Wang Conghua, Yan Fang, Zhang Yuan, Liu Haihong, Zhang Linghai
College of Mathematics, Yunnan Normal University, Kunming 650500, China.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China.
Comb Chem High Throughput Screen. 2018;21(6):411-419. doi: 10.2174/1386207321666180601080026.
A large number of experimental evidences report that the oscillatory dynamics of p53 would regulate the cell fate decisions. Moreover, multiple time delays are ubiquitous in gene expression which have been demonstrated to lead to important consequences on dynamics of genetic networks. Although delay-driven sustained oscillation in p53-based networks is commonplace, the precise roles of such delays during the processes are not completely known.
Herein, an integrated model with five basic components and two time delays for the network is developed. Using such time delays as the bifurcation parameter, the existence of Hopf bifurcation is given by analyzing the relevant characteristic equations. Moreover, the effects of such time delays are studied and the expression levels of the main components of the system are compared when taking different parameters and time delays.
The above theoretical results indicated that the transcriptional and translational delays can induce oscillation by undergoing a super-critical Hopf bifurcation. More interestingly, the length of these delays can control the amplitude and period of the oscillation. Furthermore, a certain range of model parameter values is essential for oscillation. Finally, we illustrated the main results in detail through numerical simulations.
大量实验证据表明，p53的振荡动力学可调节细胞命运决定。此外，基因表达中普遍存在多个时间延迟，已证明这些延迟会对遗传网络的动力学产生重要影响。尽管基于p53的网络中由延迟驱动的持续振荡很常见，但这些延迟在过程中的精确作用尚不完全清楚。
在此，开发了一个具有五个基本组件和两个时间延迟的网络综合模型。以这些时间延迟作为分岔参数，通过分析相关特征方程给出霍普夫分岔的存在性。此外，研究了这些时间延迟的影响，并在采用不同参数和时间延迟时比较了系统主要组件的表达水平。
上述理论结果表明，转录和翻译延迟可通过经历超临界霍普夫分岔诱导振荡。更有趣的是，这些延迟的长度可以控制振荡的幅度和周期。此外，一定范围的模型参数值对于振荡至关重要。最后，我们通过数值模拟详细说明了主要结果。
