Molecular Docking

Molecular docking aims to predict the three-dimensional structure of a protein-ligand complex; in the conventional structure-based setting, it is conditioned on an input protein structure and ligand, often starting from an apo receptor in flexible docking or a holo receptor in rigid docking. Recent co-folding models exemplified by AlphaFold 3 achieve strong accuracy in protein-ligand complex prediction, but they typically generate complexes from sequence-derived inputs and therefore do not directly use apo structures as structural priors in docking, leading to a larger conformational search space and weaker robustness in difficult or few-step settings. We present BridgeDock, a framework that adapts pretrained co-folding backbones to flexible docking by modeling the apo-to-holo transition as a diffusion bridge, allowing generation from the initial protein-ligand state rather than from Gaussian noise. To make this bridge formulation compatible with pretrained denoisers, we introduce an alignment mechanism that maps bridge states to the original denoising schedule of the pretrained model. Experiments on standard flexible docking benchmarks show that BridgeDock consistently outperforms strong co-folding baselines. Moreover, BridgeDock is computationally efficient at inference time and remains effective even with very few denoising steps.

Flexible docking is a highly practical task, aiming to predict the joint configuration of a protein-ligand complex from a protein apo structure and a ligand SMILES string. Diffusion and flow-based generative models have made this task tractable by modeling the posterior distribution over the ligand pose and the protein conformation conditioned on the apo input. The central challenge, however, remains the long-tailed apo-to-holo structure shift, where a small fraction of protein undergo large conformational changes. In this work, motivated by the practical observation that downweighting large shift examples improves generalization, and by the mixed nature of the long tail consisting of genuinely difficult examples and noisy ones, we propose to use curriculum learning for this task, gradually incorporating large conformational change examples during training. With a linear pacing function, we show that an existing method can be strongly enhanced. On the PDBBind ESMFold apo benchmark, with relaxation and confidence-based pose selection, the resulting model GCLDock achieves a 46.52% top-1 success rate (ligand RMSD less than 2A) and 40.26% when additionally requiring PoseBusters validity, outperforming existing baselines.

The Practical Molecular Optimization (PMO) benchmark standardized evaluation in molecular optimization, but it is built on simple property-based oracles that do not capture structure-based drug design. As the field has moved to docking-based objectives, evaluation practice has become unstandardized, and different methods report results on different docking tasks, often without a shared protocol for fair comparison or sample-efficiency constraints. To address this, we introduce Practical Molecular Optimization for Docking (PMO-Dock), a benchmark and protocol for docking-based optimization consisting of 25 tasks covering hit generation, lead optimization, and a new specificity task requiring strong on-target binding while penalizing off-target interactions. The protocol separates model development from final evaluation: validation tasks are used for hyperparameter tuning, and test tasks are held out for final evaluation and are not used during development. Evaluation on the test tasks is done under a strict oracle budget to reflect realistic drug-discovery settings. We benchmark four diverse high-performing methods spanning different optimization paradigms, Saturn (reinforcement learning), GenMol (discrete diffusion), Genetic-guided GFlowNet, and ChemLlama (LLM-based evolutionary search). Our results show no universally best method across tasks, additional analyses of hyperparameter transfer (cross-task and cross-category) and sensitivity show that transfer is often limited and varies by method, motivating method-dependent selection strategies. This benchmark provides a concrete standard for evaluating generalization to unseen tasks and sample efficiency under a limited test-time oracle budget.

Modeling protein-protein interactions requires accurate scoring functions that can rank potential poses (conformations) of a protein-protein complex to differentiate near-native poses from incorrect ones. Here, we propose a general framework for improving protein-protein pose ranking and other biomolecular interaction models using the LambdaLoss loss function from the Learning-to-Rank field. We test this framework by fine-tuning the energy prediction head of DFMDock with the LambdaLoss on an augmented dataset of 2.9M decoy poses derived from the DIPS dataset. On targets from the CAPRI score set benchmark, our fine-tuned ranking model LambdaDockScore is better at identifying correct poses in its top-1 and top-5 predictions compared to EuDockScore, a state-of-the-art method. LambdaDockScore also improves upon baseline DFMDock ranking performance for scoring antibody-antigen complexes and protein-protein complexes with very large or small binding interfaces.

