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Biophysics and bioengineering

Biophysics and bioengineering

Replicating how plants move

14 Jul 2021
Taken from the July 2021 issue of Physics World. Members of the Institute of Physics can enjoy the full issue via the Physics World app.

Once studied by Charles Darwin, the Venus flytrap is perhaps the most famous plant that moves at high speed. But as Daniel Rayneau-Kirkhope explains, researchers are still unearthing new scientific insights into plant motion, which could lead to novel, bio-inspired robotic structures

venus flytrap
(Courtesy: iStock/chameleonseye)

“In the absence of any other proof,” Isaac Newton is once said to have proclaimed, “the thumb alone would convince me of God’s existence.” With 29 bones, 123 ligaments and 34 muscles pulling the strings, the human hand is indeed a feat of nature’s engineering. It lets us write, touch, hold, feel and interact in exquisite detail with the world around us.

To replicate the wonders of the human hand, researchers in the field of “soft robotics” are trying to design artificial structures made from flexible, compliant materials that can be controlled and programmed by computers. Trouble is, the hand is such a complex structure that it needs lots of computing power to be properly controlled. That’s a problem when developing prosthetic hands for people who have lost an arm in, say, an accident or surgery.

Designers seeking to make their structures move are, however, finding inspiration from a surprising source: the study of movement in plants. Now if you’ve ever observed the slow movement of a leaf as it turns towards the Sun, a plant might seem an unlikely choice given that such motion occurs at just a few microns per second. But plants can also act surprisingly quickly. They disperse seeds, for example, at tens of metres per second, which is an astonishing seven orders of magnitude faster than the speed at which leaves turn to the Sun.

Quite how plants make an array of movements over such varying timescales has long fascinated scientists. What’s more, lacking any of the muscles or joints found in animals, plants have to exploit other – often ingenious – methods to induce controlled, reliable motion. And rather than being controlled by a central brain, these movements are usually the result of an external stimulus, such as gravity, light or even touch.

In trying to work out how plants move, biologists have naturally focused on the underlying biochemical signalling that triggers the motion. But what about the mechanics of the motion itself? How, in other words, does a plant move in such a precise, controlled and quick way? It’s a question that researchers have only recently started to consider from a physics points of view. As it turns out, the motions are often built into the architecture of plants themselves.

Seeds of success

Consider how a plant disperses seeds. It needs to spread them far and wide to maximize the chances of its potential descendants finding fertile ground, while also boosting the species’ resistance to disease and predators. Some, like dandelions, do this via seeds that are so light they get carried by currents of air. Others, such as burdock, have seeds with hooks that attach themselves to animals, including humans, who unwittingly transport them to new ground. Yet others, like the fern, catapult their seeds.

Figure 1

The most striking example of a catapult is found on leptosporangiate ferns, which hold the spores on the underside of leaves in tiny spherical baskets, about 0.2 mm in diameter. Each basket, known as a “sporangium”, is ringed on one side by a series of cells arranged in a semi-circle. In summer, as the weather gets warmer and drier, water between the cells in this “annulus” starts to evaporate and it stretches out to form a straight arm, with the spores held at the tip. The arm then gets bent backwards, like a catapult primed for operation (figure 1).

At this point, so much energy is stored in the annulus that the pressure of the water falls below its vapour pressure, forming bubbles in the liquid. Known as cavitation, this process releases the stored energy and the arm swings back to its initial curved shape. As a team led by Xavier Noblin from the University of Nice in France discovered in 2012, this dramatic release of energy accelerates the seeds up to 105g, flinging them from their basket into the surrounding countryside at speeds of 10 m/s (Science 335 1322).

This dramatic release of energy accelerates the seeds up to 105g, flinging them from their basket into the surrounding countryside at speeds of 10 m/s

A taste for animals

But plants don’t only need to ensure their offspring survive. They also have to find nutrition to support themselves, with most plants taking minerals from the ground and energy from the Sun. However, a few plants – roughly 0.2% of all flowering species – have an extra source of nutrition: they eat animals. The most famous example of a carnivorous plant is the Venus flytrap (Dionaea muscipula), which is native to the subtropical wetlands of the eastern US.

