Unstable cAMP wave patterns during aggregation of Dictyostelium discoideum cells

•Flow-driven unstable pattern formation of cyclic adenosine monophosphate is investigated.•A perturbed plane wave breaks up into wave patterns under the modulational instability process.•Quasi-periodic waves, spiral seeds and chaotic patterns are found to control information among D. discoideum cells.•Efficient regulation of communication between an amoebas colony is supported by right choice of system parameters.•Pattern formation process among D. discoideum cells under spontaneous fluid flow is discussed. Flow-driven formation of unstable patterns of cyclic adenosine monophosphate (cAMP) is investigated in the Martiel-Goldbeter (MG) model. This is predicted via a complex Ginzburg-Landau equation, derived from the MG model, under the so-called modulational instability process. Regions of parameters where patterns exist are discussed analytically and verified numerically. Quasi-periodic waves, spiral seeds and chaotic patterns are found to control information driven in a colony of homogeneously distributed Dictyostelium discoideum cells under the change of the extracellular cAMP degradation rate (ke), the production rate of cAMP (σ) and the advection flow velocity (Vf). Our results suggest that these quantities play a key role in the efficient regulation of communication within an amoeba colony, and the presence of the flow makes it possible to understand pattern formation process among D. discoideum cells under spontaneous fluid flow in their natural environment.