Building Markov state models along pathways to determine free energies and rates of transitions

Abstract

An efficient method is proposed for building Markov models with discrete states able to accurately describe the slow relaxation of a complex system with two stable conformations. First, the reaction pathway described by a set of collective variables between the two stable states is determined using the string method with swarms of trajectories. Then, short trajectories are initiated at different points along this pathway to build the state-to-state transition probability matrix. It is shown, using a model system, how this strategy makes it possible to use trajectories that are significantly shorter than the slowest relaxation time to efficiently build a reliable and accurate Markov model. Extensions of the method to multiple pathways, as well as some common pitfalls arising from poorly relaxed paths or an inappropriate choice of collective variables, are illustrated and discussed.

Optimal control of molecular dynamics using Markov state models

“…Recently the interest in MSMs has increased a lot, for it had been demonstrated that MSMs can be constructed even for very high dimensional systems [25]. They have been especially useful for modelling the interesting slow dynamics of biomolecules [21,[28][29][30][31][32] and materials [33] (there under the name "kinetic Monte Carlo"). If the system exhibits metastability and the jump process between the metastable sets are approximately Markovian, the corresponding MSM simply describes the Markov process that jumps between the sets with the aggregated statistics of the original process.…”

Estimation and uncertainty of reversible Markov models

“…[1][2][3][4][5][6][7] These models allow us to analyze the longest-living (metastable) sets of structures, 8 the effective transition rates between them, 9,10 the kinetic relaxation processes and their relationship to equilibrium kinetics experiments, 7,[11][12][13][14] and the thermodynamics and kinetics over multiple thermodynamic states. [15][16][17][18] A key advantage of MSMs is that they are estimated from conditional transition statistics between states, and they thus do not require the data to be in global equilibrium across all states.…”

A network of molecular switches controls the activation of the two-component response regulator NtrC

“…MSMs have been used extensively to study large-scale conformational changes involved in protein folding as well as more subtle changes involved in receptor activation and ligand binding [29][30][31][32][33][34][35][36] . This study further supports the utility of MSMs as a natural framework for understanding and quantifying changes in hydrogen bond networks or residue side chain rotations associated with many protein conformational changes in signalling networks.…”