We are all Scutoids: A brand new shape, explained

Researchers first observed the previously unnamed shape in a computer model. They then went to nature and found it in abundance. Alan Burdick writes in The New Yorker

Until last week, the world of science was unaware of the scutoid. The scutoid is a basic three-dimensional shape, like a cube or a sphere but not like either of those things. It’s more like a column with half of one end lopped off at an angle; popular accounts have described it as a twisted prism, although that’s not so helpful. “It’s a prism with a zipper,” Javier Buceta, a biophysicist at Lehigh University and one of the scutoid’s discoverers, told me excitedly. This was also not so helpful.

What matters is that mathematicians had never before conceived of the scutoid, much less given it a name. What matters even more is that scutoids turn out to be everywhere, especially in living things. The shape, however odd, is a building block of multicellular organisms; complex life might never have emerged on Earth without it. Its existence, Buceta said, “allows you to understand the fundamentals of morphogenesis and development—how cells act together when they’re forming and developing.”

One of the many mysteries of living cells is how they manage to blossom into coherent many-celled units. A person or a platypus begins as a single cell, which divides into more cells, which also divide and subdivide. Some of these, the epithelial cells, are destined to become tissues and organs. The cells collect into layers, which bend and fold into greater-than sums: ovaries, kidneys, a heart. In part, it’s a packing challenge, a geometry problem; as the layers twist and curve, the individual cells change shape in accordance with the whole, and they do so as efficiently as possible.

Buceta offered the analogy of a Roman arch. You can form rectangular cobblestones into a straight row, but to form a curve the stones must be reshaped so that one face—the bottom end, on the inside of the arch—is smaller than the top face. The stone is no longer rectangular; it’s more like a pyramid with the pointy end lopped off. Mathematicians call that shape a frustum.

Similar dynamics apply in biology. When epithelial cells pack together in a layer of flat tissue, each will often take the shape of a column with five or six sides—a prism. As the tissue grows and bends, some cells deform, with one end becoming wider than the other; this allows the tissue to have a larger area on its outer surface than it does on its inner side. Biologists had long assumed that these cells acquire the shape of frusta, as in a Roman arch. (A frustum may be four-sided, like a pyramid, but it also can have more sides than that.) But, as Buceta and his colleagues reported in Nature Communications, that isn’t always the case. “The way those cells pack together in three dimensions is actually kind of weird,” Buceta said.

Read the full feature here.

(Photograph: Luisma Escudero/The New Yorker)

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