Skip to main content
SpringerLink
Log in

Deciphering Fate Decision in Normal and Cancer Stem Cells: Mathematical Models and Their Experimental Verification

  • Chapter
  • First Online:
Mathematical Methods and Models in Biomedicine

Abstract

All tissues in the body are derived from stem cells (SCs). SCs are undifferentiated cells with two essential properties: unlimited replication capacity and the ability to differentiate into one or more specialized cell types. Embryonic SCs are pluripotent, meaning that they can give rise to nearly all cell types. Non-embryonic, adult SCs are found in various tissues and are capable of generating a limited set of tissue-specific cell types. The first discovered and most extensively studied type of adult SC is the hematopoietic SC, found in the bone marrow, which can give rise to all lineages of mature blood cells [12, 84]. Organ-specific SCs have been identified in many other tissues, including the liver, skin, brain, and mammary gland (see [19] for review).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Adams, J.M., Strasser, A.: Is tumor growth sustained by rare cancer stem cells or dominant clones? Cancer Res. 68, 4018–4021 (2008)

    Article  Google Scholar 

  2. Agrawal, S., Archer, C., Schaffer, D.V.: Computational models of the Notch network elucidate mechanisms of context-dependent signaling. PLoS Comput. Biol. 5, e1000390 (2009)

    Article  Google Scholar 

  3. Agur, Z., Kogan, Y., Levi, L., Harrison, H., Lamb, R., Kirnasovsky, O.U., Clarke, R.B.: Disruption of a quorum sensing mechanism triggers tumorigenesis: A simple discrete model corroborated by experiments in mammary cancer stem cells. Biol Direct. 5, 20 (2010)

    Article  Google Scholar 

  4. Agur, Z., Daniel, Y., Ginosar, Y.: The universal properties of stem cells as pinpointed by a simple discrete model. J. Math. Biol. 44, 79–86 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Agur, Z., Kirnasovsky, O.U., Vasserman, G., Tencer-Hershkowicz, L., Kogan, Y., Harrison, H., Lamb, R., Clarke, R.B.: Dickkopf1 regulates fate decision and drives breast cancer stem cells to differentiation: An experimentally supported mathematical model. PLoS One 6, e24225 (2011)

    Article  Google Scholar 

  6. Al-Hajj, M., Wicha, M.S., Benito-Hernandez, A., Morrison, S.J., Clarke, M.F.: Prospective identification of tumorigenic breast cancer cells. Proc Natl Acad Sci USA 100, 3983–3988 (2003)

    Article  Google Scholar 

  7. Alon Eron, S.: Maximizing lifespan in view of constant hazards during stem cells proliferation: A mathematical model. MA Thesis, Tel-Aviv University, Tel Aviv (2006)

    Google Scholar 

  8. Bankhead, A., Magnuson, N.S., Heckendorn, R.B.: Cellular automaton simulation examining progenitor hierarchy structure effects on mammary ductal carcinoma in situ. J. Theor. Biol. 246, 491–498 (2007)

    Article  Google Scholar 

  9. Bao, S., Wu, Q., McLendon, R.E., Hao, Y., Shi, Q., Hjelmeland, A.B., Dewhirst, M.W., Bigner, D.D., Rich. J.N.: Glioma stem cells promote radioresistance by preferential activation of the DNA damage response. Nature, 444, 756–760 (2006)

    Article  Google Scholar 

  10. Bassler, B.L.: How bacteria talk to each other: Regulation of gene expression by quorum sensing. Curr Opin Microbiol 2, 582–587 (1999)

    Article  Google Scholar 

  11. Baum, C.M., Weissman, I.L., Tsukamoto, A.S., Buckle, A.M., Peault, B.: Isolation of a candidate human hematopoietic stem-cell population. Proc Natl Acad Sci USA 89, 2804–2808 (1992)

