Computational Modelling of Waddington’s Epigenetic Landscape for Stem Cell Reprogramming

Zheng Jie

Assistant Professor Medical Informatics Research LabSchool 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

Mohammad, H. P., & Baylin, S. B. (2010). Linking cell signaling and the epigenetic

machinery. Nature biotechnology, 28(10), 1033-1038.

Gene regulatory

network

Signaling pathwaysEpigenetic

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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Counteracting differentiation forces allow for

Human iPSC Reprogramming [2]

• 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]

[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 with lineage

specifiers. Cell stem cell, 13, 341-350.

Seesaw model

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• Modeling methods– Theoretical models are constructed to describe the biological regulations of RNA transcription, signal transduction and epigenetic

modifications

Description Method Publications Related workA model for a two-gene network

ODE (Menten equations)Landscape

(16) Sui Huang’s quasi-potential landscape

A combination of fuzzy theory and petri network

Fuzzy petri network (17) Boolean network

Two isolated models for Wnt and Notch respectively and a combined model

ODE (Mension equations) (18) General method for signaling modeling(19,20)

A model for Notch and BMP4 with core GRN

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

Table 1. Mathematical models of global dynamics in reprogramming or differentiation.

Method• Construction of the transcriptional network

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Lineage1

Pluripotency

factors

Lineage2

For one gene,

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• Mathematical modelling of the transcriptional network

For a network,

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• Continuous Model– Mathematical modeling of global dynamics

Parameters

Description

Noise term

Degradation rate

i

i

fi = dtdxi /

• Parameter inference

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52 parameters in the 10 ODEs

Simulated Annealing was used to infer the parameters

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• Construction of the probabilistic landscape

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.

Assume that the noise is Gaussian distribution and the individual probability are

independent, then

The numerical result of U can be solved by finite difference method (FDM)

P(x,t) is the probability of certain expression state x at time t which possesses the

quasi-potential of

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We performed the parameter inference method on a theoretical seesaw network [1]

with 14 parameters.

Results

[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

The Landscape of the 4-gene network

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Parameter inference on the 10-gene network with 52 parameters.

Results

Simulated Annealing

The Landscape of the 10-gene network

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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.

Simulations of stem cell reprogramming

Discussion and future work

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• 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

Thank you!

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