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The Scutoid: additional solution for three-dimensional packing

The Scutoid: additional solution for three-dimensional packing

Tissues flex into intricate three-dimensional forms that lead to organs as an embryo grows. This process’s building blocks are epithelial cells, which create the outer layer of skin, for example. They also line all animals’ blood arteries and organs.

These cells are closely packed together. It has been suggested that epithelial cells acquire either columnar or bottle-like forms to accommodate the bending that happens during embryonic development.

A group of scientists investigated this phenomenon further and found a new geometric form in the process, which they named scutoid due to its resemblance to the scutellum—the posterior portion of an insect thorax or midsection. They discovered that during tissue bending, epithelial cells adopt a previously unknown form that allows the cells to consume less energy while maintaining packing integrity.

“During the modeling process, the results we saw were weird,” says Buceta. “Our model predicted that as the curvature of the tissue increases, columns and bottle-shapes were not the only shapes that cells may develop. To our surprise, the additional shape didn’t even have a name in math! One does not normally have the opportunity to name a new shape.”

A mathematical model for curved epithelia uncovers a novel geometrical solid. a Scheme representing planar columnar/cubic monolayer epithelia. Cells are simplified as prisms. b Scheme illustrating an invagination or fold in a columnar/cubic monolayer epithelium. Cells adopt the called “bottle shape” that would be simplified as frusta. c Mathematical model for an epithelial tube. A Voronoi diagram is drawn on the surface of a cylinder (representing the apical surface of the epithelial tube). The seeds of each Voronoi cells are projected in an outer cylinder (representing the basal surface of the epithelial tube). This can induce a topological change, a cell intercalation. Yellow and blue cells are neighbours in the apical surface but not in the basal surface. The reciprocal occurs for red and green cells. Ra, radius from the centre of the cylinders to the apical surface. Rb, radius from the centre of the cylinders to the basal surface. d Modelling clay figures illustrating two scutoids participating in a transition and two schemes for scutoids solids. Scutoids are characterized by having at least a vertex in a different plane to the two bases and present curved surfaces. e A dorsal view of a Protaetia speciose beetle of the Cetoniidae family. The white lines highlight the resemblance of its scutum, scutellum and wings with the shape of the scutoids. Illustration from Dr. Nicolas Gompel, with permission. f 3D reconstruction of the cells forming a tube with Rb/Ra=2.5 Rb/Ra=2.5. The four-cell motif (green, yellow, blue, and red cells) shows an apico-basal cell intercalation. g Detail of the apico-basal transition, showing how the blue and yellow cells contact in the apical part, but not in the basal part. The figure also shows that scutoids present concave surfaces
3D tissue packing of curved epithelia. a Example of Drosophila salivary gland and its processed images. Scale bar = 100 μm. b Confocal images showing the apico-basal cell intercalation of epithelial cells marked with green, yellow, red, and blue pseudo-colors. The green cell participates in two apico-basal transitions. c 3D reconstruction of the same cells labeled in b using the same color code. The image confirms the presence of concave surfaces predicted by the mathematical model

To validate the model’s predictions, the researchers looked at the three-dimensional packing of different tissues in various species. The experimental results verified that epithelial cells adopted morphologies and three-dimensional packing patterns anticipated by the computer model, finding preliminary evidence of the twisted prism in the epithelial tissue of both fruit flies and zebrafish.

Using biophysical methods, the team contends that scutoids stabilize three-dimensional packing and make it more energy-efficient. “We have unlocked nature’s way to attaining effective epithelial bending,” says Buceta.

However, because this type of skin cell is seen in all species, the team believes that identifying the form might be a watershed moment in how we think about the epithelium. The researchers believe their results will lead to a novel new understanding of the three-dimensional organization of epithelial organs.

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“For example, if you are looking to grow artificial organs, this discovery could help you build a scaffold to encourage this kind of cell packing, accurately mimicking nature’s way to efficiently develop tissues,” says Buceta.

Scutoids are a geometrical solution to three-dimensional packing of epithelia, Pedro Gómez-Gálvez, Pablo Vicente-Munuera, Antonio Tagua, Cristina Forja, Ana M. Castro, Marta Letrán, Andrea Valencia-Expósito, Clara Grima, Marina Bermúdez-Gallardo, Óscar Serrano-Pérez-Higueras, Florencia Cavodeassi, Sol Sotillos, María D. Martín-Bermudo, Alberto Márquez, Javier Buceta & Luis M. Escudero

Published: July 2018
DOI: https://doi.org/10.1038/s41467-018-05376-1

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