Intrinsic noise induced state transition in coupled positive and negative feedback genetic circuit

It is well known that gene regulatory circuits can be modeled by the deterministic or stochastic approach. In this paper, a three-component coupled positive and negative feedback genetic circuit is firstly modeled deterministically by Hill kinetics. Then, a corresponding stochastic model is also investigated by using Gellispie's stochastic simulation. Some typical dynamical behaviors of the genetic circuit are further discussed based on the bifurcation analysis of deterministic system, including monostability, bistability, excitability, and oscillation. This paper aims to further investigate the effect of intrinsic noise inherently in stochastic models on steady states transition. It includes: i) For the parameters in deterministically bistable region, intrinsic noise may induce bistable switch for the not too large system volume, which can be observed by the generation of a new stable steady state; ii) For the parameters in deterministically excitable region, intrinsic noise may induce periodic switch for the very large system volume, which can be observed by the stabilization of another unstable steady state and the switching between two stable states; iii) When time delays are introduced in these two models, similar phenomena can be observed. The above results will certainly increase the understanding of the inner relationships between different modeling for the genetic circuit. It sheds some light on the real- world engineering applications, such as the engineering design of synthetic circuits.