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Structure-based Drug Design with Equivariant Diffusion Models

Arne Schneuing, Charles Harris, Yuanqi Du, Kieran Didi, Arian Jamasb, Ilia Igashov, Weitao Du, Carla Gomes, Tom Blundell, Pietro Lio, Max Welling, Michael Bronstein, Bruno Correia

arXiv:2210.13695v3q-bio.BMcs.LG

TL;DR

SBDD needs methods that can generate target-specific ligands beyond autoregressive de novo design and task-specific retraining. The paper introduces DiffSBDD, an SE(3)-equivariant conditional diffusion model, and reports faithful distribution learning plus flexible constrained and property-directed design through sampling changes.

  • Problem

    Existing SBDD methods commonly generate ligands autoregressively or require task-specific models and datasets for broader design problems.

  • Method

    DiffSBDD is an SE(3)-equivariant 3D-conditional diffusion model that generates ligands and binding conformations conditioned on protein pockets.

  • Results

    DiffSBDD captures molecular-property distributions more accurately than autoregressive baselines and supports constrained, partial, negative, and property-optimization designs through sampling strategies.

  • Takeaways & Limitations

    One pretrained DiffSBDD model can address multiple SBDD design objectives without retraining specialized models for each task.

Abstract

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Structure-based drug design (SBDD) aims to design small-molecule ligands that bind with high affinity and specificity to pre-determined protein targets. Generative SBDD methods leverage structural data of drugs in complex with their protein targets to propose new drug candidates. These approaches typically place one atom at a time in an autoregressive fashion using the binding pocket as well as previously added ligand atoms as context in each step. Recently a surge of diffusion generative models has entered this domain which hold promise to capture the statistical properties of natural ligands more faithfully. However, most existing methods focus exclusively on bottom-up de novo design of compounds or tackle other drug development challenges with task-specific models. The latter requires curation of suitable datasets, careful engineering of the models and retraining from scratch for each task. Here we show how a single pre-trained diffusion model can be applied to a broader range of problems, such as off-the-shelf property optimization, explicit negative design, and partial molecular design with inpainting. We formulate SBDD as a 3D-conditional generation problem and present DiffSBDD, an SE(3)-equivariant diffusion model that generates novel ligands conditioned on protein pockets. Our in silico experiments demonstrate that DiffSBDD captures the statistics of the ground truth data effectively. Furthermore, we show how additional constraints can be used to improve the generated drug candidates according to a variety of computational metrics. These results support the assumption that diffusion models represent the complex distribution of structural data more accurately than previous methods, and are able to incorporate additional design objectives and constraints changing nothing but the sampling strategy.

1 Introduction

DiffSBDD frames structure-based drug design as 3D-conditional generation with an SE(3)-equivariant diffusion model, enabling de novo, constrained, partial, and property-optimized design from one pretrained model.

  • 1 Introduction: DiffSBDD is an SE(3)-equivariant 3D-conditional diffusion model for generating ligands conditioned on protein pockets.The model respects translation, rotation, and permutation symmetries.
  • 1 Introduction: DiffSBDD can optimize arbitrary molecular properties by combining noise/denoise sampling with an evolutionary algorithm.The workflow evaluates candidates with property oracles or score functions and iteratively searches for improved molecules.
  • 1 Introduction: A single pretrained model supports constrained design tasks including scaffold hopping, fragment growing, and fragment merging through substructure inpainting.The replacement method keeps known molecular regions fixed while generating new atoms, without retraining on specialized datasets.
  • 1 Introduction: Diffusion training applies varying noise to real ligand structures, then learns denoising transitions from Gaussian noise toward the molecular data manifold.Proteins and ligands are represented as 3D point clouds processed as graphs with distance-based edge cutoffs.
  • 1 Introduction: The study evaluates unconstrained de novo generation, partial molecular redesign, and iterative property improvement to test diffusion models across SBDD tasks.These applications use additional constraints or sampling strategies rather than specialized retraining.

3 DiffSBDD captures the data distribution faithfully

DiffSBDD is evaluated for how faithfully it learns molecular-property distributions on CrossDocked and Binding MOAD test targets, relative to autoregressive baselines.

