Totally asymmetric exclusion process with site-wise dynamic disorder

TL;DR

This paper extends the TASEP model to include dynamic obstacles that attach and detach from sites, revealing effects on particle flow, clustering, and phase behavior, with applications to gene transcription.

Contribution

It introduces a novel TASEP variant with site-wise dynamic disorder and analyzes its phase behavior and particle clustering effects.

Findings

Defects cause particle clustering despite translation invariance.

The model exhibits a symmetric or skewed current-density relationship depending on defect dynamics.

Mean-field theory accurately predicts phase boundaries and current-density relationships.

Abstract

We propose an extension of the totally asymmetric simple exclusion process (TASEP) in which particles hopping along a lattice can be blocked by obstacles that dynamically attach/detach from lattice sites. The model can be thought as TASEP with site-wise dynamic disorder. We consider two versions of defect dynamics: (i) defects can bind to any site, irrespective of particle occupation, (ii) defects only bind to sites which are not occupied by particles (particle-obstacle exclusion). In case (i) there is a symmetric, parabolic-like relationship between the current and particle density, as in the standard TASEP. Case (ii) leads to a skewed relationship for slow defect dynamics. We also show that the presence of defects induces particle clustering, despite the translation invariance of the system. For open boundaries the same three phases as for the standard TASEP are observed, albeit the position of phase boundaries is affected by the presence of obstacles. We develop a simple mean-field theory that captures the model's quantitative behaviour for periodic and open boundary conditions and yields good estimates for the current-density relationship, mean cluster sizes and phase boundaries. Lastly, we discuss an application of the model to the biological process of gene transcription.