A new class of enhanced kinetic sampling methods for building Markov state models

Abstract

Markov state models (MSMs) and other related kinetic network models are frequently used to study the long-timescale dynamical behavior of biomolecular and materials systems. MSMs are often constructed bottom-up using brute-force molecular dynamics (MD) simulations when the model contains a large number of states and kinetic pathways that are not known a priori. However, the resulting network generally encompasses only parts of the configurational space, and regardless of any additional MD performed, several states and pathways will still remain missing. This implies that the duration for which the MSM can faithfully capture the true dynamics, which we term as the validity time for the MSM, is always finite and unfortunately much shorter than the MD time invested to construct the model. A general framework that relates the kinetic uncertainty in the model to the validity time, missing states and pathways, network topology, and statistical sampling is presented. Performing additional calculations for frequently-sampled states/pathways may not alter the MSM validity time. A new class of enhanced kinetic sampling techniques is introduced that aims at targeting rare states/pathways that contribute most to the uncertainty so that the validity time is boosted in an effective manner. Examples including straightforward 1D energy landscapes, lattice models, and biomolecular systems are provided to illustrate the application of the method. Developments presented here will be of interest to the kinetic Monte Carlo community as well.

Protobiotic Systems Chemistry Analyzed by Molecular Dynamics

“…The second approach to be explored involves a relatively recent development in the field, employing Markov state modeling (MSM) methods [89,90]. In this approach, many short molecular dynamics simulations define the underlying energy landscape, allowing both thermodynamic and kinetic constants to be inferred [90].…”

Self-optimized construction of transition rate matrices from accelerated atomistic simulations with Bayesian uncertainty quantification

“…We emphasize that although all trajectory information is used in the individual rate calculations, we only use first passage information in the Bayesian posterior (17).…”

“…The local completeness of the TAD exploration is assessed using a Bayesian framework . TAMMBER then invokes the mathematics of absorbing Continuous Time Markov Chains (CTMC) [13][14][15][16][17][18] to provide a global exploration completeness metric, the expected residence time in the known configuration space. This completeness metric is then systematically optimized using a parallel resource allocation protocol.…”

“…The mathematics of absorbing CTMC have previously been used to accelerate kinetic Monte Carlo simulations of superbasin escape 13 and highly heterogeneous glassy systems 14,15 though in both of these cases the the chains were fully specified and this partitioning into two groups was made for computational convenience. Estimation of the unknown rate for each state has previously been investigated in molecular dynamics simulations of biological systems 17,18 , whilst high temperature dynamics has also been used to estimate the degree of sampling completeness in individual states 16 which is closely related to estimation of the unknown rate. The central novelty of this work is both the robust form of our estimators for the unknown escape rate from each state and an expression for the expected decrease in the unknown rate with additional computational work.…”

A generalised mechano-kinetic model for use in multiscale simulation protocols

“…The MSM comprises of a series of discrete states with associated transition rates between them (see Figure 1), and those rates satisfy the Markov property of being 'memoryless', in that the current transition rates are state occupation probabilities are not affected by any of the previous transitions. What gives an MSM its predictive power is that the states themselves are not arbitrarily defined, but instead are calculated through an exploration of a dynamic energy landscape, either analytically or via simulation [27]. Local energy minima can be isolated and identified as the central loci of a set of discrete kinetic states.…”