Mathematical modelling of the spatio-temporal response of cytotoxic T-lymphocytes to a solid tumour

Mathematical Medicine and Biology

Volumn 21, Issue 1, 2004, Pages 1-34

  Matzavinos, Anastasios ^a   Chaplain, Mark A J ^a   Kuznetsov, Vladimir A ^b  

^a UNIVERSITY OF DUNDEE   (United Kingdom)

^b EUNICE KENNEDY SHRIVER NATIONAL INSTITUTE OF CHILD HEALTH AND HUMAN DEVELOPMENT   (United States)

Author keywords

Chemokines; Immune response; Solid tumour growth; Spatiotemporal heterogeneity; T lymhocytes

Indexed keywords

BIFURCATION (MATHEMATICS); BIOCHEMISTRY; CELLS; CYTOLOGY; DISEASES; IMMUNE SYSTEM; LINEAR STABILITY ANALYSIS; NONLINEAR EQUATIONS; NUMERICAL MODELS; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PEPTIDES; VACCINES;

CHEMOKINES; CYTOTOXIC; IMMUNE CELLS; IMMUNE RESPONSE; SOLID TUMOR GROWTH; SOLID TUMORS; SPATIOTEMPORAL HETEROGENEITIES; T-LYMHOCYTES; TUMOR GROWTH; TUMOUR CELLS;

TUMORS;

CHEMOKINE;

ANGIOGENESIS; CARCINOGENESIS; CELL GROWTH; CELL INTERACTION; CELLULAR DISTRIBUTION; CHEMOTAXIS; CYTOTOXIC T LYMPHOCYTE; DORMANCY; GEOMETRY; HUMAN; IMMUNE RESPONSE; IMMUNE SYSTEM; LYMPHOCYTE ACTIVATION; LYMPHOCYTE MIGRATION; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; REVIEW; SOLID TUMOR; TUMOR ASSOCIATED LEUKOCYTE; TUMOR GROWTH;

EID: 1642348723     PISSN: 14778599     EISSN: None     Source Type: Journal    
DOI: 10.1093/imammb/21.1.1     Document Type: Review

References (89)

