Proteins evolve under a myriad of biophysical selection pressures that collectively control the patterns of amino acid substitutions. These evolutionary pressures are sufficiently consistent over time and across protein families to produce substitution patterns, summarized in global amino acid substitution matrices such as BLOSUM, JTT, WAG, and LG, which can be used to successfully detect homologs, infer phylogenies, and reconstruct ancestral sequences. Although the factors that govern the variation of amino acid substitution rates have received much attention, the influence of thermodynamic stability constraints remains unresolved. Here we develop a simple model to calculate amino acid substitution matrices from evolutionary dynamics controlled by a fitness function that reports on the thermodynamic effects of amino acid mutations in protein structures. This hybrid biophysical and evolutionary model accounts for nucleotide transition/transversion rate bias, multi-nucleotide codon changes, the number of codons per amino acid, and thermodynamic protein stability. We find that our theoretical model accurately recapitulates the complex yet universal pattern observed in common global amino acid substitution matrices used in phylogenetics. These results suggest that selection for thermodynamically stable proteins, coupled with nucleotide mutation bias filtered by the structure of the genetic code, is the primary driver behind the global amino acid substitution patterns observed in proteins throughout the tree of life.

中文翻译：

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蛋白质结构进化的热力学模型解释了经验性氨基酸取代矩阵

蛋白质在无数生物物理选择压力下进化，这些压力共同控制氨基酸取代的模式。这些进化压力随时间和跨蛋白质家族足够一致以产生替换模式，概括为全局氨基酸替换矩阵，如 BLOSUM、JTT、WAG 和 LG，可用于成功检测同源物、推断系统发育和重建祖先序列。尽管控制氨基酸取代率变化的因素受到了广泛关注，但热力学稳定性约束的影响仍未解决。在这里，我们开发了一个简单的模型，用于根据由适应度函数控制的进化动力学计算氨基酸替代矩阵，该函数报告蛋白质结构中氨基酸突变的热力学效应。这种混合生物物理和进化模型解释了核苷酸转变/颠换率偏差、多核苷酸密码子变化、每个氨基酸的密码子数量和热力学蛋白质稳定性。我们发现我们的理论模型准确地概括了在系统发育学中使用的常见全局氨基酸替代矩阵中观察到的复杂而普遍的模式。这些结果表明，选择热力学稳定的蛋白质，再加上遗传密码结构过滤的核苷酸突变偏倚，