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.

蛋白质进化的合理表征需考量突变的接纳概率如何依赖于其所处的序列上下文（sequence context）。然而，蛋白质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维度上呈现异质性，这超出了当前模型的处理能力范畴。在此，我们借助氨基酸替换与化学反应动力学之间的相似性，构建了一套改进的蛋白质进化理论。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）原理作为分析基础。针对处于纯化选择（purifying selection）下以维持热力学稳定性（thermodynamic stability）的蛋白质开展的理论分析与计算机模拟（computer simulations）显示，替换速率与驻留氨基酸的稳定效应——即所谓的‘进化斯托克斯位移（evolutionary Stokes shift）’——可仅通过生物物理学（biophysics）原理与序列熵（sequence entropy）的效应进行预测。进一步研究表明，当上位相互作用使突变处于近乎中性状态时，替换事件会频繁发生；替换速率由上位相互作用造就此类近乎中性条件的频率所决定。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率特征，并为适应性变异的检测提供了更优的零模型（null model）。