Dynamics of relaxation to a stationary state for interacting molecular motors

TL;DR

This paper investigates how interacting molecular motors relax to a stationary state, revealing that repulsive interactions speed up relaxation while attractive ones slow it down, with potential optimal weak repulsion.

Contribution

It introduces a theoretical framework combining exclusion processes and domain-wall methods to analyze relaxation dynamics of interacting molecular motors.

Findings

Repulsive interactions lead to rapid relaxation.

Attractive interactions slow down the approach to stationarity.

Weak repulsive interactions can optimize relaxation speed.

Abstract

Motor proteins are active enzymatic molecules that drive a variety of biological processes, including transfer of genetic information, cellular transport, cell motility and muscles contraction. It is known that these biological molecular motors usually perform their cellular tasks by acting collectively, and there are interactions between individual motors that specify the overall collective behavior. One of the fundamental issues related to the collective dynamics of motor proteins is the question if they function at stationary-state conditions. To investigate this problem, we analyze a relaxation to the stationary state for the system of interacting molecular motors. Our approach utilizes a recently developed theoretical framework, which views the collective dynamics of motor proteins as a totally asymmetric simple exclusion process of interacting particles, where interactions are taken into account via a thermodynamically consistent approach. The dynamics of relaxation to the stationary state is analyzed using a domain-wall method that relies on a mean-field description, which takes into account some correlations. It is found that the system quickly relaxes for repulsive interactions, while attractive interactions always slow down reaching the stationary state. It is also predicted that for some range of parameters the fastest relaxation might be achieved for a weak repulsive interaction. Our theoretical predictions are tested with Monte Carlo computer simulations. The implications of our findings for biological systems are briefly discussed.