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

Abstract 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. Competing Interest Statement The authors have declared no competing interest. Footnotes jechave{at}unsam.edu.ar, mathilde.carpentier{at}mnhn.fr This version is a thorough revision of the manuscript in response to peer review. The main changes are: (1) The paper has been restructured, with Methods moved to the end. (2) The Results section has been completely revised to be self-contained, opening with a new model overview (Section 2.1) and including sufficient method details within each subsection for the results to be understood without reading the Methods. (3) The Introduction has been revised to focus on structural evolution, with an expanded survey of empirical studies and mechanistic models. (4) The Discussion has been substantially expanded to address the significance and limitations of the work, the performance of the model in the context of analogous problems in sequence evolution, and future directions connecting the estimated selection parameters to enzyme biology. (5) The Methods section has been expanded, particularly the description of the LFENM model and the derivation of mutational effects on structure, stability, and activation energy. (6) A toy-model illustration has been added (Supplementary Section S1, Figure S1) that derives all key quantities step by step. (7) Supplementary Tables S1, S2, and S3 have been added with dataset information and model results. (8) The title has been changed. (9) New references have been added throughout.