Differentiation, cell sorting and proportion regulation in the slug stage of Dictyostelium discoideum

Recent experimental work suggests that under normal conditions cell sorting plays an important part in maintaining and re-establishing the axial pattern of cell types in the slug stage of the cellular slime mold Dictyostelium discoideum. Following removal of the anterior zone of the slug, anterior-like cells that are normally distributed throughout the posterior of the slug rapidly migrate to the anterior end of the transected slug, and new anterior-like cells appear in the posterior portion. These results provide evidence that the direct linkage between spatial location and differentiation hypothesized in positional information models of spatial pattern formation is not universal. In this paper we develop and analyze a class of mathematical models of the slug in which cell determination can be less rigidly tied to spatial location, and which involve chemotactic cell sorting to re-establish and maintain the spatial pattern of cell types. We show that these models can reproduce the qualitative aspects of the experimental observations and that sorting takes place on the observed time scale when reasonable values of the parameters are used.