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A Mathematical Model of the Enhancement of Tumor Vaccine Efficacy by Immunotherapy

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Abstract

TGF-β is an immunoregulatory protein that contributes to inadequate antitumor immune responses in cancer patients. Recent experimental data suggests that TGF-β inhibition alone, provides few clinical benefits, yet it can significantly amplify the anti-tumor immune response when combined with a tumor vaccine. We develop a mathematical model in order to gain insight into the cooperative interaction between anti-TGF-β and vaccine treatments. The mathematical model follows the dynamics of the tumor size, TGF-β concentration, activated cytotoxic effector cells, and regulatory T cells. Using numerical simulations and stability analysis, we study the following scenarios: a control case of no treatment, anti-TGF-β treatment, vaccine treatment, and combined anti-TGF-β vaccine treatments. We show that our model is capable of capturing the observed experimental results, and hence can be potentially used in designing future experiments involving this approach to immunotherapy.

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References

  • Akhurst, R., & Derynck, R. (2001). TGF-β signaling in cancer—a double-edged sword. Trends Cell Biol., 11(11), S44–S51.

    Article  Google Scholar 

  • Baylor College of Medicine. (2006). Safety study of injections of autologous/allogeneic TGFBeta-resistant LMP2A-specific cytotoxic T lymphocytes (CTL). Bethesda: National Library of Medicine. Available from http://clinicaltrials.gov/ct/show/NCT00368082.

  • Baylor College of Medicine. (2009). Her2 and TGFBeta in treatment of Her2 positive lung malignancy (HERCREEM). Bethesda: National Library of Medicine. Available from http://clinicaltrials.gov/ct/show/NCT00368082.

  • Beyer, M., & Schultze, J. L. (2006). Regulatory T cells in cancer. Blood, 108(3), 804–811.

    Article  Google Scholar 

  • Blattman, J. N., & Greenberg, P. D. (2004). Cancer immunotherapy: a treatment for the masses. Science, 305(5681), 200–205.

    Article  Google Scholar 

  • Blattman, J. N., Antia, R., Sourdive, D. J. D., Wang, X., Kaech, S. M., Murali-Krishna, K., Altman, J. D., & Ahmed, R. (2002). Estimating the precursor frequency of naive antigen-specific CD8 T cells. J. Exp. Med., 195(5), 657–664.

    Article  Google Scholar 

  • Byrne, H., & Gourley, S. (1997). The role of growth factors in avascular tumour growth. Math. Comput. Model., 26(4), 35–55.

    Article  MathSciNet  MATH  Google Scholar 

  • Cappuccio, A., Elishmereni, M., & Agur, Z. (2006). Cancer immunotherapy by interleukin-21: potential treatment strategies evaluated in a mathematical model. Cancer Res., 66(14), 7293–7300.

    Article  Google Scholar 

  • Castiglione, F., & Piccoli, B. (2006). Optimal control in a model of dendritic cell transfection cancer immunotherapy. Bull. Math. Biol., 68(2), 255–274.

    Article  MathSciNet  Google Scholar 

  • Cerwenka, A., & Swain, S. L. (1999). TGF-β1: immunosuppressant and viability factor for T lymphocytes. Microbes Infect., 1(15), 1291–1296.

    Article  Google Scholar 

  • Clarke, D. C., & Liu, X. (2008). Decoding the quantitative nature of TGF-beta/Smad signaling. Trends Cell Biol., 18(9), 430–442.

    Article  Google Scholar 

  • Currie, G. (1972). Eighty years of immunotherapy: a review of immunological methods used for the treatment of human cancer. Br. J. Cancer, 141–153.

  • de Pillis, L. G., Radunskaya, A., & Wiseman, C. L. (2005). A validated mathematical model of cell-mediated immune response to tumor growth. Cancer Res., 65(17), 7950–7958.

    Google Scholar 

  • de Pillis, L. G., Gu, W., & Radunskaya, A. E. (2006). Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations. J. Theor. Biol., 238(4), 841–862.

    Article  Google Scholar 

  • Dermime, S., Armstrong, A., Hawkins, R. E., & Stern, P. L. (2002). Cancer vaccines and immunotherapy. Br. Med. Bull., 62, 149–162.

    Article  Google Scholar 

  • Derynck, R., Akhurst, R. J., & Balmain, A. (2001). TGF-β signaling in tumor suppression and cancer progression. Nat. Genet., 29(2), 117–129.

    Article  Google Scholar 

  • d’Onofrio, A. (2005). A general framework for modeling tumor-immune system competition and immunotherapy: mathematical analysis and biomedical inferences. Physica D, Nonlinear Phenom., 208(3–4), 220–235.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Flavell, R. A., Sanjabi, S., Wrzesinski, S. H., & Lixon-Limon, P. (2010). The polarization of immune cells in the tumour environment by TGFβ. Nat. Rev. Immunol., 10(8), 554–567.

    Article  Google Scholar 

  • Kim, P., Lee, P., & Levy, D. (2010). Emergent group dynamics governed by regulatory cells produce a robust primary t cell response. Bull. Math. Biol., 72, 611–644.

    Article  MathSciNet  MATH  Google Scholar 

  • Kim, P. S., Lee, P. P., & Levy, D. (2007). Modeling regulation mechanisms in the immune system. J. Theor. Biol., 246(1), 33–69.

