Wrinkling instability in unsupported epithelial sheets

TL;DR

This paper reveals that unsupported epithelial sheets can spontaneously wrinkle due to differential surface tension, offering a new understanding of tissue patterning independent of substrate influence.

Contribution

The authors develop an exact elasticity theory for unsupported epithelial monolayers, identifying differential surface tension as the driver of wrinkling, unlike traditional substrate-dependent mechanisms.

Findings

Epithelial sheets can wrinkle without a substrate.

Differential surface tension causes wrinkling.

The theory maps to solid plate models with a phantom substrate.

Abstract

We investigate the elasticity of unsupported epithelial monolayer and we discover that unlike a thin solid plate, which wrinkles if geometrically incompatible with the underlying substrate, the epithelium may do so even in absence of the substrate. From a cell-based model, we derive an exact elasticity theory and discover wrinkling driven by the differential apico-basal surface tension. Our theory can be mapped onto that for solid plates by introducing a phantom substrate whose stiffness is finite beyond a critical differential tension. This suggests a new mechanism for an autonomous control of tissues over the length scale of their surface patterns.