Mathematical Models in Stem Cell Differentiation and Fate Predictability

  • Wayne M. EbyEmail author
  • Natalia Coleman


We review recent mathematical models in stem cell differentiation with a focus on the role of epigenetics in cell fate determination. Gene regulatory networks can be described as a dynamical system. Within this high-dimensional system cell states correspond to attractors. This study spotlights the quasi-potential landscape to represent the transition between cell states as functions of stochastic and deterministic influences. Furthermore, we will investigate how these models apply to the area of neural differentiation, with a focus on the role of the Sonic Hedgehog (Shh), Notch, and Wnt pathways. Finally, we will discuss the epigenetic landscape model in relation to cancer and cancer stem cells.


Epigenetic landscape Mathematical model of differentiation Stochasticity Neural differentiation Notch pathway 


  1. Aebersold R, Auffray C, Baney E, Barillot E, Brazma A, Brett C, Brunak S, Butte A, Califano A, Celis J, Čufer T, Ferrell J, Galas D, Gallahan D, Gatenby R, Goldbeter A, Hace N, Henney A, Hood L, Iyengar R, Jackson V, Kallioneimi O, Klingmüller U, Polar P, Kolch W, Kyriakopoulou C, Laplace F, Lehrach H, Marcus F, Matrisian L, Nolan G, Pelkmans L, Potti A, Sander C, Seljak M, Singer D, Sorger P, Stunnenberg H, Superti-Furga G, Uhlen M, Vidal M, Weinstein J, Wigle D, Williams M, Wolkenhauer O, Zhivotovsky B, Zinovyev A, Zupan B (2009) Report on EU-USA workshop: how systems biology can advance cancer research. Med Oncol 3(1):9–17. doi: 10.1016/j.molonc.2008.11.003 Google Scholar
  2. Agarwal S, Archer C, Schaffer DV (2009) Computational models of the Notch network elucidate mechanisms of context-dependent signalling. PLoS Comput Biol 5(5):e1000390CrossRefGoogle Scholar
  3. Agur Z, Kogan Y, Levi L, Harrison H, Lamb R, Kirnasovsky OU, Clarke RB (2010) Disruption of Quorum Sensing mechanism triggers tumorigenesis: a simple discrete model corroborated by experiments in mammary stem cells. Biol Direct 5:20. doi: 10.1186/1745-6150-5-20 Google Scholar
  4. Agur Z, Kirnasovsky OU, Vasserman G, Tencer-Hershkowicz L, Kogan Y, Harrison H, Lamb R, Clarke RB (2011) Dickkopf1 regulates fate decision and drives breast cancer stem cells to differentiation: an experimentally supported mathematical model. PLoS One 6(9):e24225. doi: 10.1371/journal.pone.0024225 PubMedPubMedCentralCrossRefGoogle Scholar
  5. Andersson ER, Sandberg R, Lendahl U (2011) Notch signaling: simplicity in design, versatility in function. Development 138(17):3593–3612. doi: 10.1242/dev.063610 PubMedCrossRefGoogle Scholar
  6. Andrecut M, Halley JD, Winkler DA, Huang S (2011) A general model for binary cell fate decision gene circuits and degeneracy: indeterminacy and switch behavior in the absence of cooperativity. PLoS One 6(5):e19358. doi: 10.1371/journal.pone.0019358 PubMedPubMedCentralCrossRefGoogle Scholar
  7. Ao P (2004) Potential in stochastic differential equations: novel construction. J Phys A 37:L25CrossRefGoogle Scholar
  8. Ao P, Galas D, Hood L, Zhu X (2008) Cancer of robust intrinsic state of endogenous molecular-cellular network shaped by evolution. Med Hypotheses 70(3):678–684PubMedPubMedCentralCrossRefGoogle Scholar
  9. Ao P, Galas D, Hood L, Yin L, Zhu XM (2010) Towards predictive stochastic dynamical modeling of cancer genesis and progression. Interdiscip Sci 2(2):140–144PubMedPubMedCentralCrossRefGoogle Scholar
  10. Arenas A, Diaz-Guilera A, Perez-Vicente C (2006) Synchronization reveals topological states in complex networks. Phys Rev Lett 96:114102PubMedCrossRefGoogle Scholar
  11. Arney KL, Fisher AG (2004) Epigenetic aspects of differentiation. J Cell Sci 117:4355–4363PubMedCrossRefGoogle Scholar
  12. Artyamov MN, Das J, Kardov M, Chakraborty AK (2007) Purely stochastic binary decisions in cell signaling models without underlying deterministic bistabilities. Proc Natl Acad Sci U S A 104(48):18958–18963CrossRefGoogle Scholar
  13. Balaskas N, Ribeiro A, Panovska J, Dessaud E, Sasai N, Page KM, Briscoe J, Ribes V (2011) Gene regulatory logic for reading the Sonic hedgehog signaling gradient in the vertebrate neural tube. Cell 148(1–2):273–284. doi: 10.1016/j.cell.2011.10.047 Google Scholar
  14. Banerji CRS, Miranda-Saavedra D, Severini S, Widschwendter M, Enver T, Zhou JX, Teschendorff AE (2013) Cellular network entropy as the energy potential in Waddington’s differentiation landscape. Sci Rep 3:3039. doi: 10.1038/srep03039 PubMedPubMedCentralCrossRefGoogle Scholar
  15. Bao J, Lee HJ, Zheng JJ (2013) Genome-wide network of Wnt signaling in three pediatric cancers. Sci Rep 3:2969. doi: 10.1038/srep02969 PubMedPubMedCentralGoogle Scholar
  16. Barrio M, Burrage K, Leier A, Tian HH (2006) Oscillatory regulation of hes1: discrete stochastic delay modelling and simulation. PLoS Comput Biol 2(9):1017–1030CrossRefGoogle Scholar
  17. Barton A, Fendrik AJ (2013) Sustained vs. oscillating expressions of Ngn2, Dll1 and Hes1: a model of neural differentiation of embryonic telencephalon. J Theor Biol 328:1–8. doi: 10.1016/j.jtbi.2013.03.004 Google Scholar
  18. Barton A, Fendrik AJ, Rotondo E (2014) A stochastic model of neurogenesis controlled by a single factor. J Theor Biol 355:77–82. doi: 10.1016/j.jtbi.2014.03.038 PubMedCrossRefGoogle Scholar
  19. Baylin SB, Jones PA (2011) A decade of exploring the cancer epigenome – biological and translational implications. Nat Rev Cancer 11(10):726–734. doi: 10.1038/nrc3130 PubMedPubMedCentralCrossRefGoogle Scholar
