  We investigate a special part of the human immune system, namely the
activation of T-Cells, using stochastic tools, especially sharp large deviation
results. T-Cells have to distinguish reliably between foreign and self peptides
which are both presented to them by antigen presenting cells. Our work is based
on a model studied by Zint, Baake, and den Hollander, and originally proposed
by van den Berg, Rand, and Burroughs. We are able to dispense with some
restrictive distribution assumptions that were used previously, i.e. we
establish a higher robustness of the model. A central issue is the analysis of
two new perspectives to the scenario (two different quenched systems) in
detail. This means that we do not only analyse the total probability of a
T-Cell activation (the annealed case) but also consider the probability of an
activation of one certain T-Cell type and the probability of a T-Cell
activation by a certain antigen presenting cell (the quenched cases). Finally,
we see analytically that the probability of T-Cell activation increases with
the number of presented foreign peptides in all three cases.