    Article  Google Scholar 

  12. Becker, A.J., McCulloch, E.A., Till, J.E.: Cytological demonstration of the clonal nature of spleen colonies derived from transplanted mouse marrow cells. Nature 197, 452–454 (1963)

    Article  Google Scholar 

  13. Behrens, J., von Kries, J.P., Kuhl, M., Bruhn, L., Wedlich, D. et al.: Functional interaction of beta-catenin with the transcription factor LEF-1. Nature 382, 638–642 (1996)

    Article  Google Scholar 

  14. Borovski, T., De Sousa E Melo, F., Vermeulen, L., Medema, J.P.: Cancer stem cell niche: The place to be. Cancer Res. 71, 634–639 (2011)

    Google Scholar 

  15. Brennan, K.R., Brown, A.M.: Wnt proteins in mammary development and cancer. J Mammary Gland Biol Neoplasia 9, 119–131 (2004)

    Article  Google Scholar 

  16. Chamorro, M.N., Schwartz, D.R., Vonica, A., Brivanlou, A.H., Cho, K.R. et al.: FGF-20 and DKK1 are transcriptional targets of beta-catenin and FGF-20 is implicated in cancer and development. EMBO J. 24, 73–84 (2005)

    Article  Google Scholar 

  17. Chen, H., Paradies, N.E., Fedor-Chaiken, M., Brackenbury, R. E-cadherin mediates adhesion and suppresses cell motility via distinct mechanisms. J. Cell. Sci. 110, 345–356 (1997)

    Google Scholar 

  18. Clarke, M.F., Fuller, M.: Stem cells and cancer: Two faces of eve. Cell 124, 1111–1115 (2006)

    Article  Google Scholar 

  19. Cogle, C.R., Guthrie, S.M., Sanders, R.C., Allen, W.L., Scott, E.W., Petersen, B.E.: An overview of stem cell research and regulatory issues. Mayo Clin. Proc. 78, 993–1003 (2003)

    Google Scholar 

  20. Cook, M.M., Kollar, K., Brooke, G.P., Atkinson, K.: Cellular therapy for repair of cardiac damage after acute myocardial infarction. Int J Cell Biol. 2009, 906507 (2009)

    Google Scholar 

  21. Creighton, C.J., Li, X., Landis, M., Dixon, J.M., Neumeister, V.M., Sjolund, A., Rimm, D.L., Wong, H., Rodriguez, A., Herschkowitz, J.I. et al.: Residual breast cancers after conventional therapy display mesenchymal as well as tumor-initiating features. Proc. Natl. Acad. Sci. USA 106, 13820–13825 (2009)

    Article  Google Scholar 

  22. Deasy, M., Jankowski, R.J., Payne, T.R., Cao, B., Goff, G.P., Greenberger, J.S., Huard, J.: Modeling stem cell population growth: Incorporating terms for proliferative heterogeneity. Stem Cells 21, 536–545 (2003)

    Article  Google Scholar 

  23. Dingli, D., Michor, F.: Successful therapy must eradicate cancer stem cells. Stem Cells 24, 2603–2610 (2006)

    Article  Google Scholar 

  24. Dingli, D., Traulsen, A., Michor, F.: (A)symmetric stem cell replication and cancer. PLoS Comput. Biol. 3, e53 (2007)

    Google Scholar 

  25. Dontu, G., Jackson, K.W., McNicholas, E., Kawamura, M.J., Abdallah, W.M. et al.: Role of Notch signaling in cell-fate determination of human mammary stem/progenitor cells. Breast Cancer Res. 6, R605–R615 (2004)

    Article  Google Scholar 

  26. Drasdo, D., Hoehme, S.: A single-cell based model to tumor growth in-vitro: Monolayers and spheroids. Phys. Biol. 2, 133–147 (2005)

