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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. • Suitable ATM degradation rate induces the oscillation of p53 model with high initial conditions. • Phase transition easily occurs for stability index α around 1, large noise intensity D and small skewness parameter β of Lévy noise. • Phase transition from low stable steady state to stable limit cycle is sensitive to Lévy noise parameter. [ABSTRACT FROM AUTHOR]

The cyclic AMP (cAMP)-response element-binding protein (CREB) family of transcription factors is crucial in regulating gene expression required for long-term memory (LTM) formation. Upon exposure of sensory neurons to the neurotransmitter serotonin (5-HT), CREB1 is activated via activation of the protein kinase A (PKA) intracellular signaling pathways, and CREB2 as a transcriptional repressor is relieved possibly via phosphorylation of CREB2 by mitogen-activated protein kinase (MAPK). Song et al. [18] proposed a minimal model with only interlinked positive and negative feedback loops of transcriptional regulation by the activator CREB1 and the repressor CREB2. Without considering feedbacks between the CREB proteins, Pettigrew et al. [8] developed a computational model characterizing complex dynamics of biochemical pathways downstream of 5-HT receptors. In this work, to describe more simply the biochemical pathways and gene regulation underlying 5-HT-induced LTM, we add the important extracellular sensitizing stimulus 5-HT as well as the product Ap-uch into the Song’s minimal model. We also strive to examine dynamical properties of the gene regulatory network under the changing concentration of the stimulus, [5-HT], cooperating with the varying positive feedback strength in inducing a high state of CREB1 for the establishment of long-term memory. Different dynamics including monostability, bistability and multistability due to coexistence of stable steady states and oscillations is investigated by means of codimension-2 bifurcation analysis. At the different positive feedback strengths, comparative analysis of deterministic and stochastic dynamics reveals that codimension-1 bifurcation with respect to [5-HT] as the parameter can predict diverse stochastic behaviors resulted from the finite number of molecules, and the number of CREB1 molecules more and more preferentially resides near the high steady state with increasing [5-HT], which contributes to long-term memory formation. [ABSTRACT FROM AUTHOR]