Conghua Wang, Fang Yan, Yuan Zhang, Haihong Liu* and Linghai Zhang
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 have been demonstrated to take 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 are essential for the oscillation. Finally, we illustrated the main results in detail through numerical simulations.
DNA damage, p53, Mdm2, Wip1, Time delay, Hopf bifurcation, Oscillation.
College of mathematics, Yunnan Normal University, Kunming, 650500, College of mathematics, Yunnan Normal University, Kunming, 650500, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, College of mathematics, Yunnan Normal University, Kunming, 650500, Department of mathematics, Lehigh University, Bethlehem, 18015