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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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Related in: MedlinePlus

Six simulations for the ARF model under conditions of irradiation (IR = 25 dGy for 1 minute at time t = 1 hour).
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Figure 6: Six simulations for the ARF model under conditions of irradiation (IR = 25 dGy for 1 minute at time t = 1 hour).

Mentions: All previous models to date have used a deterministic approach to analyse the oscillatory behaviour. These models have used differential equations and mathematical functions requiring a fairly large number of parameters with the generation of oscillations being very dependent on the range of parameter values chosen. Geva-Zatorsky et al. [30] constructed six different models and found that the simplest model, which contained one intermediary and one negative feedback loop with a delay, was unable to produce multiple oscillations and that it was necessary to either introduce a positive feedback loop or a time delay term (See figure 6 of Geva-Zatorsky et al. [30]). However, these additions were not sufficient for robustness over a wide range of parameter values. The addition of a non-linear negative feedback loop, a linear positive feedback loop or a second negative feedback loop produced models that were able to demonstrate sustained oscillations over a wide range of parameters. As the models are deterministic, the outcome only depends on the initial conditions and so they cannot be used to investigate cell-cell variability. Geva-Zatorsky et al. [30] incorporated some random noise in protein production in their models and found that the introduction of low-frequency noise resulted in variability in the amplitude of the oscillations as observed experimentally. Ma et al. [32] also incorporated a stochastic component for the DNA damage component of their model which resulted in variability in the number of oscillations. However, for a dose of 2.5 Gy, they found that the majority of cells had only one peak and that a step input of DNA damage was required to obtain sustained oscillations.


Explaining oscillations and variability in the p53-Mdm2 system.

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

Six simulations for the ARF model under conditions of irradiation (IR = 25 dGy for 1 minute at time t = 1 hour).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 6: Six simulations for the ARF model under conditions of irradiation (IR = 25 dGy for 1 minute at time t = 1 hour).
Mentions: All previous models to date have used a deterministic approach to analyse the oscillatory behaviour. These models have used differential equations and mathematical functions requiring a fairly large number of parameters with the generation of oscillations being very dependent on the range of parameter values chosen. Geva-Zatorsky et al. [30] constructed six different models and found that the simplest model, which contained one intermediary and one negative feedback loop with a delay, was unable to produce multiple oscillations and that it was necessary to either introduce a positive feedback loop or a time delay term (See figure 6 of Geva-Zatorsky et al. [30]). However, these additions were not sufficient for robustness over a wide range of parameter values. The addition of a non-linear negative feedback loop, a linear positive feedback loop or a second negative feedback loop produced models that were able to demonstrate sustained oscillations over a wide range of parameters. As the models are deterministic, the outcome only depends on the initial conditions and so they cannot be used to investigate cell-cell variability. Geva-Zatorsky et al. [30] incorporated some random noise in protein production in their models and found that the introduction of low-frequency noise resulted in variability in the amplitude of the oscillations as observed experimentally. Ma et al. [32] also incorporated a stochastic component for the DNA damage component of their model which resulted in variability in the number of oscillations. However, for a dose of 2.5 Gy, they found that the majority of cells had only one peak and that a step input of DNA damage was required to obtain sustained oscillations.

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