Stochastic modelling of T-cell activation.
We investigate a specific 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 et al. (J Math Bio 57(6):841-861, 2008). 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 clonotype and the probability of a T-cell activation by a certain antigen presentation profile (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.
Institut für Angewandte Mathematik, Rheinische Friedrich-Wilhelms-Universität, Endenicher Allee 60, 53115,  Bonn, Germany, hannah.mayer@uni-bonn.de.
Hannah
H
Mayer
Anton
A
Bovier
D017951:Antigen Presentation; D000938:Antigen-Presenting Cells / Q000276:immunology; D006801:Humans; D054992:Immunological Synapses / Q000276:immunology; D008213:Lymphocyte Activation; D055641:Mathematical Concepts; D018448:Models, Immunological; D011336:Probability; D013269:Stochastic Processes; D013601:T-Lymphocytes / Q000276:immunology*