Dynamic Behavior of p53 Driven by Delay and a Microrna-34a-Mediated Feedback Loop.

The tumor suppressor protein p53 is a critical hub in the comprehensive transcriptional network that inhibits the growth of cells after acute stress stimulation. In this paper, an integrated model of the p53 signaling pathway in response to DNA damage is proposed and the p53 stability and oscillatory dynamics are analyzed. Through theoretical analysis and numerical simulation, we find that the delay as a bifurcation parameter can drive the p53-Mdm2 module to undergo a supercritical Hopf bifurcation, thereby producing oscillation behavior. Moreover, we demonstrate how the positive feedback loop formed by p53* and microRNA-34a (miR-34a) with the feature of double-negative regulation produces limit-cycle oscillations. Further, we find that miR-34a can affect the critical value of Hopf bifurcation in delay-induced p53 networks. In addition, we show that ATM, once activated by DNA damage, makes p53* undergo two Hopf bifurcations. These results revealed that both time delay and miR-34a can have tumor suppressing roles by promoting p53 oscillation or high level expression, which will provide a perspective for promoting the development of anti-cancer drugs by targeting miR-34a and time delay.