Each of the leaves on this beautiful plant ends in a pair of lobes, hinged at the middle like a clam. When a fly or other insect lands on the lobes, tiny trigger hairs make the lobes swing shut, creating a cavity that holds the prey inside. Enzyme-containing secretions from the leaf dissolve the animal’s soft tissue, allowing the plant to absorb vital nutrients before the leaf re-opens. What remains of the fly is blown away, ready for the trap to snare its next victim.

The Venus flytrap can’t afford to be slow, given that a fly will respond to movement in barely 400 ms. In fact, the flytrap snaps shut in about a quarter of that time, well before the animal has time to get away. But how does the plant act so fast? For many plants that move, the secret lies in a kind of hydraulics. By changing the concentration of ions in cells in different areas of a leaf, a plant can shift water around internally. Cells with less water shrink while those with more fluid get bigger, allowing a plant to, for example, lengthen one side of a leaf but shorten the other. The leaf can therefore move, just as contracting the bicep in your upper arm can lift your hand up.

The amount of liquid that must be moved increases with the size of the plant, but there’s a limit to how fast the liquid can travel. So without some kind of clever trickery, a plant of a given size can’t move any faster than a certain speed. What this means is that if the Venus flytrap were to shut using hydraulics alone, by the time the leaves had closed, the fly would have long flown off to safety. To exceed the speed limit imposed by the slow motion of liquids in the plant tissue, this plant uses the same physics that occurs when an umbrella blows inside out.

As described by Charles Darwin in his 1875 book Insectivorous Plants, the leaves on a Venus flytrap are convex (outwardly curved) when open, but concave (inwardly curved) when shut. Although the open state is a mechanically stable configuration, the leaves lie very near to an elastic instability. So when a fly stimulates the trigger hairs, one side of the leaf expands in volume.

Using high-speed video, a team led by L Mahadevan from Harvard University found in 2005 that the expansion pushes the leaf beyond its stability limit. It buckles, snapping shut in a few tenths of a second – just as a gust of wind can blow an umbrella inside out so it flips from one stable geometrical configuration to another (Nature 433 421). Known as the “snap-through buckling instability”, engineers exploit the effect to change the shape of carefully designed structures, but it looks like the Venus flytrap got there well before we did.

Wheels of fortune

A less-well-known carnivorous plant with interesting physics is the aquatic waterwheel (Aldrovanda vesiculosa). Native to Asia, Australia, Europe and Africa, it is an invasive, underwater plant that takes its name from the series of curved leaves arranged in a circle around the plant’s long, central stems. Though lacking a physical hinge, each leaf has two lobes, making it look like the main character in the Pac-Man video game (figure 2).

Figure 2

Just like the Venus flytrap, the leaves have a set of trigger hairs on their surface, snapping the lobes together when an insect lands on them. And for this plant too, motion powered by hydraulics alone would not be fast enough for it to catch a meal. So to capture its prey, which includes water mites and mosquito larvae, the waterwheel uses the principle of “kinematic amplification”. This is where a small, controlled input motion in one part of a structure creates a larger displacement elsewhere. You see this principle in action with a door, which you can easily swing wide open at the handle, or push open by nudging it near the hinge (albeit by applying a much bigger force).

As a team led by Anna Westermeier from the University of Freiburg, Germany, observed in 2018, the waterwheel uses the same approach by creating a tiny, hydraulically induced deformation that widens the base of the trap by a few hundredths of a millimetre. Thanks to kinetic amplification, this is enough to move the walls of the trap by about 200 times that amount, allowing the plant to close and trap prey inside – with no hinges in sight.

The rapid motion is also helped by the traps being in a constant state of “pre-stress”. Like a spring confined to a small space, the leaf has stored elastic energy, which – when motion is initiated – can be released, speeding up the movement (Proc. Roy. Soc. B 205 20180012). Provided the prey can’t pry the leaves apart, this cunning design ensures that the waterwheel doesn’t go hungry.

