Simulation of Dictyostelium Discoideum Aggregation via Reaction-Diffusion Model

We propose a reaction-diffusion model for simulation of the process of aggregation of Dictyostelium discoideum amoebae. The model is based on FitzHugh-Nagumo-type equations for cyclic adenosine 3{'}-monophosphate waves and a continuity equation for amoebae motion. We simulate the process of aggregation induced by a periodic point source and by spiral wave. We show that the aggregation pattern is formed as a result of front instabilities due to dependence of wave velocity on density of amoebae. This instability can also result in formation of wave breaks and generation of spiral waves.