  We present novel experimental results on pattern formation of signaling
Dictyostelium discoideum amoeba in the presence of a periodic array of
millimeter-sized pillars. We observe concentric cAMP waves that initiate almost
synchronously at the pillars and propagate outwards. These waves have higher
frequency than the other firing centers and dominate the system dynamics. The
cells respond chemotactically to these circular waves and stream towards the
pillars, forming periodic Voronoi domains that reflect the periodicity of the
underlying lattice. We performed comprehensive numerical simulations of a
reaction-diffusion model to study the characteristics of the boundary
conditions given by the obstacles. Our simulations show that, the obstacles can
act as the wave source depending on the imposed boundary condition.
Interestingly, a critical minimum accumulation of cAMP around the obstacles is
needed for the pillars to act as the wave source. This critical value is lower
at smaller production rates of the intracellular cAMP which can be controlled
in our experiments using caffeine. Experiments and simulations also show that
in the presence of caffeine the number of firing centers is reduced which is
crucial in our system for circular waves emitted from the pillars to
successfully take over the dynamics. These results are crucial to understand
the signaling mechanism of Dictyostelium cells that experience spatial
heterogeneities in its natural habitat.