    Article  Google Scholar 

  27. Dubrovska, A., Elliott, J., Salamone, R.J., Kim, S., Aimone, L.J., Walker, J.R., Watson, J., Sauveur-Michel, M., Garcia-Echeverria, C., Cho, C.Y., Reddy, V.A., Schultz, P.G.: Combination therapy targeting both tumor-initiating and differentiated cell populations in prostate carcinoma. Clin. Cancer Res. 16, 5692–5702 (2010)

    Article  Google Scholar 

  28. Enderling, H., Anderson, A.R., Chaplain, M.A., Beheshti, A., Hlatky, L., Hahnfeldt, P.: Paradoxical dependencies of tumor dormancy and progression on basic cell kinetics. Cancer Res. 69, 8814–8821 (2009)

    Article  Google Scholar 

  29. Fialkow, P.J.: Stem cell origin of human myeloid blood cell neoplasms. Verh. Dtsch. Ges. Pathol. 74, 43–47 (1990)

    Google Scholar 

  30. Ganguly, R., Puri, I.K., Mathematical model for the cancer stem cell hypothesis. Cell Prolif. 39, 3–14 (2006)

    Article  Google Scholar 

  31. Gatenby, R.A., Frieden, B.R.: Information dynamics in carcinogenesis and tumor growth. Mutat. Res. 568, 259–273 (2004)

    Article  Google Scholar 

  32. Gratwohl, A., Baldomero, H., Aljurf, M. et al.: Hematopoietic stem cell transplantation: A global perspective. J. Am. Med. Assoc. 303, 1617–1624 (2010)

    Article  Google Scholar 

  33. Gregory, C.A., Singh, H., Perry, A.S., Prockop, D.J.: The Wnt signaling inhibitor dickkopf-1 is required for reentry into the cell cycle of human adult stem cells from bone marrow. J. Biol. Chem. 278, 28067–28078 (2003)

    Article  Google Scholar 

  34. Harrison, D.E., Stone, M., Astle, C.M.: Effects of transplantation on the primitive immunohematopoietic stem cell. J. Exp. Med. 172, 431–437 (1990)

    Article  Google Scholar 

  35. Harrison, H., Farnie, G., Howell, S.J., Rock, R.E., Stylianou, S., Brennan, K.R., Bundred, N.J., Clarke, R.B.: Regulation of breast cancer stem cell activity by signaling through the Notch4 receptor. Cancer Res. 70, 709–718 (2010)

    Article  Google Scholar 

  36. Hart, D., Shochat, E., Agur, Z.: The growth law of primary breast cancer as inferred from mammography screening trials data. Br J Cancer 78, 382–387 (1998)

    Article  Google Scholar 

  37. Hodgkinson, T., Yuan, X.F., Bayat, A.: Adult stem cells in tissue engineering. Expert Rev. Med. Dev. 6, 621–640 (2009)

    Article  Google Scholar 

  38. Huber, A.H., Weis, W.I.: The structure of the beta-catenin/E-cadherin complex and the molecular basis of diverse ligand recognition by beta-catenin. Cell 105, 391–402 (2001)

    Article  Google Scholar 

  39. Huff, C.A., Matsui, W., Smith, B.D., Jones, R.J.: The paradox of response and survival in cancer therapeutics. Blood 107, 431–434 (2006)

    Article  Google Scholar 

  40. Huff, C.A., Wang, Q., Rogers, K., Jung, M., Borrello, I.M., Jones, R.J., Matsui, W.: Correlation of clonogenic cancer stem cell growth with clinical outcomes in multiple myeloma (MM) patients undergoing treatment with high dose cyclophosphamide and rituximab. Proc AACR Late Breaking Abstract, LB87 (2008)

    Google Scholar 

  41. Katoh, M., Katoh, M.: Notch ligand, JAG1, is evolutionarily conserved target of canonical WNT signaling pathway in progenitor cells. Int. J. Mol. Med. 17, 681–685 (2006)

    Google Scholar 

  42. Kelly, P.N., Dakic, A., Adams, J.M., Nutt, S.L., Strasser, A.: Tumor growth need not be driven by rare cancer stem cells. Science 317, 337 (2007)

