Non-catalytic Binding Sites Induce Weaker Long-Range Evolutionary Rate Gradients than Catalytic Sites in Enzymes

Enzymes exhibit a strong long-range evolutionary constraint that extends from their catalytic site and affects even distant sites, where site-specific evolutionary rate increases monotonically with distance. While protein-protein sites in enzymes were previously shown to induce only a weak conservation gradient, a comprehensive relationship between different types of functional sites in proteins and the magnitude of evolutionary rate gradients they induce has yet to be established. Here, we systematically calculate the evolutionary rate (dN/dS) of sites as a function of distance from different types of binding sites in enzymes and other proteins: catalytic sites, non-catalytic ligand binding sites, allosteric binding sites, and protein-protein interaction sites. We show that catalytic sites indeed induce significantly stronger evolutionary rate gradient than all other types of non-catalytic binding sites. In addition, catalytic sites in enzymes with no known allosteric function still induce strong long-range conservation gradients. Notably, the weak long-range conservation gradients induced by non-catalytic binding sites in enzymes is nearly identical in magnitude to those induced by ligand binding sites in non-enzymes. Finally, we show that structural determinants such as local solvent exposure of sites cannot explain the observed difference between catalytic and non-catalytic functional sites. Our results suggest that enzymes and non-enzymes share similar evolutionary constraints only when examined from the perspective of non-catalytic functional sites. Hence, the unique evolutionary rate gradient from catalytic sites in enzymes is likely driven by the optimization of catalysis rather than ligand binding and allosteric functions.