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Mathematical modelling of the inhibitory role of regulatory T cells in tumor immune response. (English) Zbl 1445.92145
Summary: The immune system against tumors acts through a complex dynamical process showing a dual role. On the one hand, the immune system can activate some immune cells to kill tumor cells (TCs), such as cytotoxic T lymphocytes (CTLs) and natural killer cells (NKs), but on the other hand, more evidence shows that some immune cells can help tumor escape, such as regulatory T cells (Tregs). In this paper, we propose a tumor immune interaction model based on Tregs-mediated tumor immune escape mechanism. When helper T cells’ (HTCs) stimulation rate by the presence of identified tumor antigens is below critical value, the coexistence (tumor and immune) equilibrium is always stable in its existence region. When HTCs stimulation rate is higher than the critical value, the inhibition rate of effector cells (ECs) by Tregs can destabilize the coexistence equilibrium and cause Hopf bifurcations and produce a limit cycle. This model shows that Tregs might play a crucial role in triggering the tumor immune escape. Furthermore, we introduce the adoptive cellular immunotherapy (ACI) and monoclonal antibody immunotherapy (MAI) as the treatment to boost the immune system to fight against tumors. The numerical results show that ACI can control TCs more, while MAI can delay the inhibitory effect of Tregs on ECs. The result also shows that the combination of both immunotherapies can control TCs and reduce the inhibitory effect of Tregs better than a single immunotherapy can control.
MSC:
92C50 Medical applications (general)
92C37 Cell biology
Software:
MATCONT
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[1] Boyle, P., Measuring progress against cancer in Europe: has the 15% decline targeted for 2000 come about?, Annals of Oncology, 14, 1312-1325 (2003)
[2] Boon, T.; Van der Bruggen, P., Human tumor antigens recognized by T lymphocytes, The Journal of Experimental Medicine, 183, 3, 725-729 (1996)
[3] De Visser, K. E.; Eichten, A.; Coussens, L. M., Paradoxical roles of the immune system during cancer development, Nature Reviews Cancer, 6, 1, 24-37 (2006)
[4] Dong, Y.; Miyazaki, R.; Miyazaki, R.; Takeuchi, Y., Mathematical modeling on helper T cells in a tumor immune system, Discrete & Continuous Dynamical Systems-B, 19, 1, 55-72 (2014) · Zbl 1309.92043
[5] Talkington, A.; Dantoin, C.; Durrett, R., Ordinary differential equation models for adoptive immunotherapy, Bulletin of Mathematical Biology, 9, 1-25 (2017)
[6] Lai, Y.-P.; Jeng, C.-J.; Chen, S.-C., The roles of CD4+T cells in tumor immunity, ISRN Immunology, 2011, 1-6 (2011)
[7] Maj, T.; Wang, W.; Crespo, J., Oxidative stress controls regulatory T cell apoptosis and suppressor activity and PD-L1-blockade resistance in tumor, Nature Immunology, 18, 12, 1332-1341 (2017)
[8] Wilson, S.; Levy, D., A mathematical model of the enhancement of tumor vaccine efficacy by immunotherapy, Bulletin of Mathematical Biology, 74, 7, 1485-1500 (2012) · Zbl 1251.92023
[9] Albert, A.; Freedman, M.; Perelson, A. S., Tumors and the immune system: the effects of a tumor growth modulator, Mathematical Biosciences, 50, 1-2, 25-58 (1980) · Zbl 0439.92004
[10] d’Onofrio, A., A general framework for modeling tumor-immune system competition and immunotherapy: mathematical analysis and biomedical inferences, Physica D, 208, 220-235 (2005) · Zbl 1087.34028
[11] Kirschner, D.; Panetta, J. C., Modeling immunotherapy of the tumor - immune interaction, Journal of Mathematical Biology, 37, 3, 235-252 (1998) · Zbl 0902.92012
