  As an injury heals, an embryo develops, or a carcinoma spreads, epithelial
cells systematically change their shape. In each of these processes cell shape
is studied extensively, whereas variation of shape from cell-to-cell is
dismissed most often as biological noise. But where do cell shape and variation
of cell shape come from? Here we report that cell shape and shape variation are
mutually constrained through a relationship that is purely geometrical. That
relationship is shown to govern maturation of the pseudostratified bronchial
epithelial layer cultured from both non-asthmatic and asthmatic donors as well
as formation of the ventral furrow in the epithelial monolayer of the
Drosophila embryo in vivo. Across these and other vastly different epithelial
systems, cell shape variation collapses to a family of distributions that is
common to all and potentially universal. That distribution, in turn, is
accounted for quantitatively by a mechanistic theory of cell-cell interaction
showing that cell shape becomes progressively less elongated and less variable
as the layer becomes progressively more jammed. These findings thus uncover a
connection between jamming and geometry that is generic -spanning jammed living
and inert systems alike- and demonstrate that proximity of the cell layer to
the jammed state is the principal determinant of the most primitive features of
epithelial cell shape and shape variation.
