Long-range interaction of multi-spiral cAMP waves in Dictyostelium discoideum amoeba aggregation

Dictyostelium discoideum (Dd) aggregation is driven by propagating waves of cyclic adenosine monophosphate (cAMP), which coordinate chemotactic motion across large cell populations. While classical models emphasize nearest-neighbor signaling via diffusive relay, growing evidence highlights the importance of long-range interactions (LRIs) in shaping wave dynamics. Here, we investigate how the interaction range influences the evolution of cAMP waves using a two-dimensional discrete FitzHugh-Nagumo-type framework. Our simulations show that LRIs act as a key control parameter governing pattern formation, yielding three distinct regimes: multi-spiral turbulence at weak coupling, coherent spiral organization at intermediate coupling, and global synchronization or homogenization at strong coupling. These transitions are quantitatively characterized using synchronization measures, spatial correlations, and spectral analysis, revealing a shift from broadband spiral activity to coherent oscillations. A weak periodic forcing term is introduced to probe the interplay between excitability and long-range coordination while preserving intrinsic dynamics. The predicted frequencies, correlation lengths, and dynamical regimes are consistent with experimental observations, demonstrating that the model captures biologically relevant scales and provides a framework linking microscopic excitability to macroscopic pattern formation.