Study On Stochastic Resonance And Random Energy Of Gene Regulatory Network

More and more evidence shows that the influence of noise on gene regulation network cannot be ignored.In this paper,we study the dynamic behaviors and mechanisms of genetic regulatory networks from the perspective of internal signal stochastic resonance(ISSR)and energy landscape.Firstly,we investigate the internal signal stochastic resonance(ISSR)phenomenon of the gene regulatory network under the excitation of Lévy noise.Numerical simulation results show that the Lévy noise can induce the periodic oscillation of the protein concentration when the control parameter is close to its bifurcation points.Furthermore,we consider the noise-induced periodic signal as the periodic excitation and study the ISSR phenomenon under the cooperation of the nonlinear system,noise-induced periodic signal and random noise.And we found that there may be a connection between the ISSR phenomenon and the bifurcation mechanism.Besides,we also investigate the effects of different noise parameters on the ISSR phenomenon.The simulation results indicate that there is an optimal interval of the stability index which can induce the ISSR phenomenon,and the skewness parameter and the position parameter have a negative correlation with the ISSR phenomenon.These results may provide a pathway to uncover the positive functional mechanism of noises in complex gene regulatory networks.Secondly,we investigate the global dynamics of gene regulatory network through the methods of bifurcation analysis and energy landscape.Our results reveal that different system parameters can induce analogous bifurcation,and exhibit rich dynamics,including monostable state,oscillations,and bistable state.These dynamics of the system are further investigated by the energy landscape.Besides,the numerical simulation results can indicate the following results: 1)Noise can extend the oscillation region of the system when the control parameter (6 is close to its bifurcation value;2)The system dynamics exhibit distinct state-to-state transition features under the excitation of noise;3)For a non-equilibrium oscillation network,the force from the negative gradient of the energy landscape attracts the system states down to the oscillation path,and the probability flux is the driving force of the oscillations.Finally,we investigate the stability of the system oscillations through the physical methods of barrier heights and entropy production rate.Our approach is quite general and can be applied to other complicated gene regulatory networks to explore the potential global dynamics.