Hunziker et al., (2010). Stress-specific response of the p53-Mdm2 feedback loop.
June 2013, model of the month by Massimo Lai
Original models: BIOMD0000000252
Cells have a remarkable capability to adapt to environmental stress, but they also possess in-built safety mechanisms that allow them tolimit their activity and even self-destruct, in case they become too badly damaged. This is a common way to protect the organism against cancer.
The peculiarity of the biochemical signals involved in cell stress responseis that they all flow into one common hub: whether the source of stress ishypoxia, DNA damage, or starvation; the end result is the activationof a particular transcription factor, the tumour suppressor protein p53. The fact that over 50% of cancer cells contain mutations in p53, suggests its central role in cancer preventions.
Depending on the type and intensity of the stress, p53 can trigger cell-cycle arrest, senescence or apoptosis, and it's therefore capable of discriminating between different inputs, and produce different downstream gene expression profiles. For example, hypoxia always produces apoptosis. But, UV irradiation initially induces cell cycle arrest, and leads to cell death only if the exposure is too severe.This is a fascinating example of how the cell to some extent capable of gauging the amount of damage, before making the drasticdecision of pushing the big red button.
The model by Hunziker and coworkers [1, BIOMD0000000252], explores how a regulatory mechanismcould account for p53's capability to produce input-specific responses: in their words, "how does the regulatory network around p53 retain this flexibility even though all inputs converge at a single node?".
In order to explore possible answers, the authors first pointed out that p53 regulation happens at two main levels: its degradation,and its activity as a transcription factor. Several proteins are involvedin the two processes, but Mdm2 (an E3 ubiquitin ligase) was singled out because it's involved in both, and because Mdm2 gene knock-out is lethal in mice.
Figure 2 Differential equations of the model. Figure adapted from 
By altering the "resting-state" parameters, the model was used to simulate several types of stress, comparing the resulting peaks in p53 concentration with available experimental data. In particular, simulated conditions were: the injection of Nutlin(i.e weaker binding of p53-Mdm2), the effect of deregulated oncogenes (decrease of the Mdm2-dependent degradation of p53), DNA damage (i.e. increased auto-ubiquitination of Mdm2, decreased ubiquitination of p53 by Mdm2, weaker binding of p53-Mdm2), and hypoxia (downregulation of Mdm2).
The system was capable of reproducing the dumped spiky oscillations of p53 levels seen in real cells, with a good qualitative agreement (Figure 3).The interpretation of the results was based on the reasonable assumption that the level of p53 is important in determining the cell decision.
The main feature of the model is the structure of the negative feedback loop, between p53 and Mdm2, with a slow transcription step and a fast inhibition step based on the formation of the p53-Mdm2 complex. Such characteristics areshared with another pathway that is triggered by numerous different inputs, namelythe regulation of the transcription factor NF-kB, involved in the immune response .Therefore, the authors suggest that this regulatory mechanism could have a generality that goes beyond the p53 pathway.
Figure 1 A diagram of the model of regulation of p53 by Mdm2. Transcription and translation of the mdm2 gene to the Mdm2 protein happen with rate constants kt and ktl, respectively; β is the spontaneous degradation rate of Mdm2 mRNA; kf and kb are the association and dissociation rate contants for the p53-Mdm2 complex; σ is the rate of production of p53, assumed to be constant; δ and α are the rates of Mdm2-mediated and Mdm2-independent degradation of p53, respectively; γ is the degradation rate of Mdm2, assumed to be independent of whether Mdm2 is bound to p53 or not. Figure taken from 
In p53, single ubiquitination inhibits the trascriptor factor activity, while polyubiquitination promotes degradation . p53 returns the favour by inhibiting the Mdm2 gene, thereby forming a negative feedback loop [3,4].The model describes the time course of the concentration of four species: nuclear-p53 (p); Mdm2 (m); Mdm2 mRNA (mm); p53-Mdm2 complex (c).A diagram of the model is given in Figure 1.The resulting 4 differential equations are given in Figure 2.
In stress-free conditions, Mdm2 maintains p53 at low concentration levels, so theinitial parameters were chosen in order to reproduce this situation.
In terms of gene expression, the main effects of stresses is to upregulate ordownregulate the expression or the degradation of p53 and Mdm2. In addition, DNAdamage lowers the affinity of Mdm2 for p53.
Figure 3 Model response to 4 different forms of stress:injection of Nutlin (black)the effect of deregulated oncogenes (green), DNA damage (blue), and hypoxia (red).The model appropriately predicted the stronger response produced by DNA damage andhypoxia, as well as the spiky oscillations of p53 levels in the cell. Figure taken from .
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