The spatial pattern of aggregation centres in the cellular slime mould.

The spatial pattern of aggregation centres of the slime mould Dictyostelium discoideum was analysed by using nearest-neighbour distributions. Both undisturbed cultures, and cultures that were initiated from cells dissociated from cultures that had already aggregated, formed non-randomly spaced patterns. However, the minimal distance between aggregates in undisturbed cultures was approximately ten times that observed in dissociated cultures. In undisturbed cultures the aggregate size is regulated as a function of cell density (Bonner + Hoffman, 1963): as cell density increases aggregate density decreases and the aggregate size consequently increases. At the same cell density more and smaller aggregates were formed by dissociated cultures than by undisturbed cultures. Nevertheless, the same cell-density-dependent regulation of aggregate density existed in the dissociated cultures. Here a model is developed to account for both the non-random spacing and the cell-density-dependent regulation of aggregate density. In this model, distance-dependent competition occurs between points in a random prepattern to generate patterns very similar to those observed in experiments. The cell-density-dependent regulation of the aggregate density can be explained by assuming that a constant fraction of the cell population has the capacity to initiate centres at the time of pattern determination regardless of the cell density. As the cell density is increased the fraction of potential centres that survive distance-dependent competition decreases and hence the aggregate size increases. These results suggest that distance-dependent competition may be a mechanism that evolved to control aggregate size at high cell densities. Results obtained with this model indicate that the decrease in aggregate size in dissociated cultures is due primarily to an increase in the fraction of the cell population capable of initiating centres. This implies that as morphogenesis progresses a greater fraction of the cell population acquire a capacity which they will not normally express. Although this increase may have a function in later stages of morphogenesis, it may also provide a way to ensure aggregation in small populations of amoebae and at low cell densities.