Skip to main content

A Structured Population Model of Competition Between Cancer Cells and T Cells Under Immunotherapy

  • Conference paper
  • First Online:
Mathematical Models of Tumor-Immune System Dynamics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 107))

Abstract

How does immunotherapy affect the evolutionary dynamics of cancer cells? Can we enhance the anti-cancer efficacy of T cells by using different types of immune boosters in combination? Bearing these questions in mind, we present a mathematical model of cancer–immune competition under immunotherapy. The model consists of a system of structured equations for the dynamics of cancer cells and activated T cells. Simulations highlight the ability of the model to reproduce the emergence of cancer immunoediting, that is, the well-documented process by which the immune system guides the somatic evolution of tumors by eliminating highly immunogenic cancer cells. Furthermore, numerical results suggest that more effective immunotherapy protocols can be designed by using therapeutic agents that boost T cell proliferation in combination with boosters of immune memory.

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

  1. Agliari, E., Barra, A., Guerra, F., Moauro, F.: A thermodynamical perspective of immune capabilities. J. Theor. Biol. 287, 48–63 (2010)

    Article  Google Scholar 

  2. Brichard, V., Dréno, B., Tessier, M.H., Rankin, E., Parmiani, G., Arienti, F., Humblet, Y., Bourlond, A., Vanwijck, R., Liénard, D., Beauduin, M., Dietrich, P.Y., Russo, V., Kerger, J., Masucci, G., Jäger, E., De Greve, J., Atzpodien, J., Brasseur, F., Coulie, P.G., van der Bruggen, P., Boon, T.: Tumor regressions observed in patients with metastatic melanoma treated with an antigenic peptide encoded by gene MAGE-3 and presented by HLA-A1. Int. J. Cancer 80, 219–230 (1999)

    Google Scholar 

  3. Bunimovich-Mendrazitsky, S., Byrne, H., Stone, L.: Mathematical model of pulsed immunotherapy for superficial bladder cancer. Bull. Math. Biol. 70, 2055–2076 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  4. Burgess, D.J.: Tumour immunogenicity: editorial selection demystified. Nat. Rev. Cancer 12, 227 (2012)

    Article  Google Scholar 

  5. Calvez, V., Korobeinikov, A., Maini, P.K.: Cluster formation for multi-strain infections with cross-immunity. J. Theor. Biol. 233, 75–83 (2005)

    Article  MathSciNet  Google Scholar 

  6. Delitala, M., Lorenzi, T.: Recognition and learning in a mathematical model for immune response against cancer. Discrete Contin. Dyn. Syst. Ser. B 18, 891–914 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  7. De Pillis, L.G., Radunskaya, A.E., Wiseman, C.L.: A validated mathematical model of cell-mediated immune response to tumor growth. Cancer Res. 65, 7950–7958 (2005)

    Google Scholar 

  8. De Pillis, L.G., Mallet, D.G., Radunskaya, A.E.: Spatial tumor-immune modeling. Comput. Math. Meth. Med. 7, 159–176 (2006)

    Article  MATH  Google Scholar 

  9. DuPage, M., Mazumdar, C., Schmidt, L.M., Cheung, A.F., Jacks, T.: Expression of tumour-specific antigens underlies cancer immunoediting. Nature 482, 405–409 (2012)

    Article  Google Scholar 

  10. Eftimie, R., Bramson, J.L., Earn, D.J.: Interactions between the immune system and cancer: a brief review of non-spatial mathematical models. Bull. Math. Biol. 73, 2–32 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  11. Guloglu, F.B., Ellis, J.S., Wan, X., Dhakal, M., Hoeman, C.M., Cascio, J.A., Zaghouani, H.: Antigen-free adjuvant assists late effector CD4 T cells to transit to memory in lymphopenic hosts. J. Immunol. 191, 1126–1135 (2013)

    Article  Google Scholar 

  12. Hillen, T., Enderling, H., Hahnfeld, P.: The tumor growth paradox and immune system-mediated selection for cancer stem cells. Bull. Math. Biol. 75, 161–184 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  13. Jäeger, E., Bernhard, H., Romero, P., Ringhoffer, M., Arand, M., Karbach, J., Ilsemann, C., Hagedorn, M., Knuth, A.: Generation of cytotoxic T-cell responses with synthetic melanoma-associated peptides in vivo: implications for tumor vaccines with melanoma-associated antigens. Int. J. Cancer 66, 162–169 (1996)

    Article  Google Scholar 

  14. Kim, P., Lee, P., Peter, P.: Dynamics and potential impact of the immune response to chronic myelogenous leukemia. PLoS Comput. Biol. 4, e1000095 (2008)

    Article  Google Scholar 

  15. Kim, P., Lee, P., Levy, D.: A theory of immunodominance and adaptive regulation. Bull. Math. Biol. 73, 1645–1665 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  16. Komarova, N., Barnes, E., Klenerman, P., Wodarz, D.: Boosting immunity by anti-viral drug therapy: a simple relationship between timing, efficacy and success. Proc. Natl. Acad. Sci. 100, 1855–1860 (2008)

