Statistically optimal continuous free energy surfaces from biased simulations and multistate reweighting
Statistically optimal continuous free energy surfaces from biased simulations and multistate reweighting
复制标题
来自有偏模拟和多态重新加权的统计最优连续自由能表面
DOI：
10.1021/acs.jctc.0c00077
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发表时间：
2020
影响因子：
5.5
通讯作者：
Ferguson, Andrew L.
中科院分区：
文献类型：
--
作者：
Shirts, Michael R.;Ferguson, Andrew L.
自由能作为一组选定的集体变量的函数通常在分子模拟中计算，对于理解和设计分子行为具有重要价值。这些自由能表面最常使用直方图技术的变体来估计，但这种方法掩盖了这些函数的两个重要方面。首先，沿着集体变量的经验观察是由离散观察的集合定义的，并且将这些观察粗化为直方图箱会导致不必要的信息丢失。其次，自由能表面本身几乎总是一个连续函数，并且由于离散化，其用直方图表示引入了固有的近似值。在这项研究中，我们将有偏模拟中观察到的离散观察结果与集体变量上推断的潜在连续概率分布联系起来，并推导出用于估计该自由能表面的无直方图技术。我们将自由能表面估计重新表述为连续试验函数和离散经验分布之间的 Kullback-Leibler 散度的最小化，并表明这相当于给定一组采样数据的试验函数的似然最大化。然后，我们提出了对这种形式主义的完全贝叶斯处理，这使得能够合并强大的贝叶斯工具，例如包含正则化先验、不确定性量化和模型选择技术。我们通过对空腔中结合有苯的 T4 溶菌酶 L99A 突变体中缬氨酸侧链的 χ 扭转进行伞式采样模拟分析，证明了这种新的形式。
Free energies as a function of a selected set of collective variables are commonly computed in molecular simulation and of significant value in understanding and engineering molecular behavior. These free energy surfaces are most commonly estimated using variants of histogramming techniques, but such approaches obscure two important facets of these functions. First, the empirical observations along the collective variable are defined by an ensemble of discrete observations, and the coarsening of these observations into a histogram bin incurs unnecessary loss of information. Second, the free energy surface is itself almost always a continuous function, and its representation by a histogram introduces inherent approximations due to the discretization. In this study, we relate the observed discrete observations from biased simulations to the inferred underlying continuous probability distribution over the collective variables and derive histogram-free techniques for estimating this free energy surface. We reformulate free energy surface estimation as minimization of a Kullback–Leibler divergence between a continuous trial function and the discrete empirical distribution and show that this is equivalent to likelihood maximization of a trial function given a set of sampled data. We then present a fully Bayesian treatment of this formalism, which enables the incorporation of powerful Bayesian tools such as the inclusion of regularizing priors, uncertainty quantification, and model selection techniques. We demonstrate this new formalism in the analysis of umbrella sampling simulations for the χ torsion of a valine side chain in the L99A mutant of T4 lysozyme with benzene bound in the cavity.