . During training,step t is uniformly sampled from T = {1, 2,…, 1000}.

[0134] Shape-conditioned molecule prediction module (SMP):

[0135] Shape prediction using INV-GNN and EQ-GNN: In some embodiments, the backward generative process (DIFF-backward) further includes the prediction modulein Equation 14 to predict the atom positions and features given thenoisy data (xt, vt) conditioned on Hs. For brevity, the subscript t in the notations is omitted whenno ambiguity arises leverages two multi-layer graph neural networks: (1) an equivariantgraph neural network, denoted as EQ-GNN, that equivariantly predicts atom positions that change under transformations, and (2) an invariant graph neural network, denoted as INV-GNN, that invariantly predicts atom features that remain unchanged under transformations. Following the previous work [12”], [27”], the translation equivariance of atom position prediction is achieved by shifting a fixed point (e.g., the center of point clouds P) to zero, and therefore only rotation equivariance needs to be considered.

[0136] In EQ-GNN, the atom position of a at the ( / + 1 )-th layer is calculated in anequivariant way as shown in Equation 23 :

[0137] In Equation 23, is the set of A-nearest neighbors of a based on atomicdistances;aggregates the neighborhood information ofdenotes the multi-head attention layer in EQ-GNN with m heads; d\j is the distance between z-th and / -th atom positions x\ and xj at the Z-th layer; M convertsinto a 3D vector viameaning pooling to adjust the atom position; VN-Lin{ ) G R3denotes the equivariant VN-based linear layer [5”]; adjusts the atom positions to fit the shape condition represented byHs, by considering the current atom positionsand the neighborhood informationThe learned atom position xf at the last layer L of EQ-GNN is used as the prediction of xi 0, which is shown in Equation 24:

[0138] Proof of Equivariance in atom coordinate prediction: A function / (x) is equivariant with respect to rotation, if given any rotation matrix R G R3'7'3, it satisfies Equation 25:

[0139] Equation 23 used in the shape-conditioned molecule prediction module is proved to predict atom coordinates in an equivariant way. As shown in Equation 23, the embedding Awhich aggregates the neighborhood information of a, is updated by atom coordinates from previous layer and embeddings from multi-head attention layer MHAX( ). MHAX( ) and remain the same with rotationis proved to be updated in an equivariant way as shown in Equation 26:^(Eq.26)

[0140] Given that mean pooling is a linear operation that respects rotation equivariance, ^^^^ ^^^^ ^^^^ ^^^^�∆ ^^^^^^^^^^^^+1� is equivariant to rotations. The vector-neuron-based linear layer VN-Lin(·) with leaky-ReLu activation function also produces rotational equivariant embeddings [5’’]. Therefore, atom coordinates ^^^^^^^^^^^^+1are proved to be updated in an equivariant way as shown in Equation 27:(Eq.27)

[0141] In INV-GNN, inspired by the previous work [27’’] and VN-Layer [5’’], the atom feature embedding ℎ^^^^^^^^+1∈ ^^^^^^^^ℎof the i-th atom aiat the (l+1)-th layer of INV-GNN is updated in an invariant way as shown in Equation 28: ^^(Eq.28)

[0142] In Equation 28, MHAh(·) ∈ ^^^^^^^^ℎdenotes the multi-head attention layer in INV-GNN. The learned atom feature embedding h at the last layer L encodes the neighborhood information of ai and the conditioned molecular shape, and is used to predict the atom features as shown in Equation 29:)

[0143] Proof of invariance in atom feature prediction: Equation 25 used in the shape- conditioned molecule prediction module is proved to update atom features in an invariant way. A function f(x) is invariant with respect to rotation, when it satisfies Equation 25.

[0144] As shown in Equation 28, atom feature embeddings ℎ^^^^^^^^+1is updated according to atomic distances ^^^^^^^^^^^^^^^^, embeddings hifrom previous layer and invariant shape embeddings VN- Inv(Hs) from the vector-neuron based invariant layer adapted

[0145] Atomic distances are invariant to transformations. Atom feature embeddings are initialized with atom feature vectors, which are also invariant to transformations. The VN-Inv(.)layer maps the equivariant shape embedding Hs ∈ R ^^^^ ^^^^×3into the invariant shape embedding hs ∈R ^^^^ ^^^^ as shown in Equation 30:

[0146] In Equation 30, ^^^^^^^^^^^^is the c-th channel of Hs; ℎ^^^^^^^^denotes the c-th channel of hs; ^·^ is the inner-product operation which the results are not changed by any rotation vector. Given that all the variables in the right-hand side of Equation 28 are invariant to rotations, the atom feature embeddings are proved to be updated in an invariant way. Therefore, the invariant atom feature embeddings lead to invariant atom feature predictions in Equation 29.

[0147] In the exemplary methods and systems, both Equivariant Condition Shape Representation Pre-training (SE) and Diffusion-based Molecule Generation (DIFF) are developed to guarantee equivariance in capturing the geometric features of objects regardless of any translation or rotation transformations.

[0148] Shape prediction using GVP: In some embodiments, the shape-conditioned molecule prediction module (SMP) is a multi-layer graph neural network (GNN) comprising L layers and employing a geometric vector perceptron as shown in Fig.3D. In the l-th layer, SMP uses the geometric vector perceptron (GVP) to learn a scalar embedding and a vectorembedding rfor atom ai in an alternative manner that guarantees the invariance of ai,l and the equivariance of r

[0064] . Intuitively, ai,l captures inherent properties (e.g., atom types) of atom ai, which are invariant of the molecule’s orientation or position in 3D space. Different from ai,l, ri,lcaptures geometric information (e.g., atom positions) of atom ai, which will change under different transformations.

[0149] Some prediction modules employ equivariant graph neural networks (EGNN)

[0065] for the prediction, which may experience limited capacity in capturing rich geometric information within molecules as it can only represent geometric features in a 3-dimensional latent space. In contrast, GVP exhibits stronger expressiveness, capable of learning latent embeddings in spaces of any dimensions

[0066] . Equipped with GVP, SMP enables the learning of effective representations for geometric information. To ensure translation equivariance, SMP shifts a fixed point (i.e., the center of shape condition P) to zero to eliminate all translations. Therefore, only rotation equivariance may be considered.

[0150] SMP also leverages shape-aware scalar embeddings�, ^and vector embeddingsto generate molecules tailored to the shape condition. SMP learnsfromusing the shaperepresentation Hsin an invariant way (Equation 33). Similarly, SMP learns ^^̂^^^^^^, ^^^^from ^^^^^^^^, ^^^^and Hsin an equivariant manner (Equation 35). In addition, SMP utilizes the bond type embeddings to enhance the understanding of relations among atoms for better prediction (Equation 36).

[0151] Particularly, SMP module estimates the type and position of the i-th atom aias shown in Equation 31:)

[0152] In Equation 27, is the predicted probability distribution across all the types ofatom features; ^^�^^0, ^^^^is the predicted position of ai; xi is the noisy position of ai; ai,L and ri,L are the invariant scalar embedding and equivariant vector embedding for atom ai, respectively. In each l- th layer, ai,land ri,lof atom aiare updated by propagating its neighborhood’s inherent features and geometric features as shown in Equation 32:

[0153] In Equation 28, GVP(·) is a function that learns ai,land ri,ljointly fromand yhi,land yi,lmay be calculated as shown in Equation 33: �(Eq.33)

[0154] In Equation 33, [·, ·] is the concatenation operation; N(i) denotes the k-nearest neighbor atoms of atom aiover the 3D space; t denotes the time step; viis the noisy feature vector of ai;andare messages to propagate information from aj to ai as will be described in Equation 36.

[0155] In Equation 33, eji,lis the attention weight used to aggregate information from neighboring atoms. Equation 34 calculates the weight eji,l to estimate how much the neighboring atom aj should contribute to the learning of hi,l and yi,l:

[0156] SMP generates the shape-aware atom scalar ^^�^^^^^^, ^^^^−1and vector embedding ^^̂^^^^^^, ^^^^1in Equation 34 using shape-aware atom representation learning (SARL):, which is shown in Equation 35: ^)

[0157] In Equation 31, function SARL(.) calculates(i.e., shape-aware atom scalar) using Equation 33 and calculates ^(i.e., vector embedding) using Equation 31. In Equation 29, the messages mji,land nji,lare calculated from the scalar embeddings (e.g., ^^�^^^^^^, ^^^^) and vector embeddings (e.g., ^^̂^^^^^^, ^^^^) of atoms as shown in Equation 36: )

[0158] In Equation 32, GVP(·) is a function that learns mji,l and nji,l jointly fromand ^ is the concatenation operation; eji,l−1is the embedding of the bond type between aiand ajcalculated in Equation 36; and djiis the distance between xiand xj.

[0159] Shape-aware atom representation learning (SARL): To generate molecules that tailored to the shape condition represented by Hs, SMP adapts the scalar embedding ai,l and the vector embedding ri,lof each atom aiinto the shape-aware scalar embeddingand the shape- aware vector embedding ^^̂^^^^^^, ^^^^by incorporating Hsat each layer. Particularly, SMP learns ^^�^^^^^^, ^^^^for each atom aiusing Hsas shown in Equation 37: ^)

[0160] In Equation 37, [·, ·] is the concatenation operation; ai,lis the scalar embedding of atom ai at the l-th layer;represents the inherent relations between ai and the molecular surface shape (e.g., the signed distance from aito the shape). SMP learns oi,lin a similar way to Equation 4 as shown in Equation 38: ^)

[0161] In Equation 38,is the dot-product between ri,l andis the column- wise Euclidean norm of the vector featureencodes the inherent geometry of shape condition and thus is shared across all the layers. Apart from scalar embeddings, SMP also incorporates shape information into the vector embeddings as shown in Equation 39:

[0162] In Equation 35, ri,l is the vector embedding of atom ai at the l-th layer; VN-MLP(·) is an equivariant VN network

[0058] that learns non-linear interactions between ri,landHsin an equivariant way.

[0163] Bond type representation learning (BTRL): To enhance the understanding of relations among atoms for better prediction, SMP utilizes the bond type embeddings (i.e., BTRL). Particularly, for the bond between ajand ai, SMP generates the bond type embedding as shown in Equation 40:^)

[0164] In Equation 40, ai,l and ri,l is the scalar embedding and vector embedding of ai, respectively; abs(·) represents the absolute difference; dji is the distance between the positions xj and xi. SMP guarantees that the predictions eij,land eji,lare invariant to the permutation of atom aiand aj. This is achieved by using two invariant operations: the sum and the absolute difference operation. To learn effective bond-type embeddings, the sum and the absolute difference of column-wise Euclidean norm of ^^^^^^^^^^^^and ^^^^^^^l^ are utilized to implicitly estimate the distance between ai and aj. When l = 0, the distance dji are directly used to calculate eji,l.

[0165] In some embodiments, the backward generative process (DIFF-backward) includes a conditional molecule prediction (CMP) to generate molecules using ligand embedding Hl, pocket embedding Hp, or both.

[0166] As shown in Fig.11, the DIFF-backward process reverses the DIFF-forward process by denoising from (xi,t, vi,t) to (xi,t−1, vi,t−1) for each atom aiat t ∈ [T, 1], conditioned on the ligand embedding Hl, or the pocket embedding Hp, or both (if not available, Hlor Hp= 0). However, the probability of xi,t−1 (same idea applies to vi,t−1) denoised from xi,t conditioned on Hland Hp, denoted as is still intractable. Inspired by the standarddiffusion process [36’], the probability of the DIFF-backward process is approximated using its forward-process posterior but still conditioned on Hland Hp, that isHp). Given that (xi,0, vi,0) is unknown in the generation process, a conditional prediction module (CMP), parameterized by θ, predicts (xi,0, vi,0) at t as shown in Equation 41:)

[0167] In Equation 41,l pare conditioned on H and H . This further simplifies conditions Hland Hpare carried out within which maybe solved in a closed form [36’]. Conditions (i.e., Hland Hp) may be extensively used at each t in CMP to estimate the ultimately generated molecules. Thus, the entire diffusion process is iteratively calibrated to generate a noise-free molecule {(xi,0, vi,0)} that conforms to the conditions.

[0168] Conditional molecule prediction module (CMP): The key to predict the noise-free molecule conditioned on Hland Hpis to determine the atom type and placement with respect to the conditions, whereas bond connections may be determined by the atoms and their distances. Towards this end, a conditional adjustment strategy over the noisy molecule {(xi,t , vi,t)} is usedto estimate As shown in Fig.11, CMP employs an effective conditionalequivariant 3D geometric convolutional neural network (CEGCNN) capturing the molecular geometry and measures its “compatibility” with the conditions. Thus, the atom placement is updated by a derived conditional geometric shift.

[0169] Specifically, at each layer l, CEGCNN learns a vector embeddingcapturing conditional geometric shift of atom ai, and a scalar embedding,, capturing conditional properties of atom aienabled by the current molecular geometry. Thus, CMP is used to calculate ^ as shown in Equation 42:)

[0170] In Equation 42, ∆ are from the last layer L, and F is a feature predictionfunction.

[0171] Conditional equivariant 3D geometric convolution neural network (CEGCNN): In each l-th layer of CEGCNN, geometric vector perceptrons are used (GVP) [37’], which exhibit very strong expressiveness, capable of learning embeddings in spaces of any dimensions [38’]. An effective conditional convolution approach is used to aggregate atom features and geometric information from ai’s neighbors (N(i)) to learn,andas shown in Equation 43: ,(Eq.43)

[0172] In Equation 39,and,are the condition-aware versions of),andvia condition-aware adaption (CAA); ^is the bond embedding and will be generated by incorporating features of atoms ajand aiand their positions in the (l-1)-th layer. The convolution uses geometric information such as atom positions, bond length, bond angles, and distances between atoms without covalent bonds, etc., as well as the conditions Hland Hp, as input in each layer. Equivariance on will be guaranteed through GVP. Atom and bond properties andgeometries in generating molecules through multi-layer geometric convolution are used to promote realistic 3D molecules.

[0173] Overall, the design of CEGCNN convolution is grounded on the fact that the interaction between atoms in a molecule, which determine molecule shapes, is determined not only by the two atoms involved but also by the influence of other atoms within the molecule, and the influence decays as the distances increase. CEGCNN “simulates” such interactionsthrough multi-layer convolution in order to precisely determine the placement and type of each atom in the generated molecules.

[0174] Condition-aware adaptation (CAA) in CMP: The geometric shift embeddingand the property scalar embedding of each atom aineed to be condition-aware. This is firstensured in CEGCNN convolution where GVP takes the conditions as input as shown in Equation 43. To further strengthen the effects of the conditions, another level of adaption is usedtoward more condition-aware as shown in Equation 44:)

[0175] In Equation 44, the condition-aware,is used as input to the CEGCNN convolution (Equation 43). Intuitivelyl plearns how the conditions H and H will modify the geometric shift in an equivariant way. For ^, its condition-aware ^,calculated as shown in Equation 45:

[0176] In Equation 45, H function considers the atom features,, the geometric shift magnitude – large change in geometry may lead to large change in atom properties, theconditions Hland Hp, and how the geometric shift will be modified via Gland Gp. A combination of condition-aware adaptation (Equation 40) and condition-aware shift (Equation 43) spanning all steps of the DIFF-backward process and intertwined in every layer of CEGCNN at each step offers a robust mechanism for systematically integrating conditions at both deep and fine-grained levels.

