Kinetic distance and kinetic maps from molecular dynamics simulation

TL;DR

This paper introduces a kinetic distance metric derived from diffusion map theory and TICA, enabling better characterization of slow conformational changes in molecular dynamics simulations without needing to specify the number of TICA dimensions.

Contribution

It develops a kinetic distance measure for Markov processes and integrates it with TICA to simplify kinetic modeling of molecular conformations.

Findings

Kinetic distance effectively distinguishes slow interconversions.

Kinetic map visualization simplifies dimensionality reduction.

Application to protein dynamics demonstrates practical utility.

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.