Competitive control of the self-renewing T cell repertoire

We develop a mathematical model for the self-renewing part of the T cell repertoire. Assuming that self-renewing T cells have to be stimulated by immunogenic MHC-peptide complexes presented on the surfaces of antigen-presenting cells, we derive a model of T cell growth in which competition for MHC-peptide complexes limits T cell clone sizes and regulates the total number of self-renewing T cells in the animal. We show that for a sufficient diversity and/or degree of cross-reactivity, the total T cell number hardly depends upon the diversity of the T cell repertoire or the diversity of the set of presented peptides. Conversely, for repertoires of lower diversity and/or cross-reactivity, steady-state total T cell numbers may be limited by the diversity of the T cells. This provides a possible explanation for the limited repertoire expansion in some, but not all, mouse T cell re-constitution experiments. We suggest that the competitive interactions described by our model underlie the normal T cells numbers observed in transgenic mice, germ-free mice and various knockout mice.