  A popular approach to analyze the dynamics of high-dimensional many-body
systems, such as macromolecules, is to project the trajectories onto a space of
slowly-varying collective variables, where subsequent analyses are made, such
as clustering or estimation of free energy profiles or Markov state models
(MSMs). However, existing "dynamical" dimension reduction methods, such as the
time-lagged independent component analysis (TICA) are only valid if the
dynamics obeys detailed balance (microscopic reversibility) and typically
require long, equilibrated simulation trajectories. Here we develop a dimension
reduction method for non-equilibrium dynamics based on the recently developed
Variational Approach for Markov Processes (VAMP) by Wu and No\'e. VAMP is
illustrated by obtaining a low-dimensional description of a single file ion
diffusion model and by identifying long-lived states from molecular dynamics
simulations of the KcsA channel protein in an external electrochemical
potential. This analysis provides detailed insights into the coupling of
conformational dynamics, the configuration of the selectivity filter, and the
conductance of the channel. We recommend VAMP as a replacement for the less
general TICA method.