1. Abbas, A. K., Lichtman, A. H. & Pober, J. S. (2000) Cellular and Molecular Immunology 4th edn. Philadelphia, PA: Saunders.
2. Adam, J. A. (1993) The dynamics of growth-factor-modified immune response to cancer growth: One dimensional models. Math. Comput. Modelling, 17, 83-106.
3. Adam, J. A. & Bellomo, N. (eds) (1997) A Survey of Models for Tumor-Immune System Dynamics. Boston: Birkhaüser.
4. Alsabti, A. (1978) Tumour dormant state. Tumour Res., 13, 1-13.
5. Bar-Eli, M. (1999) Role of interleukin-8 in tumor growth and metastasis of human melanoma. Pathobiology, 67, 12-18.
6. Berezhnaya, N. M., Yakimovich, L. V., Semenova Kobzar, R. A., Lyulkin, V. D. & Papivets, A. Yu. (1986) The effect of interleukin-2 on proliferation of explants of malignant soft-tissue tumours in diffusion chambers. Exp. Oncol., 8, 39-42.
7. Bohman, Y. V. (1976) Metastases of Corpus Uterus Cancer. Leningrad: Medicine.
8. Breslow, N., Chan, C. W., Dhom, G., Drury, R. A., Franks, L. M., Gellei, B., Lee, Y. S., Lundberg, S., Sparke, B., Sternby, N. H. & Tulinius, H. (1977) Latent carcinoma of prostate at autopsy in seven areas. Int. J. Cancer, 20, 680-688.
9. Brocker, E. B., Zwaldo, G., Holzmann, B., Macher, E. & Sorg, C. (1988) Inflammatory cell infiltrates in human melanoma at different stages of tumour progression. Int. J. Cancer, 41, 562-567.
10. Byrne, H. M. & Owen, M. R. (2001) Use of mathematical models to simulate and predict macrophage activity in diseased tissues. The Macrophage, 2nd edn. (B. Burke & C. E. Lewis, eds). Oxford: Oxford University Press.
11. Cairns, C. M., Gordon, J. R., Li, F., Baca-Estrada, M. E., Moyana, T. & Xiang, J. (2001) Lymphotaktin expression by engineered myeloma cells drives tumor regression: Mediation by CD4+ and CD8+ T cells and neutrophils expressing XCR1 receptor. J. Immunol., 167, 57-65.
12. Chaplain, M. A. J., Kuznetsov, V. A., James, Z. H. & Stepanova, L. A. (1998) Spatio-temporal dynamics of the immune system response to cancer. Mathematical Models in Medical and Health Sciences. (M. A. Horn, G. Simonett & G. Webb, eds). Nashville, TN: Vanderbilt University Press, pp. 1-20.
13. Clark, W. H. (1991) Tumour progression and the nature of cancer. Br. J. Cancer, 631-644.
14. Clark, W. H., Elder, D. E. & Vanhorn, M. (1986) The biologic forms of malignant melanoma. Human Path., 17, 443-450.
15. Cowan, D. S., Hicks, K. O. & Wilson, W. R. (1996) Multicellular membranes as an in vitro model for extravascular diffusion in tumours. Br. J. Cancer Suppl., 27, S28-S31.
16. Cross, M. C. & Hohenberg, P. C. (1993) Pattern formation outside equilibrium. Rev. Mod. Phys., 65, 851-1112.
17. Demicheli, R. (2001) Tumour dormancy: Findings and hypotheses from clinical research on breast cancer. Semin. Cancer Biol., 11, 297-305.
18. Deweger, R. A., Wilbrink, B., Moberts, R. M. P., Mans, D., Oskam, R. & den Otten, W. (1987) Immune reactivity in SL2 lymphoma-bearing mice compared with SL2-immunized mice. Cancer Immun. Immunotherapy, 24, 1191-1192.
19. Drasdo, D. & Höhme, S. (2003) Individual-based approaches to birth and death in avascular tumours. Math. Comput. Modelling, 37, 1163-1175.
20. Durand, R. E. & Sutherland, R. M. (1984) Growth and cellular characteristics of multicell spheroids. Recent Results in Cancer Research, 95, 24-49.
21. Ermentrout, G. B. (2002) Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students Software, Environments, and Tools, 14. SIAM.
22. Ermentrout, G. B., Chen, X. & Chen, Z. (1997) Transition fronts and localized structures in bistable reaction-diffusion systems. Physica D, 108, 147-167.
23. Folkman, J. (1985) How is blood-vessel growth regulated in normal and neoplastic tissue. Proc. Am. Assoc. Cancer Res., 26, 384-385.
24. Forni, G., Parmiani, G., Guarini, A. & Foa, R. (1994) Gene transfer in tumour therapy. Annals Oncol., 5, 789-794.
25. Friedl, P., Noble, P. B. & Zanker, K. S. (1995) T-Lymphocyte locomotion in a 3-dimensional collagen matrix - expression and function of cell-adhesion molecules. J. Immunol., 154, 4973-4985.
