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A model of the role of natural killer cells in immune surveillance — I

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Summary

The theory of immune surveillance of Thomas and Burnet stated in part that antigenic differences between neoplastic and normal cells provide the stimulus for their destruction by cells of the immune system. Burnet pointed to the T lymphocyte as the cell which mediated this surveillance. The existence of some form of surveillance in cases of no T lymphocyte functioning presents the possibility that surveillance, if present at all, is mediated by non T cells.

Cells identified as naturally cytotoxic killer (NK) cells appear to have properties required of a surveillance effector population. This paper utilizes properties of NK cells and the effects of interferon on this population to construct a mathematical model of the characteristics that an NK cell surveillance would have. A two level theory of immune surveillance is proposed.

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References

  1. Albert, A., Freedman, M., Perelson, A.: Tumors and the immune system: The effects of a tumor growth modulator. Math. Biosci. 50, 25–58 (1980)

    Google Scholar 

  2. Burnet, F. M.: Cancer—a biological approach. Br. Med. J. 1, 779–786 and 841–847 (1957)

    Google Scholar 

  3. Burnet, F. M.: The concept of immune surveillance. Prog. Exp. Tumor Res. 13, 1–23 (1970)

    Google Scholar 

  4. Burnet, F. M.: Immunological surveillance in neoplasia. Trans. Rev. 7, 3–25 (1971)

    Google Scholar 

  5. Cronin, Jane: Differential equations, introduction and qualitative theory. Marcel Dekker, 1980

  6. Cudkowicz, G., Hochman, P. S.: Do natural killer cells engage in regulated reaction against self to ensure homeostasis? Immunol. Rev. 44, 13–41 (1979)

    Google Scholar 

  7. DeLisi, C, Rescigno, A.: Immune surveillance and neoplasia, I. A minimal mathematical model. Bull. Math. Biol. 39, 201–221 (1977)

    Google Scholar 

  8. DeMaeyer, E., DeMaeyer-Guignard, J.: Interferons. In: Comprehensive virology, Vol. 15 (H. Fraenkel-Conrat, R. R. Wagner, eds.), pp. 205–284. Plenum 1979

  9. Eisen, M.: Mathematical models in cell biology and cancer chemotherapy. Springer-Verlag 1979

  10. Garay, R. P., Lefever, R.: A kinetic approach to the immunology of cancer: Stationary states properties of effector-target cell reactions. J. Theor. Biol. 73, 417–438 (1978)

    Google Scholar 

  11. Grossman, Z., Berke, G.: Tumor escape from immune elimination. J. Theor. Biol. 83, 267–296 (1980)

    Google Scholar 

  12. Hale, J. K.: Ordinary differential equations. Wiley-Interscience 1969

  13. Hellström, K. E., Hellström, I.: Lymphocyte mediated cytoxicity and blocking serum activity to tumor antigens. Adv. Immunol. 18, 209–277 (1974)

    Google Scholar 

  14. Herberman, R. B., Nunn, M. E., Lavrin, D. H., Asofsky, R.: Effect of antibody to θ antigen on cell-mediated immunity induced in syngeneic mice by murine sarcoma virus. J. Natl. Cancer Inst. 51, 1509–1512 (1973)

    Google Scholar 

  15. Herberman, R. B., Holden, H. T.: Natural cell-mediated immunity. Adv. Cancer Res. 27, 305–377 (1978)

    Google Scholar 

  16. Herberman, R. B., Djeu, J. Y., Kay, H. D., Ortaldo, J. R., Riccardi, C., Bonnard, G. D., Holden, H. T., Fagnani, R., Santoni, A., Puccetti, P.: Natural killer cells: Characteristics and regulation of activity. Immunol. Rev. 44, 43–70 (1979)

    Google Scholar 

  17. Kiessling, R., Hochman, P. S., Haller, O., Wigzell, H., Cudkowicz, G.: Evidence for a similar or common mechanism for natural killer cell activity and the resistance to hemopoietic grafts. Eur. J. Immunol. 7, 655–663 (1977)

    Google Scholar 

  18. Kiessling, R., Wigzell, H.: An analysis of the murine NK cell as to structure, function and biological relevance. Immunol. Rev. 44, 165–208 (1979)

    Google Scholar 

  19. Klein, G., Klein, E.: Immune surveillance against virus-induced tumors and nonrejectability of spontaneous tumors: Contrasting consequences of host versus tumor evolution. Proc. Nat. Acad. Sci. USA 74, 2121–2125 (1977)

