Lévy noise-induced phase transition in p53 gene regulatory network near bifurcation points

Abstract

The dynamics of tumor suppressor p53 is closely related to cell fate decisions in responses to various stress signals, especially p53 oscillation. In this paper, phase transition of p53 dynamics from stable steady state to oscillatory state induced by Lévy noise is investigated numerically in p53 gene regulatory network. First, we carry out bifurcation analysis of p53 protein expression levels with respect to the degradation rate of ataxia telangiectasia mutated (ATM) protein in deterministic model of the p53 gene regulatory network. The bifurcation diagram demonstrates that p53 activities can display a stable steady state, a stable limit cycle and the coexistence of a stable steady state with a stable limit cycle upon varying ATM degradation rate. Then, we investigate the influences of Lévy noise parameters on phase transition from stable steady state to stable limit cycle in stochastic model of the p53 gene regulatory network for control parameters near bifurcation points. Moreover, phase transitions are verified through autocorrelation at lag-1, variance, kurtosis, skewness and potential landscape. Our results reveal that phase transition may occur for an optimal interval of stability index α, and is positive and negative correlation with noise intensity D and skewness parameter β, respectively. Besides, phase transition from low stable steady state to stable limit cycle is sensitive to Lévy noise parameters, but it is the opposite for high one. These results may provide an insight to uncover p53 dynamics in p53 gene regulatory network upon noise.