How the bean got its twist

Legumes are among the most diverse and successful families of plants in the world. In the Neotropical rainforests, the dominant tree species are mostly legumes (unlike in Southeast Asia, where dipterocarps predominate).

Their defining feature are their eponymous fruits, which appear to have a myriad ways of breaking up to release the seeds within. Some drop to the ground and shatter, like the tubular pods of Cassia:

Broken Cassia fistula pod exposing seeds

... while others twist and contort as they dry out to present seeds to dispersers, like Acacia:

Dried up and twisted Acacia auriculiformis seed pods

Legumes are certainly not the only plants with structures that change their shapes as they desiccate. They're not the only organisms to do so, either (think of mushrooms with caps that curl upwards as they mature to release their spores). However, their ubiquity and convenient size makes them a good subject for study and experimentation.

A team of physicists and mathematicians from Israel have recently figured out the rules behind the seed pod's twist, using a legume Bauhinia variegata as the model (paper in Science behind paywall). The basic idea is that the pod wall is made of an anisotropic material, that is, its material properties are not uniform but depend on the direction that it's being manipulated in. In this case, the anisotropy results from the orientation of fibres in the wall. Expansion or shrinkage tend to happen transversely to the aligned fibres. It's also a composite material, being made from at least two layers of wall sandwiched together. These two layers, however, have their fibres aligned in different orientations. As a result, when they dry out, they want to shrink in different directions. This conflict results in a deformation of the wall that produces a helical pattern.



This understanding is not new. It's at least a hundred years old, as pointed out in the commentary article that went along with this new paper. One of the early papers cited there has been digitized by the Biodiversity Heritage Library, a very useful scholarly resource that I've used time and again to find old or obscure articles not otherwise available to the public. Unfortunately, it's written in German, so some effort was required to read it.

That old paper described a very simple experiment. Strips of paper were cut out, with the long axis of the strip either parallel, or perpendicular to the grain of the paper (its anisotropy). Wetting the paper on one side, by floating it on water, causes a curling that is directed perpendicular to the grain:

"Piece of letter-paper laid on top of water, to show its uneven expansion through imbibition. The lines on the rectangular surfaces give the direction of the original grain of the paper."

"Fig. 2. a and b are two pairs of rectangles of letter-paper, that are glued together wet. Alignment asymmetrical. The bold lines show, consistently in the later figures, the grain-lines that are closest to the observer. c such a pair twisted after drying. Fig. 3. a Two glued-together sheets of paper with symmetrical alignment. b The sheet contorted after drying."

He then went on to glue together two such strips of paper, with their grains aligned in different directions. The glue was wet, and when it dried out, the resulting strips were twisted in helical or more complicated shapes (above).

The latest research takes this much further, with an array of analytical tools. They stretched two latex sheets in perpendicular directions, and then glued them together while stretched. As a result, there is "residual stress" in the sheet.

Note that unlike the old experiments with the paper strips, these latex sheets are consistently at an angle of 90º to each other. What they varied, then, was the direction in which they cut strips from this double-sheet. They found that by varying just two parameters: the angle between the long-axis of the strip and the stress directions of the latex, and the relative width of the strip, they could reproduce a whole array of shapes (we might call this a "morphospace") that resemble what we see in nature. Additionally, by using a mathematical theory of incompatible elasticity, they were able to predict the appearances of the latex strips using just these two parameters.

These shapes fall into two major categories: "cylindrical helices" and "twisted helices". The former are like tightly-wound party streamers; they seem like they can be sewn back up to form a cylinder. The latter have a straight centre-line. This is best explained by the diagram below: "helix A" is a cylindrical helix, while "B" is a twisted helix. (The other headings relate to the original context of this image, a paper on chirality in molecular bilayers, which suggests the commonality of physical principles throughout nature. I found it while looking in Google for suitable images of ribbons.)

This is a remarkable finding that suggests a unity of cause underlying a big slice of the morphological richness we see in the natural world. It's also something that humans may be able to exploit, to develop materials that can adopt specific shapes under particular circumstances.

Biomechanics seems to promise that the dazzling multitude of form in biology can eventually be brought to our human understanding, a promise that goes back at least as far as the "first biophysicist", D'Arcy Thompson. While it reminds us that biology is subservient to the rule of physics, the ingenuity of biological solutions to physical problems never ceases to amaze me.

Sources

• S Armon, E Efrati, R Kupferman, E Sharon (2011) Geometry and mechanics in the opening of chiral seed pods. Science 333 (23 Sep 2011): 1726-1730.
• Y Forterre, J Dumais (2011) Commentary: Generating helices in nature. Science 333 (23 Sep 2011): 1715-1716.
• C Steinbrinck (1906) Über Schrumpfungs- und Kohäsionsmechanismen von Pflanzen [On the shrinkage and cohesion mechanisms of plants]. Biologisches Centralblatt 26 (20): 657-677.