A mathematical model for the immunotherapeutic control of the Th1/Th2 imbalance in melanoma

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June 2013, 18(4): 1017-1030. doi: 10.3934/dcdsb.2013.18.1017

A mathematical model for the immunotherapeutic control of the Th1/Th2 imbalance in melanoma

Yuri Kogan ^1, , Zvia Agur ^1, and Moran Elishmereni ^1,

1.	10 Hate'ena St., P.O.B. 282, Bene Ataroth 60991, Israel, Israel, Israel

Received May 2012 Revised August 2012 Published February 2013

Abstract
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Under a Creative Commons license

Aggressive cancers develop immune suppression mechanisms, allowing them to evade specific immune responses. Patients with active melanoma are polarized towards a T helper (Th) 2-type immune phenotype, which subverts effective anticancer Th1-type cellular immunity. The pro-inflammatory factor, interleukin (IL)-12, can potentially restore Th1 responses in such patients, but still shows limited clinical efficacy and substantial side effects. We developed a model for the Th1/Th2 imbalance in melanoma patients and its regulation via IL-12 treatment. The model focuses on the interactions between the two Th cell types as mediated by their respective key cytokines, interferon (IFN)-$\gamma$ and IL-10. Theoretical and numerical analysis showed a landscape consisting of a single, globally attracting steady state, which is stable under large ranges of relevant parameter values. Our results suggest that in melanoma, the cellular arm of the immune system cannot reverse tumor immunotolerance naturally, and that immunotherapy may be the only way to overturn tumor dominance. We have shown that given a toxicity threshold for IFN$\gamma$, the maximal allowable IL-12 concentration to yield a Th1-polarized state can be estimated. Moreover, our analysis pinpoints the IL-10 secretion rate as a significant factor influencing the Th1:Th2 balance, suggesting its use as a personal immunomarker for prognosis.

Keywords: cancer, interferon-$\gamma$, Interleukin-12, phase plane analysis, interleukin-10, ODE, immune system..

Mathematics Subject Classification: 92B05, 37N2.

Citation: Yuri Kogan, Zvia Agur, Moran Elishmereni. A mathematical model for the immunotherapeutic control of the Th1/Th2 imbalance in melanoma. Discrete and Continuous Dynamical Systems - B, 2013, 18 (4) : 1017-1030. doi: 10.3934/dcdsb.2013.18.1017

References:

