Biologically relevant finite-size effects in a driven lattice gas with particle pausing and dynamical defects

TL;DR

This paper investigates finite-size effects in a biological lattice gas model, extending mean-field theory, revealing discrepancies with simulations, and developing a cluster approximation to better understand transcription-related processes.

Contribution

It introduces a single-cluster approximation for finite-size effects in pTASEP, enhancing the accuracy of modeling biological transport phenomena.

Findings

Finite-size effects significantly impact system dynamics.

The single-cluster approximation improves agreement with simulations.

The extended theory applies to open boundary conditions.

Abstract

In this article we present a comprehensive study of the totally asymmetric simple exclusion process with pausing particles (pTASEP), a model initially introduced to describe RNAP dynamics during transcription. We extend previous mean-field approaches and demonstrate that the pTASEP is equivalent to the exclusion process with dynamical defects (ddTASEP), thus broadening the scope of our investigation to a larger class of problems related to transcription and translation. We extend the mean-field theory to the open boundary case, revealing the system's phase diagram and critical values of entry and exit rates. However, we identify a significant discrepancy between theory and simulations in a region of the parameter space, indicating severe finite-size effects. To address this, we develop a single-cluster approximation that captures the relationship between current and lattice size, providing a more accurate representation of the system's dynamics. Finally, we extend our approach to open boundary conditions, demonstrating its applicability in different scenarios. Our findings underscore the importance of considering finite-size effects, often overlooked in the literature, when modelling biological processes such as transcription and translation.