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Stochastic competitive exclusion in the maintenance of the naïve T cell repertoire

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Stirk, Emily R., Lythe, Grant, Berg, Hugo van den and Molina-Paris, Carmen. (2010) Stochastic competitive exclusion in the maintenance of the naïve T cell repertoire. Journal of Theoretical Biology, Vol.265 (No.3). pp. 396-410. ISSN 0022-5193

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Official URL: http://dx.doi.org/10.1016/j.jtbi.2010.05.004

Abstract

Recognition of antigens by the adaptive immune system relies on a highly diverse T cell receptor repertoire. The mechanism that maintains this diversity is based on competition for survival stimuli; these stimuli depend upon weak recognition of self-antigens by the T cell antigen receptor. We study the dynamics of diversity maintenance as a stochastic competition process between a pair of T cell clonotypes that are similar in terms of the self-antigens they recognise. We formulate a bivariate continuous-time Markov process for the numbers of T cells belonging to the two clonotypes. We prove that the ultimate fate of both clonotypes is extinction and provide a bound on mean extinction times. We focus on the case where the two clonotypes exhibit negligible competition with other T cell clonotypes in the repertoire, since this case provides an upper bound on the mean extinction times. As the two clonotypes become more similar in terms of the self-antigens they recognise, one clonotype quickly becomes extinct in a process resembling classical competitive exclusion. We study the limiting probability distribution for the bivariate process, conditioned on non-extinction of both clonotypes. Finally, we derive deterministic equations for the number of cells belonging to each clonotype as well as a linear Fokker-Planck equation for the fluctuations about the deterministic stable steady state.

Item Type:

Journal Article

Subjects:

Q Science > QR Microbiology

Divisions:

Faculty of Science > Mathematics
Faculty of Science > Centre for Systems Biology

Library of Congress Subject Headings (LCSH):

T cells -- Receptors -- Mathematical models

Journal or Publication Title:

Journal of Theoretical Biology

Publisher:

Elsevier

ISSN:

0022-5193

Official Date:

7 August 2010

Dates:

Date	Event
7 August 2010	Published

Volume:

Vol.265

Number:

No.3

Number of Pages:

Page Range:

pp. 396-410

Identifier:

10.1016/j.jtbi.2010.05.004

Status:

Peer Reviewed

Publication Status:

Published

Access rights to Published version:

Restricted or Subscription Access

Funder:

Engineering and Physical Sciences Research Council (EPSRC), Biotechnology and Biological Sciences Research Council (Great Britain) (BBSRC)

References:

