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Morphoelasticity of large bending deformations of cell sheets during development

Pierre A. Haas and Raymond E. Goldstein
Phys. Rev. E 103, 022411 – Published 22 February 2021

Abstract

Deformations of cell sheets during morphogenesis are driven by developmental processes such as cell division and cell shape changes. In morphoelastic shell theories of development, these processes appear as variations of the intrinsic geometry of a thin elastic shell. However, morphogenesis often involves large bending deformations that are outside the formal range of validity of these shell theories. Here, by asymptotic expansion of three-dimensional incompressible morphoelasticity in the limit of a thin shell, we derive a shell theory for large intrinsic bending deformations and emphasize the resulting geometric material anisotropy and the elastic role of cell constriction. Taking the invagination of the green alga Volvox as a model developmental event, we show how results for this theory differ from those for a classical shell theory that is not formally valid for these large bending deformations and reveal how these geometric effects stabilize invagination.

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  • Received 14 July 2020
  • Revised 23 November 2020
  • Accepted 7 January 2021

DOI:https://doi.org/10.1103/PhysRevE.103.022411

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

  1. Physical Systems
Physics of Living Systems

Authors & Affiliations

Pierre A. Haas1,2,* and Raymond E. Goldstein1,†

  • 1Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
  • 2Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, United Kingdom

  • *Current address: Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany; haas@pks.mpg.de
  • r.e.goldstein@damtp.cam.ac.uk

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Issue

Vol. 103, Iss. 2 — February 2021

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