Although the oscillatory dynamics of the p53 network have been extensively studied, the understanding of the mechanism of delay-induced oscillations is still limited. In this paper, a comprehensive mathematical model of p53 network is studied, which contains two delayed negative feedback loops. By studying the model with and without explicit delays, the results indicate that the time delay of Mdm2 protein synthesis can well control the pulse shape but cannot induce p53 oscillation alone, while the time delay required for Wip1 protein synthesis induces a Hopf bifurcation to drive p53 oscillation. In addition, the synergy of the two delays will cause the p53 network to oscillate in advance, indicating that p53 begins the repair process earlier in the damaged cell. Furthermore, the stability and bifurcation of the model are addressed, which may highlight the role of time delay in p53 oscillations.

中文翻译：

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时间延迟对 DNA 损伤反应中 p53 振荡的贡献。

尽管 p53 网络的振荡动力学已被广泛研究，但对延迟引起的振荡机制的理解仍然有限。本文研究了p53网络的综合数学模型，其中包含两个延迟的负反馈回路。通过研究有和没有显式延迟的模型，结果表明Mdm2蛋白合成的时间延迟可以很好地控制脉冲形状但不能单独诱导p53振荡，而Wip1蛋白合成所需的时间延迟诱导Hopf分叉来驱动p53振荡。此外，两种延迟的协同作用会导致p53网络提前振荡，表明p53在受损细胞中更早地开始了修复过程。此外，还解决了模型的稳定性和分岔问题，