An exploration of mathematical shapes could explain why skin gets wrinkled after too much time in the tub. Understanding the geometry of wrinkly skin could help design new materials that can stretch out without losing strength.
"The paper explains a mechanism that can explain the structural stability of keratin in skin and its ability to absorb very large quantities of water," said mathematician Gerd Schröder-Turk of the University of Erlangen-Nürnberg in Germany, who was not involved in the new work. "This is a major breakthrough."
Scientists and frequent bathers know that skin can absorb a tremendous amount of water, and still be a strong barrier between our bodies and the harsh outside world.
"Your skin wrinkles, yet it maintains its structure," said mathematician Myfanwy Evans of the Australian National University, lead author of the new study. "It doesn't just fall apart and dissolve into the water."
The skin's resilient stretchiness comes from an intricate network of fibrous proteins called keratin, which make up the outermost layer of the skin, as well as hair and nails. Scientists knew that skin's keratin networks were important, but the arrangement of fibers was uncertain.
Now, Evans and Australian National University colleague Stephen Hyde may have found a solution. They describe their stringy skin model in the March 8 Journal of the Royal Society Interface.
"It explains a lot of mechanical features that hadn't really been able to be explained before," Evans said.
The researchers stumbled upon the new model in a purely math-based search for interesting topological shapes. Evans studies a class of beautiful mathematical shapes called Gyroids, which show up all over the natural world, from lipid membranes to butterfly wings.
"It's an interesting fusion of maths and experimental science," Evans said. "These are popping up everywhere."
Using computer simulations, Evans and Hyde explored what would happen if you took infinitely long threads and wove them through the labyrinth of the Gyroid surface, then took the surface away. Some of the resulting 3-D woven structures were so tangled that none of the threads could move without breaking the connections between individual threads. If keratin were arranged this way, Evans says, our skin would lose its strength when it got wet.
"Losing contacts between keratin fibers means losing structural rigidity," she said.
But other weavings could expand, with threads straightening and sliding along each other without losing contact. One of these, which Evans and Hyde call G129, could swell to fill a volume seven times greater than its original shape, while keeping all its fiber connections intact - just like skin.
Suggestively, the model's version of keratin networks in dry skin matches real data almost exactly, Evans says.
"That was quite convincing evidence that it's highly likely that this model really does work," she said.
Although the model hasn't made it far from the world of abstract math, Evans and colleagues hope their models of expandable networks of fibers could be used in the bottom-up design of custom materials with controllable stretchiness. These materials could be useful for things like bandages, bulletproof vests and artificial skin, she suggests.
"This could be a really good target for bio-inspired materials," she said. "It's not a matter of testing it in the lab, it's a matter of understanding its geometry in order to understand its physical properties…. We hope this paper will put that idea out there, and maybe lead to some new interesting materials."
Images: 1) Flickr/Mathew Wilson. 2) Evans and Hyde, 2011. Video: Gerd Schröder-Turk.
"From three-dimensional weavings to swollen corneocytes." Myfanwy Evans and Stephen Hyde. Journal of the Royal Society Interface, March 8, 2011. DOI: 10.1098/rsif.2010.0722