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

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