Persistence and stability of generalized ribosome flow models with time-varying transition rates

TL;DR

This paper analyzes the dynamical properties of generalized ribosome flow models with arbitrary network structures and time-varying transition rates, establishing conditions for persistence and stability using Lyapunov functions.

Contribution

It extends existing ribosome flow models by incorporating arbitrary network topologies and time-varying rates, providing new stability and persistence results.

Findings

Persistence of the dynamics is established using CRN representation.

Stability is proven for strongly connected compartmental structures with entropy-like Lyapunov functions.

L1 contractivity is shown for periodic reaction rates with the same period.

Abstract

In this paper the qualitative dynamical properties of so-called generalized ribosome flow models are studied. Ribosome flow models known from the literature are generalized by allowing an arbitrary directed network structure between the compartments and secondly, by assuming a general time-varying rate function describing the compartmental transitions. Persistence of the dynamics is shown using the chemical reaction network (CRN) representation of the system. We show the stability of different compartmental structures including strongly connected ones with an entropy-like logarithmic Lyapunov function. The L1 contractivity of solutions is also studied in the case of periodic reaction rates having the same period. It is also shown that different Lyapunov functions may be assigned to the same model depending on the factorization of the reaction rates.