The totally asymmetric exclusion process with extended objects, a model for protein synthesis

TL;DR

This paper extends the TASEP model to include particles covering multiple sites, providing exact solutions and phase diagrams, and analyzing biological protein synthesis as a driven lattice gas with extended objects.

Contribution

It introduces an extended TASEP model for particles with spatial extent, offering exact solutions and new analytical approaches for open systems with disorder.

Findings

Exact solutions for uniform closed systems.

Modified diffusion equation for open systems.

Accurate phase diagram predictions with domain wall theory.

Abstract

The process of protein synthesis in biological systems resembles a one dimensional driven lattice gas in which the particles have spatial extent, covering more than one lattice site. We expand the well studied Totally Asymmetric Exclusion Process (TASEP), in which particles typically cover a single lattice site, to include cases with extended objects. Exact solutions can be determined for a uniform closed system. We analyze the uniform open system through two approaches. First, a continuum limit produces a modified diffusion equation for particle density profiles. Second, an extremal principle based on domain wall theory accurately predicts the phase diagram and currents in each phase. Finally, we briefly consider approximate approaches to a non-uniform open system with quenched disorder in the particle hopping rates and compare these approaches with Monte Carlo simulations.