  20. Bhattacharya S, Zhang Q, Andersen ME (2011) A deterministic map of Waddington’s epigenetic landscape for cell fate specification. BMC Syst Biol 5:85. doi: 10.1186/1752-0509-5-85 PubMedPubMedCentralCrossRefGoogle Scholar
  21. Bizarri M, Giuliani A, Cucina A, D’Anselmi F, Soto AM, Sonnenschein C (2011) Fractal analysis in a systems biology approach to cancer. Semin Cancer Biol 21(3):175–182. doi:19.1016/j.semcancer.2011.04.002CrossRefGoogle Scholar
  22. Bogdan P, Deasy BM, Gharaibeh B, Roehrs T, Marculescu R (2014) Heterogeneous stem cell dynamics: statistical model and qualitative predictions. Sci Rep 4:4826. doi: 10.1038/srep04826 PubMedPubMedCentralGoogle Scholar
  23. Brock A, Chang H, Huang S (2009) Non-genetic heterogeneity – a mutation-independent driving force for the somatic evolution of tumours. Nat Rev Genet 10(5):336–342. doi: 10.1038/nrg2556 PubMedCrossRefGoogle Scholar
  24. Cabrera MC, Hollingsworth RE, Hart EM (2015) Cancer stem cell plasticity and tumor heirarchy. World J Stem Cells 7(1):27–36PubMedPubMedCentralCrossRefGoogle Scholar
  25. Cau E, Blader P (2009) Notch activity in the nervous system: to switch or not to switch? Neural Dev 4:36. doi: 10.1186/1749-8104-4-36 PubMedPubMedCentralCrossRefGoogle Scholar
  26. Chang HH, Hemberg M, Barahona M, Ingber DE, Huang S (2008) Transcriptome-wide noise controls lineage choice in mammalian progenitor cells. Nature 453:544–547PubMedCrossRefGoogle Scholar
  27. Chickarmane V, Peterson C (2008) A computational model for understanding stem cell, trophectoderm and endoderm lineage determination. PLoS One 3:e3478PubMedPubMedCentralCrossRefGoogle Scholar
  28. Chickarmane V, Troein C, Nuber UA, Sauro HM, Peterson C (2006) Transcriptional dynamics of the embryonic stem cell switch. PLoS Comput Biol 2:e123PubMedPubMedCentralCrossRefGoogle Scholar
  29. Cinquin O, Demongeot J (2005) High-dimensional switches and the modeling of cellular differentiation. J Theor Biol 233(3):391–411PubMedCrossRefGoogle Scholar
  30. Cohen M, Page KM, Perez-Carrasco R, Barnes CP, Briscoe J (2014) A theoretical framework for the regulation of Shh morphogen-controlled gene expression. Development 141:3868–3878. doi: 10.1242/dev.112573 PubMedPubMedCentralCrossRefGoogle Scholar
  31. Cornell RA, Eisen JS (2005) Notch in the pathway: the roles of Notch signaling in neural crest development. Semin Cell Dev Biol 16:663–672PubMedCrossRefGoogle Scholar
  32. Creixell P, Schoof EM, Erler JT, Linding R (2012) Navigating cancer network attractors for tumor-specific therapy. Nat Biotech 30(9):842–847. doi: 10.1038/nbt.2345 CrossRefGoogle Scholar
  33. Crespo I, Perumal TM, Jurkowski W, del Sol A (2013) Differential cellular reprogramming determinants by differential stability analysis of gene regulatory networks. BMC Syst Biol 7:140. doi: 10.1186/1752-0509-7-140 PubMedPubMedCentralCrossRefGoogle Scholar
  34. D’Anselmi F, Valerio M, Cucina A, Galli L, Proietti S, Dinicola S, Pasqualato A, Manetti C, Ricci G, Giuliani A, Bizzarri M (2011) Metabolism and cell shape in cancer: a fractal analysis. Int J Biochem Cell Biol 43(7):1052–1058. doi: 10.1016/j.biocel.2010.05.002 PubMedCrossRefGoogle Scholar
  35. Davila-Velderrain J, Villarreal C, Alvarez-Buylla ER (2015) Reshaping the epigenetic landscape during early flower development: induction of attractor transitions by relative differences in gene decay rates. BMC Syst Biol 9:20. doi: 10.1186/s12918-015-0166-y PubMedPubMedCentralCrossRefGoogle Scholar
  36. Dewitt ND (2008) Metarandom states push cell fate. Nature Reports Stem Cells. doi: 10.1038/stemcells.2008.84
  37. Doe CQ (2008) Neural stem cells: balancing self-renewal with differentiation. Development 135:1575–1587PubMedCrossRefGoogle Scholar
  38. Doumic M, Marciniak-Czochra A, Perthame B, Zubelli JP (2011) A structured population model of cell differentiation. SIAM J Appl Math 7196:1918–1940CrossRefGoogle Scholar
  39. Dressoud E, McMahon AP, Briscoe J (2008) Pattern formation in the vertebrate neural tube: a sonic hedgehog morphogen-regulated transcriptional network. Development 135:2489–2503CrossRefGoogle Scholar
  40. Eby WM, Tabatabai MA (2014) Methods in mathematical modeling for stem cells. In: Hayat MA (ed) Stem cells and cancer stem cells, vol 12. Springer, Dordrecht, pp 201–217CrossRefGoogle Scholar
  41. Efroni S, Melcer S, Nissim-Rafinia M, Meshorer E (2009) Stem cells do play dice: a statistical physics view of transcription. Cell Cycle 8(1):43–48. doi: 10.4161/cc.8.1.7216 PubMedCrossRefGoogle Scholar
  42. Elowitz MB, Levine AJ, Siggia ED, Swain PS (2002) Stochastic gene expression in a single cell. Science 297(5584):1183–1186PubMedCrossRefGoogle Scholar
  43. Enver T, Heyworth CM, Dexter TM (1998) Do stem cells play dice? Blood 92(2):348–351PubMedGoogle Scholar
  44. Fagan MB (2011) Waddington redux: models and explanation in stem cell and systems biology. Biol Philos 27(2):179–213. doi: 10.1007/s10539-011-9294-y CrossRefGoogle Scholar
  45. Feinberg AP, Irizarry RA (2010) Evolution in health and medicine Sackler colloquium: Stochastic epigenetic variation as a driving force of development, evolutionary adaptation, and disease. Proc Natl Acad Sci U S A 107(1):1757–1764PubMedPubMedCentralCrossRefGoogle Scholar
  46. Feinberg AP, Tycko B (2004) The history of cancer epigenetics. Nat Rev Cancer 4:143–153PubMedCrossRefGoogle Scholar
