DNA damage caused by γ -irradiation initiates oscillatory expression of the p53 genetic network. Although many studies revealed the effects of the p53-Mdm2 circuit on p53 dynamics, a few studies explored the contribution of upstream kinases to p53 oscillation. In this paper, an integrated mathematical model of the p53 network in response to γ -irradiation is studied, which consists of five basic components, two ubiquitous time delays, and two negative feedback loops. It is found that recurrent p53 pulses are externally initiated by ataxia telangiectasia mutated (ATM), and the negative feedback loop formed between ATM and p53, via Wip1, plays a dominant role in generating p53 oscillation. In addition, p53 oscillation requires not only an appropriate Mdm2 negative strength but also a threshold level of Wip1 negative strength. Furthermore, the time delays required for transcription and translation of Mdm2 and Wip1 proteins are essential for p53 oscillation. In particular, the critical value of time delay for inducing oscillation and the properties of delay-driven Hopf bifurcation are theoretically analyzed. As expected, the results are clearly in consistence with biological experiments and observations.

中文翻译：

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反馈回路和时间延迟引起的p53遗传网络的振荡动力学。

γ射线辐射引起的DNA损伤启动了p53遗传网络的振荡表达。尽管许多研究揭示了p53-Mdm2回路对p53动力学的影响，但一些研究探索了上游激酶对p53振荡的影响。本文研究了一个响应于γ辐射的p53网络的集成数学模型，该模型由五个基本成分，两个无处不在的时延和两个负反馈回路组成。发现复发性p53脉冲是由共济失调毛细血管扩张突变（ATM）外部引发的，并且ATM与p53之间通过Wip1形成的负反馈回路在产生p53振荡中起主要作用。此外，p53振荡不仅需要适当的Mdm2负强度，而且还需要Wip1负强度的阈值水平。此外，Mdm2和Wip1蛋白转录和翻译所需的时间延迟对于p53振荡至关重要。特别地，从理论上分析了引起振荡的时延的临界值和时延驱动的霍普夫分支的性质。正如预期的那样，结果显然与生物学实验和观察结果一致。