Skip to main content

Part of the book series: Stem Cells and Cancer Stem Cells ((STEM,volume 13))

  • 871 Accesses

Abstract

Mathematical models provide many insights into both the biology of cancer and the optimization of its treatment. Cancer stem cells represent a novel target of cancer therapeutics. While cancer stem cells can represent a relatively small proportion of the total cells within a tumor, they are responsible for driving the dynamics of tumor growth and invasiveness. Modeling in combination with experimental validation has advanced quantitative understanding of cancer stem cells and their interaction with their microenvironment. We present here the salient features of a set of examples of mathematical models that have contributed to our current understanding of how cancer stem cells are regulated and describe further opportunities for modeling.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

  • Abkowtiz JL, Catlin SN, Guttorp P (1996) Evidence that hematopoiesis may be a stochastic process in vivo. Nat Med 2(2):190–197

    Article  Google Scholar 

  • Abkowtiz JL, Golinelli D, Harrison DE, Guttorp P (2000) In vivo kinetics of murine hematopoietic stem cell. Blood 96(10):3399–3405

    Google Scholar 

  • Abkowtiz JL, Catlin SN, McCallie MT, Guttorp P (2002) Evidence that the number of hematopoietic stem cells per animal is conserved in mammals. Blood 100(7):2665–2667

    Article  Google Scholar 

  • Anderson ARA, Chaplain MAJ, Newman EL, Steele RJC, Thompson AM (2000) Mathematical modelling of tumour invasion and metastasis. J Theor Med 2:129–154

    Article  Google Scholar 

  • Armitage P, Doll R (1954) The age distribution of cancer and a multi-stage theory of carcinogenesis. Br J Cancer 8:1–12

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Ashkenazi R, Jackson TL, Dontu G, Wicha MS (2007) Breast cancer stem cells-research opportunities utilizing mathematical modeling. Stem Cell Rev 3:176–182

    Article  PubMed  Google Scholar 

  • Benzekry S, Chapuisat G, Ciccolini J, Erlinger A, Hubert F (2011) A new mathematical model for optimizing the combination between antiangiogenic and cytotoxic drugs in oncology. C R Acad Sci Paris Ser I 350:23–28

    Article  Google Scholar 

  • Bocklandt S, Lin W, Sehl ME, Sánchez FJ, Sinsheimer JS, Horvath S, Vilain E (2011) Epigenetic predictor of age. PLoS One 6, e14821

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Bozic I, Reiter JG, Allen B, Antal T, Chatterjee K, Shah P, Moon YS, Yaqubie A, Kelly N, Le DT, Lipson EJ, Chapman PB, Diaz LA Jr, Vogelstein B, Nowak MA (2013) Evolutionary dynamics of cancer in response to targeted combination therapy. eLife 2, e00747

    Article  PubMed Central  PubMed  Google Scholar 

  • Breen EC, Hussain SK, MagpanRabkin CS, Kaslow RA, Variakojis D, Bream JH, Rinaldo CR, Ambinder RF, Martinez-Maza O (2011) B-cell stimulatory cytokines and markers of immune activation are elevated several years prior to the cytokines and markers of immune activation are elevated several years prior to the diagnosis of systemic AIDS-associated non-Hodgkin B-cell lymphoma. Cancer Epidemiol Biomarkers Prev 20:1303–1314

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Brümmendorf TH, Balabanov S (2006) Telomere length dynamics in normal hematopoiesis and in disease states characterized by increased stem cell turnover. Leukemia 20:1706–1716

    Article  PubMed  Google Scholar 

  • Butov A, Johnson T, Cypser J, Sannikov I, Volkov M, Sehl M, Yashin A (2001) Hormesis and debilitation effects in stress experiments using the nematode worm Caenorhabditis elegans: the model of balance between cell damage and HSP levels. Exp Gerontol 7:57–66

    Article  Google Scholar 

  • Butov AA, Volkov MA, Anisimov VN, Sehl ME, Yashin AI (2002) A model of accelerated aging induced by 5-bromodeoxyuridine. Biogerontology 3(3):175–182

    Article  CAS  PubMed  Google Scholar 

  • Butov AA, Carey JR, Volkov MA, Sehl ME, Yashin AI (2003) Reproduction and survival in Mediterranean fruit flies: a “protein and energy” free radical model of aging. Biogerontology 4:387–395

    Article  CAS  PubMed  Google Scholar 

  • Campisi J (2003) Cancer and ageing: rival demons? Nat Rev Cancer 3:339–349

    Article  CAS  PubMed  Google Scholar 

  • Conley SJ, Gheordunescu E, Kakarala P, Newman B, Korkaya H, Heath AN, Clouthier SG, Wicha MS (2012) Antiangiogenic agents increase breast cancer stem cells via the generation of tumor hypoxia. Proc Natl Acad Sci U S A 109:2784–2789

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Folkman J (1971) Tumor angiogenesis: therapeutic implications. N Engl J Med 285(21):1182–1186