[0177] Inference module:

[0178] In exemplary embodiments, the method includes an inference module. The inference module generates novel molecules by gradually denoising (xT, vT) to (x0, v0) using the equivariant shape-conditioned molecule prediction module. Specifically, the inference module samples xT and vT from N(0, I) and C(1 / K), respectively. After that, the inference module samples xt−1 from xt using in Equation 15. Similarly, the inference modulesamples vt−1 from vt using in Equation 16 until t reaches 1.

[0179] The inference module uses post-processing to determine bond types between atoms based on atomic distances and bond embeddings. It is a well-known issue that in diffusionmodels, the sample quality may be low [39’]. Generated molecules may be different from the condition ligands (or molecules) or may not bind well to the condition pockets. An effective strategy to mitigate this is to impose guidance [8’] during inference, using the guidance signals to modify the inference trajectories. Therefore, two classifier-free conditional guidance schemes (e.g., shape guidance and pocket guidance) are developed, which further enhances the generation process to conform to conditions.

[0180] Shape guidance (SG): In some embodiments, the inference module further includes a shape guidance module. During molecule generation, as shown in Fig.3E, additional shape guidance may be utilized by pushing the predicted atoms to the shape of the condition molecule Mx. This approach is motivated by previous work

[0067] , which demonstrates that incorporating additional guidance into conditional diffusion models may further ensure the generated objects closely following the given condition. Different from the shape for conditions, when used as guidance, molecule shapes were defined as a set of points Q sampled according to atom positions in the condition molecule Mx

[0023] .This design may lead to improved generation performance. Particularly, for each atom ai in Mx, 10, 20, 30, 40, 50, etc. points are randomly sampled into Q from a Gaussian distribution centered at xi. Given the predicted atom position ^^�^^0, ^^^^at step t, the shape guidance is applied by adjusting the predicted positions to Q as shown in Equation 46: ^^(Eq.46)

[0181] In Equation 46, σ > 0 is the weight used to balance the prediction ^^�^^0, ^^^^and the adjustment;is the Euclidean distance between ^^�^^0, ^^^^and z�,is the set of k- nearest neighbors of in Q based on d(·); γ > 0 is a distance threshold. By doing theadjustment shown in Equation 46, the predicted atom positions will be pushed to those of Mx when they are sufficiently far away. Additionally, the shape guidance is applied exclusively for steps t = T, T − 1,…, S, where S > 1, not for all the steps, and thus it only adjusts predicted atom positions when there are a lot of noises, and the prediction needs more guidance.

[0182] Protein Pocket Guidance (PG): Pocket-conditioned molecule generation (PMG) is applied when atoms in the generated molecules are too close to the protein pocket atoms K. Such close proximity may lead to steric clashes and thus undesirable binding affinities. To address this issue, as shown in Fig.3F, pocket guidance may be used in DiffSMol to further adjust atom positions in direction 328 and maintain sufficient distances between molecule atoms 324 andprotein atoms 326. Particularly, DiffSMol refines the atom positions in the generated molecules based on K as shown in Equation 47: ^^^^^ ^^^^^(Eq.47)

[0183] In Equation 47, xtis the sampled atom positions at the step t; N(xt; K) is the set of k- nearest neighbors of xt within the protein atoms K; d(xt, z) is the distance between xt and z, and calculates the unit vector in the direction that moves xtfar from z. A threshold, ρ, isintroduced to assess if protein atoms and molecule atoms are too close. This threshold is identified from known protein-ligand complexes in the training dataset. A hyper-parameter, ^, may also be introduced to control the margin. Different from the shape guidance that is applied on predicted atom positions, the pocket guidance is applied on the noisy atomic positions, xt. This pocket guidance design benefits the generated molecules in their binding affinities to protein pockets.

[0184] Algorithmic implementation for exemplary embodiments:

[0185] Figs.4A – 4C shows algorithms implementing the method in the exemplary embodiments. Algorithm S1 in Fig.4A describes the molecule generation process of the method. Given a known ligand Mx, the method generates a novel molecule Mythat has a similar shape to Mx and thus potentially similar binding activity. The method may also take the protein pocket K as input and adjust the atoms of generated molecules for optimal fit and improved binding affinities. Specifically, the method first calculates the shape embedding Hsfor Mxusing the shape encoder SE-enc described in Algorithm S2 shown in Fig.4B.

[0186] Based on Hs, the method then generates a novel molecule with a similar shape to Mx using the diffusion-based generative model DIFF as in Algorithm S3 shown in Fig.4C. During generation (i.e., inference), the method may use shape guidance to directly modify the shape of My to closely resemble the shape of Mx. When the protein pocket K is available, the method may also use pocket guidance to ensure that Myis specifically tailored to closely fit within K.

[0187] Related Work

[0188] Diffusion Models: Diffusion models [1’] are a class of deep generative models capable of generating new data samples from a target data distribution. This is achieved by gradually transforming random noise into a sample that follows the target distribution through an iterative denoising process. Diffusion models have demonstrated remarkable performance in many applications [2’–6’]. The forward process of diffusion model is a Markov chain that adds a small Gaussian noise to the original data x0at each step t ∈ [1, T] as shown in Equation 48:^)

[0189] In Equation 48,is the variance schedule, and N (·, ·) is the Gaussian distribution. To reverse the forward process, xT∼ N(0, I) is first sampled. However, the reverse distribution p(xt−1 | xt) is intractable, but it may be approximated by the tractable forward process posterior q(xt−1|xt , x0) as shown in Equation 49: ^)

[0190] In Equation 49, since x0is unknown during inference, q(xt−1|xt, x0) may be further approximated by a parameterized form qθand estimated. Diffusion models may be further tailored to generate samples from conditional distributions (e.g., Stable Diffusion [7’]), and to include guidance in the sampling process [8’].

[0191] Molecule generation: A variety of deep generative models have been developed to generate molecules in 1D [9’] or 2D [10’], [11’]. However, they fall short in capturing 3D structures of molecules, which are critical for determining their biological activities. Recent efforts have been dedicated to generating molecules in 3D [12’–18’] for LBDD and SBDD, respectively. However, there has been no model that may perform both.

[0192] Methods [13’], [14’] for LBDD often rely on ligand shapes as conditions and employ generative models to create potential binding molecules. Among these methods, SQUID [13’] combines a fragment-based generative model with a rotatable-bond scoring model. The former generates molecules using variational autoencoders (VAEs) [19’] and decodes fragments sequentially based on the shapes of condition ligands. The latter adjusts the angles of rotatable bonds among fragments to match the condition shapes. Considered state-of-the-art for LBDD, SQUID has limitations. SQUID generates molecules with fixed bond lengths and angles, potentially resulting in unrealistic molecule geometries. Meanwhile, SQUID fails to account for the effects of various poses, potentially leading to molecules of low binding affinities. An alternative approach Shape2Mol [14’] encodes 3D shapes of molecules into latent embeddings and then generates fragments sequentially based on these embeddings. Unfortunately, Shape2Mol lacks equivariance [20’], a key property ensuring consistent representation of 3D geometric information, regardless of its orientation or location in 3D space. Additionally, being fragment-based, it faces similar challenges as SQUID.

[0193] Methods for SBDD may be categorized as VAE-based [21’], [22’], autoregression- based [15’], [16’], [23’–25’], and diffusion-based methods [17’], [18’], [26’–29’], [29’–33’], and diffusion models demonstrate better performance. TargetDiff, a conditional diffusion model that sequentially denoises both continuous atom coordinates and categorical atom types in noisymolecules, while learning condition pocket representation, was developed

[0017] . TargetDiff was further enhanced into DecompDiff by utilizing data-dependent prior distributions over molecular arms and scaffolds

[0018] . The high-binding molecular arms were iteratively identified from generated molecules, and the binding affinities of the molecular arms were optimized by incorporating these arms as priors

[0026] . A pre-trained protein-ligand binding affinity predictor was employed to infer protein-ligand interaction priors and incorporated these priors into diffusion models

[0027] . Two strategies were introduced

[0028] , including condition and inpainting: the condition strategy considers protein pockets as fixed contexts, and the inpainting strategy jointly learns distributions of pocket and molecular atoms. Despite their promise, current models for SBDD often experience limited capability of deeply and effectively integrating conditions in the diffusion process, and the generated molecules may be very deviated from the conditions. EXAMPLES EXAMPLE 1: SHAPE-CONDITIONED DIFFUSION MODELS WITH GUIDANCE (DIFFSMOL)

[0194] The exemplary DiffSMol method generates binding molecules based on the shapes of known ligands. An overview of the DiffSMol system is shown in Fig.3A. Building on the principle that molecules with similar shapes tend to have similar binding activities, DiffSMol consists of two modules: (1) a pre-trained equivariant shape embedding (SE) module that learns expressive latent embeddings for the shapes of condition molecules (e.g., ligands), and (2) an equivariant molecule diffusion model (DIFF) that explicitly considers shape embeddings (SE) to generate new 3D molecules with similar shapes to condition molecules. Particularly, given a condition molecule, SE represents its shape as a point cloud with points sampled over its molecular surface. SE learns to map this point cloud into a latent embedding Hsusing an encoder-decoder framework. Conditioned on the shape embedding Hs, DIFF learns to generate molecules with desired shapes and realistic topologies in an equivariant way. Particularly, DIFF utilizes equivariant graph neural networks to learn shape-aware atom embeddings and generate molecules tailored to the shape condition. DIFF also leverages bond types as a training signal to fully capture the inherent topologies of molecules. During inference, DIFF utilizes shape guidance to further direct the generated molecules toward the shape condition. Besides shape guidance, when the structure of the protein binding pocket is available, DIFF employs pocket guidance to adjust the atom positions of generated molecules for optimal binding affinities with the binding pocket. This design enables the applicability of the exemplary DiffSMol method for pocket-conditioned molecule generation. The theory of the exemplary DiffSMol method is described above.EXPERIMENT 1:

[0195] The following study employs the generative AI method (e.g., DiffSMol) to generate molecules in 3D that effectively bind to a protein target and have realistic structures (e.g., empirically correct bond angles and bond lengths). DiffSMol was used to further modify the generated 3D structures in an iterative manner via shape guidance to better resemble the ligand shapes. DiffSMol was also used to tailor the generated molecules toward optimal binding affinities under the guidance of protein pockets.

[0196] Hyper-parameters:

[0197] In the study, a plurality of hyper parameters for Shape Embedding (SE) optimization and DIFF optimization. Specifically, Table 2 shows the dimension of all the hidden layers including: VN-DGCNN layers shown in Equation 3, MLP layers shown in Equation 4, VN-Inv layer shown in Equation 4, and the dimension dp of generated shape latent embeddings Hsin the parameter space of SE. Table 2. Hyper-parameters

[0198] The study determined the optimal hyper-parameters according to the mean squared errors of the predictions of signed distances for 1,000 validation molecules. The optimal dimension of all the hidden layers is 256, and the optimal dimension dpof shape latent embedding Hsis 128. The optimal number of points |P| in the point cloud P is 512. The study sampled 1,024 query points in Z for each molecule shape. The study constructed graphs from point clouds, which were employed to learn Hswith VN-DGCNN layer shown in Equation 3, using the k-nearest neighbors based on Euclidean distance with k = 20. The study set the number of VN-DGCNN layers as 4. The study set the number of MLP layers in the decoder shown in Equation 4 as two. The study set the number of VN-Inv layers as one.

[0199] The study optimized the SE model via Adam with its parameters (0.950, 0.999), learning rate 0.001, and batch size 16 [1]. The study evaluated the validation loss every 2,000 training steps. The study scheduled to decay the learning rate with a factor of 0.6 and a minimumlearning rate of 1e-6 if the validation loss did not decrease in five consecutive evaluations. The optimal SE model had 28,300 learnable parameters. The study trained the SE model with ∼156,000 training steps. The training took 80 hours with the study’s GPUs. The trained SE model achieved the minimum validation loss at 152,000 steps.

[0200] Materials:

[0201] The study evaluated the effectiveness of DiffSMol in both shape-conditioned molecule generation (SMG) and pocket-conditioned molecule generation (PMG) paradigms. For SMG, following a previous study

[0023] , the study evaluated whether DiffSMol could generate realistic 3D molecules that have shapes similar to condition molecules

[0023] . For PMG, the following previous studies

[0025] ,

[0026] , and

[0027] assessed, given target protein pockets, whether DiffSMol could generate molecules with high binding affinities and realistic structures. Particularly, for SMG, the study evaluated DiffSMol and its variant with shape guidance, referred to as DiffSMol+s, against the state-of-the-art SMG baselines in terms of shape similarity, diversity, and realism of generated molecules. For PMG, the study compared both DiffSMol and DiffSMol+s with pocket guidance, referred to as DiffSMol+p and DiffSMol+s+p, to state-of-the-art PMG baselines to investigate if DiffSMol could effectively generate realistic molecules binding towards protein targets. Different from PMG baselines trained on sparse protein-ligand complex data, DiffSMol was trained on large-scale molecule data for better generation.

[0202] SMG baseline: To evaluate the effectiveness of DiffSMol in generating molecules with similar shapes to condition molecules, the study compared DiffSMol and DiffSMol+s with a SMG baseline SQUID and a virtual screening (VS) method. In previous studies, SQUID used a variable λ to balance the interpolation (i.e., λ denotes interpolation level) and extrapolation in the latent space

[0023] . The instant study included SQUID with λ = 0.3 and SQUID with λ = 1.0

[0023] . VS was used to screen through the training set to identify molecules with high shape similarities with the condition molecule.

[0203] PMG baseline: To evaluate the effectiveness of DiffSMol in generating molecules binding towards target protein pockets, the study compared DiffSMol+p and DiffSMol+s+p with four PMG baselines, including AR,

[0025] Pocket2Mol,

[0026] TargetDiff,

[0027] and DecompDiff

[0028] . For DecompDiff, the study excluded DecompDiff with protein pocket priors from the comparison, and only included DecompDiff with known ligand priors. This was due to the substantially lower performance of DecompDiff with protein pocket priors in generating molecules with desirable drug-likeness compared to other methods.

[0204] Data for SMG: Data for SMG Following SQUID

[0023] , the study used molecules in the MOSES dataset

[0031] , with their 3D conformers calculated by RDKit

[0032] . The study used the same training and testing split as in SQUID. SQUID further modified the generated conformers into artificial ones, by adjusting acyclic bond distances to their empirical means and fixing acyclic bond angles using heuristic rules. Unlike SQUID, the study did not make any additional adjustments to the calculated 3D conformers, as DiffSMol was designed with sufficient flexibility to accept any 3D conformers as input. Limited by the predefined fragment library, SQUID also removed molecules with fragments not present in its fragment library. In contrast, the study kept all the molecules, as DiffSMol was not based on fragments. As a result, the study’s training set included 1,593,653 molecules. The same set of 1,000 molecules as in SQUID was used for testing. For hyper-parameter tuning, the study randomly sampled 1,000 molecules from the training set for validation.

