The mathematical and mechanical mystery of interlocking shells.
By Ian Connellan
Bivalve molluscs include marine creatures such as clams, mussels, oysters and scallops.
At first glance, the bivalve brachiopods – lamps shells – seem to closely resemble bivalve molluscs, but in fact they’re not closely related.
It’s known that the most recognisable trait of bivalve seashells – the two valves that fit together perfectly when closed – has evolved in them from a common, shell-less, ancestor.
Bivalve shells have been described for hundreds of years. While their functional advantage is clear, there’s been no understanding of how the perfectly fitting valve feature is generated.
Now, an Anglo-French team led by Derek Moulton from Oxford University has created a mathematical model to explain how geometry and mechanical forces combine to generate the interlocking shells of bivalves.
Their study is published in Proceedings of The National Academy Of Sciences.
The two sides of oyster shells and other bivalves fit together seamlessly and continue to match up precisely even when environmental influences or injuries perturb the shell’s shape as it grows.
Moulton and his team investigated how the interlocking edges develop physically by creating a mathematical model of shell growth.
The shell edges of bivalves and brachiopods grow throughout the animal’s life. There are differences in mode of secretions and anatomy between bivalves and brachiopods, but the shells of both groups are incrementally secreted at the margin by a thin membranous elastic organ called the mantle.
A different part of the mantle creates each half of the shell. The mantle first secretes the periostracum, a thin soft organic layer that serves as a matrix for the calcium carbonate of the shell.
The authors considered the geometry and mechanics of each half of the mantle, which are constrained by the influence of one lobe on another and the rigid nature of the shell secreted.
The model reveals that a toothed or wavy edge, as opposed to a flat edge, occurs when the mantle grows faster than the shell edge, causing it to buckle.
The interlocking pattern is then created and maintained because the mechanical buckling instability is constrained by the force of one shell against the other.
In addition, the intricate patterning on some brachiopods is due to a secondary mechanical instability, according to the authors.