26. Gatenby, R. A. (1995) Models of tumor-host intearcation as competing populations: Implications for tumor biology and treatment. J. Theor. Biol., 176, 447-455.
27. Gatenby, R. A. (1996) Application of competition theory to tumour growth: Implications for tumour biology and treatment. Eur. J. Cancer, 32A, 722-726.
28. Aguirre Ghiso, J. A. (2002) Inhibition of FAK signaling activated by urokinase receptor induces dormancy in human carcinoma cells in vivo. Oncogene, 21, 2513-2524.
29. Giovarelli, M., Cappello, P., Forni, G., Salcedo, T., Moore, P. A., LeFleur, D. W., Nardelli, B., Carlo, E. D., Lollini, P. L., Ruben, S., Ullrich, S., Garotta, G. & Musiani, P. (2000) Tumor rejection and immune memory elicited by locally released LEC chemokine are associated with an impressive recruitment of APCs, lymphocytes and granulocytes. J. Immunol., 164, 3200-3206.
30. Holmberg, L. & Baum, M. (1996) Work on your theories!. Nature Med., 2, 844-846.
31. Ioannides, C. G. & Whiteside, T. L. (1993) T-cell recognition of human tumours - implications for molecular immunotherapy of cancer. Clin. Immunol. Immunopath., 66, 91-106.
32. Jaaskelainen, J., Maenpaa, A., Patarroyo, M., Gahmberg, C. G., Somersalo, K., Tarkkanen, J., Kallio, M. & Timonen, T. (1992) Migration of recombinant IL-2-activated T-cells and natural killer cells in the intercellular space of human H-2 glioma spheroids in vitro - a study on adhesion molecules involved. J. Immunol., 149, 260-268.
33. Kawakami, Y., Nishimura, M. I., Restifo, N. P., Topalian, S. L., O'Neil, B. H., Shilyansky, J., Yannelli, J. R. & Rosenberg, S. A. (1993) T-cell recognition of human-melanoma antigens. J. Immunotherapy, 14, 88-93.
34. Kelly, C. E., Leek, R. D., Byrne, H. M., Cox, S. M., Harris, A. L. & Lewis, C. E. (2002) Modelling macrophage infiltration into avascular tumours. J. Theor. Med., 4, 21-38.
35. Kobayashi, R., Ohta, T. & Hayase, Y. (1995) Self-organized pulse generator. Physica D, 84, 162-170.
36. Kuznetsov, V. A. (1979) Dynamics of cellular immune anti-tumor reactions. I. Synthesis of a multi-level model. Mathematical Methods in the Theory of Systems. (V. D. Fedorov, ed.). Frunze: Kyrghyz State University, pp. 57-71 (In Russian)
37. Kuznetsov, V. A. (1991) A mathematical model for the interaction between cytotoxic lymphocytes and tumor cells. Analysis of the growth, stabilization and regression of the B cell lymphoma in mice chimeric with respect to the major histocompatibility complex. Biomed. Sci., 2, 465-476.
38. Kuznetsov, V. A. (1992) Dynamics of Immune Processes During Tumor Growth. Moscow: Nauka, (In Russian)
39. Kuznetsov, V. A. & Knott, G. D. (2001) Modeling tumor regrowth and immunotherapy. Math. Comput. Modelling, 33, 1275-1287.
40. Kuznetsov, V. A., Makalkin, I. A., Taylor, M. A. & Perelson, A. S. (1994) Nonlinear dynamics of immunogenic tumours: Parameter estimation and global bifurcation analysis. Bull. Math. Biol., 56, 295-321.
41. Kuznetsov, V. A. & Puri, R. K. (1999) Kinetic analysis of the high affinity forms of interleukin (IL)-13 receptors: Suppression of IL-13 binding by IL-2 receptor γ chain. Biophys. J., 77, 154-172.
42. Kuznetsov, V. A. & Stepanova, L. A. (1992) Space-time waves and dissipative structures in a model of growth of tumours infiltrated by immune lymphocytes. Lecture Notes of the ICB Seminars Biosystems. (G. I. Marchuk & A. Werynski, eds). Warsaw, Poland: International Center for Biocybernetics, pp. 68-111.
43. Kuznetsov, V. A., Zhivoglyadov, V. P. & Stepanova, L. A. (1993) Kinetic approach and estimation of the parameters of cellular interaction between the immune system and a tumour. Arch. Immunol. Therap. Exp., 41, 21-32.
44. Kwok, C. S., Cole, S. E. & Liao, S. K. (1988) Uptake kinetics of monoclonal antibodies by human malignant melanoma multicell spheroids. Cancer Res., 48, 1856-1863.
45. Kyle, A. H., Chan, C. T. & Minchinton, A. I. (1999) Characterization of three-dimensional tissue cultures using electrical impedance spectroscopy. Biophys. J., 76, 2640-2648.
46. Lee, J., Moran, J. P., Fenton, B. M., Koch, C. J., Frelinger, J. G., Keng, P. C. & Lord, E. M. (2000a) Alteration of tumour response to radiation by interleukin-2 gene transfer. Br. J. Cancer, 82, 937-944.
