Exponential equilibration of genetic circuits using entropy methods

TL;DR

This paper demonstrates exponential convergence to equilibrium in a continuum genetic circuit model using entropy methods, providing explicit bounds and extending results to multi-gene networks with numerical validation.

Contribution

It introduces entropy-based analysis to prove exponential equilibration in a continuum genetic circuit model, including multi-gene networks, with explicit bounds and numerical simulations.

Findings

Exponential convergence to equilibrium with explicit bounds.

Asymptotic equilibration in multi-gene networks under certain conditions.

Numerical simulations confirming theoretical results.

Abstract

We analyse a continuum model for genetic circuits based on a partial integro-differential equation initially proposed in Friedman, Cai \& Xie (2006) as an approximation of a chemical master equation. We use entropy methods to show exponentially fast convergence to equilibrium for this model with explicit bounds. The asymptotic equilibration for the multidimensional case of more than one gene is also obtained under suitable assumptions on the equilibrium stationary states. The asymptotic equilibration property for networks involving one and more than one gene is investigated via numerical simulations.