Oscillatory Dynamics of p53 Genetic Network Induced by Feedback Loops and Time Delays

DNA damage caused by γ -irradiation initiates oscillatory expression of the p53 genetic network. Although many studies revealed the effects of the p53-Mdm2 circuit on p53 dynamics, a few studies explored the contribution of upstream kinases to p53 oscillation. In this paper, an integrated mathematical model of the p53 network in response to γ -irradiation is studied, which consists of five basic components, two ubiquitous time delays, and two negative feedback loops. It is found that recurrent p53 pulses are externally initiated by ataxia telangiectasia mutated (ATM), and the negative feedback loop formed between ATM and p53, via Wip1, plays a dominant role in generating p53 oscillation. In addition, p53 oscillation requires not only an appropriate Mdm2 negative strength but also a threshold level of Wip1 negative strength. Furthermore, the time delays required for transcription and translation of Mdm2 and Wip1 proteins are essential for p53 oscillation. In particular, the critical value of time delay for inducing oscillation and the properties of delay-driven Hopf bifurcation are theoretically analyzed. As expected, the results are clearly in consistence with biological experiments and observations.