  47. Ferrell JE (2012) Bistability, bifurcations, and Waddington’s epigenetic landscape. Curr Biol 22(11):R458–R466. doi: 10.1016/j.cub.2012.03.045 PubMedPubMedCentralCrossRefGoogle Scholar
  48. Fessler E, Dijkgraaf FE, DeSousa E, Mederria JP (2013) Cancer stem cell dynamics in tumor progression and metastasis: is the microenvironment to blame? Cancer Lett 341(1):97–104PubMedCrossRefGoogle Scholar
  49. Fisher R, Pusztai L, Swanton C (2013) Cancer heterogeneity: implications for targeted therapeutics. Brit J Cancer 108:479–485. doi: 10.1038/bjc.2012.581 PubMedPubMedCentralCrossRefGoogle Scholar
  50. Flöttman M, Scharp T, Klipp E (2012) A stochastic model of epigenetic dynamics in somatic cell reprogramming. Front Physiol 3:216CrossRefGoogle Scholar
  51. Formosa-Jordan P, Ibañes M (2014) Competition in notch signaling with cis enriches cell fate decisions. PLoS One 9(4):e95744PubMedPubMedCentralCrossRefGoogle Scholar
  52. Furusawa C, Kaneko K (1998) Emergence of rules in cell society: differentiation, hierarchy, and stability. Bull Math Biol 60:659PubMedCrossRefGoogle Scholar
  53. Furusawa C, Kaneko K (2001) Theory of robustness of irreversible differentiation in a stem cell system: Chaos hypothesis. J Theor Biol 209(4):395–416PubMedCrossRefGoogle Scholar
  54. Furusawa C, Kaneko K (2009) Chaotic expression dynamics implies pluripotency: when theory and experiment meet. Biol Direct 4:17. doi:10.1.1186/1745-6150-4-17PubMedPubMedCentralCrossRefGoogle Scholar
  55. Furusawa C, Kaneko K (2012) A dynamical-systems view of stem cell biology. Science 338:215–217. doi: 10.1126/science.1224311 PubMedCrossRefGoogle Scholar
  56. Garcia-Ojalvo J, Martinez Arias A (2012) Towards a statistical mechanics of cell fate decisions. Curr Opin Genet Dev 22(6):619–626. doi: 10.1016/j.gde.2012.10.004 PubMedCrossRefGoogle Scholar
  57. Glauche I, Lorenz R, Hasenclever D, Roeder I (2009) A novel view of stem cell development: analyzing the shape of cellular genealogies. Cell Prolif 42(2):248–263. doi: 10.1111/j.1365-2184.2009.00586.x PubMedCrossRefGoogle Scholar
  58. Goldberg AD, Allis CD, Bernstein E (2007) Epigenetics: a landscape takes shape. Cell 128:635–638. doi: 10.1016/j.cell.2007.02.006 PubMedCrossRefGoogle Scholar
  59. Gupta PB, Fillmore CM, Jiang G, Shapira SD, Tao K, Kuperwasser C, Lander ES (2011) Stochastic state transitions give rise to phenotypic equilibrium in populations of cancer cells. Cell 146(4):633–644PubMedCrossRefGoogle Scholar
  60. Hackett JA, Surani MA (2014) Regulatory principles of pluripotency: from the ground state up. Cell Stem Cell 15(4):416–430. doi: 10.1016/j.stem.2014.04.015 PubMedCrossRefGoogle Scholar
  61. Hagemann AIH, Scholpp S (2012) The tale of the three brothers – Shh, Wnt, and Fgf during development of the thalamus. Front Neurosci 6:76. doi: 10.3389/frnins.2012.00076 PubMedPubMedCentralCrossRefGoogle Scholar
  62. Halley JD, Winlker DA, Burden FR (2008) Toward a Rosetta stone for the stem cell genome: Stochastic gene expression, network architecture, and external influences. Stem Cell Res 1(3):157–168PubMedCrossRefGoogle Scholar
  63. Halley JD, Burden FG, Winkler DA, Kalkan T, Huang S, Smith A (2009) Stem cell decision making and critical-like exploratory networks. Stem Cell Res 2(3):165–177. doi: 10.1016/j.scr.2009.03.001 PubMedCrossRefGoogle Scholar
  64. Han L, Shi S, Gong T, Zhang Z, Sun X (2013) Cancer stem cells: therapeutic implications and perspectives in cancer therapy. Acta Pharm Sinica B 3(2):65–75. doi: 10.1016/j.apsb.2013.02.006 CrossRefGoogle Scholar
  65. Hanna J, Saha K, Pando B, van Zon J, Lengner CJ, Creyghton MP, van Oudenaarden A, Jaenisch R (2009) Direct cell reprogramming is a stochastic process amenable to acceleration. Nature 462(7273):595–601. doi: 10.1038/nature08592 PubMedPubMedCentralCrossRefGoogle Scholar
  66. Hendrix MJC, Seftor EA, Seftor REB, Kasemeier-Kulesa PM, Postovit LM (2007) Reprogramming metastatic tumour cells with embryonic microenvironments. Nat Rev Cancer 7:246–255PubMedCrossRefGoogle Scholar
  67. Herberg M, Zerjatke T, de Back W, Glauche I, Roeder I (2015) Image-based quantification and mathematical modeling of spatial heterogeneity in ESC colonies. Cytometry Part A 87:481–490. doi: 10.1002/cyto.a.22598 CrossRefGoogle Scholar
  68. Hernandez-Vargas H, Sincic N, Ouzounova M, Herceg Z (2009) Epigenetic signatures in stem cells and cancer stem cells. Epigenomics 1(2):261–280PubMedCrossRefGoogle Scholar
  69. Heron EA, Finkenstadt B, Rand PA (2007) Bayesian inference for dynamic transcriptional regulation: the Hes1 system as a case study. Bioinformatics 23:2596–2603PubMedCrossRefGoogle Scholar
  70. Hitchler MJ, Domann FE (2012) Redox regulation of the epigenetic landscape in cancer: a role for metabolic reprogramming in remodeling the epigenome. Free Radic Biol Med 53(11):2178–2187. doi: 10.1016/j.freeradbiomed.2012.09.028 PubMedPubMedCentralCrossRefGoogle Scholar
  71. Hood L, Tian Q (2012) Systems approach to biology and disease enable translational systems medicine. Genom Proteom Bioinform 10:181–185CrossRefGoogle Scholar
  72. Hood L, Balling R, Auffrey C (2012a) Revolutionizing medicine in the 21st century through systems approaches. Biotechnol J 7(8):992–1001PubMedPubMedCentralCrossRefGoogle Scholar
  73. Hood L, Omenn GS, Moritz RL, Aebersold R, Yamamoto KR, Amos M, Hunter-Cevera J, Locasio L et al (2012b) New and improved proteomic technologies for understanding complex biological systems: addressing a grand challenge in the life sciences. Proteomics 12:2773PubMedPubMedCentralCrossRefGoogle Scholar
