Markov models of molecular kinetics: Generation and validation

Abstract

Markov state models of molecular kinetics (MSMs), in which the long-time statistical dynamics of a molecule is approximated by a Markov chain on a discrete partition of configuration space, have seen widespread use in recent years. This approach has many appealing characteristics compared to straightforward molecular dynamics simulation and analysis, including the potential to mitigate the sampling problem by extracting long-time kinetic information from short trajectories and the ability to straightforwardly calculate expectation values and statistical uncertainties of various stationary and dynamical molecular observables. In this paper, we summarize the current state of the art in generation and validation of MSMs and give some important new results. We describe an upper bound for the approximation error made by modeling molecular dynamics with a MSM and we show that this error can be made arbitrarily small with surprisingly little effort. In contrast to previous practice, it becomes clear that the best MSM is not obtained by the most metastable discretization, but the MSM can be much improved if non-metastable states are introduced near the transition states. Moreover, we show that it is not necessary to resolve all slow processes by the state space partitioning, but individual dynamical processes of interest can be resolved separately. We also present an efficient estimator for reversible transition matrices and a robust test to validate that a MSM reproduces the kinetics of the molecular dynamics data.

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

“…In this study, we use extensive MD simulations to build a Markov state model (MSM) for estimating the thermodynamics and kinetic properties of NtrC dynamics. MSMs reduce the complex conformational landscape of a protein to a set of metastable conformational states and the rates of transition between them [18][19][20] . The MSM of NtrC reveals a network of molecular switches that control NtrC activation and identifies metastable states on the NtrC conformational free energy landscape that could be targeted for inhibitor design.…”

Efficient Construction of Mesostate Networks from Molecular Dynamics Trajectories

“…It has been argued that at the level of coarse Markov state models, details of the algorithm are not important. 37 Note again that the aforementioned algorithms are general data processing tools with a modular definition of similarity, and that dedicated grouping schemes as discussed may be available. 19,27,28 In this contribution, we propose a tree-based algorithm that relies on partitioning according to a preset schedule of threshold criteria operating at each level of the tree.…”

“…38,39 Alternatively, fixed partition algorithms such as the approximate K-centers (K-medoids) algorithms 40,41 are in use. 15,19,37,42 All aforementioned methods scale superlinearly with dataset size (because in fixed partitioning schemes, the number of mesostates, K, will have to be proportional to N unless sampling is exhaustive). Post-processing of initial results may involve application of similar or more rigorous algorithms such as strictly hierarchical schemes.…”

“…It is undesirable to have many parameters or system-specific performance characteristics because the structure of the data is not known a priori. The simplest class of approaches is based on the Leader algorithm 36 (in Prinz et al 37 referred to a regular space clustering). 38,39 Alternatively, fixed partition algorithms such as the approximate K-centers (K-medoids) algorithms 40,41 are in use.…”

Communication: Microsecond peptide dynamics from nanosecond trajectories: A Langevin approach

“…[8][9][10][11][12][13][14][15][16] This is achieved by partitioning the continuous MD a) Present address: Biozentrum, University of Basel and Swiss Institute of Bioinformatics, Basel, Switzerland. b) A. Rzepiela and N. Schaudinnus contributed equally to this work.…”