aks are due to free radicals in these reactions. Depending on its concentration, H2O2 A Model for ATM Sensor induces two types of DNA lesions: DNA single- and double-strand breaks. DNA single-strand breaks are dominant under H2 O2 stress, but these lesions are efficiently repaired and do not appear to mediate the cytotoxic response. On the other hand, DNA double-strand breaks seldom occur under H2 O2 stress, 
but they are toxic and potentially induce apoptosis. In addition, after IR stress, DNA double-strand breaks are generated and ATM proteins are phosphorylated. The true mechanism of this process has not been understood yet. However, one of the targets of ATM phosphorylation is suggested to be the Nbs1 protein, which associates with the conserved DSB repair factors Mre11 and Rad50. The phosphorylated ATM phosphorylates itself, and it is suggested that ATM is autophosphorylated within 15 min after exposure to 0.5 Gy IR, which induces only 18 DNA breaks, approximately. However, it has not been known how ATM detects a small number of DSBs and activates signalling cascades. In this paper, we propose a mathematical model of the ATM phosphorylation process after a stochastic generation of a small number of DSBs regardless of the source of damage. In our model, we assume that 12504917 DSBs are generated under DNA damage, repair proteins bind to them and become DSB-RP complexes, and DSBs are repaired. The numbers of DSBs and DSBCs are very small and these processes are stochastic. We will see that we can calculate theoretical values for the mean numbers of DSBs and DSBCs by using the number of repair proteins and rate constants of repair processes. The produced DSBs and DSBCs phosphorylate ATM which autophosphorylates itself. We will find that DSBs are not successfully repaired and the number of DSBs increases when the number of repair proteins is small, but when sufficient repair proteins exist, the number of DSBs is suppressed to low levels. Also, we will find that autophosphorylation of ATM induces bifurcation of the phosphorylated ATM. Depending on the total concentration of ATM, the fixed points of ATM will have three types of steady state diagrams: monostable, reversible bistable, and irreversible bistable diagrams. Of these steady-state diagrams, bistability emerges when the total concentration of ATM increases, and the concentration of ATM exhibits switch-like behaviour in the presence of such bistabilities. Furthermore, we will see that the time to detection after the DNA damage decreases when the total concentration of ATM increases. Results where DSB denotes DNA DMXAA site double strand breaks, RP denotes repair proteins, DSBC denotes DSB and repair protein complexes, and RDSB denotes the repaired DSB. The constants, c1, cz, c{, c3, represent the stochastic rate constants . Also, the associated rate laws are hi X,ci, where i is a reaction type and X ~XDSB,XRP,XDSBC,XRDSB is the current state of each reaction species) of the 10604535 system. These chemical reactions occur stochastically, thus the fluctuations of the number of molecules which are produced in these reactions are stochastic processes. For example, the production of DSBs is a zeroth-order reaction, and the hazard of the reaction is h1 X,c1 ~c1: 2 The repair process of the DSBs is a second-order reaction, and the combined hazard of the reaction is hz X,cz ~cz XDSB XRP: 2 2 2 3 The failed and succeeded repair processes are first-order reactions, and we respectively denote the combined hazards of each
