Department of Chemistry, King's College London, SE1 1DB London, U.K.
Department of Physics and Astronomy, University College London, WC1E 6BT London, U.K.
J Chem Theory Comput. 2021 Apr 13;17(4):2022-2033. doi: 10.1021/acs.jctc.0c01151. Epub 2021 Mar 17.
A variety of enhanced statistical and numerical methods are now routinely used to extract important thermodynamic and kinetic information from the vast amount of complex, high-dimensional data obtained from molecular simulations. For the characterization of kinetic properties, Markov state models, in which the long-time statistical dynamics of a system is approximated by a Markov chain on a discrete partition of configuration space, have seen widespread use in recent years. However, obtaining kinetic properties for molecular systems with high energy barriers remains challenging as often enhanced sampling techniques are required with biased simulations to observe the relevant rare events. Particularly, the calculation of diffusion coefficients remains elusive from biased molecular simulation data. Here, we propose a novel method that can calculate multidimensional position-dependent diffusion coefficients equally from either biased or unbiased simulations using the same formalism. Our method builds on Markov state model analysis and the Kramers-Moyal expansion. We demonstrate the validity of our formalism using one- and two-dimensional analytic potentials and also apply it to data from explicit solvent molecular dynamics simulations, including the water-mediated conformations of alanine dipeptide and umbrella sampling simulations of drug transport across a lipid bilayer. Importantly, the developed algorithm presents significant improvement compared to standard methods when the transport of solute across three-dimensional heterogeneous porous media is studied, for example, the prediction of membrane permeation of drug molecules.
现在，各种增强的统计和数值方法被常规用于从分子模拟中获得的大量复杂高维数据中提取重要的热力学和动力学信息。对于动力学性质的描述，马尔可夫状态模型已经在近年来得到了广泛的应用，其中系统的长时间统计动力学由配置空间离散分区上的马尔可夫链来近似。然而，对于具有高能量势垒的分子体系，获得动力学性质仍然具有挑战性，因为通常需要使用有偏的模拟来进行增强采样，以观察相关的罕见事件。特别是，从有偏的分子模拟数据中计算扩散系数仍然难以捉摸。在这里，我们提出了一种新的方法，该方法可以使用相同的形式从有偏或无偏的模拟中同样地计算多维位置相关的扩散系数。我们的方法基于马尔可夫状态模型分析和 Kramers-Moyal 展开。我们使用一维和二维解析势来证明我们的形式的有效性，并且还将其应用于来自显式溶剂分子动力学模拟的数据，包括丙氨酸二肽的水介导构象和药物跨脂质双层的伞形采样模拟。重要的是，与标准方法相比，当研究溶质在三维非均相多孔介质中的传输时，所开发的算法呈现出显著的改进，例如，预测药物分子的膜渗透。
