Directional sensing and streaming in Dictyostelium aggregation

We merge the Kessler-Levine simple discrete model for Dictyostelium cyclic adenosine monophosphate (cAMP) production and diffusion with the Dilão-Hauser directional sensing aggregation mechanism. The resulting compound model describes all the known transient patterns that emerge during Dictyostelium aggregation, which include the spontaneous formation of cAMP self-sustained target and spiral waves and streaming. We show that the streaming patterns depend on the speed of the amoebae, on the relaxation time for the production of cAMP, on the cAMP degradation rate, and on directional sensing. Moreover, we show that different signaling centers emerge during Dictyostelium aggregation.