Slow-fast systems in cell biology: switches and oscillators

Geometric singular perturbation theory (GSPT) founded by Fenichel has been successfully used in many areas of mathematical biology, e.g. mathematical neuroscience and calcium signaling. However, slow-fast analysis and GSPT of mathematical models arising in cell biology is much less established. The main reason seems to be that the corresponding models typically do not have an obvious slow-fast structure of the standard form. Nevertheless, many of these models exhibit some form of hidden slow-fast dynamics, which can be utilized in the analysis.

In this talk I will explain some of the main concepts of GSPT in the context of a non-trivial application. I will present a geometric analysis of a novel type of relaxation oscillations involving two different switches in a model for the NF − $\kappa$B signaling pathway.