Steady-state properties of a totally asymmetric exclusion process with particles of arbitrary size

TL;DR

This paper analyzes the steady-state properties of a generalized TASEP with particles of arbitrary size, using mean field approximations and simulations to understand phase behavior and currents relevant to biological systems.

Contribution

It introduces a refined mean field approach and Monte Carlo simulations to accurately predict steady-state currents and phase diagrams for TASEP with particles of any size.

Findings

Local equilibrium distributions yield accurate currents in the maximal current phase.

Refined mean field approach provides exact expressions for currents and phase boundaries.

Monte Carlo simulations support the theoretical predictions.

Abstract

The steady-state currents and densities of a one-dimensional totally asymmetric exclusion process (TASEP) with particles that occlude an integer number ($d$) of lattice sites are computed using various mean field approximations and Monte Carlo simulations. TASEP's featuring particles of arbitrary size are relevant for modeling systems such as mRNA translation, vesicle locomotion along microtubules, and protein sliding along DNA. We conjecture that the nonequilibrium steady-state properties separate into low density, high density, an maximal current phases similar to those of the standard ($d=1$) TASEP. A simple mean field approximation for steady-state particle currents and densities is found to be inaccurate. However, we find {\it local equilibrium} particle distributions derived from a discrete Tonks gas partition function yield apparently exact currents within the maximal current phase. For the boundary-limited phases, the equilibrium Tonks gas distribution cannot be used to predict currents, phase boundaries, or the order of the phase transitions. However, we employ a refined mean field approach to find apparently exact expressions for the steady state currents, boundary densities, and phase diagrams of the $d\geq 1$ TASEP. Extensive Monte Carlo simulations are performed to support our analytic, mean field results.