Beyond Stability Constraints: A Biophysical Model of Enzyme Evolution with Selection on Stability and Activity

Proteins trace trajectories in sequence space as their amino acids become substituted by other amino acids. The number of substitutions per unit time, the rate of evolution, varies among sites because of biophysical constraints. Several properties that characterize sites' local environments have been proposed as biophysical determinants of site-specific evolutionary rates. Thus, rate increases with increasing solvent exposure, increasing flexibility, and decreasing local packing density. For enzymes, rate increases also with increasing distance from the protein's active residues, presumably due to functional constraints. The dependence of rates on solvent accessibility, packing density, and flexibility has been mechanistically explained in terms of selection for stability. However, as I show here, a stability-based model fails to reproduce the observed rate-distance dependence, overestimating rates close to the active residues and underestimating rates of distant sites. Here, I pose a new biophysical model of enzyme evolution with selection for stability and activity (MSA) and compare it with a stability-based counterpart (MS). Testing these models on a structurally and functionally diverse dataset of monomeric enzymes, I found that MSA fits observed rates better than MS for most proteins. While both models reproduce the observed dependence of rates on solvent accessibility, packing, and flexibility, MSA fits these dependencies somewhat better. Importantly, while MS fails to reproduce the dependence of rates on distance from the active residues, MSA accounts for the rate-distance dependence quantitatively. Thus, the variation of evolutionary rate among enzyme sites is mechanistically underpinned by natural selection for both stability and activity.