Modelling apical constriction in epithelia using elastic shell theory

Complex structures from patterned cell sheets

The formation of three-dimensional structures from patterned epithelial sheets plays a key role in tissue morphogenesis. An important class of morphogenetic mechanisms relies on the spatio-temporal control of apical cell contractility, which can result in the localized bending of cell sheets and in-plane cell rearrangements. We have recently proposed a modified vertex model that can be used to systematically explore the connection between the two-dimensional patterns of cell properties and the emerging three-dimensional structures. Here we review the proposed modelling framework and illustrate it through the computational analysis of the vertex model that captures the salient features of the formation of the dorsal appendages during Drosophila oogenesis.This article is part of the themed issue 'Systems morphodynamics: understanding the development of tissue hardware'.

Shape Transformations of Epithelial Shells

Regulated deformations of epithelial sheets are frequently foreshadowed by patterning of their mechanical properties. The connection between patterns of cell properties and the emerging tissue deformations is studied in multiple experimental systems, but the general principles remain poorly understood. For instance, it is in general unclear what determines the direction in which the patterned sheet is going to bend and whether the resulting shape transformation will be discontinuous or smooth. Here these questions are explored computationally, using vertex models of epithelial shells assembled from prismlike cells. In response to rings and patches of apical cell contractility, model epithelia smoothly deform into invaginated or evaginated shapes similar to those observed in embryos and tissue organoids. Most of the observed effects can be captured by a simpler model with polygonal cells, modified to include the effects of the apicobasal polarity and natural curvature of epithelia. Our models can be readily extended to include the effects of multiple constraints and used to describe a wide range of morphogenetic processes.

Regulation of tissue morphodynamics: an important role for actomyosin contractility

Forces arising from contractile actomyosin filaments help shape tissue form during morphogenesis. Developmental events that result from actomyosin contractility include tissue elongation, bending, budding, and collective migration. Here, we highlight recent insights into these morphogenetic processes from the perspective of actomyosin contractility as a key regulator. Emphasis is placed on a range of results obtained through live imaging, culture, and computational methods. Combining these approaches in the future has the potential to generate a robust, quantitative understanding of tissue morphodynamics.

Generating suspended cell monolayers for mechanobiological studies

Cell monolayers line most of the surfaces and cavities in the human body. During development and normal physiology, monolayers sustain, detect and generate mechanical stresses, yet little is known about their mechanical properties. We describe a cell culture and mechanical testing protocol for generating freely suspended cell monolayers and examining their mechanical and biological response to uniaxial stretch. Cells are cultured on temporary collagen scaffolds polymerized between two parallel glass capillaries. Once cells form a monolayer covering the collagen and the capillaries, the scaffold is removed with collagenase, leaving the monolayer suspended between the test rods. The suspended monolayers are subjected to stretching by prying the capillaries apart with a micromanipulator. The applied force can be measured for the characterization of monolayer mechanics. Monolayers can be imaged with standard optical microscopy to examine changes in cell morphology and subcellular organization concomitant with stretch. The entire preparation and testing protocol requires 3-4 d.