Spatial Pattern Formation During Aggregation of the Slime Mould Dictyostelium discoideum

Stream formation and spiral wave behaviour during the aggregation of Dictyostelium discoideum (Dd)are studied in a model based on the Martiel-Goldbeter equations for cAMP relay, combined with chemotactic motion of Ddcells. The results show that stream formation occurs if the turnover rate of intracellular cAMP is increased. This increase in the turnover rate of cAMP [in]leads to a dependence of the speed of the cAMP wave on the cell density. We propose that this dependence of wave speed on cell density is the underlying mechanism for stream formation. Besides stream formation, increasing the turnover rate of cAMP [in]also results in a spiral wave period that decreases during aggregation, a phenomenon that is commonly observed in situ. Furthermore, the dependence of wave speed on cell density is measured empirically. The speed of the cAMP wave is found to decrease as the wave travels from high to low cell density. This indicates that in situ, wave speed does depend on cell denisty.