Variational Approach to Molecular Kinetics

Self Cite

121

153

Reversibility is a key concept in Markov models and master-equation models of molecular kinetics. The analysis and interpretation of the transition matrix encoding the kinetic properties of the model rely heavily on the reversibility property. The estimation of a reversible transition matrix from simulation data is, therefore, crucial to the successful application of the previously developed theory. In this work, we discuss methods for the maximum likelihood estimation of transition matrices from finite simulation data and present a new algorithm for the estimation if reversibility with respect to a given stationary vector is desired. We also develop new methods for the Bayesian posterior inference of reversible transition matrices with and without given stationary vector taking into account the need for a suitable prior distribution preserving the meta-stable features of the observed process during posterior inference.

“…Choosing strictly positive starting parameters according to (35) results in valid iterates from (34). In analogy to the reversible case, we iterate (34) and (35) …”

Section: Reversible Estimation For Given Stationary Vectormentioning

confidence: 99%

“…24,31,32 The error incurred by the discretization and by the subsequent approximation of the jump-process as a Markov process can be systematically controlled and evaluated. 7,[33][34][35] a) B. Trendelkamp-Schroer and H. Wu contributed equally to this work. b) Electronic mail: frank.noe@fu-berlin.…”

Section: Introductionmentioning

confidence: 99%

Estimation and uncertainty of reversible Markov models

Trendelkamp-Schroer

Paul

et al. 2015

Self Cite

121

153

“…51,54 However, there is an important conceptual difference. In these works, the eigenvectors are evaluated with the aim to approximate the transfer operator, which describes the dynamics without explicitly constructing a MSM.…”

Section: A Variational Approachmentioning

confidence: 99%

Nonparametric variational optimization of reaction coordinates

Banushkina

Krivov

2015

State of the art realistic simulations of complex atomic processes commonly produce trajectories of large size, making the development of automated analysis tools very important. A popular approach aimed at extracting dynamical information consists of projecting these trajectories into optimally selected reaction coordinates or collective variables. For equilibrium dynamics between any two boundary states, the committor function also known as the folding probability in protein folding studies is often considered as the optimal coordinate. To determine it, one selects a functional form with many parameters and trains it on the trajectories using various criteria. A major problem with such an approach is that a poor initial choice of the functional form may lead to sub-optimal results. Here, we describe an approach which allows one to optimize the reaction coordinate without selecting its functional form and thus avoiding this source of error.

“…31,39,40 Recently, a variational theorem for evaluating MSMs has been introduced, which enables the modeler to select the best MSM for a system based on its distance from a theoretical upper limit. 41,42 In this work, we reanalyze twelve ultra-long protein folding MD datasets. 5,18,34,43 For each system, we create MSMs with many protocol choices and utilize the variational theorem introduced by Noé and Nüske 41 as a metric for crossvalidation 44 to determine how different modeling choices affect the quality of the MSM as defined by its ability to detect and represent the systems' long-time scale dynamical processes.…”

Section: Introductionmentioning

confidence: 99%

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

Husic

McGibbon

Sultan

et al. 2016

119

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