[0205] Data for PMG: Following the previous studies [25–28], the study used the CrossDocked2020 benchmark dataset

[0033] with protein-ligand complex data to evaluate DiffSMol. During evaluation, for DiffSMol, the study directly utilized the model trained on the MOSES without fine-tuning on the complex data. For all the PMG baselines, the study used the model checkpoints released by the authors. All PMG baselines were trained on the training set of CrossDocked2020 [25–28], which included 11,915 unique ligands, 15,207 unique proteins, and 100,000 protein-ligand complexes in total. Note that the PMG baselines were designed specifically for protein-ligand complex data and may not accept molecule data as input. Thus, the study did not tune PMG baselines on the MOSES training set. The study used the same test dataset as in the previous studies [25–28], which included 100 protein-ligand complexes with novel proteins. Note that the MOSES dataset focused on molecules with a number of atoms ranging from 8 to 27. In this evaluation, the study did not consider complexes with out-of- distribution ligands (i.e., ligands with more than 27 atoms). Thus, the study excluded 28 complexes from the test set of CrossDocked2020.

[0206] Evaluation of DiffSMol in SMG: Following SQUID

[0023] , the study applied DiffSMol, DiffSMol+s and all SMG baselines to generate 50 molecules per test molecule for evaluation. For VS, following SQUID, the study randomly sampled 500 training molecules for each test molecule. The study then identified and selected the top-50 molecules from the 500 molecules that have the highest shape similarities to the test molecule.

[0207] Evaluation of DiffSMol in PMG: The study directly utilized the DiffSMol model trained on the MOSES dataset for the evaluation against PMG baseline methods. Following previous PMG baselines [25–28], the study used DiffSMol+p, and DiffSMol+s+p to generate100 molecules for each test protein-ligand complex. For DiffSMol+p and DiffSMol+s+p, the study used SE to encode the shapes of ligands in test protein-ligand complexes into shape embeddings. Then, the study used DiffSMol+p and DiffSMol+s+p to generate molecules conditioned on these embeddings. For baselines, the study directly used molecules generated from AR, Pocket2Mol and TargetDiff, as provided by TargetDiff [2], to calculate evaluation metrics. For DecompDiff, the study used the model checkpoints released by the authors to generate 100 molecules for each test protein-ligand complex.

[0208] Metrics for SMG: To evaluate the performance of DiffSMol and SMG baselines in generating molecules with similar shapes to condition molecules, the study used shape similarity (referred to as Sims) and molecular graph similarity (referred to as Simg) as evaluation metrics. Higher Sims and lower Simg suggested that generated molecules may have similar binding activities and substantially different molecular graphs compared to condition molecules (e.g., ligands). The study calculated the shape similarity Simsvia the overlapped volumes between two aligned molecules following the literature

[0023] . Each generated molecule is aligned with the condition molecule by the ROCS tool

[0034] . For the molecular graph similarity Simg, the study used the Tanimoto similarity, calculated by RDKit

[0032] , over Morgan fingerprints between the generated and condition molecule. Based on Simsand Simg, the study calculated the following three metrics using the set of 50 generated molecules per condition molecule, and reported the average of these metrics across all condition molecules in the test set: (1) #d% relates to the percentage of molecules in each set with Sims>0.8 and Simgsmaller than a threshold δg(i.e., graph similarity constraints), referred to as desirable molecules; (2) Divd relates to the diversity among desirable molecules within each set, calculated as 1 minus the average pairwise graph similarity; (3) #n% relates to the percentage of desirable molecules in each set that cannot be found in the MOSES dataset. The study selected 0.8 as the threshold of Simsfor desirable molecules. This threshold was chosen to ensure that the selected desirable molecules had highly similar shapes, and thus, similar binding activities to condition molecules. During evaluation, the study used test molecules as condition molecules for the generation.

[0209] Metrics for PMG: The study evaluated the performance of DiffSMol and PMG baselines in generating molecules binding towards protein targets. Following previous studies

[0027] ,

[0028] , the study evaluated the binding affinities, drug-likeness, and diversity of generated molecules. For binding affinity, the study used Vina Scores (Vina S) calculated by AutoDock Vina

[0015] as an evaluation metric. The study also considered the optimized poses from the generated 3D molecules in evaluation. Specifically, the study used Vina Minimization (Vina M) and Vina Dock (Vina D) calculated from AutoDock Vina as evaluation metrics. Vina M andVina D optimized the poses by local energy minimization and global search optimization, respectively

[0015] . For drug-likeness, the study evaluated whether the generated molecules are drug-like using QED scores

[0016] and synthesizable using synthesizability scores (SA)

[0035] . The study also calculated the diversity as defined in the previous paragraph among generated molecules. Following previous studies

[0027] ,

[0028] , the study reported the average and median of the above metrics across all test complexes.

[0210] Metrics for evaluation of molecule quality: The study evaluated the quality of generated molecules based on their realism for both SMG and PMG. The study used a comprehensive set of metrics to evaluate the stability, 3D structures, and 2D structures of generated molecules. For stability, the study calculated atom and molecule stability of generated molecules. Atom stability measured the proportion of atoms that had the right valency, while molecule stability measured the proportion of generated molecules that all the atoms were stable. For 3D structures and 2D structures, the study used the same metrics as in previous study

[0036] . Particularly, for 3D structures, the study used root mean square deviations (RMSDs) and Jensen- Shannon (JS) divergences of bond lengths, bond angles and dihedral angles to evaluate the quality of 3D molecule structures.

[0211] RMSDs were used to measure the discrepancies between the generated 3D structures of molecules and their optimal structures identified by RDKit toolkit

[0032] via energy minimization. In addition, the JS divergences of bond lengths, bond angles and dihedral angles measured the divergences between the generated molecules and the real molecules (i.e., training molecules) regarding the 3D structures. Smaller divergence values indicated that the generated molecules had these properties more similar to those of training molecules and thus more realistic. To evaluate the quality of 2D molecule structures, the study primarily assessed if the bonds and rings within the generated molecules are similar to those in real molecules. Particularly, for bonds, the study evaluated the JS divergences in terms of bond counts per atom and bond types (single, double, triple, and aromatic). For rings, the study compared both the counts of all rings and the counts of rings of varying sizes (n-sized rings) in the generated molecules to those in real molecules using JS divergences. Furthermore, the study measured if the generated molecules capture the frequent rings in real molecules. To be specific, the study calculated the number of overlapping rings observed in the top-10 frequent ring types of both generated and real molecules. Note that the study considered different molecules to calculate JS divergences when comparing against SMG and PMG baselines. For SMG, the study used the training molecules in the MOSES dataset. For PMG, the study used the ligands in the training protein-ligand complexes of CrossDocked2020.

[0212] Experimental Results:

[0213] Comparison on generating desirable molecules in SMG: The study evaluated DiffSMol, DiffSMol+s and state-of-the-art SMG baselines in generating desirable molecules.

[0214] The study defined desirable molecules as those satisfying δgand with shape similarities larger than 0.8. These molecules had highly similar shape with the condition molecules (e.g., ligands), and thus, could also have desirable binding activities [4]. In this analysis, for each method, the study calculated the possibility of generating desirable molecules (i.e., #d%), the diversity and the novelty among these molecules (i.e., Divd and #n%) under different graph similarity constraints (i.e., δg=0.3, 0.5, 0.7, and 1.0).

[0215] Table 3 shows the comparison on desirable molecules for SMG between virtual screening (VS), SQUID (λ=0.3), SQUID (λ=1.0), DiffSMol, and DiffSMol+s. In the Table 3, δg denotes a graph similarity constraint; #d% denotes a percentage of generated molecules that are desirable, satisfying δg, and exhibiting high Sims (Sims ≥ 0.8); Divd denotes a diversity among the desirable molecules; and #n% denotes a percentage of desirable molecules that may not be found in the MOSES dataset. Best values are in bold, and second-best values are underlined. Table 3. Comparison on Desirable Molecules for SMG

[0216] As shown in Table 3, DiffSMol and DiffSMol+s consistently outperformed all the baseline methods (e.g., VS, SQUID) in terms of all the metrics. For example, when δg=0.3, at #d%, DiffSMol+s (61.4%) demonstrated a substantial improvement of 448.2% compared to the best baseline SQUID (λ=1.0) (11.2%). In terms of Divd, DiffSMol (0.762) also substantially outperformed the best baseline VS (0.736) by 2.3%. At #n%, both DiffSMol and DiffSMol+s ensured that nearly all the generated desirable molecules were novel (99.8% for DiffSMol and 99.9%for DiffSMol+s), substantially outperforming the best baseline SQUID with λ=1.0 (96.9%) by 3.1% and 3.0%, respectively. When δg=0.5, 0.7, or 1.0, a similar trend is observed. Specifically, when δg=0.5, at #d%, DiffSMol+s (70.9%) establishes a notable improvement of225.2% compared to the best baseline method SQUID with λ=0.3 (21.8%). At Divd and #n%, DiffSMol and DiffSMol+s also demonstrated top performance among all the methods. When δg=0.7, at #d%, DiffSMol+s (71.0%) also achieves a remarkable improvement of 158.2% over the best baseline method SQUID with λ=0.3 (27.5%). The superior performance of DiffSMol and DiffSMol+s in #d%, Divd, and #n%, particularly at small δg, indicates their strong capacity in generating novel molecules that had desirable shapes and distinct graph structures compared to the condition molecules, thereby facilitating the process of drug development.

[0217] In Table 3, DiffSMol and DiffSMol+s consistently outperformed SQUID with λ=0.3 and 1.0 in terms of all the metrics. A key distinction between DiffSMol and SQUID was that SQUID generated molecules by sequentially predicting fragments. However, during fragment prediction, their poses were not fully considered, leading to suboptimal prediction accuracy and limited generation performance. On the other hand, by directly arranging atoms, DiffSMol and DiffSMol+s explicitly considered the 3D atom positions when generating molecules, and thus, achieved remarkable improvement over SQUID as shown in Table 3.

[0218] Different from DiffSMol and SQUID which directly generated desirable molecules, VS screened over randomly sampled training molecules to identify molecules of interest. However, VS cannot ensure optimal precision design, resulting in the suboptimal performance of VS at #d%. In addition, due to the reliance on existing molecules, VS cannot discover novel molecules. In contrast, DiffSMol can effectively generate novel molecules with desirable shapes, making it a promising tool for discovering novel drug candidates.

[0219] Comparing DiffSMol+s and DiffSMol, Table 3 shows that incorporating shape guidance into DiffSMol substantially boosts its effectiveness in generating desirable molecules. For example, when δg=0.3, at #d%, DiffSMol+s (61.4%) substantially outperforms DiffSMol (28.4%) by 116.2%. when δg=0.5, 0.7, and 1.0, DiffSMol+s also achieved a considerable improvement of 119.5%, 119.1% and 119.1%, respectively, compared to DiffSMol. In the meantime, DiffSMol+s retained similar performance with DiffSMol in terms of the diversity and novelty of generated desirable molecules. These results signified that shape guidance effectively improved the ability of DiffSMol in generating molecules that had similar shapes to condition molecules without degrading the novelty and diversity among generated molecules.

[0220] Quality comparison between desirable molecules generated by DiffSMol and SQUID: The study evaluated the quality of desirable molecules generated from DiffSMol, DiffSMol+s, and baseline methods in terms of stability, 3D structures, and 2D structures. Table 4 presents the performance comparison in the quality of desirable molecules generated by different methods (e.g., SQUID, DiffSMol, DiffSMol+s) when the graph similarity constraint δgwas 0.3.In this analysis, the study focused on desirable molecules that may have high utility in drug development. The study also excluded the search algorithm VS and considered only generative models, such as DiffSMol and SQUID, in this analysis. Table 4. Comparison on quality of generated molecules between DiffSMol and SQUID (δg=0.3)

[0221] As shown in Table 4, “atom stability” denotes the portion of stable atoms that have the correct vacancy; “molecule stability” denotes the proportion of generated molecules with all atoms stable; RMSD denotes the root mean square deviation between the generated 3D structures of molecules and their optimal conformations; “JS. bond lengths” denotes the Jensen- Shannon (JS) divergences of bond lengths; “JS. bond angles” denotes the JS divergences of bond angles; “JS. dihedral angles” denotes the JS divergences of dihedral angles; “JS. number of bonds per atom” denotes the JS divergences of bond counts per atom; “JS. basic bonds types” denotes the JS divergences of basic bond types; “JS. number of rings” denotes the JS divergences of counts of all rings; “JS. number of n-sized rings” denotes the JS divergences of counts of n-sized rings; and “Number of intersecting rings” denotes the number of rings observed in the top-10 frequent rings of both generated and real molecules.

[0222] As shown in Table 4, DiffSMol generated molecules with comparable quality to baselines in terms of stability, 3D structures, and 2D structures. For example, in stability, Table 4 shows that DiffSMol and DiffSMol+s either achieved comparable performance or fell slightly behind SQUID (λ=0.3) and SQUID (λ=1.0) in atom stability and molecule stability. Particularly, DiffSMol achieved similar performance with SQUID (λ=0.3) and SQUID (λ=1.0) in atom stability (0.993 for DiffSMol vs 0.996 for SQUID with λ of 0.3 and 1.0). In terms of molecule stability, DiffSMol underperformed SQUID (λ=0.3) by 6.5%. However, DiffSMol stilldemonstrated strong effectiveness in generating stable molecules, with 89.1% of generated molecules being stable.

[0223] Table 4 also shows that DiffSMol and DiffSMol+s generated molecules with more realistic 3D structures compared to SQUID. Particularly, for RMSD, DiffSMol and DiffSMol+s outperformed the best baseline SQUID (λ=1.0) by 0.8% and 2.2%, respectively. In addition, DiffSMol and DiffSMol+s also established a notable improvement of 4.6% and 6.3% over the best baseline SQUID (λ=0.3) in JS. bond lengths. In terms of JS. bond angles and JS. dihedral angles, DiffSMol and DiffSMol+s outperformed the best baseline SQUID (λ=0.3) by 30.9% and 25.7%, and by 15.6% and 14.6%, respectively. SQUID fixed the bond lengths and angles within the generated molecules, leading to the discrepancy in 3D structures between the generated molecules and real molecules. Conversely, DiffSMol and DiffSMol+s used a data-driven manner to infer distances and angles between atoms. This design enabled DiffSMol and DiffSMol+s to achieve superior performance in generating molecules with realistic 3D structures.

[0224] Table 4 also presents that DiffSMol and DiffSMol+s achieved comparable performance with SQUID in generating realistic 2D molecule structures. Particularly, for JS. number of bonds per atom, DiffSMol and DiffSMol+s substantially outperformed the best baseline SQUID (λ=0.3) by 77.8% and 73.9%, respectively. In terms of JS. basic bond types, DiffSMol and DiffSMol+s underperformed SQUID (λ=0.3) considerably. DiffSMol and DiffSMol+s also achieved substantially better performance (0.042 and 0.048) than SQUID with λ=0.3 (0.309) in JS. number of rings. DiffSMol and DiffSMol+s slightly underperformed SQUID in terms of JS. number of n-sized rings and the number of intersecting rings. These results signified that DiffSMol and DiffSMol+s, though not explicitly leverage fragments as SQUID did, may still generate molecules with realistic 2D structures.