47. Lee, L. F., Hellendall, R. P., Wang, Y., Haskilla, J. S., Mukaida, N., Matsushima, K. & Ting, J. P. (2000b) IL-8 reduces tumorigenicity of human ovarian cancer in vivo due to neutrophil infiltration. J. Immunol., 164, 2769-2775.
48. Lefever, R. & Erneux, T. (1984) On the growth of cellular tissues under constant and fluctuating environmental conditions. Nonlinear Electrodynamics in Biological Systems. (W. Ross & A. Lawrence, eds). New York: Plenum, pp. 287-305.
49. Loeffler, D., Heppner, G. & Lord, E. (1988) Influence of hypoxia on T lymphocytes in solid tumours. Proc. Am. Assoc. Cancer Res., 29, 378.
50. Loeffler, D. & Ratner, S. (1989) In vivo localization of lymphocytes labeled with low concentrations of HOECHST-33342. J. Immunol. Meth., 119, 95-101.
51. Lord, E. M. & Burkhardt, G. (1984) Assessment of in situ host immunity to syngeneic tumours utilizing the multicellular spheroid model. Cell. Immunol., 85, 340-350.
52. Lord, E. M. & Nardella, G. (1980) The multicellular tumour spheroid model. 2. characterization of the preliminary allograft response in unsensitized mice. Transplantation, 29, 119-124.
53. MacSween, R. N. M. & Whaley, K. (eds) (1992) Muir's Textbook of Pathology 13th edn. London: Arnold.
54. Marušić, M., Bajzer, Ž., Vuk-Pavlović, S. & Freyer, J. P. (1994a) Analysis of the growth of multicellular tumour spheroids by mathematical models. Cell Prolif., 27, 73-94.
55. Marušić, M., Bajzer, Ž., Vuk-Pavlović, S. & Freyer, J. P. (1994b) Tumour growth in vivo and as multicellular spheroids compared by mathematical models. Bull. Math. Biol., 56, 617-631.
56. Merkin, J. H. & Sadiq, M. A. (1996) The propagation of travelling waves in an open cubic autocatalytic chemical system. IMA J. Appl. Math., 57, 273-309.
57. Murphy, C. & Newsholme, P. (1999) Macrophage-mediated lysis of a beta-cell line, tumour necrosis factor-alpha release from bacillus Calmette-Guerin (BCG)-activated murine macrophges and interleukin-8 release from human monocytes are dependent on extracellular glutamine concentration and glutamine metabolism. Clin. Sci., 96, 89-97.
58. Naumov, G. N., MacDonald, I. C., Weinmeister, P. M., Kerkvliet, N., Nadkarni, K. V., Wilson, S. M., Morris, V. L., Groom, A. C. & Chambers, A. F. (2002) Persistence of solitary mammary carcinoma cells in a secondary site: A possible contributor to dormancy. Cancer Res., 62, 2162-2168.
59. Nesvetov, A. M. & Zhdanov, A. S. (1981) Relationship of the morphology of the immune response and the histological structure of tumours in stomach cancer patients. Voprosy Onkologii, 27, 25-31.
60. Nomiyama, H., Hieshima, K., Nakayama, T., Sakaguchi, T., Fujisawa, R., Tanase, S., Nishiura, H., Matsuno, K., Takamori, H., Tabira, Y., Yamamoto, T., Miura, R. & Yoshie, O. (2001) Human CC chemokine liver-expressed chemokine/CCL16 is a functional ligand for CCR1, CCR2 and CCR5, and constitutively expressed by hepatocytes. Int. Immunol., 13, 1021-1029.
61. Nowak, M. A. & May, R. M. (2000) Virus Dynamics: Mathematical Principles of Immunology and Virology. Oxford: Oxford University Press.
62. O'Connell, J., Bennett, M. W., O'Sullivan, G. C., Collins, J. K. & Shanahan, F. (1999) The Fas counterattack: Cancer as a site of immune privilege. Immunol. Today, 20, 46-50.
63. Owen, M. R. & Sherratt, J. A. (1997) Pattern formation and spatio-temporal irregularity in a model for macrophage-tumour interactions. J. Theor. Biol., 189, 63-80.
64. Owen, M. R. & Sherratt, J. A. (1998) Modelling the macrophage invasion of tumours: Effects on growth and composition. IMA J. Math. Appl. Med. Biol., 15, 165-185.
65. Owen, M. R. & Sherratt, J. A. (1999) Mathematical modelling of macrophage dynamics in tumours. Math. Models Meth. Appl. Sci., 9, 513-539.
66. Prehn, R. T. (1994) Stimulatory effects of immune reactions upon the growths of untransplanted tumours. Cancer Res., 54, 908-914.
67. Prigogine, I. & Lefever, R. (1980) Stability problems in cancer growth and nucleation. Comp. Biochem. Physiol., 67, 389-393.