    Article  Google Scholar 

  17. Kolev, M., Kozlowska, E., Lachowicz, M.: A mathematical model for single cell cancer-immune system dynamics. Math. Comput. Model. 41, 1083–1095 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  18. Kzhyshkowska, J., Marciniak-Czochra, A., Gratchev, A.: Perspectives of mathematical modelling for understanding of macrophage function. Immunobiology 212, 813–825 (2007)

    Article  Google Scholar 

  19. Ledzewicz, U., d’Onofrio, A., Schattler, H.: Tumor development under combination treatments with anti-angiogenic therapies. Mathematical methods and models in biomedicine. Lecture Notes on Mathematical Modelling in the Life Sciences, pp. 311–337. Springer, New York (2013)

    Google Scholar 

  20. Lollini, P.L., Palladini, A., Pappalardo, F., Motta, S.: Predictive models in tumor immunology. In: Bellomo, N., De Angelis, E. (eds.) Selected Topics in Cancer Modeling, vol. 4, pp. 363–384. Birkhäuser, Boston (2008)

    Google Scholar 

  21. Lorenzi, T., Lorz, A., Restori, G.: Asymptotic dynamics in populations structured by sensitivity to global warming and habitat shrinking. Acta Appl. Math. (2013). doi:10.1007/s10440-013-9849-9

    Google Scholar 

  22. Lorz, A., Lorenzi, T., Clairambault, J., Escargueil, A., Perthame, B.: Effects of space structure and combination therapies on phenotypic heterogeneity and drug resistance in solid tumors (2013, preprint)

    Google Scholar 

  23. Matzavinos, A., Chaplain, M.A.J., Kuznetsov, V.A.: Mathematical modelling of the spatio-temporal response of cytotoxic T-lymphocytes to a solid tumor. Math. Med. Biol. 21, 1–34 (2004)

    Article  MATH  Google Scholar 

  24. Palucka, K., Banchereau, J.: Cancer immunotherapy via dendritic cells. Nat. Rev. Cancer 12, 265–277 (2012)

    Article  Google Scholar 

  25. Perelson, A., Weisbuch, G.: Immunology for physicists. Rev. Mod. Phys. 69, 1219–1268 (1997)

    Article  Google Scholar 

  26. Plesa, A., Ciuperca, G., Genieys, S., Louvet, V., Pujo-Menjouet, L., Dumontet, C., Volpert, V.: Diagnostics of the AML with immunophenotypical data. Math. Mod. Nat. Phen. 2, 104–123 (2006)

    Article  MathSciNet  Google Scholar 

  27. Ravkov, E.V., Williams, M.A.: The magnitude of CD4+ T cell recall responses is controlled by the duration of the secondary stimulus. J. Immunol. 183, 2382–2389 (2009)

    Article  Google Scholar 

  28. Ricupito, A., Grioni, M., Calcinotto, A., Hess Michelini, R., Longhi, R., Mondino, A., Bellone, M.: Booster vaccinations against cancer are critical in prophylactic but detrimental in therapeutic settings. Cancer Res. 73, 3545–3554 (2013)

    Article  Google Scholar 

  29. Rosenberg, S.A., Yannelli, J.R., Yang, J.C., Topalian, S.L., Schwartzentruber, D.J., Weber, S.J., Parkinson, D.R., Seipp, C.A., Einhorn, J.H., White, D.E.: Treatment of patients with metastatic melanoma with autologous tumorinfiltrating lymphocytes and interleukin 2. J. Natl. Cancer Inst. 86, 1159–1166 (1994)

    Article  Google Scholar 

  30. Semino, C., Martini, L., Queirolo, P., Cangemi, G., Costa, R., Alloisio, A., Ferlazzo, G., Sertoli, M.R., Reali, U.M., Ratto, G.B., Melioli, G.: Adoptive immunotherapy of advanced solid tumors: an eight year clinical experience. Anticancer Res. 19, 5645–5649 (1999)

    Google Scholar 

Download references

Acknowledgements

This work has been partially supported by the FIRB project—RBID08PP3J, the Fondation Sciences Mathématiques de Paris (FSMP) and by a public grant overseen by the French National Research Agency (ANR) as part of the “Investissements d’Avenir” program (reference: ANR-10-LABX-0098).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marcello Delitala .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this paper

Cite this paper

Delitala, M., Lorenzi, T., Melensi, M. (2014). A Structured Population Model of Competition Between Cancer Cells and T Cells Under Immunotherapy. In: Eladdadi, A., Kim, P., Mallet, D. (eds) Mathematical Models of Tumor-Immune System Dynamics. Springer Proceedings in Mathematics & Statistics, vol 107. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1793-8_3

Download citation

Publish with us

Policies and ethics