AUSTIN, TEXAS--The intricately ruffled edges of lettuce leaves may arise from a single simple physical principle, physicists have found. But accounting for the exact pattern of curlicues may require mathematics more often associated with Einstein than with endive.
Biophysicists have long sought simple physical explanations for seemingly complex biological phenomena. In recent years, for example, researchers have shown that the spiral patterns of seeds in sunflowers and similar plants emerge automatically if the face of the flower grows only where the mechanical stresses in the tissue are greatest. And now physicists may have found an elegant explanation of the frills that adorn many leaves and flower petals.
Those frills are not encoded one by one in a plant's genes but arise simply because the plant's leaves grow faster along their edges than in their centers, argue Benoit Roman of the French National Center for Scientific Research in Paris, Eran Sharon of the University of Texas, Austin, and colleagues. The researchers found that similar patterns arise when a plastic sheet is torn because the tearing permanently stretches one edge of the sheet while leaving the opposing edge the same length. A stretched sheet can't lie flat, so its torn edge must curl, Roman told a meeting of the American Physical Society here on 6 March. And that suggests leaves develop such shapes simply by growing more rapidly along their extremities.
Yet physicists aren't sure how the exact pattern of frills arises, and to find out they're employing differential geometry, the same type of mathematics Einstein used to describe the warping of space and time. Leaves and torn sheets generally wear ruffles upon ruffles, so that if the edge of the leaf or sheet is magnified it essentially looks as curly as it did before. Roman and Sharon argue that this pattern arises because when the sheet is stretched severely, it becomes geometrically impossible to take up all the slack with ruffles of similar sizes. In frustration, the sheet sprouts ruffles of all sizes, Roman says, and the exact distribution depends on the sheet's thickness. And in spite of the contortions, some tension remains in the sheet.
Not so, argue Arezki Boudaoud of the École Normale Supérieure in Paris and Basile Audoly of the University of Paris. Their calculations show that a variety of shapes will nicely accommodate the slack, and that the torn sheet strikes a balance between curling to take up slack and trying to stay flat to reduce its energy, Boudaoud told scientists at the meeting. "There are many such allowed geometric shapes," he says, "and the elastic energy selects the best one."