68. Puri, R. K. & Siegel, J. P. (1993) Interleukin-4 and cancer therapy. Cancer Invest., 11, 473-486.
69. Ratner, S. & Heppner, G. H. (1986) Mechanisms of lymphocyte traffic in neoplasia. Anticancer Res., 6, 475-482.
70. Reisenberger, K., Egarter, C., Vogl, S., Sternberger, B., Kiss, H. & Husslein, P. (1996) The transfer of interleukin-8 across the human placenta perfused in vitro. Obstet Gynecol., 87, 613-616.
71. Retsky, M. W., Wardwell, R. H., Swartzendruber, D. E. & Headley, D. L. (1987) Prospective computerized simulation of breast-cancer - comparison of computer-predictions with 9 sets of biological and clinical data. Cancer Res., 47, 4982-4987.
72. Rothstein, T. L., Mage, M. G., Mond, J. & McHugh, L. L. (1978) Guinea pig antiserum to mouse cytotoxic T-lymphocytes and their precursor. J. Immunol., 120, 209-215.
73. Satyamoorthy, K., Li, G., Vaidya, B., Kalabis, J. & Herlyn, M. (2002) Insulin-like growth factor-I-induced migration of melanoma cells is mediated by interleukin-8 induction. Cell Growth Differ., 13, 87-93.
74. Schirrmacher, V. (2001) T-cell immunity in the induction and maintenance of a tumour dormant state. Semin. Cancer Biol., 11, 285-295.
75. Schwartzentruber, D. J., Topalian, S. L., Mancini, M. & Rosenberg, S. A. (1991) Specific release of granulocyte-macrophage colony-stimulating factor, tumour necrosis factor-α and IFN-γ by human tumour-infiltrating lymphocytes after autologous tumour stimulation. J. Immunol., 146, 3674-3681.
76. Sherratt, J. A., Eagan, B. T. & Lewis, M. A. (1997) Oscillations and chaos behind predator-prey invasion: Mathematical artifact or ecological reality?. Phil. Trans. R. Soc. Lond. B, 352, 21-38.
77. Sherratt, J. A., Lewis, M. A. & Fowler, A. C. (1995) Ecological chaos in the wake of invasion. Proc. Natl. Acad. Sci. USA, 92, 2524-2528.
78. Sherratt, J. A., Perumpanani, A. J. & Owen, M. R. (1999) Pattern formation in cancer. On Growth and Form: Spatio-temporal Pattern Formation in Biology. (M. A. J. Chaplain, G. D. Singh & J. C. McLachlan, eds). New York: Wiley.
79. Siu, H., Vitetta, E. S., May, R. D. & Uhr, J. W. (1986) Tumour dormancy regression of BCL tumour and induction of a dormant tumour state in mice chimeric at the major histocompatibility complex. J. Immunol., 137, 1376-1382.
80. Sordat, B., MacDonald, H. R. & Lees, R. K. (1980) The multicellular spheroid as a model tumour allograft. 3. morphological and kinetic analysis of spheroid infiltration and destruction. Transplantation, 29, 103-112.
81. Sozzani, S., Luini, W., Molino, M., Jilek, P., Bottazzi, B. & Cerletti, C. (1991) The signal transduction pathway involved in the migration induced by a monocyte chemotactic cytokine. J. Immunol., 147, 2215-2221.
82. Sutherland, R. M. (1988) Cell and environment interactions in tumor microregions: The multicell spheroid model. Science, 240, 177-184.
83. Suzuki, Y., Liu, C. M., Chen, L. P., Bennathan, D. & Wheelock, E. F. (1987) Immune regulation of the L5178Y murine tumour dormant state. 2. interferon gamma requires tumour necrosis factor to restrain tumour cell growth in peritoneal cell cultures from tumour dormant mice. J. Immunol., 139, 3146-3152.
84. Udagawa, T., Fernandez, A., Achilles, E. G., Folkman, J. & D'Amato, R. J. (2002) Persistence of microscopic human cancers in mice: alterations in the angiogenic balance accompanies loss of tumor dormancy. FASEB J., 16, 1361-1370.
85. Uhr, J. W. & Marches, R. (2001) Dormancy in a model of murine B cell lymphoma. Semin. Cancer Biol., 11, 277-283.
86. Uhr, J. W., Tucker, T., May, R. D., Siu, H. & Vitetta, E. S. (1991) Cancer dormancy: Studies of the murine BCL lymphoma. Cancer Res. (Suppl.), 51, 5045s-5053s.
87. Webb, S. D., Sherratt, J. A. & Fish, R. G. (2002) Cells behaving badly: A theoretical model for the Fas/FasL system in tumour immunology. Math. Biosci., 179, 113-129.
88. Wheelock, E. F., Weinhold, K. J. & Levich, J. (1981) The tumour dormant state. Adv. Cancer Res., 34, 107-140.
89. Wilson, K. M. & Lord, E. M. (1987) Specific (EMT6) and non-specific (WEHI-164) cytolytic activity by host cells infiltrating tumour spheroids. Br. J. Cancer, 55, 141-146.