Mean field approaches to the totally asymmetric exclusion process with quenched disorder and large particles

TL;DR

This paper investigates a biological lattice gas model with large particles and quenched disorder, using mean field methods and simulations to understand protein synthesis dynamics.

Contribution

It extends mean field approaches to include large particles and correlations, improving accuracy in modeling disordered biological transport systems.

Findings

Mean field equations effectively describe the system.

Two-point correlations improve the match with simulations.

A new numerical technique accelerates current computation.

Abstract

The process of protein synthesis in biological systems resembles a one dimensional driven lattice gas in which the particles (ribosomes) have spatial extent, covering more than one lattice site. Realistic, nonuniform gene sequences lead to quenched disorder in the particle hopping rates. We study the totally asymmetric exclusion process with large particles and quenched disorder via several mean field approaches and compare the mean field results with Monte Carlo simulations. Mean field equations obtained from the literature are found to be reasonably effective in describing this system. A numerical technique is developed for computing the particle current rapidly. The mean field approach is extended to include two-point correlations between adjacent sites. The two-point results are found to match Monte Carlo simulations more closely.