[1]	J. M. Kirkwood, A. A. Tarhini, M. C. Panelli, S. J. Moschos, H. M. Zarour, L. H. Butterfield and H. J. Gogas, Next generation of immunotherapy for melanoma, J. Clin. Oncol., 26 (2008), 3445-3455.
[2]	G. P. Dunn, A. T. Bruce, H. Ikeda, L. J. Old and R. D. Schreiber, Cancer immunoediting: From immunosurveillance to tumor escape, Nat. Immunol., 3 (2002), 991-998.
[3]	W. H. Fridman, F. Pages, C. Sautes-Fridman and J. Galon, The immune contexture in human tumours: impact on clinical outcome, Nat. Rev. Cancer, 12 (2012), 298-306.
[4]	A. J. Cochran, R. R. Huang, J. Lee, E. Itakura, S. P. L. Leong and R. Essner, Tumour-induced immune modulation of sentinel lymph nodes, Nat. Rev. Immunol., 6(9) (2006), 659-670.
[5]	L. Lauerova, L. Dusek, M. Simickova, I. Kocak, M. Vagundova, J. Zaloudik and J. Kovarik, Malignant melanoma associates with Th1/Th2 imbalance that coincides with disease progression and immunotherapy response, Neoplasma, 49 (2002), 159-166.
[6]	R. Botella-Estrada, M. Escudero, J. E. O'Connor, E. Nagore, B. Fenollosa, O. Sanmartin, C. Requena and C. Guillen, Cytokine production by peripheral lymphocytes in melanoma, Eur. Cytokine Netw., 16 (2005), 47-55.
[7]	W. K. Nevala, C. M. Vachon, A. A. Leontovich, C. G. Scott, M. A. Thompson and S. N. Markovic, Evidence of systemic Th2-driven chronic inflammation in patients with metastatic melanoma, Clin. Cancer Res., 15 (2009), 1931-1939.
[8]	W. Dummer, J. C. Becker, A. Schwaaf, M. Leverkus, T. Moll and E. B. Brocker, Elevated serum levels of interleukin-10 in patients with metastatic malignant melanoma, Melanoma Res., 5 (1995), 67-68.
[9]	A. M. Lana, D. R. Wen and A. J.Cochran, The morphology, immunophenotype and distribution of paracortical dendritic leucocytes in lymph nodes regional to cutaneous melanoma, Melanoma Res., 11 (2001), 401-410.
[10]	R. Botella-Estrada, F. Dasi, D. Ramos, E. Nagore, M. J. Herrero, J. Gimenez, C. Fuster, O. Sanmartin, C. Guillen and S. Alino, Cytokine expression and dendritic cell density in melanoma sentinel nodes, Melanoma Res., 15 (2005), 99-106.
[11]	J. H. Lee, H. Torisu-Itakara, A. J. Cochran, A. Kadison, Y. Huynh, D. L. Morton and R. Essner, Quantitative analysis of melanoma-induced cytokine-mediated immunosuppression in melanoma sentinel nodes, Clin. Cancer Res., 11 (2005), 107-112.
[12]	T. Tatsumi, L. S. Kierstead, E. Ranieri, L. Gesualdo, F. P. Schena, J. H. Finke, R. M. Bukowski, J. Mueller-Berghaus, J. M. Kirkwood, W. W. Kwok and W. J. Storkus, Disease-associated bias in T helper type 1 (Th1)/Th2 CD4+ T cell responses against MAGE-6 in HLA-DRB10401+ patients with renal cell carcinoma or melanoma, J. Experimental Medicine, 196 (2002), 619-628.
[13]	D. D. Kharkevitch, D. Seito, G. C. Balch, T. Maeda, C. M. Balch and K. Itoh, Characterization of autologous tumor-specific T-helper 2 cells in tumor-infiltrating lymphocytes from a patient with metastatic melanoma, Int. J. Cancer, 58 (1994), 317-323.
[14]	G. Trinchieri, Interleukin-12: A proinflammatory cytokine with immunoregulatory functions that bridge innate resistance and antigen-specific adaptive immunity, Annu. Rev. Immunol., 13 (1995), 251-276.
[15]	M. P. Colombo and G. Trinchieri, Interleukin-12 in anti-tumor immunity and immunotherapy, Cytokine Growth Factor Rev., 13 (2002), 155-168.
[16]	G. Trinchieri, Interleukin-12 and the regulation of innate resistance and adaptive immunity, Nat. Rev. Immunol., 3 (2003), 133-146.
[17]	M. Del Vecchio, E. Bajetta, S. Canova, M. T. Lotze, A. Wesa, G. Parmiani and A. Anichini, Interleukin-12: biological properties and clinical application, Clin. Cancer Res., 13 (2007), 4677-4685.
[18]	M. A. Cheever, Twelve immunotherapy drugs that could cure cancers, Immunol. Rev., 222 (2008), 357-368.
[19]	Z. Agur, From the evolution of toxin resistance to virtual clinical trials: The role of mathematical models in oncology, Future Oncol., 6 (2010), 917-927.
[20]	R. Eftimie, J. L. Bramson and D. J. Earn, Interactions between the immune system and cancer: A brief review of non-spatial mathematical models, Bull. Math. Biol., 73 (2011), 2-32. doi: 10.1007/s11538-010-9526-3.
[21]	D. Kirschner and J. C. Panetta, Modeling immunotherapy of the tumor-immune interaction, J. Math. Biol., 37 (1998), 235-252.