Allen, L.J.S., 2003. An Introduction to Stochastic Processes with Applications to Biology. Prentice Hall.
Arstila, T.P., Casrouge, A., Baron, V., Even, J., Kanellopoulos, J., Kourilsky, P., 1999. A direct estimate of
the human T cell receptor diversity. Science 286, 958{961.
Bain, L.J., Engelhardt, M., 2000. Introduction to Probability and Mathematical Statistics. Duxbury Press.
Begon, M., Harper, J.L., Townsend, C.R., 1990. Ecology: Individuals, Populations and Communities. Blackwell's
Sci., Oxford, UK.
Bousso, P., Levraud, J-P., Kourilsky, P., Abastado, J-P., 1999. The composition of a primary T cell response is
largely determined by the timing of recruitment of individual T cell clones. J. Exp. Med. 189, 1591{1600.
Clancy, D., O'Neill, P.D., Pollett, P.K., 2001. Approximations for the long-term behaviour of an open-population
epidemic model. Methodology and Computing in Appl. Probab. 3, 75{95.
Correia-Neves, M., Waltzinger, C., Mathis, D., Benoist, C., 2001. The shaping of the T cell repertoire. Immunity
14, 21{32.
Darroch, J.N., Seneta, E., 1967. On quasi-stationary distributions in absorbing continuous time finite Markov
chains. J. Appl. Probab. 4, 192{196.
Davenport, M.P., Price, D.A., McMichael, A.J., 2007. The T cell repertoire in infection and vaccination: implications
for control of persistent viruses. Curr. Opin. Immunol. 19, 294{300.
de Boer, R.J., Perelson, A.S., 1993. How diverse should the immune system be? Proc. Royal Soc. London B
252, 171{175.
de Boer, R.J., Perelson, A.S., 1994. T cell repertoires and competitive exclusion. J. Theor. Biol. 169, 375{390.
de Boer, R.J., Perelson, A.S., 1997. Competitive control of the self-renewing T cell repertoire. Int. Immunol.
9, 779{790.
Edelstein-Keshet, L., 1988. Mathematical models in biology, 1st edition. McGraw-Hill.
Ernst, B., Lee, D-S., Chang, J.M., Sprent, J., Surh, C.D., 1999. The peptide ligands mediating positive selection
in the thymus control T cell survival and homeostatic proliferation in the periphery. Immunity 11, 173{181.
Ferreira, C., Barthlott, T., Garcia, S., Zamoyska, R., Stockinger, B., 2000. Differential survival of nafive CD4
and CD8 T cells. J. Immunol. 165, 3689{3694.
Freitas, A.A., Rocha, B., 1999. Peripheral T cell survival. Curr. Opin. Immunol. 11, 152{156.
Freitas, A.A., Rocha, B., 2000. Population biology of lymphocytes: the
ight for survival. Annu. Rev. Immunol.
18, 83{111.
Gibson, K.L., Wu, Y-C., Barnett, Y., Duggan, O., Vaughan, R., Kondeatis, E., Nilsson, B-O., Wikby, A.,
Kipling, D., Dunn-Walters, D.K., 2009. B cell diversity decreases in old age and is correlated with poor health
status. Aging Cell 8, 18{25.
Gillespie, D.T., 1976. A general method for numerically simulating the stochastic time evolution of coupled
chemical reactions. J. Comp. Phys. 22, 403{434.
Grimmett, G., Stirzaker, D., 2001. Probability and random processes, 3rd edition. Oxford University Press.
Goldrath, A.W., Bevan, M.J., 1999. Selecting and maintaining a diverse T cell repertoire. Nature 402, 255{262.
Goronzy, J.J., Lee, W-W., Weyand, C.M., 2007. Aging and T cell diversity. Exp. Gerontol. 42, 400{406.
Guide, M.U., 1998. MATLAB, The MathWorks. Inc., Natick, MA 5.
Iglehart, D.L., 1964. Multivariate competition processes. Annals. Math. Statist. 35, 350{361.
Jost, L., 2007. Partitioning diversity into independent alpha and beta components. Ecology 88, 2427{2439.
Kedzierska, K., Venturi, V., Field, K., Davenport, M.P., Turner, S.J., Doherty, P.C., 2006. Early establishment
of diverse T cell receptor profiles for in
uenza-specific CD8+CD62Lhi memory T cells. Proc. Natl. Acad. Sci.
USA 103, 9184{9189.
Krangel, M.S., Hernandez-Munain, C., Lauzurica, P., McMurry, M., Roberts, J.L., Zhong, X-P., 1998. Developmental
regulation of V(D)J recombination at the TCR locus. Immunol. Rev. 165, 131{147.
Mahajan, V.S., Leskov, I.B., Chen, J., 2005. Homeostasis of T cell diversity. Cellular and Molecular Immunology
2, 1{10.
O'Conner, D., Friedrich, T., Hughes, A., Allen, T.M., Watkins, D., 2001. Understanding cytotoxic T lymphocyte
escape during simian immunodeficiency virus infection. Immunol. Rev. 183, 115{126.
Pollett, P.K., 1995. The determination of quasistationary distributions directly from the transition rates of an
absorbing Markov chain. Math. Comp. Modelling 22, 279{287.
Reuter, G.E.H., 1961. Competition Process. Proc. Fourth Berkeley Symp. Math. Statist. Prob. II, 421{430.
Stirk, E.R., Molina-Pars, C., van den Berg, H.A., 2008. Stochastic niche structure and diversity maintenance
in the T cell repertoire. J. Theor. Biol. 255, 237{249.
Taylor, H.M., Karlin, S., 1998. An Introduction to Stochastic Modelling, 3rd edition. Academic Press.
Troy, A.E., Shen, H., 2003. Cutting edge: homeostatic proliferation of peripheral T lymphocytes is regulated
by clonal competition. J. Immunol. 170, 672{676.
van den Berg, H.A., Burroughs, N.J., Rand, D.A., 2001. A reliable and safe T cell repertoire based on lowa
finity T cell receptors. J. Theor. Biol. 209, 465{486.
van den Berg, H.A., Burroughs, N.J., Rand, D.A., 2002. Quantifying the strength of ligand antagonism in TCR
triggering. Bull. Math. Biol. 64, 781{808.
van den Berg, H.A., Rand, D.A., 2003. Antigen presentation on MHC molecules as a diversity filter that enhances
immune efficacy. J. Theor. Biol. 224, 249{267.
Van Kampen, N.G., 1961. A power series expansion of the master equation. Canadian J. Phys. 39, 551{567.
Van Kampen, N.G., 2007. Stochastic Processes in Physics and Chemistry, 3rd edition. North-Holland Personal
Library.
Wynn, K.K., Fulton, Z., Cooper, L., Silins, S.L., Gras, S., Archbold, J.K., Tynan, F.E., Miles, J.J., McCluskey,
J., Burrows, S.R., Rossjohn, J., Khanna, R., 2008. Impact of clonal competiton for peptide-MHC complexes on the CD8+ T cell repertoire selection in a persistent viral infection. Blood 111, 4283{4292.