[0225] Shape and graph similarities analysis: The study analyzed the distributions of shape and graph similarities between condition molecules and all molecules generated from DiffSMol and SQUID. The study conducted this analysis to (1) assess the capacity of DiffSMol and SQUID in generating molecules with similar shapes to condition molecules (e.g., ligands); and (2) compare the strategies in DiffSMol and SQUID to further improve shape similarities. In this analysis, for each condition molecule, the study used all 50 molecules generated by DiffSMol, DiffSMol+s, SQUID with λ=0.3 and SQUID with λ=1.0.

[0226] Figs.5A – 5D, for each method, each shows a heatmap with the x-axis representing shape similarities (i.e., Sims) and the y-axis representing graph similarities (i.e., Simg). Each grid in this heatmap shows the percentage of molecules that had shape and graph similarities within specific ranges, and the grid color represented the scale of the percentage (e.g., a darker colorindicated a higher percentage). In each heatmap, the vertical black line marked the average of shape similarities, and the horizontal black line marked the average of graph similarities.

[0227] Both DiffSMol and SQUID developed specific strategies to enhance the shape similarity. Particularly, DiffSMol incorporated shape guidance (i.e., DiffSMol+s) to iteratively modify the generated 3D structures to better resemble the known ligand shapes. On the other hand, SQUID leveraged a balance variable λ to control the interpolation level during generation. A lower λ indicated stronger interpolation, and thus, better shape similarity but worse graph similarity.

[0228] As shown in Figs.5A – 5D, the shape guidance in DiffSMol+s effectively boosts the shape similarities of generated molecules without degrading their graph similarities. Specifically, Fig.5A and Fig.5B show that compared to DiffSMol, DiffSMol+s achieved a higher average shape similarity (0.824 for DiffSMol+s vs 0.771 for DiffSMol) and comparable average graph similarity (0.230 for DiffSMol+s and 0.229 for DiffSMol). However, Fig.5C and Fig.5D shows a different trend for SQUID: by decreasing λ from 1.0 to 0.3, there existed a trade-off between shape similarity and graph similarity. To be specific, SQUID (λ=0.3) achieved superior average shape similarity (0.740) while inferior average graph similarity (0.349), compared to SQUID (λ=1.0) (0.699 for average shape similarity and 0.235 for average graph similarity). These results suggested that compared to adjusting the interpolation level (λ) as in SQUID, including shape guidance may effectively enhance shape similarities of generated molecules without compromising graph similarities.

[0229] Table 5 shows the shape similarity (i.e., Sims) and graph similarity (i.e., Simg) of molecules generated from VS, SQUID, DiffSMol and DiffSMol+s under different graph similarity constraints (δg=1.0, 0.7, 0.5, 0.3). Table 5. Similarity comparison on SMG

[0230] As shown in Table 5, δg denotes the graph similarity constraint; avgASims denotes the average of shape similarities between the condition molecules and generated molecules with avgASimgdenotes the average of graph similarities between the condition molecules and generated molecules with Simg <= δg; avgMSims denotes the maximum of shape similarities between the condition molecules and generated molecules with Simg<= δg; avgMSimg denotes the maximum of graph similarities between the condition molecules and the molecules with the maximum shape similarities with Simg <= δg; “std” denotes the standard deviation; and “↑” represents higher values are better, and “↓” represents lower values are better. Best values are in bold, and second-best values are underlined.

[0231] The study calculated evaluation metrics using all the generated molecules satisfying the graph similarity constraints. Particularly, when δg=1.0, the study did not filter out any molecules based on the constraints and directly calculated metrics on all the generatedmolecules. When δg=0.7, 0.5 or 0.3, the study considered only generated molecules with similarities lower than δg. Based on Sims (i.e., shape similarities) and Simg (i.e., graph similarities), the study calculated the following metrics using the subset of molecules with Simglower than δg, from a set of 50 generated molecules for each test molecule and reported the average of these metrics across all test molecules: (1) avgASims measures the average Sims across each subset of generated molecules with Simg lower than δg; (2) avgASimgcalculates the average Simgfor each set; (3) avgMSimsdetermines the maximum Simswithin each set; (4) avgMSimg measures the Simg of the molecule with maximum Sims in each set.

[0232] As shown in Table 5, DiffSMol and DiffSMol+s demonstrated outstanding performance in terms of the average shape similarities (i.e., avgASims) and the average graph similarities (i.e., avgASimg) among generated molecules. Specifically, when δg=0.3, DiffSMol+s achieved a substantial 10.5% improvement in avgASims over the best baseline VS. In terms of avgASimg, DiffSMol+s also achieved highly comparable performance with VS (0.217 vs 0.211, in avgASimg, lower values indicated better performance). This trend remained consistent when applying various similarity constraints (i.e., δg) as shown in Table 5.

[0233] Similarly, DiffSMol and DiffSMol+s demonstrated superior performance in terms of the average maximum shape similarity across generated molecules for all test molecules (avgMSims), as well as the average graph similarity of the molecules with the maximum shape similarities (avgMSimg). Specifically, at avgMSims, Table 5 shows that DiffSMol+s outperformed the best baseline SQUID (λ=0.3) when δg=0.3, 0.5, and 0.7, and only underperformed it by 0.7% when δ=1.0. The molecules generated by DiffSMol+s with the maximum shape similarities had substantially lower graph similarities (i.e., avgMSimg) compared to those generated by SQUID (λ=0.3). As evidenced by these results, DiffSMol+s featured strong capacities of generating molecules with similar shapes yet novel graph structures compared to the condition molecule, facilitating the discovery of promising drug candidates.

[0234] Table 5 also shows that by incorporating shape guidance, DiffSMol+s substantially outperformed DiffSMol in both avgASimsand avgMSims, while maintaining comparable graph similarities (i.e., avgASimg and avgMSimg). Particularly, when δg=0.3, DiffSMol+s establishes a considerable improvement of 6.9% and 4.9% over DiffSMol in avgASimsand avgMSims, respectively. Meanwhile, DiffSMol+s achieved the same avgASimgwith DiffSMol and only slightly underperformed DiffSMol in avgMSimg (0.223 vs 0.220). The superior performance of DiffSMol+s suggested that the incorporation of shape guidance effectively boosted the shape similarities of generated molecules without compromising graph similarities.

[0235] Validity and novelty comparison: The study evaluated the ability of DiffSMol and SQUID to generate molecules with valid and novel 2D molecular graphs. The study calculated the percentages of the valid and novel molecules among all the generated molecules.

[0236] Table 6 shows comparison on Validity and Novelty between DiffSMol and SQUID. As shown in Table 6, #v% denotes the percentage of generated molecules that are valid; #n% denotes the percentage of valid molecules that are novel; and #v&n% denotes the percentage of generated molecules that are valid and novel. Best values are in bold. Table 6. Comparison on validity and novelty between DiffSMol and SQUID

[0237] As shown in Table 6, both DiffSMol and DiffSMol+s outperformed SQUID with λ=0.3 and λ=1.0 in generating novel molecules. Particularly, almost all valid molecules generated by DiffSMol and DiffSMol+s were novel (99.8% and 99.9% at #n%), while the best baseline SQUID with λ=0.3 achieved 98.4% in novelty. In terms of the percentage of valid and novel molecules among all the generated ones (#v&n%), DiffSMol and DiffSMol+s also outperformed SQUID with λ=0.3 and λ=1.0. At #v%, DiffSMol (99.1%) and DiffSMol+s (99.2%) slightly underperformed SQUID with λ=0.3 and λ=1.0 (100.0%) in generating valid molecules. SQUID guaranteed the validity of generated molecules by incorporating valence rules into the generation process and ensuring it to avoid fragments that violate these rules. Conversely, DiffSMol and DiffSMol+s used a data-driven approach to learn the generation of valid molecules. These results suggested that, even without integrating valence rules, DiffSMol and DiffSMol+s may still achieve a high percentage of valid and novel generated molecules.

[0238] Additional quality comparison between molecules generated by DiffSMol and SQUID: Similar to Table 4, the study presented the performance comparison on the quality of desirable molecules generated by different methods under different graph similarity constraints δg=0.5, 0.7 and 1.0, as detailed in Table 7, Table 8, and Table 9, respectively.Table 7. Comparison on quality of generated molecules between DiffSMol and SQUID (δg=0.5)Table 8. Comparison on quality of generated molecules between DiffSMol and SQUID (δg=0.7)Table 9. Comparison on quality of generated molecules between DiffSMol and SQUID (δg=1.0)

[0239] As shown in each Table 7, Table 8, and Table 9, “atom stability” denotes the portion of stable atoms that have the correct vacancy; “molecule stability” denotes the proportion of generated molecules with all atoms stable; RMSD denotes the root mean square deviation between the generated 3D structures of molecules and their optimal conformations; “JS. bond lengths” denotes the Jensen-Shannon (JS) divergences of bond lengths; “JS. bond angles” denotes the JS divergences of bond angles; “JS. dihedral angles” denotes the JS divergences of dihedral angles; “JS. number of bonds per atom” denotes the JS divergences of bond counts per atom; “JS. basic bonds types” denotes the JS divergences of basic bond types; “JS. number of rings” denotes the JS divergences of counts of all rings; “JS. number of n-sized rings” denotes the JS divergences of counts of n-sized rings; and “Number of intersecting rings” denotes the number of rings observed in the top-10 frequent rings of both generated and real molecules.

[0240] Overall, these tables show that under varying graph similarity constraints, DiffSMol and DiffSMol+s may always generate desirable molecules with comparable quality to baselines in terms of stability, 3D structures, and 2D structures. These results demonstrated the strong effectiveness of DiffSMol and DiffSMol+s in generating high-quality desirable molecules with stable and realistic structures in both 2D and 3D. This enabled the high utility of DiffSMol and DiffSMol+s in discovering promising drug candidates.

[0241] Case study for SMG: Figs.6A – 6D show three generated molecules from VS, SQUID with λ=0.3, and DiffSMol+s given the same condition molecule. Each molecule had the highest shape similarity among the 50 candidates generated by each method. As shown in Fig. 6D, the molecule generated by DiffSMol+s had higher shape similarity (0.883) with the condition molecule in Fig.6A than those from the baseline methods (i.e., 0.768 for VS shown in Fig.6B and 0.759 for SQUID with λ=0.3 shown in Fid.6C). Particularly, Fig.6D shows the molecule from DiffSMol+s having the surface shape most similar to that of the condition molecule. On the contrary, the molecules generated from VS in Fig.6B and SQUID with λ=0.3 in Fig.6C show noticeable misalignments when compared to the condition molecule. This comparison demonstrated the superior ability of DiffSMol+s to generate molecules with highly similar 3D shapes to the condition molecule in Fig.6A. In terms of graph similarities, all these generated molecules have low graph similarities with the condition molecule. The ability togenerate molecules that had similar 3D shapes yet different molecular graphs demonstrated the potential high utility of DiffSMol+s in facilitating the drug development.

[0242] Comparison on generating desirable molecules for PMG: The study evaluated the effectiveness of DiffSMol against state-of-the-art PMG baselines in generating molecules binding towards specific protein pockets. All the baselines required protein-ligand complex data for training and generated molecules by explicitly modeling their interactions with protein binding pockets. Different from these baselines, DiffSMol did not require complex data and consumes molecules for training. Note that protein-ligand complex data was expensive and thus highly limited. In contrast, there existed several high-quality and large-scale molecule databases [31, 37]. By consuming molecule data for training, DiffSMol may leverage the rich data for better generation. DiffSMol further enhanced the binding molecule generation by incorporating pocket guidance.

[0243] The study utilized two variants of DiffSMol for evaluation: DiffSMol with pocket guidance (i.e., DiffSMol+p) and DiffSMol with both pocket and shape guidance (i.e., DiffSMol+s+p). In this section, the study evaluated DiffSMol+p, DiffSMol+s+p and PMG baselines in both effectiveness and efficiency. Following previous studies

[0027] ,

[0028] , in terms of the effectiveness, the study evaluated the binding affinity, drug-likeness, and diversity of molecules generated from DiffSMol+p, DiffSMol+s+p and all PMG baselines. Regarding efficiency, the study reported the inference time of all methods used to generate molecules.

[0244] Table 10 shows the comparison on desirable molecules for PMG between DiffSMol+p, and DiffSMol+s+p, and PMG baselines. In other words, the study reported the performance of all methods in Table 10. Table 10. Overall comparison on PMG

[0245] As shown in Table 10, “Vina S” denotes the binding affinities between the initially generated poses of molecules and the protein pockets; “Vina M” denotes the binding affinities between the poses after local structure minimization and the protein pockets; “Vina D: denotes the binding affinities between the poses determined by AutoDock Vina

[0015] and the protein pockets; “HA” denotes the percentage of generated molecules with Vina D higher than those of condition molecules; “QED” denotes the drug-likeness score; “SA” denotes the synthesizability score; “Div” denotes the diversity among generated molecules; and “time” denotes the time cost to generate molecules. Best values are in bold, and the second-best values are underlined.

[0246] In Table 10, DiffSMol+p and DiffSMol+s+p showed remarkable efficiency over baselines by using pocket guidance instead of directly modeling these pockets. Specifically, DiffSMol+p and DiffSMol+s+p generated 100 molecules in 48 and 58 seconds on average, respectively, while the most efficient baseline TargetDiff took 1,252 seconds. The superior efficiency enabled DiffSMol+p and DiffSMol+s+p to generate more than 10x molecules than baselines in the same time duration. Therefore, for baselines, the study applied them to generate 100 molecules for each test protein target. For DiffSMol, the study generated 1,000 molecules and selected the top 100 molecules for comparison based on their Vina S, QED, and SA scores..

[0247] As shown in Table 10, DiffSMol+p and DiffSMol+s+p achieved the second-best and best performance in terms of the binding affinities of generated molecules. Particularly, DiffSMol+p and DiffSMol+s+p demonstrated the second-best (-5.53 kcal / mol) and best (-5.81 kcal / mol) average Vina S, with 17.7% and 13.2% improvement over the best baseline AR (-5.06 kcal / mol). Similarly, for Vina scores obtained from locally minimized poses (i.e., Vina M), DiffSMol+p and DiffSMol+s+p also achieved the second-best (-6.37 kcal / mol) and best (-6.50 kcal / mol) performance, outperforming the best baseline TargetDiff (-6.20 kcal / mol) by 11.5% and 9.5%. Moreover, for Vina D, a score calculated from poses optimized by global search, DiffSMol+p and DiffSMol+s+p again yielded the second-best (-7.19 kcal / mol) and third-best performance (-7.16 kcal / mol) and only slightly underperformed the best baseline TargetDiff (- 7.37 kcal / mol). These results demonstrated that even without explicitly training on protein- ligand complexes, DiffSMol+p and DiffSMol+s+p may still generate molecules with superiorbinding affinities towards protein targets in terms of Vina S, Vina M, and Vina D, compared to PMG baselines. Note that the study considered Vina M and Vina D in evaluation, as it was a common practice in drug development to find more favorable binding poses of candidates through pose optimization

[0038] .

