Helical structures through simple mechanical rules

Structures of this kind commonly occurs in nature. How do we generate them artificially? Here is a review of a work that gives a simple thumb rule.

Macroscopic helical structures formed by organisms include seashells, horns, plant tendrils, and seed pods (see the figure, panel A). The helices that form are chiral; like wood screws, they have a handedness. Some are helicoids, twisted helices with saddle-like curvature and a straight centerline; others are cylindrical helices with cylindrical curvature and a helical centerline. Studies of the mechanisms underlying the formation of helicoid or helical ribbons and of the transitions between these structures (1–4) have left an important question unanswered: How do the molecular organization of the material and its global geometrical features interact to create a diversity of helical shapes? On page 1726 of this issue, Armon et al. (5) explore the rich phenomenology associated with slender strips made of mutually opposing “molecular” layers, taking a singular botanical structure—the Bauhinia seed pod—as their inspiration. They show that a single component, namely a flat strip with a saddle-like intrinsic curvature, is sufficient to generate a wide variety of helical shapes.

Morphology

Recently there have appeared some interesting works on biological morphology development. They help us understanding how a particular pattern, e.g., fingerprints and intestine, comes about under basic mechanical laws [http://www.nature.com/nphys/journal/v7/n9/full/nphys2088.html?WT.ec_id=NPHYS-201109].

Thierry Savin and colleagues refer to Thompson's tome in their investigation, published in Nature, of the elaborate looped morphology that arises in the vertebrate gut (Nature 476, 57–62; 2011). Using experiment, simulation, and an innovative physical mock-up comprising rubber tubing stitched to latex, they have examined the forces arising from relative growth between the gut tube and a neighbouring sheet of tissue known as the dorsal mesentery. The study reveals a mechanism for the formation of loops based on differential strain between the two tissues.

© SPL

This is a timely nod to Thompson's century-old ideas, given the recent surge of physicists and mathematicians into the biological sciences, problem-solving artillery engaged. In another paper, published in Physical Review Letters, Edouard Hannezo, Jacques Prost and Jean-Francçois Joanny adopt a similarly mechanical approach to understanding the complex structures seen lining the small intestine (pictured), invoking an analogy with the buckling of metallic plates under compression (Phys. Rev. Lett. 107, 078104; 2011). They have developed a model that implicates cellular division and death as sources of internal stress, which in turn influences morphology and induces mechanical feedback on organ and tissue development.

Why does it grow in the observed way ?

Crystal growth has been all the time an intriguing but complicated problem. The macroscopic shape depends in a subtle way on several factors, such as the properties of the surroundings. Indebted to the increasing power of computers, physicists are enabled to simulate a real growth. On the other hand, experiments also provide important insights. "Despite the many parameters involved, theorists have predicted that icicles, as well as other natural features like stalactites, should all converge to the same shape as they grow. In a paper appearing in Physical Review E, Antony Chen and Stephen Morris at the University of Toronto, Canada, describe an experimental setup that allows them to image icicles as they grow under controlled conditions, and test these predictions. They mounted a camera through a slot in the side of a refrigerator, within which icicles formed as water dripped from a nozzle and onto a rotating wooden support. Rotating the support helps even out the effects of drafts and temperature gradients." [http://physics.aps.org/synopsis-for/10.1103/PhysRevE.83.026307]