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18 June 2024

Scutoids, the Geometry of Cells

Estimated reading time Time 4 to read

Biology textbooks depict the generic cell as more or less spherical in shape, although it has been known for more than a century that this image of a squishy ball is misleading: cells have a rigid but changeable internal skeleton, or cytoskeleton, which determines its shape, whether it is a neuron or a muscle fibre. The shape of cells is an important area of research because it is closely related to their function. But there is still so much to learn that only recently a team of Spanish researchers discovered a new geometric cell shape that has curiously become a new pop icon of scientific culture, even cited in Marvel comics: the scutoid.

BBVA-OpenMind-Yanes-Escutoides la geometria de las celulas_1 The so-called Voronoi diagrams are irregular mosaic tiles, so that each tessera contains all the points of the plane that are closer to the so-called "seed" point of that tessera than to those of the others. Credit: Balu Ertl / CC BY-SA 4.0
The so-called Voronoi diagrams are irregular mosaic tiles, so that each tessera contains all the points of the plane that are closer to the so-called “seed” point of that tessera than to those of the others. Credit: Balu Ertl / CC BY-SA 4.0

While generic cells are represented as rounded shapes, those that form part of compact structures, such as the epithelium lining the intestine, are often drawn in 3D as prisms or parallelepipeds. This is a simplification, but the truth is that in order to pack themselves into such tissues, cells have to compress against one another, and this is not just passive compaction, as neighbouring cells are stitched together by protein complexes that form rivets between them and allow them to communicate.

Traditionally, it was assumed that epithelial cells compacted in this way adopt a prism-like shape, like a truncated pyramid (the part of a pyramid between two parallel planes) or a prismatoid (like a prism, but with faces that are irregular polygons). In 2018, a collaboration between biomedical scientists, bioengineers and mathematicians, co-led by the University of Seville, computationally analysed the organisation of a curved epithelium, such as the one lining the duct of a gland, where the cells have their apices forming the inner surface of the tube and their bases are held by a basement membrane.

BBVA-OpenMind-Yanes-Escutoides la geometria de las celulas_2 The name scutoid was eventually adopted as a formal name because of its resemblance to the scutellum, a part of the thorax of certain beetles. Credit: Tsekhmister/Getty Images.
The name scutoid was eventually adopted as a formal name because of its resemblance to the scutellum, a part of the thorax of certain beetles. Credit: Tsekhmister/Getty Images.

The researchers noted that, according to evidence from studies of fruit fly epithelia—one of the most commonly used animal models— each cell contacts different neighbours along its axis between the apex and the base, which is incompatible with a trunk or a prismatoid, where a cell would have the same neighbours on its upper and lower face. According to the computational model used by the authors, these two faces of the epithelium would be organised according to the so-called Voronoi diagrams, irregular mosaic tiles, so that each tessera contains all the points of the plane that are closer to the so-called “seed” point of that tessera than to those of the others.

Once the two Voronoi diagrams were defined on the upper and lower faces of the epithelium, the researchers saw that they were different: as in the published studies, each cell did not contact the same neighbours on both faces. By defining the bodies that join the two mosaics with computational analysis, the result is a shape that can be defined as a prismatoid with at least one vertex between the apex and the base, which draws a “Y” line. Study co-director Javier Buceta, from Lehigh University in Pennsylvania, defined it to The New Yorker magazine as “a prism with a zipper”; but with the peculiarity that the faces are not necessarily flat, as they can be twisted. “To the best of our knowledge, this type of geometric figures had been previously undescribed,” the authors write in their study published in Nature Communications.

From science to pop icon

The name scutoid, according to the researchers, was initially chosen as an inside joke in reference to the project’s co-director, Luis María Escudero, but was eventually adopted as a formal name because of its resemblance to the scutellum, a part of the thorax of certain beetles. The shape of the scutellum allows for 3D compaction of the cells into a curved tissue in a way that “makes their packing energetically efficient,” according to the authors. “Here we propose that such geometric conformation is one of nature’s solutions to epithelial bending,” they conclude. The authors found that scutoids appear in real tissues, such as the salivary glands of fly larvae.

BBVA-OpenMind-Yanes-Escutoides la geometria de las celulas_3_ENG According to Escudero and his collaborators, the finding of scutoids "paves the way to understanding the three-dimensional organisation of epithelial organs," which applies to organ and tumour formation. Original: Scutoid Vector: Lasunncty - based on: Prism, frusta, prismatoid and scutoid.jpg de Scutoid, CC BY-SA 4.0.
According to Escudero and his collaborators, the finding of scutoids “paves the way to understanding the three-dimensional organisation of epithelial organs,” which applies to organ and tumour formation. Original: Scutoid Vector: Lasunncty – based on: Prism, frusta, prismatoid and scutoid.jpg de Scutoid, CC BY-SA 4.0.

According to Escudero and his collaborators, the finding of scutoids “paves the way to understanding the three-dimensional organisation of epithelial organs,” which applies to organ and tumour formation. “This is fundamental not only for an understanding of tissue architecture during development and disease, but to the fields of tissue and organ engineering,” one of the great promises of regenerative medicine. 

The work of the Spanish researchers has already been followed up: a Swiss study found scutoid-like but more irregular shapes in the developing lung epithelium, which they named “punakoids” because of their resemblance to a rock formation in Punakaiki, New Zealand. Meanwhile, a team of physicists in Ireland and the UK found scutoids in the organisation of foam bubbles in ordinary dishwasher soap. In 2024, Escudero and his collaborators at the University of Seville and the Universities of Stanford and California at San Diego have documented how, during the embryonic development of starfish, cells first adopt a spherical shape, then transform into cubes and finally into scutoids as they proliferate and compact. 

A Swiss study found scutoid-like but more irregular shapes in the developing lung epithelium, which they named "punakoids" because of their resemblance to a rock formation in Punakaiki, New Zealand. Credit: Shaycobs/Getty Images.
A Swiss study found scutoid-like but more irregular shapes in the developing lung epithelium, which they named “punakoids” because of their resemblance to a rock formation in Punakaiki, New Zealand. Credit: Shaycobs/Getty Images.

What the discoverers of scutoids did not expect was the impact their discovery would have outside the world of science. “We’ve been lucky in that scutoids have become a pop icon,” Escudero wrote on X (formerly Twitter), mentioning that these shapes have been featured in jewellery, furniture, slippers and even cremation urns, and there are already numerous models on the internet for 3D printing them. But what surprised the researcher most was their appearance in a Fantastic Four comic book published by Marvel in June 2023, where the character of Reed Richards, aka Mr. Fantastic, explains scutoids to his partner Johnny Storm, aka The Human Torch. “Scutoids are kicking down the biggest door in pop culture,” Escudero wrote.

Javier Yanes

Main picture credit:  Ufuk Fuat Tekin/Getty Images.

 

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