Abstract

Most systems of scientific interest are interacting many-body systems. One typically describes their kinetics in terms of a low-dimensional reaction coordinate, which in general is influenced by the entire system. The dynamics of such a reaction coordinate is governed by the generalized Langevin equation (GLE), an integro-differential stochastic equation, and involves a memory function [1]. I discuss a few examples where the GLE can be used to interpret and model data in different fields of science.

Protein-folding kinetics is typically described as Markovian (i.e., memoryless) diffusion in a one-dimensional free energy landscape. By analysis of large-scale molecular-dynamics simulation trajectories of fast-folding proteins from the Shaw group using the special-purpose computer ANTON , I demonstrate that the friction characterizing protein folding exhibits significant memory with a decay time that is of the same order as the folding and unfolding times [2,3]. Memory friction effects lead to anomalous and drastically modified protein kinetics. For the set of proteins for which simulations are available, it is shown that the folding and unfolding times are not dominated by the free-energy barrier but rather by the non-Markovian friction.

Memory effects are also present for non-equilibrium systems. Using an appropriate non-equilibrium formulation of the GLE , it is demonstrated that the motion of living organisms is characterized by memory friction, which allows to characterize internal feedback loops of such organisms and to classify and sort individual organisms [4]. The GLE can be even used to predict complex phenomena such as weather data.

[1] Generalized Langevin equation with a nonlinear potential of mean force and nonlinear memory friction from a hybrid projection scheme Cihan Ayaz , Laura Scalfi , Benjamin A. Dalton, and Roland R. Netz PHYSICAL REVIEW E 105 , 054138 (2022)

[2] Non-Markovian modeling of protein folding, Cihan Ayaza, Lucas Tepper, Florian N. Brünig, Julian Kappler, Jan O. Daldrop, Roland R. Netz Proc. Natl Acad. Sci. 118, e2023856118 (2021)

[4] Fast protein folding is governed by memory-dependent friction Benjamin A. Dalton, Cihan Ayaz, Lucas Tepper, and Roland R. Netz. Proc. Natl Acad. Sci. 120, e2220068120 (2023), DOI : 10.1073/pnas.2220068120

[4] Data-driven classification of individual cells by their non-Markovian motion Anton Klimek, Debasmita Mondal, Stephan Block, Prerna Sharma, and Roland R. Netz Biophysical Journal 123, 1–11, May 7, 2024, https://doi.org/10.1016/j.bpj.2024.03.023