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STUDIA UNIVERSITATIS BABEŞ – BOLYAI, BIOLOGIA, LV, 1, 2010, p. 67-79 ON THE CONDITIONS FOR WHICH THE Atm PROTEIN CAN SWITCH OFF THE DNA DAMAGE SIGNAL IN A p53 MODEL OMID RABIEIMOTLAGH 1 and ZAHRA AFSHARNEZHAD 2 SUMMARY. In this paper, we consider a recently developed p53 model which simulates interactions between the proteins p53, Mdm2, Atm and DNA damage signal. We apply analytic methods to answer this question: how can the Atm protein contribute positively in DNA healing process? Indeed, we determine regions of parameters into which the Atm protein can switch off damage signals, or conversely, it can lead DNA to a permanent damage. Keywords: DNA healing; Mdm2 protein; Atm protein Introduction Today, it is probably well known that one of the key players in cancer development is p53, a tumor suppressor. The p53 protein is a transcription factor encoded by a gene whose disruption is associated with approximately 50 to 55 percent of human cancers. The p53 protein acts as a checkpoint in the cell cycle, either preventing or initiating programmed cell death (apoptosis) (Cohen et al., 2008). Regarding to the recent experimental observations, biologists consider three major functions for the p53 protein, as, it arrests the cell cycle, thereby giving the cell time to correct any DNA damage, activates transcription of gene indirectly responsible of DNA repair and can be cause of apoptosis (Chicharmane et al., 2007; Vogelstein et al., 2000). We know that p53 regulates itself through its interaction with an intermediate protein which is called Mdm2 (Harris and Levine, 2005). A recent elementary model which is motivated biologically, formulates this interaction as below n n x& = α0 + α1x /( k1 + x ) − γ 1xy −γ 2x (1) 4 4 y& = α 2 + α3x /( k2 + x ) − γ 3y, where x (t) and y (t) are dimensionless and stand respectively for [p35] (t) and [Mdm2] (t) , [2]. In the first equation above, α 0 shows the production rate of p53, the second therm with coefficient α 1 exists due to positive feedback of p53 on 1 Corresponding author, Dept. of Math., University of Birjand, Birjand, Iran, email: omid.rabiei@gmail.com 2 Dept. of Math., Ferdowsi University of Mashhad, Mashhad,Iran, email: afsharnezhad@um.ac.ir
O. RABIEIMOTLAGH, Z. AFSHARNEZHAD itself and it is described with a Hill coefficient n ∈ N which determines the degree of cooperativity of the ligand of p53 binding to the enzyme or receptor (Hill, 1910). The third term represents the active process of ubiquitination of p53 by Mdm2 and the fourth term represents the degradation of p53 independently of Mdm2. Similarly, in the second equation above, α 2 shows the production rate of Mdm2, and second term with coefficient α 3 represents the activation of Mdm2 by p53 with Hill coefficient 4 , and the third term represents the degradation of Mdm2 (Chicharmane et al., 2007; Vogelstein et al., 2000; McLure and Lee, 1998). Another factor in the cell cycle process which acts as a damage sensor, signaling presence of DNA damage, is the Atm protein (Banin et al., 1998: Kurz and Lees-Miller, 2004), The Atm-p protein, a phosphorylated form of Atm, associates in the cell cycle process by controlling production rate of p53. This is the motivation for improving the model (1) by the new model n n x& = z + α1x /( k1 + x ) −γ 1xy −γ 2x (2) 4 4 y& = α 2 + α3x /( k2 + x ) − γ 3y, where z (t) denotes [Atm-p] (t) . Experimental observations show that amount of Atm and Atm-p holds for the conservative equation [Atm] (t) +[Atm-p] (t) = µ , for a positive real constant µ . Also, they are in a reaction for which the phosphorylated form Atm-p promotes further phosphorylation of Atm, hence, once a small amount of Atm-p is produced, it leads to further increase in Atm-p, until all the Atm is converted into its phosphorylated form. This should occur only when a significant DAN damage occurs. So, this process is modelled by the equation z& = α1s z( µ − z)/( k1s + µ − z) −α 2sz/(( k0d + w)( k2s + z)). Here, w (t) =[Dmg] (t) denotes the DNA damage signal, representing amount of DNA damages, and µ − z (t) = µ − [Atm-p] (t) denotes amount of the Atm protein [2]. The first term of the above equation, with coefficient α 1s shows phosphorylation rate of the Atm protein and the second term, with coefficient α 2s shows dephosphorylation rate of the Atm protein. The parameter k 1 controls dependence of phosphorylation rate of the Atm protein to amount of Atm. Similarly, the parameters s k 2 s and k 0 d control dependence of dephosphorylation rate of the Atm protein to amount of Atm-p and damage signal. In order to complete the chain of this interaction, finally, we have to take in account that DNA is repaired by combined actions of Atm-p and p53 which can be modelled as below . w& = −α wzx. d 68
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