[12] Amarnath, S.; Mangus, C. W.; Wang, J. C. M., The PDL1-PD1 Axis converts human TH1 cells into regulatory T cells, Science Translational Medicine, 3, 111, 111-120 (2011)
[13] Spain, L.; Diem, S.; Larkin, J., Management of toxicities of immune checkpoint inhibitors, Cancer Treatment Reviews, 44, 51-60 (2016)
[14] Peggs, K. S.; Quezada, S. A.; Korman, A. J.; Allison, J. P., Principles and use of anti-CTLA4 antibody in human cancer immunotherapy, Current Opinion in Immunology, 18, 2, 206-213 (2006)
[15] Hurwitz, A. A.; Foster, B. A.; Kwon, E. D., Combination immunotherapy of primary prostate cancer in a transgenic mouse model using CTLA-4 blockade, Cancer Research, 60, 9, 2444-2448 (2000)
[16] Egen, J. G.; Kuhns, M. S.; Allison, J. P., CTLA-4: new insights into its biological function and use in tumor immunotherapy, Nature Immunology, 3, 7, 611-618 (2002)
[17] Takahashi, T.; Tagami, T.; Yamazaki, S., Immunologic self-tolerance maintained by Cd25+Cd4+Regulatory T cells constitutively expressing cytotoxic T lymphocyte-associated antigen 4, The Journal of Experimental Medicine, 192, 2, 303-310 (2000)
[18] Ma, Y.-F.; Chen, C.; Li, D., Targeting of interleukin (IL)-17A inhibits PDL1 expression in tumor cells and induces anticancer immunity in an estrogen receptor-negative murine model of breast cancer, Oncotarget, 8, 5, 7614-7624 (2016)
[19] Jordan, K. R.; Borges, V.; Mccarter, M. D., Abstract 1671: immunosuppressive myeloid-derived suppressor cells expressing PDL1 are increased in human melanoma tumor tissue, Cancer Research, 74, 1671 (2014)
[20] Baldelli, E.; Calvert, V.; Hodge, K. A., Abstract 5656: quantitative measurement of PDL1 expression across tumor types using laser capture microdissection and reverse phase protein microarray, Cancer Research, 77, 5656 (2017)
[21] West, E. E.; Jin, H.-T.; Rasheed, A.-U., PD-L1 blockade synergizes with IL-2 therapy in reinvigorating exhausted T cells, Journal of Clinical Investigation, 123, 6, 2604-2615 (2013)
[22] Francisco, L. M.; Sage, P. T.; Sharpe, A. H., The PD-1 pathway in tolerance and autoimmunity, Immunological Reviews, 236, 1, 219-242 (2010)
[23] Brady, B., Dramatic survival benefit with nivolumab in melanoma, Cancer Research, 6, OF7 (2016)
[24] Kazandjian, D.; Suzman, D. L.; Blumenthal, G., FDA approval summary: nivolumab for the treatment of metastatic non‐small cell lung cancer with progression on or after platinum‐based chemotherapy, The Oncologist, 21, 5, 634-642 (2016)
[25] Voena, C.; Chiarle, R., Advances in cancer immunology and caner immuntherapy, Cancer Research, 21, 125-133 (2016)
[26] Stepanova, N. V., Course of the immune reaction during the development of a malignant tumour, Cancer Research, 24, 917-923 (1979)
[27] Kuznetsov, V. A.; Makalkin, I. A.; Taylor, M. A.; Perelson, A. S., Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis, Bulletin of Mathematical Biology, 56, 2, 295-321 (1994) · Zbl 0789.92019
[28] Sotolongo-Costa, O.; Morales Molina, L.; Rodríguez Perez, D.; Antoranz, J. C.; Chacón Reyes, M., Behavior of tumors under nonstationary therapy, Physica D: Nonlinear Phenomena, 178, 3-4, 242-253 (2003) · Zbl 1011.92028
[29] Galach, M., Dynamics of the tumor-immune system competition-the effect of time delay, International Journal of Applied Mathematics and Computer Science, 13, 395-406 (2003) · Zbl 1035.92019
[30] de Pillis, L. G.; Gu, W.; Radunskaya, A. E., Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations, Journal of Theoretical Biology, 238, 4, 841-862 (2006)
