Markov Models of Molecular Kinetics

Abstract

a. Introduction The Journal of Chemical Physics article collection on Markov Models of Molecular Kinetics (MMMK)features recent advances developing and using Markov State Models (MSMs) 1-6 in atomistic molecular simulations and related applications -see 7-10 for recent MSM reviews. MSMs have been an important driving force in molecular dynamics (MD), as they facilitate divide-and-conquer integration of short, distributed MD simulations into long-timescale predictions, they are conceptually simple and provide readily-interpretable models of kinetics and thermodynamics.Most MSM estimation approaches proceed by a sequence, or pipeline, of data processing steps that is also represented by MSM software packages [11][12][13] , and typically includes:1. Featurization: The MD coordinates are transformed into features, such as residue distances, contact maps or torsion angles 11,12,14,15 , that form the input of the MSM analysis. Dimension reduction:The dimension is reduced to much fewer (typically 2-100) slow collective variables (CVs), [16][17][18][19][20][21][22][23][24][25][26] . The resulting coordinates may be scaled, in order to embed them in a metric space whose distances correspond to some form of dynamical distance 27,28 . Discretization:The space may be discretized by clustering the projected data 4,7,11,[29][30][31][32][33] , typically resulting in 100-1000 discrete "microstates". MSM estimation:A transition matrix or rate matrix describing the transition probabilities or rate between the discrete states at some lag time τ is estimated 5,6,34,35 .5. Coarse-graining: In order to get an easier interpretable kinetic model, the MSM from step 5 is often coarse-grained to a few states [36][37][38][39][40][41][42][43][44] .Some method skip or combine some of these steps, novel machine learning methods attempt to integrate most or all of them in an end-to-end learning framework.

Markov state models from hierarchical density-based assignment

“…In the present work this is done by using the time-lagged independent coordinate analysis (TICA) [26][27][28] . Many other dimensionality reduction methods are available in the literature 7,30,32,33 .…”

“…These improvements leave us with the additional burden of having to analyze extremely large data sets including Cartesian coordinates of many-atom systems with (potentially) femtosecond resolution. In the last 15 years, Markov State Models (MSMs) have become established as a useful approach for both the analysis and interpretation of MD simulations [6][7][8] . Starting from one or multiple MD trajectories, MSMs provide an integrated framework for constructing a network model of metastable states such that biomolecular dynamics are described as memory-less jump processes.…”

Capturing the Flexibility of a Protein-Ligand Complex: Binding Free Energies from Different Enhanced Sampling Techniques

“…However, this opti-mization step can only yield CV that reliably cover all slow DOF if the corresponding slow motions have been sampled at least once in exploratory simulations before. Apart from improving the CV for MTD simulations, the data obtained from such exploratory simulations may also be used to build Markov State Models (MSM) and apply adaptive sampling schemes [55][56][57] or to construct an adaptive bias with a neural network 54 . Systematically improved CV from exploratory simulations thus open the gate to various modern techniques to calculate thermodynamic and kinetic quantities; however, CV optimization was not required for the other enhanced sampling techniques used here and thus beyond the scope of the present study.…”

Binding Free Energy of Protein/Ligand Complexes Calculated using Dissociation Parallel Cascade Selection Molecular Dynamics and Markov State Model

“…By selecting snapshots with longer intermolecular distances, our group previously used dissociation PaCS-MD (dPaCS-MD) to generate dissociation pathways of tri-N-acetyl-dglucosamine from hen egg white lysozyme [26], of the transactivation domain of p53 protein (p53-TAD) from murine double-minute clone 2 protein (MDM2) protein [30], and of an N-terminal fragment of the bacterial flagellar rotor protein FliM from the signaling protein CheY [28]. We built an MSM model using dPaCS-MD trajectories to investigate the dissociation mechanisms by describing states based on ligand/protein geometry [29,31]. Using this combination, we obtained binding free energies of the protein/ligand complexes in accordance with the experimentally determined values.…”