A gene that plays a crucial role in the regulation of cell life and death is the tumour suppressor gene p53, which encodes protein p53. The p53 tumour suppressor protein is regarded as the “guardian of the genome”, which is a transcription factor, that activates genes that result in DNA repair, cell cycle arrest, senescence (permanent cell cycle arrest) or apoptosis (programmed cell death) in response to various stress signals that could induce genetic instability. Recent individual cell studies have indicated that p53 activation is highly regulated in response to stress conditions and in unstressed normal proliferating cells. The aim of this research is to investigate the design principles behind the precise regulation of p53 activation. We develop a mathematical model using delay differential equations that incorporate the most recently found molecular interactions and genes regulated by p53, such as p53 activation of MdmX and Wip1, in the core regulation of p53 in normal proliferating cells and cells under DNA damage stress. We model the p53 core regulatory feedback mechanisms that control p53 levels. Experiments have shown that after DNA damage – DNA double-strand breaks (DSBs) – p53 levels show a series of repeated pulses. Whereas in non-stressed conditions with intrinsic DNA damage, one or two spontaneous pulses (basal dynamics) were observed. Figure 1 shows a schematic diagram of the model hypothesis. We found that the core regulatory network consists of ATM, Mdm2, MdmX, Wip1 and p53, and it reproduced simulations consistent with the experimental findings. Our results show that the p53 spontaneous pulses are due to intrinsic DNA double strand breaks in normal proliferating cells. Local parameter sensitivity analysis identified Wip1 as the major component that controlled the period of p53 oscillations. Despite its simplicity, our model is a mechanistic model that presents a dynamic hypothesis of molecular interactions that control p53 activation.

1. LINCOLN
UNIVERSITY
Mathematical modelling of p53 basal
dynamics and DNA damage
response
Student name: Ket Hing Chong
Supervisors: Prof. Sandhya Samarasinghe
Prof. Don Kulasiri
Centre for Advanced Computational
Solutions (C-fACS)
1

2. Outline
• Introduction ─ p53 signalling network
• Problems ─ Quantitative p53 responses
• Methods ─ Deterministic modelling
• Results ─ Computer simulation results
• Summary
2

3. Background:
• The tumour suppressor protein, p53, is regarded as
“the guardian of the genome” (Lane, 1992)
• Normal p53 protects us from cancer
Introduction
• To stop cell cycle progression in response to
conditions that could induce genetic instability,
such as DNA damage ─DNA double strand breaks
(DSBs).
One of the p53 functions:
3

4. Adapted from Hunziker, PhD Thesis, 2010 & Batchelor et al., Nature Reviews Cancer, 2009
The p53 signalling network
4

5. The p53 signalling network
Adapted from Hunziker, PhD Thesis, 2010 & Batchelor et al., Nature Reviews Cancer, 2009
p53 auto-regulation
5

6. p53 dynamics in stress and
non-stressed conditions
Loewer et al., Cell, 2010
p53 is active p53 is not active
Problem 1:
p21 was induced p21 stayed at basal levels
p21 induction
Problem 2:
(period: 4-7 hours);
6

7. Proposed model
7

8. Methods: Deterministic modelling
• Use delay differential equations (DDEs)
• 19 Eqns and 78 parameters
• The model of DDEs were solved by using
XPP
One of the equations:
𝑑[𝑝53]
𝑑𝑡
= 𝑠𝑝53 + 𝑒5
[𝑃53𝑝 𝑡 − 𝜏5 + 𝑃53𝑝𝑝 𝑡 − 𝜏5 ]4
𝐾𝑝53
4
+ [𝑃53𝑝(𝑡 − 𝜏5) + 𝑃53𝑝𝑝 𝑡 − 𝜏5 ]4
− 𝛿𝑝53[𝑝53]
8
Rate of change for p53 mRNA
parameter: 𝛿𝑝53 =0.03

9. Results:
Loewer et al., Cell, 2010
Stressed non-stressed
Problem 1
period: 5.8 hours
(Experiments 4-7 hours)
0.06-0.5 𝜇M
9

10. Results:
Loewer et al., Cell, 2010
Stressed non-stressed
Problem 2
p21 was induced p21 stayed at basal levels
10

11. 32
19 69
49
Wip1 mRNA
degradation
rate
Wip1 protein
degradation
rate
ATM auto-
activation rate
Wip1
transcription
delay
Local Parameter sensitivity analysis
Nominal parameter period: 5.8 hours (Experiments 4-7 hours)
11

12. Model predictions: 3 targets in reactivating p53
Wip1 mRNA degradation rate
p53
oscillations
are lost
12

13. ATM auto-activation rate
Wip1 protein degradation rate
Model predictions: 3 targets in reactivating p53 (cont.)
p53
oscillations
are lost
13

