A tug-of-war between stretching and bending in living cell sheets

Abstract

The balance between stretching and bending deformations characterizes shape transitions of thin elastic sheets. While stretching dominates the mechanical response in tension, bending dominates in compression after an abrupt buckling transition. Recently, experimental results in suspended living epithelial monolayers have shown that, due to the asymmetry in surface stresses generated by molecular motors across the thickness $e$ of the epithelium, the free edges of such tissues spontaneously curl out-of-plane, stretching the sheet in-plane as a result. This suggests that a competition between bending and stretching sets the morphology of the tissue margin. In this study, we use the framework of non-euclidean plates to incorporate active pre-strain and spontaneous curvature to the theory of thin elastic shells. We show that, when the spontaneous curvature of the sheet scales like $1/e$, stretching and bending energies have the same scaling in the limit of a vanishingly small thickness and therefore both compete, in a way that is continuously altered by an external tension, to define the three-dimensional shape of the tissue.

References in corpus (8)

• Elastic theory of unconstrained non-Euclidean plates
• Mechanics of active surfaces
• The von Karman equations for plates with residual strain
• Collective dynamics of actomyosin cortex endow cells with intrinsic mechanosensing properties
• Dynamics of a $Volvox$ Embryo Turning Itself Inside Out
• Stability boundaries for wrinkling in highly stretched elastic sheets
• Curvature-Driven Morphing of Non-Euclidean Shells
• Nonlinear and Nonlocal Elasticity in Coarse-Grained Differential-Tension Models of Epithelia

Cited by in corpus (2)

• Review: How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale
• Cut it out: Out-of-plane stresses in cell sheet folding of Volvox embryos