Stochastic Modelling of T-Cell-Activation

TL;DR

This paper uses stochastic modeling and large deviation theory to analyze T-Cell activation, improving robustness of the model and exploring different probabilistic perspectives on immune response.

Contribution

It extends previous models by removing restrictive assumptions and introduces detailed analysis of quenched systems in T-Cell activation modeling.

Findings

Probability of T-Cell activation increases with foreign peptides

Robustness of the model is enhanced by relaxing distribution assumptions

Analysis of quenched systems provides new insights into immune response

Abstract

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.