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Mathematical modelling of p53 basal dynamics and DNA damage response

Significance Statement

Cancer is a genetic disease. The most convincing evidence is the findings reported that about half of cancers contain mutations in a major tumour suppressor gene known as p53. p53 is well-known as the guardian of the genome due to the protective effects exerted by p53. Under stressed conditions, p53 protein increases its pulse generation. Recent experimental findings from single cell studies uncovered spontaneous pulses of protein p53 (basal dynamics) under normal proliferation conditions and repeated pulses of p53 under stressed conditions. Experiments carried out by a team of researchers at Harvard Medical School also suggest p53 pulses are excitable such that once initiated they complete a pulse. Scientists are curious to know what controls these responses and how p53 works to protect us under normal and stress conditions. Based on a previous mathematical model, we modified and improved the model by incorporating the core feedback regulators of p53.

The major finding: The model constructed was able to reproduce experimental findings and further dynamical system analysis suggests how stress signal controls p53 dynamics that link to cell fate decisions (Figure below). Importantly, the model demonstrated there is a threshold stress signal that activates p53 pulses. The threshold signal is like a safety threshold for turning on p53 activation for DNA damage repair and cell cycle arrest — to prevent abnormal cells from dividing. Importantly, the study suggests that the spontaneous pulses are due to intrinsic DNA damage from normal biochemical processes.  The model analysis also suggested p53 pulses are Type II excitable, which indicates that information processing is similar to neurons. Thus, our study has employed known molecular interactions to formulate an advanced model that can be used for gaining insights into how it functions as a transcription factor in regulating gene expression that controls cell fate. This model can be used to study perturbations to the network or make prediction of a strategy to reactivate p53 functions in cancer cells.

Mathematical modelling of p53 basal dynamics and DNA damage response- . Global Medical Discovery

Figure Legend: Signal Response Curve from Bifurcation Diagram (left) that explains p53 dynamics (Cell Responses) for different stress levels (right)

 The bifurcation diagram consists of saddle-node and Hopf bifurcations that offer theoretical explanation for how p53 dynamics decide cell fate.

  1. For low stress signal, p53 stays at basal levels – corresponds to cell homeostasis (SN1)
  2. For stress signal above a threshold value of 0.04, p53 starts to pulse- corresponds to DNA damage repair (SN2).
  3. For stress signal above the first Hopf bifurcation point (HB1), p53 starts to oscillate in a stable limit cycle – corresponds to cell cycle arrest and DNA damage repair.
  4. For higher stress signal above the second Hopf bifurcation point (HB2), p53 pulses and reach a high steady state – corresponds to activation of apoptosis.

Figure (permission from Math Biosci. Journal)

Journal Reference

Chong KH1, Samarasinghe S2, Kulasiri D3. Math Biosci. 2015 ;259:27-42.

Show Affiliations

1Integrated Systems Modelling Group and Centre for Advanced Computational Solutions (C-fACS), Lincoln University, Christchurch, New Zealand.

2Integrated Systems Modelling Group and Centre for Advanced Computational Solutions (C-fACS), Lincoln University, Christchurch, New Zealand; Department of Informatics and Enabling Technologies, Lincoln University, Christchurch, New Zealand. Electronic address: [email protected]

3Integrated Systems Modelling Group and Centre for Advanced Computational Solutions (C-fACS), Lincoln University, Christchurch, New Zealand; Department of Molecular Biosciences, Lincoln University, Christchurch, New Zealand. 


The p53 tumour suppressor protein is a transcription factor that activates genes that result in cell cycle arrest, DNA damage repair, senescence or apoptosis. Recent individual cell studies have indicated that p53 activation is highly regulated in response to stressed conditions and non-stressed (normal proliferating) conditions in cells. The aim of this research is to investigate the design principles behind the precise regulation of p53 activation, under normal and stressed conditions. We extended the Sun et al. (2011)mathematical model of delay differential equations by incorporating the most recently found molecular interactions and hypotheses. In particular, we found that the core regulatory network consists of ATM, Mdm2, MdmX, Wip1 and p53. Our model of the p53 core regulatory feedback mechanisms can reproduce a series of repeated pulses in stressed conditions with appropriate induction of cell cycle arrest, and one or two spontaneous pulses (basal dynamics) in non-stressed conditions and these are consistent with the recent experimental findings. Our results show that the p53 spontaneous pulses are due to intrinsic DNA double strand breaks in normal proliferating cells, and p53 auto-regulation (positive feedback loop) allows threshold activation of p53 in generating these pulses. It also shows that its dynamics are excitable; bifurcation analysis revealed a spectrum of p53 behaviour under stressed and non-stressed (normal) conditions on the basis of stress signal activation rate, and characterised p53 dynamics as Type II excitability. Additionally, the model makes testable predictions on pharmacological intervention to reactivate p53. Importantly, we reveal novel findings on the mechanism of threshold activation of p53 pulsatile and oscillatory dynamics that are important for its physiological function as the guardian of the genome.

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