Competitive control of the self-renewing T cell repertoire

We develop a mathematical model for the self-renewing part of the T cellrepertoire. Assuming that self-renewing T cells have to be stimulated byimmunogenic MHC-peptide complexes presented on the surfaces ofantigen-presenting cells, we derive a model of T cell growth in whichcompetition for MHC-peptide complexes limits T cell clone sizes andregulates the total number of self-renewing T cells in the animal. We showthat for a sufficient diversity and/or degree of cross-reactivity, thetotal T cell number hardly depends upon the diversity of the T cellrepertoire or the diversity of the set of presented peptides. Conversely,for repertoires of lower diversity and/or cross-reactivity, steady-statetotal T cell numbers may be limited by the diversity of the T cells. Thisprovides a possible explanation for the limited repertoire expansion insome, but not all, mouse T cell re-constitution experiments. We suggestthat the competitive interactions described by our model underlie thenormal T cells numbers observed in transgenic mice, germ-free mice andvarious knockout mice.