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Flexibility-conditioned protein structure design with flow matching
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Introduces BackFlip, a sequence-independent SE(3)-equivariant predictor of per-residue flexibility from backbone structure, and FliPS, a flexibility-conditioned flow matching model (extending GAFL) that generates backbones matching a target flexibility profile verified by MD.
Problem
Generative protein structure design is restricted to static properties (motifs, symmetries, binders), and generated proteins are overly rigid; there is no way to condition backbone generation on per-residue flexibility, which is important for function.
Approach
Define a local RMSF flexibility measure from MD, train an SE(3)-equivariant backbone flexibility predictor (BackFlip) without sequence input, and use it both to annotate PDB/SCOPe data and as a differentiable auxiliary loss in a conditional flow matching model (FliPS) built on GAFL, plus a BackFlip-based screening step to rank samples.
Key results
- BackFlip reaches Pearson r=0.80 and MAE 0.17 Å against MD local RMSF on 129 unseen ATLAS test proteins, versus 0.16 for B-factor and 0.54 for negative pLDDT.
- FliPS top-ranked samples achieve average MD-profile correlation r=0.70 (existing profiles) and 0.78 (hand-drawn profiles) for domain-sized proteins, above RFdiffusion-BFS (0.58/0.56) and FoldFlow2-BFS (0.45/0.50).
- For bigger proteins (200-300 residues), FliPS top samples reach r=0.79 vs 0.41 for RFdiffusion-BFS and 0.35 for FoldFlow2-BFS.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use BackFlip instead of negative pLDDT to predict local RMSF | Flexibility prediction on ATLAS test proteins · ATLAS test set | Global r: 0.54 (0.00) -> 0.80 (0.00) | Helped |
| Use BackFlip instead of negative pLDDT to predict local RMSF | Flexibility prediction on de novo proteins · De novo proteins | Global r: 0.48 (0.00) -> 0.73 (0.00) | Helped |
| Condition generation on the target flexibility profile | FliPS compared with unconditionally sampled structures · 4 hand-drawn profiles, lengths 200–300, BackFlip on all samples | r: -0.00 (0.00) -> 0.76 (0.00) | Helped |
| Use FliPS conditioning rather than RFdiffusion with flexibility screening | Flexibility-conditioned protein generation · 10 existing profiles, MD of top samples | r: 0.58 (0.03) -> 0.70 (0.02) | Helped |
| Use FliPS conditioning rather than FoldFlow2 with flexibility screening | Flexibility-conditioned protein generation · 10 hand-drawn profiles, MD of top samples | r: 0.50 (0.03) -> 0.78 (0.01) | Helped |
| Add BackFlip guidance with static scale 5 (ablation) | FliPS unconditional flow · BackFlip guidance target profile, lengths 200–300 | r: 0.47 (0.05) -> 0.73 (0.01) | Helped |
| Add BackFlip guidance with static scale 10 (ablation) | FliPS unconditional flow · BackFlip guidance target profile, lengths 200–300 | Median scRMSD: 1.15 (0.04) -> 7.58 (0.53) | Hurt |
| Use a linear BackFlip-guidance schedule (ablation) | FliPS unconditional flow · BackFlip guidance target profile, lengths 200–300 | Median scRMSD: 2.78 (0.13) -> 1.60 (0.07) | Helped |
| Scale BackFlip guidance by protein length instead of using a static scale of 5 (ablation) | FliPS unconditional flow · BackFlip guidance target profile, lengths 200–300 | MAE: 0.30 (0.01) -> 0.25 (0.01) | Helped |
| Replace FliPS conditional flow with unconditional flow (ablation) | FliPS · BackFlip guidance target profile, lengths 200–300 | r: 0.89 (0.00) -> 0.47 (0.05) | Hurt |
| Use length-scaled BackFlip guidance in FrameFlow rather than conditional FliPS (ablation) | FrameFlow · BackFlip guidance target profile, lengths 200–300 | Median scRMSD: 2.78 (0.12) -> 3.23 (0.14) | Hurt |
Surprising findings
- Conditioned FliPS samples have higher scRMSD than unconditional samples, and scRMSD correlates with flexibility even on designable natural SCOPe proteins, questioning scRMSD as a designability criterion for flexible backbones.
- BackFlip guidance applied to unconditional models underperforms the conditionally trained FliPS and often produces physically invalid backbones at high guidance scales.
Limitations
- Flexibility ground truth is defined from 300 ns MD, which may not capture functional motions on longer timescales.
- MD-derived flexibility has fundamental uncertainty between replicas (ceiling r around 0.8).
- Conditioned samples have higher scRMSD and lower designability than unconditional baselines.
Experimental setup
Datasets: ATLAS PDB SCOPe FrameFlow-generated de novo backbones RFdiffusion-generated de novo backbones
Benchmarks: ATLAS test set de novo proteins MD set SCOPe hand-drawn flexibility profiles
Metrics: Pearson correlation MAE scRMSD TM-score novelty diversity helix/strand percentage
Baselines: RFdiffusion FoldFlow2 FrameFlow FlexPert-3D SCOPe natural proteins negative pLDDT B-factor
Builds on: GAFL FrameFlow FoldFlow AlphaFold2 structure module Invariant Point Attention
Closest papers by meaning
- Learning to engineer protein flexibility (ICLR 2025 · similarity 0.91)
- Predicting directional flexibility in proteins (NeurIPS 2026 · similarity 0.88)
- Sequence-Augmented SE(3)-Flow Matching For Conditional Protein Generation (NeurIPS 2024 · similarity 0.88)
- SE(3)-Stochastic Flow Matching for Protein Backbone Generation (ICLR 2024 · similarity 0.87)
- Learning conformational ensembles of proteins based on backbone geometry (NeurIPS 2025 · similarity 0.87)
- Proteina: Scaling Flow-based Protein Structure Generative Models (ICLR 2025 · similarity 0.87)
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