  74. Howk CL (2010) A mathematical model for IL6-induced differentiation of neural progenitor cells on a micropatterned polymer substrate. Dissertation, Iowa State UniversityGoogle Scholar
  75. Howk CL, Levine HA, Smiley MW, Mallapragada SK, Nilsen-Hamilton M, Oh J, Sakaguchi DS (2012) A mathematical model for selective differentiation of neural progenitor cells on micropatterned polymer substrates. Math Biosci 238(2):65–79. doi: 10.1016/j.mbs.2012.04.001 PubMedPubMedCentralCrossRefGoogle Scholar
  76. Huang S (2007) Cell fates as attractors – stability and flexibility of cellular phenotype. In: Endothelial biomedicine, 1st edn. Cambridge University Press, New York, pp 1761–1779Google Scholar
  77. Huang S (2009a) Non-genetic heterogeneity of cells in development: more than just noise. Development 136:3853–3862. doi: 10.1242/dev.035139 PubMedPubMedCentralCrossRefGoogle Scholar
  78. Huang S (2009b) Reprogramming cell fates: reconciling rarity with robustness. Bioessays 31(5):546–560. doi: 10.1002/bies.200800189 PubMedCrossRefGoogle Scholar
  79. Huang S (2010) Cell lineage determination in state space: a systems view brings flexibility to dogmatic canonical rules. PLoS Biol 8(5):e1000380PubMedPubMedCentralCrossRefGoogle Scholar
  80. Huang S (2011) Systems biology of stem cells: three useful perspectives to help overcome the paradigm of linear pathways. Phil Trans R Soc B 366:2247–2259PubMedPubMedCentralCrossRefGoogle Scholar
  81. Huang S (2012a) The molecular and mathematical basis of Waddington’s epigenetic landscape: a framework for post-Darwinian biology? Bioessays 43(2):149–157. doi: 10.1002/bies.2011100031 CrossRefGoogle Scholar
  82. Huang S (2012b) Tumor progression: chance and necessity in Darwinian and Lamarckian somatic (mutationless) evolution. Prog Biophys Mol Biol 110(1):69–86PubMedCrossRefGoogle Scholar
  83. Huang S (2013) Genetic and non-genetic instability in tumor progression: link between the fitness landscape and the epigenetic landscape of cancer cells. Cancer Metast Rev 32(3–4):423–448. doi: 10.1007/s10555-013-9435-7 CrossRefGoogle Scholar
  84. Huang S, Ingber DE (2007) A non-genetic basis for cancer progression and metastasis: self-organizing attractors in cell regulatory networks. Breast Dis 26:27–54Google Scholar
  85. Huang S, Kauffman S (2013) How to escape the cancer attractor: rationale and limitations of multi-target drugs. Semin Cancer Biol 23(4):270–278. doi: 10.1016/j.semcancer.2013.06.003 PubMedCrossRefGoogle Scholar
  86. Huang S, Eichler G, Bar-Yam Y, Ingber DE (2005) Cell fates as high-dimensional attractor states of a complex gene regulatory network. Phys Rev Lett 94:128701PubMedCrossRefGoogle Scholar
  87. Huang S, Guo YP, May G, Enver T (2007) Bifurcation dynamics of cell fate decision in bipotent progenitor cells. Dev Biol 305:695–713PubMedCrossRefGoogle Scholar
  88. Huang S, Ernberg I, Kauffman S (2009) Cancer attractors: a systems view of tumors from a gene network dynamics and developmental perspective. Semin Cell Dev Biol 20(7):869–876. doi: 10.1016/j.semcdb.2009.07.003 PubMedPubMedCentralCrossRefGoogle Scholar
  89. Jaeger J, Irons D, Monk N (2012) The inheritance of process: a dynamical systems approach. J Exp Zool B 318(8):591–612CrossRefGoogle Scholar
  90. Johnston I (2012) The chaos within: exploring noise in cellular biology. Significance 9(4):17–21. doi: 10.1111/j.1740-9713.2012.00586.x CrossRefGoogle Scholar
  91. Johnston IG, Gaal B, Pires das Neves R, Enver T, Iborra FJ, Jones NS (2012) Mitochondrial variability as a source of extrinsic cellular noise. PLoS Comput Biol 8(3):e1002416PubMedPubMedCentralCrossRefGoogle Scholar
  92. Joksimovic M, Yun BA, Kitappa R, Anderegg AM, Chang WW, Taketo MM, McRay RD, Awatrami RB (2009) Wnt antagonism of Shh facilitates midbrain floor plate neurogenesis. Nat Neurosci 12(2):125–131PubMedCrossRefGoogle Scholar
  93. Jost D (2014) Bifurcation in epigenetics: implications in development, proliferation, and diseases. Phys Rev E 89:010701(R). doi: 10.1103/PhysRevE.89.010701 CrossRefGoogle Scholar
  94. Kaern M, Elston TC, Blake WJ, Collins JJ (2005) Stochasticity in gene expression: from theories to phenotypes. Nat Rev Genet 6:451–464PubMedCrossRefGoogle Scholar
  95. Kaneko K (2009) Relationship among phenotypic plasticity, phenotypic fluctuations, robustness, and evolvability: Waddington’s legacy revisited under the spirit of Einstein. J Biosci 34(4):529–532PubMedCrossRefGoogle Scholar
  96. Kaneko K (2011) Characterization of stem cells and cancer cells on the basis of gene expression profile stability, plasticity, and robustness. Bioessays 33(6):403–413. doi: 10.1002/bies.201000153 PubMedCrossRefGoogle Scholar
  97. Kaneko K, Yomo T (1997) Isologous diversification: a theory of cell differentiation. Bull Math Biol 59(1):139–196PubMedCrossRefGoogle Scholar
  98. Karamboulas C, Ailles L (2013) Developmental signaling pathways in cancer stem cells of solid tumors. BBA 1830(2):2481–2495PubMedGoogle Scholar
  99. Kauffman SA (1969) Metabolic stability and epigenesis in randomly connected nets. J Theor Biol 22:437–467PubMedCrossRefGoogle Scholar
  100. Kida YS, Kawamura T, Wei Z, Sogo T, Jacinto S, Shigeno A, Kushige H, Yoshihara E, Liddle C, Ecker JR, Yu RT, Atkins AR, Downes M, Evans RM (2015) ERRs mediate a metabolic switch required for somatic cell reprogramming to pluripotency. Cell Stem Cell 16(5):547–555. doi: 10.1016/j.stem.2015.03.001 PubMedCrossRefGoogle Scholar
