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

Emily R. Stirk (1) , Grant Lythe (1) , Hugo A. van den Berg (2) , Carmen Molina-París (1)

1 Department of Applied Mathematics
2 University of Warwick [Coventry]

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.

Mots clés: T cell homeostasis; TCR diversity; Stochastic bivariate birth and death process; Niche overlap; Large expansion

Emily R. Stirk, Grant Lythe, Hugo A. van den Berg, Carmen Molina-París. Stochastic competitive exclusion in the maintenance of the naïve T cell repertoire. Journal of Theoretical Biology, 2010, 265 (3), pp.396. ⟨10.1016/j.jtbi.2010.05.004⟩. ⟨hal-00608419⟩