Curvature and spiral geometry in aggregation patterns of Dictyostelium discoideum

Abstract

Aggregation patterns of the slime mould Dictyostelium discoideum were recorded using dark-field equipment combined with video techniques. Computerized image processing allowed the analysis of wave collision structures, expanding concentric circles and rotating spirals in terms of wave velocity and front geometry, as previously done in the Belousov-Zhabotinskii reaction, a chemical system showing similar patterns. We verified the linear relationship between the normal velocity and the curvature of wave fronts predicted by a reaction-diffusion model. The proportionality factor, which in this case is the diffusion coefficient of the chemical signal transmitter cAMP establishing communication between the cells, was determined to be 0.66×10-5cm2s-1. From measurements of positively curved circular waves, we could roughly estimate the critical radius of wave propagation Rcrit (approximately 200_m); which means that up to 500 cells are necessary to form a center of an aggregation structure. Furthermore, we analyzed the geometrical parameters of spiral wave patterns and estimated the core radius ro to be approximately equal to 300_m.