  • 3 DiffSBDD captures the data distribution faithfully: The evaluation compares DiffSBDD with Pocket2Mol and ResGen using publicly available code and weights.These autoregressive models represent the previous state-of-the-art comparison class for SBDD in the study.
  • 3 DiffSBDD captures the data distribution faithfully: Generated and real-ligand distributions are compared with Wasserstein distances across QED, SA, LogP, Vina, and CNN affinity scores.The metrics cover drug-likeness, synthetic accessibility, hydrophobicity, and target-affinity estimates.
  • 3 DiffSBDD captures the data distribution faithfully: DiffSBDD generally captures natural-ligand molecular properties more accurately than autoregressive baselines while sampling significantly faster.Pocket2Mol particularly matches CrossDocked Vina scores, whereas DiffSBDD better approximates GNINA CNN affinity.
  • 3 DiffSBDD captures the data distribution faithfully: DiffSBDD and Pocket2Mol produce Vina-score distributions centered near reference ligands, but DiffSBDD has greater spread.The wider spread includes both lower-scoring molecules and candidates that may bind more tightly than native counterparts.
  • 3 DiffSBDD captures the data distribution faithfully: The same qualitative observation extends to the Binding MOAD dataset, which contains experimentally determined binding complexes.The passage notes that docking scores there are lower on average than corresponding reference-ligand scores.

4 Generating novel chemical matter from known substructures

DiffSBDD uses inpainting to design molecular regions around fixed substructures, supporting scaffold hopping, elaboration, fragment linking, growing, and merging without retraining task-specific models. Fixed complementary regions can improve docking scores, while resampling helps integrate generated and original regions into coherent molecules.

  • Inpainting strategy: DiffSBDD’s replacement method adds new atoms around fixed molecular regions to support scaffold hopping, fragment growing, and related inpainting tasks.The method applies denoising to the whole molecule while replacing predictions for known regions with their ground-truth noised versions.
  • Applications: Molecular inpainting was demonstrated for scaffold hopping, scaffold elaboration, fragment merging, fragment growing, and fragment linking.The experiments used a DiffSBDD model trained on Binding MOAD, including an Eg5 inhibitor scaffold-hopping example.
  • Inpainting regimes: DiffSBDD-de novo designs new motifs around fixed substructures, whereas DiffSBDD-diversify redesigns existing regions through partial noising.De novo sampling explores the chemical fitness landscape, while diversification locally explores around prior chemical and topological compositions.
  • Docking results: −7.74 kcal/mol is the average Vina score for DiffSBDD-de novo linker design, compared with −5.69 for DiffSBDD-baseline.For scaffold elaboration, scores improved from −5.69 kcal/mol to −8.10 kcal/mol; for scaffold hopping, they improved to −7.60 kcal/mol.
  • Sample refinement: Resampling improves molecular connectivity by iteratively refining intermediate states before continuing denoising.Minimal resampling produced chemically valid but disjointed structures, whereas more iterations yielded coherent molecules in complex modifications.

5 Molecule optimization: iterative search for better molecule candidates

DiffSBDD supports iterative molecule optimization by partially noising and denoising candidates, optionally guided by an evolutionary algorithm and property score. Experiments improved drug-likeness, synthetic accessibility, binding affinity, and kinase selectivity, although docking optimization could reduce molecular quality.

  • Optimization procedure: Partial noising followed by denoising samples diverse candidates near the starting molecule while maintaining shape and chemical complementarity.This local exploration does not directly optimize a specified property unless combined with an optimization procedure.
  • Trade-off: Subsequent generations continuously optimized docking score at the expense of molecular quality.Figure 4 reports single-property optimization over 8 QED generations, 7 SA generations, and 3 docking-score generations.
  • Optimization procedure: An evolutionary algorithm extends partial noising and denoising to optimize specific molecular properties without additional fine-tuning.At each stage, the method generates 100 new molecules from the previous generation or the original molecule.
  • Single-property optimization: QED increased from 0.35 to a mean of 0.43 during optimization of the 5NDU inhibitor while maintaining high similarity to the original molecule.The same experiments also rescued the seed molecule’s low synthetic accessibility and optimized binding affinity after a few rounds.
  • Specificity optimization: After 5 rounds, kinase optimization improved on-target docking from −7.2 to −13.9 kcal/mol and off-target docking from −10.8 to −8.7 kcal/mol.The procedure combined positive design against BIKE, negative design against MPSK1, and pruning of candidates that regressed on either docking score.

