In this talk I will introduce a mathematical model of naive T cell homeostasis. The number of naive T cells in the peripheral pool is regulated by IL-7 signalling, and T cell receptor diversity is regulated by peptide-MHC signalling. The development of a mathematical model requires understanding the key molecular, cellular and population processes involved in peripheral naive T cell homeostasis. In order to do so, we make use of state-of-the-art experimental evidence to develop a model of IL-7 binding to its IL-7 receptor (IL-7R), internalisation, recycling, degradation, and synthesis. At the cellular level, we introduce the idea of survival and proliferation thresholds for naive T cells in the presence of IL-7. These elements allow us to define a population model of resting and cycling naive T cells, that includes the dynamics of extra-cellular IL-7. The model is then used to parameterise recent experiments by Hogan et al (2013).
I will conclude with a discussion of how mathematical model, together with biochemical data, can help us improve our understanding of receptor-regulated cellular responses.