[22]	F. Nani and H. I. Freedman, A mathematical model of cancer treatment by immunotherapy, Math. Biosci., 163 (2000), 159-199. doi: 10.1016/S0025-5564(99)00058-9.
[23]	L. G. de Pillis, W. Gu and A. E. Radunskaya, Mixed immunotherapy and chemotherapy of tumors: Modeling, applications and biological interpretations, J. Theor. Biol., 238 (2006), 841-862. doi: 10.1016/j.jtbi.2005.06.037.
[24]	A. Cappuccio, M. Elishmereni and Z. Agur, Cancer immunotherapy by interleukin-21: Potential treatment strategies evaluated in a mathematical model, Cancer Res, 66 (2006), 7293-7300.
[25]	A. Cappuccio, M. Elishmereni and Z. Agur, Optimization of interleukin-21 immunotherapeutic strategies, J. Theor. Biol., 248 (2007), 259-266. doi: 10.1016/j.jtbi.2007.05.015.
[26]	M. Elishmereni, Y. Kheifetz, H. Sondergaard, R. V. Overgaard and Z. Agur, An integrated disease/pharmacokinetic/pharmacodynamic model suggests improved interleukin-21 regimens validated prospectively for mouse solid cancers, PLoS Comput. Biol., 7 (2011), e1002206.
[27]	N. Kronik, Y. Kogan, V. Vainstein and Z. Agur, Improving alloreactive CTL immunotherapy for malignant gliomas using a simulation model of their interactive dynamics, Cancer Immunol. Immunother., 57 (2008), 425-439.
[28]	N. Kronik, Y. Kogan, M. Elishmereni, K. Halevi-Tobias, S. Vuk-Pavlovic and Z. Agur, Predicting outcomes of prostate cancer immunotherapy by personalized mathematical models, PLoS One, 5 (2010), e15482.
[29]	Y. Kogan, K. Halevi-Tobias, M. Elishmereni, S. Vuk-Pavlovic and Z. Agur, Reconsidering the paradigm of cancer immunotherapy by computationally aided real-time personalization, Cancer Res., 72 (2012), 2218-2227.
[30]	E. Jager, V. H. van der Velden, J. G. te Marvelde, R. B. Walter, Z. Agur and V. Vainstein, Targeted drug delivery by gemtuzumab ozogamicin: mechanism-based mathematical model for treatment strategy improvement and therapy individualization, PLoS One, 6 (2011), e24265.
[31]	Z. Agur and S. Vuk-Pavlovic, Mathematical modeling in immunotherapy of cancer: Personalizing clinical trials, Mol. Ther., 20 (2012), 1-2.
[32]	F. Castiglione and B. Piccoli, Cancer immunotherapy, mathematical modeling and optimal control, J. Theor. Biol., 247 (2007), 723-732. doi: 10.1016/j.jtbi.2007.04.003.
[33]	L. G. de Pillis, A. E. Radunskaya and C. L. Wiseman, A validated mathematical model of cell-mediated immune response to tumor growth, Cancer Res., 65 (2005), 7950-7958.
[34]	M. A. Fishman and A. S. Perelson, Th1/Th2 cross regulation, J. Theor. Biol., 170 (1994), 25-56.
[35]	M. A. Fishman and L. A. Segel, Modeling immunotherapy for allergy, Bull. Math. Biol., 58 (1996), 1099-1121.
[36]	M. A. Fishman and A. S. Perelson, Th1/Th2 differentiation and cross-regulation, Bull. Math. Biol., 61 (1999), 403-436.
[37]	A. Yates, C. Bergmann, J. L. Van Hemmen, J. Stark and R. Callard, Cytokine-modulated regulation of helper T cell populations, J. Theor. Biol., 206 (2000), 539-560.
[38]	C. Bergmann, J. L. Van Hemmen and L. A.Segel, Th1 or Th2: How an appropriate T helper response can be made, Bull. Math. Biol., 63 (2001), 405-430.
[39]	A. Yates, R. Callard and J. Stark, Combining cytokine signalling with T-bet and GATA-3 regulation in Th1 and Th2 differentiation: a model for cellular decision-making, J. Theor. Biol., 231 (2004), 181-196. doi: 10.1016/j.jtbi.2004.06.013.
[40]	R. E. Callard, Decision-making by the immune response, Immunol. Cell Biol., 85 (2007), 300-305.
[41]	F. Gross, G. Metzner and U. Behn, Mathematical modeling of allergy and specific immunotherapy: Th1-Th2-Treg interactions, J. Theor. Biol., 269 (2011), 70-78.
[42]	M. L. Disis, Immunologic biomarkers as correlates of clinical response to cancer immunotherapy, Cancer Immunol. Immunother., 60 (2011), 433-442.
[43]	J. P. Leonard, M. L. Sherman, G. L. Fisher, L. J. Buchanan, G. Larsen, M. B. Atkins, J. A. Sosman, J. P. Dutcher, N. J. Vogelzang and J. L. Ryan, Effects of single-dose interleukin-12 exposure on interleukin-12-associated toxicity and interferon-gamma production, Blood, 90 (1997), 2541-2548.
[44]	J. M. Weiss, J. J. Subleski, J. M. Wigginton, R. H. Wiltrout, Immunotherapy of cancer by IL-12-based cytokine combinations, Expert Opin. Biol. Ther., 7 (2007), 1705-1721.