6 Conclusion

DiffSBDD applies SE(3)-equivariant diffusion to generate ligands conditioned on protein pockets and to address redesign and optimization tasks with sampling constraints. The authors conclude that constrained learning-based tools can support drug-development pipelines, while purely de novo design remains challenging and better benchmarks are needed.

  • Conclusion: Substructure redesign and optimization techniques improve computational docking and drug-likeness scores for candidate compounds.The paper frames these constraints as useful for medicinal-chemistry design specifications.
  • Scope and outlook: Purely de novo design of novel chemical matter remains challenging, while constrained learning-based tools are described as ready for incorporation into drug-development pipelines.The authors also identify more informative metrics and reliable benchmarks as important for reducing reliance on visual inspection and expert judgment.

7 Methods

DiffSBDD uses equivariant diffusion to generate and redesign 3D molecular structures while preserving relevant geometric symmetries and protein-pocket context. Its inpainting procedure fixes selected atoms during reverse diffusion, enabling constrained molecular design without retraining.

  • Denoising diffusion: DDPMs learn to reverse a Markovian process that adds noise to molecular data, generating samples by denoising from noise.The model predicts Gaussian noise during training and uses the prediction to estimate the underlying data representation.
  • Denoising diffusion: DiffSBDD represents molecules as atomic point clouds with 3D coordinates and categorical atom features, then applies a fixed noise process across diffusion steps.The representation is zdata = [x, h], where x contains coordinates and h contains categorical features.
  • Geometric equivariance: The model enforces SE(3)-equivariance so conditional ligand likelihoods and generated samples transform consistently under rotations and translations, while excluding reflections.Reflection sensitivity is retained because reflections can alter chirality and molecular properties.
  • Geometric equivariance: SE(3)GNN layers break reflection symmetry by adding a cross-product-dependent coordinate-update term while retaining the original equivariant graph-network structure.The cross product changes sign under reflection, making the layer sensitive to reflections.
  • Molecular inpainting: For molecular inpainting, fixed atoms are diffused at each step and replace the model’s corresponding predictions, allowing arbitrary ligand-pocket regions to be masked without retraining.The fixed representation is translated to align centers of mass and remains unperturbed in the final sample.
  • Evaluation: Evaluation uses Vina Score, QED, SA, Lipinski compliance, Diversity, and Inference Time to assess generated-molecule quality and sampling efficiency.Docking scores are calculated after local minimization with GNINA or, when specified, redocking with QuickVina2.

Appendix A Note on Variational Lower Bound

The model is trained by optimizing a variational lower bound, implemented in practice as a mean-squared noise-prediction loss. Pocket coordinates provide a reference frame that removes the need for the usual translation-equivariant subspace trick.

  • Variational objective: Training maximizes the variational lower bound through prior, reconstruction, and diffusion-loss components.The prior loss is computed exactly, whereas the reconstruction loss is estimated.
  • Variational objective: In practice, the model minimizes mean squared error between sampled noise and predicted noise across randomly sampled diffusion time steps.This objective is equivalent to the variational formulation up to a multiplicative factor.
  • Conditional coordinates: Pocket-node coordinates define a reference frame, allowing samples to be translated to a unique location and making translation equivariance irrelevant.At inference, the pocket center of mass can be subtracted before likelihood evaluation and restored after sampling.
  • Conditional coordinates: The conditional implementation retained linear-subspace sampling because changing the approach did not appear to affect conditional-model performance.The subspace approach remains necessary for the joint model.

Number of resampling steps

Resampling is evaluated as a way to improve inpainting placement without sacrificing molecular metrics. Increasing the resampling count brings generated molecules closer to the pocket, with the positional benefit saturating at r = 10.

  • Experimental setup: r = 1, r = 5, and r = 10 were tested for all test pockets, with denoising steps reduced proportionally to offset resampling’s sampling-time cost.The resampling strategy slows sampling by approximately a factor of r, motivating striding.
  • Positional effect: r = 1 places generated molecules farther from the presumed pocket center than the conditional model, while increasing r reduces this displacement.The improvement approaches the conditional model’s average displacement and appears to saturate at r = 10.
  • Molecular metrics: Additional resampling steps and the shortened denoising trajectory do not degrade the reported molecular metrics.The same model trained with T = 500 diffusion steps was used in all three cases.
  • Molecular metrics: Average docking scores improve slightly with resampling, possibly reflecting better pre-docking positioning of generated ligands in the pockets.The passage presents improved positioning as a possible explanation rather than an established mechanism.

