Sustained oscillations in the MAP kinase cascade

TL;DR

This paper investigates conditions under which the MAP kinase cascade exhibits sustained oscillations due to Hopf bifurcations, using geometric singular perturbation theory to extend findings from simple to complex models.

Contribution

It identifies parameter regimes for oscillations in the MAP kinase cascade and demonstrates how geometric singular perturbation theory generalizes bifurcation results.

Findings

Hopf bifurcations lead to periodic oscillations in the cascade

Geometric singular perturbation theory extends simple model results

Conditions for sustained oscillations are characterized

Abstract

The MAP kinase cascade is a network of enzymatic reactions arranged in layers. In each layer occurs a multiple futile cycle of phosphorylations. The fully phosphorylated substrate then serves as an enzyme for the layer below. This papers focusses on the existence of parameters for which Hopf bifurcations occur and generate periodic orbits. Furthermore it is explained how geometric singular perturbation theory allows to generalize results from simple models to more complex ones.