Flexible macromolecular docking offers high-fidelity predictions of biomolecular interactions, but remains prohibitively expensive at scale. Among existing approaches, LightDock leverages Glowworm Swarm Optimization (GSO) for accuracy, yet suffers from limited parallelism, irregular computation, and severe load imbalance, preventing efficient execution on GPU supercomputers. We present SparkleDock, a scalable GSO-based docking framework enabling near-real-time flexible docking. We redesign GSO to expose massive fine-grained parallelism at the glowworm-agent level, and restructure the dominant energy scoring computation into a Tensor Core-compatible formulation, enabling efficient execution of irregular pairwise interactions through structured matrix operations. We further introduce a performance-model-driven scheduling for load balancing and out-of-core scaling across GPUs. SparkleDock achieves 9.7 $\times$ and 18.9 $\times$ speedups over LightDock on single A100 and H100 GPU, and delivers over two orders of magnitude acceleration at scale. On 512 GPUs, it reduces docking time from hours to seconds, enabling large-scale, high-fidelity virtual screening previously impractical with flexible docking.

Structure-prediction networks built on co-evolutionary statistics have transformed protein-based drug discovery, yet their accuracy does not extend to peptide therapeutics--an increasingly important modality defined by non-canonical residues, macrocyclization, and complex topologies. We introduce Vilya-2, a diffusion transformer that extends the all-atom representation of Vilya-1 from modeling individual molecules to modeling their interactions with protein targets. This all-atom representation enables transfer learning between different molecular types, and delivers highly accurate structural modeling of peptides across sizes, classes, and compositions bound to therapeutically relevant targets. By generating diverse structural ensembles and ranking them with calibrated confidence, Vilya-2 recovers 59.1% of peptide interfaces to sub-2 Å backbone RMSD, far exceeding the performance of a representative co-folding model even when that model is given the bound receptor as a template. In addition, Vilya-2 is state-of-the-art at small-molecule docking, and generalizes to novel protein-small molecule complexes unlike those seen in training. It also generalizes to modeling molecular conformations of diverse macrocycles and disulfide-stapled miniproteins several-fold larger than any molecule seen in training. Finally, Vilya-2 can be used as a foundation model, and fine-tuned to enrich for active compounds in hit-to-lead campaigns. By unifying predictive accuracy with broad generalizability across chemical space, Vilya-2 is the structure-prediction oracle that de novo peptide design pipelines require--establishing the all-atom approach as a general foundation for the design and evaluation of de novo peptide therapeutics.

A hallmark of neurodegenerative diseases such as Alzheimer's and Parkinson's is the aberrant aggregation of proteins into amyloid fibrils, and small molecules that selectively bind to these fibrils hold promise as diagnostics, imaging probes, and therapeutics. Predicting how such ligands bind to fibril targets, however, presents two fundamental challenges. First, resolved co-crystal structures of amyloid-ligand complexes are exceptionally scarce; even with recent advances in cryo-EM only a handful have been structurally characterized, making supervised training of docking models impractical for this target class. Second, amyloid fibrils present a binding mode fundamentally different from globular proteins: ligands intercalate into longitudinal cross-$β$ grooves and stack cooperatively along the fibril axis, a geometry that existing docking models are not designed to capture. To address these challenges, we present CORAL (COopeRative Amyloid Ligand docking), a reinforcement learning framework that trains a generative docking model to produce ligand pose distributions tailored to the cross-$β$ groove geometry. Our reward explicitly incorporates cooperative ligand-ligand stacking energy alongside protein-ligand docking affinity, directly capturing the distinctive binding geometry of amyloid fibrils. We further introduce a curated evaluation set of amyloid-ligand complexes constructed from model-generated poses validated by domain experts. Experiments on both experimentally resolved structures and this evaluation set demonstrate improved pose quality and binding affinity correlation over existing docking baselines. Our project page is available at https://sunyasheng.github.io/projects/CORAL.

