Bifurcation of Transition Paths Induced by Coupled Bistable Systems

TL;DR

This paper investigates how coupling multiple bistable systems affects their transition paths, revealing bifurcation phenomena and providing a criterion to predict such bifurcations, with implications for gene circuit dynamics.

Contribution

The paper introduces a criterion to predict bifurcation of transition paths in coupled bistable systems and validates it through numerical simulations of gene circuit models.

Findings

Transition paths in coupled bistable systems can bifurcate.

Bifurcation lowers the energy barrier, facilitating transitions.

Transition rate decreases exponentially with system size when no bifurcation occurs.

Abstract

We discuss the transition paths in a coupled bistable system consisting of interacting multiple identical bistable motifs. We propose a simple model of coupled bistable gene circuits as an example, and show that its transition paths are bifurcating. We then derive a criterion to predict the bifurcation of transition paths in a generalized coupled bistable system. We confirm the validity of the theory for the example system by numerical simulation. We also demonstrate in the example system that, if the steady states of individual gene circuits are not changed by the coupling, the bifurcation pattern is not dependent on the number of gene circuits. We further show that the transition rate exponentially decreases with the number of gene circuits when the transition path does not bifurcate, while a bifurcation facilitates the transition by lowering the quasi-potential energy barrier.