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

The embryos of the green alga Volvox are spherical sheets of cells that turn themselves inside out at the close of their development through a program of cell shape changes. This process of inversion is a simple model for the mathematical analysis of morphogenesis [1], yet shares many features with processes such as gastrulation in higher organisms. In Volvox carteri, inversion 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 in V. carteri is arrested if some cell shape changes are inhibited, but the mechanical basis for these observations has remained unclear. 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 [2].
[1] S Höhn, AR Honerkamp-Smith, PA Haas, P Khuc Trong, and RE Goldstein, Phys. Rev. Lett. 114, 178101 (2015); PA Haas, SSMH Höhn, AR Honerkamp-Smith, JB Kirkegaard, and RE Goldstein, PLOS Biol. 16, e2005536 (2018).
[2] PA Haas and RE Goldstein, Phys. Rev. E (2018, in press), arXiv:1808.00828.