Embryonic inversion inVolvox carteri: The flipping and peeling of elastic lips

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.

Efficient snap-through of spherical caps by applying a localized curvature stimulus

“…The process is as follows: To begin, we coat a metal ball-bearing (R sphere ∈ [12, 75] mm) with viscous polydimethylsiloxane (PDMS), ensuring a relatively uniform thickness [36]. Once the PDMS has cured, we use a laser-cut (Epilog Laser Helix, 75W) ring (inner radius R p ∈ [2,65] A second green layer is added. f. Once the green layer is cured, a PDMS cap (cut from a sphere of the same size, in the same manner as a.-d.) of radius Rp is centered at the top of the sphere.…”

“…Thus, the Volvox embryo must entirely invert itself during morphogenesis. To do so, cells in a "bend region" adopt a wedge shape, which creates a localized curvature that leads to an eventual instability reminiscient of snap-through [1,2]. Depending on the species, the bend region either propagates from the open phialopore (located at the pole), where four lips peel back to drive type-A inversion, or begins at the equator, where invagination leads to type-B inversion [3].…”

“…Depending on the species, the bend region either propagates from the open phialopore (located at the pole), where four lips peel back to drive type-A inversion, or begins at the equator, where invagination leads to type-B inversion [3]. Arrested inversion of mutant Volvox has been linked to insufficient size of the bend region or intrinsic curvature therein [2].…”

Volvox and volvocine green algae

“…This developmental bifurcation gives rise to a post-cleavage embryo containing ~ 2000 small somatic-precursor cells arranged like a hollow-ball with 12-16 exterior-facing large gonidialprecursor cells in predictable evenly spaced locations around the embryo's anterior region. The remarkable process of inversion immediately follows embryonic cleavage and involves a sequence of coordinated cell shape changes that enable the embryo to turn itself completely inside-out and assume its adult configuration with outward-oriented somatic precursors and interiorly located gonidial precursors [33]. Anterior-posterior (A-P) embryonic polarity and the presence of cytoplasmic bridges connecting post-mitotic blastomeres are key derived features that enable inversion to occur [34][35][36][37].…”

“…Volvox is amenable to most standard methods of microscopic imaging including single plane illumination microscopy (SPIM, a.k.a. light sheet microscopy) to study development and morphogenesis [33,57], and video microscopy to study motility and flagella dynamics. A recent study was able to establish in vitro motility in "zombie" Volvox whose cells were permeabilized but whose flagella could be re-activated in the presence of ATP and calcium to investigate flagella responses to calcium signaling [54].…”