Simulation ofDictyostelium DiscoideumAggregation via Reaction-Diffusion Model

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Abstract
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.