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Time-lapse footage has revealed remarkable detail about how a lily blooms

By Victoria Gill
Science and nature reporter, BBC News
Tuesday, 22 March 2011

Writing in the Proceedings of the National Academy of Sciences, researchers said that the discovery shows why the flowers' petals have characteristically crinkled edges.

The footage's careful measurements reveal that the lily petals grow longer at the edges than in the middle.

This puts stress on the bud, eventually bursting it open.

PhD student Haiyi Liang and Professor L Mahadevan from Harvard University, Boston, Massachusetts, US carried out the research.

The scientists marked a lily bud with dots along each petal's edge and "midrib" or central vein.

These dots were markers that enabled them to measure every change in the size and shape of the flower as it went from bud to bloom.

"I noticed that petals of some flowers are wrinkled and thought that perhaps [these wrinkles were] functional and may play a role in opening," Professor Mahadevan told BBC News. "So I decided to look at it more carefully."

The scientists placed a lily (Lilium casablanca) with its stem immersed in water and filmed it for four and a half days until the flower was fully open.

The experiment revealed that the petals' edges elongated up to 40% more than their midribs.

This difference in the rate and amount of growth created stress that eventually burst open the bud, and resulted in petals with their familiar wrinkles.

The scientists wrote in their paper that, "in addition to infusing a scientific aesthetic into a thing of beauty," their study could aid the design of tiny motors or switches.

"Someone might be inspired to use this natural design, where the edges drive the interior, to build an actuator - a film that changes shape," explained Professor Mahadevan.

"That might be useful as a means to store information or to flip a switch.

"[But] that's not what drove me at all to work on the problem.

"I study nature because I am curious, like all of us. But if we can learn some general principle that someone else might put to use, that is fantastic."


SEAS Harvard (Nov 23, 2009); NSF; R&D Magazine; Science Daily; EurekAlert!, ...


The cause behind the characteristic shape of a long leaf revealed

Cambridge, Mass. – November 23, 2009 – Applied mathematicians dissected the morphology of the plantain lily (Hosta lancifolia), a characteristic long leaf with a saddle-like arc midsection and closely packed ripples along the edges. The simple cause of the lily's fan-like shape—elastic relaxation resulting from bending during differential growth—was revealed by using an equally simple technique, stretching foam ribbons.

Haiyi Liang, a postdoctoral student at Harvard's School of Engineering and Applied Sciences (SEAS), and L. Mahadevan, the Lola England de Valpine Professor of Applied Mathematics at SEAS and a core faculty member of the Wyss Institute for Biologically Inspired Engineering, were inspired to study the formation of laminae (thin leaf-like structures) because they are so commonplace in biology.

The work had its origins in conversations that Mahadevan had with experimental biologists Mimi Koehl at the University of California, Berkeley and Wendy Silk from the University of California, Davis, who showed him examples of such morphologies in long submarine algal blades.

"These blades have rippled edges when they grow in slowly moving water. When they are transplanted to environments that have rapidly moving water, they generate new blades which are much narrower," says Mahadevan. "This example of phenotypic plasticity, or the ability of the algae to change their shape in response to environmental forces, led to a paper co-authored with Koehl and Silk last year that focused primarily on the experimental findings."

Inspired by this, Mahadevan and Liang developed an analog model to understand how a long leaf is formed by pulling flat, foam ribbons, measuring approximately 4.3" x 1.5" (about the size of a large bookmark), beyond their elastic limit and then letting them go. These stretching strains were applied preferentially to the horizontal edges so that the foam ribbon naturally forms a saddle-like shape when it relaxes. In the same scenario, but with a four-fold increase of strain on the horizontal edges, ripples will form along the edges, producing a series of small undulating waves.

An equivalent growth-induced strain, highest along the edges and lessening toward the middle, occurs as a long leaf grows, leading to the elegant arc and serrated surface of the leaves in plants like the lily. This effect is widely seen, says Mahadevan, in a variety of common objects and activities.

"When knitting a scarf, as the number of stitches is increased as the knitter moves away from the center, the material forms a saddle shape. As the edge length becomes much larger ripples begin to appear. The same effect can be seen when thin potato slices are dropped into hot oil to make chips. You end up with a bulbous middle and wrinkled edges," he explains.

The researchers also dissected the leaves of the plantain lily to show that elastic strain resulting from differential growth led to the patterns seen in real leaves. From this simple experiment, the researchers then developed a mathematical model explaining the shape, using a combination of scaling concepts, stability analysis, and numerical simulations.

"While the phenomena has been studied previously, researchers did not consider the role of finite size of a leaf on the stability or the effect of boundaries. Further, our study characterizes, mathematically, the range of parameters that quantify the shape and diversity in leaf morphology," adds Mahadevan.

The resulting model has application in understanding a variety of artificial systems such as non-uniform thermal expansion, hydraulic swelling, and plasticity induced shape changes in thin laminae.


MRS Materials News (October 25, 2007)

Cover Paper: Journal of the Royal Society Interface


Understanding the elasticity of twisted filaments
(Journal of the Royal Society - Interface)

Filaments with intrinsic handedness such as chiral carbon nanotubes and DNA twist when they are stretched, similar to helical springs. A new study now shows that both the geometry and the deformation mechanism influence the sense of the twist, with rather surprising results; compressed carbon nanotubes unwind at large strains, while stretched DNA overwinds initially. Model simulations highlight microstructure design principles that can be used to tailor such mechanically coupled response in nanoscale devices. As affirmation, Nature has already adopted these design principles, with examples ranging from spiral growth and propulsion, to grain spiral evolution in several classes of trees.

  APS Tip Sheet (May 6, 2006)  

Carbon Nanotubes Turn Translation into Rotation
Haiyi Liang and Moneesh Upmanyu
Phys. Rev. Let. 96, 165501 (2006)

Some DNA molecules may serve as handy micromachines to convert rotational motion into linear translation, an important function for positioning minuscule parts in microscopic devices. Researchers at the école Normale Supérieure in France made the micro-translators by securing one end of a palindromic DNA molecule and untwisting the other end of the helical molecule. A palindromic DNA molecule consists of an amino acid chain that reads the same forwards and backwards, just as is true of the letters in palindromic words such as “rotator” and “deified.” The researchers found that by grasping the end of a DNA molecule with a pair of magnetic tweezers and twisting in the opposite direction of the molecule’s helix, the DNA would buckle in the middle and form a cross-shaped molecule (see for an example of palindromic and cruciform DNA). Cruciform DNA is shorter than the linear configuration, and grows ever shorter as the molecule is untwisted.

Meanwhile, researchers at the Colorado School of Mines have shown theoretically that carbon nanotubes can perform the reverse task, i.e. converting linear motion to rotation. Simulations show that stretching or compressing a carbon nanotube along its length makes it twist, provided the nanotube has a helical, spring-like structure. Future experiments will be needed to confirm the phenomenon.

Converting rotational motion to translation and converting translational motion to rotation are vital tasks in macroscopic machines that are usually performed by worm screws and gears. Unfortunately, they are are difficult to duplicate on small scales. Together, these two studies suggest that DNA molecules and carbon nanotubes could solve the problem, and may soon be important components in micromachine parts bins that researchers will turn to when assembling tiny, complex machines.


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