Perturbation theory analysis of competition in a heterogeneous population

Physica D: Nonlinear Phenomena

Volumn 175, Issue 1-2, 2003, Pages 109-126

  Utzny, C ^a   Burroughs, N J ^b  

^a CHU PURPAN   (France)

^b UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

Apoptosis; Competition; Immunological memory; Perturbation analysis; Population dynamics; Selection; Structuring

Indexed keywords

IMMUNOLOGY; INTEGRODIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES;

HETEROGENEOUS POPULATION;

CELLS;

EID: 0037437760     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(02)00678-4     Document Type: Article

References (29)

1. McMichael A.J., Phillips R.E., Escape of human immunoddeficiency virus from immune control. Annu. Rev. Immunol. 15:1997;271-296.
2. Berger A., Berek C., Apel M., Maturation of the immune response in germinal centers. Cell. 67:1991;1121-1129.
3. Kepler T.B., Perelson A.S., Cyclic reentry for germinal center B cells and the efficiency of affinity maturation. Immunol. Today. 14:1993;412-512.
4. Bachmann M.F., Speiser D.E., Ohashi P.S., Functional maturation of an antiviral cytotoxic T-cell response. J. Virol. 71:1997;5764-5768.
5. Boniface J.J., Savage A., Davis M.M., A kinetic T cell receptor repertoire selection during an immune response. Immunity. 10:1999;482-492.
6. McHeyzer-Williams M.G., Davis M.M., Antigen-specific development of primary and memory T cells in vivo. Science. 268:1995;106-111.
7. Ahmed R., Gray D., Immunological memory and protective immunity: understanding their relation. Science. 272:1996;54-60.
8. Dutton R.W., Bradley L.M., Swain S.L., T cell memory. Annu. Rev. Immunol. 16:1998;201-223.
9. Zimmermann C., Prévost-Blondel A., Blaser C., Pircher H., Kinetics of the response of naïve and memory CD8 T cells to antigen: similarities and differences. Eur. J. Immunol. 29:1999;284-290.
10. Duke R.C., Cohen J.J., IL-2 addiction-withdrawal of growth-factor activates a suicide program in dependent T cells. Lymphokine Res. 5:1986;289-299.
11. Broome H.E., Dargan C.M., Bessent E.F., Krajewski S., Reed J.C., Apoptosis and Bcl-2 expression in cultured murine splenic T cells. Immunology. 84:1995;375-382.
12. Akbar A.N., Salmon M., Cellular environment and apoptosis: tissue microenvironments control activated T cell death. Immunol. Today. 18:1997;72-74.
13. Cantrell D.A., Smith K.A., The interleukin-2 T-cell system a new cell growth model. Science. 224:1984;1312-1316.
14. DeBoer R.J., Perelson A.S., T cell repertoires and competitive exclusion. J. Theor. Biol. 169:1994;375-390.
15. G.F. Webb, Theory of nonlinear age-dependent population dynamics, in: E.J. Tafts, Z. Nansted (Eds.), Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, 1985.
16. J.A.J. Metz, O. Dieckmann, The dynamics of physiologically structured populations, Springer Lecture Notes in Biomathematics, vol. 68, Springer, Heidelberg, 1986.
17. Gyllenberg M., Webb F., A nonlinear structured population-model of tumor-growth with quiesence. J. Math. Biol. 28:1990;671-694.
18. de Roos A.M., Claessen C., Persson L., Dwarfs and giants: cannibalism and competition in size-structured populations. Am. Nat. 155:2000;219-237.
19. Mittler J., Pilyugin S., Antia R., Modelling T cell proliferation: an investigation of the Hayflick limit. J. Theor. Biol. 186:1997;117-129.
20. J. Thèze (Ed.), The Cytokine Network and Immune Functions, Oxford University Press, Oxford, UK, 1999.
21. A. Thomson (Ed.), Cytokine Handbook, Academic Press, San Diego, USA, 1998.
22. Lenardo M., Ka-Ming C.F., Hornung F., McFarland H., Siegel H., Wang J., Zheng L., Mature T lymphocyte apoptosis - immune regulation in a dynamic and unpredictable antigenic environment. Annu. Rev. Immunol. 17:1999;221-253.
23. Scheel-Toellner D., Pilling D., Akbar A.N., Hardie D., Lombardie G., Salmon M., Buckley C.D., Lord J.M., Inhibition of T cell apoptosis by IFN-. β rapidly reverses nuclear translocation of protein kinases Eur. J. Immunol. 29:1999;1041-1050.
24. Akbar A.N., Brothwick N.J., Wickremasinghe R.G., Panayoitidis P., Pilling D., Bofill M., Krajewski S., Reed J.C., Salmon M., Interleukin-2 receptor common. γ -chain signaling cytokines regulate activated T-cell apoptosis in response to growth factor withdrawal: selective induction of anti-apoptotic (bcl-2, bcl-xL) but not pro-apoptotic (bax, bcl-xS) gene expression Eur. J. Immunol. 26:1996;294-299.
25. Waldmann T.A., The multi-subunit interleukin-2 receptor. Annu. Rev. Biochem. 58:1989;875-911.
26. Utzny C., Burroughs N.J., Stability of a diverse immunological memory is determined by T cell population dynamics. Bull. Math. Biol. 63:2001;685-713.
27. Diekmann O., de Roos A.M., Metz J.A.J., Studying the dynamics of structured population-models - a versatile technique and its application to daphnia. Am. Nat. 139:1992;123-147.
28. Lynch D.H., Ramsdell F., Alderson M.R., Fas and Fasl in the homeostatic regulation of the immune responses. Immunol. Today. 16:1995;569-574.
29. C.R. Mackay, Homing of naive, memory and effector Lymphocytes. Curr. Opin. Immunol. 5 (1993) 423-427.