Steady state distributions in generalized exclusion processes

TL;DR

This paper advances the analysis of the ASEP model by refining the probabilistic Boolean network approach to compute steady state distributions, including explicit structure matrices and methods applicable to multi-species exclusion processes.

Contribution

It introduces simplified and general methods for computing structure matrices of Boolean functions, extending the PBN approach to multi-valued logic networks.

Findings

Explicit structure matrices for common transitions

Simplified method for Boolean function structure matrices

Extension to multi-valued logic networks for multi-species processes

Abstract

The asymmetric simple exclusion process (ASEP) is a model of particle transport used in the study of biological processes such as mRNA translation. In 2014, Zhao and Krishnan introduced a new approach for analyzing the ASEP using probabilistic Boolean networks (PBN). In this paper, we revisit and further explore the PBN approach, with focus on computing steady state distributions. Explicit forms of the structure matrices of some common transitions are obtained. In addition, we derive a simplified method for computing the structure matrices of Boolean functions and a general method for writing the Boolean functions. These methods are also extended to multi-valued logic networks for application in multi-species exclusion processes.