The asiatic lily’s graceful geometry invites observational and quantitative study. Credit: Flickr user KingsbraeGarden.
The “lily white” has inspired
centuries’ worth of rich poetry and art, but when it comes to the science of
how and why those delicately curved petals burst from the bud, surprisingly
little is known.
Now, however, mathematics has revealed
that differential growth and ruffling at the edges of each petal—not in the
midrib, as commonly suggested—provide the driving force behind the lily’s
The research, conducted at Harvard’s School of Engineering and Applied Sciences (SEAS),
contradicts earlier theories regarding growth within the flower bud. The
petals, in fact, behave like leaves.
Published online in the Proceedings of the National Academy
of Sciences, the findings characterize the blooming process using
mathematical theory, observation, and experiment.
“That differences in planar growth
strains can lead to shape changes has been known for some time,” says
principal investigator L. Mahadevan, the Lola England de Valpine Professor of
Applied Mathematics at SEAS. “But showing that it is at work and dominant
in lily blooming is new, as our measurements and simple theory show.”
“What is most surprising is that a
subject that is so rich in metaphor—the blooming of a flower—had been studied
so little from a quantitative perspective.”
Mahadevan collaborated with Haiyi Liang,
formerly a postdoctoral fellow at SEAS and now a professor at the Univ. of Science
and Technology of China in Hefei.
Together, they studied the asiatic lily Lilium casablanca, the bud of which
comprises three inner petals wrapped in three outer sepals.
A stiff midrib runs along the center of
each petal and sepal, protecting the structure of the developing flower bud.
The edges of the sepals also rest in grooves along the midribs of the petals,
forming a locking mechanism that holds the bud closed until the growth inside
reaches a critical point.
It was previously suggested that growth in
the midribs might provide enough internal stress for the petals to burst out of
their casing. Another plausible theory held that if the internal (adaxial) face
of each petal and sepal grew faster than the external (abaxial) face, the
flower would eventually be forced to bend outward. In some plants, these
mechanisms do drive the blooming process.
Liang and Mahadevan’s new research shows that
in the lily, however, midrib growth and differential adaxial/abaxial growth
play only minor roles. Rapid growth and wrinkling at the periphery of the
petals actually create the stress within the bud that forces it to burst open.
The researchers used observation and
experimentation to measure growth in various parts of the petals and to
determine which types of growth are necessary for blooming. They then
characterized the process mathematically in order to quantify, synthesize, and
generalize their observations beyond the specific instance (see videos at
The findings contradict common assumptions
about the lily, but they do seem to vindicate one unlikely theorist: German
literary master Johann Wolfgang von Goethe.
In a 1790 essay, “Metamorphosis of
Plants,” Goethe proposed that petals and leaves could be homologous,
meaning that they are both derived from one ancestral form.
“In a sense,” says Mahadevan,
“we have quantified one aspect of the similarity by showing that in
addition to being laminae (like blades), the morphologies of petals and leaves
are often determined by similar principles.”
“In particular, leaves have rippled
edges due to gradients in growth in the plane that lead to the edge growing
more than the middle, a phenomenon that Liang and I demonstrated in 2009,”
he adds. “Here, we build on and generalize these results to show that
lilies bloom using a mechanism that is similar to leaf growth, except that the
petals are curved objects.”
In addition to his appointment at SEAS,
Mahadevan is a Professor of Organismic and Evolutionary Biology at Harvard, a
Core Faculty Member of the Wyss Institute for Biologically Inspired Engineering
at Harvard, an affiliate of the Harvard Department of Physics, and a member of
the Kavli Institute for Bionano Science and Technology.
His previous research, often inspired by
beauty in nature, has investigated questions such as how snakes slither and how the Venus fly trap snaps its jaws.
The question of how the lily blooms,
Mahadevan says, “is just one more small instance of being inspired by and
curious about the natural world around us, a subject that fascinates us all,
child and adult alike.”
The research also has immediate practical
applications in materials science involving thin films and elastic sheets, and
it may affect the development of devices such as sensors and actuators that
mimic the mechanism of blooming.