    Article  CAS  PubMed  Google Scholar 

  • Foo J, Drummond MW, Clarkson B, Holyoake T, Michor F (2009) Eradication of chronic myeloid leukemia stem cells: a novel mathematical model predicts no therapeutic benefit of adding G-CSF to imatinib. PLoS Comput Biol 5(9), e1000503. doi:10.1371/journal.pcbi.1000503

    Article  PubMed Central  PubMed  Google Scholar 

  • Jain RK (2001) Normalizing tumor vasculature with anti-angiogenic therapy: a new paradigm for combination therapy. Nat Med 7(9):987–989

    Article  CAS  PubMed  Google Scholar 

  • Jain RK, Tong RT, Munn LL (2007) Effect of vascular normalization by antiangiogenic therapy on interstitial hypertension, peritumor edema, and lymphatic metastasis: insights from a mathematical Model. Cancer Res 67(6):2729–2735

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Kohandel M, Kardar M, Milosevic M, Sivaloganathan S (2007) Dynamics of tumor growth and combination of anti-angiogenic and cytotoxic therapies. Phys Med Biol 52:3665–3677

    Article  CAS  PubMed  Google Scholar 

  • Korkaya H, Liu S, Wicha MS (2011) Breast cancer stem cells, cytokine networks, and the tumor microenvironment. J Clin Invest 121:3804–3809

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Li L, Neaves WB (2006) Normal stem cells and cancer stem cells: the niche matters. Cancer Res 66:4553–4557

    Article  CAS  PubMed  Google Scholar 

  • Liao D, Johnson RS (2007) Hypoxia: a key regulator of angiogenesis in cancer. Cancer Metastasis Rev 26(2):281–290

    Article  CAS  PubMed  Google Scholar 

  • Mantzaris NV, Webb S, Othmer HG (2004) Mathematical modeling of tumor-induced angiogenesis. J Math Biol 49:111–187

    Article  PubMed  Google Scholar 

  • Michaud M, Balardy L, Moulis G, Gaudin C, Peyrot C, Vellas B, Cesari M, Nourhashemi F (2013) Proinflammatory cytokines, aging, and age-related diseases. J Am Med Dir Assoc S1525–8610(13):00280–00286

    Google Scholar 

  • Michor F, Hughes TP, Iwasa Y, Branford S, Shah NP, Sawyers CL, Nowak MA (2005) Dynamics of chronic myeloid leukaemia. Nature 435:1267–1270

    Article  CAS  PubMed  Google Scholar 

  • Scott JG, Basanta D, Anderson AR, Gerlee P (2013) A mathematical model of tumour self-seeding reveals secondary metastatic deposits as drivers of primary tumour growth. J R Soc Interface 10(82):20130011. doi:10.1098/rsif.2013.0011

    Article  PubMed Central  PubMed  Google Scholar 

  • Sehl ME, Sinsheimer JS, Zhou H, Lange KL (2009) Differential destruction of stem cells: implications for targeted cancer stem cell therapy. Cancer Res 69:9481–9489

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Sharpless NE, DePinho RA (2004) Telomeres, stem cells, senescence, and cancer. J Clin Invest 113:160–168

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Shepherd BE, Kiem HP, Lansdorp PM, Dunbar CE, Aubert G, LaRochelle A, Seggewiss R, Guttorp P, Abkowitz JL (2007) Hematopoietic stem-cell behavior in nonhuman primates. Blood 110(6):1806–1813

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Sun Z, Komarova N (2012) Stochastic modeling of stem-cell dynamics with control. Math Biosci 240:231–240

    Article  PubMed Central  PubMed  Google Scholar 

  • Tang M, Gonen M, Quintas-Cardama A, Cortes J, Kantarjian H, Field C, Hughes TP, Branford S, Michor F (2011) Dynamics of chronic myeloid leukemia response to long-term targeted therapy reveal treatment effects on leukemic stem cells. Blood 118(6):1622–1631

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Teicher BA (1994) Hypoxia and drug resistance. Cancer Metastasis Rev 13:139–168

    Article  CAS  PubMed  Google Scholar 

  • Teschendorff AE, Menon U, Gentry-Maharaj A, Ramus SJ, Weisenberger DJ, Shen H, Campan M, Noushmehr H, Bell CG, Maxwell AP, Savage DA, Mueller-Holzner E, Marth C, Kocjan G, Gayther SA, Jones A, Beck S, Wagner W, Laird PW, Jacobs IJ, Widschwendter M (2010) Age-dependent DNA methylation of genes that are suppressed in stem cells is a hallmark of cancer. Genome Res 20:440–446

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Till JE, McCulloch EA, Siminovitch L (1964) A stochastic model of stem cell proliferation, based on the growth of spleen colony-forming cells. Proc Natl Acad Sci U S A 51(1):29–36

    Article  PubMed Central  CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mary E. Sehl .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Myat, H.S., Sehl, M.E. (2015). Cancer Stem Cell Dynamics and Regulation. In: Hayat, M. (eds) Stem Cells and Cancer Stem Cells, Volume 13. Stem Cells and Cancer Stem Cells, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-7233-4_7

Download citation

Publish with us

Policies and ethics