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A New Model for How Wrinkled Organs Get Their Shapes

You might think wrinkles are only skin deep, but there’s a lot more to the topic than anti-aging cream and laundry. The brain is a wrinkly object for a reason, as are flames, fingerprints, raisins, elephants, and the ridges in your teeth. Understanding how and why wrinkles emerge in developing biological organs like the brain could inform treatments for conditions like lissencephaly (the absence of wrinkles in the cerebral cortex), and possibly even diseases like Alzheimer’s and macular degeneration.

An embryonic mouse brain and some other organs, including the lab-grown organoid shown here (center), don’t follow the wrinkling model that scientists thought they did. If they followed the conventional model, where the inner core is thickest the outer layer would also be thickest. 
Image Credit:  Center image reprinted by permission from Springer Nature Customer Service Centre GmbH: Springer Nature. Nature Physics, Human brain organoids on a chip reveal the physics of folding, Eyal Karzbrun et al.
 © 2018.
That topic—how wrinkles develop—is the subject of new research recently published in the American Physical Society’s journal Physical Review X by an interdisciplinary team that includes physicists and an engineer from Syracuse University and biologists from Memorial Sloan Kettering Career Center. In a surprising discovery, the group showed that a universal model for how the brain and other organs get their shapes isn't quite as universal as people had thought. They also developed a more inclusive wrinkling model that reveals a deep connection between biology and physics.

Since the heyday of bellbottoms and funk music, scientists have been describing how developing brains and other organs wrinkle by using a model based on elastic solids. Imagine that you have two materials, one that forms a solid inner core and one that forms a solid layer around that core. The two materials stick together and both have elasticity—meaning that when you push or pull on them, they push or pull back. As Syracuse physicist Tyler Engstrom explains, when the outer layer grows faster than the inner core, the system buckles and wrinkles to alleviate stresses caused by the growth mismatch. That’s the basic idea of the elastic solid model.

Engstrom works in a theoretical physics group that is just beginning to collaborate with biologists. While looking at an image of a developing mouse cerebellum one day, for what he says “was probably the twentieth time,” something clicked. An embryonic mouse cerebellum has an inner core and an outer layer. As the cerebellum develops, the outer layer grows much faster than the inner layer and causes the organ to wrinkle. It should be a prototypical case of bilayer wrinkling. But looking at the wrinkles this time, Engstrom realized that something wasn’t quite right.

Scientists typically consider wrinkles to be thickness oscillations in the substrate, or inner core, but the outer layer can have thickness oscillations too. What caught Engstrom’s attention in the image was that where the inner core was thickest, the outer layer was thinnest and vice versa. That’s not typical.

Engstrom’s postdoc advisor Jen Schwarz secured NSF funding to investigate whether this was even allowed by the long-accepted conventional model, and they set to work with the help of team members Teng Zhang at Syracuse, and Andrew Lawton and Alex Joyner at Memorial Sloan Kettering. Using mathematical models and computer simulations, the team analyzed the elastic solid model. They found that according to the model, the thickest spots in the two layers must always line up.

The trouble is, they don’t. The team found three cases, including the developing cerebellum that started it all, where the relationship between the thicknesses was exactly the opposite of this.

“In this work, we’ve come up with a new and rigorous way to test for elastic wrinkling behavior, and (surprise!) three biological systems don’t pass the test,” says Engstrom. “These aren’t some obscure biological systems either, but include part of the eye, and the cerebellum which is a major part of the
brain,” he says.

These failures highlighted the need for a new and better model of the developing cerebellum and these other systems. Inspired by the types of cells in each layer and how they interact, the team created one. Their new model leads to different outcomes depending on the details of the system, including outcomes like the shapes Engstrom saw in the original image. Among other things, the new model shows that, for some organs, it’s more accurate to treat the top layer of the system as a liquid rather than an elastic solid.

“The biology gives us hints for how we should treat the fast-growing layer in a physics model, and if we listen to those hints, we arrive at a fluid layer that is mechanically constrained by fiber-like cells,” says Engstrom. “That may sound like a subtle difference from an elastic solid, but it means that the wrinkling phenomenon is governed by a completely different set of parameters–parameters that are associated with specific biological cells and processes,” he explains.

Put another way, you can’t model the wrinkling process of certain organs using physics alone, you have to take into account the biology of the system. This work is a great example of just how important it is for scientists in different fields to work together. Many systems don’t just operate on physics, biology, or chemistry alone—nor do they care which field claims them. To get at the factors underlying diseases and effective treatments, we need interdisciplinary collaboration.

“I liken biophysics to a relatively young genre of music–there will always be new melodies to write
down, but right now there are still compositional structures to create as well,” says Engstrom.

It should come as no surprise that the story of our journey toward understanding biology is full of twists, turns and—yes—wrinkles. But where will the next one pop up? Finding out is the fun of it.

Kendra Redmond

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