LAUSR

The rate of evolution varies among sites within proteins. In enzymes, two rate gradients are observed: rate decreases with increasing local packing and it increases with increasing distance from catalytic residues. The rate-packing gradient would be mainly due to stability constraints and is well reproduced by biophysical models with selection for protein stability. However, stability constraints are unlikely to account for the rate-distance gradient. Here, to explore the mechanistic underpinnings of the rate gradients observed in enzymes, I propose a stability-activity model of enzyme evolution, MSA. This model is based on a two-dimensional fitness function that depends on stability, quantified by ΔG, the enzyme's folding free energy, and activity, quantified by ΔG*, the activation energy barrier of the enzymatic reaction. I test MSA on a diverse data set of enzymes, comparing it with two simpler models: MS, which depends only on ΔG, and MA, which depends only on ΔG*. I found that MSA clearly outperforms both MS and MA and it accounts for both the rate-packing and rate-distance gradients. Thus, MSA captures the distribution of stability and activity constraints within enzymes, explaining the resulting patterns of rate variation among sites.