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Equivariant Scalar Fields for Molecular Docking with Fast Fourier Transforms
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Learns protein and ligand equivariant scalar fields (ESFs) via E3NN so that docking scores are cross-correlations that can be optimized over rigid-body poses with FFTs, amortizing computation across poses and ligands.
Problem
Molecular docking pose optimization is slow because classical scoring functions require expensive sampling over ligand rigid-body poses; the goal is a learned scoring function whose form permits rapid optimization.
Approach
Define the score as a sum over channels of the cross-correlation of learned multi-channel ligand and protein scalar fields parameterized by equivariant graph neural networks (E3NN), so translations and rotations can be searched in one shot with FFTs over R^3 and SO(3), with precomputation amortized over proteins, conformers and ligands.
Key results
- On ESMFold test structures, ESF-N-TS attains top-ranked pose RMSD of 1.64 Å and ESF-TS 1.38 Å, versus Vina 2.43 Å and Gnina 2.19 Å in decoy scoring.
- Per-pose scoring takes 1.0 µs (TS) and 8.2 µs (RS), several orders of magnitude faster than Vina (3.4 ms) and Gnina (13.0 ms).
- On PDE10A conformer docking, amortization gives a 45x overall runtime speedup (67 s to 1.5 s) while matching baseline success rates (~73%).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use equivariant scalar-field scoring (ESF-TS) instead of Vina | Decoy pose scoring · PDBBind test ESMFold structures | Top RMSD: 2.43 -> 1.38 | Helped |
| Use equivariant scalar-field scoring (ESF-TS) instead of Vina | Decoy pose scoring · PDBBind test crystal structures | Top RMSD: 0.54 -> 0.59 | Mixed |
| Add rotational and translational training noise (ablation) | ESF rigid conformer docking with translational FFT · PDBBind test ESMFold structures | % <2 Å: 31 -> 46 | Helped |
| Add rotational and translational training noise (ablation) | ESF rigid conformer docking with rotational FFT · PDBBind test ESMFold structures | % <2 Å: 32 -> 47 | Helped |
| Add rotational and translational training noise (ablation) | ESF rigid conformer docking with translational FFT · PDBBind test crystal structures | % <2 Å: 70 -> 72 | Helped |
| Add rotational and translational training noise (ablation) | ESF rigid conformer docking with rotational FFT · PDBBind test crystal structures | % <2 Å: 71 -> 73 | Helped |
| Use rotational FFT instead of translational FFT (ablation) | ESF rigid conformer docking · PDBBind test ESMFold structures | % <2 Å: 31 -> 32; 46 -> 47 | Mixed |
| Use translational scoring instead of rotational scoring (ablation) | ESF decoy scoring · PDBBind test ESMFold structures | Top RMSD: 1.75 -> 1.38 | Helped |
| Amortize protein-level precomputation across ligands | ESF-RF rigid conformer docking · PDE10A | Runtime: 67 s -> 1.5 s | Helped |
Surprising findings
- Learned scoring is more robust on ESMFold predicted structures than Vina and Gnina, despite being competitive on crystal structures.
- On crystal structures, DiffDock's confidence model achieves higher <2 Å AUROC (0.96) than the proposed method (0.87-0.92).
Limitations
- Evaluated only on simplified tasks (decoy scoring and rigid conformer docking) without torsional flexibility, conformer search, or refinement.
- Median RMSD in rigid docking is worse than baselines on crystal structures (about 1.0-1.1 Å vs 0.32-0.33 Å) due to coarse search grid and lack of refinement.
- Total per-complex runtime is comparable to or slower than baselines when precomputation is included for PDBBind.
Experimental setup
Datasets: PDBBind ESMFold structures of PDBBind test complexes PDE10A crystal structures (77 PDB IDs, 70 used)
Benchmarks: PDBBind test decoy scoring PDBBind crystal and ESMFold rigid conformer docking PDE10A cross-docking
Metrics: AUROC top RMSD top rank % under 2 Å RMSD median RMSD runtime
Baselines: Vina Gnina TANKBind DiffDock
Builds on: E3NN Gnina Vina TANKBind
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