Molecular docking predicts how a small molecule binds to a protein and is a key bottleneck in drug discovery. Classical scoring functions sum empirical pairwise contacts, blind to quantum-mechanical effects like orbital charge transfer that govern binding specificity. We introduce Q-Score, encoding GNN-predicted orbital donor-acceptor energies into a weighted graph and scoring binding by solving a maximum-weight vertex clique problem via Digitized-Counterdiabatic QAOA. Each interaction anchor maps to one qubit and compatibility constraints become edges. Across 11 protein targets, DC-QAOA recovers the exact optimum on 8 at 10 qubits. On 1000 AI-generated molecules, Q-Score is orthogonal to classical scoring with Spearman rho of 0.05, driven by orbital quality with rho of 0.90, and free of molecular-weight bias, enriching for strong orbital interactions at twice the random rate. DC-QAOA achieves a mean approximation ratio of 0.94 with 52 percent exact. Execution of 1000 circuits on IBM Eagle confirms 6-qubit solvability on NISQ hardware.

Molecular docking requires reasoning jointly about ligand pose and protein flexibility. Most diffusion-based docking models predict torsional updates with generic Euclidean heads that ignore the periodic geometry of angular variables. This mismatch is especially limiting in flexible docking, where ligand conformations and pocket side chains co-adapt to form the bound complex. Here, we introduce Harmony, a harmonic torsional diffusion framework for flexible protein-ligand docking. Harmony parameterizes ligand and side-chain torsional score fields as derivatives of learned harmonic potentials on the circle, which are noised mode by mode in the Fourier basis owing to the properties of variance-exploding diffusion on the torus. This construction makes periodicity explicit and gives the model a frequency-aware inductive bias over rotameric motion. On the PDBBind benchmark, Harmony improves ligand pose accuracy and pocket all-atom reconstruction over recent flexible docking methods. On PoseBusters, it improves the physical validity of generated complexes. Case studies on EBNA1 and KRAS G12D illustrate the method's behavior on a polar and a shallow binding site, respectively. Together, these results indicate that aligning the score parameterization with the geometry of the diffusion process is a simple and effective lever for improving flexible docking.

Nucleic acids are increasingly recognized as therapeutic targets beyond conventional protein-centered drug discovery, yet accurate and efficient docking of small molecules to nucleic acid structures remains challenging. Physics-based docking methods often show limited accuracy and efficiency, whereas deep learning approaches are constrained by the scarcity of experimentally resolved nucleic acid-ligand complexes. Here, we present NucleoDock, a deep learning framework for nucleic acid-small molecule docking. To address data scarcity, NucleoDock combines physics-guided large-scale pretraining on millions of docking-generated synthetic complexes with fine-tuning on curated experimental co-crystal structures. It further integrates sequence- and structure-informed nucleotide representations with atomistic three-dimensional features to capture both biological context and binding-site geometry. A mixture density network-based geometric scoring head is used to model conditional interaction-distance distributions for pose ranking. On an external benchmark of 125 nucleic acid-ligand complexes, NucleoDock achieved a top-1 success rate of 56 percent at an RMSD cutoff of 2.0 Angstrom, outperforming rDock with 29 percent, while generating 100 poses in approximately 5 seconds per complex. Retrospective virtual screening on the ROBIN benchmark further showed improved early enrichment. NucleoDock represents a step toward bridging the methodological gap between protein- and nucleic acid-directed computational drug discovery.

