Too packed to change: side-chain packing and site-specific substitution rates 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 are solvent accessibility and packing density. The packing density measure that best correlates with rates is the weighted contact number (WCN), the sum of inverse square distances between a site's C α and the C α of the other sites. 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 C α packing, mutations replace side chains. Here, we 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 contact density. We tested this prediction on a data set of structurally and functionally diverse monomeric enzymes. We compared side-chain contact density with main-chain contact density measures and with relative solvent accessibility (RSA). We found that side-chain contact density is the best predictor of rate variation among sites (it explains 39.2% of the variation). Moreover, the independent contribution of main-chain contact density measures and RSA are negligible. Thus, as predicted by the stress theory, site-specific evolutionary rates are determined by side-chain packing.