Department of Mathematics, Yunnan Normal University, Kunming 650500, China.
Key Laboratory of Complex System Modeling and Application for Universities in Yunnan, Kunming 650500, China.
Math Biosci Eng. 2023 Jan;20(2):2321-2347. doi: 10.3934/mbe.2023109. Epub 2022 Nov 18.
The tumor suppressor protein P53 can regulate the cell cycle, thereby preventing cell abnormalities. In this paper, we study the dynamic characteristics of the P53 network under the influence of time delay and noise, including stability and bifurcation. In order to study the influence of several factors on the concentration of P53, bifurcation analysis on several important parameters is conducted; the results show that the important parameters could induce P53 oscillations within an appropriate range. Then we study the stability of the system and the existing conditions of Hopf bifurcation by using Hopf bifurcation theory with time delays as the bifurcation parameter. It is found that time delay plays a key role in inducing Hopf bifurcation and regulating the period and amplitude of system oscillation. Meanwhile, the combination of time delays can not only promote the oscillation of the system but it also provides good robustness. Changing the parameter values appropriately can change the bifurcation critical point and even the stable state of the system. In addition, due to the low copy number of the molecules and the environmental fluctuations, the influence of noise on the system is also considered. Through numerical simulation, it is found that noise not only promotes system oscillation but it also induces system state switching. The above results may help us to further understand the regulation mechanism of the P53-Mdm2-Wip1 network in the cell cycle.
肿瘤抑制蛋白 P53 可以调节细胞周期，从而防止细胞异常。在本文中，我们研究了时滞和噪声影响下 P53 网络的动态特性，包括稳定性和分岔。为了研究几个因素对 P53 浓度的影响，对几个重要参数进行了分岔分析；结果表明，在适当的范围内，重要参数可以诱导 P53 振荡。然后，我们利用时滞作为分岔参数的时滞 Hopf 分岔理论研究了系统的稳定性和 Hopf 分岔的存在条件。结果表明，时滞在诱导 Hopf 分岔和调节系统振荡的周期和幅度方面起着关键作用。同时，时滞的组合不仅可以促进系统的振荡，而且提供了良好的鲁棒性。适当改变参数值可以改变分岔临界点，甚至改变系统的稳定状态。此外，由于分子的拷贝数低和环境波动，还考虑了噪声对系统的影响。通过数值模拟发现，噪声不仅促进了系统的振荡，而且诱导了系统状态的切换。上述结果可能有助于我们进一步了解 P53-Mdm2-Wip1 网络在细胞周期中的调控机制。
