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The model is constructed based on the core regulatory network of p53 and is an improved model from the one (deterministic model) proposed by Sun et al. (2011). We aim to develop a model that is consistent with the limited experimental data, and can be used to make further predictions or gain insights into p53 regulation in light of new experimental findings. P53 regulation involves many post- translational modifications such as phosphorylation, ubiquitination, acetylation, methylation and sumoylation (Bode & Dong, 2004). Our model is a simplified representation that includes

phosphorylation, acetylation and degradation mediated by Mdm2. The main differences in our model compared to Sun et al. (2011) model are that in our model: 1) p53 auto regulation (positive feedback loop) is included; 2) MdmX is included; 3) Mdm2 and MdmX inhibit p53 acetylation; 4) p53- Mdm2, Mdm2-MdmX and p53-MdmX complexes are represented explicitly as variables. The model (equations) was integrated with XPPAUT, a software program freely downloadable from

www.math.pitt.edu/~bard/xpp/xpp.html.

Figure 4.1 shows a schematic diagram of the model. When cells are exposed to stress, for example gamma irradiation, it causes DNA double-strand breaks (DSBs). The DSB is the input into the model. (For simplicity, the number of DSBs is represented by DSB, a model parameter which could be plural or singular). The DSB activate the protein kinase, ataxia telangiectasia mutated (ATM) stress

signalling molecule and these stress signals are further amplified by ATM intermolecular auto- phosphorylation at Serine 1981 (Bakkenist & Kastan, 2003). The DSB caused ATM phosphorylation results in a cascade of phosphorylation activities that activates p53 (Figure 4-1 green arrows, turn on p53) (Cheng & Chen, 2010). Firstly, ATM phosphorylation of Mdm2 prevents the ability of Mdm2 binding to p53 and degradation of p53 (Maya et al., 2001). At the same time, Mdm2 switches the target of ubiquitination from p53 to itself and MdmX, and thus facilitates p53 activation (Wade et al., 2010). Secondly, ATM phosphorylation of p53 on the N terminus Serine 15 further disrupts Mdm2 binding and stabilizes p53. Note that ATM also activates check point kinase 2 (Chk2), which then phosphorylates p53 on Serine 20 (Cheng & Chen, 2010). However, Chk2 is not included in our model

for simplicity since Chk2 concentration is relatively constant (Kastan & Bartek, 2004). Finally, ATM also phosphorylates MdmX. Phosphorylation of MdmX enhances binding, ubiquitination and degradation by Mdm2 (Cheng & Chen, 2010).

Figure 4-1 Schematic representation of the model. A schematic diagram incorporates the molecular interactions of the p53 core regulatory network. For clarity, a few model interactions are not shown.

Phosphorylated p53 (P53p) can be further phosphorylated at different sites, represented by P53pp. It is assumed that both P53p and P53pp activate the transcription of p53 itself (Deffie et al., 1993; Wang & El-Deiry, 2006). P53p and P53pp also activate the transcription of mdm2, mdmx and Wip1. We adopted the transcriptional time delay of 30 min and translation/translocation delay of 10 min proposed by Ma et al. (2005). The up-regulation of Wip1 plays a role in modulating ATM-dependent signalling pathway, and attenuating the p53 response. Wip1 function as a phosphatase that

dephosphorylates ATM, p53, Mdm2, and MdmX (Figure 4-1 red arrows, turn off p53) (Wade et al., 2010). Wip1 reverses the stress signal protein ATMp and p53p to un-phosphorylated form, resetting ATM and p53 to non-active state (Lu et al., 2005; Shreeram et al., 2006). Thus, Wip1 creates a p53

negative feedback mechanism that attenuates the stress signal and p53 activation. Moreover, Wip1 dephosphorylates Mdm2 and MdmX; these dephosphorylations stabilize Mdm2 and MdmX and then lead to the inhibition of p53 activities (Lu et al., 2007; Zhang et al., 2009c). Therefore, p53 activation by ATM is rapid because ATM is sensitive to stress signal (Bakkenist & Kastan, 2003), and feedback from Wip1 ensures that p53 activation in general is not in sustained active state that promotes cell cycle arrest and apoptosis, which can have strong anti-growth effect (Vousden & Lane, 2007). MdmX inhibits p53 mainly by forming a p53-MdmX complex (Cheng & Chen, 2010), and this is represented by a reversible reaction of p53-MdmX complex (C3) formation and dissociation (Figure 4-2). MdmX also regulates p53 levels by modulating Mdm2 levels and E3 ligase activity towards p53 ubiquitination and degradation through the heterodimers Mdm2-MdmX (C2) (Linke et al., 2008), and this reversible reaction is represented by the reaction of Mdm2-MdmX complex (C2) formation and dissociation. The p53-Mdm2 complex (C1) formation and dissociation is also included in this model to represent the binding and unbinding between Mdm2 and p53 protein molecules (Schon et al., 2002).

Moreover, Mdm2 is assumed to inhibit p53 activity by repressing p53 acetylation. This assumption is based on the experimental results that demonstrated that Mdm2 suppresses p300/CBP acetylation of p53, where p300 and CBP are acetyltransferases that function as co-activators to promote p53 acetylation (Ito et al., 2001). Similarly, MdmX was also reported to suppress p300/CBP acetylation of p53 (Sabbatini & McCormick, 2002) and both Mdm2 and MdmX inhibition of p53 acetylation are represented by a barred arrow in Figure 4-1. These inhibitions by Mdm2 and MdmX of p53

acetylation were modelled as competitive inhibition reactions (See Eqn. 4.10). Acetylated p53 (P53a) is assumed to activate p21, a gene that encodes protein P21, which acts as a cyclin-dependent kinase (Cyclin E/cdk2) inhibitor to arrest cell cycle, and causes G1 arrest (Kastan & Bartek, 2004). For clarity, not all model interactions are shown in Figure 4-1 and Figure 4-2. These interactions are listed below:

1. Mdm2 protein and heterodimer C2 promote P53 protein degradation (see Eqn. 4.7) Figure 4-2 Formation and dissociation of complexes in the core regulation of p53.

2. P21 protein degradation is mediated by heterodimer C2 (Jin et al., 2008) (see Eqn. 4.11) 3. DSB induces Mdm2 protein degradation (Ciliberto et al., 2005) (see Eqn. 4.12)

4. Mdm2p promotes auto-ubiquitination and degradation of Mdm2 (see Eqn. 4.13)