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Single-cell data-driven mathematical model reveals possible molecular mechanisms of embryonic stem-cell differentiation

1 School of Mathematics and Statistics, Wuhan University, Wuhan, P. R. China
2 School of Science, East China Jiaotong University, Nanchang, P. R. China

Special Issues: Systems biology: Modeling of dynamical diseases and cancer

Embryonic development is widely studied due to its application in disease treatment. The published literature demonstrated that Krüppel-like factor 8(KLF8) plays an important role in modulating mesendoderm to definitive endoderm (DE) differentiation. However, it is not clear how KLF8 interacts with other key genes and affects the differentiation process. To qualitatively and quantitatively explore the molecular mechanisms of KLF8 during the differentiation of human embryonic stem cells (hESCs) in detail, we developed a mathematical model to describe the dynamics between KLF8 and two other significant genes, E-cadherin(CDH1) and Zinc-finger E-box-binding homeobox1(ZEB1). Based on the single-cell RNA-seq data, the model structure and parameters were obtained using particle swarm optimization (PSO). The bifurcation analysis and simulation results reveal that the system can exhibit a complex tristable transition, which corresponds to the three states of embryonic development at the single-cell level. We further predict that the novel important gene KLF8 promotes the formation of DE cells by reciprocal inhibition between CDH1 and KLF8 and promotion of the expression of ZEB1. These results may help to shed light on the biological mechanism in the differentiation process of hESCs.
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Keywords embryonic stem cells(ESCs); single-cell data; bifurcation; molecular mechanisms; tristability

Citation: Xiao Tu, Qinran Zhang, Wei Zhang, Xiufen Zou. Single-cell data-driven mathematical model reveals possible molecular mechanisms of embryonic stem-cell differentiation. Mathematical Biosciences and Engineering, 2019, 16(5): 5877-5896. doi: 10.3934/mbe.2019294


