使用间接伞形取样量化各种形状和大小体积的密度波动
Quantifying density fluctuations in volumes of all shapes and sizes using indirect umbrella sampling
摘要：
水的密度波动是一个重要的统计力学观测，它与多体相关性，以及疏水水化和相互作用有关。在固体水表面的局部水密度波动也被提议作为其疏水性的量度。这些波动可以通过计算在感兴趣的探针体积$v$中观察到$N$水的概率$P_v(N)$来量化。当$v$很大时，使用分子动力学模拟计算$P_v(N)$是具有挑战性的，因为观察到非常少的水的概率是指数小的，并且用于克服该问题的标准程序（$N$中的伞形取样）导致不期望的冲力。Patel等人[J. Phys. Chem. B，114，1632（2010）]最近开发了一种间接伞形取样（INDUS）方法，其对粗粒颗粒数进行取样以获得立方体积的$P_v(N)$。在这里，我们提出并展示了这种方法的扩展到其他基本形状，如球体和圆柱体，以及这些体积的集合。我们进一步描述了INDUS在NPT系综中的实现，并计算了广泛压力范围内的$P_v(N)$分布。我们的方法可能是特别感兴趣的特征蛋白质，纳米管和相关系统的界面的疏水性。
英文摘要：
Water density fluctuations are an important statistical mechanical observable that is related to many-body correlations, as well as hydrophobic hydration and interactions. Local water density fluctuations at a solid-water surface have also been proposed as a measure of its hydrophobicity. These fluctuations can be quantified by calculating the probability, $P_v(N)$, of observing $N$ waters in a probe volume of interest $v$. When $v$ is large, calculating $P_v(N)$ using molecular dynamics simulations is challenging, as the probability of observing very few waters is exponentially small, and the standard procedure for overcoming this problem (umbrella sampling in $N$) leads to undesirable impulsive forces. Patel et al. [J. Phys. Chem. B, 114, 1632 (2010)] have recently developed an indirect umbrella sampling (INDUS) method, that samples a coarse-grained particle number to obtain $P_v(N)$ in cuboidal volumes. Here, we present and demonstrate an extension of that approach to other basic shapes, like spheres and cylinders, as well as to collections of such volumes. We further describe the implementation of INDUS in the NPT ensemble and calculate $P_v(N)$ distributions over a broad range of pressures. Our method may be of particular interest in characterizing the hydrophobicity of interfaces of proteins, nanotubes and related systems.
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