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The main goal here is to estimate a lower bound for the level of the p53 protein which is necessary for the DNA damage is repaired by a coeffective work of activated p53 and ATM-p. We consider a system of ODEs as the mathematical model of interactions between the proteins p53, Mdm2, and ATM-p. The model is biologically motivated and can simulate effects of proteins on the DNA damage suppression. It is shown that positive amounts of ATM-p may force the system to pass through a saddle node bifurcation which in turn indicates the lower bound for p53. We see that if the amount of p53 is less that the lower bound then the DNA damage is not suppressed. Finally we use the bifurcation equation and show that how the Hill coefficient of p53 must be controlled in order to optimize the healing process.

Keywords: p53-Mdm2 oscillatory model, ATM-p protein, Saddle node bifurcation, Center Manifold, Hill constant.