Computational Modelling of
Waddington’s Epigenetic Landscape
for Stem Cell Reprogramming
Zheng Jie
Assistant Professor
Medical Informatics Research Lab
School of Computer Engineering
Nanyang Technological University
8 Dec. 2014
Sharing Session, Complexity Institute, NTU
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Outline
• Background
• Method
– Construction of the gene regulatory network
– Mathematical modeling of global dynamics
• Result
– Parameter inference
– Drawing Waddington’s epigenetic landscape
– Simulation of reprogramming
• Discussion and future work
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Gene Regulatory Network (GRN)
Hecker et al. BioSystems, 2009
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• Waddington’s Epigenetic Landscape
Gene regulatory
network
Signaling
pathways
Mohammad, H. P., & Baylin, S. B. (2010). Linking cell signaling and the epigenetic
machinery. Nature biotechnology, 28(10), 1033-1038.
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Epigenetic
modifications
Background
• Stem cell reprogramming
– Somatic cells can regain the pluripotent potential through
reprogramming treatment by different cocktails, e.g. the combinations
of transcriptional factors, small chemical compounds, growth factors
stimulus and epigenetic modifiers. The reprogrammed cells are called
induced pluripotent stem cells (iPSC).
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• Generation of iPSCs by pluripotent factors
Takahashi, K., & Yamanaka, S. (2006). Induction of pluripotent stem cells from mouse
embryonic and adult fibroblast cultures by defined factors. Cell, 126(4), 663-676.
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• Generation of iPSCs by lineage specifiers
GFP images of iPS colonies generated with
KM+GATA3+SOX1 (G3S1KM),
KM+GATA3+SOX3 (G3S3KM),
KM+GATA6+SOX1 (G6S1KM),
KM+GATA6+SOX3 (G6S3KM),
KM+GATA6+GMNN (G6GmKM),
KM+PAX1+SOX1 (P1S1KM), KM+PAX1+SOX3
(P1S3KM), and OSKM. [1]
Seesaw model
Counteracting differentiation forces allow
for Human iPSC Reprogramming [2]
[1] Shu, et al. (2013) Induction of pluripotency in mouse somatic cells with lineage
specifiers. Cell, 153, 963-975.
[2] Montserrat, et al. (2013) Reprogramming of human fibroblasts to pluripotency 7
with lineage specifiers. Cell stem cell, 13, 341-350.
• Modeling methods
– Theoretical models are constructed to describe the biological
regulations of RNA transcription, signal transduction and
epigenetic modifications
Table 1. Mathematical models of global dynamics in reprogramming or differentiation.
Description
A model for a two-gene network
Method
ODE (Menten equations)
Landscape
Fuzzy petri network
Publications
(16)
ODE (Mension equations)
(18)
ODE (non-contact model Narula,
2010)
Consider enhancer, promoter
(21)
A model for three-gene network
ODE (Hill equation, considering
protein complex binding)
(22)
(16)
A model for epigenetic regulations
during reprogramming
Epigenetic regulatory rules with
assigned probabilities
(23)
Probabilistic Boolean
network
A combination of fuzzy theory and
petri network
Two isolated models for Wnt and
Notch respectively and a combined
model
A model for Notch and BMP4 with
core GRN
(17)
Related work
Sui Huang’s quasipotential landscape
Boolean network
General method for
signaling
modeling(19,20)
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Method
• Construction of the transcriptional network
Pluripotency
factors
Lineage1
Lineage2
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• Mathematical modelling of the transcriptional network
For one gene,
For a network,
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• Continuous Model
– Mathematical modeling of global dynamics
fi = dxi / dt
Parameters
Description
i
Noise term
i
Degradation rate
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• Parameter inference


52 parameters in the 10 ODEs
Simulated Annealing was used to infer the parameters
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• Construction of the probabilistic landscape
Assume that the noise is Gaussian distribution and the individual
probability are independent, then
P(x,t) is the probability of certain expression state x at time t which
possesses the quasi-potential of
The numerical result of U can be solved by finite difference method (FDM)
Zhou, J., Aliyu, M., Aurell, E. and Huang, S. (2012) Quasi-potential landscape in complex multi-stable
systems. Journal of the Royal Society, Interface / the Royal Society, 9, 3539-3553.
Li, C. and Wang, J. (2013) Quantifying cell fate decisions for differentiation and reprogramming of a
human stem cell network: landscape and biological paths. PLoS computational biology, 9.
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Results
We performed the parameter inference method on a theoretical seesaw
network [1] with 14 parameters.
[1] Shu, et al. (2013) Induction of pluripotency in mouse somatic cells with
lineage specifiers. Cell, 153, 963-975.
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Parameter inference result of 4-gene network
Simulated Annealing
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The Landscape of the 4-gene network
Results
Parameter inference on the 10-gene network with 52 parameters.
Simulated Annealing
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The Landscape of the 10-gene network
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Simulations of stem cell reprogramming
Figure. Reprogramming simulations by lineage specifiers and pluripotency factors.
(a) Reprogramming experiments induced by Oct4, Sox2, Klf4 and Myc.
(b) Reprogramming experiments induced by Gata6, Sox1, Klf4 and Myc.
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Discussion and future work
• We implemented a preliminary model of Waddington’s
epigenetic landscape
• We have simulated the reprogramming process under various
experimental conditions, which predicts a relatively low
success rate of reprogramming, consistent with experiments.
• In future, we will:
– Integrate transcriptional regulations with signal transduction and
epigenetic modifications
– Modelling with real data
– Simulate the process of cellular ageing
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Acknowledgements
MOE AcRF Tier 1 Seed Grant on
Complexity
PhD Scholarships from NTU
PhD:
Ms. Chen Haifen
Mr. Zhang Fan
Mr. Mishra Shital Kumar
Ms. Guo Jing
Research Fellow :
Dr. Zhang Xiaomeng
Dr. Liu Hui
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Thank you!
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