Mapping mechanical stress in curved epithelia of designed size and shape

Abstract

The function of organs such as lungs, kidneys and mammary glands relies on the three-dimensional geometry of their epithelium. To adopt shapes such as spheres, tubes and ellipsoids, epithelia generate mechanical stresses that are generally unknown. Here we engineered curved epithelial monolayers of controlled size and shape and mapped their state of stress. We designed pressurized epithelia with circular, rectangular and ellipsoidal footprints. We developed a computational method to map the stress tensor in these epithelia. This method establishes a direct correspondence between epithelial shape and mechanical stress without assumptions of material properties. In epithelia with spherical geometry spanning more than one order of magnitude in radius, we show that stress weakly increases with areal strain in a size-independent manner. In epithelia with rectangular and ellipsoidal cross-section we found pronounced stress anisotropies consistent with the asymmetric distribution of tractions measured at the cell-substrate contact line. In these anisotropic profiles, cell shape tended to align with the direction of maximum principal stress but this alignment was non-universal and depended on epithelial geometry. Besides interrogating the fundamental mechanics of epithelia over a broad range of sizes and shapes, our approach will enable a systematic study of how geometry and stress influence epithelial fate and function in three-dimensions.

Mechanobiological approaches to synthetic morphogenesis: learning by building

“…This mechanism identified in a synthetic system was later established in vivo during drosophila gastrulation [63]. More recent studies also took advantage of closed-dome structures to map stresses on domes of different shapes [61] and built domes from human stem cells [7], with an elongated footprint to mimic the neural tube geometry. Here, stem cells seeded on rectangular patterns were covered with Matrigel and subsequently self-organized into a tissue bilayer.…”

“…Domes are curved, lumenized epithelial structures attached to a substrate [60,61] (Figure 2C-C'). They can be used to model lumen-filled in vivo organs like the healthy blastocyst or the otic vesicle, as well as diseased organs like the polycystic kidney, with more control than free-floating 3D spheres that we discussed above.…”

A morphoelastic theory of biological shells: Application to the Volvox globator invagination

“…Folding is a distinctive feature of embryonic transformation allowing to acquire a three-dimensional structure driven either by differential growth [3] or by active contractility [4]. In both case, folding emerges as a mechanoadaptation process with the formation of invaginations/evaginations as the cellular tissue behaves as an elastic membrane [5,6]. In many biological system models, folding may lead to the inversion of the cellular assembly, in order to fulfil a biological function, such as the assembly of the adult exoskeleton in the Drosophila disc [7] and the telencefalic develoment in mammals and teleosts [8].…”

Mechanics of epithelial tissue subjected to controlled pressure

“…Not just 2D shape, epithelial monolayers are also able to respond to curvature by regulating cell migration, orientation, cell/nucleus size, and shape (Marín-Llauradó et al, 2022, Schamberger et al, 2022 (see fig 2.3 C). For example, an epithelial monolayer on hemispheres of elastomers acts as a fluid with increasing curvature (Tang et al, 2022).…”

“…Second, epithelial domes, where MDCK cells pump ions to form fluid-filled blisters, have been used (Lever, 1979). Recently, my colleagues, Ernest Latorre and Ariadna Marin-Llaurado, have enhanced control over the curvature, shape, and size of the domes (Latorre et al, 2018, Marín-Llauradó et al, 2022, details on this system in the next chapter. These experiments showed that elasticity measurements of the monolayer were two orders of magnitude larger than those of individual cellular parts, and the monolayer could sustain more than 200% strain before the rupture of cell-cell junctions.…”