title: Stochastic competitive exclusion in the maintenance of the naïve T cell repertoire.
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.
authors.affiliation: Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK.
authors.forename: Emily R
authors.initials: ER
authors.lastname: Stirk
authors.forename: Grant
authors.initials: G
authors.lastname: Lythe
authors.forename: Hugo A
authors.initials: HA
authors.lastname: van den Berg
authors.forename: Carmen
authors.initials: C
authors.lastname: Molina-París
mesh_terms: D001324:Autoantigens / Q000276:immunology*; D003198:Computer Simulation; D006706:Homeostasis / Q000276:immunology; D006801:Humans; D008390:Markov Chains; D018448:Models, Immunological; D011948:Receptors, Antigen, T-Cell / Q000276:immunology*; D017634:Self Tolerance / Q000276:immunology*; D013269:Stochastic Processes; D013601:T-Lymphocytes / Q000276:immunology*
chemical_list: D001324:Autoantigens; D011948:Receptors, Antigen, T-Cell