p53-Mdm2 loop controlled by a balance of its feedback strength and effective dampening using ATM and delayed feedback

When the genomic integrity of a cell is challenged, its fate is determined in part by signals conveyed by the p53 tumour suppressor protein. It was observed recently that such signals are not simple gradations of p53 concentration, but rather a counter-intuitive limit-cycle behaviour. Based on a careful mathematical interpretation of the experimental body of knowledge, we propose a model for the p53 signalling network and characterise the p53 stability and oscillatory dynamics. In our model, ATM, a protein that senses DNA damage, activates p53 by phosphorylation. In its active state, p53 has a decreased degradation rate and an enhanced transactivation of Mdm2, a gene whose protein product Mdm2 tags p53 for degradation. Thus the p53-Mdm2 system forms a negative feedback loop. However, the feedback in this loop is delayed, as the pool of Mdm2 molecules being induced by p53 at a given time will mark for degradation the pool of p53 molecules at some later time, after the Mdm2 molecules have been transcribed, exported out of the nucleus, translated and transported back into the nucleus. The analysis of our model demonstrates how this time lag combines with the ATM-controlled feedback strength and effective dampening of the negative feedback loop to produce limit-cycle oscillations. The picture that emerges is that ATM, once activated by DNA damage, makes the p53-Mdm2 oscillator undergo a supercritical Hopf bifurcation. This approach yields an improved understanding of the global dynamics and bifurcation structure of our time-delayed, negative feedback model and allows for predictions of the behaviour of the p53 system under different perturbations.     

Steady States and Oscillations in the p53/Mdm2 Network

p53 is activated in response to events compromising the genetic integrity of a cell. Recent data show that p53 activity does not increase steadily with genetic damage but rather fluctuates in an oscillatory fashion (Lahav et al., Nature Genetics, 36, 147-150, 2004). Theoretical studies suggest that oscillations can arise from a combination of positive and negative feedbacks or from a long negative feedback loop alone. Both negative and positive feedbacks are present in the p53/Mdm2 network, but it is not known what roles they play in the oscillatory response to DNA damage. We developed a mathematical model of p53 oscillations based on positive and negative feedbacks in the p53/Mdm2 network. According to the model, the system reacts to DNA damage by moving from a stable steady state into a region of stable limit cycles. Oscillations in the model are born with large amplitude, which guarantees an all-or-none response to damage. As p53 oscillates, damage is repaired and the system moves back to a stable steady state with low p53 activity. The model reproduces experimental data in quantitative detail. We suggest new experiments for dissecting the contributions of negative and positive feedbacks to the generation of oscillations.     

Predicted Functions of MdmX in Fine-Tuning the Response of p53 to DNA Damage

Tumor suppressor protein p53 is regulated by two structurally homologous proteins, Mdm2 and MdmX. In contrast to Mdm2, MdmX lacks ubiquitin ligase activity. Although the essential interactions of MdmX are known, it is not clear how they function to regulate p53. The regulation of tumor suppressor p53 by Mdm2 and MdmX in response to DNA damage was investigated by mathematical modeling of a simplified network. The simplified network model was derived from a detailed molecular interaction map (MIM) that exhibited four coherent DNA damage response pathways. The results suggest that MdmX may amplify or stabilize DNA damage-induced p53 responses via non-enzymatic interactions. Transient effects of MdmX are mediated by reservoirs of p53∶MdmX and Mdm2∶MdmX heterodimers, with MdmX buffering the concentrations of p53 and/or Mdm2. A survey of kinetic parameter space disclosed regions of switch-like behavior stemming from such reservoir-based transients. During an early response to DNA damage, MdmX positively or negatively regulated p53 activity, depending on the level of Mdm2; this led to amplification of p53 activity and switch-like response. During a late response to DNA damage, MdmX could dampen oscillations of p53 activity. A possible role of MdmX may be to dampen such oscillations that otherwise could produce erratic cell behavior. Our study suggests how MdmX may participate in the response of p53 to DNA damage either by increasing dependency of p53 on Mdm2 or by dampening oscillations of p53 activity and presents a model for experimental investigation.     

