Integrating evolutionary and protein language model representations for thermodynamically consistent stability prediction

At fixed thermodynamic conditions, protein stability changes obey reversal antisymmetry and path independence, but learned predictors need not satisfy these properties. Explicit alignment-derived evolutionary information may also complement single-sequence protein language model representations, motivating their integration under clearly defined physical constraints. Here, we develop a training-free strategy that combines thermodynamic constraints with complementary sequence representations. We first introduce EvoPhi-DDG, a potential-based adaptation of the alignment-conditioned evolutionary predictor MSAesm_ddG. By antisymmetrizing its predictions and setting the hidden biases to zero, we express stability changes as differences of a learned, evolution-informed effective potential conditioned on the mutation site and alignment context. This guarantees exact reversal consistency and exact same-site transitivity under fixed alignment contexts while preserving predictive accuracy. We further extend the adapted predictor to multiple substitutions through a background-aware construction that preserves whole-variant antisymmetry. We then combine EvoPhi-DDG with the previously published JanusDDG using fixed, equal weight averaging to test predictive complementarity without additional training. The ensemble preserves exact antisymmetry and reduces multisite pathway-closure RMSE relative to JanusDDG across all evaluated path lengths. Furthermore, the ensemble outperforms both components on S669 and S96, achieving Pearson correlations of 0.59 and 0.55, respectively, compared with 0.55 and 0.52 for JanusDDG and 0.53 and 0.48 for EvoPhi-DDG. On the multiple-substitution benchmark PTmul-NR, the ensemble achieves a Pearson correlation of 0.66, improving on JanusDDG's 0.61 and matching the EvoPhi-DDG extension at the reported precision. Together, these findings distinguish two benefits: averaging complementary predictions improves accuracy, whereas the potential-based reformulation strengthens physical consistency. They support the integration of alignment-conditioned and single-sequence representations without additional training, while separating predictive improvements from mathematical guarantees.