On the Conditions of Hopf Bifurcation for ATM Protein and DNA Damage Signal Model; Cuts off the DNA Healing Process

In this paper, we consider some available models and then introduce a model which simulates the interaction between ATM protein and DNA damage signal, which motivated biologically. Next we find a Hopf bifurcation for this system. Biologically we find a region for the DNA damage signal and ATM protein where solutions in this region are not of those solutions that DNA healing process occurs on these. In fact entering solutions in this region aren’t biologically appropriate solutions.