Aims and Objective: 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.
Method: 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.
Result and Conclusion: 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.