This study develops an integrated model of the p53-Mdm2 interaction composed of five basic components and time delay in the DNA damage response based on the existing research work. Some critical factors, including time delay, system parameters, and their interactions in the p53-Mdm2 system are investigated to examine their effects on the oscillatory behaviour induced by Hopf bifurcation. It is shown that the positive feedback formed between p53 and the activity of Mdm2 in the cytoplasm can cause a slight decrease in the amplitude of the p53 oscillation. The length of the time delay plays an important role in determining the amplitude and period of the oscillation and can significantly extend the parameter range for the system to demonstrate oscillatory behaviour. The numerical simulation results are found to be in good agreement with the published experimental observation. It is expected that the results of this research would be helpful to better understand the biological functions of p53 pathway and provide some clues in the treatment of cancer.

中文翻译：

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p53-Mdm2 反馈模块中 Hopf 分叉引起的振荡。


本研究在现有研究工作的基础上，开发了由五个基本成分组成的p53-Mdm2相互作用的集成模型以及DNA损伤反应的时间延迟。研究了一些关键因素，包括时间延迟、系统参数及其在 p53-Mdm2 系统中的相互作用，以检查它们对 Hopf 分岔引起的振荡行为的影响。结果表明，p53与细胞质中Mdm2活性之间形成的正反馈可以导致p53振荡幅度略有下降。时间延迟的长度在确定振荡的幅度和周期方面起着重要作用，并且可以显着扩展系统展示振荡行为的参数范围。数值模拟结果与已发表的实验观察结果非常吻合。预计该研究结果将有助于更好地了解p53通路的生物学功能，并为癌症的治疗提供一些线索。