Abstract

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

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. We derive a continuum theory for a simple differential-tension model of a two-dimensional epithelial monolayer 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 nonlinear and nonlocal elastic behaviour at the continuum level.

Shape-Shifting Polyhedral Droplets:

Cooled oil emulsion droplets in aqueous surfactant solution have been observed to flatten into a remarkable host of polygonal shapes with straight edges and sharp corners, but different driving mechanisms — (i) a partial phase transition of the bulk oil phase and (ii) buckling of the interfacially frozen surfactant monolayer — have been proposed. Combining experiment and theory, we analyse the initial stages of the phase diagram of these ‘shape-shifting’ droplets, during which a polyhedral droplet flattens into a polygonal platelet. Using reflected-light microscopy, we reveal how an icosahedral droplet evolves through an intermediate octahedral stage to flatten into a hexagonal platelet. This behaviour is reproduced by a theoretical model of the phase transition mechanism, but the buckling mechanism can only reproduce the flattening if surface tension decreases by several orders of magnitude during cooling so that the flattening is driven by buoyancy.