Interplay between finite resources and local defect in an asymmetric simple exclusion process

TL;DR

This paper extends the asymmetric simple exclusion process to include a controlled entrance and a defect site, revealing how finite resources and local defects influence particle flow and density, with implications for biological transport mechanisms.

Contribution

It introduces a modified exclusion model with a controlled entry point and defect, providing theoretical and simulation insights into their combined effects on transport dynamics.

Findings

Current remains constant despite increasing particle supply.

Particles redistribute without increasing overall flow.

Steady-state profiles match biological transport observations.

Abstract

When particle flux is regulated by multiple factors such as particle supply and varying transport rate, it is important to identify the respective dominant regimes. We extend the well-studied totally asymmetric simple exclusion model to investigate the interplay between a controlled entrance and a local defect site. The model mimics cellular transport phenomena where there is typically a finite particle pool and non-uniform moving rates due to biochemical kinetics. Our simulations reveal regions where, despite an increasing particle supply, the current remains constant while particles redistribute in the system. Exploiting a domain wall approach with mean-field approximation, we provide a theoretical ground for our findings. The results in steady state current and density profiles provide quantitative insights into the regulation of the transcription and translation process in bacterial protein synthesis. We investigate the totally asymmetric simple exclusion model with controlled entrance and a defect site in the bulk to mimic the finite particle pool and non-uniform moving rates in particle transport processes.