Elasticity and glocality: initiation of embryonic inversion in Volvox.

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Haas, Pierre A 
Goldstein, Raymond E  ORCID logo  https://orcid.org/0000-0003-2645-0598

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 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 behaviour, we illustrate how appropriate local deformations can overcome global constraints to initiate inversion.

Volvox, cell sheet folding, embryonic inversion, Elasticity, Models, Biological, Volvox
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J R Soc Interface
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The Royal Society
Engineering and Physical Sciences Research Council (EP/M017982/1)
EPSRC (1345122)
Wellcome Trust (097855/Z/11/Z)
We thank Stephanie H¨ohn, Aurelia R. HonerkampSmith and Philipp Khuc Trong for extensive discussions. This work was supported in part by an EPSRC studentship (PAH), an EPSRC Established Career Fellowship (REG), and a Wellcome Trust Senior Investigator Award (REG).