    Article  MathSciNet  Google Scholar 

  • Kirschner, D., & Panetta, J. C. (1998). Modeling immunotherapy of the tumor-immune interaction. J. Math. Biol., 37(3), 235–252.

    Article  MATH  Google Scholar 

  • Kirschner, D., Jackson, T., & Arciero, J. (2003). A mathematical model of tumor-immune evasion and siRNA treatment. Discrete Contin. Dyn. Syst., Ser. B, 4(1), 39–58.

    Article  MathSciNet  Google Scholar 

  • Kogan, Y., Forys, U., Shukron, O., Kronik, N., & Agur, Z. (2010). Cellular immunotherapy for high grade gliomas: mathematical analysis deriving efficacious infusion rates based on patient requirements. SIAM J. Appl. Math., 70(6), 1953–1976.

    Article  MathSciNet  MATH  Google Scholar 

  • Kolev, M. (2005). A mathematical model for single cell cancer immune system dynamics. Math. Comput. Model., 41, 1083–1095.

    Article  MathSciNet  MATH  Google Scholar 

  • Kuznetsov, V., Makalkin, I., Taylor, M., & Perelson, A. (1994). Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. Bull. Math. Biol.

  • Llopiz, D., Dotor, J., Casares, N., Bezunartea, J., Díaz-Valdés, N., Ruiz, M., Aranda, F., Berraondo, P., Prieto, J., Lasarte, J. J., Borrás-Cuesta, F., & Sarobe, P. (2009). Peptide inhibitors of transforming growth factor-β enhance the efficacy of antitumor immunotherapy. Int. J. Cancer, 125(11), 2614–2623.

    Article  Google Scholar 

  • Michelson, S., & Leith, J. (1991). Autocrine and paracrine growth factors in tumor growth: a mathematical model. Bull. Math. Biol., 53(4), 639–656.

    Google Scholar 

  • Murphy, K., Travers, P., Walport, M., et al. (2008). Immunobiology. New York: Garland Science.

    Google Scholar 

  • Paillard, F. (2000). Immunosuppression mediated by tumor cells: a challenge for immunotherapeutic approaches. Hum. Gene Ther., 11(5), 657–658.

    Article  Google Scholar 

  • Reiss, M. (1999). TGF-β and cancer. Microbes Infect., 1(15), 1327–1347.

    Article  Google Scholar 

  • Ribas, A., Butterfield, L. H., Glaspy, J. A., & Economou, J. S. (2003). Current developments in cancer vaccines and cellular immunotherapy. J. Clin. Oncol., 21(12), 2415–2432.

    Article  Google Scholar 

  • Ribba, B., Colin, T., & Schnell, S. (2006). A multiscale mathematical model of cancer, and its use in analyzing irradiation therapies. Theor. Biol. Med. Model., 3, 7.

    Article  Google Scholar 

  • Rosenberg, S. A. (2001). Progress in human tumour immunology and immunotherapy. Nature, 411(6835), 380–384.

    Article  Google Scholar 

  • Rosenberg, S. A., Yang, J. C., & Restifo, N. P. (2004). Cancer immunotherapy: moving beyond current vaccines. Nat. Med., 10(9), 909–915.

    Article  Google Scholar 

  • Sakaguchi, S., Yamaguchi, T., Nomura, T., & Ono, M. (2008). Regulatory T cells and immune tolerance. Cell, 133(5), 775–787.

    Article  Google Scholar 

  • Sakaguchi, S., Miyara, M., Costantino, C. M., & Hafler, D. A. (2010). FOXP3+ regulatory T cells in the human immune system. Nat. Rev. Immunol., 10(7), 490–500.

    Article  Google Scholar 

  • Terabe, M., Ambrosino, E., Takaku, S., O’Konek, J. J., Venzon, D., Lonning, S., McPherson, J. P., & Berzofsky, J. A. (2009). Synergistic enhancement of CD8+ T cell-mediated tumor vaccine efficacy by an anti-transforming growth factor-β monoclonal antibody. Clin. Cancer Res., 15(21), 6560–6569.

    Article  Google Scholar 

  • Wang, S. E., Hinow, P., Bryce, N., Weaver, A. M., Estrada, L., Arteaga, C. L., & Webb, G. F. (2009). A mathematical model quantifies proliferation and motility effects of TGF-β on cancer cells. Comput. Math. Methods Med., 10(1), 71–83.

    Article  MathSciNet  MATH  Google Scholar 

  • Wilson, S. N., Lee, P., & Levy, D. (2010). A mathematical model of the primary T cell response with contraction governed by adaptive regulatory T cells. In K. E. Herold, W. E. Bentley, & J. Vossoughi (Eds.), Proceedings IFMBE (Vol. 32, pp. 209–212). Berlin: Springer.

    Google Scholar 

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Acknowledgements

The authors would like to thank Jim Greene for his helpful comments. This work was supported in part by the joint NSF/NIGMS program under Grant Number DMS-0758374 and in part by Grant Number R01CA130817 from the National Cancer Institute. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Cancer Institute or the National Institutes of Health.

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  1. Department of Mathematics and Center for Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, College Park, MD, 20742, USA

    Shelby Wilson & Doron Levy

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  1. Shelby Wilson
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  2. Doron Levy
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Correspondence to Doron Levy.

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Wilson, S., Levy, D. A Mathematical Model of the Enhancement of Tumor Vaccine Efficacy by Immunotherapy. Bull Math Biol 74, 1485–1500 (2012). https://doi.org/10.1007/s11538-012-9722-4

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