This article has been reviewed according to Science X's editorial process and policies. Editors have highlighted the following attributes while ensuring the content's credibility: Kaushik Bhattacharya is an engineer and materials scientist, but he has always been fascinated by seashells. Part of the draw is the "beautiful" idea that even simple organisms like mollusks can construct wonderfully complex structures over and over again, even in differing environments.
He marvels at nature's engineering capabilities. "Manufacturing materials is a nasty, difficult process," Bhattacharya says. "How does nature do it so nicely in such simple organisms?" Bhattacharya, Caltech's Howell N.
Tyson, Sr., professor of mechanics and materials science, and postdoctoral scholar Huan Liu have now figured out a mathematical way to explain the puzzling reproducibility of mollusk shells—the animals' ability to make roughly the same shell, regardless of the challenges that an individual mollusk might face. This mathematical method can reliably reproduce the characteristic shells of almost any class of mollusk—from the coiled shell of a nautilus to the fanlike shell of a scallop—beginning with nothing more than three elements: the shape at the leading edge of a developing shell (what the researchers call the "curve" element); a scaling factor that reflects how fast a shell expands; and the angle of the shell's rotation, whether it is making the tight spirals of a tower snail or the wide swooping whorls of a nautilus, for example. The mollusk-shell growth process is both passive, meaning it happens without additional control, and energy efficient—and the scientists now hope to emulate this ability to make other materials with complex shapes, such as specialized manifolds for jet engines.
Bhattacharya and Liu, a Cecil and Sally Drinkward postdoctoral fellow at Caltech, describe their findings in a paper published in the journal Proceedings of the National Academy of Sciences on Oct. 23. About a year ago, Bhattacharya mentioned his interest in molluscan shells to Liu, noting that shell growth had to be governed by "some simple rule which is done repeatedly," he recalls. "It can't be that the mollusk is sensing the whole shape and then adding to it in a clever way." By studying a variety of real seashells, including the conelike shells of some sea snails and the hinged two-part shells of bivalves, Liu saw that the growth lines of each shell had the same shape as the one before it.
Like tree rings, these growth lines are laid down sequentially over time. As a mollusk grows, its mantle secretes material that the organism then makes into its shell, creating ridges or bands with each new growth. Liu and Bhattacharya quickly realized that the growing edge of the first shell that forms in the mollusk's embryo—what is known as a protoconch—repeated one set of actions over and over.
The growth lines only differed by a scaling factor, or scalar, and a turn, or rotation. This suggested that a concept from mathematics called a Lie group (pronounced "lee") would be a natural way of describing seashell growth. (In this context, "group" is a collection of actions that can be combined or undone.) In a Lie group, those actions change smoothly rather than in fixed steps, and this characteristic makes them ideal for describing a process in which the same small operation is executed repeatedly. By treating the shell's growth as a Lie group that acts on the shell's growing edge, the researchers could work out a growth law—a mathematical formula that explains how the growing edge transforms as the shell grows.
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