  101. Kim J, Orkin SH (2011) Embryonic stem cell-specific signatures in cancer: insights into genomic regulatory networks and implications for medicine. Genome Med 3(11):75. doi: 10.1186/gm291 Google Scholar
  102. Kim YK, Wang J (2007) Potential energy landscape and robustness of a gene regulatory network: toggle switch. PLoS Comput Biol 3(3):e60. doi: 10.1371/journal.pcbi.0030060 PubMedPubMedCentralCrossRefGoogle Scholar
  103. Kirparissides A, Koutinas M, Moss T, Newman J, Pistikopoulos EN, Mantalaris A (2011) Modelling the Delta1/Notch1 pathway: in search of the mediator(s) of neural stem differentiation. PLoS One 6(2):e14668. doi: 10.1371/journal.pone.0014668 CrossRefGoogle Scholar
  104. Kobayashi T, Kageyama R (2010) Hes1 oscillation: making variable choices for stem cell differentiation. Cell Cycle 9:207–208PubMedCrossRefGoogle Scholar
  105. Kobayashi T, Kageyama R (2011) Hes1 oscillations contribute to heterogeneous differentiation responses in embryonic stem cells. Genes 2(1):219–228. doi: 10.3390/genes2010219 PubMedPubMedCentralCrossRefGoogle Scholar
  106. Kogan Y, Halevi-Tobias KE, Hochman G, Baczmanski AK, Leyns L, Agur Z (2012) A new validated mathematical model of the Wnt signaling pathway predicts effective combinational therapy by sFRP and Dkk. Biochem J 444:115–125PubMedCrossRefGoogle Scholar
  107. Laedwig J, Koch P, Brüstle O (2013) Leveling Waddington: the emergence of direct programming and the loss of cell fate heirarchies. Nat Rev Mol Cell Biol 14:225–236. doi: 10.1038/nrm3543 CrossRefGoogle Scholar
  108. Lai K, Robertson MJ, Schaffer DV (2004) The Sonic hedgehog signaling system as a bistable genetic switch. Biophys J 86(5):2748–2757PubMedPubMedCentralCrossRefGoogle Scholar
  109. Landler AD (2011) The individuality of stem cells. BMC Biol 9:40. doi: 10.1186/1741-7007-9-40
  110. Lang AH, Li H, Collins JJ, Mehta P (2014) Epigenetic landscapes explain partially reprogrammed cells and identify key reprogramming genes. PLoS Comput Biol 10(8):e1003734. doi: 10.1371/journal.pcbi.1003734 PubMedPubMedCentralCrossRefGoogle Scholar
  111. Lei J (2011) Recent progress in hematological dynamics. Adv Mech (Li Xue Jin Dian Chn) 42(3):294–313Google Scholar
  112. Lei J, Levin SA, Nie Q (2014) Mathematical model of adult stem cell regeneration with cross-talk between genetic and epigenetic regulation. Proc Natl Acad Sci U S A 111(10):E880–E887. doi: 10.1073/pnas.1324267111 PubMedPubMedCentralCrossRefGoogle Scholar
  113. Li C, Wang J (2013a) Quantifying cell fate decisions for differentiation and reprogramming of a human stem cell network: network and biological paths. PLoS Comput Biol 9(8):e1003165. doi: 10.1371/journal/pcbi.1003165 PubMedPubMedCentralCrossRefGoogle Scholar
  114. Li C, Wang J (2013b) Quantifying Waddington landscapes and paths of non-adiabatic cell fate decisions for differentiation reprogramming and transdifferentiation. J R Soc Interface 10:20130787PubMedPubMedCentralCrossRefGoogle Scholar
  115. Li C, Wang J (2014) Quantifying the underlying landscape and paths of cancer. J R Soc Interface 11:20140774PubMedPubMedCentralCrossRefGoogle Scholar
  116. Li S, Liu Y, Liu Z, Wang R (2015) Bifurcation dynamics and determination of alternate cell fates in bipotent progenitor cells. Cogn Neurodyn 9(2):221–229PubMedPubMedCentralCrossRefGoogle Scholar
  117. Lilja T, Heldring N, Hermanson O (2013) Like a rolling histone: epigenetic regulation of neural stem cells and brain development by factors controlling histone acetylation and methylation. BBA 1830(2):2354–2360PubMedGoogle Scholar
  118. Lotem J, Sachs L (2006) Epigenetics and the plasticity of differentiation in normal and cancer stem cells. Oncogene 25(59):7663–7672PubMedCrossRefGoogle Scholar
  119. Lovrics A, Gao Y, Juhasz B, Bock I, Byrne HM, Dinnyes A, Kovacs KA (2014) Boolean modelling reveals new regulatory connections between transcription factors orchestrating the development of the ventral spinal cord. PLoS One 9(11):e111430. doi: 10.1371/journal.pone.0111430 PubMedPubMedCentralCrossRefGoogle Scholar
  120. Lu C, Thompson CB (2012) Metabolic regulation of epigenetics. Cell Metab 16:9–17PubMedPubMedCentralCrossRefGoogle Scholar
  121. MacArthur BD (2014) Collective dynamics of stem cell populations. Proc Natl Acad Sci U S A 111(10):3653–3654. doi: 10.1073/pnas.1401030111 PubMedPubMedCentralCrossRefGoogle Scholar
  122. MacArthur BD, Lemischka IR (2013) Statistical mechanics of pluripotency. Cell 154(3):484–489PubMedCrossRefGoogle Scholar
  123. MacArthur BD, Ma’ayan A, Lemischka IR (2008a) Toward stem cell systems biology: from molecules to networks and landscapes. Cold Spr Harb Symp Quant Biol 73:211–215CrossRefGoogle Scholar
  124. MacArthur BD, Please CP, Oreffo RO (2008b) Stochasticity and the molecular mechanisms of induced pluripotency. PLoS One 3:e3086PubMedPubMedCentralCrossRefGoogle Scholar
  125. MacArthur BD, Ma’ayan A, Lemischka IR (2009) Systems biology of stem cell fate and cellular reprogramming. Nat Rev Mol Cell Biol 10(10):672–681. doi: 10.1038/nrm2766 PubMedPubMedCentralGoogle Scholar
  126. MacLean AL, Kirk P, Stumpf MPH (2015) Cellular population dynamics control the robustness of the stem cell niche. Biol Open 4:1420–1426. doi: 10.1101/021881
  127. Malouf GG, Taube JH, Lu Y, Roysarkar T, Panjarian S, Estecio MRH, Jelinek J, Yamazaki J, Raynal MJN, Long H, Tahara T, Tinnirello A, Ramachandran P, Zhang XY, Liang S, Mani SA, Issa JPJ (2013) Architecture of epigenetic reprogramming following Twist1-mediated epithelial-mesenchymal transition. Geonome Biol 14:R144. doi: 10.1186/gb-2013-14-12-r144 CrossRefGoogle Scholar
