Toolbox for quantifying memory in dynamics along reaction coordinates

Alessio Lapolla,Aljaž Godec

doi:10.1103/physrevresearch.3.l022018

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.

Highlights

The dynamics of complex, high-dimensional physical systems such as complex biomolecules is frequently described by means of memoryless, Markovian diffusion along a low-dimensional reaction coordinate [1,2,3,4,5,6,7,8,9,10]
We presented a set of complementary methods to quantify conclusively the degree and duration of memory in a time series of a reaction coordinate qt
The analysis determines whether the dynamics of qt has memory and quantifies the magnitude and duration of memory and complements the recently proposed “test for Markovianity” based on transition paths [42]

Summary

Toolbox for quantifying memory in dynamics along reaction coordinates

The dynamics of complex, high-dimensional physical systems such as complex biomolecules is frequently described by means of memoryless, Markovian diffusion along a low-dimensional reaction coordinate [1,2,3,4,5,6,7,8,9,10] Such simplified models often accurately describe selected observations in experiments [11,12,13,14,15] and computer simulations [1,6,7]. Our approach is twofold—(i) we quantify violations of the Chapman-Kolmogorov equation in a time series of the monitored true dynamics and (ii) we compare the true dynamics to a constructed nominally memoryless diffusion in the free energy and diffusion landscape of the true dynamics This assumes all hidden degrees of freedom to be at equilibrium constrained by the instantaneous value of the observable.

ALESSIO LAPOLLA AND ALJAŽ GODEC

Conclusion