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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. [Copyright &y& Elsevier]

Abstract: The reliability of the immune response to pathogenic challenge depends critically on the size and diversity of the T cell repertoire. We study naïve T cell repertoire diversity maintenance by a stochastic model that incorporates the concept of competition between T cells for survival stimuli emanating from self-antigen presenting cells (APCs). In the mean field approximation we show that clonotype extinction is certain and compute mean extinction times. We introduce the concept of mean niche overlap and show that clones with a mean niche overlap greater than one have a short repertoire lifespan. This selection differential induces minimal recognition commonality between T cell receptors (TCRs) resulting in a diverse T cell repertoire. [Copyright &y& Elsevier]