Advertisement

Bulletin of Mathematical Biology

, Volume 80, Issue 5, pp 1059–1083 | Cite as

Ordinary Differential Equation Models for Adoptive Immunotherapy

  • Anne Talkington
  • Claudia Dantoin
  • Rick DurrettEmail author
Special Issue : Mathematical Oncology

Abstract

Modified T cells that have been engineered to recognize the CD19 surface marker have recently been shown to be very successful at treating acute lymphocytic leukemias. Here, we explore four previous approaches that have used ordinary differential equations to model this type of therapy, compare their properties, and modify the models to address their deficiencies. Although the four models treat the workings of the immune system in slightly different ways, they all predict that adoptive immunotherapy can be successful to move a patient from the large tumor fixed point to an equilibrium with little or no tumor.

Keywords

Chimeric antigen receptor T cells ODE models Stability analysis Saturating response Acute lymphoblastic leukemia 

Notes

Acknowledgements

Funding was provided by National Science Foundation (Grant No. DMS 1505215).

References

  1. de Pillis L, Radunskaya AE (2006) Mixed immunotherapy and chemotherapy of tumors: modeling, appplications and biological interpretations. J Theor Biol 238:841–862CrossRefGoogle Scholar
  2. de Pillis L, Radunskaya AE, Wiseman CL (2005) A validated mathematical model of cell-mediated immune response to tumor growth. Cancer Res 65:7950–7958Google Scholar
  3. Dong Y, Miyazaki R, Takeuchi Y (2014) Mathematical modeling on helper T cells in a tumor immune system. Discrete Continuous Dyn Syst B 19:55–71MathSciNetCrossRefzbMATHGoogle Scholar
  4. Eshhar Z, Waks T, Gross G, Schindler DG (1993) Specific activation and targeting of cytotoxic lymphocytes through chimeric single chains consisting of antibody-binding domains and the \(\gamma \) or \(\zeta \) subunits of the immunoglobulin and T-cell receptors. Proc Natl Acad Sci 90:720–724CrossRefGoogle Scholar
  5. Grupp SA et al (2013) Chimeric antigen receptor-modified T cells for acute lymphoid leukemia. N Engl J Med 368:1509–1518CrossRefGoogle Scholar
  6. Janeway CA, Travers P, Walport M, Shlomicki MJ (2001) Immunobiology: the immune system in health and disease. Garland Publishing Company, New YorkGoogle Scholar
  7. Kirschner D, Panetta JC (1998) Modeling immunotherapy of the tumor-immune interaction. J Math Biol 37:235–252CrossRefzbMATHGoogle Scholar
  8. Kuznetsov VA, Makalkin IA, Taylor MA, Perleson AS (1994) Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. Bull Math Biol 56:295–321Google Scholar
  9. Maude SL et al (2014) Chimeric antigen receptor T cells for sustained remission in leukemia. N Engl J Med 371:1507–1517CrossRefGoogle Scholar
  10. Mohri H et al (2001) Increased turnover of \(T\) lymphocytes in HIV-1 infection and its reduction by anti-viral therapy. J Exp Med 194(9):1277–1287CrossRefGoogle Scholar
  11. Moore HN, Li NK (2004) A mathematical model for chronic myelogenous leukemia (CML) and T cell interaction. J Theor Biol 227:513–523MathSciNetCrossRefGoogle Scholar
  12. Park TS, Rosenberg SA, Morgan RA (2011) Treating cancer with genetically engineered T cells. Trends Biotechnol 29:550–557CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2017

Authors and Affiliations

  • Anne Talkington
    • 1
  • Claudia Dantoin
    • 2
  • Rick Durrett
    • 3
    Email author
  1. 1.Bioinformatics and Computational BiologyUniversity of North CarolinaChapel HillUSA
  2. 2.Departments of Chemistry and Electrical and Computer EngineeringDuke UniversityDurhamUSA
  3. 3.Department of MathematicsDuke UniversityDurhamUSA

Personalised recommendations