A Max-Plus Model of Ribosome Dynamics During mRNA Translation

TL;DR

This paper models ribosome movement during mRNA translation using max-plus algebra and timed event graphs, providing analytical and numerical insights into protein production rates and ribosome density.

Contribution

It introduces a max-plus algebra-based deterministic model of ribosome dynamics during translation, linking discrete event systems with biological processes.

Findings

Analytical expressions for protein production rate

Exact match between model and simulations

Quantitative insights into ribosome density

Abstract

We examine the dynamics of the translation stage of cellular protein production, in which ribosomes move uni-directionally along mRNA strands building an amino acid chain as they go. We describe the system using a timed event graph - a class of Petri net useful for studying discrete events which take a finite time. We use max-plus algebra to describe a deterministic version of the model, calculating the protein production rate and density of ribosomes on the mRNA. We find exact agreement between these analytical results and numerical simulations of the deterministic case.