A Toolbox for Quantifying Memory in Dynamics Along Reaction Coordinates

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.

arXiv commentRevised version with additional examples; accepted for publication in Phys. Rev. Res

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• General theory for localizing the where and when of entropy production meets single-molecule experiments
• Perspective: Time irreversibility in systems observed at coarse resolution
• Model-free inference of memory in conformational dynamics of a multi-domain protein
• On the emergence of memory in equilibrium versus non-equilibrium systems
• Memory effects in colloidal motion under confinement and driving
• Time- and ensemble-average statistical mechanics of the Gaussian Network Model
• The impact of memory on learning sequence-to-sequence tasks
• Dynamics of micro and nanoscale systems in the weak-memory regime: A mathematical framework beyond the Markov approximation
• Weak-Memory Dynamics in Discrete Time