Collective variables for the study of long-time kinetics from molecular trajectories: theory and methods.
Collective variables are an important concept to study high-dimensional dynamical systems, such as molecular dynamics of macromolecules, liquids, or polymers, in particular to define relevant metastable states and state-transition or phase-transition. Over the past decade, a rigorous mathematical theory has been formulated to define optimal collective variables to characterize slow dynamical processes. Here we review recent developments, including a variational principle to find optimal approximations to slow collective variables from simulation data, and algorithms such as the time-lagged independent component analysis. Using these concepts, a distance metric can be defined that quantifies how slowly molecular conformations interconvert. Extensions and open questions are discussed.
Department of Mathematics and Computer Science, FU Berlin, Arnimallee 6, 14195 Berlin, Germany. Electronic address: frank.noe@fu-berlin.de.
Frank
F
Noé
Center for Theoretical Biological Physics, and Department of Chemistry, Rice University, 6100 Main Street, Houston, TX 77005, United States. Electronic address: cecilia@rice.edu.
Cecilia
C
Clementi
D007700:Kinetics; D056004:Molecular Dynamics Simulation