  128. Matsuda S, Yan T, Mizutani A, Sota T, Hiramoto Y, Prieto-Villa M, Chen L, Satoh A, Kudoh T, Kasai T et al (2014) Cancer stem cells maintain a heirarchy of differentiation by creating their niche. Int J Cancer 135(1):127–136CrossRefGoogle Scholar
  129. Menendez JA, Alarcón T (2014) Metabostemness a new cancer hallmark. Front Oncol 4:262PubMedPubMedCentralCrossRefGoogle Scholar
  130. Menendez JA, Corominas-Faja B, Cuyás E, Alarcón T (2014) Metabostemness: metabolepigenetic reprogramming of cancer stem-cell functions. Oncoscience 1(12):803–806PubMedPubMedCentralCrossRefGoogle Scholar
  131. Mettetal JT, Muzzey D, Pedraza JM, Ozbudak EM, van Oudenaarden A (2006) Predicting stochastic gene expression dynamics in single cells. Proc Natl Acad Sci U S A 103(19):7304–7309PubMedPubMedCentralCrossRefGoogle Scholar
  132. Miller-Jensen K, Dey SS, Schaffer DV, Arkin AP (2011) Varying virulence: epigenetic control of expression noise and disease processes. Cell Trends Biotech 29(10):517–525CrossRefGoogle Scholar
  133. Momiji H, Monk NAM (2009) Oscillatory Notch-pathway activity in a delay model of neuronal differentiation. Phys Rev E 80(2):021930. doi: 10.1103/PhysRevE.80.021930 CrossRefGoogle Scholar
  134. Moore A (2012) Towards the new evolutionary synthesis: gene regulatory networks as information integrators. Bioessays 34:87PubMedCrossRefGoogle Scholar
  135. Morris R, Sancho-Martinez I, Sharpee TO, Belmonte JCI (2011) Mathematical approaches to modeling development and reprogramming. Proc Natl Acad Sci U S A 111(14):5076–5082. doi: 10.1073/pnas.1317150111 CrossRefGoogle Scholar
  136. Muñoz P, Iliou MS, Esteller M (2012) Epigenetic alterations involved in cancer stem cell reprogramming. Med Oncol 6(6):620–636. doi:j.molonc.2012.10.006Google Scholar
  137. Panovska-Griffiths J, Page KM, Briscoe J (2012) A gene regulatory motif that generates oscillatory or multiway switch outputs. J R Soc Interface 10:20120826. doi: 10.1098/rsif.2012.0826 PubMedCrossRefGoogle Scholar
  138. Paździorek PR (2014) Mathematical model of stem cell differentiation and tissue regeneration with stochastic noise. Bull Math Biol 76:1642–1669PubMedPubMedCentralCrossRefGoogle Scholar
  139. Pedraza JM, van Oudenaarden A (2005) Noise propagation in gene networks. Science 307(5717):1965–1969PubMedCrossRefGoogle Scholar
  140. Peltier J, Schaffer DV (2010) Systems biology approaches to understanding stem cell fate choice. IET Syst Biol 4(1):1–11. doi: 10.1049/iet-syb.2009.0011 PubMedCrossRefGoogle Scholar
  141. Pera EM, Ikeda A, Eivers E, DeRobertis EM (2003) Integration of IGF, FGF, and anti-BMP signals via Smad1 phosphorylation in neural induction. Genes Dev 17(24):3023–3028PubMedPubMedCentralCrossRefGoogle Scholar
  142. Pfeuty B (2015) A computational model for the coordination of neural progenitor self-renewal and differentiation through Hes1 dynamics. Development 142(3):477–485PubMedCrossRefGoogle Scholar
  143. Pisco AO, Huang S (2015) Non-genetic cancer cell plasticity and therapy-induced stemness in tumor relapse: ‘What does not kill me strengthens me’. Brit J Canc 112:1725–1732. doi: 10.1038/bjc.2015.146 CrossRefGoogle Scholar
  144. Prasanphanich AF, Arencibia CA, Kemp ML (2014) Redox processes inform multivariate transdifferentiation trajectories associated with TGFβ-induced epithelial-mesenchymal transition. Free Rad Biol Med 7:76. doi: 10.1016/j.freeradbiolmed.2014.07.032 Google Scholar
  145. Pujadas E, Feinberg A (2012) Regulated noise in the epigenetic landscape of development and disease. Cell 148(6):1123–1131. doi: 10.1016/j.cell.2012.02.045 PubMedPubMedCentralCrossRefGoogle Scholar
  146. Qiu X, Ding S, Shi T (2012) From understanding the development landscape of the canonical fate-switch pair to constructing a dynamic landscape for two-step neural differentiation. PLoS One 7(12):e49271. doi: 10.1371/journal.pone.0049271 PubMedPubMedCentralGoogle Scholar
  147. Rabajante JF, Babierra AL (2015) Branching and oscillations in the epigenetic landscape of cell-fate determination. Prog Biophys Mol Biol 117:240–249. doi: 10.1016/j.pbiomolbio.2015.01.006 PubMedCrossRefGoogle Scholar
  148. Rabajante JF, Talaue CO (2015) Equilibrium switching and mathematical properties of nonlinear interaction networks with concurrent antagonism and self-stimulation. Chaos Solitons Fractals 73:166–182CrossRefGoogle Scholar
  149. Rabajante JF, Babierra AL, Tubay JM, Jose EC (2015) Mathematical modeling of cell-fate specification: from simple to complex epigenetics. Stem Cell Epigenetics 2:e752. doi:10.14800/sce.752Google Scholar
  150. Raj A, van Oudenaarden A (2008) Nature, nurture, or choice: stochastic gene expression and its consequences. Cell 135:216–226PubMedPubMedCentralCrossRefGoogle Scholar
  151. Rao CV, Wolf DM, Arkin AP (2002) Control, exploitation, and tolerance of intracellular noise. Nature 420:231–237PubMedCrossRefGoogle Scholar
  152. Raser JM, O’Shea EK (2005) Noise in gene expression: origins, consequences, and control. Science 309(5473):2010–2013PubMedPubMedCentralCrossRefGoogle Scholar
  153. Ridden SJ, Chang HH, Zhgalakis KC, MacArthur BD (2015) Entropy, ergodicity, and stem cell multipotency. Phys Rev Lett 115:208103. doi: 10.1103/PhysRevLett.115.208103
  154. Roeder I, Glauche I (2006) Towards an understanding of lineage specification in hematopoietic stem cells: a mathematical model for the interaction of transcription factors GATA-1 and PU.1. J Theor Biol 241:852–865PubMedCrossRefGoogle Scholar