show all references

References:

[1]	J. M. Kirkwood, A. A. Tarhini, M. C. Panelli, S. J. Moschos, H. M. Zarour, L. H. Butterfield and H. J. Gogas, Next generation of immunotherapy for melanoma, J. Clin. Oncol., 26 (2008), 3445-3455.
[2]	G. P. Dunn, A. T. Bruce, H. Ikeda, L. J. Old and R. D. Schreiber, Cancer immunoediting: From immunosurveillance to tumor escape, Nat. Immunol., 3 (2002), 991-998.
[3]	W. H. Fridman, F. Pages, C. Sautes-Fridman and J. Galon, The immune contexture in human tumours: impact on clinical outcome, Nat. Rev. Cancer, 12 (2012), 298-306.
[4]	A. J. Cochran, R. R. Huang, J. Lee, E. Itakura, S. P. L. Leong and R. Essner, Tumour-induced immune modulation of sentinel lymph nodes, Nat. Rev. Immunol., 6(9) (2006), 659-670.
[5]	L. Lauerova, L. Dusek, M. Simickova, I. Kocak, M. Vagundova, J. Zaloudik and J. Kovarik, Malignant melanoma associates with Th1/Th2 imbalance that coincides with disease progression and immunotherapy response, Neoplasma, 49 (2002), 159-166.
[6]	R. Botella-Estrada, M. Escudero, J. E. O'Connor, E. Nagore, B. Fenollosa, O. Sanmartin, C. Requena and C. Guillen, Cytokine production by peripheral lymphocytes in melanoma, Eur. Cytokine Netw., 16 (2005), 47-55.
[7]	W. K. Nevala, C. M. Vachon, A. A. Leontovich, C. G. Scott, M. A. Thompson and S. N. Markovic, Evidence of systemic Th2-driven chronic inflammation in patients with metastatic melanoma, Clin. Cancer Res., 15 (2009), 1931-1939.
[8]	W. Dummer, J. C. Becker, A. Schwaaf, M. Leverkus, T. Moll and E. B. Brocker, Elevated serum levels of interleukin-10 in patients with metastatic malignant melanoma, Melanoma Res., 5 (1995), 67-68.
[9]	A. M. Lana, D. R. Wen and A. J.Cochran, The morphology, immunophenotype and distribution of paracortical dendritic leucocytes in lymph nodes regional to cutaneous melanoma, Melanoma Res., 11 (2001), 401-410.
[10]	R. Botella-Estrada, F. Dasi, D. Ramos, E. Nagore, M. J. Herrero, J. Gimenez, C. Fuster, O. Sanmartin, C. Guillen and S. Alino, Cytokine expression and dendritic cell density in melanoma sentinel nodes, Melanoma Res., 15 (2005), 99-106.
[11]	J. H. Lee, H. Torisu-Itakara, A. J. Cochran, A. Kadison, Y. Huynh, D. L. Morton and R. Essner, Quantitative analysis of melanoma-induced cytokine-mediated immunosuppression in melanoma sentinel nodes, Clin. Cancer Res., 11 (2005), 107-112.
[12]	T. Tatsumi, L. S. Kierstead, E. Ranieri, L. Gesualdo, F. P. Schena, J. H. Finke, R. M. Bukowski, J. Mueller-Berghaus, J. M. Kirkwood, W. W. Kwok and W. J. Storkus, Disease-associated bias in T helper type 1 (Th1)/Th2 CD4+ T cell responses against MAGE-6 in HLA-DRB10401+ patients with renal cell carcinoma or melanoma, J. Experimental Medicine, 196 (2002), 619-628.
[13]	D. D. Kharkevitch, D. Seito, G. C. Balch, T. Maeda, C. M. Balch and K. Itoh, Characterization of autologous tumor-specific T-helper 2 cells in tumor-infiltrating lymphocytes from a patient with metastatic melanoma, Int. J. Cancer, 58 (1994), 317-323.
