Data from: Sequence entropy of folding and the absolute rate of amino acid substitutions

Adequate representations of protein evolution should consider how the acceptance of mutations depends on the sequence context in which they arise. However, epistatic interactions among sites in a protein result in hererogeneities in the substitution rate, both temporal and spatial, that are beyond the capabilities of current models. Here we use parallels between amino acid substitutions and chemical reaction kinetics to develop an improved theory of protein evolution. We constructed a mechanistic framework for modelling amino acid substitution rates that uses the formalisms of statistical mechanics, with principles of population genetics underlying the analysis. Theoretical analyses and computer simulations of proteins under purifying selection for thermodynamic stability show that substitution rates and the stabilization of resident amino acids (the ‘evolutionary Stokes shift’) can be predicted from biophysics and the effect of sequence entropy alone. Furthermore, we demonstrate that substitutions predominantly occur when epistatic interactions result in near neutrality; substitution rates are determined by how often epistasis results in such nearly neutral conditions. This theory provides a general framework for modelling protein sequence change under purifying selection, potentially explains patterns of convergence and mutation rates in real proteins that are incompatible with previous models, and provides a better null model for the detection of adaptive changes.对蛋白质演化的合理表征，应当考量突变的接受度如何取决于其所处的序列背景。然而，蛋白质各位点间的上位相互作用（epistatic interactions）会导致替换速率在时间与空间上呈现异质性，这是当前模型无法覆盖的范畴。本研究借助氨基酸替换（amino acid substitutions）与化学反应动力学（chemical reaction kinetics）之间的相似性，构建了一套改进的蛋白质演化理论。我们搭建了一个用于建模氨基酸替换速率的机制性框架，该框架采用统计力学（statistical mechanics）的形式体系，并以群体遗传学（population genetics）原理作为分析的底层基础。针对热力学稳定性开展纯化选择（purifying selection）的蛋白质的理论分析与计算机模拟结果显示，替换速率与驻留氨基酸的稳定效应——即所谓“进化斯托克斯位移（evolutionary Stokes shift）”——仅可通过生物物理学与序列熵（sequence entropy）的效应予以预测。此外，本研究证实，当上位相互作用引发近乎中性的状态时，替换事件将占据主导；替换速率由上位性导致此类近乎中性状态的频率所决定。该理论为纯化选择下的蛋白质序列变化建模提供了通用框架，有望解释真实蛋白质中与既往模型不符的趋同演化模式与突变速率特征，并为适应性变化（adaptive changes）的检测提供了更优的零模型（null model）。