A mathematical model for cell sorting,migration and shape in the slug stage ofDictyostelium discoideum

A mathematical model for cell sorting and migration in the slug stage of cellular slime moldsDictyostelium discoideum is proposed. Assuming that a slug is a “mixed fluid” of prespore and prestalk cells, a set of equations which describe the dynamics of cell distribution, internal pressure and velocity of hte slug are derived from the balance formula of individual cell movement. These equations are analyzed to obtain the spatial patterns of the two types of cells at dynamical equilibrium and the relationship between the migration velocity and the slug size. The body shape of the elongated slug at the migrating stage is also investigated, taking account of the law of surface tension. The stable shapes of slugs with different volumes are explicity obtaained and the existence of critical size of a slug is suggested.