Harmonic Oscillations in Homeostatic Controllers: Dynamics of the p53 Regulatory System

Homeostatic mechanisms are essential for the protection and adaptation of organisms in a changing and challenging environment. Previously, we have described molecular mechanisms that lead to robust homeostasis/adaptation under inflow or outflow perturbations. Here we report that harmonic oscillations occur in models of such homeostatic controllers and that a close relationship exists between the control of the p53/Mdm2 system and that of a homeostatic inflow controller. This homeostatic control model of the p53 system provides an explanation why large fluctuations in the amplitude of p53/Mdm2 oscillations may arise as part of the homeostatic regulation of p53 by Mdm2 under DNA-damaging conditions. In the presence of DNA damage p53 is upregulated, but is subject to a tight control by Mdm2 and other factors to avoid a premature apoptotic response of the cell at low DNA damage levels. One of the regulatory steps is the Mdm2-mediated degradation of p53 by the proteasome. Oscillations in the p53/Mdm2 system are considered to be part of a mechanism by which a cell decides between cell cycle arrest/DNA repair and apoptosis. In the homeostatic inflow control model, harmonic oscillations in p53/Mdm2 levels arise when the binding strength of p53 to degradation complexes increases. Due to the harmonic character of the oscillations rapid fluctuating noise can lead, as experimentally observed, to large variations in the amplitude of the oscillation but not in their period, a behavior which has been difficult to simulate by deterministic limit-cycle models. In conclusion, the oscillatory response of homeostatic controllers may provide new insights into the origin and role of oscillations observed in homeostatically controlled molecular networks.     

Recurrent initiation: a mechanism for triggering p53 pulses in response to DNA damage

DNA damage initiates a series of p53 pulses. Although much is known about the interactions surrounding p53, little is known about which interactions contribute to p53's dynamical behavior. The simplest explanation is that these pulses are oscillations intrinsic to the p53/Mdm2 negative feedback loop. Here we present evidence that this simple mechanism is insufficient to explain p53 pulses; we show that p53 pulses are externally driven by pulses in the upstream signaling kinases, ATM and Chk2, and that the negative feedback between p53 and ATM, via Wip1, is essential for maintaining the uniform shape of p53 pulses. We propose that p53 pulses result from repeated initiation by ATM, which is reactivated by persistent DNA damage. Our study emphasizes the importance of collecting quantitative dynamic information at high temporal resolution for understanding the regulation of signaling pathways and opens new ways to manipulate p53 pulses to ask questions about their function in response to DNA damage.     

A theoretical exploration of birhythmicity in the p53-Mdm2 network

Experimental observations performed in the p53-Mdm2 network, one of the key protein modules involved in the control of proliferation of abnormal cells in mammals, revealed the existence of two frequencies of oscillations of p53 and Mdm2 in irradiated cells depending on the irradiation dose. These observations raised the question of the existence of birhythmicity, i.e. the coexistence of two oscillatory regimes for the same external conditions, in the p53-Mdm2 network which would be at the origin of these two distinct frequencies. A theoretical answer has been recently suggested by Ouattara, Abou-Jaoudé and Kaufman who proposed a 3-dimensional differential model showing birhythmicity to reproduce the two frequencies experimentally observed. The aim of this work is to analyze the mechanisms at the origin of the birhythmic behavior through a theoretical analysis of this differential model. To do so, we reduced this model, in a first step, into a 3-dimensional piecewise linear differential model where the Hill functions have been approximated by step functions, and, in a second step, into a 2-dimensional piecewise linear differential model by setting one autonomous variable as a constant in each domain of the phase space. We find that two features related to the phase space structure of the system are at the origin of the birhythmic behavior: the existence of two embedded cycles in the transition graph of the reduced models; the presence of a bypass in the orbit of the large amplitude oscillatory regime of low frequency. Based on this analysis, an experimental strategy is proposed to test the existence of birhythmicity in the p53-Mdm2 network. From a methodological point of view, this approach greatly facilitates the computational analysis of complex oscillatory behavior and could represent a valuable tool to explore mathematical models of biological rhythms showing sufficiently steep nonlinearities.     

Intrinsic noise and Hill dynamics in the p53 system

The p53 feedback loop can induce cellular senescence, cell cycle arrest and apoptosis in response to various stresses, including DNA damage, hypoxia and nutrient deprivation. Using a stochastic model of the negative feedback circuit involving p53 and its inhibitor Mdm2, we present the different oscillatory dynamics at the single-cell and population-cell levels as described in the experiments, and the resonant nature of the oscillations is captured. The stationary distributions of protein populations are characterized by non-Gaussian nature which is due to the interplay between time delay and nonlinearity of reactions.     

