Markov state models of biomolecular conformational dynamics

Abstract

It has recently become practical to construct Markov state models (MSMs) that reproduce the long-time statistical conformational dynamics of biomolecules using data from molecular dynamics simulations. MSMs can predict both stationary and kinetic quantities on long timescales (e.g. milliseconds) using a set of atomistic molecular dynamics simulations that are individually much shorter, thus addressing the well-known sampling problem in molecular dynamics simulation. In addition to providing predictive quantitative models, MSMs greatly facilitate both the extraction of insight into biomolecular mechanism (such as folding and functional dynamics) and quantitative comparison with single-molecule and ensemble kinetics experiments. A variety of methodological advances and software packages now bring the construction of these models closer to routine practice. Here, we review recent progress in this field, considering theoretical and methodological advances, new software tools, and recent applications of these approaches in several domains of biochemistry and biophysics, commenting on remaining challenges.

Figure 1

Schematic illustrating important properties of MSMs and their construction. (A) A metastable four-well potential. (B) Eigenfunctions of the Markov operator (solid) and eigenfunctions approximated by the eigenvectors of a MSM using four states separating the four basins. (C) Implied timescales plot. The MSM timescales (solid) converge to the true relaxation timescales with increasing observation interval, or lag time, τ, but may do so only slowly. PMM timescales [3] (dashed) converge rapidly. (D) MSM construction. Using some state space discretization, the simulation trajectories are mapped to discrete trajectories. From these, the transition matrix P is estimated whose largest eigenvalues/eigenvectors approximate the true largest eigenvalues/eigenfunctions. P is then analyzed for molecular observables of interest.