Gaussian Markov transition models of molecular kinetics

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.