Kinetic Distance and Kinetic Maps from Molecular Dynamics Simulation

Abstract

Characterizing macromolecular kinetics from molecular dynamics (MD) simulations requires a distance metric that can distinguish slowly-interconverting states. Here we build upon diffusion map theory and define a kinetic distance for irreducible Markov processes that quantifies how slowly molecular conformations interconvert. The kinetic distance can be computed given a model that approximates the eigenvalues and eigenvectors (reaction coordinates) of the MD Markov operator. Here we employ the time-lagged independent component analysis (TICA). The TICA components can be scaled to provide a kinetic map in which the Euclidean distance corresponds to the kinetic distance. As a result, the question of how many TICA dimensions should be kept in a dimensionality reduction approach becomes obsolete, and one parameter less needs to be specified in the kinetic model construction. We demonstrate the approach using TICA and Markov state model (MSM) analyses for illustrative models, protein conformation dynamics in bovine pancreatic trypsin inhibitor and protein-inhibitor association in trypsin and benzamidine.

Dimensional reduction of Markov state models from renormalization group theory

“…Fig.7f shows the five more relevant conformations composing each of the three macrostates superposed together. These conformations are very similar to those predicted in a previous MSM analysis on BPTI dynamics, based on the of Robust Perron-Cluster Cluster Analysis (PCCA+) -see [27] and references thereien-. This shows that the RGC scheme is able to correctly predict the metastable configurations, with accuracy comparable with that of PCCA-based schemes.…”

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

“…35,54,55 In contrast to PCA, tICA describes the slowest degrees of freedom in a dataset by finding linear combinations of features that maximize autocorrelation time. Both PCA 39,47,[56][57][58][59][60][61][62] and tICA 21,35,38,39,46,49,55,63,64 have been used in the analysis of protein folding and conformational change. PCA or tICA FIG. 1.…”

Multiensemble Markov models of molecular thermodynamics and kinetics

“…In addition to breakthroughs in computer hardware (16), simulation software (17)(18)(19), and distributed computing (20,21), a key technology to reconcile swarms of individually short simulations to long-time kinetics are kinetic models, such as Markov state models (MSMs) (22)(23)(24)(25)(26)(27)(28). A key advantage of Markov state modeling over many other approaches is that it integrates well with dimension reduction and clustering techniques (29)(30)(31)) that can process high-dimensional data, and can thus treat complex kinetics that are not well described by few states or reaction coordinates (13,(32)(33)(34). A limitation of MSMs is that they rely on the rare events being reversibly sampled in the underlying MD simulation data.…”