Embryonic Inversion in $Volvox~carteri$: The Flipping and Peeling of Elastic Lips

TL;DR

This paper models the mechanical process of embryonic inversion in Volvox carteri, focusing on the elastic deformation of the lips that facilitate the flipping and peeling of the embryo during development.

Contribution

It introduces an averaged elastic theory to explain the mechanics behind the inversion process, linking cell shape changes to mechanical behavior.

Findings

Inversion involves elastic deformation of lips during embryo flipping.

Inhibition of cell shape changes arrests inversion, explained by mechanical model.

The model aligns with experimental observations of inversion mechanics.

Abstract

The embryos of the green alga $Volvox~carteri$ are spherical sheets of cells that turn themselves inside out at the close of their development through a programme of cell shape changes. This process of inversion is a model for morphogenetic cell sheet deformations; it starts with four lips opening up at the anterior pole of the cell sheet, flipping over and peeling back to invert the embryo. Experimental studies have revealed that inversion is arrested if some of these cell shape changes are inhibited, but the mechanical basis for these observations has remained unclear. Here, we analyse the mechanics of this inversion by deriving an averaged elastic theory for these lips and we interpret the experimental observations in terms of the mechanics and evolution of inversion.