Elasticity and Glocality: Initiation of Embryonic Inversion in $Volvox$

Abstract

Elastic objects across a wide range of scales deform under local changes of their intrinsic properties, yet the shapes are $glocal$, set by a complicated balance between local properties and global geometric constraints. Here, we explore this interplay during the inversion process of the green alga $Volvox$, whose embryos must turn themselves inside out to complete their development. This process has recently been shown [S. Höhn $etal.$, $Phys.Rev.Lett.$ $\text{114}$, 178101 (2015)] to be well described by the deformations of an elastic shell under local variations of its intrinsic curvatures and stretches, although the detailed mechanics of the process have remained unclear. Through a combination of asymptotic analysis and numerical studies of the bifurcation behavior, we illustrate how appropriate local deformations can overcome global constraints to initiate inversion.

10 pages, 8 figures

References in corpus (5)

• Green Algae as Model Organisms for Biological Fluid Dynamics
• Dynamics of Snapping Beams and Jumping Poppers
• Geometrically controlled snapping transitions in shells with curved creases
• Dynamics of a $Volvox$ Embryo Turning Itself Inside Out
• Osmotic buckling of spherical capsules

Cited by in corpus (7)

• Curvature-Driven Morphing of Non-Euclidean Shells
• Morphoelasticity of Large Bending Deformations of Cell Sheets during Development
• Likely equilibria of stochastic hyperelastic spherical shells and tubes
• The nonlinear buckling behavior of a complete spherical shell under uniform external pressure and homogenous natural curvature
• Embryonic Inversion in $Volvoxcarteri$: The Flipping and Peeling of Elastic Lips
• Likely oscillatory motions of stochastic hyperelastic solids
• Cut it out: Out-of-plane stresses in cell sheet folding of Volvox embryos