2 August 2018
Alan Rendall
Institue of Mathematics
University of Mainz, Germany
This talk is concerned with mathematical models describing events during the first few minutes after the encounter of a naive mature T cell with its antigen. I will describe results obtained with Eduardo Sontag showing that some of these models exhibit behaviour which had not previously been noticed such as multiple steady states and damped oscillations. In addition I will discuss features of the response function which are predicted by this type of model although this was previously not believed possible. An example is that under some circumstances the response is a decreasing function of the dissociation time of the antigen from the T cell receptor. It can be concluded that these features can be explained by events in the first few minutes and do not require later events to be taken into account. These results illustrate how mathematical studies of a model of a biological system can complement approaches based on simulations and heuristics.