Elasticity and Glocality: Initiation of Embryonic Inversion in ${\it Volvox}$
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arXiv
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| Format: | Preprint |
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2015
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| _version_ | 1866914194370068480 |
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| author | Haas, Pierre A. Goldstein, Raymond E. |
| author_facet | Haas, Pierre A. Goldstein, Raymond E. |
| contents | Elastic objects across a wide range of scales deform under local changes of their intrinsic properties, yet the shapes are ${\it glocal}$, 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 ${\it Volvox}$, whose embryos must turn themselves inside out to complete their development. This process has recently been shown [S. Höhn ${\it et~al}.$, ${\it Phys. Rev. Lett.}$ $\textbf{114}$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1507_01439 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Elasticity and Glocality: Initiation of Embryonic Inversion in ${\it Volvox}$ Haas, Pierre A. Goldstein, Raymond E. Soft Condensed Matter Cell Behavior Elastic objects across a wide range of scales deform under local changes of their intrinsic properties, yet the shapes are ${\it glocal}$, 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 ${\it Volvox}$, whose embryos must turn themselves inside out to complete their development. This process has recently been shown [S. Höhn ${\it et~al}.$, ${\it Phys. Rev. Lett.}$ $\textbf{114}$, 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. |
| title | Elasticity and Glocality: Initiation of Embryonic Inversion in ${\it Volvox}$ |
| topic | Soft Condensed Matter Cell Behavior |
| url | https://arxiv.org/abs/1507.01439 |