Driven diffusive systems with mutually interactive Langmuir kinetics

TL;DR

This paper studies a driven one-dimensional exclusion process with interactive Langmuir kinetics, revealing how mutual interactions influence phase behavior and boundary effects, supported by analytical solutions and Monte Carlo simulations.

Contribution

It introduces a modified exclusion process with neighbor-dependent attachment/detachment rates and provides analytical and numerical analysis of its phase behavior.

Findings

Mutual interactions alter boundary effects on phase transitions.

Analytical solutions agree with Monte Carlo simulations.

Phase diagrams illustrate the impact of interactions on system states.

Abstract

We investigate the simple one-dimensional driven model, the totally asymmetric exclusion process, coupled to mutually interactive Langmuir kinetics. This model is motivated by recent studies on clustering of motor proteins on microtubules. In the proposed model, the attachment and detachment rates of a particle are modified depending upon the occupancy of neighbouring sites. We first obtain continuum mean-field equations and in certain limiting cases obtain analytic solutions. We show how mutual interactions increase (decrease) the effects of boundaries on the phase behavior of the model. We perform Monte Carlo simulations and demonstrate that our analytical approximations are in good agreement with the numerics over a wide range of model parameters. We present phase diagrams over a selective range of parameters.