  155. Roeder I, Radtke F (2009) Stem cell biology meets systems biology. Development 163:3525–3530CrossRefGoogle Scholar
  156. Rué P (2013) Transient and stochastic dynamics in cellular processes. Dissertation, Universitat Politècnica de CatalunyaGoogle Scholar
  157. Ruiz i Altaba A, Sanchez P, Dahmane N (2002) Gli and hedgehog in cancer: tumors, embryos, and stem cells. Nat Rev Canc 2:361–372. doi: 10.1038/nrc796 Google Scholar
  158. Saade M, Gutiérrez-Vallejo I, Le Dréau G, Rabadán MA, Miguez DG, Buceta J, Martí E (2013) Sonic hedgehog signaling switches the model of division in the developing nervous system. Cell Rep 4(3):492–503. doi: 10.1016/j.celrep.2013.06.038 PubMedCrossRefGoogle Scholar
  159. Saha K, Schaffer DV (2006) Signal dynamics in Sonic hedgehog tissue patterning. Development 133(5):889–900. doi: 10.1242/dev.02254 PubMedCrossRefGoogle Scholar
  160. Salnikov AV, Liu L, Gladkich J, Salnikova O, Ryschich E, Mattern J, Moldenhauer G, Werner J, Schemmer P, Büchler MW, Herr I (2012) Hypoxia induces EMT in low and highly aggressive pancreatic tumor cells but only cells with cancer stem cell characteristics acquire pronounced migratory potential. PLoS One 7(9):e46391. doi: 10.1371/journal.pone.0046391 PubMedPubMedCentralCrossRefGoogle Scholar
  161. Scharp T (2010) Mathematical modeling of stem cell reprogramming. Dissertation, Humboldt University, BerlinGoogle Scholar
  162. Scharp T (2014) Systems biology approaches to somatic cell reprogramming reveal new insights into the order of events, transcriptional and epigenetic control of the process. Dissertation, Humboldt University, BerlinGoogle Scholar
  163. Shaughnessy DT, McAllister K, Worth L, Haugen AC, Meyer JN, Domann FE, Van Houten B, Mostoslavsky R, Bultman SJ, Baccarelli AA, Begley TJ, Sobol RW, Hirschey MD, Ideker T, Santos JH, Copeland WC, Tice RR, Balshaw DM, Tyson FL (2014) Mitochondria, energetics, epigenetics, and cellular response to stress. Environ Health Perspect 122(12):1271–1278PubMedPubMedCentralGoogle Scholar
  164. Shi X, Zhang Z, Zhan X, Cao M, Satoh T, Akira S, Shpargel K, Magnuson T, Li Q, Wang R, Wang C, Ge K, Wu J (2014) An epigenetic switch induced by Shh signalling regulates gene activation during development and medulloblastoma growth. Nat Commun 5:425. doi: 10.1038/ncomms6425 Google Scholar
  165. Shimojo H, Ohtsuka T, Kageyama R (2008) Oscillations in Notch signaling regulate maintenance of neural progenitors. Neuron 58:52–64PubMedCrossRefGoogle Scholar
  166. Shvartsman SY, Baker RE (2012) Mathematical models of morphogen gradients and their effects on gene expression. WIREs Dev Biol 1(5):715–730. doi: 10.1002/wdev.55 CrossRefGoogle Scholar
  167. Siegal ML, Bergman A (2002) Waddington’s canalization revisited: developmental stability and evolution. Proc Natl Acad Sci U S A 99(16):10528–10532. doi: 10.1073/pnas.1023039999 PubMedPubMedCentralCrossRefGoogle Scholar
  168. Sisan DR, Halter M, Hubbard JB, Plant AL (2012) Predicting rates of cell state change caused by stochastic fluctuations using a data-driven landscape model. Proc Natl Acad Sci U S A 109(47):19262–19267PubMedPubMedCentralCrossRefGoogle Scholar
  169. Stern CD (2005) Neural induction: old problems, new findings, yet more questions. Development 132:2007–2021PubMedCrossRefGoogle Scholar
  170. Stockholm D, Benchaouir R, Picot J, Rameau P, Neildez TM, Landini G, Laplace-Bailhe C, Paldi A, Huang S (2007) The origin of phenotypic heterogeneity in a clonal cell population in vitro. PLoS One 2:e394. doi: 10.1371/journal.pone.0000394 PubMedPubMedCentralCrossRefGoogle Scholar
  171. Süel GM, Kulkarni RP, Dworkin J, Garcia-Ojalvo J, Elowitz MB (2007) Tunability and noise dependence in differentiation dynamics. Science 315:1716–1719PubMedCrossRefGoogle Scholar
  172. Sun Z, Komarova NL (2012) Stochastic modeling of stem-cell dynamics with control. Math Biosci 240(2):231–240. doi: 10.1016/j.mbs.2012.08.004 PubMedPubMedCentralCrossRefGoogle Scholar
  173. Sun Z, Komarova NL (2015) Stochastic control of proliferation and differentiation in stem cell dynamics. J Math Biol 71(4):883–901. doi: 10.1007/s00285-014-0835-2 PubMedCrossRefGoogle Scholar
  174. Suzuki N, Furusawa C, Kaneko K (2011) Oscillatory protein expression dynamics endows stem cells with robust differentiation potential. PLoS One 6(11):e27232. doi: 10.1371/journal.pone.0027232 PubMedPubMedCentralCrossRefGoogle Scholar
  175. Swain PS, Elowitz MB, Siggia ED (2002) Intrinsic and extrinsic contributions to stochasticity in gene expression. Proc Natl Acad Sci U S A 99:12795–12800PubMedPubMedCentralCrossRefGoogle Scholar
  176. Tabatabai M, Eby W, Bursac Z (2012) Oscillabolastic model, a new model for oscillatory growth dynamics, applied to the analysis of Hes1 gene expression and Ehrlich ascites tumor growth. J Biomed Inform 45(3):401–407. doi: 10.1016/j.jbi.2011.11.016 PubMedCrossRefGoogle Scholar
  177. Tang M, Villaescusa JC, Luo S, Guitarte C, Lei S, Miyamoto Y, Taketo MM, Arenas E, Huang EJ (2010) Interactions of Wnt/beta-catenin signaling and sonic hedgehog regulate the neurogenesis of ventral midbrain dopamine neurons. J Neurosci 30(27):9280–9291PubMedPubMedCentralCrossRefGoogle Scholar
  178. Tecarro E, Bui T, Lisi M, Sater A, Uzman A (2009) A simple model of two interacting signaling pathways in embryonic Xenopus laevis. Dsc Cont Dynam Syst (Suppl):753–760Google Scholar