Sticky subject

Another fascinating carnivorous plant is the Cape sundew (Drosera capensis). Native to South Africa, this beautiful plant has long, thin leaves covered with hair-like tentacles. They secrete a sticky fluid that forms a drop at the tip of each tentacle. When an insect lands on the leaf, it gets stuck on the sticky surface, which curls over, trapping the unfortunate animal. This process brings more of the plant’s digestive glands into contact with the prey, maximizing its nutritional intake (figure 3).

Cape sundew

This genera of plant so fascinated Darwin that he once claimed to “care more about Drosera than the origin of all the species in the world”. However, it was only in 2019 that an interdisciplinary research collaboration led by Caterina La Porta and Stefano Zapperi at the University of Milan, of which I was a part, worked out the full mechanical details of this strange motion and the biochemical signalling that triggers it.

Using an optical microscope, the upper and lower layers of cells in the Cape sundew leaf were found to have different shapes. The lower layer has elongated cells running down the length of the leaf, while the upper layer has more circular cells. When the plant is stimulated, either by an insect landing on its surface or a drop of milk being placed on its surface (as we did in our experiments), the plant alters the internal pressure of its cells, which change size in response.

Much like a balloon, where the inflated shape depends a lot on its initial, deflated shape, the upper and lower cells respond differently to the pressure change, with the long cells on the bottom of the leaf extending much more than the rounder cells on the upper layer. This differential rate of growth changes the overall geometry of the leaf, which curls up around its prey like a forefinger on a hand beckoning inwards (Proc. Nat. Acad. Sci. 116 18777).

The bending, in other words, is literally encoded in the cellular structure of Cape sundew’s leaf, which converts a uniform biochemical signal into an asymmetric response. Inspired by this behaviour, our collaboration realized that the Cape sundew could also be useful for soft robotics. That’s because an artificial hand, say, has to respond in a predictable way to a particular input: it needs a pre-determined motion from a given stimulus. We therefore began planning new artificially structured metamaterials that could do just that.

Using an ordinary plastic, we built an artificial, bi-layer structure that copied the behaviour of the Cape sundew plant (figure 4). The upper layer is made of hexagons where two of the sides are pulled in, which is a geometry well known to get thicker when stretched (i.e. has a negative Poisson’s ratio). The lower layer had the same structure, but with a single extra link added to each lattice unit cell. This geometry acts more conventionally by getting thinner when stretched (i.e. has a positive Poisson’s ratio).

figure 4

This bilayer structure was easy to manufacture and had far-reaching mechanical consequences. Computer simulations showed that our material would curl up into a circle if air were pumped into the voids in the material – just like the plant that inspired it. What’s more, we found we could also make this material deform from its initial, flat configuration into a circle by compressing it from its sides. In other words, there was more than one way to trigger this hingeless behaviour.

It’s not too fanciful to imagine a soft material like this, where the motion is built into the architecture, being used to make robotic fingers or limbs that can curl up or straighten out on demand. By replacing conventional rigid hinges, such materials could allow robots to grasp fragile objects without damaging them, such as plates, glasses and cups from a dishwasher. They would need less computational power and none of the complicated feedback loops that are normally required to stop robots from unintentionally smashing objects in their grasp.

Robotic future

From self-cleaning windows inspired by superhydrophobic lotus leaves to surgical staples inspired by porcupine quills, our work is just part of a growing trend for novel, practical applications inspired by mechanisms found in plants and animals. But rather than simply copying animals or plants to create robots, researchers are seeking to tease out the basic principles and mechanics, marrying them with modern engineering materials to create an entirely new generation of machines.

What is wonderful about following nature’s lead is that we know that the mechanics work. Living things we see all around us have been tested over thousands and millions of years, with faulty designs long since weeded out. If a plant seed dispersal mechanism does not work, its species will become extinct; if a plant cannot get food reliably, it will die. Newton may have seen God’s presence in a thumb, but one wonders what he would have made of a robotic plant-inspired hand.

 

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