    Google Scholar 

  20. Koo, G. C., Jacobsen, J. B., Hammerling, G. J., Hammerling, U.: Antigenic profile of murine natural killer cells. J. Immunol. 125, 1003–1006 (1980)

    Google Scholar 

  21. Lefever, R., Garay, R. P.: A mathematical model of the immune surveillance against cancer. In: Theoretical immunology (G. I. Bell, A. S. Perelson, G. H. Pimbley, Jr., eds.), pp. 481–518. Marcel Dekker 1978

  22. Lefever, R., Garay, R. P.: Local description of immune tumor rejection. In: Biomathematics and cell kinetics (A. J. Valleron, P. D. M. Macdonald, eds.), pp. 333–344. Elsevier/North-Holland 1978

  23. Lohmann-Matthes, M. L., Roder, J.: Promonocytes have the functional characteristics of natural killer cells. J. Immunol. 123, 1883–1886 (1979)

    Google Scholar 

  24. Merrill, S. J.: A mathematical model of tumor growth and cytotoxic blocking activity. Math. Biosci. 47, 79–89 (1979)

    Google Scholar 

  25. Naor, D.: Suppressor cells: Permitters and promoters of malignancy. Adv. Immunol. 29, 45–125 (1979)

    Google Scholar 

  26. Oldham, R. K., Siwarski, D., McCoy, J. L., Plata, E. J., Herberman, R. B.: Evaluation of a cell-mediated cytotoxicity assay utilizing 125Iododeoxyuridine-labeled tissue culture target cells. Natl. Cancer Inst. Monograph 37, 49–58 (1973)

    Google Scholar 

  27. Prehn, R. T.: Discussion. In: Immune surveillance (R. T. Smith, M. Landy, eds.), pp. 451–462. Academic Press 1970

  28. Rescigno, A., DeLisi, C.: Immune surveillance and neoplasia, II. A two-stage mathematical model. Bull. Math. Biol. 39, 487–497 (1977)

    Google Scholar 

  29. Roder, J. C., Lohmann-Matthes, M. L., Domzig, W., Wigzell, H.: The beige mutation in the mouse, II. Selectivity of the natural (NK) cell defect. J. Immunol. 123, 2174–2181 (1979)

    Google Scholar 

  30. Rygaard, J., Poulsen, C. O.: The nude mouse versus the hypothesis of immunological surveillance. Trans. Rev. 28, 43–61 (1976)

    Google Scholar 

  31. Saksela, E., Timonen, T., Ranki, A., Häyre, P.: Morphological and functional characterization of isolated effector cells responsible for human natural killer activity to fetal fibroblasts and to cultural cell line targets. Immunol. Rev. 44, 71–123 (1979)

    Google Scholar 

  32. Santoli, D., Koprowski, H.: Mechanisms of activation of human natural killer cells against tumor and virus-infected cells. Immunol. Rev. 44, 125–163 (1979)

    Google Scholar 

  33. Swan, G. W.: Some current mathematical topics in cancer research. University Microfilms 1977

  34. Thames, H. D.: Mathematical models of dose and cell cycle effects in multifraction radiotherapy. In: Modeling and differential equations in biology (T. A. Burton, ed.), pp. 51–105. Marcel Dekker 1980

  35. Thomas, L.: Reactions to homologous tissue antigens and relation to hypersensitivity. In: Cellular and humoral aspects of the hypersensitive states (H. S. Lawrence, ed.), pp. 529–532. Hoeber 1959

  36. Timonen, T., Saksela, E., Virtanen, L, Cantell, K.: Natural killer cells are responsible for the interferon production induced in human lymphocytes by tumor cell contact. Eur. J. Immunol. 10, 422–427 (1980)

    Google Scholar 

  37. Welsh, R. M., Karre, K., Hansson, M., Kunkel, L. A., Kiessling, R. W.: Interferon-mediated protection of normal and tumor target cells against lysis by mouse natural killer cells. J. Immunol. 126, 219–225 (1981)

    Google Scholar 

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Authors and Affiliations

  1. Division of Applied Mathematics, Lefschetz Center for Dynamical Systems, Brown University, 02912, Providence, RI

    Stephen J. Merrill

  2. Department of Mathematics, Statistics and Computer Science, Marquette University, 53233, Milwaukee, WI, USA

    Stephen J. Merrill

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  1. Stephen J. Merrill
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This research has been supported in part by the National Science Foundation under grant #NSF-Eng. 7904852

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Merrill, S.J. A model of the role of natural killer cells in immune surveillance — I. J. Math. Biology 12, 363–373 (1981). https://doi.org/10.1007/BF00276923

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  • DOI: https://doi.org/10.1007/BF00276923

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