[14]	G. Trinchieri, Interleukin-12: A proinflammatory cytokine with immunoregulatory functions that bridge innate resistance and antigen-specific adaptive immunity, Annu. Rev. Immunol., 13 (1995), 251-276.
[15]	M. P. Colombo and G. Trinchieri, Interleukin-12 in anti-tumor immunity and immunotherapy, Cytokine Growth Factor Rev., 13 (2002), 155-168.
[16]	G. Trinchieri, Interleukin-12 and the regulation of innate resistance and adaptive immunity, Nat. Rev. Immunol., 3 (2003), 133-146.
[17]	M. Del Vecchio, E. Bajetta, S. Canova, M. T. Lotze, A. Wesa, G. Parmiani and A. Anichini, Interleukin-12: biological properties and clinical application, Clin. Cancer Res., 13 (2007), 4677-4685.
[18]	M. A. Cheever, Twelve immunotherapy drugs that could cure cancers, Immunol. Rev., 222 (2008), 357-368.
[19]	Z. Agur, From the evolution of toxin resistance to virtual clinical trials: The role of mathematical models in oncology, Future Oncol., 6 (2010), 917-927.
[20]	R. Eftimie, J. L. Bramson and D. J. Earn, Interactions between the immune system and cancer: A brief review of non-spatial mathematical models, Bull. Math. Biol., 73 (2011), 2-32. doi: 10.1007/s11538-010-9526-3.
[21]	D. Kirschner and J. C. Panetta, Modeling immunotherapy of the tumor-immune interaction, J. Math. Biol., 37 (1998), 235-252.
[22]	F. Nani and H. I. Freedman, A mathematical model of cancer treatment by immunotherapy, Math. Biosci., 163 (2000), 159-199. doi: 10.1016/S0025-5564(99)00058-9.
[23]	L. G. de Pillis, W. Gu and A. E. Radunskaya, Mixed immunotherapy and chemotherapy of tumors: Modeling, applications and biological interpretations, J. Theor. Biol., 238 (2006), 841-862. doi: 10.1016/j.jtbi.2005.06.037.
[24]	A. Cappuccio, M. Elishmereni and Z. Agur, Cancer immunotherapy by interleukin-21: Potential treatment strategies evaluated in a mathematical model, Cancer Res, 66 (2006), 7293-7300.
[25]	A. Cappuccio, M. Elishmereni and Z. Agur, Optimization of interleukin-21 immunotherapeutic strategies, J. Theor. Biol., 248 (2007), 259-266. doi: 10.1016/j.jtbi.2007.05.015.
[26]	M. Elishmereni, Y. Kheifetz, H. Sondergaard, R. V. Overgaard and Z. Agur, An integrated disease/pharmacokinetic/pharmacodynamic model suggests improved interleukin-21 regimens validated prospectively for mouse solid cancers, PLoS Comput. Biol., 7 (2011), e1002206.
[27]	N. Kronik, Y. Kogan, V. Vainstein and Z. Agur, Improving alloreactive CTL immunotherapy for malignant gliomas using a simulation model of their interactive dynamics, Cancer Immunol. Immunother., 57 (2008), 425-439.
[28]	N. Kronik, Y. Kogan, M. Elishmereni, K. Halevi-Tobias, S. Vuk-Pavlovic and Z. Agur, Predicting outcomes of prostate cancer immunotherapy by personalized mathematical models, PLoS One, 5 (2010), e15482.
