Mathematical and computational analysis of intracelluar dynamics 4

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Chapter p53-MDM2 Oscillations Intracellular protein levels of p53 and MDM2 have been shown to oscillate in response to ionizing radiation. p53 and MDM2 are members of the p53-AKT network studied previously in the preceding chapters. In particular, the p53-AKT network embeds the p53-MDM2 negative feedback loop, which has been attributed to cause the p53-MDM2 oscillations upon ionizing radiation induced DNA damage. This chapter reviews the reported experimental observations of p53-MDM2 oscillations (Section 4.1), and the corresponding mathematical models that have been developed in the last few years to simulate them (Section 4.2). The consequences of p53-MDM2 oscillations on the predicted p53-AKT bistable switch are studied in the following chapter. 4.1 Experimental evidence of p53 oscillations Oscillations in p53 protein levels were initially reported in cell population studies where damped oscillations were observed in response to DNA damage; see, for examples, Figures to of Collister et al. (1998) and Figure of Bar-Or et al. (2000); Ohnishi et al., 1999. Damped oscillation means that the oscillation amplitude decreases with subsequent pulses. Collister et al. (1998) observed that protein levels of p53, p21 (a target gene of p53) and MDM2 showed damped oscillations in cell 68 populations of human wild-type and Bloom’s syndrome patients’ fibroblast, following induction of DNA damage either by 20 J/m2 of UV radiation or 2.5 Gy of ionizing radiation (IR). Interestingly, the oscillation profiles between wild-type and cancerprone Bloom’s syndrome patients’ cell populations are markedly distinct when induced under identical experimental conditions. On the other hand, Bar-Or et al. (2000) reported damped oscillations of p53 and MDM2 protein levels in cell populations of mouse fibroblasts and human breast cancer epithelial MCF-7 cells, following 5Gy of IR. The dynamics of the p53-MDM2 oscillator are clarified after single-cell experiments on MCF7 cells revealed that these oscillations are sustained as long as IR-induced (up to 10 Gy) DNA damage persisted, and could last for at least three days: Figure 2D of Lahav et al. (2004), Figure 1B of Geva-Zatorsky et al. (2006); Ramalingam et al., 2007. Reproducible observations include the following: periods of oscillation are to hrs; peaks of MDM2 oscillations lag behind p53 peak for 1.5 to 2.5 hrs; periods of oscillations decrease with increasing IR intensity; and peaks of p53 pulses display considerably more variations than their oscillation periods (GevaZatorsky et al., 2006). Based on the positive correlation between the observed numbers of p53 pulses with IR intensity (Lahav et al., 2004), the p53 response to DNA damage has been referred to as a digital counter, with number of pulses signaling which p53 target genes to induce. Despite that, the number of pulses among cells showed variability when they are exposed to the same IR intensity (GevaZatorsky et al., 2006) – in fact, one would obtain damped oscillations observed in cell population studies by taking the average of the time-courses of p53 or MDM2 protein levels from each individual cell. 69 Consistent with cell population and single-cell studies, p53-MDM2 oscillations are also observed in the intestine and spleen of living mice upon totalbody-irradiation with Gy of IR; see Figure of Hamstra et al. (2006). As expected, the oscillations are damped, with periods ranging from 4.5 to hrs. Notably, p53-dependent transcription of PTEN upon irradiation-induced DNA damage has been reported in MCF-7 (human breast cancer epithelial), human colon carcinoma (HCT116), A172 (human glioblastoma), MEF (mouse embryonic fibroblasts) and tissues of mouse small intestine, colon, kidney and liver (Feng et al., 2007; Wang et al., 2005; Stambolic et al., 2001; Trotman and Pandolfi, 2003; Singh et al., 2002] where p53 oscillations are also observed (Bar-Or et al., 2000; Lahav et al., 2004; Geva-Zatorsky et al., 2006; Hamstra et al., 2006; Ohnishi et al., 1999; Ramalingam et al., 2007). 4.2 Review of p53-MDM2 mathematical models This section reviews the recent mathematical models developed to describe the dynamics of the p53-MDM2 oscillator in a cell population (Bar-Or et al., 2000) or in a single cell (Ciliberto et al., 2005; Ma et al., 2005; Wagner et al., 2005; GevaZatorsky et al., 2006; Zhang et al., 2006; Bottani and Grammaticos, 2007). These models focus on reproducing experimental observations as well as on the underlying mechanisms. Common to them is the postulation that the mechanistic origin of the abovementioned oscillations is the negative feedback loop between p53 and MDM2. In the models, which are formulated by ODEs and rate expressions similar to the 70 kinetic models formulated in the preceding chapter, the p53-MDM2 oscillator is kickstarted by IR-induced DSBs (DNA double strand breaks), which lead to posttranslational modifications (PTMs) of p53 and MDM2 proteins (reviewed in Sections 2.2.2 and 2.3 of Chapter 2). These PTM events prolong the time required by MDM2 to degrade p53. Generally, these models generate p53-MDM2 oscillations using two mechanisms, as discussed below. The first group of models demonstrated the importance of a time-delay mechanism to generate oscillations (Bar-Or et al., 2000; Ma