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 Sharing Session, Complexity Institute, NTU 1

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 2

Gene Regulatory Network (GRN) Hecker et al. BioSystems,

4 Waddington’s Epigenetic Landscape Mohammad, H. P., & Baylin, S. B. (2010). Linking cell signaling and the epigenetic machinery. Nature biotechnology, 28(10), Gene regulatory network Signaling pathways 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). 5

6 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),

7 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, [2] Montserrat, et al. (2013) Reprogramming of human fibroblasts to pluripotency with lineage specifiers. Cell stem cell, 13, Seesaw model

8 Modeling methods –Theoretical models are constructed to describe the biological regulations of RNA transcription, signal transduction and epigenetic modifications DescriptionMethodPublicationsRelated work A 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 9 Lineage1 Pluripotency factors Lineage2

For one gene, 10 Mathematical modelling of the transcriptional network For a network,

11 Continuous Model –Mathematical modeling of global dynamics ParametersDescription Noise term Degradation rate f i =

Parameter inference 12  52 parameters in the 10 ODEs  Simulated Annealing was used to infer the parameters

13 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, 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

14 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,

15 Parameter inference result of 4-gene network Simulated Annealing

The Landscape of the 4-gene network

17 Parameter inference on the 10-gene network with 52 parameters. Results Simulated Annealing

The Landscape of the 10-gene network 18

19 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 20 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

21 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! 22