ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Ivanchenko M. V. Competition in the two­component model of the immune T-cell ensemble. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 3, pp. 33-45. DOI: 10.18500/0869-6632-2010-18-3-33-45

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 129)
Article type: 
537.86, 530.182

Competition in the two­component model of the immune T-cell ensemble

Ivanchenko Mihail Vasilevich, Lobachevsky State University of Nizhny Novgorod

We study the process of competition in the two­component model of the immune T­cells ensemble that underpins the selection mechanism of the most efficient T­cell species (clonotypes). We demonstrate the absence of periodic oscillations, determine the regions of coexistence, partial and mutual extinction of clonotypes. Applicability of the mean field approximation is analyzed. The biological implications of the results are discussed.

  1. Arecchi FT, Boccaletti S, Ramazza PL. Pattern formation and competition in nonlinear optics. Physic Reports. 1999;318:1–83. DOI: 10.1016/S0370-1573(99)00007-1.
  2. Afraimovich VS, Nekorkin VI, Osipov GV, Shalfeev VD. Stability, Structures and Chaos in Nonlinear Synchronization Networks. Singapore: World Scientific; 1994.
  3. Kuramoto Y. Chemical oscillations, waves and turbulence. Tokio: Springer; 1984.
  4. Koronovskii AA., Trubetskov DI. Nonlinear dynamics in action. Saratov: Publ. of GosUNTs «College»; 2002. (in Russian).
  5. Murray JD. Mathematical Biology. Berlin-Heidelberg: Springer-Verlag; 2002.
  6. Rabinovich MI, Varona P, Selverston AI, Abarbanel HDI. Dynamical principles in neuroscience. Rev. Mod. Phys. 2006;78(4):1213–1265. DOI: 10.1103/RevModPhys.78.1213.
  7. Nekorkin VI, Shapin DS, Dmitrichev AS. et al. Heteroclinic contours and self-replicated solitary waves in a reaction-diffusion lattice with complex threshold excitation. Physica D. 2008;237:2463–2475. DOI: 10.1016/j.physd.2008.03.035
  8. Jameson SC. Maintainting the norm: T-cell homeostasis. Nature Reviews Immunology. 2002;2(8):547–556. DOI: 10.1038/nri853.
  9. Perelson A, Weisbuch G. Immunology for physicists. Reviews of Modern Physics. 1997;69(4):1219–1268. DOI: 10.1103/RevModPhys.69.1219.
  10. Freitas AA, Rocha BB. Lymphocyte lifespans: homeostasis, selection and competition. Immun. Today. 1993;14(1):25–29. DOI: 10.1016/0167-5699(93)90320-K.
  11. De Boer R, Perelson A. Competitive control of the self-renewing T cell repertoire. International Immunology. 1997;9(5):779–790. DOI: 10.1093/intimm/9.5.779.
  12. Stirk ER, Molina-Paris C, van den Berg H. Stochastic niche structure and diversity maintenance in the T cell repertoire. J. Theor. Biol. 2008;255(2):237–249. DOI: 10.1016/j.jtbi.2008.07.017.
  13. Gillespie DT. Stochastic simulation of chemical kinetics. Annu. Rev. Phys. Chem. 2007;58:35–55. DOI: 10.1146/annurev.physchem.58.032806.104637.
  14. Stirk E, Lythe G, van den Berg H, Hurst G, Molina-Paris C. The limiting conditional probability distribution in a stochastic model of T cell repertoire maintenance. Math. Biosciences; 2010 (in print).
Short text (in English):
(downloads: 89)