Commute Maps: Separating Slowly Mixing Molecular Configurations for Kinetic Modeling.

Identification of the main reaction coordinates and building of kinetic models of macromolecular systems require a way to measure distances between molecular configurations that can distinguish slowly interconverting states. Here we define the commute distance that can be shown to be closely related to the expected commute time needed to go from one configuration to the other, and back. A practical merit of this quantity is that it can be easily approximated from molecular dynamics data sets when an approximation of the Markov operator eigenfunctions is available, which can be achieved by the variational approach to approximate eigenfunctions of Markov operators, also called variational approach of conformation dynamics (VAC) or the time-lagged independent component analysis (TICA). The VAC or TICA components can be scaled such that a so-called commute map is obtained in which Euclidean distance corresponds to the commute distance, and thus kinetic models such as Markov state models can be computed based on Euclidean operations, such as standard clustering. In addition, the distance metric gives rise to a quantity we call total kinetic content, which is an excellent score to rank input feature sets and kinetic model quality.