In many applications of evolutionary inference, a model of protein evolution needs to be fitted to the amino acid variation at individual sites in a multiple sequence alignment. Most existing models fall into one of two extremes: Either they provide a coarse-grained description that lacks biophysical realism (e.g., dN/dS models), or they require a large number of parameters to be fitted (e.g., mutation–selection models). Here, we ask whether a middle ground is possible: Can we obtain a realistic description of site-specific amino acid frequencies while severely restricting the number of free parameters in the model? We show that a distribution with a single free parameter can accurately capture the variation in amino acid frequency at most sites in an alignment, as long as we are willing to restrict our analysis to predicting amino acid frequencies by rank rather than by amino acid identity. This result holds equally well both in alignments of empirical protein sequences and of sequences evolved under a biophysically realistic all-atom force field. Our analysis reveals a near universal shape of the frequency distributions of amino acids. This insight has the potential to lead to new models of evolution that have both increased realism and a limited number of free parameters.

在进化推理的许多应用中，需要将蛋白质进化模型拟合到多序列比对中单个位点的氨基酸变异。大多数现有模型都属于两个极端之一：要么提供缺乏生物物理真实性的粗粒度描述（例如，dN / dS模型），或者它们需要拟合大量参数（例如，突变选择模型）。在这里，我们问是否有可能采取中间立场：我们能否在严格限制模型中自由参数的数量的同时获得位点特定氨基酸频率的真实描述？我们表明，具有单个自由参数的分布可以准确地捕获比对中大多数位点的氨基酸频率变化，只要我们愿意将我们的分析限制为通过排名而不是通过氨基酸同一性来预测氨基酸频率。该结果同样适用于经验蛋白质序列的比对和在生物物理现实的全原子力场下进化的序列。我们的分析揭示了氨基酸频率分布的近乎普遍的形状。