Dynamical reweighting methods for Markov models

Abstract

Conformational dynamics is essential to biomolecular processes. Markov State Models (MSM) are widely used to elucidate dynamic properties of molecular systems from unbiased Molecular Dynamics (MD). However, the implementation of reweighting schemes for MSMs to analyze biased simulations is still at an early stage of development. Several dynamical reweighing approaches have been proposed, which can be classified as approaches based on (i) Kramers rate theory, (ii) rescaling of the probability density flux, (iii) reweighting by formulating a likelihood function, (iv) path reweighting. We present the state-of-the-art and discuss the methodological differences of these methods, their limitations and recent applications.

Enhanced sampling without borders: on global biasing functions and how to reweight them

“…transition rates), which are particularly challenging to recover. 127,128 Therefore, different reweighting approaches have been developed that either focus on reconstruction of thermodynamic quantities, or additionally perform reweighting of the system's kinetics. In the following, we will discern between these two incentives as "phase-space reweighting" and "dynamic reweighting".…”

“…We are providing a condensed overview of both types of reweighting approaches, for a more detailed discussion we refer the interested reader to dedicated reviews and the original literature. 124,[127][128][129]…”

Estimation of Binding Rates and Affinities from Multiensemble Markov Models and Ligand Decoupling

“…A great improvement to this situation has come from the introduction of so-called multi-ensemble Markov Model (MEMM) estimators, which use trajectory data collected from multiple thermodynamic ensembles to make MSM estimates of thermodynamics and kinetics. [35][36][37][38][39] The essential idea, as applied to ligand binding, is to collect energy snapshots and metastable state transitions in biased thermodynamic ensembles that are not limited by rare event sampling, in order to make more statistically significant estimates of rates and affinities for the unbiased ensemble. One of these estimators, the transition-based reweighting analysis method (TRAM) of Wu et al, 37 has been used to estimate the slow dissociation of small-molecule and peptide ligands using harmonic bias potentials.…”

Path probability ratios for Langevin dynamics -- exact and approximate

“…Starting points for the derivation of dynamical reweighting methods are Kramers rate theory [10][11][12][13] , the likelihood function for estimating the transition probabilities from MD trajectories [14][15][16][17] , or a discretization of the Fokker-Planck equation 7,[18][19][20] . The methods differ in the ease of use and the severity of the assumptions they make 21 .…”