Mathematicians' Study Of How The Lily Blooms Has Implications For Sensor Development And Other Applications In Materials Science

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 bloom.



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 this week in the journal 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 University 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.



Source:

Caroline Perry

Harvard University