    Article  Google Scholar 

  43. Kim, S.U., de Vellis, J.: Stem cell-based cell therapy in neurological diseases: A review. J. Neurosci. Res. 87, 2183–2200 (2009)

    Article  Google Scholar 

  44. Kirnasovsky, O.U., Kogan, Y., Agur, Z.: Analysis of a mathematical model for the molecular mechanism of mammary stem cell fate decision. Math. Model. Nat. Phenom. 3, 78–89 (2008)

    Article  MathSciNet  Google Scholar 

  45. Kirnasovsky, O.U., Kogan, Y., Agur, Z.: Resilience in stem cell renewal: Development of the Agur-Daniel-Ginossar model. Disc. Cont. Dyn. Systems 10, 129–148 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  46. Kofahl, B., Wolf, J.: Mathematical modelling of Wnt/beta-catenin signalling. Biochem. Soc. Trans. 38, 1281–1285 (2010)

    Article  Google Scholar 

  47. Kogan, Y., Halevi-Tobias, K.E., Hochman, G., Baczmanska, A.K., Leyns, L., Agur, Z.: A new validated mathematical model of the Wnt signaling pathway predicts effective combinational therapy by sFRP and Dkk. Biochem. J. 444, 115–125 (2012)

    Article  Google Scholar 

  48. Kogan, Y., Hochman, G., Vainstein V., Shukron O., Lankenau, A., Boysen, B., Lamb, R., Berkman, T., Clarke, R.B., Duschl, C., Agur, Z.: Evidence for power law tumor growth and implications for cancer radiotherapy. Submitted

    Google Scholar 

  49. Kozusko, F., Bajzer, Z.: Combining Gompertzian growth and cell population dynamics. Math. Biosci. 185, 153–167 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  50. LaBarge, M.A.: The difficulty of targeting cancer stem cell niches. Clin. Cancer 16, 3121–3129 (2010)

    Article  Google Scholar 

  51. Lander, A.D., Gokoffski, K.K., Wan, F.Y.M., Nie, Q., Calof, A.L.: Cell lineages and the logic of proliferative control. PLoS Biol. 7, e1000015 (2009)

    Article  Google Scholar 

  52. Lapidot, T., Sirard, C., Vormoor, J., Murdoch, B., Hoang, T., et al.: A cell initiating human acute myeloid leukaemia after transplantation into SCID mice. Nature 17, 645–648 (1994)

    Article  Google Scholar 

  53. Lee, E., Salic, A., Kruger, R., Heinrich, R., Kirschner, M.W.: The roles of APC and Axin derived from experimental and theoretical analysis of the Wnt pathway. PLoS Biol. 1, e10 (2003)

    Article  Google Scholar 

  54. Lenz, D., Mok, K., Lilley, B., Kulkarni, R., Wingreen, N., Bassler, B.: The small RNA chaperone Hfq and multiple small RNAs control quorum sensing in Vibrio harveyi and Vibrio cholerae. Cell 118, 69–82 (2004)

    Article  Google Scholar 

  55. Li, L., Xie, T.: Stem cell niche: Structure and function. Annu. Rev. Cell Dev. Biol. 21, 605–631 (2005)

    Article  MathSciNet  Google Scholar 

  56. Li, X., Lewis, M.T., Huang, J., Gutierrez, C., Osborne, C.K., Wu, M.F., Hilsenbeck, S.G., Pavlick, A., Zhang, X., Chamness, G.C. et al.: Intrinsic resistance of tumorigenic breast cancer cells to chemotherapy. J. Natl. Cancer Inst. 100, 672–679 (2008)

    Article  Google Scholar 

  57. Lobo, N.A., Shimono, Y., Qian, D., Clarke, M.F.: The biology of cancer stem cells. Annu. Rev. Cell Dev. Biol. 23, 675–699 (2007)

