Krivov, SV orcid.org/0000-0002-3493-0068 (2022) Additive eigenvectors as optimal reaction coordinates, conditioned trajectories, and time-reversible description of stochastic processes. The Journal of Chemical Physics, 157 (1). 014108. 014108-. ISSN 0021-9606
Abstract
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.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2022 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
Keywords: | Diffusion; Markov Chains; Models, Biological; Probability; Stochastic Processes |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Biological Sciences (Leeds) > School of Molecular and Cellular Biology (Leeds) > Biological Dynamics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 21 Jul 2022 12:29 |
Last Modified: | 21 Jul 2022 12:29 |
Status: | Published |
Publisher: | American Institute of Physics |
Identification Number: | 10.1063/5.0088061 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:189295 |