We theoretically investigate the mechanical stability of three-dimensional (3D ) foam geometry in a cell sheet and apply its understandings to epithelial integrity and cell delamination. Analytical calculations revealed that the monolayer integrity of cell sheet is lost to delamination by a spontaneous symmetry breaking, inherently depending on the 3D foam geometry of cells; i. e., the instability spontaneously appears when the cell density in the sheet plane increases and/or when the number of neighboring cellsdecreases, as observed in vivo. The instability is also facilitated by the delaminated cell-specific force generation upon lateral surfaces, which are driven by cell-intrinsic genetic programs during cell invasion and apoptosis in physiology. In principle, this instability emerges from the force balance on the lateral boundaries among cells. Additionally, taking into account the cell-intrinsic force generation on apical and basal sides , which are also broadly observed in morphogenesis, homeostasis, and carcinogenesis, we found apically/basally directed cell delaminations and pseudostratified structures, which could universally explain mechanical regulations of epithelial geometries in both physiology and pathophysiology{\it   .
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 .
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We theoretically investigate the mechanical stability of
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
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) foam geometry in a cell sheet and apply its understandings to epithelial integrity and cell delamination. Analytical calculations revealed that the monolayer integrity of cell sheet is lost to delamination by a spontaneous symmetry breaking, inherently depending on the
) vertex model to investigate the mechanical stability of cells arranged in a monolayer with
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of cells; i. e.,
. 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,
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instability spontaneously appears when the cell density in
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
D
sheet plane increases and/or when the number of neighboring cellsdecreases, as observed in vivo. The instability is also facilitated by the delaminated cell-specific force generation upon lateral surfaces, which are driven by cell-intrinsic genetic programs during cell invasion and apoptosis in physiology. In principle, this instability emerges from the force balance on the lateral boundaries among cells. Additionally, taking into account the cell-intrinsic force generation on
R
, which are also broadly observed in morphogenesis, homeostasis, and carcinogenesis, we found apically/basally directed cell delaminations and pseudostratified structures, which could universally explain mechanical regulations of epithelial geometries in both physiology and pathophysiology
. Although our analyses are based on a simple mechanical model, our results are in accordance with observations of epithelial monolayers
A
in vivo
A
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