Oscillatory Behaviors of Delayed p53 Regulatory Network with microRNA 192 in DNA Damage Response

This study develops a general model of delayed p53 regulatory network in the DNA damage response by introducing microRNA 192-mediated positive feedback loop based on the existing research work. 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 192 (miR-192) with the feature of double-negative regulation produces oscillations. Further, a comparison is given to demonstrate that microRNA 192-mediated positive feedback loop affects the robustness of system oscillations. In addition, we show that ataxia telangiectasia mutated kinase (ATM), once activated by DNA damage, makes p53* undergo two Hopf bifurcations. These results reveal that both time delay and miR-192 play 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-192 and time delay.