[0248] Table 10 also shows that DiffSMol+p and DiffSMol+s+p were able to generate molecules with better binding affinities than condition molecules (i.e., known ligands). Particularly, DiffSMol+p and DiffSMol+s+p achieved the best (79.92%) and second-best (78.75%) performance in terms of the average percentage of generated molecules with Vina D higher than those of known ligands (i.e., HA). The superior performance in HA demonstrated the high utility of DiffSMol+p and DiffSMol+s+p in generating promising drug candidates with better binding affinities than known ligands.

[0249] Table 10 further presents the superior performance of DiffSMol+p and DiffSMol+s+p in metrics related to drug-likeness and diversity. Particularly, for drug-likeness, DiffSMol+p and DiffSMol+s+p achieved the best (0.77) and second-best (0.76) QED scores, respectively, with 31.0% and 29.3% improvement over the best baseline Pocket2Mol (0.58). DiffSMol+p and DiffSMol+s+p also achieved the second (0.72) and third (0.70) SA scores, and only slightly fell behind the best baseline Pocket2Mol (0.76). In terms of the diversity among generated molecules, DiffSMol+p and DiffSMol+s+p underperformed the baselines. The inferior diversity may be attributed to the design of DiffSMol+p and DiffSMol+s+p that generated molecules with similar shapes to the ligands. This design allowed DiffSMol+p and DiffSMol+s+p to generate molecules with desired drug-likeness while may slightly degrade the diversity among generated molecules.

[0250] When comparing DiffSMol+p and DiffSMol+s+p, Table 10 shows that overall, DiffSMol+s+p with shape guidance may generate molecules with higher binding affinities compared to DiffSMol+p. To be specific, for Vina S and Vina M, DiffSMol+s+p outperformed DiffSMol+p by 5.1% and 2.0%, respectively. At Vina D, the performance of DiffSMol+s+p and DiffSMol+p was highly comparable. These results indicated that even with pocket guidance, including additional shape guidance may further enhance the generation of binding molecules.

[0251] Quality comparison for PMG: In addition to binding affinities, drug-likeness, and diversity, the study also evaluated the quality of molecules generated by DiffSMol+p, DiffSMol+s+p, and all the PMG baselines. The study assessed the quality of these molecules across multiple dimensions, including stability, 3D structures, and 2D structures, using the same metrics as in Table 4. To ensure a fair comparison, instead of using molecules from the MOSESdataset to calculate the JS divergence metrics as in Table 4, the study used the known ligands from the baselines’ training set (i.e., CrossDocked2020) to calculate JS divergences.

[0252] Table 11 shows a comparison on quality of generated molecules by PMG baselines (e.g., AR, Pocket2Mol, TargetDiff, DecompDiff), DiffSMol+p, and DiffSMol+s+p. In other words, the study reported the performance of all methods in terms of molecule quality in Table 11. Table 11. Comparison on quality of generated molecules for PMG

[0253] As shown in Table 11, “atom stability” denotes the portion of stable atoms that have the correct vacancy; “molecule stability” denotes the proportion of generated molecules with all atoms stable; RMSD denotes the root mean square deviation between the generated 3D structures of molecules and their optimal conformations; “JS. bond lengths” denotes the Jensen- Shannon (JS) divergences of bond lengths; “JS. bond angles” denotes the JS divergences of bond angles; “JS. dihedral angles” denotes the JS divergences of dihedral angles; “JS. number of bonds per atom” denotes the JS divergences of bond counts per atom; “JS. basic bonds types”denotes the JS divergences of basic bond types; “JS. number of rings” denotes the JS divergences of counts of all rings; “JS. number of n-sized rings” denotes the JS divergences of counts of n-sized rings; and “Number of intersecting rings” denotes the number of rings observed in the top-10 frequent rings of both generated and real molecules. “↑” represents higher values are better, and “↓” represents lower values are better.

[0254] Table 11 shows that DiffSMol+p and DiffSMol+s+p achieved higher or at least comparable performance with all base-lines in most quality metrics. Specifically, for stability, Table 11 shows that DiffSMol+p and DiffSMol+s+p either achieved comparable performance or slightly fell behind the baselines in atom stability and molecule stability. Particularly, DiffSMol+p achieved the second-best performance in atom stability and only slightly underperformed the best baseline TargetDiff (0.934 vs 0.949). DiffSMol+p also achieved the best performance in molecule stability. DiffSMol+s+p underperformed DiffSMol+p in both atom stability and molecule stability but still outperformed Pocket2Mol and AR in atom stability and Pocket2Mol, TargetDiff, and DecompDiff in molecule stability. These results demonstrated the effectiveness of DiffSMol+p and DiffSMol+s+p in generating binding molecules with high stability.

[0255] In terms of 3D structures, overall, both DiffSMol+p and DiffSMol+s+p achieved similar performance compared to the baselines. Particularly, DiffSMol+p and DiffSMol+s+p achieved the best (0.274) and second-best performance (0.278) in terms of JS. bond lengths. For JS. dihedral angles, DiffSMol+p and DiffSMol+s+p also outperformed the best baseline DecompDiff by 8.9% and 8.4%, respectively. In terms of RMSD, DiffSMol+p and DiffSMol+s+p underperformed the best base-line Pocket2Mol and achieved very comparable performance (0.663 for DiffSMol+p and 0.675 for DiffSMol+s+p) with the second-best baseline AR (0.656). For JS. bond angles, both DiffSMol+p and DiffSMol+s+p again underperformed the best baseline DecompDiff and achieved the second and fourth performance among all the methods. The overall comparable performance of DiffSMol+p and DiffSMol+s+p against the PMG methods in these metrics demonstrated their ability to generate molecules with realistic 3D structures.

[0256] For 2D structures, both DiffSMol+p and DiffSMol+s+p demonstrated comparable performance with the PMG baselines. Specifically, for JS. basic bond types, DiffSMol+p and DiffSMol+s+p achieved the second and third performance (0.061 and 0.080), and only slightly underperformed the best baseline Pocket2Mol (0.055). For JS. number of rings, DiffSMol+p and DiffSMol+s+p also achieved the best and second performance among all the methods. Similarly, in terms of the number of intersecting rings, DiffSMol+s+p again achieved the bestperformance, while DiffSMol+p slightly underperformed DiffSMol+p by just one ring (6 vs 7). DiffSMol+p and DiffSMol+s+p underperformed the best baseline TargetDiff in JS. number of bonds per atom. For JS. number of n-sized rings, DiffSMol+p and DiffSMol+s+p also underperformed the best baseline Pocket2Mol and achieved the second and third performance. These results highlight that compared to the PMG methods, DiffSMol+p and DiffSMol+s+p had similar performance in generating molecules with realistic 2D structures.

[0257] Case studies for Targets:

[0258] DiffSMol may generate binding molecules that serve as promising drug candidates. To demonstrate this ability, the study highlighted three molecules generated by DiffSMol+s+p for two drug targets, cyclin-dependent kinase 6 (CDK6) and neprilysin (NEP). CDK6 plays a critical role in cell proliferation by regulating cell cycle progression. Inhibiting CDK6 may disrupt the abnormal cell cycles of cancer cells, making it a valuable therapeutic target for cancers

[0039] . NEP may help prevent amyloid plaque formation associated with Alzheimer’s disease, making it an important target for therapies to potentially slow the disease’s progression

[0040] . The study used an existing protein-ligand complex for CDK6 (e.g., PDBID:4AUA), and an existing protein-ligand complex for NEP (e.g., PDBID:1R1H), respectively, from Protein Data Bank (PDB)

[0041] and generated 1,000 molecules for each of the targets. Both complexes were included in the test set for PMG. For each target, the study prioritized the best molecule based on their Vina S, QED

[0016] , SA

[0035] , toxicity scores calculated by ICM

[0042] and absorption, distribution, metabolism, excretion, and toxicity (ADMET) metrics calculated by admetSAR 2.0

[0043] .

[0259] Figs.7A – 7C show drug candidate (i.e., generated molecule) NL-001 for CDK6, Figs.8A – 8C show drug candidate NL-002 for CDK6, and Figs.9A – 9C show drug candidate NL-003 for NEP. The 3D structures of these molecules and their binding poses were generated by DiffSMol+s+p without any post-processing such as energy minimization or docking. All the generated 3D structures were validated to be realistic by their close match, with an RMSD of less than 2Å, to minimized structures from the Cartesian MMFF minimization algorithm

[0044] .

[0260] Table 12 shows drug properties (e.g., Vina S, Vina M, Vina D, QED, SA, etc.) of the generated molecules NL-001, NL-002, and NL-003.Table 12. Drug properties of generated molecules

[0261] Generated molecules NL-001 and NL-002 for CDK6: Figs.7A – 7C show a generated molecule, referred to as NL-001, for CDK6 and its structures and binding interactions with the CDK6 binding pocket. Specifically, Fig.7A presents a molecular graph of the molecule. As shown in Fig.7C, molecule NL-001 fit well within the CDK binding pocket (green pocket) and formed hydrophobic interactions with the surrounding residues, such as T107, D104, L152, A162, etc. The interactions were further illustrated in Fig.7B. This effective binding resulted in a better Vina S of -6.817 kcal / mol (shown in Table 12) for the generated molecule NL-001, compared to the Vina S (0.736 kcal / mol, not shown) of the 4AU ligand in the complex 4AUA. Local minimization and docking refinement may further improve the Vina M score of NL-001 to -7.251 kcal / mol and the Vina D score of NL-001 to -8.319 kcal / mol asshown in Table 12, respectively, outperforming the 4AU ligand (-5.939 kcal / mol for Vina M and -7.592 kcal / mol for Vina D) (not shown).

[0262] In addition to the binding activity, the molecule NL-001 in Figs.7A – 7C also demonstrated favorable properties that were important for drug development, including drug- likeness, synthesizability, toxicity, and ADMET profiles. The molecule NL-001met the Lipinski rule of five criteria

[0017] , with a QED score of 0.834 (shown in Table 12), higher than that of 4AU ligand (0.773, not shown). The molecule NL-001’s synthetic accessibility (SA) score of 0.720 (shown in Table 12) suggested favorable synthesizability. The molecule NL-001 also had a low toxicity score (0.236) as shown in Table 12. To fully evaluate its potential as a drug candidate, the study compared its ADMET profile with those of three FDA-approved CDK6 inhibitors, including Abemaciclib

[0045] , Palbociclib

[0046] , and Ribociclib

[0047] . The results showed that the molecule NL-001had comparable or even better ADMET properties in metrics crucial for cancer drug development, compared to those approved drugs. For example, same as the approved drugs, the molecule NL-001was predicted to be negative for carcinogenicity

[0048] and nephrotoxicity

[0049] . Notably, the molecule NL-001 had a higher score than all the approved drugs in plasma protein binding (not shown), indicating its capacity to be distributed throughout the body and reach the target site.

[0263] Figs.8A – 8C present another drug candidate for CDK6 generated by DiffSMol, referred to as NL-002. Specifically, Fig.8A presents a molecular graph of the molecule. As shown in Fig.8C, molecule NL-002 fit well within the CDK binding pocket (green pocket) and formed hydrophobic interactions with the surrounding residues, such as V101, D102, L152, A162, etc. The interactions were further illustrated in Fig.8B.

[0264] The molecule NL-002 had similar properties to NL-001, with a Vina S score of - 6.970 kcal / mol, a Vina M score of -7.605 kcal / mol, and a Vina D score of -8.986 kcal / mol as shown in Table 12, showing its strong binding affinity to CDK6. Notably, NL-002 had a low toxicity score (0.000) and did not have any known toxicity-inducing functional groups detected as shown in Table 12

[0042] . NL-002 also had a similar ADMET profile as NL-001, suggesting it may be another strong drug candidate for CDK6.

[0265] Generated molecule NL-003 for NEP: Figs.9A – 9C shows the generated molecule, referred to NL-003, for NEP. Specifically, Fig.9A presents a molecular graph of the molecule NL-003. Fig.9C shows how the molecule NL-003 bound to the NEP ligand binding pocket through hydrogen bonds with residues W693 and E584 and hydrophobic interactions. Such interactions were further illustrated in Fig.9B. This resulted in a lower Vina S (-11.953 kcal / mol, in Table 12) of this molecule NL-003 than that of the BIR ligand in complex 1R1H (-9.399 kcal / mol, not shown). Through local minimization and docking refinement, the molecule NL-003 yielded lower Vina M (-12.165 kcal / mol, in Table 12) and Vina D (-12.308 kcal / mol, in Table 12) than the Vina M (-9.505 kcal / mol, not shown) and Vina D (-9.561 kcal / mol, not shown) of BIR ligand.

[0266] The molecule NL-003 in Figs.9A – 9C also had favorable properties in terms of drug-likeness, synthesizability, toxicity, and ADMET profiles. Particularly, the molecule NL- 003 met Lipinski’s rule of five and achieved a QED score of 0.772 as shown in Table 12, which was substantially higher than that of BIR ligand (0.463, not shown). NL-003 also demonstrated a favorable SA score of 0.570 for synthesizability as shown in Table 12. The molecule NL-003 was also predicted to be non-toxic and did not have any known toxicity-inducing functional groups detected as shown in Table 12

[0042] . It also had a promising ADMET profile comparable to those of three approved drugs, Donepezil, Galantamine, and Rivastigmine, for Alzheimer’s disease

[0050] , specifically in metrics crucial for Alzheimer’s disease drug development. For example, the molecule NL-003 was predicted to be permeable to the blood-brain barrier that was essential for treating Alzheimer’s disease

[0051] and negative for carcinogenicity

[0048] , same as the approved drugs.

[0267] All three molecules NL-001, NL-002, and NL-003 had high binding affinities in terms of Vina S, Vina M and Vina D, and favorable QED and SA values. In addition, all of them meet the Lipinski’s rule of five criteria [4]. In terms of physicochemical properties, all these properties of NL-001, NL-002 and NL-003, including number of rotatable bonds, molecule weight, LogP value, number of hydrogen bond doners and acceptors, and molecule charges, fall within the desired range of drug molecules. This indicated that these molecules may potentially have good solubility and membrane permeability, essential qualities for effective drug absorption.

[0268] The generated molecules NL-001, NL-002, and NL-003 also demonstrated promising safety profiles based on the predictions from ICM [5]. In terms of drug-induced liver injury prediction scores, all three molecules had low scores (0.188 to 0.376) as shown in Table 12, indicating a minimal risk of hepatotoxicity. In Table 12, NL-001 and NL-002 fell under ‘Ambiguous / Less concern’ for liver injury, while NL-003 was categorized under ’No concern’ for liver injury. Moreover, all three molecules had low toxicity scores (0.000 to 0.236) as shown in Table 12. NL-002 and NL-003 did not have any known toxicity-inducing functional groups as shown in Table 12. NL-001 and NL-003 were also predicted not to include any known bad groups that lead to inappropriate features. These attributes highlighted the potential of NL-001, NL-002, and NL-003 as promising treatments for cancers and Alzheimer’s disease.