    Article  Google Scholar 

  58. Loeb, L.A.: A mutator phenotype in cancer. Cancer Res. 61, 3230–3239 (2001)

    Google Scholar 

  59. Loeffler, M., Stein, R., Wichmann, H.E., Potten, C.S., Kaur, P., Chwalinski, S.: Intestinal cell proliferation. I. A comprehensive model of steady-state proliferation in the crypt. Cell Tissue Kinet. 19, 627–645 (1986)

    Google Scholar 

  60. Loeffler, M., Wichmann, H.E.: A comprehensive mathematical model of stem cell proliferation which reproduces most of the published experimental results. Cell Tissue Kinet. 13, 543–561 (1980)

    Google Scholar 

  61. Marciniak-Czochra, A., Stiehl, T., Ho, A., Jaeger, W., Wagner, W.: Modeling of asymmetric cell division in hematopoietic stem cells-regulation of self-renewal is essential for efficient repopulation. Stem Cells Dev. 18, 377–386 (2009)

    Article  Google Scholar 

  62. Matsui, W., Wang, Q., Barber, J.P., Brennan, S., Smith, B.D., Borrello, I., McNiece, I., Lin, L., Ambinder, R.F., Peacock, C. et al.: Clonogenic multiple myeloma progenitors, stem cell properties, and drug resistance. Cancer Res. 68, 190–197 (2008)

    Article  Google Scholar 

  63. Matsumoto, S.: Islet cell transplantation for Type 1 diabetes. J. Diabetes 2, 16–22 (2010)

    Article  Google Scholar 

  64. Meineke, F.A., Potten, C.S., Loeffler, M.: Cell migration and organization in the intestinal crypt using a lattice-free model. Cell Prolif., 34, 253–266 (2001)

    Article  Google Scholar 

  65. Metallo, C.M., Mohr, J.C., Detzel, C.J., De Pablo, J.J., Van Wie, B.J., Palecek S.P.: Engineering the stem cell microenvironment. Biotechnol. Prog. 23, 18–23 (2007)

    Article  Google Scholar 

  66. Michor, F., Hughes, T.P., Iwasa, Y., Branford, S., Shah, N.P. et al.: Dynamics of chronic myeloid leukaemia. Nature, 435, 1267–1270 (2005)

    Article  Google Scholar 

  67. Michor, F., Nowak, M.A., Frank, S.A., Iwasa, Y.: Stochastic elimination of cancer cells. Proc. Biol. Sci. 270, 2017–2024 (2003)

    Article  Google Scholar 

  68. Mueller, M.T., Hermann, P.C., Witthauer, J., Rubio-Viqueira, B., Leicht, S.F., Huber, S., Ellwart, J.W., Mustafa, M., Bartenstein, P., D’Haese, J.G., Schoenberg, M.H., Berger, F., Jauch, K.W., Hidalgo, M., Heeschen, C.: Combined targeted treatment to eliminate tumorigenic cancer stem cells in human pancreatic cancer. Gastroenterology 137, 1102–1113 (2009)

    Article  Google Scholar 

  69. O’Rourke, S.F., McAneney, H., Hillen, T.: Linear quadratic and tumour control probability modelling in external beam radiotherapy. J. Math. Biol. 58, 799–817 (2009)

    Article  MathSciNet  Google Scholar 

  70. Peltier, J., Schaffer, D.V.: Systems biology approaches to understanding stem cell fate choice. IET Syst. Biol. 4, 1–11 (2010)

    Article  Google Scholar 

  71. Piotrowska, M.J., Widera, D., Kaltschmidt, B., an der Heiden, U., Kaltschmidt, C.: Mathematical model for NF-kappaB-driven proliferation of adult neural stem cells. Cell Prolif. 39, 441–455 (2006)