[29]	Y. Kogan, K. Halevi-Tobias, M. Elishmereni, S. Vuk-Pavlovic and Z. Agur, Reconsidering the paradigm of cancer immunotherapy by computationally aided real-time personalization, Cancer Res., 72 (2012), 2218-2227.
[30]	E. Jager, V. H. van der Velden, J. G. te Marvelde, R. B. Walter, Z. Agur and V. Vainstein, Targeted drug delivery by gemtuzumab ozogamicin: mechanism-based mathematical model for treatment strategy improvement and therapy individualization, PLoS One, 6 (2011), e24265.
[31]	Z. Agur and S. Vuk-Pavlovic, Mathematical modeling in immunotherapy of cancer: Personalizing clinical trials, Mol. Ther., 20 (2012), 1-2.
[32]	F. Castiglione and B. Piccoli, Cancer immunotherapy, mathematical modeling and optimal control, J. Theor. Biol., 247 (2007), 723-732. doi: 10.1016/j.jtbi.2007.04.003.
[33]	L. G. de Pillis, A. E. Radunskaya and C. L. Wiseman, A validated mathematical model of cell-mediated immune response to tumor growth, Cancer Res., 65 (2005), 7950-7958.
[34]	M. A. Fishman and A. S. Perelson, Th1/Th2 cross regulation, J. Theor. Biol., 170 (1994), 25-56.
[35]	M. A. Fishman and L. A. Segel, Modeling immunotherapy for allergy, Bull. Math. Biol., 58 (1996), 1099-1121.
[36]	M. A. Fishman and A. S. Perelson, Th1/Th2 differentiation and cross-regulation, Bull. Math. Biol., 61 (1999), 403-436.
[37]	A. Yates, C. Bergmann, J. L. Van Hemmen, J. Stark and R. Callard, Cytokine-modulated regulation of helper T cell populations, J. Theor. Biol., 206 (2000), 539-560.
[38]	C. Bergmann, J. L. Van Hemmen and L. A.Segel, Th1 or Th2: How an appropriate T helper response can be made, Bull. Math. Biol., 63 (2001), 405-430.
[39]	A. Yates, R. Callard and J. Stark, Combining cytokine signalling with T-bet and GATA-3 regulation in Th1 and Th2 differentiation: a model for cellular decision-making, J. Theor. Biol., 231 (2004), 181-196. doi: 10.1016/j.jtbi.2004.06.013.
[40]	R. E. Callard, Decision-making by the immune response, Immunol. Cell Biol., 85 (2007), 300-305.
[41]	F. Gross, G. Metzner and U. Behn, Mathematical modeling of allergy and specific immunotherapy: Th1-Th2-Treg interactions, J. Theor. Biol., 269 (2011), 70-78.
[42]	M. L. Disis, Immunologic biomarkers as correlates of clinical response to cancer immunotherapy, Cancer Immunol. Immunother., 60 (2011), 433-442.
[43]	J. P. Leonard, M. L. Sherman, G. L. Fisher, L. J. Buchanan, G. Larsen, M. B. Atkins, J. A. Sosman, J. P. Dutcher, N. J. Vogelzang and J. L. Ryan, Effects of single-dose interleukin-12 exposure on interleukin-12-associated toxicity and interferon-gamma production, Blood, 90 (1997), 2541-2548.
[44]	J. M. Weiss, J. J. Subleski, J. M. Wigginton, R. H. Wiltrout, Immunotherapy of cancer by IL-12-based cytokine combinations, Expert Opin. Biol. Ther., 7 (2007), 1705-1721.

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