Dynamic Analysis Of Regulation Mechanisms When Cells In Response To DNA Damage

Various stress could cause DNA damage,a defense mechanism that is crucial for protecting the integrity of the genomic and inhibiting tumorigenesis.The tumor suppressor p53 has a crucial role in preventing tumor-igenesis,and its encoded production is p53 protein which plays a crucial role in preventing tumorigenesis.Previously,it was proposed that cell fate after DNA damage is governed by p53 levels,namely,a low levels of p53 leads to transient growth arrest and cell survival,whereas a high levels promotes irreversible apoptosis.Therefore,it is a meaningful and important task to study how regulate the levels of p53 in the system.In particular,the delays involved in transcription and translation are critical.As we all know,the transcriptional and translational processes are the basic steps of gene expression in cells,which are not only slow but also are complex.As a result,a lot of works has proved that the time delay will induce oscillation of the system,so studying the effects of the time delay in p53 network is very important too.In this paper,we add the time delay to the p53 network and attempt to find the main factors that regulate the levels of p53 by studying the kinetic behavior of p53.These results may provide a new approach for the treatment of cancer.The main contents are as follows:In chapter 1,we described the research background and significance of p53;the de-velopment of p53 gene network model;the main research contents and the theorems and definitions.In chapter 2,we use experimental data to developed a three-dimensional delayed mathematical model,with the aim of understanding how the time delays required for transcription and translation in Mdm2 gene expression affect oscillatory behaviour in p53-Mdm2 network.Considering the time delays as the bifurcation parameter,the explicit algorithms for determining the conditions of Hopf bifurcation are studied by analyzing the associated characteristic equation.Moreover,the direction and stability of the bifurcating periodic solutions are determined in detail by applying the normal form theory and the center manifold reduction.Finally,numerical simulations are carried out to illustrate the main results.In chapter 3,we extend the three-dimensional model to get a five-dimensional delayed mathematical model of p53 network with two time delays.The same method in chapter 2 is used to study the asymptotic stability of the model at the positive equilibrium point and to determine the existence of the Hopf bifurcation;the direction;stability and period of the solution.Additionally,in addition to considering the decisive role of time delay,the effects of five model parameters on system dynamics behavior are considered separately when working with time delays.Finally,the model is numerically simulated to illustrate the main results.In chapter 4,we summarize the full text and introduce the innovations and deficiencies of this article in detail.