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Introduction

We'll consider a three-dimensional ODE model (introduced in ``Unified mechanism for relay and oscillation of cyclic AMP in Dictyostelium discoideum'' by A. Goldbeter and L. A. Segel, Proc. Natl. Acad. Sci. USA 74:1543-1547, 1977, may be downloaded from JSTOR) for the dynamic behavior of the cAMP signalling system for Dictyostelium discoideum. The three variables in this model correspond to intracellular ATP, intracellular cAMP, and extracellular cAMP. Depending on parameters, this model can display either excitability or oscillations. As for FitzHugh's simplification of the Hodgkin/Huxley equations (see Computer Lab Tutorial 2), here it is possible to eliminate a "fast" variable. This gives a two-dimensional system of equations which can be understood in terms of nullclines, etc. Indeed, this analysis shows that the dynamics of squid giant axons and slime molds might have some nice qualitative similarities.



Jeffrey M. Moehlis 2001-10-10