D.3 O(3)-equivariance of the learned likelihood

The learned likelihood is O(3)-equivariant when the prior and denoising transitions are equivariant under orthogonal transformations. The construction uses an equivariant context-dependent mean and isotropic transition distributions.

  • Likelihood equivariance: The learned sample likelihood is O(3)-equivariant under orthogonal transformations of the ligand and pocket coordinates.The proof combines equivariance of the prior and transition probabilities.
  • Architecture: The SE(3)-equivariant architecture modifies the coordinate update using centered cross-product terms, making it sensitive to reflections while retaining rotational equivariance.The resulting graph neural networks are called SE(3)GNNs.

E.1 Discussion of Equivariance

The equivariance discussion explains how a centered cross-product coordinate update distinguishes rotations from reflections. A toy chirality experiment is used to test whether the resulting network can classify R and S centers.

  • SE(3)GNN construction: For an orthogonal transformation R, the output remains equivariant only when det(R) = 1; reflections introduce an additional symmetry-breaking summand.Thus rotations are preserved, whereas orientation-reversing transformations are intentionally distinguished.
  • SE(3)GNN construction: The cross-product transformation law contributes the determinant-dependent factor that separates orientation-preserving rotations from reflections.The derivation uses Ra × Rb = det(R)R(a × b).
  • Toy experiment: A tetrahedral-chirality classification experiment compares EGNN and SE(3)GNN models on right-handed (R) versus left-handed (S) centers.The reported results are presented in Table E2, with reference results taken from prior work.

F.1 Sampling statistics

The sampling analysis evaluates generated molecules using dataset counts, molecular-property distributions, size–score relationships, validity metrics, and protein-context fidelity. Full-atom pocket representations generally provide stronger protein-interaction and pose-conditioning results than coarse-grained Cα representations, while Cα models are faster.

  • Property distributions: Generated molecules are assessed against reference ligands using computational-score distributions and Wasserstein distances, including drug-likeness, hydrophobicity, synthetic accessibility, and affinity-related scores.The score distributions are visualized for Binding MOAD, while ligand size is examined because QuickVina scores correlate with heavy-atom count.
  • Molecular metrics: Validity measures chemically acceptable molecules, connectivity measures the absence of disconnected fragments, and uniqueness and novelty quantify diversity relative to generated and training-set molecules.Validity is based mainly on RDKit valence checks; uniqueness and novelty are computed from canonical SMILES strings.
  • Molecular metrics: Only a small fraction of generated molecules is invalid, but fragmentation is more common; all models nevertheless produce diverse molecules unseen during training.Largest fragments can be selected for downstream processing when molecules are fragmented.
  • Protein representation: Full-atom pocket models outperform Cα models on the Vina metric, whereas ligand-centric metrics show little dependence on protein representation.Cα models offer significantly faster training and inference, supporting their use during model development and preliminary analyses.
  • Protein representation: For full-atom models, QuickVina often leaves generated conformations nearly unchanged after redocking, with RMSD below 2 Å, whereas Cα models show weaker pocket-context conditioning.Cα-generated poses barely improve over random RDKit conformers, likely because side-chain clashes require docking correction.

F.6 Random generated molecules

Random samples and supplementary experiments illustrate DiffSBDD’s molecular outputs, its inpainting and fragment-based design settings, and how resampling or diffusion-step choices affect generated molecules.

  • Random generated molecules: Randomly selected molecules generated by different models are presented as qualitative samples of model output.The cited figure provides examples without reporting a numerical comparison.
  • Molecular design applications: Molecular inpainting supports scaffold hopping, scaffold elaboration, fragment merging, fragment growing, and fragment linking using fixed molecular context and newly generated atoms.Fragment merging combines fragments from overlapping binding sites, including an example using two SARS-CoV-2 NSP3 fragment structures.
  • Sampling choices: The number of noising and denoising steps affects molecular properties, with measurements taken across timestep values using 200 sampled molecules at each value.The timestep sweep alone does not explicitly optimize a property unless combined with the evolutionary algorithm.
  • Model context: Diffusion models learn molecular data distributions through a denoising reverse process and can generate molecules conditioned on three-dimensional protein context.The broader geometric-learning context motivates architectures that respect symmetries in molecular representations.
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