Everything you wanted to know about Markov State Models but were afraid to ask

Abstract

Simulating protein folding has been a challenging problem for decades due to the long timescales involved (compared with what is possible to simulate) and the challenges of gaining insight from the complex nature of the resulting simulation data. Markov State Models (MSMs) present a means to tackle both of these challenges, yielding simulations on experimentally relevant timescales, statistical significance, and coarse grained representations that are readily humanly understandable. Here, we review this method with the intended audience of non-experts, in order to introduce the method to a broader audience. We review the motivations, methods, and caveats of MSMs, as well as some recent highlights of applications of the method. We conclude by discussing how this approach is part of a paradigm shift in how one uses simulations, away from anecdotal single-trajectory approaches to a more comprehensive statistical approach.

Figure 1

The population of the folded state was monitored throughout the ensemble of 545 trajectories (black). The same population can be calculated by propagating the initial populations using MSM dynamics (blue). That both agree to within error suggests that the MSM accurately models the folding kinetics in this molecular dynamics dataset [8]. The model was constructed from simulations of a fast-folding villin headpiece mutant [9]. This figure was reproduced from Ref. [8].

Figure 2

The MSM-estimated equilibrium populations can be used to calculate the free energies of microstates. Here the lowest free energy states (most populated) are structurally similar to the experimentally determined crystal structure. The model was constructed from simulations of a fast-folding villin headpiece mutant [8]. This figure was reproduced from Ref. [8].

Figure 3

The top 15 pathways of NTL9 folding were calculated using TPT. Each node represents a macrostate and is sized by the equilibrium free energy −kt log(P). The edges are sized by the folding flux through each segment, so the dominant pathways are depicted by larger arrows. This figure was reproduced from Ref. [21].