A theoretical model for p53 dynamics: Identifying optimal therapeutic strategy for its activation and stabilization

The activation and stabilization of tumor suppressor p53 are very important in preventing cells from becoming cancerous. Hence, many experimental works have been carried out to investigate p53’s dynamics through its interactions with other proteins and its therapeutic applications for the treatment of cancers. In this work, by analyzing a theoretical model, we attempt to search for an optimal therapeutic strategy that guarantees the activation and stabilization of p53. For this purpose, we introduce a new mathematical model including oncogene activation and ARF, which are recognized as crucial for tumor suppression but have not yet been considered in most theoretical works. Through mathematical modeling and numerical simulations, we confirm several important properties of p53 dynamics: the role of the oncogene-mediated activation of ARF as an important factor for the activation and stabilization of p53, the necessity of time delays in negative feedback loops to guarantee sustained p53 oscillations, and the digital behavior of p53 pulses. Furthermore, we propose that the binding of ARF to Mdm2 and enhancing the degradation of Mdm2 is an efficient strategy for therapeutic targeting, which may assure the activation and stabilization of p53.     

Role of the histone acetyl transferase Tip60 in the p53 pathway

The histone acetyl transferase Tip60 (HTATIP) shares many properties with the tumor suppressor p53 (TP53). Both proteins are involved in the cellular response to DNA damage, are subjected to proteasomal digestion following Mdm2-mediated ubiquitination, and accumulate after UV irradiation. We found here that knock-down of Tip60 affects the p53-dependent response following actinomycin D treatment, most likely because it inhibits p21 (CDKN1A) accumulation. Moreover, Tip60 is required for p53 to activate the endogenous p21 promoter, suggesting that it functions as a p53 co-activator. However, we also found that knock-down of Tip60 increases the turnover rate of p53 under normal growth conditions. Tip60 interferes with Mdm2-mediated degradation of p53, probably because it affects its subcellular localization. Taken together, our results suggest that Tip60 plays a double role in the p53 pathway: under normal growth conditions, Tip60 contributes to maintain a basal pool of p53 by interfering with its degradation; following DNA damage, Tip60 functions as p53 co-activator. That these two distinct roles are linked during the p53-dependent response is an attractive hypothesis.     

Oscillations of the p53-Akt Network: Implications on Cell Survival and Death

Intracellular protein levels of p53 and MDM2 have been shown to oscillate in response to ionizing radiation (IR), but the physiological significance of these oscillations remains unclear. The p53-MDM2 negative feedback loop – the putative cause of the oscillations – is embedded in a network involving a mutual antagonism (or positive feedback loop) between p53 and AKT. We have shown earlier that this p53-AKT network predicts an all-or-none switching behavior between a pro-survival cellular state (low p53 and high AKT levels) and a pro-apoptotic state (high p53 and low AKT levels). Here, we show that upon exposure to IR, the p53-AKT network can also reproduce the experimentally observed p53 and MDM2 oscillations. The present work is based on the hypothesis that the physiological significance of the experimentally observed oscillations could be found in their role in regulating the switching behavior of the p53-AKT network between pro-survival and pro-apoptotic states. It is shown here that these oscillations are associated with a significant decrease in the threshold level of IR at which switching from a pro-survival to a pro-apoptotic state occurs. Moreover, oscillations in p53 protein levels induce higher levels of expression of p53-target genes compared to non-oscillatory p53, and thus influence cell-fate decisions between cell cycle arrest/DNA damage repair versus apoptosis.     

The promyelocytic leukemia protein protects p53 from Mdm2-mediated inhibition and degradation

The p53 protein is kept labile under normal conditions. This regulation is governed largely by its major negative regulator, Mdm2. In response to stress however, p53 accumulates and becomes activated. For this to occur, the inhibitory effects of Mdm2 have to be neutralized. Here we investigated the role of the promyelocytic leukemia protein (PML) in the activation of p53 in response to stress. We found that PML is critical for the accumulation of p53 in response to DNA damage under physiological conditions. PML protects p53 from Mdm2-mediated ubiquitination and degradation, and from inhibition of apoptosis. PML neutralizes the inhibitory effects of Mdm2 by prolonging the stress-induced phosphorylation of p53 on serine 20, a site of the checkpoint kinase 2 (Chk2). PML recruits Chk2 and p53 into the PML nuclear bodies and enhances p53/Chk2 interaction. Our results provide a novel mechanistic explanation for the cooperation between PML and p53 in response to DNA damage.