Estimation and uncertainty of reversible Markov models

Trendelkamp-Schroer, Benjamin; Wu, Hao; Paul, Fabian; Noé, Frank

doi:10.1063/1.4934536

Cited by 127 publications

(168 citation statements)

References 66 publications

Supporting

Mentioning

153

Contrasting

Order By: Relevance

“…V D, we reported that MSM time scales differ widely across models constructed from different features. To a lesser extent, this is also the case for time scales predicted by MSMs that have indistinguishable scores; in other words, time scales across indistinguishably good models differ more than their intra-model uncertainties [82][83][84][85][86][87][88] account for. This is likely due to the fact that each model is built from a different state decomposition and is thus describing a (perhaps subtly) different process.…”

Section: Discussionmentioning

confidence: 93%

Optimized parameter selection reveals trends in Markov state models for protein folding

Husic

McGibbon

Sultan

et al. 2016

The Journal of Chemical Physics

119

View full text Add to dashboard Cite

As molecular dynamics simulations access increasingly longer time scales, complementary advances in the analysis of biomolecular time-series data are necessary. Markov state models offer a powerful framework for this analysis by describing a system's states and the transitions between them. A recently established variational theorem for Markov state models now enables modelers to systematically determine the best way to describe a system's dynamics. In the context of the variational theorem, we analyze ultra-long folding simulations for a canonical set of twelve proteins [K. Lindorff-Larsen et al., Science 334, 517 (2011)] by creating and evaluating many types of Markov state models. We present a set of guidelines for constructing Markov state models of protein folding; namely, we recommend the use of cross-validation and a kinetically motivated dimensionality reduction step for improved descriptions of folding dynamics. We also warn that precise kinetics predictions rely on the features chosen to describe the system and pose the description of kinetic uncertainty across ensembles of models as an open issue. Published by AIP Publishing. [http://dx

show abstract

Section: Discussionmentioning

confidence: 93%

Optimized parameter selection reveals trends in Markov state models for protein folding

Husic

McGibbon

Sultan

et al. 2016

The Journal of Chemical Physics

119

View full text Add to dashboard Cite

show abstract

“…This analysis of the systematic bias is based on the approximation of rare transitions between subgraphs in various types of MSMs [eqs. (3), (25), or (59)], which allowed us to proceed with analytical derivations beyond the results previously published in the literature, [23][24][25][26] and obtain the analytical result given by Eq. (64).…”

mentioning

confidence: 99%

Theoretical restrictions on longest implicit time scales in Markov state models of biomolecular dynamics

Sinitskiy

Pande

2018

The Journal of Chemical Physics

View full text Add to dashboard Cite

Markov state models (MSMs) have been widely used to analyze computer simulations of various biomolecular systems. They can capture conformational transitions much slower than an average or maximal length of a single molecular dynamics (MD) trajectory from the set of trajectories used to build the MSM. A rule of thumb claiming that the slowest implicit timescale captured by an MSM should be comparable by the order of magnitude to the aggregate duration of all MD trajectories used to build this MSM has been known in the field. However, this rule have never been formally proved. In this work, we present analytical results for the slowest timescale in several types of MSMs, supporting the above rule. We conclude that the slowest implicit timescale equals the product of the aggregate sampling and four factors that quantify: (1) how much statistics on the conformational transitions corresponding to the longest implicit timescale is available, (2) how good the sampling of the destination Markov state is, (3) the gain in statistics from using a sliding window for counting transitions between Markov states, and (4) a bias in the estimate of the implicit timescale arising from finite sampling of the conformational transitions. We demonstrate that in many practically important cases all these four factors are on the order of unity, and we analyze possible scenarios that could lead to their significant deviation from unity. Overall, we provide for the first time analytical results on the slowest timescales captured by MSMs. These results can guide further practical applications of MSMs to biomolecular dynamics and allow for higher computational efficiency of simulations.2

show abstract

“…With detailed balance constraints, the maximum likelihood of Eq. 6 has no closed-form solution but can be iteratively solved (28,62,63).…”

Section: Trammentioning

confidence: 99%

Multiensemble Markov models of molecular thermodynamics and kinetics

Paul

Wehmeyer

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

200

249

View full text Add to dashboard Cite

We introduce the general transition-based reweighting analysis method (TRAM), a statistically optimal approach to integrate both unbiased and biased molecular dynamics simulations, such as umbrella sampling or replica exchange. TRAM estimates a multiensemble Markov model (MEMM) with full thermodynamic and kinetic information at all ensembles. The approach combines the benefits of Markov state models—clustering of high-dimensional spaces and modeling of complex many-state systems—with those of the multistate Bennett acceptance ratio of exploiting biased or high-temperature ensembles to accelerate rare-event sampling. TRAM does not depend on any rate model in addition to the widely used Markov state model approximation, but uses only fundamental relations such as detailed balance and binless reweighting of configurations between ensembles. Previous methods, including the multistate Bennett acceptance ratio, discrete TRAM, and Markov state models are special cases and can be derived from the TRAM equations. TRAM is demonstrated by efficiently computing MEMMs in cases where other estimators break down, including the full thermodynamics and rare-event kinetics from high-dimensional simulation data of an all-atom protein–ligand binding model.

show abstract

Estimation and uncertainty of reversible Markov models

Cited by 127 publications

References 66 publications

Optimized parameter selection reveals trends in Markov state models for protein folding

Optimized parameter selection reveals trends in Markov state models for protein folding

Theoretical restrictions on longest implicit time scales in Markov state models of biomolecular dynamics

Multiensemble Markov models of molecular thermodynamics and kinetics

Contact Info

Product

Resources

About