  In cell extrusion, a cell embedded in an epithelial monolayer loses its
apical or basal surface and is subsequently squeezed out of the monolayer by
neighboring cells. Cell extrusions occur during apoptosis,
epithelial-mesenchymal transition, or pre-cancerous cell invasion. They play
important roles in embryogenesis, homeostasis, carcinogenesis, and many other
biological processes. Although many of the molecular factors involved in cell
extrusion are known, little is known about the mechanical basis of cell
extrusion. We used a three-dimensional (3D) vertex model to investigate the
mechanical stability of cells arranged in a monolayer with 3D foam geometry. We
found that when the cells composing the monolayer have homogeneous mechanical
properties, cells are extruded from the monolayer when the symmetry of the 3D
geometry is broken due to an increase in cell density or a decrease in the
number of topological neighbors around single cells. Those results suggest that
mechanical instability inherent in the 3D foam geometry of epithelial
monolayers is sufficient to drive epithelial cell extrusion. In the situation
where cells in the monolayer actively generate contractile or adhesive forces
under the control of intrinsic genetic programs, the forces act to break the
symmetry of the monolayer, leading to cell extrusion that is directed to the
apical or basal side of the monolayer by the balance of contractile and
adhesive forces on the apical and basal sides. Although our analyses are based
on a simple mechanical model, our results are in accordance with observations
of epithelial monolayers {\it in vivo} and consistently explain cell extrusions
under a wide range of physiological and pathophysiological conditions. Our
results illustrate the importance of a mechanical understanding of cell
extrusion and provide a basis by which to link molecular regulation to physical
processes.
