Studying the effect of perturbations on protein structure is a basic approach in protein research. Important problems, such as predicting pathological mutations and understanding patterns structural evolution, have been addressed by computational simulations based on modelling mutations as forces and predicting deformations using the Linear Response Approximation. In single mutation-response scanning simulations, a sensitivity matrix is obtained by averaging deformations over point mutations. In double mutation-response scanning simulations, a compensation matrix is obtained by minimizing deformations over pairs of mutations. These very useful simulation-based methods may be too slow to deal with large supra-molecular complexes, such as a ribosome or a virus capsid, or large number of proteins, such as the human proteome, which limits their applicability. To address this issue, I derived analytical closed formulas to calculate the sensitivity and compensation matrices directly, without simulations. Here, I present these derivations and show that the resulting analytical methods are much faster than their simulation counterparts, and that where the simulation methods are approximate, the analytical methods are exact by design.

中文翻译：

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快速准确的蛋白质单突变和双突变响应扫描

研究微扰对蛋白质结构的影响是蛋白质研究的基本方法。通过基于将突变建模为力并使用线性响应近似来预测变形的计算模拟已解决了重要问题，例如预测病理突变和理解模式结构演变。在单突变响应扫描模拟中，通过对点突变的平均变形来获得灵敏度矩阵。在双突变响应扫描模拟中，通过最小化成对突变的变形来获得补偿矩阵。这些非常有用的基于模拟的方法可能太慢，无法处理大型超分子复合物（如核糖体或病毒衣壳）或大量蛋白质（如人蛋白质组），这限制了它们的适用性。为了解决这个问题，我导出了解析的封闭公式，无需仿真即可直接计算灵敏度和补偿矩阵。在这里，我介绍了这些推导，并表明所得的分析方法比其模拟方法要快得多，并且在模拟方法为近似值的情况下，分析方法在设计上是精确的。