Tian Chengzhe, Mitarai Namiko
Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark.
J Chem Phys. 2016 Jun 7;144(21):215102. doi: 10.1063/1.4953242.
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.
我们讨论了由相互作用的多个相同双稳基序组成的耦合双稳系统中的转变路径。我们提出了一个耦合双稳基因电路的简单模型作为示例，并表明其转变路径是分叉的。然后，我们推导了一个准则来预测广义耦合双稳系统中转变路径的分叉。我们通过数值模拟证实了该理论对示例系统的有效性。我们还在示例系统中证明，如果单个基因电路的稳态不受耦合影响，分叉模式不依赖于基因电路的数量。我们进一步表明，当转变路径不分叉时，转变速率随基因电路数量呈指数下降，而分叉通过降低准势能垒促进转变。
