Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Modeling the stem cell hypothesis: Investigating the effects of cancer stem cells and TGF−β on tumor growth

1 Department of Biology, St. Mary’s College of Maryland, 47645 College Drive, St. Mary’s City, MD 20686, USA
2 Department of Mathematics and Computer Science, St. Mary’s College of Maryland, 47645 College Drive, St. Mary’s City, MD 20686, USA
3 Department of Mathematics, Lafayette College, 730 High Street, Easton, PA 18042, USA
4 National Cancer Institute, 9000 Rockville Pike Bethesda, MD 20892, USA
5 Department of Mathematics and Computer Science, St. Joseph’s College, 245 Clinton AVE, Brooklyn, NY 11205, USA

Special Issues: Practical Insights from Cancer Models

We propose a mathematical model to describe the interaction of cancer stem cells, tumor cells, and the immune system in order to better understand tumor growth in the presence of cancer stem cells. We consider the system in two scenarios: with no-treatment and with a chemotherapy treatment regimen. We develop a system of differential equations, fit the parameters to experimental data, and perform sensitivity and stability analysis. The model simulations show that the tumor cells grow as predicted with no-treatment and that with chemotherapy, which targets only the tumor cells, the cancer will eventually relapse. As chemotherapy does not target the cancer stem cells, we conclude that the tumor cells recover due to the presence of cancer stem cells.
  Article Metrics


1. T. Reya, S. J. Morrison, M. F. Clark, et al., Stem cells, cancer, and cancer stem cells, Nature, 414 (2001), 105–111.

2. M. Al-Hajj, M. S. Wicha, A. Benito-Hernandez, et al., Prospective identification of tumorigenic breast cancer cells, Proc. Nat. Acad. Sci., 100 (2003), 3983–3988.

3. T. Kondo, T. Setoguchi and T. Taga, Persistence of a small subpopulation of cancer stem-like cells in the C6 glioma cell line, Proc. Nat. Acad. Sci., 101 (2004), 781–786.

4. A. Cozzio, E. Passegué, P.M. Ayton, et al., Similar MLL-associated leukemias arising from self-renewing stem cells and short-lived myeloid progenitors, Gene Dev., 17 (2003), 3029–3035.

5. S. K. Singh, I. D. Clarke, T. Hide, et al., Cancer stem cells in nervous system tumors, Oncogene, 23 (2004), 7267.

6. X. Yuan, J. Curtin, Y. Xiong, et al., Isolation of cancer stem cells from adult glioblastoma multi-forme, Oncogene, 23 (2004), 9392.

7. A. T. Collins, P. A. Berry, C. Hyde, et al., Prospective identification of tumorigenic prostate cancer stem cells, Cancer Res., 65 (2005), 10946–10951.

8. , N. Haraguchi, H. Inoue, F. Tanaka, et al., Cancer stem cells in human gastrointestinal cancers, Human Cell, 19 (2006), 24–29.

9. C. Li, D. G. Heidt, P. Dalerba, et al., Identification of pancreatic cancer stem cells, Cancer Res., 67 (2007), 1030–1037.

10. I. Zucchi, S. Sanzone, S. Astigiano, et al., The properties of a mammary gland cancer stem cell, P. Natl. A. Sci., 104 (2007), 10476–10481.

11. S. Ma, K. Chan, L. Hu, et al., Identification and characterization of tumorigenic liver cancer stem/progenitor cells, Gastroenterology, 132 (2007), 2542–2556.

12. A. Kreso and J. Dick, Evolution of the cancer stem cell model, Cell Stem Cell, 14 (2014), 275–291.

13. , K. Dzobo, D. A. Senthebane, A. Rowe, et al., Cancer stem cell hypothesis for therapeutic inno-vation in clinical oncology? Taking the root Out, not chopping the leaf, OMICS A J. Integ. Bio., 20 (2016), 681–691.

14. A. L. Allan, S. A. Vantyghem, A. B. Tuck, et al., Tumor dormancy and cancer stem cells: impli-cations for the biology and treatment of breast cancer metastasis, Breast Dis., 26 (2006), 87–98.

15. D. Beier, P. Hau, M. Proescholdt, et al., CD133+ and CD133- glioblastoma-derived cancer stem cells show differential growth characteristics and molecular profiles, Cancer Res., 67 (2007), 4010–4015.

16. , H. Lopez-Bertoni, Y. Li and J. Laterra, Cancer stem cells: dynamic entities in an ever-evolving paradigm, Bio. Med., 7 (2015), 1–10.

17. P. Wang, W. Wan, S. Xiong, et al., Cancer stem-like cells can be induced through dedifferentia-tion under hypoxic conditions in glioma, hepatoma and lung cancer, Cell Death Discov., 3 (2017), 16105.

18. Y. Xu, C. So, H. Lam, et al., Apoptosis reversal promotes cancer stem cell-like cell formation, Neoplasia, 20 (2018), 295–303.

19. P. Grandics, The cancer stem cell: Evidence for its origin as an injured autoreactive T Cell, Molec. Cancer, 5 (2006), 1–6.

