Cells of Dictyostelium discoideum show patterns of cyclic adenosine 3'
, 5'-monophosphate (cAMP) waves during the aggregation process. The de
tails of the temporal evolution of the pattern depend on the initial c
ell density as well as the specific strain. Here, we simulate this pro
cess by generalizing the Martiel-Goldbeter biochemical kinetics to inc
lude the coupling of the cAMP signaling to the expression levels of ag
gregation-stage genes. This model naturally explains the formation of
spiral waves at high cell density as well as the surprising results of
recent wave-resetting experiments.