Oscillation induced by Hopf bifurcation in the p53-Mdm2 feedback module

This study develops an integrated model of the p53-Mdm2 interaction composed of five basic components and time delay in the DNA damage response based on the existing research work. Some critical factors, including time delay, system parameters, and their interactions in the p53-Mdm2 system are investigated to examine their effects on the oscillatory behaviour induced by Hopf bifurcation. It is shown that the positive feedback formed between p53 and the activity of Mdm2 in the cytoplasm can cause a slight decrease in the amplitude of the p53 oscillation. The length of the time delay plays an important role in determining the amplitude and period of the oscillation and can significantly extend the parameter range for the system to demonstrate oscillatory behaviour. The numerical simulation results are found to be in good agreement with the published experimental observation. It is expected that the results of this research would be helpful to better understand the biological functions of p53 pathway and provide some clues in the treatment of cancer.