Bifurcation of transition paths induced by coupled bistable systems

TY - JOUR

T1 - Bifurcation of transition paths induced by coupled bistable systems

AU - Tian, Chengzhe

AU - Mitarai, Namiko

PY - 2016/6/7

Y1 - 2016/6/7

N2 - 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.

AB - 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.

U2 - 10.1063/1.4953242

DO - 10.1063/1.4953242

M3 - Journal article

C2 - 27276971

SN - 0021-9606

VL - 144

JO - The Journal of Chemical Physics

JF - The Journal of Chemical Physics

IS - 21

M1 - 215102

ER -