[0269] Comparison on absorption, distribution, metabolism, excretion, and toxicity (ADMET) profiles between NL-001, NL-002, and NL-003 and approved drugs: Fig.10A shows a table comparing the ADMET profiles (e.g., Ames mutagenesis, Acute oral toxicity, Eye corrosion, etc.) among NL-001, NL-002, and approved drugs (e.g., Abemaciclib, Palbociclib, and Ribociclib) targeting CDK6. In Fig.10A, “†” indicates crucial properties where a positive outcome (“+”) is desired; for acute oral toxicity (c), a higher category (e.g., “III”) is desired; and for carcinogenicity (trinary), “Non-required” is desired. In Fig.10A, “ ” indicates crucial properties where a negative result (“-”) is desired; for plasma protein binding, a lower value is desired; and for water solubility, values higher than -4 are desired [9].

[0270] As shown in Fig.10A, the generated molecules, NL-001 and NL-002, exhibited comparable ADMET profiles with those of the approved CDK6 inhibitors (i.e., drugs). Both molecules NL-001 and NL-002 demonstrated good potential in most crucial properties, including Ames mutagenesis, favorable oral toxicity, carcinogenicity, estrogen receptor binding, high intestinal absorption and favorable oral bioavailability. Although the generated molecules were predicted as positive in hepatotoxicity and mitochondrial toxicity, all the approved drugs were also predicted as positive in these two toxicity. This result suggested that these issues might stem from the limited prediction accuracy rather than being specific to the generated molecules. Notably, NL-001 displayed a potentially better plasma protein binding score compared to other molecules, which may improve its distribution within the body. Overall, these results indicated that NL-001 and NL-002 may be promising candidates for further drug development.

[0271] Fig.10B shows a table comparing the ADMET profiles (e.g., Ames mutagenesis, Acute oral toxicity, Eye corrosion, etc.) among NL-003 targeting NEP and approved drugs (e.g., Donepezil, Galantamine, and Rivastigmine) for Alzheimer’s disease. In Fig.10B, “†” indicates crucial properties where a positive outcome (“+”) is desired; for acute oral toxicity (c), a higher category (e.g., “III”) is desired; and for carcinogenicity (trinary), “Non-required” is desired. In Fig.10B, “ ” indicates crucial properties where a negative result (“-”) is desired; for plasma protein binding, a lower value is desired; and for water solubility, values higher than -4 are desired [9].

[0272] Generally, NL-003 exhibited a comparable ADMET profile with the three approved drugs (e.g., Donepezil, Galantamine, and Rivastigmine). Notably, same as other approved drugs, NL-003 was predicted to be able to penetrate the blood brain barrier, a crucial property for Alzheimer’s disease. In addition, NL-003 demonstrated a promising safety profile in terms ofAmes mutagenesis, favorable oral toxicity, carcinogenicity, estrogen receptor binding, high intestinal absorption, nephrotoxicity and so on. These results suggested that NL-003 may be promising candidates for the drug development of Alzheimer’s disease.

[0273] Discussion:

[0274] Related Work: A variety of deep generative models have been developed to generate molecules using various molecule representations, including generating SMILES string representations

[0019] , or 2D molecular graph representations

[0011] ,

[0020] . However, these representations fall short in capturing the 3D structures of molecules, which are critical for understanding their biological activities and certain properties. Recent studies have developed 3D molecule generation methods. For example, an equivariant diffusion model was developed employing an equivariant network to jointly predict both the positions and features of all atoms

[0021] . In 3D molecule generation, two types of methods have been developed. Motivated by ligand-based drug design (LBDD), the first type of methods, referred to as shape-conditioned molecule generation (SMG) methods, generates molecules with similar shapes to condition molecules (e.g., ligands). The second type of methods, referred to as pocket-conditioned molecule generation (PMG) methods, is motivated by structure-based drug design (SBDD) and generates binding molecules to a target protein pocket.

[0275] Previous SMG methods

[0022] ,

[0023] generally leverage shapes as conditions and use generative models such as variational autoencoders (VAE) [7] to generate potentially binding molecules. Among SMG methods, Adams and Coley

[0023] developed SQUID, which consists of a fragment-based generative model and a rotatable-bond scoring model. The fragment-based generative model generates molecules using VAE and sequentially decodes fragments based on the shapes of condition molecules (e.g., ligands), while the rotatable-bond scoring model adjusts the angles of rotatable bonds between fragments to adapt to the condition shapes. An encoder- decoder framework, referred to as Shape2Mol, which first encode 3D shapes of molecules into latent embeddings and then generate fragments sequentially based on these embeddings to build molecules. Previous studies

[0018] demonstrated the potential of diffusion models for generating binding molecules conditioned on shapes. By improving the shape-conditioned molecule prediction module (SMP), the study has significantly enhanced the performance of DiffSMol.

[0276] DiffSMol is fundamentally different from SQUID. SQUID, as a fragment-based method, generates molecules by sequentially adding fragments. When predicting the next fragments, however, SQUID fails to consider the effects of their various poses, and thus, may lead to inaccurate fragment predictions. Due to the sequential nature, the prediction errors may be accumulated and may substantially degrade the generation performance. Different fromSQUID, DiffSMol generates molecules by directly arranging atoms in the 3D space using diffusion models. This design explicitly considers the influence of varying 3D atom positions in the generation process, leading to effective generations. In addition, by using only fragments in a predefined library, SQUID may struggle to generate diverse molecules, while DiffSMol ensures superior diversity by allowing for the generation of any fragments. DiffSMol also captures the flexibility of bonding geometries in real 3D molecules by generating molecules with flexible bond lengths and angles. However, SQUID may only generate molecules with fixed bond lengths and angles, leading to the discrepancy in 3D structures between the generated molecules and real molecules.

[0277] DiffSMol is also different from Shape2Mol. DiffSMol is specifically designed to be equivariant under any rotations and translations of the shape condition, allowing for better sampling efficiency

[0024] . Conversely, Shape2Mol is not equivariant, and thus, suffers from limited training efficiency. In addition, different from DiffSMol, Shape2Mol is a fragment-based approach and may experience the same issues for SQUID.

[0278] For PMG, previous work [25–28] has been focused on directly utilizing protein pockets as a condition and generating molecules binding towards these pockets. These methods may be grouped into three categories: VAE-based, autoregressive model-based, and diffusion model-based. Among VAE-based methods, a conditional VAE model was developed

[0029] to generate atomic density grids based on the density grids of protein pockets. The generated atomic density grids are then converted to molecules. Several autoregressive models

[0025] ,

[0026] ,

[0030] also have been developed to generate binding molecules by sequentially adding atoms into the 3D space conditioned on protein pocket atoms. Particularly, an autoregressive model AR was developed

[0025] to estimate the probability density of atoms’ occurrences in the 3D space conditioned on protein pockets. AR sequentially adds atoms based on these estimations to construct molecules. AR was improved

[0026] into Pocket2Mol by incorporating a more efficient atom sampling strategy. Pocket2Mol determines the positions of newly added atoms by predicting their relative positions to previously added atoms. Diffusion models are also very popular in PMG. A conditional diffusion model TargetDiff was developed

[0027] to generate molecules based on protein pockets by sequentially denoising both continuous atom coordinates and categorical atom types in noisy molecules. The TargetDiff was further improved

[0028] into DecompDiff by utilizing data-dependent prior distributions over molecular arms and scaffolds. These priors are derived from either known ligands or protein pockets.

[0279] PMG methods require protein-ligand complex data for training. However, such data is expensive and thus highly limited. The sparse ground-truth binding ligands confine thesemethods in exploring a wide range of molecules with desired properties. In contrast, DiffSMol may learn from rich molecule data, improving its ability to generate effective and novel binding molecules.

[0280] Integrating protein targets for binding molecule generation: For PMG, DiffSMol with pocket guidance (DiffSMol+p and DiffSMol+s+p) may effectively generate molecules with high binding affinities toward protein targets. The pocket guidance enabled DiffSMol+p and DiffSMol+s+p to consider the geometric information of protein binding pockets when generating binding molecules. In addition to geometric information, incorporating other information about protein pockets may further enable molecules generated in high quality. For example, the physicochemical properties of amino acid sequences within the binding pockets, such as polarity, electrostatics, and hydrophobicity, may affect the strength of interactions between proteins and molecules

[0052] . Therefore, a generative model considering these properties may produce molecules that better conformed to what was expected based on pharmaceutical chemistry, shortening their pathways to be induced into downstream tasks of drug development. Identifying and integrating essential properties of protein binding pockets into molecule generation may be an interesting yet challenging future research direction.

[0281] Multi-objective molecule generation: When developing a molecule into a drug, in addition to its binding affinity to the protein target, many other properties also need to be considered, such as drug-likeness, synthesizability, toxicity, metabolism, and cell permeability

[0053] . Similar to other molecule generation methods

[0012] , [25–27], DiffSMol primarily emphasized molecule binding affinities. Although DiffSMol’s generated binding molecules may have favorable ADMET profiles, properties beyond binding affinities and shapes may not specifically be optimized by design in the molecules out of DiffSMol. Consequently, the generated molecules may need to go through further optimization and refinement to gain other necessary properties in order to become viable drug candidates. Towards this end, a multi- objective genAI model that generates molecules exhibiting multiple properties simultaneously and satisfying multiple objectives (e.g., high drug-likeness, high synthesizability) may be demanded, which calls for a significant future research endeavor, though out of the scope of this study.

[0282] In vitro validation: In vitro experimental validation is necessary for accessing in silico generated molecules for further investigation into real-world therapeutic agents. Even when all the desired properties may be ideally incorporated into the generative process, which, by itself, may be nontrivial, these properties of the generated molecules remain unclear until they are experimentally confirmed. Meanwhile, other unanticipated properties may emerge dueto the unknown interactions between the molecules and the complex biological systems, which may also require rigorous in vitro testing. Despite its crucial importance, systematic in vitro validation for genAI generated molecules remains challenging

[0054] . This process would start from effective sampling or prioritization of generated molecules to identify a feasible and manageable subset for in vitro experiments. Then, determining and executing viable synthesis reactions to make those molecules, if they do not exist, may also pose substantial difficulties

[0055] .

[0283] Conclusions: The exemplary DiffSMol method generates binding molecules with realistic 3D structures based on the shapes of known ligands. DiffSMol utilizes pre-trained shape embeddings and a customized diffusion model for binding molecule generation. To better resemble the known ligand shapes, DiffSMol also modifies the generated 3D molecules iteratively under the guidance of the ligand shapes. Additionally, DiffSMol may leverage the geometric information of protein binding pockets and tailor the generated molecules toward optimal binding affinities. Experimental results demonstrated that DiffSMol outperformed shape-conditioned molecule generation (SMG) methods in generating molecules with highly similar shapes to known ligands, while incorporating shape guidance further boosts this performance. When compared to pocket-conditioned molecule generation (PMG) methods, DiffSMol with pocket guidance also achieves exceptional performance in generating molecules with high binding affinities. The case studies involving two critical drug targets showed that DiffSMol may generate binding molecules with desirable drug properties. EXAMPLE 2: ADVANCED SHAPE-CONDITIONED DIFFUSION-BASED MODELS (mDiffSMol)

[0284] The exemplary mDiffSMol method generates molecules resembling the shapes of given ligands (i.e., ligand-conditioned) and thus binding to the ligands’ targets, or binding to given pockets (i.e., pocket-conditioned), or both. The exemplary mDiffSMol is aphoristic conditional diffusion model for both LBDD and SBDD that better ensures conformity with the conditions via in-depth integration of conditions through-out every step and different levels of the generation process. Conditional guidance is also implemented in the exemplary mDiffSMol to further strengthen the conformity during inference. mDiffSMol potentially generates more realistic and lifelike molecules due to comprehensive 3D geometry learning. Meanwhile, the exemplary mDiffSMol consistently guarantees SE(3) equivariance.

[0285] Fig.11 presents the overview of mDiffSMol, which features four key modules: (a) Equivariant Condition Representation Pre-training (ECRPT), which comprises innovative, self- supervised formulations and optimizations to learn equivariant representations for conditions,and a novel joint contrastive fine-tuning strategy to further improve the representations learning; (b) Forward Diffusion Process (CDMG-f), which incrementally adds noises to the molecules; (c) Backward Generative Process (CDMG-b), which transforms random noise into new molecules. The CDMG-b process comprises a conditional equivariant 3D geometric convolutional neural network (CEGCNN) that operates on the geometric structures of noisy molecules. By deeply integrating ligand and / or pocket conditions within each layer, CEGCNN leverages local-global geometric information of the noisy molecules, as well as the conditions, to precisely determine the structures of the generated molecules; and (d) Conditional guidance (CDMG-g), which comprises guiding schemes to direct generation towards better condition conformity. The theory of the exemplary mDiffSMol method is described above. EXAMPLE 3: SHAPE-GUIDED DIFFUSION-BASED (SHAPEMOL)

[0286] The exemplary ShapeMol method consists of an equivariant shape embedding (SE) module that maps 3D molecular surface shapes to latent embeddings, and an equivariant diffusion model (DIFF) that generates 3D molecules conditioned on these embeddings.

[0287] Fig.13 presents the overview of the ShapeMol method, which employs point cloud construction, shape embedding (SE) module, and diffusion module (DIFF). As shown in Fig.13, the SE module comprises a shape embedding encoder (SE-enc) and a shape embedding decoder (SE-dec). Additionally, the DIFF module employs a forward diffusion process (DIFF-forward) and a backward generative process (DIFF-backward). The theory of the exemplary ShapeMol method is described above. EXPERIMENT 2:

[0288] The following study employs the generative AI method (e.g., ShapeMol) to generate molecules in 3D that generates molecules that retain 3D molecular shapes similar to the given shape condition.

[0289] Data:

[0290] Following SQUID [2’’], the study used molecules in the MOSES dataset [22’’], with their 3D conformers calculated by RDKit [16’’]. The study used the same training and test split as in SQUID. SQUID further modified the generated conformers into artificial ones, by adjusting acyclic bond distances to their empirical means and fixing acyclic bond angles using heuristic rules. Unlike SQUID, the study did not make any additional adjustments to the calculated 3D conformers, as ShapeMol was designed with sufficient flexibility to accept any 3D conformers as input and generate 3D molecules without restrictions on fixed bond lengths or angles. Limited by the predefined fragment library, SQUID also removed molecules withfragments not present in its fragment library. In contrast, the study kept all the molecules, as ShapeMol was not based on fragments. The training dataset contained 1,593,653 molecules, out of which a random set of 1,000 molecules was selected for validation. Both the ShapeMol-enc (i.e., SE-enc) and DIFF models were trained using this training set.1,000 test molecules (i.e., conditions) as used in SQUID were used to test ShapeMol.

