Thickness of epithelia on wavy substrates: measurements and continuous models

TL;DR

This study investigates how epithelial tissue thickness varies on wavy substrates, comparing experimental measurements with continuum models, and finds that active stress modeling best explains the observed patterns.

Contribution

It introduces a continuum mechanics model incorporating active stress to accurately describe epithelial thickness variations on sinusoidal substrates.

Findings

Epithelial thickness follows substrate profile at long wavelengths.

Cells are thicker in valleys than ridges at short wavelengths.

Active stress model aligns well with experimental data.

Abstract

We measured the thickness of MDCK epithelia grown on substrates with a sinusoidal profile. We show that while at long wavelength the profile of the epithelium follows that of the substrate, at short wavelengths cells are thicker in valleys than on ridges. This is reminiscent of the so-called {\guillemotleft} healing length {\guillemotright} in the case of a thin liquid film wetting a rough solid substrate. We explore the ability of continuum mechanics models to account for these observations. Modeling the epithelium as a thin liquid film, with surface tension, does not fully account for the measurements. Neither does modeling the epithelium as a thin incompressible elastic film. On the contrary, the addition of an apical active stress gives satisfactory agreement with measurements, with one fitting parameter, the ratio between the active stress and the elastic modulus.