Singular perturbation analysis of cAMP signalling in Dictyostelium discoideum aggregates

Abstract

In this paper, we use singular perturbation methods to study the structure of travelling waves for some reaction-di®usion models obtained from the Martiel-Goldbeter and Goldbeter-Segel's models of cAMP signalling in Dictyostelium discoideum. As a consequence, we derive analytic formulae for quantities like wave speed, maximum concentration and other magnitudes in terms of the di®erent biochemical constants that appear in the model.