Oscillatory Behavior Of P53-Mdm2 Network Driven By Time Delay

Cancer is one of the most terrible diseases in human diseases,and it is also the main cause of death in modern humans.All types of cancer have one thing in common: they are caused by mutations in genes that cause cell division and abnormal proliferation.In this paper,we start with one of the major tumor suppressor genes,p53,and discuss the dynamic behavior of p53 gene regulatory network by analyzing the stability of the equilibrium point of the corresponding differential equation.The main contents are as follows:In chapter 1,we briefly describe the research background and significance of p53,the development of p53 gene regulatory network and the main work of this paper.In Chapter 2,we study the dynamics of a five-dimensional p53-Mdm2 network with two delays,and further explore how the time delay required for transcription and translation in Mdm2 gene expression affects the oscillation behavior of the p53-Mdm2 network.Firstly,the time delay is taken as a branch parameter,by analyzing the corresponding characteristic equations at the equilibrium point,the stability of the model at the equilibrium point and the conditions for the existence of the Hopf branch are studied.Secondly,the Hopf bifurcation properties(direction,stability,and period of the bifurcation solution)are obtained by applying the canonical theory and the central manifold theorem.Finally,the theoretical results are verified by numerical simulation.In Chapter 3,on the basis of the Chapter 2,a five-dimensional mathematical model of p53-Mdm2 network with a time delay and positive feedback loop is proposed.The stability of the model’s positive equilibrium point and the nature of the Hopf branch are studied by using a similar method in Chapter 2.In addition,besides considering the main role of time delay,the effects of three model parameters and time delay on the oscillation behavior of the system are also considered.In particular,we also study how the positive feedback loop between p53 and Mdm2 affects the oscillation behavior of the system.Finally,numerical simulations are carried out to verify the correctness of the conclusions and to illustrate the main results.In chapter 4,we summarize the full text and introduce the innovation of this article and the work will be done next.