Abstract
The morphogenetic movement and cell sorting in cell aggregates from the mound stage to the migrating slug stage of the cellular slime mold Dictyostelium discoideum were studied using a mathematical model. The model postulates that the motive force generated by the cells is in equilibrium with the internal pressure and mechanical resistance. The moving boundary problem derived from the force balance equation and the continuity equation has stationary solutions in which the aggregate takes the shape of a spheroid (or an ellipse in two-dimensional space) with the pacemaker at one of its foci, moving at a constant speed. Numerical calculations in two-dimensional space showed that an irregularly shaped aggregate changes its shape to become an ellipse as it moves. Cell aggregates consisting of two cell types differing in motive force exhibit cell sorting and become elongated, suggesting the importance of prestalk/prespore differentiation in the morphogenesis of Dictyostelium.
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