Toolbox for quantifying memory in dynamics along reaction coordinates

Abstract

Memory effects in time series of experimental observables are ubiquitous, have important consequences for the interpretation of kinetic data, and may even affect the function of biomolecular nanomachines such as enzymes. Here we propose a set of complementary methods for quantifying conclusively the magnitude and duration of memory in a time series of a reaction coordinate. The toolbox is general, robust, easy to use, and does not rely on any underlying microscopic model. As a proof of concept we apply it to the analysis of memory in the dynamics of the end-to-end distance of the analytically solvable Rouse-polymer model, an experimental time series of extensions of a single DNA hairpin measured by optical tweezers, and the fraction of native contacts in a small protein probed by atomistic molecular dynamics simulations.