Before revision:  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 softens this decrease. Finally we show that multiplicative noises facilitate the bifurcation of transition paths .
After revision:  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 .