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.

中文翻译：

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通过偏差模拟和多状态重加权获得统计上最优的连续自由能面。

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，在理解和工程化分子行为方面具有重要价值。这些自由能表面最常用的是使用直方图技术的变体来估算，但是这种方法掩盖了这些功能的两个重要方面。首先，沿着集体变量的经验观测值由一组离散观测值定义，并且将这些观测值粗化为直方图bin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，由于离散化，它的直方图表示引入了固有近似。在这个研究中，我们将偏差模拟中观察到的离散观测结果与推断出的集体变量上潜在的连续概率分布相关联，并推导出无直方图的技术来估算该自由能面。我们将自由能表面估计重新构造为连续试验函数和离散经验分布之间的Kullback-Leibler散度的最小值，并表明这等效于给定一组采样数据的试验函数的似然最大化。然后，我们对这种形式主义提出了完全的贝叶斯方法，从而可以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。