Escuela de Ciencia y Tecnología, Universidad Nacional de San Martín, Martín de Irigoyen 3100, 1650 San Martín, Buenos Aires Argentina.
BMC Evol Biol. 2014 Apr 9;14:78. doi: 10.1186/1471-2148-14-78.
Protein sites evolve at different rates due to functional and biophysical constraints. It is usually considered that the main structural determinant of a site's rate of evolution is its Relative Solvent Accessibility (RSA). However, a recent comparative study has shown that the main structural determinant is the site's Local Packing Density (LPD). LPD is related with dynamical flexibility, which has also been shown to correlate with sequence variability. Our purpose is to investigate the mechanism that connects a site's LPD with its rate of evolution.
We consider two models: an empirical Flexibility Model and a mechanistic Stress Model. The Flexibility Model postulates a linear increase of site-specific rate of evolution with dynamical flexibility. The Stress Model, introduced here, models mutations as random perturbations of the protein's potential energy landscape, for which we use simple Elastic Network Models (ENMs). To account for natural selection we assume a single active conformation and use basic statistical physics to derive a linear relationship between site-specific evolutionary rates and the local stress of the mutant's active conformation.We compare both models on a large and diverse dataset of enzymes. In a protein-by-protein study we found that the Stress Model outperforms the Flexibility Model for most proteins. Pooling all proteins together we show that the Stress Model is strongly supported by the total weight of evidence. Moreover, it accounts for the observed nonlinear dependence of sequence variability on flexibility. Finally, when mutational stress is controlled for, there is very little remaining correlation between sequence variability and dynamical flexibility.
We developed a mechanistic Stress Model of evolution according to which the rate of evolution of a site is predicted to depend linearly on the local mutational stress of the active conformation. Such local stress is proportional to LPD, so that this model explains the relationship between LPD and evolutionary rate. Moreover, the model also accounts for the nonlinear dependence between evolutionary rate and dynamical flexibility.
由于功能和生物物理限制，蛋白质位点以不同的速率进化。通常认为，一个位点进化速率的主要结构决定因素是其相对溶剂可及性（RSA）。然而，最近的一项比较研究表明，主要的结构决定因素是位点的局部堆积密度（LPD）。LPD 与动态灵活性有关，动态灵活性也与序列变异性相关。我们的目的是研究连接位点的 LPD 与其进化速率的机制。
我们考虑了两种模型：经验灵活性模型和机械应力模型。灵活性模型假设位点特异性进化速率随动态灵活性线性增加。我们在这里引入的应力模型将突变建模为蛋白质势能景观的随机扰动，对于这些扰动，我们使用简单的弹性网络模型（ENM）。为了考虑自然选择，我们假设只有一个活跃构象，并使用基本统计物理学来推导位点特异性进化速率与突变的活跃构象的局部应力之间的线性关系。我们在一个大型和多样化的酶数据集上比较了这两种模型。在对蛋白质的逐个研究中，我们发现对于大多数蛋白质，应力模型的性能优于灵活性模型。将所有蛋白质汇总在一起，我们表明应力模型得到了证据的总权重的强烈支持。此外，它解释了序列变异性对灵活性的观察到的非线性依赖性。最后，当控制突变压力时，序列变异性与动态灵活性之间几乎没有剩余相关性。
我们根据该机制开发了一种进化的机械应力模型，根据该模型，一个位点的进化速率预计与活跃构象的局部突变压力呈线性相关。这种局部压力与 LPD 成正比，因此该模型解释了 LPD 与进化速率之间的关系。此外，该模型还解释了进化速率与动态灵活性之间的非线性关系。
