Nüske, F. and Wu, H. and Wehmeyer, C. and Clementi, C. and Noé, F. (2017) Markov State Models from short nonEquilibrium Simulations  Analysis and Correction of Estimation Bias. J. Chem. Phys., 146 . 094104.

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Official URL: http://dx.doi.org/10.1063/1.4976518
Abstract
Many stateoftheart methods for the thermodynamic and kinetic characterization of large and complex biomolecular systems by simulation rely on ensemble approaches, where data from large numbers of relatively short trajectories are integrated. In this context, Markov state models (MSMs) are extremely popular because they can be used to compute stationary quantities and longtime kinetics from ensembles of short simulations, provided that these short simulations are in “local equilibrium” within the MSM states. However, over the last 15 years since the inception of MSMs, it has been controversially discussed and not yet been answered how deviations from local equilibrium can be detected, whether these deviations induce a practical bias in MSM estimation, and how to correct for them. In this paper, we address these issues: We systematically analyze the estimation of MSMs from short nonequilibrium simulations, and we provide an expression for the error between unbiased transition probabilities and the expected estimate from many short simulations. We show that the unbiased MSM estimate can be obtained even from relatively short nonequilibrium simulations in the limit of long lag times and good discretization. Further, we exploit observable operator model (OOM) theory to derive an unbiased estimator for the MSM transition matrix that corrects for the effect of starting out of equilibrium, even when short lag times are used. Finally, we show how the OOM framework can be used to estimate the exact eigenvalues or relaxation time scales of the system without estimating an MSM transition matrix, which allows us to practically assess the discretization quality of the MSM. Applications to model systems and molecular dynamics simulation data of alanine dipeptide are included for illustration. The improved MSM estimator is implemented in PyEMMA of version 2.3.
Item Type:  Article 

Subjects:  Physical Sciences > Physics Physical Sciences > Chemistry Mathematical and Computer Sciences > Artificial Intelligence > Machine Learning 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics > Comp. Molecular Biology 
ID Code:  2002 
Deposited By:  BioComp Admin 
Deposited On:  06 Jan 2017 18:09 
Last Modified:  19 Jun 2017 16:38 
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