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. doi:10.1016/j.jtbi.2010.05.004

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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:	15
Page Range:	pp. 396-410
DOI:	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)

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