20. H. Lou and M. Dean, Targeted therapy for cancer stem cells: the patched pathway and ABC transporters, Oncogene, 26 (2007), 1357.

21. J. N. Rich, Cancer stem cells in radiation resistance, Cancer Res., 67 (2007), 8980–8984.

22. N. V. Margaryan, H. Hazard-Jenkins, M. A. Salkeni, et al., The stem cell phenotype of aggressive breast cancer cells, Cancers, 11 (2019), 340.

23. S. Pece, D. Disalvatore, D. Tosoni, et al., Identification and clinical validation of a multigene assay that interrogates the biology of cancer stem cells and predicts metastasis in breast cancer: A retrospective consecutive study, EBioMedicine, (2019), In press.

24. G. L. Gravina, A. Mancini, A. Colapietro, et al., The small molecule ephrin receptor inhibitor, GLPG1790, reduces renewal capabilities of cancer stem cells, showing anti-tumour efficacy on preclinical glioblastoma models, Cancers, 11 (2019), 359.

25. B. Bao, Z. Wang, S. Ali, et al., Metformin inhibits cell proliferation, migration and invasion by attenuating CSC function mediated by deregulating miRNAs in pancreatic cancer cells, Cancer Prevent. Res., 5 (2012), 355–364.

26. L. MacDonagh, M. F. Gallagher, B. French, et al., Targeting the cancer stem cell marker, alde-hyde dehydrogenase 1, to circumvent cisplatin resistance in NSCLC, Oncotarget, 8 (2017), 72544–72563.

27. J. J. Huang and G. C. Blobe, Dichotomous roles of TGF-β in human cancer, Biochem. Soc. Trans., 44 (2016), 1441–1454.

28. A. Dahmani and J. Delisle, TGF-β in T cell biology: Implications for cancer immunotherapy, Cancers, 10 (2018), 194.

29. D. A. Thomas and J. Massague, TGF-β directly targets cytotoxic T cell functions during tumor evasion of immune surveillance, Cancer Cell, 8 (2005), 369–380.

30. S. Mariathasan, S. J. Turley, D. Nickles, et al., TGF-β attenuates tumour response to PD-L1 block-ade by contributing to exclusion of T cells, Nature, 554 (2018), 544.

31. V. Ingangi, M. Minopoli, C. Ragone, et al., Role of microenvironment on the fate of disseminating cancer stem cells, Front. Onc., 9 (2019), 82.

32. F. Mami-Chouaib, C. Blanc, S. Corgnac, et al., Resident memory T cells, critical components in tumor immunology, J. Immunother. Cancer , 6 (2018), 87.

33. P. C. Rosato, S. Wijeyesinghe, J. M. Stolley, et al., Virus-specific memory T cells populate tumors and can be repurposed for tumor immunotherapy, Nat. Comm., 10 (2019), 567.

34. N. Badrinath and S. Y. Yoo, Recent advances in cancer stem cell-targeted immunotherapy, Can- cers, 11 (2019), 310.

35. F. Vahidian, P. H. G. Dujif, E. Safarzadeh, et al., Interactions between cancer stem cells, immune system and some environmental components: friends or foes?, Immunol. Lett., 208 (2019), 19–29.

36. I. A. Voutsadakis, Immune ligands for cytotoxic T lymphocytes (CTLS) in cancer stem cells (CSCS), Front. Biosci., 23 (2018), 563–583.

37. N. D. Price, G. Foltz, A. Madan, et al., Systems biology and cancer stem cells, J. Cell. Molec. Med., 12 (2008), 97–110.

38. S. L. Weekes, B. Barker, S. Bober, et al., A multicompartment mathematical model of cancer stem cell-driven tumor growth dynamics, B. Math. Biol., 7 (2014), 1762–1782.

39. S. Wilson and D. Levy, A mathematical model of the enhancement of tumor vaccine efficacy by immunotherapy, B. Math. Biol., 7 (2012), 1485–1500.

40. C. Loizides, D. Iacovides, M. M. Hadjiandreou, et al., Model-based tumor growth dynamics and therapy response in a mouse model of De Novo Carcinogenesis, PLoS ONE, 10 (2015), e0143840.

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

42. A. L. Garner, Y. Y. Lau, D. W. Jordan, et al., Implications of a simple mathematical model to cancer cell population dynamics, Cell Prolif., 39 (2006), 15–28.

43. D. Dingli and F. Michor, Successful therapy must eradicate cancer stem cells, Stem Cells, 4 (2006), 2603–2610.

44. D. Dingli, A. Traulsen and J. M. Pacheco, Stochastic dynamics of hematopoietic tumor stem cells, Cell Cyc., 6 (2007), 461–466.

45. R. Ashkenazi, T. L. Jackson, G. Dontu, et al., Breast cancer stem cells-research opportunities utilizing mathematical modeling, Stem Cell Rev., 3 (2007), 176–182.

46. R. Ganguly and I. K. Puri, Mathematical model for chemotherapeutic drug efficacy in arresting tumour growth based on the cancer stem cell hypothesis, Cell Prolif., 40 (2007), 338–354.