[31] Bunimovich-Mendrazitsky, S.; Byrne, H.; Stone, L., Mathematical model of pulsed immunotherapy for superficial bladder cancer, Bulletin of Mathematical Biology, 70, 7, 2055-2076 (2008) · Zbl 1147.92013
[32] Radunskaya, A.; Kim, R.; Woods, T., Mathematical modeling of tumor immune interactions: a closer look at the role of a PD-L1 inhibitor in cancer immunotherapy, Spora: A Journal of Biomathematics, 4, 25-41 (2018)
[33] Shu, Y.; Huang, J.; Dong, Y.; Takeuchi, Y., Mathematical modeling and bifurcation analysis of pro- and anti-tumor macrophages, Applied Mathematical Modelling, 88, 758-773 (2020)
[34] Piretto, E.; Delitala, M.; Ferraro, M., How combination therapies shape drug resistance in heterogeneous tumoral populations, Letters in Biomathematics, 5, 2, S160-S177 (2018)
[35] Dritschel, H.; Waters, S.; Roller, A.; Byrne, H., A mathematical model of cytotoxic and helper T cell interactions in a tumour microenvironment, Letters in Biomathematics, 5, 2, S36-S68 (2018)
[36] Dong, Y.; Huang, G.; Miyazaki, R.; Takeuchi, Y., Dynamics in a tumor immune system with time delays, Applied Mathematics and Computation, 252, 99-113 (2015) · Zbl 1338.92046
[37] Yu, M.; Dong, Y.; Takeuchi, Y., Dual role of delay effects in a tumour-immune system, Journal of Biological Dynamics, 11, 2, 334-347 (2017)
[38] Yu, M.; Huang, G.; Dong, Y.; Takeuchi, Y., Complicated dynamics of tumor-immune system interaction model with distributed time delay, Discrete & Continuous Dynamical Systems-B, 25, 7, 2391-2406 (2020) · Zbl 1443.92083
[39] Caravagna, G.; d’Onofrio, A.; Milazzo, P.; Barbuti, R., Tumour suppression by immune system through stochastic oscillations, Journal of Theoretical Biology, 265, 3, 336-345 (2010) · Zbl 1460.92047
[40] George, J. T.; Levine, H., Stochastic modeling of tumor progression and immune evasion, Journal of Theoretical Biology, 458, 148-155 (2018) · Zbl 1406.92297
[41] Ren, H.-P.; Yang, Y.; Baptista, M. S.; Grebogi, C., Tumour chemotherapy strategy based on impulse control theory, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 375, 2088, 20160221 (2017) · Zbl 1404.92103
[42] Deng, Y.; Liu, M., Analysis of a stochastic tumor-immune model with regime switching and impulsive perturbations, Applied Mathematical Modelling, 78, 482-504 (2020) · Zbl 07193089
[43] Mahlbacher, G. E.; Reihmer, K. C.; Frieboes, H. B., Mathematical modeling of tumor-immune cell interactions, Journal of Theoretical Biology, 469, 47-60 (2019) · Zbl 1411.92081
[44] Hale, J. K., Theory of Functional Differential Equations (1977), New York, NY, USA: Springer, New York, NY, USA
[45] Dhooge, A.; Govaerts, W.; Kuznetsov, Y. A., Matcont, ACM SIGSAM Bulletin, 38, 1, 21-22 (2004) · Zbl 1086.65538
[46] Facciabene, A.; Motz, G. T.; Coukos, G., T-regulatory cells: key players in tumor immune escape and angiogenesis, Cancer Research, 72, 9, 2162-2171 (2012)
[47] Shitara, K.; Nishikawa, H., Regulatory T cells: a potential target in cancer immunotherapy, Annals of the New York Academy of Sciences, 1417, 1, 104-115 (2018)
[48] Zhang, T.; Wang, J.; Li, Y.; Jiang, Z.; Han, X., Dynamics analysis of a delayed virus model with two different transmission methods and treatments, Advances in Difference Equations, 1, 2020 (2020)
[49] Zhang, H.; Zhang, T., The stationary distribution of a microorganism flocculation model with stochastic perturbation, Applied Mathematics Letters, 103, 106217 (2020) · Zbl 1441.60041
[50] Zhang, T.; Gao, N.; Gao, N.; Wang, T.; Liu, H.; Jiang, Z., Global dynamics of a model for treating microorganisms in sewage by periodically adding microbial flocculants, Mathematical Biosciences and Engineering, 17, 1, 179-201 (2020)
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