Markov state models based on milestoning

Abstract

Markov state models (MSMs) have become the tool of choice to analyze large amounts of molecular dynamics data by approximating them as a Markov jump process between suitably predefined states. Here we investigate "Core Set MSMs," a new type of MSMs that build on metastable core sets acting as milestones for tracing the rare event kinetics. We present a thorough analysis of Core Set MSMs based on the existing milestoning framework, Bayesian estimation methods and Transition Path Theory (TPT). We show that Core Set MSMs can be used to extract phenomenological rate constants between the metastable sets of the system and to approximate the evolution of certain key observables. The performance of Core Set MSMs in comparison to standard MSMs is analyzed and illustrated on a toy example and in the context of the torsion angle dynamics of alanine dipeptide.

Optimal control of molecular dynamics using Markov state models

“…In such cases the accurate computation of the committors as functions on state space is infeasible even on the most powerful computers. Yet the matrix pair (L, M ) can be accurately estimated from one long realization of x t or from many independent short realizations [35].…”

“…As outlined in Remark 1 we typically do not have access to the committor functions in molecular dynamics applications, but to the matrix pair (M,L) instead. Fortunately, the matrix F can also be accurately estimated from one long realization of the process (x t ) or from many independent shorter realizations without knowing the committor functions [35].…”

“…Our further considerations are based on the MSM (standard MSM with 250 states and a lag time of 500 time units) constructed in [35]. Our target function is f = 1 B with B = [ 130, 50]⇥[ 100, 50], meaning that we want to maximize the population of the ↵-helix conformation while suppressing the -sheet conformation without putting too much energy into the system.…”

Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions

“…Such projections onto discrete sets of states naturally lead to descriptions of the dynamics in terms of Markov state models 14 or coarse master equations 15,16 with discrete timestepping or continuous dynamics, respectively. Coarse master equations and Markov state models have attracted much attention because they can be constructed directly from molecular dynamics simulations, [15][16][17][18][19][20][21] with the aim to capture the dynamics of most interest, occurring over long time scales. The success of such models, however, strongly depends on the ability to decompose conformation space into a set of meaningful metastable states, associated with low free energy (meta)basins.…”

Catch bond-like kinetics of helix cracking: Network analysis by molecular dynamics and Milestoning

“…A related algorithm 47 was proposed in the context of the Markov State Model. [48][49][50] As used in the current study, the following algorithm finds the MaxFlux path:…”