et al., 2005; Wagner et al., 2005; Geva-Zatorsky et al., 2006; Bottani and Grammaticos, 2007); these models are also referred to as delay oscillators (Goldbeter, 2002; Monk, 2003). In the model proposed by Bar-Or et al. (2000) to simulate damped p53-MDM2 oscillations that match experimental observations in a cell population, a postulated intermediary part list is used to produce a time-delay between p53 activation and p53-dependent induction of MDM2. They demonstrated that only biologically meaningful damped p53 and MDM2 oscillations are obtained for intermediate lengths of the time-delay. On the other hand, models of Ma et al. (2005), Wagner et al. (2005), Geva-Zatorsky et al. (2006: Model IV) and Bottani and Grammaticos (2007) considers the time-delay due to the transcription and translation of MDM2 proteins; mRNA of MDM2 is included in the models. These models generate sustained oscillations upon DNA damage in individual cells. Notably, Geva-Zatorsky et al. (2006) show that the model could generate sustained oscillations over a broad range of kinetic parameters that match experimental observations. 71 In the second group of models (Ciliberto et al., 2005; Geva-Zatorsky et al., 2006: Model V; Zhang et al., 2006), the p53-MDM2 negative feedback loop is supplemented with a positive feedback loop to generate sustained oscillations observed in single cells; these models are also referred to as relaxation oscillators (Pomerening et al., 2003; Tyson et al., 2003). These models differed in the manner at which the positive loop is connected to the oscillator. For instance, in the model of Ciliberto et al. (2005), the positive loop is implemented as an abstract reaction step in which p53 inhibits the translocation of cytoplasmic MDM2 to the nucleus and thereby inhibiting MDM2-mediated degradation of p53. This abstract step is inspired by the mutual antagonism loop between p53 and AKT. It will be shown in the next chapter that the explicit modeling of the p53-AKT network not only generates steady-state bifurcation diagrams that are distinct from those reported by them, but also provides insights and predictions about the biological functions of such oscillations. In addition, three different connectivity of the positive loop is considered by Zhang et al. (2006) namely, MDM2-mediated activation of p53, a p53 self-activation loop and a MDM2 self-activation loop. Interestingly, Geva-Zatorsky et al. (2006: Model VI) show that a model that has two negative feedback loops on p53 could also generate sustained oscillations over a wide range of kinetic parameters values. Taken together, these models demonstrate that there are several biologically plausible networks that could generate oscillations matching experimental observations. Besides the mechanistic differences, these models can also be differentiated by how the oscillations are born. For instance, oscillations are born from a Hopf bifurcation in the models of Bar-Or et al. (2000), Ma et al. (2005), Wagner et al. (2005) and Zhang et al. (2006: Models and 3). In contrast, 72 oscillations are born from an unstable saddle node, or a homoclinic or saddle-node invariant cycle (SNIC) bifurcation, by models of Ciliberto et al. (2005) and Zhang et al. (2006: Model 2). In fact, dynamic differences between oscillations born from a Hopf or homoclinic bifurcation can be used to identify biologically more plausible models, as discussed in more detail in Section 5.8 of Chapter 5. Alternatively, stochastic models of the p53-MDM2 feedback loop have been developed to explain variability in p53 oscillations at the single-cell level (Proctor and Gray, 2008). Proctor and Gray (2008) consider two separate mechanisms to kick start the oscillator upon DNA damage in their stochastic models – ATM-mediated posttranslational modifications of p53 and MDM2, and ARF-mediated inhibition of MDM2. The first mechanism has been utilized in several published p53-MDM2 models (Ma et al., 2005; Wagner et al., 2005). The model that use the second mechanism however, could not match experimental observations that initial p53 pulse is higher than subsequent pulses. 4.3 Summary The various independent reports on the manifestation of sustained p53 and MDM2 oscillations after DNA damage on different cell types indicate that such a phenomenon is reproducible in vitro and in vivo. Notably, recent efforts in mathematical modeling of the p53-MDM2 network have illuminated the biophysical mechanisms and conditions for the manifestation of such oscillations. Specifically, a p53-MDM2 network that is either supplemented with a positive feedback loop or a 73 time-delay mechanism or both, is more plausible to generate sustained oscillations over a wide range of kinetic parameters values. 74 . observations of p53-MDM2 oscillations (Section 4. 1), and the corresponding mathematical models that have been developed in the last few years to simulate them (Section 4. 2). The consequences of p53-MDM2. levels of p53, p21 (a target gene of p53) and MDM2 showed damped oscillations in cell 69 populations of human wild-type and Bloom’s syndrome patients’ fibroblast, following induction of DNA. periods of oscillation are 4 to 7 hrs; peaks of MDM2 oscillations lag behind p53 peak for 1.5 to 2.5 hrs; periods of oscillations decrease with increasing IR intensity; and peaks of p53 pulses
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