×

A mathematical model of the enhancement of tumor vaccine efficacy by immunotherapy. (English) Zbl 1251.92023

Summary: TGF-\(\beta\) is an immunoregulatory protein that contributes to inadequate antitumor immune responses in cancer patients. Recent experimental data suggest that TGF-\(\beta\) 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-\(\beta\) and vaccine treatments. The mathematical model follows the dynamics of the tumor size, TGF-\(\beta\) 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-\(\beta\) treatment, vaccine treatment, and combined anti-TGF-\(\beta\) 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.

MSC:

92C50 Medical applications (general)
93A30 Mathematical modelling of systems (MSC2010)
65C20 Probabilistic models, generic numerical methods in probability and statistics
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Akhurst, R., & Derynck, R. (2001). TGF-{\(\beta\)} signaling in cancer–a double-edged sword. Trends Cell Biol., 11(11), S44–S51.
[2] 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 .
[3] 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 .
[4] Beyer, M., & Schultze, J. L. (2006). Regulatory T cells in cancer. Blood, 108(3), 804–811. · doi:10.1182/blood-2006-02-002774
[5] Blattman, J. N., & Greenberg, P. D. (2004). Cancer immunotherapy: a treatment for the masses. Science, 305(5681), 200–205. · doi:10.1126/science.1100369
[6] 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. · doi:10.1084/jem.20001021
[7] Byrne, H., & Gourley, S. (1997). The role of growth factors in avascular tumour growth. Math. Comput. Model., 26(4), 35–55. · Zbl 0898.92018 · doi:10.1016/S0895-7177(97)00143-X
[8] 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. · doi:10.1158/0008-5472.CAN-06-0241
[9] Castiglione, F., & Piccoli, B. (2006). Optimal control in a model of dendritic cell transfection cancer immunotherapy. Bull. Math. Biol., 68(2), 255–274. · Zbl 1334.92191 · doi:10.1007/s11538-005-9014-3
[10] Cerwenka, A., & Swain, S. L. (1999). TGF-{\(\beta\)}1: immunosuppressant and viability factor for T lymphocytes. Microbes Infect., 1(15), 1291–1296. · doi:10.1016/S1286-4579(99)00255-5
[11] Clarke, D. C., & Liu, X. (2008). Decoding the quantitative nature of TGF-beta/Smad signaling. Trends Cell Biol., 18(9), 430–442. · doi:10.1016/j.tcb.2008.06.006
[12] Currie, G. (1972). Eighty years of immunotherapy: a review of immunological methods used for the treatment of human cancer. Br. J. Cancer, 141–153.
[13] 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.
[14] 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. · doi:10.1016/j.jtbi.2005.06.037
[15] Dermime, S., Armstrong, A., Hawkins, R. E., & Stern, P. L. (2002). Cancer vaccines and immunotherapy. Br. Med. Bull., 62, 149–162. · doi:10.1093/bmb/62.1.149
[16] Derynck, R., Akhurst, R. J., & Balmain, A. (2001). TGF-{\(\beta\)} signaling in tumor suppression and cancer progression. Nat. Genet., 29(2), 117–129. · doi:10.1038/ng1001-117
[17] 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. · Zbl 1087.34028 · doi:10.1016/j.physd.2005.06.032
[18] 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. · Zbl 1209.92028 · doi:10.1007/s11538-010-9526-3
[19] Flavell, R. A., Sanjabi, S., Wrzesinski, S. H., & Lixon-Limon, P. (2010). The polarization of immune cells in the tumour environment by TGF{\(\beta\)}. Nat. Rev. Immunol., 10(8), 554–567. · doi:10.1038/nri2808
[20] 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. · Zbl 1189.92013 · doi:10.1007/s11538-009-9463-1
[21] Kim, P. S., Lee, P. P., & Levy, D. (2007). Modeling regulation mechanisms in the immune system. J. Theor. Biol., 246(1), 33–69. · doi:10.1016/j.jtbi.2006.12.012
[22] Kirschner, D., & Panetta, J. C. (1998). Modeling immunotherapy of the tumor-immune interaction. J. Math. Biol., 37(3), 235–252. · Zbl 0902.92012 · doi:10.1007/s002850050127
[23] 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. · Zbl 1083.37531 · doi:10.3934/dcdsb.2004.4.39
[24] 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. · Zbl 1211.37109 · doi:10.1137/08073740X
[25] Kolev, M. (2005). A mathematical model for single cell cancer immune system dynamics. Math. Comput. Model., 41, 1083–1095. · Zbl 1085.92019 · doi:10.1016/j.mcm.2005.05.004
[26] Kuznetsov, V., Makalkin, I., Taylor, M., & Perelson, A. (1994). Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. Bull. Math. Biol. · Zbl 0789.92019
[27] 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-{\(\beta\)} enhance the efficacy of antitumor immunotherapy. Int. J. Cancer, 125(11), 2614–2623. · doi:10.1002/ijc.24656
[28] Michelson, S., & Leith, J. (1991). Autocrine and paracrine growth factors in tumor growth: a mathematical model. Bull. Math. Biol., 53(4), 639–656.
[29] Murphy, K., Travers, P., Walport, M., et al. (2008). Immunobiology. New York: Garland Science.
[30] Paillard, F. (2000). Immunosuppression mediated by tumor cells: a challenge for immunotherapeutic approaches. Hum. Gene Ther., 11(5), 657–658. · doi:10.1089/10430340050015554
[31] Reiss, M. (1999). TGF-{\(\beta\)} and cancer. Microbes Infect., 1(15), 1327–1347. · doi:10.1016/S1286-4579(99)00251-8
[32] 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. · doi:10.1200/JCO.2003.06.041
[33] 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. · doi:10.1186/1742-4682-3-7
[34] Rosenberg, S. A. (2001). Progress in human tumour immunology and immunotherapy. Nature, 411(6835), 380–384. · doi:10.1038/35077246
[35] Rosenberg, S. A., Yang, J. C., & Restifo, N. P. (2004). Cancer immunotherapy: moving beyond current vaccines. Nat. Med., 10(9), 909–915. · doi:10.1038/nm1100
[36] Sakaguchi, S., Yamaguchi, T., Nomura, T., & Ono, M. (2008). Regulatory T cells and immune tolerance. Cell, 133(5), 775–787. · doi:10.1016/j.cell.2008.05.009
[37] 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. · doi:10.1038/nri2785
[38] 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-{\(\beta\)} monoclonal antibody. Clin. Cancer Res., 15(21), 6560–6569. · doi:10.1158/1078-0432.CCR-09-1066
[39] 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-{\(\beta\)} on cancer cells. Comput. Math. Methods Med., 10(1), 71–83. · Zbl 1317.92027 · doi:10.1080/17486700802171993
[40] 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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.