title: Sustained oscillations in the MAP kinase cascade.
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 paper 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.
authors.affiliation: Freie Universität Berlin, Germany. Electronic address: jhell@zedat.fu-berlin.de.
authors.forename: Juliette
authors.initials: J
authors.lastname: Hell
authors.affiliation: Johannes Gutenberg-Universität Mainz, Germany. Electronic address: rendall@uni-mainz.de.
authors.forename: Alan D
authors.initials: AD
authors.lastname: Rendall