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Harmonic Self-Conditioned Flow Matching for joint Multi-Ligand Docking and Binding Site Design
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Proposes HarmonicFlow, a self-conditioned flow matching model over ligand 3D coordinates with a harmonic prior, and FlowSite, which extends it to jointly generate pocket residue types for designing small-molecule binding sites.
Problem
Designing protein binding pockets for one or multiple small molecules without prior knowledge of the ligand's 3D binding pose, which requires jointly solving docking and sequence design.
Approach
Flow matching over ligand Cartesian coordinates with a harmonic (graph Laplacian) prior, x1-prediction, and self-conditioning borrowed from recycling, extended with a jointly generated discrete residue-type flow that is trained with self-conditioning and a fake-ligand augmentation.
Key results
- HarmonicFlow reaches 42.8% RMSD<2Å on PDBBind time-split distance-pockets vs 20.8% for product-space diffusion.
- FlowSite recovers 47.0% of binding-site residues on Binding MOAD vs 39.4% for PiFold without ligand, approaching the 51.4% oracle with ground-truth ligand pose.
- On Binding MOAD multi-ligand docking, HarmonicFlow achieves 44.4% RMSD<2Å vs 39.7% for EigenFold Diffusion.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use HarmonicFlow instead of Product Space Diffusion | PDBBind pocket-level docking · PDBBind sequence similarity split, Distance-Pocket | %<2 RMSD: 27.2 -> 30.1 | Helped |
| Use HarmonicFlow instead of Product Space Diffusion | PDBBind pocket-level docking · PDBBind sequence similarity split, Radius-Pocket | %<2 RMSD: 16.1 -> 20.5 | Helped |
| Use HarmonicFlow instead of EigenFold Diffusion | multi-ligand docking · Binding MOAD multi-ligands | %<2 RMSD: 39.7 -> 44.4 | Helped |
| Jointly generate ligand structure and binding-site residue types with FlowSite rather than use PiFold with a 2D ligand | binding-site recovery · PDBBind sequence similarity | Recovery: 44.5 -> 49.5 | Helped |
| Replace the harmonic prior with an isotropic Gaussian prior (ablation) | HarmonicFlow · PDBBind sequence similarity, Radius-Pocket | %<2 RMSD: 20.5 -> 17.0 | Hurt |
| Predict (x1 - x0) instead of x1 (ablation) | HarmonicFlow · PDBBind sequence similarity, Radius-Pocket | %<2 RMSD: 20.5 -> 11.9 | Hurt |
| Replace refinement TFN layers with standard TFN layers (ablation) | HarmonicFlow · PDBBind sequence similarity, Radius-Pocket | %<2 RMSD: 20.5 -> 13.7 | Hurt |
| Remove refinement loss (ablation) | HarmonicFlow · PDBBind sequence similarity, Radius-Pocket | %<2 RMSD: 20.5 -> 9.8 | Hurt |
| Remove structure self-conditioning (ablation) | HarmonicFlow · PDBBind sequence similarity, Radius-Pocket | %<2 RMSD: 20.5 -> 14.3 | Hurt |
| Set conditional-flow σ to 0 rather than 0.5 (ablation) | HarmonicFlow · PDBBind sequence similarity, Radius-Pocket | %<2 RMSD: 20.5 -> 18.3 | Hurt |
| Remove side-chain torsion loss (ablation) | FlowSite · PDBBind sequence similarity | Recovery: 49.5 -> 47.7 | No clear effect |
| Add Gaussian noise to backbone coordinates (ablation) | FlowSite · PDBBind sequence similarity | Recovery: 49.5 -> 42.4 | Hurt |
Surprising findings
- Parameterizing the vector field to predict x1 rather than velocity works better for molecular structure generation, per ablations.
- Only equivariant layers without invariant graph attention yields much worse residue recovery (35.3% vs 47.0%).
Limitations
- Blind docking results are preliminary and HarmonicFlow underperforms product-space diffusion on sequence-split top-5 and top-10 sampling.
- Binding site recovery is a proxy metric; recovery may not reflect binding affinity or designs that are functional, and multiple valid solutions are not captured.
- No discriminator/confidence model is used, so the docking comparison covers only the generative component.
Experimental setup
Datasets: PDBBind v2020 Binding MOAD
Benchmarks: PDBBind Binding MOAD
Metrics: RMSD < 2 Å success rate median RMSD sequence recovery BLOSUM score
Baselines: DiffDock product-space diffusion EigenFold Diffusion ProteinMPNN PiFold DiffDock-Pocket Autodock Vina
Builds on: conditional flow matching EigenFold DiffDock PiFold AlphaFold2 recycling
Closest papers by meaning
- Generalized Protein Pocket Generation with Prior-Informed Flow Matching (NeurIPS 2024 · similarity 0.90)
- Prior-Guided Flow Matching for Target-Aware Molecule Design with Learnable Atom Number (NeurIPS 2025 · similarity 0.89)
- Energy-Based Flow Matching for Generating 3D Molecular Structure (ICML 2025 · similarity 0.89)
- Template-Guided 3D Molecular Pose Generation via Flow Matching and Differentiable Optimization (NeurIPS 2025 · similarity 0.88)
- Integrating Protein Dynamics into Structure-Based Drug Design via Full-Atom Stochastic Flows (ICLR 2025 · similarity 0.88)
- Re-Dock: Towards Flexible and Realistic Molecular Docking with Diffusion Bridge (ICML 2024 · similarity 0.88)
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