Nonlinear and Nonlocal Elasticity in Coarse-Grained Differential-Tension Models of Epithelia

Abstract

The shapes of epithelial tissues result from a complex interplay of contractile forces in the cytoskeleta of the cells in the tissue, and adhesion forces between them. A host of discrete, cell-based models describe these forces by assigning different surface tensions to the apical, basal, and lateral sides of the cells. These differential-tension models have been used to describe the deformations of epithelia in different living systems, but the underlying continuum mechanics at the scale of the epithelium are still unclear. Here, we derive a continuum theory for a simple differential-tension model of a two-dimensional epithelium and study the buckling of this epithelium under imposed compression. The analysis reveals how the cell-level properties encoded in the differential-tension model lead to linear, nonlinear as well as nonlocal elastic behavior at the continuum level.

11 pages, 5 figures

References in corpus (7)

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Cited by in corpus (7)

• Theory of nematic and polar active fluid surfaces
• Morphoelasticity of Large Bending Deformations of Cell Sheets during Development
• Wrinkling instability in unsupported epithelial sheets
• A tug-of-war between stretching and bending in living cell sheets
• Likely oscillatory motions of stochastic hyperelastic solids
• Geometry of T1 transitions in epithelia
• (Un)buckling mechanics of epithelial monolayers under compression