A Toolbox for Quantifying Memory in Dynamics Along Reaction Coordinates

TL;DR

This paper introduces a versatile set of methods to quantify the magnitude and duration of memory effects in time-series data of reaction coordinates, aiding interpretation of kinetic data across various systems.

Contribution

It presents a general, robust toolbox for analyzing memory in reaction coordinate dynamics without relying on microscopic models.

Findings

Applied to Rouse-polymer model, DNA hairpin, and protein simulations.

Demonstrated effectiveness in quantifying memory effects.

Provided insights into the timescales of memory in different systems.

Abstract

Memory effects in time-series of experimental observables are ubiquitous, have important cosequences 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.