Gaussian Markov transition models of molecular kinetics

The Journal of Chemical Physics
Hao Wu, Frank Noé

Abstract

The slow processes of molecular dynamics (MD) simulations--governed by dominant eigenvalues and eigenfunctions of MD propagators--contain essential information on structures of and transition rates between long-lived conformations. Existing approaches to this problem, including Markov state models and the variational approach, represent the dominant eigenfunctions as linear combinations of a set of basis functions. However the choice of the basis functions and their systematic statistical estimation are unsolved problems. Here, we propose a new class of kinetic models called Markov transition models (MTMs) that approximate the transition density of the MD propagator by a mixture of probability densities. Specifically, we use Gaussian MTMs where a Gaussian mixture model is used to approximate the symmetrized transition density. This approach allows for a direct computation of spectral components. In contrast with the other Galerkin-type approximations, our approach can automatically adjust the involved Gaussian basis functions and handle the statistical uncertainties in a Bayesian framework. We demonstrate by some simulation examples the effectiveness and accuracy of the proposed approach.

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Citations

Feb 8, 2016·The Journal of Chemical Physics·Feliks NüskeFrank Noé
Nov 18, 2015·Journal of Chemical Theory and Computation·Martin K SchererFrank Noé
Nov 18, 2015·Journal of Chemical Theory and Computation·Frank Noé, Cecilia Clementi
Jan 4, 2018·Nature Communications·Andreas MardtFrank Noé
Nov 24, 2019·The Journal of Chemical Physics·Frank Noé, Edina Rosta
May 5, 2021·Chemical Reviews·Aldo GlielmoAlessandro Laio
Jan 13, 2018·Journal of the American Chemical Society·Brooke E Husic, Vijay S Pande
Apr 17, 2018·Journal of Chemical Theory and Computation·Florian LitzingerCecilia Clementi

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