Why structural divergence varies among residues in enzyme evolution: contributions of mutation, stability, and activity constraints.

In enzyme evolution, structural divergence varies among residues, forming residue-dependent structural divergence profiles. The evolutionary constraints that determine these profiles remain unclear. We build on the mutation-stability-activity (MSA) model, a mechanistic mutation-selection model previously developed for sequence evolution. In the MSA model, mutations become fixed or are lost depending on their effects on stability and activity, with parameters aS and aA controlling selection on stability and activity, respectively. The Linearly Forced Elastic Network Model (LFENM) is used to calculate mutational effects on structure, stability, and activity. As substitutions accumulate, structural changes build up unevenly across residues, producing a structural divergence profile that depends on how each residue responds to mutation and on how strongly selection acts on stability and activity. Applied to 34 enzyme families, the MSA model recapitulates observed structural divergence profiles, and nested model comparisons show that mutation, stability, and activity constraints each contribute. However, the balance among these constraints varies widely across families: mutation always contributes substantially, but stability and activity contributions range from negligible to dominant, so any of the three can prevail in a given family. These variations have distinct origins: the mutation contribution depends on how unevenly the protein's flexibility is distributed across residues, while the stability and activity contributions depend on how strongly selection acts, as quantified by aS and aA. The MSA model thus recovers family-specific selection strengths from structural divergence profiles, suggesting these profiles encode information not only about enzyme architecture but also about the selective regime under which enzymes evolve.