14. Results:
• Our model simulation results were consistent with
the experimental findings
Summary
Contribution:
• The model advances our understanding of the
mechanisms underlying p53 regulation
• 3 targets to modulate p53 oscillations and function
Wip1 mRNA degradation rate
Wip1 protein degradation rate
ATM auto-activation rate
14

15. THANK YOU
QUESTIONS & ANSWERS
source:
http://www.techtransfer.harvard.edu/crop/investigators/investigator.php?id=27
15
Individual cells study of p53 dynamics (Lahav et al., Nature Genetics, 2004)

16. Quantitative experimental measurements
in individual cells
Individual cells study of
p53 dynamics (Lahav et
al., Nature Genetics, 2004)
• MCF7 cell line
• The fluorescent protein
fusion system
• γ-irradiation DNA
damage
• Live-cell time-lapse
microscopy
source:
http://www.techtransfer.harvard.edu/crop/investigators/investigator.php?id=27
16

17. Previous model
(Sun et al., PLoS One, 2011)
• Deterministic model (does not capture p53 basal
dynamics)
Our model
• Modified and improved their deterministic
model (to capture p53 basal dynamics)
• Two new components:
1. p53 auto-regulation
2. MdmX
17

18. Results:
• Our model simulation results were consistent with
the experimental findings
Summary
Contribution:
• The model advances our understanding of
mechanisms underlying the p53 regulation
• Provides some for predictions of p53-based
therapy..
Future Work:
• Incorporate the apoptotic switch activated by p53
18

19. Questions
1. Can we construct a quantitative mathematical
model to explain the repeated pulses and
spontaneous pulses?
2. What are the mechanisms that regulate p53
activation of p21 in arresting cell cycle?
Previous model
(Sun et al., PLoS One, 2011)
• Deterministic model (does not capture p53
basal dynamics)
• Stochastic model
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20. Table 1 Parameters used in the mathematical model
39 𝑘𝑎𝑡𝑚1 ATM induced P53 phosphorylation 0.8 𝜇𝑀 −1
𝑚𝑖𝑛−1
40 𝑘𝑎𝑡𝑚2 ATM induced Mdm2 phosphorylation 0.02 𝜇𝑀 −1
𝑚𝑖𝑛−1
41 𝑘𝑎𝑡𝑚3 ATM induced Mdmx phosphorylation 0.02 𝜇𝑀 −1
𝑚𝑖𝑛−1
42 𝑘𝑤𝑖𝑝1 Wip1 induced P53p dephosphorylation 1.3 𝜇𝑀 −1
𝑚𝑖𝑛−1
43 𝑘𝑤𝑖𝑝2 Wip1 induced Mdm2p dephosphorylation 0.5 𝜇𝑀 −1
𝑚𝑖𝑛−1
44 𝑘𝑤𝑖𝑝3 Wip1 induced Mdmxp dephosphorylation 0.2 𝜇𝑀 −1
𝑚𝑖𝑛−1
45 𝑘𝑤𝑖𝑝4 Wip1 induced ATMp dephosphorylation 1.5 𝜇𝑀 −1
𝑚𝑖𝑛−1
46 𝑘𝐷𝑆𝐵 DSB induced ATM activation rate 0.0005 𝑚𝑖𝑛−1
47 DSB Double Strand Break (300 approximately 10 Gy 𝛾-
irradiation)
300 Unit of 1
𝑑[𝐴𝑇𝑀𝑝]
𝑑𝑡
= 𝑘𝐷𝑆𝐵
𝐷𝑆𝐵
𝐷𝑆𝐵 + 𝐾𝐷𝑆𝐵
𝐴𝑇𝑀 + 𝑘𝑎𝑢𝑡𝑜 𝐴𝑇𝑀𝑝 𝐴𝑇𝑀 − 𝑘𝑏𝑎𝑠𝑎𝑙 𝐴𝑇𝑀𝑝
−𝑘𝑤𝑖𝑝4[𝑊𝑖𝑝1][𝐴𝑇𝑀𝑝]
20

21. Activation of p53 using small
molecules : Nutlin, HLI98, RITA
Marine & Lozano, Cell Death and Differentiation, 2010
Mechanisms of action of the small molecules
21

22. Mdm2 promotes ubiquitination and
proteasomal-dependent degradation of p53
Marine & Lozano, Cell Death and Differentiation, 2010
p53-Mdm2 negative feedback loop
Check points
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23. Post-translational modifications (PTM)
modulate p53 activity
1. ubiquitination
2. phosphorylation
3. acetylation
p53
Ub
p53 p53
Ub
Ub
Ub
p53
P
p53 p53
P
P
P
p53
A
p53 p53
A
A
A
Mdm2
HAUSP
ATM
WIP1
HAT
HDAC
Unstable
stable &
active
(feedback
regulators)
stable &
active (p21)
HAT=Histone Acetyl Transferase
HDAC=Histone Deacetylase Complex
11 sites
17 sites
11 sites
23