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Explaining oscillations and variability in the p53-Mdm2 system.

Proctor CJ, Gray DA - BMC Syst Biol (2008)

Bottom Line: We describe two stochastic mechanistic models of the p53/Mdm2 circuit and show that sustained oscillations result directly from the key biological features, without assuming complicated mathematical functions or requiring more than one feedback loop.The models predict more regular oscillations if ARF is present and suggest the need for further experiments in ARF positive cells to test these predictions.Our work illustrates the importance of systems biology approaches to understanding the complex role of p53 in both ageing and cancer.

View Article: PubMed Central - HTML - PubMed

Affiliation: Centre for Integrated Systems Biology of Ageing and Nutrition, Institute for Ageing and Health, Newcastle University, Newcastle upon Tyne, UK. c.j.proctor@ncl.ac.uk

ABSTRACT

Background: In individual living cells p53 has been found to be expressed in a series of discrete pulses after DNA damage. Its negative regulator Mdm2 also demonstrates oscillatory behaviour. Attempts have been made recently to explain this behaviour by mathematical models but these have not addressed explicit molecular mechanisms. We describe two stochastic mechanistic models of the p53/Mdm2 circuit and show that sustained oscillations result directly from the key biological features, without assuming complicated mathematical functions or requiring more than one feedback loop. Each model examines a different mechanism for providing a negative feedback loop which results in p53 activation after DNA damage. The first model (ARF model) looks at the mechanism of p14ARF which sequesters Mdm2 and leads to stabilisation of p53. The second model (ATM model) examines the mechanism of ATM activation which leads to phosphorylation of both p53 and Mdm2 and increased degradation of Mdm2, which again results in p53 stabilisation. The models can readily be modified as further information becomes available, and linked to other models of cellular ageing.

Results: The ARF model is robust to changes in its parameters and predicts undamped oscillations after DNA damage so long as the signal persists. It also predicts that if there is a gradual accumulation of DNA damage, such as may occur in ageing, oscillations break out once a threshold level of damage is acquired. The ATM model requires an additional step for p53 synthesis for sustained oscillations to develop. The ATM model shows much more variability in the oscillatory behaviour and this variability is observed over a wide range of parameter values. This may account for the large variability seen in the experimental data which so far has examined ARF negative cells.

Conclusion: The models predict more regular oscillations if ARF is present and suggest the need for further experiments in ARF positive cells to test these predictions. Our work illustrates the importance of systems biology approaches to understanding the complex role of p53 in both ageing and cancer.

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Deterministic solution for the ARF model.
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Figure 12: Deterministic solution for the ARF model.

Mentions: In order to show that the variability in the oscillations is qualitatively different from those seen in deterministic simulations, we also performed deterministic simulations on the models (Figures 12 and 13). In the ARF model, oscillations are still produced but interestingly, the deterministic version of the ATM model predicts only one peak followed by fairly constant levels of total p53 and Mdm2 but at a level higher than the initial values. The lack of oscillations may be either due to the averaging effect since there is variability in the period in this model, or due to the approximation used to derive the reaction rate equations in the deterministic simulation. We carried out 1000 repeat simulations of the stochastic ATM model and compared the mean with the deterministic simulation. We found that the plot of the mean was very similar to the deterministic output, confirming that the lack of oscillations was due to the averaging effect (data not shown). Therefore the stochastic model shows stochastic oscillations consistent with the data for single cell measurements, whereas the deterministic model loses the oscillations due to averaging out effects. The averaging effect is due to the inter-cell variability in the oscillatory period and although the cells are synchronised for the first peak, they are unsynchronised for all the following peaks. Therefore the oscillations in the different cells cancel out. This is also observed experimentally if measurements are taken for a population of cells rather than individual cells [35].


Explaining oscillations and variability in the p53-Mdm2 system.

Proctor CJ, Gray DA - BMC Syst Biol (2008)

Deterministic solution for the ARF model.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2553322&req=5

Figure 12: Deterministic solution for the ARF model.
Mentions: In order to show that the variability in the oscillations is qualitatively different from those seen in deterministic simulations, we also performed deterministic simulations on the models (Figures 12 and 13). In the ARF model, oscillations are still produced but interestingly, the deterministic version of the ATM model predicts only one peak followed by fairly constant levels of total p53 and Mdm2 but at a level higher than the initial values. The lack of oscillations may be either due to the averaging effect since there is variability in the period in this model, or due to the approximation used to derive the reaction rate equations in the deterministic simulation. We carried out 1000 repeat simulations of the stochastic ATM model and compared the mean with the deterministic simulation. We found that the plot of the mean was very similar to the deterministic output, confirming that the lack of oscillations was due to the averaging effect (data not shown). Therefore the stochastic model shows stochastic oscillations consistent with the data for single cell measurements, whereas the deterministic model loses the oscillations due to averaging out effects. The averaging effect is due to the inter-cell variability in the oscillatory period and although the cells are synchronised for the first peak, they are unsynchronised for all the following peaks. Therefore the oscillations in the different cells cancel out. This is also observed experimentally if measurements are taken for a population of cells rather than individual cells [35].

Bottom Line: We describe two stochastic mechanistic models of the p53/Mdm2 circuit and show that sustained oscillations result directly from the key biological features, without assuming complicated mathematical functions or requiring more than one feedback loop.The models predict more regular oscillations if ARF is present and suggest the need for further experiments in ARF positive cells to test these predictions.Our work illustrates the importance of systems biology approaches to understanding the complex role of p53 in both ageing and cancer.

View Article: PubMed Central - HTML - PubMed

Affiliation: Centre for Integrated Systems Biology of Ageing and Nutrition, Institute for Ageing and Health, Newcastle University, Newcastle upon Tyne, UK. c.j.proctor@ncl.ac.uk

ABSTRACT

Background: In individual living cells p53 has been found to be expressed in a series of discrete pulses after DNA damage. Its negative regulator Mdm2 also demonstrates oscillatory behaviour. Attempts have been made recently to explain this behaviour by mathematical models but these have not addressed explicit molecular mechanisms. We describe two stochastic mechanistic models of the p53/Mdm2 circuit and show that sustained oscillations result directly from the key biological features, without assuming complicated mathematical functions or requiring more than one feedback loop. Each model examines a different mechanism for providing a negative feedback loop which results in p53 activation after DNA damage. The first model (ARF model) looks at the mechanism of p14ARF which sequesters Mdm2 and leads to stabilisation of p53. The second model (ATM model) examines the mechanism of ATM activation which leads to phosphorylation of both p53 and Mdm2 and increased degradation of Mdm2, which again results in p53 stabilisation. The models can readily be modified as further information becomes available, and linked to other models of cellular ageing.

Results: The ARF model is robust to changes in its parameters and predicts undamped oscillations after DNA damage so long as the signal persists. It also predicts that if there is a gradual accumulation of DNA damage, such as may occur in ageing, oscillations break out once a threshold level of damage is acquired. The ATM model requires an additional step for p53 synthesis for sustained oscillations to develop. The ATM model shows much more variability in the oscillatory behaviour and this variability is observed over a wide range of parameter values. This may account for the large variability seen in the experimental data which so far has examined ARF negative cells.

Conclusion: The models predict more regular oscillations if ARF is present and suggest the need for further experiments in ARF positive cells to test these predictions. Our work illustrates the importance of systems biology approaches to understanding the complex role of p53 in both ageing and cancer.

Show MeSH
Related in: MedlinePlus