The Study On The Dynamics Of The Tumor Suppressor Gene P53

When the genomic integrity of a cell is challenged, its fate is determined in part by signals conveyed by the tumor suppressor protein. It was observed in the experiments that p53 protein can respond to DNA damage or Hypoxia by various stresses (both intrinsic and extrinsic to the cell), such as physical or chemical factors, including gamma or UV irradiation, ionizing radiation, as well as reaction with oxidative free radicals, activate and regulate its downstream genes to initiate the program of cell cycle arrest to repair the damaged DNA, or the program of cell apoptosis when the damage to DNA is too severe to repair. No matter how p53 responds to the signal, it is able to control the limitless reproduction of cells effectively, and thus to prevent the tumor.The Mdm2 oncogene, an important negative regulator of tumor suppressor gene p53, plays an extremely important role in regulating the level of p53 and stabilizing organisms. p53 induces the expression of Mdm2 gene, whereas the expressed product Mdm2 protein negatively regulates p53, so they form a p53-Mdm2 negative feedback loop based on protein level. p53 and Mdm2 are two important nodes respectively in the signaling transduction network, and the negative feedback loop between both of them is the core of this network. The central work of the study in this passage is the dynamics of p53.For convenience, the paper discusses just the dynamics of p53 in individual living cells, and the main work is embodied in chaps three and four. The analytical stationary state solutions-stationary points to the equations from the ready-made model with three variables about p53 and its dynamical equations have been obtained, the nonlinear equations have been made linear by using nonlinear dynamical method, and then using linear stability theorem and Routh-Hurwitz criterion the stability of the stationary points has been analyzed. In order to make it easy to generate oscillations for the system and given the details of the interaction between p53 and Mdm2, we introduce time lags based on the original model, as well as two new variables-active p53 and signal. Besides, DNA damage switch is introduced to control p53 network on or off, and thus we found the modified model. Without DNA damage, p53 network is off, so it stays in the steady state; whereas DNA damage is present, p53 network is turned on, the signal S is activated, and the system responds to DNA damage in the form of oscillations. At the end of the passage, we have reduced five variables to three under certain condition, namely inactivated p53, Mdm2 and signal, so reduced model can be obtained, and it is also able to generate limit-cycle oscillations easily. The dynamical properties are compared with that of the model without reduction, only to find they both have extremely similar limit cycles, and the reduced model can reflect partly the dynamical properties of its prototype, so to a great extant, the modified model is reduced.