Towards a General Function Describing T Cell Proliferation

We propose a new function for describing the rate of T cell proliferation in response to peptides on antigen presenting cells. The model improves an earlier model of ours by allowing for a true maximum proliferation rate of the T cells. This is achieved by a simple change of variables that markedly relaxes the conditions for a conventional quasi-steady state assumption. Our new model has the same ``ecological'' properties as our previous one. Thus the natural competition in the model allows for regulation of T cell population size in the presence of continuous stimulation by antigen. An important feature is the competitive exclusion of T cell clones recognizing the same peptide with different affinities allowing for ``affinity selection.'' We also develop models for the population dynamics of experienced, naive, and activated T cells. These T cell sub-populations compete with one another for antigen. In models with lymphokine production we obtain a ``proliferation threshold'' that allows for tolerance.