Ribosome Flow Model on a Ring

TL;DR

The paper analyzes the ribosome flow model on a ring (RFMR), a mean field approximation of ASEP with periodic boundary conditions, showing convergence to equilibrium and entrainment to periodic rates, with implications for gene expression modeling.

Contribution

It provides a dynamical systems analysis of RFMR, demonstrating convergence properties and periodic entrainment, advancing understanding of cyclic mRNA translation.

Findings

RFMR admits a continuum of equilibrium points.

Every RFMR trajectory converges to an equilibrium.

RFMR entrains to periodic transition rates.

Abstract

The asymmetric simple exclusion process (ASEP) is an important model from statistical physics describing particles that hop randomly from one site to the next along an ordered lattice of sites, but only if the next site is empty. ASEP has been used to model and analyze numerous multiagent systems with local interactions including the flow of ribosomes along the mRNA strand. In ASEP with periodic boundary conditions a particle that hops from the last site returns to the first one. The mean field approximation of this model is referred to as the ribosome flow model on a ring (RFMR). The RFMR may be used to model both synthetic and endogenous gene expression regimes. We analyze the RFMR using the theory of monotone dynamical systems. We show that it admits a continuum of equilibrium points and that every trajectory converges to an equilibrium point. Furthermore, we show that it entrains to periodic transition rates between the sites. We describe the implications of the analysis results to understanding and engineering cyclic mRNA translation in-vitro and in-vivo.