Three biophysical constraints determine the variation of structural divergence among residues in enzyme evolution

Structural divergence varies across residue positions in homologous enzyme families, forming residue-dependent structural divergence profiles. The evolutionary constraints that shape these profiles and the underlying physical and biological principles remain unclear. To address this question, we develop a Mutation-Stability-Activity (MSA) model of enzyme structure evolution. In MSA, mutations arise randomly and fix with probabilities that depend on their effects on folding stability, {Delta}{Delta}G, and catalytic activation energy, {Delta}{Delta}G{ddagger}, scaled by two selection-strength parameters, aS and aA. To calculate {Delta}{Delta}G and {Delta}{Delta}G{ddagger}, and predict mutant structures, we use the coarse-grained Linearly Forced Elastic Network Model (LFENM). Applied to 34 enzyme families, MSA recapitulates observed structural divergence profiles. To identify which constraints shape these profiles, we compare four progressively complex nested models: uniform divergence (M0), mutation model (MM), mutation-stability model (MS), and the full mutation-stability-activity model (MSA). Each successive model provides improved fit to observations, demonstrating that mutation, stability, and activity constraints influence structural divergence profiles. Decomposing MSA predictions shows that the relative contributions of the mutation, stability, and activity components vary widely among enzyme families. We find that contributions vary among families because underlying factors vary: mutation contributions depend on internal flexibility heterogeneity, while stability and activity contributions depend on their respective external selection strengths (aS, aA). MSA provides quantitative, family-level estimates of these selection strengths, enabling future studies to link them to context-level properties such as expression, metabolic role, and specificity.