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Zero-shot protein stability prediction by inverse folding models: a free energy interpretation
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Derives a free-energy interpretation of inverse folding log-likelihood ratios for zero-shot stability prediction, showing the standard log-ratio is a single-sample importance sampling estimate and that multi-sample folded ensembles and unfolded-state terms improve correlations.
Problem
Zero-shot prediction of protein stability changes (ΔΔG) with inverse folding models lacks a formal link to thermodynamic free energies; the standard log-likelihood ratio is used without theoretical justification.
Approach
Expresses ΔΔG as a difference of pseudo free-energy changes for folded and unfolded macro-states, estimated via importance sampling with an inverse folding model; the standard log-ratio emerges as a one-sample Monte Carlo estimate of the folded term, and unfolded-state terms (MC sampling, single-residue fragments, disordered-region amino acid statistics) and multi-sample folded ensembles (MD, BioE
Key results
- Multi-sample folded ensembles from MD improve Protein G Pearson correlation from 0.66 (single structure) to 0.70 and VAMP-seq from 0.51 to 0.53 with ESM-IF.
- Using disordered-region amino acid statistics as the unfolded state gives the best results, e.g. Protein G 0.72 with multi-sample folded ensemble.
- BioEmu ensembles (20 samples) give almost identical performance to MD ensembles (Protein G 0.69 vs 0.70 for multi-sample folded).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace one folded structure with an ensemble of sampled structures (ablation) | ESM-IF zero-shot stability prediction · Protein G and VAMP-seq | Pearson correlation: 0.66 (0.02) -> 0.7 (0.03); 0.51 (0.01) -> 0.53 (0.01) | Helped |
| Replace one folded structure with an ensemble of sampled structures (ablation) | ESM-IF zero-shot stability prediction · Guerois | Pearson correlation: 0.63 (0.02) -> 0.6 (0.03) | Mixed |
| Add IDP amino-acid frequencies as the unfolded-state model (ablation) | ESM-IF zero-shot stability prediction · Protein G | Pearson correlation: 0.66 (0.02) -> 0.69 (0.02); 0.7 (0.02) -> 0.72 (0.02) | Helped |
| Add IDP amino-acid frequencies as the unfolded-state model (ablation) | ESM-IF zero-shot stability prediction · VAMP-seq | Pearson correlation: 0.51 (0.01) -> 0.52 (0.01); 0.53 (0.01) -> 0.54 (0.01) | Helped |
| Add IDP amino-acid frequencies as the unfolded-state model (ablation) | ESM-IF zero-shot stability prediction · Guerois | Pearson correlation: 0.63 (0.02) -> 0.64 (0.02); 0.6 (0.03) -> 0.62 (0.03) | Mixed |
| Add the p(a) sequence correction (ablation) | ESM-IF folded-only prediction · Protein G | Pearson correlation: 0.66 (0.02) -> 0.67 (0.02); 0.7 (0.03) -> 0.71 (0.02) | Helped |
| Add the p(a) sequence correction (ablation) | ESM-IF folded-only prediction · Guerois | Pearson correlation: 0.63 (0.02) -> 0.63 (0.02); 0.6 (0.03) -> 0.61 (0.03) | No clear effect |
| Add the p(a) sequence correction (ablation) | ESM-IF folded-only prediction · VAMP-seq | Pearson correlation: 0.51 (0.01) -> 0.51 (0.01); 0.53 (0.01) -> 0.54 (0.01) | No clear effect |
| Use Monte Carlo sampling to model the unfolded state (ablation) | ESM-IF stability prediction · Protein G and Guerois | Pearson correlation: 0.66 (0.02) -> 0.66 (0.02); 0.63 (0.02) -> 0.59 (0.02) | Hurt |
| Replace unfolded Monte Carlo samples with a short fragment from the folded structure (ablation) | ESM-IF stability prediction · Protein G | Pearson correlation: 0.66 (0.02) -> 0.67 (0.02) | Helped |
| Use ProteinMPNN instead of ESM-IF (ablation) | Zero-shot stability prediction · Protein G | Pearson correlation: 0.66 (0.02) -> 0.4 (0.03); 0.72 (0.02) -> 0.58 (0.02) | Hurt |
| Replace MD structural ensembles with BioEmu-generated ensembles (ablation) | ESM-IF zero-shot stability prediction · Protein G | Pearson correlation: 0.7 (0.02) -> 0.69 (0.02); 0.71 (0.02) -> 0.70 (0.02); 0.72 (0.02) -> 0.72 (0.02) | No clear effect |
Surprising findings
- Monte Carlo sampled unfolded-state ensembles generally perform worse than the simple log-odds baseline.
- ESM2-based sequence compensation terms are detrimental on Protein G and Guerois, although they help on VAMP-seq.
Limitations
- Experiments are a proof-of-concept with limited choices of models for each term; the space of possible models is not exhaustively explored.
- Assumptions such as equal beta representativeness across sequences and state determined by structure only are approximate.
- The framework does not explain the correlation of inverse-folding likelihoods with absolute stabilities.
Experimental setup
Datasets: Protein G B1 domain stability data Guerois/ProTherm FoldX benchmark VAMP-seq TPMT and PTEN mega-scale stability dataset (ProteinGym subset) MobiDB curated disorder annotations
Benchmarks: Protein G Guerois VAMP-seq mega-scale stability subset
Metrics: Pearson correlation Spearman correlation
Baselines: ESM-IF log-likelihood ratio ProteinMPNN ESM2 sequence compensation
Builds on: ESM-IF free energy perturbation ProteinMPNN
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