[0291] Baselines:

[0292] The study compared ShapeMol and ShapeMol+g (i.e., ShapeMol with guidance) with the state-of-the-art baseline SQUID and a virtual screening method over the training dataset, denoted as VS. SQUID was the only generative baseline that generated 3D molecules conditioned on molecule shapes. SQUID consisted of a fragment-based generative model based on variational autoencoder that sequentially decoded fragments from molecule latent embeddings and shape embeddings, and a rotatable bond scoring framework that adjusted the angles of rotatable bonds between fragments to maximize the 3D shape similarity with the condition molecule. VS aimed to sift through the training set to identify molecules with high shape similarities with the condition molecule. For SQUID, the study assessed two interpolation levels, λ = 0.3 and 1.0 (prior) [2’’] For SQUID, ShapeMol and ShapeMol+g, the study generated 50 molecules for each testing molecule (i.e., condition) as the candidates for evaluation. For VS, the study randomly sampled 500 training molecules for each testing molecule and considered the top-50 molecules with the highest shape similarities as candidates for evaluation.

[0293] Evaluation Metrics:

[0294] The study used shape similarity Sims(sx, sy) and molecular graph similarity Simg(Mx, My) to measure the generated new molecules My with respective to the condition Mx. Higher Simsand meanwhile lower Simgindicated better model performance. The study also measured the diversity (div) of the generated molecules, calculated as 1 minus average pair-wise Simgamong all generated molecules. Higher div indicated better performance.

[0295] The study calculated the shape similarity Sims(sx, sy) via the overlap volumes between two aligned molecules [2’’]. Each molecule candidate Myfor evaluation was aligned with the condition molecule Mx by the ShaEP tool [34’’]. For the molecular graph similarity Simg(Mx, My), the study used the Tanimoto similarity over Morgan fingerprints between Mxand Mycalculated by RDKit [16’’].

[0296] Preliminary results:

[0297] In a previous study [40’], a ligand-condition diffusion model ShapeMol was built, which uses a ligand condition embedding learned from its point cloud (via recovering signed distances of randomly sampled query points), an equivariant graph neural network [41’] topredict atom positions, and an invariant graph neural network [41’] to predict atom features. ShapeMol+g (i.e., ShapeMol with guidance) uses a k-nearest neighbor-based approach to guide generation by ligand conditions.

[0298] The results in Table 13 demonstrate that, compared to the state-of-the-art method SQUID [13’], the preliminary model ShapeMol+g is able to generate new molecules that are drug-like (QED > 0.542), more similar to the condition ligand (Sims) in 3D shapes. Also, a simple guidance is able to improve condition conformity (ShapeMol+g vs ShapeMol on Sims). Table 13. Results on ligand-conditioned molecule generation

[0299] As shown in Table 13, “#v%” denotes the percentage of valid molecules; “#u%” denotes the percentage of unique molecules; “QED” denotes the average druglikeness; “Sims / Simg” denotes the average of shape / graph similarities between the condition molecules and generated molecules; and “Divd” denotes molecule diversity.

[0300] Figs.12A – 12C present an example of generated molecules. ShapeMol is able to generate 3D molecules (Fig.12C) more similar to the condition ligand (Fig.12A) compared to SQUID (Fig.12B). The results are promising, demonstrating the effectiveness of conditional diffusion model in generating new molecules for LBDD. The exemplary mDiffSMol includes conditional diffusion for both LBDD and SBDD, which provides powerful representation learning for conditions, sophisticated and powerful integration of conditions during generation, and enhanced guidance.

[0301] Performance comparison:

[0302] Overall comparison: Table 14 presents the overall comparison of shape-conditioned molecule generation among VS, SQUID, ShapeMol and ShapeMol+g. Table 14. Overall comparison on shape-conditioned molecule generation

[0303] As shown in Table 14, “#c%" denotes the percentage of connected molecules; “#u%” denotes the percentage of unique molecules; “QED” denotes the average drug-likeness of generated molecules; “avgSims / avgSimg”: the average of shape or graph similarities between the condition molecules and generated molecules; “std" denotes the standard deviation; “maxSims” denotes the maximum of shape similarities between the condition molecules and generated molecules; “maxSimg” denotes the graph similarities between the condition molecules and the molecules with the maximum shape similarities; and “div” denotes the diversity among the generated molecules.

[0304] As shown in Table 14, ShapeMol+g achieved the highest average shape similarity 0.746±0.036, with 2.3% improvement from the best base-line VS (0.729±0.039), although at the cost of a slightly higher graph similarity (0.241±0.050 in ShapeMol+g vs 0.226±0.038 in VS). This indicated that ShapeMol+g could generate molecules that align more closely with the shape conditions than those in the dataset. Furthermore, ShapeMol+g achieved the second-best performance in maximum shape similarity (maxSims) at 0.852±0.034 among all the methods. While ShapeMol underperformed the best baseline (0.904±0.070 for SQUID with λ=0.3) on this metric, ShapeMol+g achieved substantially lower maximum graph similarity maxSimgof 0.247±0.068 compared with the best baseline (0.549±0.243). This highlighted the ability of ShapeMol+g in generating molecules that resemble the shape conditions. ShapeMol+g also achieved the lowest standard deviation values on both the average and maximum shape similarities (0.036 and 0.034, respectively) among all the methods, further demonstrating its ability to consistently generate molecules with high shape similarities.

[0305] As shown in Table 14, ShapeMol+g performed substantially better than ShapeMol on 3D shape similarity metrics (e.g., 0.746±0.036 vs 0.689±0.044 on avgSims). The superior performance of ShapeMol+g highlighted the importance of shape guidance in the generative process. Although ShapeMol underperformed ShapeMol+g, ShapeMol still outperformed SQUID with λ=1.0 in terms of the avgSims(i.e., 0.689±0.044 vs 0.670±0.069).

[0306] In terms of the quality of generated molecules, 98.7% of molecules from ShapeMol+g and 98.8% from ShapeMol were connected, and every connected molecule wasunique. SQUID with λ values of 0.3 or 1.0 ensures the 100% connectivity among generated molecules by sequentially attaching fragments. However, out of these connected molecules, 94.2% and 95.0% were unique for SQUID with λ value of 0.3 or 1.0, respectively. In terms of the drug-likeness (QED), both ShapeMol+g and ShapeMol achieved QED values (e.g., 0.749 for ShapeMol+g) close to those of SQUID with λ as 0.3 and 1.0 (e.g., 0.760 for SQUID with λ=0.3). All the generative methods produced slightly inferior QED values to real molecules (0.795 for VS). In terms of diversity, ShapeMol+g and ShapeMol achieved higher diversity values (e.g., 0.703±0.053 for ShapeMol+g) than SQUID with λ=1.0 (0.677±0.065), though slightly lower than SQUID with λ=0.3 and VS. Overall, ShapeMol and ShapeMol+g were able to generate connected, unique and diverse molecules with good drug-likeness scores.

[0307] Unlike SQUID, which neglected distorted bonding geometries in real molecules and limited itself to generating molecules with fixed bond lengths and angles, both ShapeMol and ShapeMol+g were able to generate molecules without such limitations. Given the superior performance of ShapeMol+g in shape-conditioned molecule generation, ShapeMol serves as a tool for ligand-based drug design.

[0308] Comparison of diffusion weighting schemes: While previous methods [20’’] applied uniform weights on different diffusion steps, ShapeMol used different weights (i.e., ^^^^^^^^^^^^in Eq. 17). The study demonstrated the effectiveness of this new weighting scheme by training two DIFF modules with the varying step weights ^^^^^^^^^^^^(with δ = 10 in Eq.17) and uniform weights, respectively, while fixing all the other hyper-parameters in ShapeMol and ShapeMol+g.

[0309] Table 15 presents the performance comparison between ShapeMol and ShapeMol+g. Table 15. Comparison of diffusion weighting schemes between ShapeMol and ShapeMol+g

[0310] As shown in Table 15, “weights" denotes different weighting schemes; “JS divergence of bond” denotes the Jensen-Shannon (JS) divergence of bond length among all the bond types (“bond") between real molecules and generated molecules; and “JS divergence of C- C” denotes the Jensen-Shannon (JS) divergence of the carbon-carbon single bonds (“C-C") between real molecules and generated molecules.

[0311] The results in Table 15 showed that the different weights on different steps substantially improved the quality of the generated molecules. Specifically, ShapeMol with different weights ensured higher molecular connectivity and drug-likeness than that with uniform weights (98.8% vs 89.4% for connectivity; 0.748 vs 0.660 for QED). ShapeMol with different weights also produced molecules with bond length distributions closer to those of real molecules (i.e., lower Jensen-Shannon divergence), for example, the Jensen-Shannon (JS) divergence of bond lengths between real and generated molecules decreased from 0.115 to 0.095 when different weights were applied. The same trend may be observed for ShapeMol+g, for which the different weights also improved the generated molecule qualities. Since ^^^^^^^^^^^^increased as the noise level in the data decreased , the results in Table 15 demonstrated the effectiveness of the new weighting scheme in promoting new molecules generated more similarly to real ones when the noise level in data was small.

[0312] Parameter study: A parameter study was conducted to evaluate the impact of the distance threshold γ (Eq.42) and the step threshold S (Eq.42) in the shape guidance. Particularly, using the same trained DIFF module, the study sampled molecules with different values of γ and S and present the results in Table 16. Table 16. Parameter study in shape guidance

[0313] As shown in Table 16, “γ” denotes distance threshold in shape guidance; “S” denotes step threshold in shape guidance; “JS. bond” denotes the JS divergence of bond length distributions of all the bond types between real molecules and generated molecules; and All the others are identical to those in Table 15.

[0314] As shown in Table 16, the average shape similarities avgSims and maximum shape similarities maxSims consistently decreased as γ and S increased. For example, when S = 50, avgSimsand maxSimsdecreased from 0.794 to 0.763 and 0.890 to 0.861, respectively, as γ increased from 0.2 to 0.6. Similarly, when γ = 0.2, avgSimsand maxSimsdecreased from 0.794 to 0.746 and 0.890 to 0.852, respectively, as S increased from 50 to 300. Larger γ and S indicated stronger shape guidance in ShapeMol+g. These results demonstrated that stronger shape guidance in ShapeMol+g may effectively induce higher shape similarities between the given molecule and generated molecules.

[0315] As shown in Table 3, incorporating shape guidance enabled a trade-off between the quality of the generated molecules (QED), and the shape similarities (avgSimsand maxSims) between the given molecule and the generated ones. For example, when γ = 0.2, QED increased from 0.630 to 0.749 and avgSims decreased from 0.794 to 0.746 as S increased from 50 to 300. These results indicated the effects of γ and S in guiding molecule generation conditioned on given shapes.

[0316] Case study: Figs.14B – 14D show three generated molecules from three methods (e.g., VS, SQUID, ShapeMol) given the same condition molecule shown in Fig.14A. As shown in Fig.14D, the molecule generated by ShapeMol has higher shape similarity (0.835) with the condition molecule than those from the baseline methods (0.759 for VS in Fig.14B and 0.749 for SQUID in Fig.14C). Particularly, the molecule from ShapeMol has the surface shape most similar to that of the condition molecule. All three molecules in Figs.14B – 14D have low graph similarities with the condition molecule in Fig.14A and higher QED scores than the condition molecule in Fig.14A. This example shows the ability of ShapeMol to generate molecules that are more similar in 3D shape to condition molecules than those from baseline methods.

[0317] Discussion:

[0318] The study developed a generative model ShapeMol to generate 3D molecules conditioned on the 3D shape of given molecules. The exemplary ShapeMol utilized a pre-trained equivariant shape encoder to generate equivariant embeddings for 3D shapes of given molecules. Conditioned on the embeddings, ShapeMol learned an equivariant diffusion model to generate novel molecules. To improve the shape similarities between the given molecule and the generated ones, the study developed ShapeMol+g, which incorporated shape guidance to push the generated atom positions to the shape of the given molecule.

[0319] The study compared ShapeMol and ShapeMol+g against state-of-the-art baseline methods. Experimental results demonstrated that ShapeMol and ShapeMol+g generates molecules with higher shape similarities, and competitive qualities compared to the base-linemethods. In future studies, generating 3D molecules jointly conditioned on the shape and the electro-static may be explored, considering that the electrostatic of molecules may also determine the binding activities of molecules. Configuration of Certain Implementations

[0320] The construction and arrangement of the systems and methods as shown in the various implementations are illustrative only. Although only a few implementations have been described in detail in this disclosure, many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes, and proportions of the various elements, values of parameters, mounting arrangements, use of materials, colors, orientations, etc.). For example, the position of elements may be reversed or otherwise varied, and the nature or number of discrete elements or positions may be altered or varied. Accordingly, all such modifications are intended to be included within the scope of the present disclosure. The order or sequence of any process or method steps may be varied or re-sequenced according to alternative implementations. Other substitutions, modifications, changes, and omissions may be made in the design, operating conditions, and arrangement of the implementations without departing from the scope of the present disclosure.

[0321] The present disclosure contemplates methods, systems, and program products on any machine-readable media for accomplishing various operations. The implementation of the present disclosure may be implemented using existing computer processors, or by a special purpose computer processor for an appropriate system, incorporated for this or another purpose, or by a hardwired system. Implementations within the scope of the present disclosure include program products including machine-readable media for carrying or having machine-executable instructions or data structures stored thereon. Such machine-readable media can be any available media that can be accessed by a general purpose or special purpose computer or other machine with a processor. By way of example, such machine-readable media can comprise RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to carry or store desired program code in the form of machine-executable instructions or data structures, and which can be accessed by a general purpose or special purpose computer or other machine with a processor.

[0322] When information is transferred or provided over a network or another communications connection (either hardwired, wireless, or a combination of hardwired or wireless) to a machine, the machine properly views the connection as a machine-readablemedium. Thus, any such connection is properly termed a machine-readable medium. Combinations of the above are also included within the scope of machine-readable media. Machine-executable instructions include, for example, instructions and data which cause a general-purpose computer, special purpose computer, or special purpose processing machines to perform a certain function or group of functions.

[0323] Although the figures show a specific order of method steps, the order of the steps may differ from what is depicted. Also, two or more steps may be performed concurrently or with partial concurrence. Such variation will depend on the software and hardware systems chosen and on designer choice. All such variations are within the scope of the disclosure. Likewise, software implementations could be accomplished with standard programming techniques with rule-based logic and other logic to accomplish the various connection steps, processing steps, comparison steps and decision steps.

[0324] Each and every feature described herein, and each and every combination of two or more of such features, is included within the scope of the present invention, provided that the features included in such a combination are not mutually inconsistent.

[0325] Although example embodiments of the disclosed technology are explained in detail herein, it is to be understood that other embodiments are contemplated. Accordingly, it is not intended that the disclosed technology be limited in its scope to the details of construction and arrangement of components set forth in the following description or illustrated in the drawings. The disclosed technology is capable of other embodiments and of being practiced or carried out in various ways.

[0326] It must also be noted that, as used in the specification and the appended claims, the singular forms “a,” “an” and “the” include plural referents unless the context clearly dictates otherwise. Ranges may be expressed herein as from “about” or “approximately” one particular value and / or to “about” or “approximately” another particular value. When such a range is expressed, other exemplary embodiments include from the one particular value and / or to the other particular value.

