University of Leeds, Astbury Center for Structural Molecular Biology, Faculty of Biological Sciences, University of Leeds, Leeds LS2 9JT, United Kingdom.
J Chem Phys. 2022 Jul 7;157(1):014108. doi: 10.1063/5.0088061.
A fundamental way to analyze complex multidimensional stochastic dynamics is to describe it as diffusion on a free energy landscape-free energy as a function of reaction coordinates (RCs). For such a description to be quantitatively accurate, the RC should be chosen in an optimal way. The committor function is a primary example of an optimal RC for the description of equilibrium reaction dynamics between two states. Here, additive eigenvectors (addevs) are considered as optimal RCs to address the limitations of the committor. An addev master equation for a Markov chain is derived. A stationary solution of the equation describes a sub-ensemble of trajectories conditioned on having the same optimal RC for the forward and time-reversed dynamics in the sub-ensemble. A collection of such sub-ensembles of trajectories, called stochastic eigenmodes, can be used to describe/approximate the stochastic dynamics. A non-stationary solution describes the evolution of the probability distribution. However, in contrast to the standard master equation, it provides a time-reversible description of stochastic dynamics. It can be integrated forward and backward in time. The developed framework is illustrated on two model systems-unidirectional random walk and diffusion.
分析复杂多维随机动力学的一种基本方法是将其描述为在自由能景观上的扩散-自由能是反应坐标（RCs）的函数。为了使这种描述具有定量准确性，RC 应该以最佳方式选择。配分函数是描述两个状态之间平衡反应动力学的最佳 RC 的主要示例。在这里，加性本征向量（addevs）被认为是解决配分函数限制的最佳 RC。推导出了马科夫链的 addev 主方程。该方程的稳态解描述了具有相同最佳 RC 的轨迹的子集合，用于正向和时间反转动力学的子集合。这样的轨迹子集合的集合，称为随机本征模，可以用于描述/近似随机动力学。非稳态解描述了概率分布的演化。然而，与标准主方程相比，它提供了随机动力学的时间可逆描述。它可以在时间上向前和向后集成。所开发的框架在两个模型系统-单向随机游走和扩散上进行了说明。
