Morphoelasticity of Large Bending Deformations of Cell Sheets during Development

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 emphasise 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 stabilise invagination.

arXiv comment29 pages, 6 figures; corrected and expanded version

References in corpus (10)

• Elastic theory of unconstrained non-Euclidean plates
• Green Algae as Model Organisms for Biological Fluid Dynamics
• Morphogenesis of growing soft tissues
• Dynamics of a $Volvox$ Embryo Turning Itself Inside Out
• Curvature-Driven Morphing of Non-Euclidean Shells
• Geometry of wave propagation on active deformable surfaces
• Elasticity and Glocality: Initiation of Embryonic Inversion in $Volvox$
• Nonlinear and Nonlocal Elasticity in Coarse-Grained Differential-Tension Models of Epithelia
• The Elastic Theory of Shells using Geometric Algebra
• Embryonic Inversion in $Volvoxcarteri$: The Flipping and Peeling of Elastic Lips

Cited by in corpus (5)

• An asymptotically consistent morphoelastic shell model for compressible biological structures with finite-strain deformations
• Mechanics of poking a cyst
• Buckling by disordered growth
• Cut it out: Out-of-plane stresses in cell sheet folding of Volvox embryos
• Elasticity and plasticity of epithelial gap closure