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De novo Protein Design Using Geometric Vector Field Networks
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Proposes Vector Field Network (VFN), a frame-based structure encoder using learnable vector computations between frame-anchored virtual atoms, applied to protein diffusion (VFN-Diff) and inverse folding (VFN-IF, VFN-IFE with ESM).
Problem
Protein structure encoders for de novo design must model residue backbone frames without atom-level features, and prior frame-based encoders such as IPA are limited by a single pooled distance scalar ("atom representation bottleneck").
Approach
A vector field operator applies learnable linear-like weights to 3D virtual atom coordinates expressed in a common local frame, outputting multiple geometric vectors (decomposed into unit directions and RBF-encoded lengths) that feed attention-based residue and virtual-atom updates; real backbone atoms can also be used as virtual atoms.
Key results
- In protein diffusion, VFN-Diff reaches 67.04% scTM>0.5 designability vs. 53.58% for FrameDiff (8 sequences, 500 steps, noise 1.0).
- VFN-IF achieves 54.74% sequence recovery on CATH 4.2 vs. 51.66% for PiFold; VFN-IF+ trained on the full PDB reaches 57.14%.
- VFN-IFE (VFN with ESM via LoRA) reaches 62.67% recovery on CATH 4.2 vs. 55.65% for LM-Design.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace FrameDiff's IPA point attention with VFN | FrameDiff · Protein diffusion, Noise Scale 1.0 | scTM0.5 (%): 53.58% -> 67.04% | Helped |
| Replace FrameDiff's IPA point attention with VFN | FrameDiff · Protein diffusion, Noise Scale 1.0 | diversity (%): 51.98% -> 66.54% | Helped |
| Equip VFN-IF with ESM and LoRA | VFN-IF · CATH 4.2 | sequence recovery (%): 55.65% -> 62.67% | Helped |
| Train VFN-IF on the entire PDB dataset | VFN-IF · CATH 4.2 | sequence recovery (%): 54.74% -> 57.14% | Helped |
| Use VFN-IF rather than PiFold | Inverse folding · CATH 4.2 | sequence recovery (%): 51.66% -> 54.74% | Helped |
| Use VFN-Diff + VFN-IFE instead of FrameDiff + MPNN | Whole protein-design pipeline · One-shot, Noise Scale 1.0 | scTM>0.5 (%): 37.25% -> 45.43% | Helped |
| Remove edge features (ablation) | VFN-IF · CATH 4.2, 15 layers | sequence recovery (%): 54.08 -> 54.7 | Helped |
| Use 32 vectors instead of 16 (ablation) | VFN-IF · CATH 4.2 | sequence recovery (%): 53.97 -> 54.28 | Helped |
| Use 64 vectors instead of 32 (ablation) | VFN-IF · CATH 4.2 | sequence recovery (%): 54.28 -> 53.63 | Hurt |
| Use V-MLP rather than regular MLP (ablation) | VFN-IF · CATH 4.2 | sequence recovery (%): 53.42 -> 54.28 | Helped |
| Add the vector field operator (ablation) | VFN-IF · CATH 4.2 | sequence recovery (%): 35.43 -> 54.28 | Helped |
| Add g_i,j to edge aggregation (ablation) | VFN-IF · CATH 4.2 | sequence recovery (%): 53.05 -> 54.28 | Helped |
Surprising findings
- Removing the entire vector field operator drops recovery from 54.28% to 35.43%, showing the operator is critical.
- VFN-IF with only 5 layers (52.68%) already beats a 10-layer PiFold, and VFN-IF does not saturate with depth as PiFold does.
Limitations
- Structure recovery and whole-pipeline results are one-shot evaluations with limited sample sizes.
- Comparison with RFDiffusion was deliberately excluded as out of scope.
- Diversity and pdbTM metrics were modified from FrameDiff's protocol, making comparisons less standard.
Experimental setup
Datasets: CATH 4.2 TS50 TS500 PDB
Benchmarks: CATH 4.2 TS50 TS500
Metrics: sequence recovery perplexity scTM scRMSD designability diversity pdbTM
Baselines: IPA (FrameDiff) PiFold ProteinMPNN LM-Design ESM-IF GVP AlphaDesign StructGNN GraphTrans GCA
Builds on: FrameDiff PiFold invariant point attention (IPA) ESM LM-Design
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