Dynamics Of A P53-Mdm2 Gene Regulatory Network Model With Delay Effect

When DNA is stimulated and damaged,p53 levels rise rapidly in response to ex-ternal stimuli.As the stimulation is small and causes less damage,the p53 gene causes cells to temporarily stop growing to repair the damage and then return to normal levels.p53 protein levels rise sharply would start apoptosis process make the cell apoptosis and inhibition of cancer cells.The above control cell death process is controlled by the p53protein.In gene transcription and translation to protein is a complex and slow process.Therefore,in the process of time delay is inevitable.In previous studies have proved that the time delay has important influence on dynamic character of system.So the research of time delay effects on p53 gene regulation and control system is also very important.This article will focus on research on the influence of time delay of the system,From the perspective of time delay,new ideas are provided for the research and treatment of cancer.The main contents are as follows:The first chapter,We analyzed the importance of p53 in cancer pathogenesis and cancer treatment.Current major research findings and advances in p53;The main work of this paper.The second chapter,we studied the effects of two time delays on two types of cells stimulated by chemotherapy drugs.First of all,for the sensitive cell model,we studied the effect of time delay on the system by appropriate assumptions and mathematical deformation and using the local Hopf bifurcation theory.The time delay?₂of p53-Wip1negative feedback loop was set as zero,and the time delay?₁of p53-Mdm2 was taken as the bifurcation parameter to obtain the existence conditions of Hopf bifurcation at the positive equilibrium point.Secondly,the direction,stability and period of bifurcation periodic solution are determined according to the central manifold theorem and canonical type theory.Finally,some theoretical results are verified by numerical simulation and the effects of two time delays and important parameters are studied.The third chapter,based on the second chapter,we studied the effects of time delay on the system from the network composed of p53-Mdm2 and p53-PTEN-Akt.Using the same method as the second chapter studies the model in the condition of the existence of positive equilibrium of the Hopf branch and the nature of the branch.Finally,the theoretical results are verified through the numerical simulation analysis and study two time delay,and the function of some important parameters.The fourth chapter summarizes the whole paper and gives the innovation,shortcom-ings and the direction of our research.