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Multiple Markov transition matrix method: Obtaining the stationary probability distribution from multiple simulations
Author(s) -
Sakuraba Shun,
Kitao Akio
Publication year - 2009
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.21186
Subject(s) - markov chain , stochastic matrix , statistical physics , stationary distribution , probability distribution , non equilibrium thermodynamics , molecular dynamics , histogram , distribution (mathematics) , matrix (chemical analysis) , continuous time markov chain , markov process , mathematics , computer science , markov model , algorithm , balance equation , physics , chemistry , thermodynamics , computational chemistry , statistics , artificial intelligence , mathematical analysis , chromatography , image (mathematics)
We herein propose the multiple Markov transition matrix method (MMMM), an algorithm by which to estimate the stationary probability distribution from independent multiple molecular dynamics simulations with different Hamiltonians. Applications to the potential of mean force calculation in combination with the umbrella sampling method are presented. First, the performance of the MMMM is examined in the case of butane. Compared with the weighted histogram analysis method (WHAM), the MMMM has an advantage with respect to the reasonable evaluation of the stationary probability distribution even from nonequilibrium trajectories. This method is then applied to Met‐enkephalin nonequilibrium simulation. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009