Mitsuta Yuki, Asada Toshio
Department of Chemistry, Osaka Metropolitan University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan.
RIMED, Osaka Metropolitan University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan.
J Chem Theory Comput. 2024 Aug 13;20(15):6531-6548. doi: 10.1021/acs.jctc.4c00282. Epub 2024 Aug 5.
Umbrella sampling (US) is an effective method for calculating free-energy landscapes (FELs). However, the complexity of controlling the sampling positions complicates multidimensional FEL calculations. In this study, we proposed a method for controlling sampling by optimizing the US parameters. This method comprises the introduction of a target point and the optimization of the parameters to sample a window around this point. We approximated each window to normal distributions using an umbrella integration method and calculated the divergences between the window distributions and the state distributed at the target position by a variationally enhanced sampling method. Thus, the minimization of the divergence facilitated sampling around the target point, after which the parameters could be optimized on the fly while performing equilibration simulation. In practice, our method employs bias potentials with off-diagonal terms, ensuring a more efficient calculation of multidimensional FEL. Additionally, we developed an algorithm for determining the target point for automated FEL search; the algorithm samples in a specified direction while controlling the overlap of distributions. We performed three different FEL calculations as examples: (1) the calculation of the permeation of a water molecule through a lipid bilayer (one-dimensional FEL), (2) the calculation of the internal structural changes in alanine dipeptide in water (two-dimensional FEL), and (3) the calculation of the internal structural changes from a β-strand structure to an α-helix structure in alanine decapeptide (Ala10, 16-dimensional FEL). These results confirmed that our method could control the number of US windows and calculate the high-dimensional FELs that could not be evaluated by the conventional US method.
伞形抽样（US）是一种计算自由能景观（FEL）的有效方法。然而，控制抽样位置的复杂性使多维FEL计算变得复杂。在本研究中，我们提出了一种通过优化US参数来控制抽样的方法。该方法包括引入一个目标点并优化参数以对该点周围的一个窗口进行抽样。我们使用伞形积分方法将每个窗口近似为正态分布，并通过变分增强抽样方法计算窗口分布与目标位置处分布状态之间的散度。因此，散度的最小化有助于在目标点周围进行抽样，之后可以在进行平衡模拟时即时优化参数。在实际应用中，我们的方法采用带有非对角项的偏置势，确保更高效地计算多维FEL。此外，我们开发了一种用于确定自动FEL搜索目标点的算法；该算法在控制分布重叠的同时沿指定方向进行抽样。我们以三个不同的FEL计算为例：（1）水分子通过脂质双层的渗透计算（一维FEL），（2）水中丙氨酸二肽内部结构变化的计算（二维FEL），以及（3）丙氨酸十肽（Ala10，16维FEL）从β链结构到α螺旋结构的内部结构变化计算。这些结果证实了我们的方法可以控制US窗口的数量，并计算传统US方法无法评估的高维FEL。
