Analysis of Markov Models

Abstract

When accurately estimated and validated, Markov model transition matrices contain information of the long-time molecular kinetics and thermodynamic properties of the molecular system studied, approximated on the discrete state space. Thus, many quantities of interest to the molecular scientist can now be calculated from the Markov model transition matrix rather than from a “direct” analysis of the underlying simulation data. The advantage over a direct analysis is that the Markov model provides straightforward access to some quantities that direct analyses do not, such as the equilibrium relaxation timescales and the assignment to transition processes via the eigenvalues and eigenvectors of the transition matrix. Moreover, Markov models permit a rigorous assessment of the statistical estimation error of any quantity calculated from the transition matrix, as described in the previous chapter. This chapter describes the following quantities that can be calculated from transition matrices: (1) Eigenvectors and Eigenvalues and their relation to equilibrium relaxation timescales and structural changes. (2) Metastable states. (3) Transition pathways. All quantities are illustrated on a simple discrete protein folding example.

Part of this article, including figures has been originally published in J.H. Prinz, B. Keller, F. Noé: “Probing molecular kinetics with Markov models: metastable states, transition pathways and spectroscopic observables”, Phys. Chem. Chem. Phys. 13, pp. 16912–16927 (2011)—Reproduced by permission of The Royal Society of Chemistry.