    Google Scholar 

  72. Polakis, P.: Wnt signaling and cancer. Genes Dev. 14, 1837–1851 (2000)

    Google Scholar 

  73. Prudhomme, W.A., Duggar, K.H., Lauffenburger, D.A.: Cell population dynamics model for deconvolution of murine embryonic stem cell self-renewal and differentiation responses to cytokines and extracellular matrix. Biotechnol. Bioeng. 88, 264–272 (2004)

    Article  Google Scholar 

  74. Reya, T., Clevers, H.: Wnt signalling in stem cells and cancer. Nature 434, 843–850 (2005)

    Article  Google Scholar 

  75. Reya, T., Morrison, S.J., Clarke, M.F., Weissman, I.L.: Stem cells, cancer, and cancer stem cells. Nature 414, 105–111 (2001)

    Article  Google Scholar 

  76. Rubinfeld, B., Albert, I., Porfiri, E., Fiol, C., Munemitsu, S. et al.: Binding of GSK3beta to the APC-beta-catenin complex and regulation of complex assembly. Science 272, 1023–1026 (1996)

    Article  Google Scholar 

  77. Sell, S.: Cancer and stem cell signaling: A guide to preventive and therapeutic strategies for cancer. Stem Cell Rev. 3, 1–6 (2007)

    Article  Google Scholar 

  78. Sell, S.: Stem cell origin of cancer and differentiation therapy. Crit. Rev. Oncol. Hematol. 51, 1–28 (2004)

    Article  Google Scholar 

  79. Sneddon, J.B., Werb, Z.: Location, location, location: The cancer stem cell niche. Cell Stem Cell 1, 607–611 (2007)

    Article  Google Scholar 

  80. Stiehl, T., Marciniak-Czochra, A.: Characterization of stem cells using mathematical models of multistage cell lineages. Math. Comp. Model. 53, 1505–1517 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  81. Stosich, M.S., Mao, J.J.: Adipose tissue engineering from human adult stem cells: Clinical implications in plastic and reconstructive surgery. Plast. Econstr. Surg. 119, 71–83 (2007)

    Article  Google Scholar 

  82. Swanson, K.R., Harpold, H.L., Peacock, D.L., Rockne, R., Pennington, C., Kilbride, L., Grant, R., Wardlaw, J.M., Alvord, E.C. Jr.: Velocity of radial expansion of contrast-enhancing gliomas and the effectiveness of radiotherapy in individual patients: A proof of principle. Clin Oncol (R Coll Radiol) 4, 301–308 (2008)

    Google Scholar 

  83. Takebe, N., Ivy, S.P.: Controversies in cancer stem cells: Targeting embryonic signaling pathways. Clin. Cancer Res. 16, 3106–3112 (2010)

    Google Scholar 

  84. Till, J.E., McCulloch, E.A.: A direct measurement of the radiation sensitivity of normal mouse bone marrow cells. Radiat. Res. 14, 213–222 (1961)

    Article  Google Scholar 

  85. Tomlinson, I.P.M., Bodmer, W.F.: Failure of programmed cell death and differentiation as causes of tumors: Some simple mathematical models. Proc. Natl. Acad. Sci. USA 92, 1130–1134 (1995)

    Article  Google Scholar 

  86. Trounson, A., Thakar, R.G., Lomax, G., Gibbons, D.: Clinical trials for stem cell therapies. BMC Med. 9, 52 (2011)

    Article  Google Scholar 

  87. Tuch, B.E.: Stem cells—a clinical update. Aust. Fam. Physician. 35, 719–721 (2006)

    Google Scholar 

  88. Uchida, N., Sutton, R.E., Friera, A.M., He, D., Reitsma, M.J., Chang, W,C., Veres, G., Scollay, R., Weissman, I.L.: HIV, but not murine leukemia virus, vectors mediate high efficiency gene transfer into freshly isolated G0/G1 human hematopoietic stem cells. Proc. Natl. Acad. Sci. USA 95, 11939–11944 (1998)

