Noise-induced Switch And Coherent Switch In Multistable Systems

Multistability phenomena are ubiquitous in the field of nature and science.The theory of multistability has become an important criterion to explain cell differentiation and development.In consequence of complexity of biological systems,it is difficult to reveal the mechanism of multistability from natural biological systems.Based on characteristics of natural cell fate control systems,some synthetic multistable circuits that are helpful to understand similar natural multistable circuits have been proposed.Gene expression process involves noise due to low copy number of molecules.Previous studies have shown that noise can induce switch and coherent switch in bistable systems.However,there is limited research on the impact of noise on switching behaviour of multistable systems.Recently,someone has proposed a new synthetic mechanism for generating multiple stable steady states,called MultiFate circuit.It has not yet been paid much attention that the effect of noise on switching behavior of MultiFate system.Therefore,in this paper,we investigate the effect of Gaussian white noise on switching behavior of two-gene MultiFate-2 system and three-gene MultiFate-3 system.For MultiFate-2 system,it can generate two,three,or even four stable steady states.We investigate the influence of noise on switching behavior of MultiFate-2 system with two and three stable steady states.The numerical results indicate that additive noise caused by environmental fluctuations can affect switching behavior of MultiFate-2 system.Compared with existing bistable systems,in a tristable system,a certain intensity of additive noise can induce MultiFate-2 system to switch from a single gene in high expression state to two genes in high expression state.Starting with two genes in high expression state,MultiFate-2 system does not switch,which can be explained from the perspective of the attraction domain.The vector field diagram of MultiFate-2 system of three stable steady states shows that the attraction domain of two genes in high expression state is larger than that of a single gene in high expression state.Our research also indicates that a certain intensity of additive noise induces coherent switch in MultiFate-2 system with two stable steady states.For MultiFate-3 system,it can generate four,six,seven,or even ten stable steady states.We investigate the influence of noise on switching behavior of MultiFate-3 system with four and seven stable steady states.The numerical results indicate that additive noise caused by environmental fluctuations can affect switching behavior of MultiFate-3system.In heptatable system,a certain intensity of additive noise can induce MultiFate-3system to switch.Compared to the high expression state of a single gene,high expression of two or three genes as initial state,it is difficult for MultiFate-3 system to switch,which may be because the attraction domains of the latter two types of stable steady states are bigger.In a certain intensity of additive noise induces coherent switch in MultiFate-3system with four stable steady states.Compared to a single gene in high expression state,a very low intensity of additive noise can induce coherent switch from three genes in low expression state.This is because the attraction domain of three genes in low expression state is smaller than that of a single gene in high expression state.We designed algorithms to calculate mean first passage time and mean residence time,thereby quantifying the relationship between noise and switching behavior of MultiFate-2system and MultiFate-3 system.Compared with bistable systems,the switching behavior of multistable systems is more diverse.Hope that this article can provide reference significance for understanding the switching behavior of natural multistable systems.