StrucNS reveals interaction-weighted network topology as the driving predictor of absolute stability of natural and de novo proteins

MOTIVATION: Folded protein function requires stability, yet mapping structure and sequence to a fitness landscape remains difficult. The protein fold is the physical realization of complex, spatially-sensitive physicochemical interactions; quantitatively elucidating how these subtle relationships dictate thermodynamic stability remains challenging. We present StrucNS, a mathematical framework that identifies principles governing protein fitness by employing network science to learn physicochemical relationships between residues and their stability contributions directly from the protein fold. While the fold is traditionally viewed as the phenotypic consequence of the underlying chemical forces, we represent the fold as a network topology to decode the physicochemical dependencies that govern protein stability. Unlike language models reliant on high-dimensional evolutionary embeddings, StrucNS extracts these signals directly from the interaction-weighted network topology. Evolutionary independence uniquely suits StrucNS for de novo design prediction. RESULTS: Despite reduced dimensionality and training depth, StrucNS outperforms unsupervised ESM-2 and ProteinMPNN on predicting mutational stability across three miniprotein test sets. StrucNS performs comparably to supervised UniRep in predicting absolute stability of de novo designs and outperforms supervised UniRep and supervised ESM-2 in predicting mutational stability of multi mutants far outside its training regime. Feature analysis reveals network topology drive predictive power. SHAP analysis reveals high degree and low modularity of polar/hydrophobic mixed subnetworks as influential features, which highlights connectivity between the hydrophobic core and protein surface as predictive of stability contrary to the conventional focus on the hydrophobic core. Revelation of predictive topological features underscores the utility of interpretability. AVAILABILITY: Source codes and datasets: https://github.com/Hackel-Group-CEMS/StrucNS and https://zenodo.org/records/20497907.