Mechanical state, material properties and continuous description of an epithelial tissue

Abstract

During development, epithelial tissues undergo extensive morphogenesis based on coordinated changes of cell shape and position over time. Continuum mechanics describes tissue mechanical state and shape changes in terms of strain and stress. It accounts for individual cell properties using only a few spatially averaged material parameters. To determine the mechanical state and parameters in the Drosophila pupa dorsal thorax epithelium, we severed in vivo the adherens junctions around a disc-shaped domain comprising typically a hundred cells. This enabled a direct measurement of the strain along different orientations at once. The amplitude and the anisotropy of the strain increased during development. We also measured the stress-to-viscosity ratio and similarly found an increase in amplitude and anisotropy. The relaxation time was of the order of 10 s. We propose a space -time, continuous model of the relaxation. Good agreement with experimental data validates the description of the epithelial domain as a continuous, linear, visco-elastic material. We discuss the relevant time and length scales. Another material parameter, the ratio of external friction to internal viscosity, is estimated by fitting the initial velocity profile. Together, our results contribute to quantify forces and displacements, and their time evolution, during morphogenesis.

Direct laser manipulation reveals the mechanics of cell contacts in vivo

“…Notably, so-called vertex models (31), usually based on energy minimization, do not incorporate energy dissipation and thus, cannot predict the tissue dynamics. Here, we propose a vertex-based model, which bridges usual vertex models and continuum mechanics with finite elements approaches that integrate viscoelastic constitutive behavior (32,33). In addition, it captures the nontrivial two-timescale relaxation dynamics evidenced by pull-and-release experiments.…”

Measuring forces and stressesin situin living tissues

“…The initial velocity of wound margin retraction or closure after ablation measures the stress-to-viscosity ratio within the tissue. Alternatively, severing a large circle (Bonnet et al, 2012;Etournay et al, 2015) reveals at once the main directions of stress and its anisotropy (Fig. 2Ca,Cb).…”

“…Such experiments also helped to understand how planar cell polarity can control mechanics during dorsal thorax morphogenesis (Bonnet et al, 2012), and how the wing morphogenesis is affected by tensions at its boundaries (Etournay et al, 2015).…”

Mechanisms and mechanics of cell competition in epithelia

“…The live epithelium can be visualized using imaging during pupal stages. At these stages, cells divide but the overall size of the tissue remains relatively constant 81 , and thus tissue pressure is expected to rise. During this time, many cells at the prospective dorsal midline undergo delamination.…”

“…Nevertheless, there is a need for validation with experimental measurements of forces within tissues. The most successful approach so far involves ablating individual junctions with an infrared laser and inferring the tension from the initial speed of vertex recoil 81,84 . Because this method is invasive and samples only a small number of junctions, alternative approaches are needed.…”