Quantum mechanics

Epithelial tissue

Scale (ratio)

Biology

Geometric shape

Distribution (mathematics)

Genetics

Physics

Mathematics

Epithelium

Condensed matter physics

Mathematical analysis

Geometry

Cell

Biological system

Biophysics

Jamming

Nature Physics

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 variability of shape from cell to cell is regarded most often as biological noise. But where do cell shape and its variability come from? Here we report that cell shape and shape variability are mutually constrained through a relationship that is purely geometrical. That relationship is shown to govern processes as diverse as maturation of the pseudostratified bronchial epithelial layer cultured from non-asthmatic or asthmatic donors, and formation of the ventral furrow in the Drosophila embryo. Across these and other epithelial systems, shape variability collapses to a family of distributions that is common to all. That distribution, in turn, is accounted for 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 suggest a connection between jamming and geometry that spans living organisms and inert jammed systems, and thus transcends system details. Although molecular events are needed for any complete theory of cell shape and cell packing, observations point to the hypothesis that jamming behaviour at larger scales of organization sets overriding geometric constraints. Epithelial cells are shown to scale via a shape distribution that is common to a number of different systems, suggesting that cell shape and shape variability are constrained through a relationship that is purely geometrical.

Geometric constraints during epithelial jamming