Too packed to change: site-specific substitution rates and side-chain packing in protein evolution

In protein evolution, due to functional and biophysical constraints, the rates of amino acid substitution differ from site to site. Among the best predictors of site-specific rates is packing density. The packing density measure that best correlates with rates is the weighted contact number (WCN), the sum of inverse square distances between the site’s Cα and the other Cα . According to a mechanistic stress model proposed recently, rates are determined by packing because mutating packed sites stresses and destabilizes the protein’s active conformation. While WCN is a measure of Cα packing, mutations replace side chains, which prompted us to consider whether a site’s evolutionary divergence is constrained by main-chain packing or side-chain packing. To address this issue, we extended the stress theory to model side chains explicitly. The theory predicts that rates should depend solely on side-chain packing. We tested these predictions on a data set of structurally and functionally diverse monomeric enzymes. We found that, on average, side-chain contact density (WCNρ ) explains 39.1% of among-sites rate variation, larger than main-chain contact density (WCNα ) which explains 32.1%. More importantly, the independent contribution of WCNα is only 0.7%. Thus, as predicted by the stress theory, site-specific evolutionary rates are determined by side-chain packing.