  179. Thattai M, van Oudenaarden A (2004) Stochastic gene expression in fluctuating environments. Genetics 167:523–530PubMedPubMedCentralCrossRefGoogle Scholar
  180. Tian Q, Price ND, Hood L (2012) Systems cancer medicine: towards realization of predictive, preventive, personalized and participatory (P4) medicine. J Intern Med 271(2):111–121. doi: 10.1111/j.1365-2796.2011.02498.x PubMedPubMedCentralCrossRefGoogle Scholar
  181. Tsai JH, Yang J (2013) Epithelial-mesenchymal plasticity in carcinoma metastasis. Genes Dev 27:2192–2206. doi: 10.1101/gad.225334.113 PubMedPubMedCentralCrossRefGoogle Scholar
  182. Tuck DP, Miranker W (2010) Modeling the clonal heterogeneity of stem cells. Theor Biol Med Model 7:44. doi: 10.1186/1742-4682-7-44 PubMedPubMedCentralCrossRefGoogle Scholar
  183. Ulloa F, Marti E (2010) Wnt won the war: antagonistic role of Wnt over Shh controls dorso-ventral patterning of the vertebrate neural tube. Dev Dyn 239(1):69–76. doi: 10.1002/dvdy.22058 PubMedGoogle Scholar
  184. van Ooyen A (2011) Using theoretical models to analyse neural development. Nat Rev Neurosci 12:311–326. doi: 10.1038/nrn3031 PubMedCrossRefGoogle Scholar
  185. Veloso FA (2015) A general theory of differentiated multicellularity. bioRXiv. doi: 10.1101/016840
  186. Verd B, Cromback A, Jaeger J (2014) Classification of transient behaviours in a time-dependent toggle switch model. BMC Syst Biol 8:43PubMedPubMedCentralCrossRefGoogle Scholar
  187. Waddington C (1942) The epigenotype. Endeavour 1:18–20Google Scholar
  188. Waddington C (1957) The strategy of the genes: a discussion of some aspects of theoretical biology. George Allen & Unwin, LondonGoogle Scholar
  189. Wang JQ, Wu KJ (2015) Epigenetic regulation of epithelial-mesenchymal transition by hypoxia in cancer: targets and therapy. Curr Pharm Des 21(10):1272–1278. doi: 10.2174/1381612821666141211145610 Google Scholar
  190. Wang E, Lenferink A, O’Connor-McCourt M (2007) Cancer systems biology: exploring cancer-associated genes on cellular networks. Cell Mol Life Sci 64(14):175–1762CrossRefGoogle Scholar
  191. Wang J, Xu L, Wang E (2008) Potential landscape and flux framework of nonequilibrium networks: robustness, dissipation, and coherence of biochemical oscillations. Proc Natl Acad Sci U S A 105:12271–12276. doi: 10.1073/pnas.0800579105 PubMedPubMedCentralCrossRefGoogle Scholar
  192. Wang J, Xu L, Wang E, Huang S (2010a) The “potential” landscape of genetic circuits imposes the arrow of time in stem cell differentiation. Biophys J 99(1):29–39. doi: 10.1016/j.bpj.2010.03.058 PubMedPubMedCentralCrossRefGoogle Scholar
  193. Wang J, Zhang K, Wang E (2010b) Kinetic paths, time scale, and underlying landscapes: a path integral framework to study global natures of nonequilibrium systems and networks. J Chem Phys 133:125103. doi: 10.1063/1.3478547 PubMedCrossRefGoogle Scholar
  194. Wang J, Zhang K, Xu L, Wang E (2011a) Quantifying the Waddington landscape and biological paths for development and differentiation. Proc Natl Acad Sci U S A 108:8257–8262PubMedPubMedCentralCrossRefGoogle Scholar
  195. Wang R, Liu K, Chen L, Aihara K (2011b) Neural fate decisions mediated by trans-activation and cis-inhibition in Notch signaling. Bioinform 27(22):3158–3165CrossRefGoogle Scholar
  196. Wray J, Kalkan T, Smith AG (2010) The ground state of pluripotency. Biochem Soc Trans 38(4):1027-1032. doi:  10.1042/BST0381027 Google Scholar
  197. Yamada Y, Watanabe A (2010) Epigenetic codes in stem cells and cancer stem cells. Adv Genet 70:177–199PubMedCrossRefGoogle Scholar
  198. Yamanaka S (2009) Elite and stochastic models for induced pluripotent stem cell generation. Nature 460:49–52PubMedCrossRefGoogle Scholar
  199. Youssefpour H (2013) Mathematical modelling of cancer stem cells and intervention methods. Dissertation, University of California, IrvineGoogle Scholar
  200. Yu W, Gius D, Onyago P, Muldoon-Jacobsd K, Karp J, Feinberg AP, Cui H (2008) Epigenetic silencing of tumour suppressor gene p15 by its antisense RNA. Nature 451:202–206PubMedPubMedCentralCrossRefGoogle Scholar
  201. Zaraisky AG (2007) Neural induction: new achievements and prospects. Mol Biol 41(2):173–186. doi: 10.1134/S002689330702001X CrossRefGoogle Scholar
  202. Zernicka-Goetz M, Huang S (2010) Stochasticity versus determinism in development: a false dichotomy? Nat Rev Genet 11:743–744. doi: 10.1038/nrg2886 PubMedCrossRefGoogle Scholar
  203. Zhou JX, Huang S (2011) Understanding gene circuits at cell-fate branch points for rational cell reprogramming. Trends Genet 27:55–62PubMedCrossRefGoogle Scholar
  204. Zhou JX, Aliyu MDS, Aurell E, Huang S (2012) Quasi-potential landscape in complex multi-state systems. J R Soc Interface 9:3539–3553PubMedPubMedCentralCrossRefGoogle Scholar
  205. Zhou D, Wu D, Li Z, Qian M, Zhang MQ (2013) Population dynamics of cancer cells with cell state conversions. Quant Biol 1(3):201–208. doi: 10.1007/s40484-013-0014-2 PubMedPubMedCentralCrossRefGoogle Scholar
  206. Zhou D, Shao L, Spitz DR (2014a) Reactive oxygen species in normal and tumor stem cells. Adv Cancer Res 122:1–67PubMedPubMedCentralCrossRefGoogle Scholar
  207. Zhou JX, Pisco AO, Qian H, Huang S (2014b) Nonequilibrium population dynamics of phenotype conversion of cancer cells. PLoS One 9:e110714PubMedPubMedCentralCrossRefGoogle Scholar

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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Mathematics Department/Biology DepartmentNew Jersey City UniversityJersey CityUSA

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