    Article  Google Scholar 

  89. Underhill, G.H., Bhatia, S.N.: High-throughput analysis of signals regulating stem cell fate and function. Curr. Opin. Chem. Biol. 11, 357–366 (2007)

    Article  Google Scholar 

  90. Vainstein, V., Kirnasovsky, O.U., Kogan, Y., Agur, Z.: Strategies for cancer stem cell elimination: Insights from mathematical modeling. J. Theor. Biol. 298, 32–41 (2012)

    Article  MathSciNet  Google Scholar 

  91. van Leeuwen, I.M., Mirams, G.R., Walter, A., Fletcher, A., Murray, P., Osborne, J., Varma, S., Young, S.J., Cooper, J., Doyle, B. et al.: An integrative computational model for intestinal tissue renewal. Cell Prolif. 42, 617–636 (2009)

    Article  Google Scholar 

  92. Wicha, M.S., Liu, S., Dontu, G.: Cancer stem cells: An old idea—a paradigm shift. Cancer Res. 66, 1883–1890 (2006)

    Article  Google Scholar 

  93. Wright, K.T., Masri, W.E., Osman, A., Chowdhury, J., Johnson, W.E.: Concise review: Bone marrow for the treatment of spinal cord injury: Mechanisms and clinical applications. Stem Cells 29, 169–178 (2011)

    Article  Google Scholar 

  94. Zardawi, S.J., O’Toole, S.A., Sutherland, R.L., Musgrove, E.A.: Dysregulation of Hedgehog, Wnt and Notch signalling pathways in breast cancer. Histol. Histopathol. 24, 385–398 (2009)

    Google Scholar 

  95. Zhang, X.P., Zheng, G., Zou, L., Liu, H.L., Hou, L.H., Zhou, P., Yin, D.D., Zheng, Q.J., Liang, L., Zhang, S.Z., Feng, L., Yao, L.B., Yang, A.G., Han, H., Chen, J.Y.: Notch activation promotes cell proliferation and the formation of neural stem cell-like colonies in human glioma cells. Mol. Cell. Biochem. 307, 101–108 (2008)

    Article  Google Scholar 

  96. Zhu, X., Zhou, X., Lewis, M.T., Xia, L., Wong, S.: Cancer stem cell, niche and EGFR decide tumor development and treatment response: A bio-computational simulation study. J. Theor. Biol. 269, 138–149 (2011)

    Article  Google Scholar 

Download references

Acknowledgments

We thank Yuri Kogan and Karin Halevi-Tobias for helpful discussions and support, Karen Marron for helpful advice and careful editing of the manuscript, and the Chai Foundation for supporting the study.

Author information

Authors and Affiliations

  1. Institute for Medical BioMathematics, 10 Hate’ena St., Bene Ataroth, Israel

    Gili Hochman & Zvia Agur

Authors
  1. Gili Hochman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zvia Agur
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gili Hochman .

Editor information

Editors and Affiliations

  1. , Mathematics and Statistics, Southern Illinois University Edwardsvill, Edwardsville, 62026, Illinois, USA

    Urszula Ledzewicz

  2. , Electrical and Systems Engineering, Washington University, Brookings Drive 1, Saint Louis, 63130, Missouri, USA

    Heinz Schättler

  3. Mathematical Biosciences Institute, Ohio State University, W. 18th Avenue 231, Columbus, 43210-1292, Ohio, USA

    Avner Friedman

  4. Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel

    Eugene Kashdan

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Hochman, G., Agur, Z. (2013). Deciphering Fate Decision in Normal and Cancer Stem Cells: Mathematical Models and Their Experimental Verification. In: Ledzewicz, U., Schättler, H., Friedman, A., Kashdan, E. (eds) Mathematical Methods and Models in Biomedicine. Lecture Notes on Mathematical Modelling in the Life Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4178-6_8

Download citation

Publish with us

Policies and ethics

Search

Navigation