  • 1. J. A. Thomson, J. Itskovitz-Eldor, S. S. Shapiro, et al., Blastocysts Embryonic Stem Cell Lines Derived from Human, Science, 282 (1998), 1145–1147.
  • 2. C. E. Murry, M. A. Laflamme, X. Yang, et al., Human embryonic-stem-cell-derived cardiomyocytes regenerate non-human primate heart, Nature, 510 (2014), 273–277.
  • 3. P. P. Tam and D. A. Loebel, Gene function in mouse embryogenesis: get set for gastrulation, Nat. Rev. Genet., 8 (2007), 368–381.
  • 4. A. Adamo, I. Paramonov, M. J. Barrero, et al., LSD1 regulates the balance between self-renewal and differentiation in human embryonic stem cells, Nat. Cell Biol., 13 (2011), 652–659.
  • 5. L. Chu, J. Zhang, J. A. Thomson, et al., Single-cell RNA-seq reveals novel regulators of human embryonic stem cell differentiation to definitive endoderm, Genome Biol., 17 (2016), 173.
  • 6. S. Larabee, H. Coia, G. Gallicano, et al., miRNA-17 Members that Target Bmpr2 Influence Signaling Mechanisms Important for Embryonic Stem Cell Differentiation In Vitro and Gastrulation in Embryos, Stem Cells Dev., 24 (2015), 354–371.
  • 7. R. A. Young, L. A. Boyer, T. I. Lee, et al., Core Transcriptional Regulatory Circuitry in Human Embryonic Stem Cells, Cell, 122 (2005), 947–956.
  • 8. L. W. Jeffrey, T. A. Beyer, J. L. Wrana, et al., Switch enhancers interpret TGF- and Hippo signaling to control cell fate in human embryonic stem cells, Cell Rep., 5 (2013), 1611–1624.
  • 9. J. Rossant, J. S. Draper, A. Nagy, et al., Establishment of endoderm progenitors by SOX transcription factor expression in human embryonic stem cells, Cell Stem Cell, 3 (2008), 182–195.
  • 10. N. Ivanova, Z. Wang, S. Razis, et al., Distinct lineage specification roles for NANOG, OCT4, and SOX2 in human embryonic stem cells, Cell Stem Cell, 10 (2012), 440–454.
  • 11. A. F. Schier, A. Regev, D. Gennert, et al., Spatial reconstruction of single-cell gene expression data, Nat. Biotechnol., 33 (2015), 495–502.
  • 12. J. L. Rinn, C. Trapnell, T. S. Mikkelsen, et al., The dynamics and regulators of cell fate decisions are revealed by pseudotemporal ordering of single cells, Nat. Biotechnol., 32 (2014), 381–386.
  • 13. J. Tan and X. Zou, Complex dynamical analysis of a coupled network from innate immune responses, Int. J. Bifurcat. Chaos, 23 (2013), 1350180.
  • 14. S. Jin, D. Wang and X. Zou, Trajectory control in nonlinear networked systems and its applications to complex biological systems, SIAM J. Appl. Math, 78 (2018), 629–649.
  • 15. S. Jin, F. Wu and X. Zou, Domain control of nonlinear networked systems and applications to complex disease networks, Discrete Cont. Dyn. B, 22 (2017), 2169–2206.
  • 16. X. Shu, D. Pei, S. Wei, et al., A sequential EMT-MET mechanism drives the differentiation of human embryonic stem cells towards hepatocytes, Nat. Commun., 8 (2017), 15166.
  • 17. M. A. Nieto, J. P. Thiery, R. Y. Huang, et al., Epithelial-mesenchymal transitions in development and disease, Cell, 139 (2009), 871–890.
  • 18. J. P. Thiery and J. P. Sleeman, Complex networks orchestrate epithelial-mesenchymal transitions, Nat. Rev. Mol. Cell Biol., 7 (2006), 131–142.
  • 19. H. Peinado, F. Portillo and A. Cano, Transcriptional regulation of cadherins during development and carcinogenesis, Int. J. Dev. Biol., 48 (2004), 365–375.
  • 20. A. Voulgari and A. Pintzas, Epithelial mesenchymal transition in cancer metastasis: mechanisms, markers and strategies to overcome drug resistance in the clinic, Biochim. Biophys. Acta, 1796 (2009), 75–90.
  • 21. J. Zhao, X. Wang, M. Hung, et al., Krüppel-Like Factor 8 Induces Epithelial to esenchymal Transition and Epithelial Cell Invasion, Cancer Res., 67 (2007), 7184–7193.
  • 22. Y. Ma, X. Zheng, K. Chen, et al., ZEB1 promotes the progression and metastasis of cervical squamous cell carcinoma via the promotion of epithelial-mesenchymal transition, Int. J. Clin. Exp. Pathol., 8 (2015), 11258–11267.
  • 23. D. Chen, Y. Chu, S. Li, et al., Knock-down of ZEB1 inhibits the proliferation, invasion and migration of gastric cancer cells, Chin. J. Cell. Mol. Immunol., 33 (2017), 1073–1078.
  • 24. B. L. Li, J. M. Cai, F. Gao, et al., Inhibition of TBK1 attenuates radiation-induced epithelial-mesenchymal transition of A549 human lung cancer cells via activation of GSK-3β and repression of ZEB1, Lab. Invest., 94 (2014), 362–370.
  • 25. J. Comijn, G. Berx, Roy F. van, et al., The two-handed E box binding zinc finger protein SIP1 down-regulates E-cadherin and induces invasion, Mol. Cell, 7 (2001), 1267–1278.
  • 26. M. Moes, E. Friederich, A. Sol, et al., A novel network integrating a mi-RNA 203/SNAI1 feedback loop which regulates epithelial to mesenchymal transition, PloS One, 7 (2012), e35440.
  • 27. U. Alon, An Introduction to Systems Biology: Design Principles of Biological Circuits, 1st edition, Taylor & Francis Inc, Boca Raton, FL, 2006.
  • 28. D. Chu, N. R. Zabet and B. Mitavskiy, Models of transcription factor binding: Sensitivity of activation functions to model assumptions, J. Theor. Biol., 257 (2009), 419–429.
  • 29. J. Kennedy and R. Eberhart, Particle swarm optimization, Proceedings of ICNN'95, International Conference on Neural Networks, Perth, WA, Australia, 4 (1995), 1942–1948.
  • 30. D. Gillespie, Exact Stochastic Simulation of Coupled Chemical Reactions, J. Phys. Chem., 81 (1977), 2340–2361.
  • 31. X.Xiang, Y.Chen, X.Zou, etal., UnderstandinginhibitionofviralproteinsontypeIIFNsignaling pathways with modeling and optimization, J. Theor. Biol., 265 (2010), 691–703.
  • 32. S. Shin, O. Rath, K. Cho, et al., Positive- and negative-feedback regulations coordinate the dynamic behavior of the Ras-Raf-MEK-ERK signal transduction pathway, J. Cell Sci., 122 (2009), 425–435.
  • 33. T. Tian and K. Burrage, Stochastic models for regulatory networks of the genetic toggle switch, Proc. Natl. Acad. Sci., 103 (2006), 8372–8377.
  • 34. M. R. Birtwistle, J. Rauch, B. N. Kholodenko, et al., Emergence of bimodal cell population responses from the interplay between analog single-cell signaling and protein expression noise, BMC Syst. Biol., 16 (2012), 109.
  • 35. L. K. Nguyen, M. R. Birtwistle, B. N. Kholodenko, et al., Stochastic models for regulatory networks of the genetic toggle switch, Proc. Natl. Acad. Sci., 103 (2006), 8372–8377.


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