From Multisets to Profiles: Recovering Per-Residue Protein Stability from Unassigned High-Throughput Measurements

Protein local stability --- the residue-resolved opening free energy --- governs many biological functions, but per-residue experimental measurement is scarce. Recent advances in hydrogen–deuterium exchange mass spectrometry (HDX-MS) allow high-throughput measurements, yet returns an unordered multiset of per-residue values with no assignment to positions. We recover the missing assignment with a per-residue predictor model that requires only sequence and native state structure and needs no HDX-MS input at inference. The model is pretrained on synthetic, residue-resolved physics priors (Best–Vendruscolo estimation on native structures or molecular-dynamics ensembles) and finetuned on large-scale unassigned HDX-MS dataset through a permutation-invariant order-statistics loss. On residue-assigned HDX-NMR benchmark, the model ranks and assigns per-residue opening free energy substantially better than the classical structure-based estimators. In addition, the model captures mutational effects on stability while the classical estimators are insensitive to mutations. These results show that identity-ambiguous measurements can supervise a transferable assignment model, provided a low-fidelity prior supplies a roughly correct starting point.