Multiple Time Delays Induced Dynamics of p53 Gene Regulatory Network

p53 dynamics plays an important role in determining cell arrest or apoptosis upon DNA damage response. In this paper, based on a p53 gene regulatory network composed of its core regulator ATM, Mdm2 and Wip1, the effect of multiple time delays in transcription and translation of Mdm2 and Wip1 gene expression on p53 dynamics are investigated through theoretical and numerical analyses. The stability of the positive equilibrium point and the existence of Hopf bifurcation are demonstrated through analyzing the associated characteristic equation of the corresponding linearized system in five cases. Detailed numerical simulations and bifurcation analyses are performed to support the theoretical results. The results show that with the increase of a time delay, the positive equilibrium point becomes unstable, and the p53 dynamics presents an oscillating state. These results reveal that time delay has a significant impact on p53 dynamics and may provide a useful insight into developing anti-cancer therapy.

Pid Controller Design for Multiple Time Delays System

This paper presents an approach of stabilization and control of time invariant linear system of an arbitrary order that include several time delays. In this work, the stability is ensured by PI, PD and PID controller. The method is analytical and needs the knowledge of transfer function parameters of the plant. It permits to find stability region by the determination of p K , i K and d K gains.