The earwig’s delicate, paper-thin wings can open 10x their folded size due to its origami-like creases – Credit: ETH Zurich / Purdue University

(Article by Rohini Subrahmanyam originally published by Knowable Magazine)

As the microscopic, tear-shaped *Lacrymaria olor * swims around hunting for food, it does something remarkable: In a blink, the tiny protist extends its neck more than 30 times its body length, snatching up unwitting prey.

Then, just as quickly, the neck withdraws, returning to its original size. The movement is akin to a six-foot human suddenly stretching their neck some 200 feet and then snapping it back to normal.

This acrobatic behavior had been observed for more than a hundred years, yet only in 2024 did scientists finally understand how L. olor manages to whip out and store its neck so deftly.

The tiny hunter uses a kind of cellular origami: It folds its external membrane in pleats that it can unfold, deploy, and retract at will.

“This particular origami, which we named Lacrygami — humans did not invent it, nature invented it,” says Stanford University bioengineer Manu Prakash.

Like releasing tightly spooled fishing line, the tiny, single-celled hunter Lacrymaria olor can rapidly extend its neck 30 times its body size and just as quickly whip it back into itself.

Anyone who has dabbled in origami knows that it can be frustratingly complicated, yet somehow its intricate folds have arisen naturally many times in living things. In recent years, scientists have taken a closer look at these complex folds of the biological realm, such as in delicate insect wings, a chick’s developing gut, or the lightning-fast neck of L. olor.

Some of what they’re finding is inspiring practical applications such as drones and robots, but the nature of origami itself is enough to keep scientists fascinated. Origami exists at a particular boundary, says Harvard University physicist Lakshminarayanan Mahadevan, “where there is just enough balance between constraints and freedom, so that you can do remarkable things.”

Frontiers in space

Japanese people started practicing origami some time around the sixth century, but it wasn’t until about 40 years ago that scientists and engineers began investigating origami in earnest. Early studies focused on usefulness in space: With origami, one could tightly pack solar panel arrays on a rocket for unfolding later on.

Japanese astrophysicist Koryo Miura published what became a standard folding technique for such applications in 1985. Called the Miura-ori, this rigid fold is made of mountain and valley creases; it’s essentially a pattern of closely packed parallelograms.

With one pull, you can unfurl an entire folded sheet, such as a map or an array of solar panels, and then just as easily fold it up again. In 1995, the fold was used to efficiently pack solar panel arrays in Japan’s Space Flyer Unit satellite.

Curved creases don’t fold flatly along a straight line, they fold along a curve, like a folded-over shirt collar. They are trickier than a standard flat crease; as you fold along a curve, the crease changes direction ever so slightly at every point. So, at each point, the sheet needs to fold in two directions: radially along the crease, where the two parts of the sheet bend like a hinge and come closer, and tangentially to the crease. Because the crease is curved, every part of it is angled slightly differently.

It turns out that earwigs stretch their wings ever so slightly at the curved crease along the wing’s middle. It manages this stretching with an elastic protein called resilin that can store and release energy like a spring. In the middle of the earwig wing — a spot the researchers call the mid-wing mechanism — the resilin is distributed both symmetrically and asymmetrically. The former helps the wing’s creases extend, like a stretchy spring, and the latter gives the creases the energy to rotate, like a bendy spring. Together, the two types of springs help to lock the wing in position, whether folded or unfolded.

Incorporating the stretchy springs into the folds was key to capturing the behavior of the wing, says Arrieta, who calls the approach “spring origami.”

After modeling how the insect wing folded mathematically, the researchers designed and 3D-printed a membrane that incorporated springs and could fold up on its own.

With some origami applications, the creases have to be folded in the right order to get the final shape. That requires a lot of control, says Arrieta. In contrast, a bistable structure has only two states, open and closed. “It’s just a little bit of effort and boom! the thing deploys.”

Eventually these bistable, foldable structures (see them openin this GIF) might be deployed as wings for drones, helping them fold up more compactly. Inspired by the earwig wing (in the video below), engineers incorporated a spring-like mechanism into a self-folding structure that may have applications in robotics.

Lo and be-fold

The single-celled hunter *L. olor * presented a similar puzzle — and a similar solution. The scientists knew that the protist’s body had microtubule proteins that give it a helical structure, the way rods give tents their shape. But could those microtubules help explain its massively extending, then retracting, neck?

After all, the membrane can’t just appear and disappear, says Prakash, so where does it come from and where does it go?

On a trip to Japan, Prakash saw chochin lanterns that have paper stretched over bamboo frames and realized that the membrane of the single-celled creature might similarly stretch out over the bamboo-like microtubules. By testing this paper-based set-up using origami with his kids, he discovered that “there is a very easy way to fold and unfold this architecture.”

Cross-checking with L. olor’s microscopy data confirmed his hunch: The protist’s cell is folded up into pleats using curved creases, and anchored to a scaffold of helical microtubules. Opening and closing of these pleats drives the extraordinary extending neck.

Folding and storing the membrane and microtubules in this curved, helical fashion allows the cell to keep a lot of its gelatinous cytoplasm in a ready-to-release configuration. But L. olor doesn’t just release all that cytoplasm at once, says study coauthor Eliott Flaum, Prakash’s former graduate student who is now a biophysicist at the European Molecular Biology Laboratory in Heidelberg, Germany. “It can control the neck length,” she says. “And that is only possible if it had really fine control over the material being stored.”

It exerts this fine control with the help of what are called singularities — points or kinks along the curved creases where the membrane sharply goes from being folded to being unfolded. Similar to resilin and the mid-wing mechanism in the earwigs, these points concentrate a lot of the bending energy when the membrane is all folded up. And by controlling how these points move, L. olor is able to rapidly unfurl its pleats and just as easily fold them back up again.

As the little hunter either deploys or reels its neck back in, the singularities move along with the neck — ensuring that all the creases open and fold back in sequentially — in the same way every time. Thus L. olor perfectly folds and unfolds its origami without fail — like the pleats of an accordion that open and tuck themselves back in.

“Mathematically, it does not allow any other folds,” says Prakash, “which is why it’s so robust — the cell folds and unfolds tens of thousands of times and does not make a mistake.”

Learn more about nature’s fantastic folding below…

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