  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.

Soft Condensed Matter;Tissues and Organs