Many machine learning problems involve data supported on curved spaces such as spheres, rotation groups, hyperbolic spaces, and general Riemannian manifolds, where Euclidean geometry can distort distances, averages, and the resulting optimal transport (OT) problem. Existing manifold OT methods have pursued amortized out-of-sample maps, while entropic regularization has made discrete OT more scalable, but these advantages have remained largely disjoint. We propose Entropic Riemannian Neural Optimal Transport (Entropic RNOT), a unified framework that combines intrinsic entropic OT with amortized out-of-sample evaluation on Riemannian manifolds. Our method learns a single target-side Schrödinger potential through a neural pullback parameterization, recovers the induced Gibbs coupling, and uses the resulting conditional laws to construct intrinsic transport surrogates. These include barycentric projections on Cartan-Hadamard manifolds and heat-smoothed conditional surrogates on stochastically complete manifolds, the latter turning possibly atomic target laws into absolutely continuous ones. For fixed regularization $\varepsilon>0$, we prove that the proposed hypothesis class recovers the entropic optimal coupling in strong probabilistic metrics. As consequences, barycentric surrogates converge in $L^2$, while heat-smoothed surrogates are stable at fixed heat time and asymptotically unbiased as the heat time vanishes. The guarantees hold for compactly supported data on possibly noncompact manifolds. Empirically, our method matches or improves over Euclidean, tangent-space, and log-Euclidean baselines on benchmarks over $\mathbb{S}^2$, $\mathrm{SO}(3)$, $\mathrm{SPD}(3)$, $\mathrm{SE}(3)$, and $\mathbb{H}^2$, scales favorably relative to discrete manifold Sinkhorn, and in a protein-ligand docking application, refines poses on $\mathrm{SE}(3)$ without retraining or per-instance optimization.

Virtual screening performance depends heavily on the chosen docking and scoring methods. Recent AI-based tools such as DiffDock and NMDN have reported strong benchmark results, but their practical utility on realistic, experimentally-derived datasets remains unclear. Here we perform a large-scale evaluation on the LIT-PCBA library (15 targets, 578,295 ligand-target pairs with experimentally confirmed actives and inactives). We compare AutoDock-GPU and DiffDock for pose generation, followed by rescoring with GNINA and NMDN. We further evaluate rank-based consensus strategies and supervised machine learning models trained on docking features. GNINA rescoring of AutoDock-GPU poses (AutoDock-GNINA) emerged as the strongest single method with a median EF1% of 2.14. DiffDock-based approaches underperformed relative to AutoDock-GNINA, particularly on challenging targets such as OPRK1. Carefully designed consensus ranking improved robustness but did not surpass the best single scorer. Supervised ML re-ranking delivered the largest gains, achieving a median EF1% of 4.49 (+110% over AutoDock-GNINA). Our results highlight that even the best classical+ML hybrid workflows provide only modest early enrichment on realistic benchmarks. We conclude that no single docking method dominates across targets and that rigorously validated, cost-effective combinations with supervised re-ranking currently offer the most practical value for virtual screening.

Dual-target structure-based drug design aims to generate a single ligand together with two pocket-specific binding poses, each compatible with a corresponding target pocket, enabling polypharmacological therapies with improved efficacy and reduced resistance. Existing approaches typically rely on staged pipelines, which either decouple the two poses via conditional-independence assumptions or enforce overly rigid correlations, and therefore fail to jointly generate two target-specific binding modes. To address this, we propose FuseDiff, an end-to-end diffusion model that jointly generates a ligand molecular graph and two pocket-specific binding poses conditioned on both pockets. FuseDiff features a message-passing backbone with Dual-target Local Context Fusion (DLCF), which fuses each ligand atom's local context from both pockets to enable expressive joint modeling while preserving the desired symmetries. Together with explicit bond generation, FuseDiff enforces topological consistency across the two poses under a shared graph while allowing target-specific geometric adaptation in each pocket. To support principled training and evaluation, we derive a dual-target training set and use an independent held-out test set for evaluation. Experiments on the benchmark and a real-world dual-target system show that FuseDiff achieves state-of-the-art docking performance and enables the first systematic assessment of dual-target pose quality prior to docking-based pose search.

Predicting a protein--ligand binding pose is central to structure-based drug design, yet current docking methods still struggle to combine speed, accuracy and physical plausibility. We introduce Matcha, which refines a ligand pose by three flow-matching stages in translation, rotation and torsion space, then minimizes, filters and ranks candidates with GNINA. Across the benchmarks considered, Matcha attains the strongest physical plausibility and runs about $28\times$ faster than modern large-scale co-folding models. Code and benchmarking artifacts are available at https://github.com/LigandPro/Matcha and archived at https://doi.org/10.5281/zenodo.23568093. Model checkpoints are archived at https://doi.org/10.5281/zenodo.23569055.