[0327] By “comprising” or “containing” or “including” is meant that at least the named compound, element, particle, or method step is present in the composition or article or method, but does not exclude the presence of other compounds, materials, particles, method steps, even if the other such compounds, material, particles, method steps have the same function as what is named.

[0328] Unless otherwise expressly stated, it is in no way intended that any method set forth herein be construed as requiring that its steps be performed in a specific order. Accordingly,where a method claim does not actually recite an order to be followed by its steps or it is not otherwise specifically stated in the claims or descriptions that the steps are to be limited to a specific order, it is no way intended that an order be inferred, in any respect. This holds for any possible non-express basis for interpretation, including: matters of logic with respect to arrangement of steps or operational flow; plain meaning derived from grammatical organization or punctuation; the number or type of embodiments described in the specification.

[0329] While the methods and systems have been described in connection with certain embodiments and specific examples, it is not intended that the scope be limited to the particular embodiments set forth, as the embodiments herein are intended in all respects to be illustrative rather than restrictive.

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Claims

CLAIMS What is claimed is:

1. A method of generating a 3D model of a small molecule comprising: generating a starting structure, wherein the starting structure is defined by atom positions and atom features; providing the starting structure to a trained conditional diffusion model; and generating, via the trained conditional diffusion model, the 3D model of a small molecule, wherein generating comprises: removing variance from the atom position and atom feature data of the starting structure in a backwards diffusion process to generate the 3D model of the small molecule, wherein constraints, based on a latent embedding of a target ligand (Hs) (i.e. condition) that is equivariant to transformations, are applied during the backward diffusion process.

2. The method of claim 1, wherein the latent embedding (Hs) of the target ligand is generated by: generating, using an autoencoder, the latent embedding of the target ligand from a point cloud derived from a molecular surface of the target ligand; and determining, by the autoencoder, a signed distance of a randomly sampled point from the point cloud of the target ligand, wherein the autoencoder comprises an encoder having vector neurons and a decoder comprising multilayer perceptrons.

3. The method of claim 1, wherein constraints are applied by: providing the latent embedding of the target ligand (Hs) and variance from the atom position and atom feature data to a geometric vector perceptron model (GVP, eq. 28); determining, by a first module, shape-aware scalar embeddings and shape-aware vector embeddings of atoms using the latent embedding of the target ligand and the starting structure; determining, by a second module, bond-type weighting factors of each pair of atoms of the starting structure;determining, by the geometric vector perceptron model, a scalar embedding and a vector embedding using the shape-aware scalar embeddings, the shape-aware vector embeddings, and the bond-type weighting factors; and estimating an atom type and position for each atom of the starting structure.

4. The method of claim 1, wherein the constraints are applied by: determining, by a first multi-layer graph neural network comprising comprises atom type attention layers, an atom type for each atom of the starting structure using the latent embedding of the target ligand; and determining, by a second multi-layer graph neural network comprising atom position attention layers, a position for each atom of the starting structure.

5. The method of claim 1, wherein the constraints are additionally based on a second latent embedding of a pocket of interest (Hp) that is equivariant to transformations; wherein the second latent embedding of the pocket of interest (Hp) is generated using at least an autoencoder configured to generate the latent embedding of a set of residues and atoms of the pocket of interest by masking off randomly selected atoms; wherein the autoencoder comprises an encoder comprising vector neurons; and wherein the latent embedding of the target ligand and the second latent embedding of the pocket of interest are modified (e.g., fine-tuned) relative to each other using a contrastive learning operation.

6. The method of claim 5, wherein the constraints are applied by: providing the latent embedding of the target ligand, the latent embedding of the pocket of interest and the starting structure to a molecule prediction model; determining, by a convolutional neural network (CNN), a geometric shift embedding and an atomic feature embedding using the latent embedding of the target ligand, the latent embedding of the pocket of interest and noisy data, wherein, at each layer of the CNN, geometric vector perceptrons are used; determining, by a first module, condition-aware geometric shift embeddings; determining, by a second module comprising, a condition-aware atomic feature embedding;repeating the determination of the geometric shift embedding and atomic feature embedding using the condition-aware geometric shift embedding and the condition-aware atomic feature embedding; and estimating an atom type and position for each atom of the starting structure.

7. The method of any one of claims 1-6, wherein the trained conditional diffusion model is trained by: receiving 3D models of known molecules; generating a shape latent embedding of each 3D model of known molecules, wherein a shape latent embedding is generated using at least an autoencoder configured to generate the latent embedding of the target ligand from a point cloud derived from a molecular surface of the target ligand; wherein the autoencoder comprises an encoder having vector neurons; wherein the autoencoder comprises a decoder comprising multilayer perceptrons, wherein the decoder determines a signed distance of a randomly sampled point from the point cloud of the target ligand; adding variance to atom position and atom feature data of the 3D models of known molecules in a forward diffusion process; removing variance from the atom position and atom feature data of the 3D models of known molecules in a backwards diffusion process, conditioned on the respective shape latent embeddings; comparing, using a loss function, a resulting atom position and atom feature data from the backwards diffusion process to the atom position and atom feature data of a respective 3D model of a known molecule; and adjusting weights of the backward diffusion process based on the comparison.

8. The method of claim 1, wherein the constraints are applied by: determining a distance of an atom of the starting structure to one or more atoms of a pocket of interest; and based on a determination that the atom of the starting structure is within a pre-defined distance to the one or more atoms of the pocket of interest, moving the atom of the starting structure to a position away from an atom of the one or more atoms of the pocket of interest by a given distance (e.g. pocket guidance).

9. The method of claim 1, wherein the constraints are applied by: determining a distance of an atom of the starting structure to one or more atoms of the target ligand; and based on a determination that the atom of the starting structure is outside a pre-defined distance from the target ligand, moving the atom of the starting structure to a position closer to an atom of the one or more atoms of the target ligand a given distance, wherein the constrained starting structure forms a shape more similar to the target ligand. (e.g. shape guidance) 10. The method of any one of claims 1-9, wherein the small molecule comprises a binding portion of an antibody-antigen, a binding portion of a protein, or a ligand.

11. A system having a processor and memory having instructions stored thereon, wherein execution of the instructions by the processor causes the processor to perform any one of the methods of claims 1-10.

12. A non-transitory computer readable medium having instructions stored thereon, wherein execution of the instructions by a processor causes the processor to perform any one of the methods of claims 1-10.

13. A method comprising: generating, via a trained conditional diffusion model, a 3D model of a small molecule conditioned on a shape latent embedding of a molecular shape of an input molecule to yield molecules with a similar shape to an input molecule, wherein the trained conditional diffusion model comprises: a 3D shape autoencoder that embeds the molecular shape of the input molecule into a shape latent embedding, and wherein the shape latent embeddings are equivariant to transformations; and a backward diffusion process and employs the trained conditional diffusion model to generate atom features and atom positions to form the 3D model of a small molecule, guided by the shape latent embedding.

14. The method of claim 13, wherein the 3D shape autoencoder is configured to learn latent embeddings of a molecular shape from a point cloud derived from a molecular surface of an input molecule, wherein an encoder of the 3D shape autoencoder comprises vector neurons and is configured to produce shape latent embeddings that are equivariant to transformations of the 3D model of a small molecule; and wherein the 3D shape autoencoder is trained to predict, via a decoder, if a randomly sampled point of the molecular shape is located within the point cloud or outside of the point cloud.

15. The method of claim 13, wherein the backward diffusion process within the trained conditional diffusion model comprises transformer-based layers to predict atom positions and atom types, wherein each layer includes an atom type attention layer and an atom position attention layer, wherein the atom type attention layer employs, at least, as inputs: atom type embeddings from previous layers, distances between atoms, neighboring atom type embeddings, and shape latent embeddings to generate an atom type output; and wherein the atom position attention layer employs, at least, as inputs, updated atom type embeddings, distance between atoms, relative position, neighboring atom type embeddings and shape latent embeddings to generate an atom position difference.

16. The method of claim 13, wherein the backward diffusion process comprises steps of: providing the shape latent embedding to a geometric vector perceptron model (GVP, eq. 28); determining, by a first module, shape-aware scalar embeddings and shape-aware vector embeddings of atoms using the shape latent embedding; determining, by a second module, bond-type weighting factors of each pair of atoms of the 3D model of a small molecule; determining, by the geometric vector perceptron model, a scalar embedding and a vector embedding using the shape-aware scalar embeddings, the shape-aware vector embeddings, and the bond-type weighting factors; and estimating an atom type and an atom position of the 3D model of a small molecule.

17. The method of claim 13, wherein the trained conditional diffusion model further comprises: a pocket of interest autoencoder that embeds the molecular shape of a pocket of interest into a latent embedding of the pocket of interest (Hp), wherein the latent embedding of the pocket of interest (Hp) is generated in part using an autoencoder, wherein the pocket of interest autoencoder is configured to learn the latent embedding of a set of residues and atoms of the pocket of interest by masking off randomly selected atoms; wherein the autoencoder comprises an encoder comprises vector neurons, and wherein the encoder is configured to produce latent embeddings that are equivariant to transformations of the pocket of interest; and wherein the shape latent embedding and the latent embedding of the pocket of interest (Hp) are fine-tuned relative to each other using contrastive learning; and wherein the backward diffusion process is guided by the shape latent embedding and the latent embedding of the pocket of interest (Hp).

18. The method of claim 17, wherein the backward diffusion process comprises steps of: determining, by a convolutional neural network (CNN), a geometric shift embedding and an atomic feature embedding using the shape latent embedding, latent embedding of the pocket of interest (Hp), and wherein, at each layer of the CNN, geometric vector perceptrons are used; determining, by a first module, condition-aware geometric shift embeddings; determining, by a second module comprising, a condition-aware atomic feature embedding; repeating the determination of the geometric shift embedding and atomic feature embedding using the condition-aware geometric shift and condition-aware atomic feature embedding; and estimating an atom type and position for each atom of the 3D model of a small molecule.

19. The method of claim 18, wherein the backward diffusion process further comprises steps of: determining a distance of an atom of the 3D model of a small molecule to an atom of the pocket of interest; andwherein, based on a determination that the atom from the 3D model of a small molecule is too close to an atom of the pocket of interest, moving the atom from the input molecule away from the atom of the pocket of interest a given distance. (e.g. pocket guidance) 20. The method of claim 18, wherein the backward diffusion process further comprises steps of: determining a distance of an atom from the 3D model of a small molecule to an atom of the input molecule, wherein, based on a determination that the atom of the 3D model of a small molecule is too far from the input molecule, moving the atom of the 3D model of a small molecule closer to the atom of the input molecule a given distance; and wherein the atom positions of the 3D model of a small molecule form a shape more similar to the input molecule. (e.g. shape guidance) 21. The method of any one of claim 13-20, wherein the 3D model of a small molecule comprises a binding portion of an antibody-antigen, a binding portion of a protein, or a ligand.

22. A system having a processor and memory having instructions stored thereon, wherein execution of the instructions by the processor causes the processor to perform any one of the methods of claims 13-21.

23. A non-transitory computer readable medium having instructions stored thereon, wherein execution of the instructions by a processor causes the processor to perform any one of the methods of claims 13-21.

24. A method of training a diffusion model for prediction of 3D models of small molecules, the method comprising: receiving 3D models of known molecules; determining a shape latent embedding of each 3D model of known molecules; adding variance to atom position and atom feature data of the 3D models of known molecules in a forward diffusion process;removing variance from the atom position and atom feature data of the 3D models of known molecules in a backwards diffusion process, conditioned on the respective shape latent embeddings; comparing, using a loss function, a resulting atom position and atom feature data from the backwards diffusion process to the atom position and atom feature data of a respective 3D model of a known molecule; and adjusting weights of the backward diffusion process based on the comparison.

25. The method of claim 24, wherein the conditional diffusion model comprises a 3D shape autoencoder that embeds a molecular shape of a respective 3D model of a known molecule into a latent embedding, and wherein the shape latent embedding is equivariant to transformations; wherein the 3D shape autoencoder is configured to learn latent embeddings of a molecular shape from a point cloud derived from a molecular surface of the respective 3D model of a known molecule; and wherein an encoder of the 3D shape autoencoder comprises vector neurons and is configured to produce shape latent embeddings that are equivariant to transformations of 3D molecules; wherein the 3D shape autoencoder is trained to predict, via a decoder, if a randomly sampled point within the respective 3D model of a known molecule is located within the point cloud or outside of the point cloud.

26. The method of claim 24, wherein the conditional diffusion model comprises transformer- based layers to predict atom positions and atom types, wherein each layer includes an atom type attention layer and an atom position attention layer, wherein the atom type attention layer employs, at least, as inputs: atom type embeddings from previous layers, distances between atoms, neighboring atom type embeddings, and shape latent embeddings to generate an atom type output; and wherein the atom position attention layer employs, at least, as inputs, updated atom type embeddings, distance between atoms, relative position, neighboring atom type embeddings and shape latent embeddings to generate an atom position difference.

27. The method of claim 24, wherein the backward diffusion process comprises steps of:providing the shape latent embedding to a geometric vector perceptron model (GVP, eq. 25); determining, by a first module, shape-aware scalar embeddings and shape-aware vector embeddings of atoms using the shape latent embedding; determining, by a second module, bond-type weighting factors of each pair of atoms; determining, by the geometric vector perceptron model, a scalar embedding and a vector embedding using the shape-aware scalar embeddings, the shape-aware vector embeddings, and the bond-type weighting factors; and estimating an atom type and an atom position.

28. The method of claim 24, wherein the conditional diffusion model further comprises: a 3D pocket of interest autoencoder that embeds a molecular shape of a pocket of interest into a latent embedding of the pocket of interest (Hp), wherein the latent embedding of the pocket of interest (Hp) is generated in part using an autoencoder, wherein the 3D pocket of interest autoencoder is configured to learn the latent embedding of residuals and atoms of the pocket of interest by masking off randomly selected atoms; wherein the autoencoder comprises an encoder comprises vector neurons, and wherein the encoder is configured to produce latent embeddings that are equivariant to transformations of the 3D pocket of interest; and wherein the shape latent embedding and the pocket of interest latent embedding are fine- tuned relative to each other using contrastive learning; and wherein the backward diffusion process is conditioned on the shape latent embedding and the pocket of interest latent embedding.

29. The method of claim 28, wherein the conditional diffusion model further comprises steps of: determining, by a convolutional neural network (CNN), a geometric shift embedding and an atomic feature embedding using the shape latent embedding, the pocket of interest latent embedding, and a set of noisy atomic data, wherein, at each layer of the CNN, geometric vector perceptrons are used; determining, by a first module, condition-aware geometric shift embeddings using; determining, by a second module comprising, a condition-aware atomic feature embedding;repeating the determination of the geometric shift embedding and atomic feature embedding using the condition-aware geometric shift and condition-aware atomic feature embedding; and estimating an atom type and position for each atom.

30. A system having a processor and memory having instructions stored thereon, wherein execution of the instructions by the processor causes the processor to perform any one of the methods of claims 24-29.

31. A non-transitory computer readable medium having instructions stored thereon, wherein execution of the instructions by a processor causes the processor to perform any one of the methods of claims 24-29.

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