47. S. E. Kern and D. Shibata, The fuzzy math of solid tumor stem cells: a perspective, Cancer Res., 67 (2007), 8985–8988.

48. H. Zhong, S. Brown, S. Devpura, et al., Kinetic modeling of tumor regression incorporating the concept of cancer stem-like cells for patients with locally advanced lung cancer, Theor. Biol. Med. Model, 15 (2018), 23.

49. M. E. Sehl and M. S. Wicha, Modeling of interactions between cancer stem cells and their mi-croenvironment: Predicting clinical response, Cancer Sys. Bio. Met. Prot. (ed. L. Von Stechow), Springer New York, 2018.

50. S. A. M. Tonekaboni, A. Dhawan and M. Kohandel, Mathematical modelling of plasticity and phenotype switching in cancer cell populations, Math. Biosci., 283 (2017), 30–37.

51. S. Michelson and J. Leith, Autocrine and paracrine growth factors in tumor growth: A mathemat-ical model, B. Math. Biol., 53 (1991), 639–656.

52. G. Ascolani and P. Liò, Modeling TGF-β in early stages of cancer tissue dynamics, PLoS ONE, 9 (2014), 1–20.

53. S. Khatibi, H. J. Zhu, J. Wagner, et al., Mathematical model of TGF-β signalling: Deedback coupling is consistent with signal switching, BMC Sys. Bio., 11 (2017), 48.

54. D. Krijgsman, M. Hokland and P. J. Juppen, The role of natural killer T cells in cancer-A pheno-typical and functional approach, Front. Immun., 9 (2018), 367.

55. E. Vivier, D. H. Raulet, A. Moretta, et al., Innate or adaptive immunity? The example of natural killer cells, Science, 331 (2011), 44–49.

56. M. Hashimoto, A. O. Kamphorst, S. J. Im, et al., CD8 T cell exhaustion in chronic infection and cancer: opportunities for interventions, Ann. Rev. Med., 69 (2018), 301–318.

57. I. P. da Silva, A. Gallois, S. Jimenez-Baranda, et al., Reversal of NK-cell exhaustion in advanced melanoma by Tim-3 blockade, Cancer Immunol. Res., 2 (2014), 410–422.

58. E. Bae, H. Seo, I. Kim, et al., Roles of NKT cells in cancer immunotherapy, Arch. Pharm. Res., (2019), In press.

59. A. Cerwenka and L. L. Lanier, Natural killers join the fight against cancer, Science, 359 (2018), 1460–1461.

60. Y. Takeuchi and H. Nishikawa, Roles of regulatory T cells in cancer immunity, Int. Immunol., 28 (2016), 401–409.

61. A. Friedman, Mathematical Biology: Modeling and Analysis, Amer. Math. Monthly, 127 (2018), ISBN: 978-1-4704-4715-1.

62. J. C. Arciero, T. L. Jackson and D. E. Kirschner, A mathematical model of tumor-immune evasion and siRNA treatment, Disc. Cont. Dyn. Sys. Series B, 4 (2004), 39–58.

63. L. G. de Pillis, W. Gu and A. E. Radunskaya, Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations, J. Theor. Biol., 238 (2006), 841–862.

64. H. Haario, M. Laine, A. Mira, et al., Efficient adaptive MCMC, Stat. Comput., 26 (2006), 339–354.

65. R. B. Diasio and B. B. Harris, Clinical pharmacology of 5-fluorouracil, Clin. Pharmoacokin., 16 (1989), 215–237.

66. N. Petrelli, L. Herrera, Y. Rustum, et al., A prospective randomized trial of 5-fluorouracil ver-sus 5-fluorouracil and high-dose leucovorin versus 5-fluorouracil and methotrexate in previously untreated patients with advanced colorectal carcinoma. J. Clin. Onc., 5 (1987), 1559–1565.

67. I. E. Smith, R. P. A'Hern, G. A. Coombes, et al., A novel continuous infusional 5-fluorouracil-based chemotherapy regimen compared with conventional chemotherapy in the neo-adjuvant treat-ment of early breast cancer: 5 year results of the TOPIC trial. Ann. Onc., 15 (2004), 751–758.

68. F. X. Caroli-Bosc, J. L. Van Laethem, P. Michel, et al., A weekly 24-h infusion of high-dose 5-fluorouracil (5-FU)+ leucovorin and bi-weekly cisplatin (CDDP) was active and well tolerated in patients with non-colon digestive carcinomas, Eur. J. Cancer, 37 (2001), 1828–1832.

69. S. Marino, I. B. Hogue, C. J. Ray, et al., A methodology for performing global uncertainty and sensitivity analysis in systems biology, J. Theor. Biol., 254 (2009), 178–196.

70. L. Wu, W. Blum, C. Zhu, et al., Putative cancer stem cells may be the key target to inhibit cancer cell repopulation between the intervals of chemoradiation in murine mesothelioma, BMC Cancer, 18 (2018), 471.

71. H. Liu, L. Lv and K. Yang, Chemotherapy targeting cancer stem cells, Am. J. Cancer Res., 5 (2015), 880–893.

© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved