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October 20, 2014

In previous articles (Crumpling, August 27, 2012, Packing, November 30, 2010 and Packing and Filling, May 17, 2012), I've discussed crumpling, packing and filling, and stacking. Crumpling involvestwo-dimensional objects, such as a sheet of paper, while packing, filling, and stacking involve three-dimensional objects, such as granular materials.

Additional to these two- and three-dimensional processes, there' s an important one-dimensional material process, folding. The most important example of folding is protein folding. Proteins are biological macromolecules formed when a polypeptide, which is a linear chain of amino acid residues, folds into a three-dimensional structure. Just as the isomeric forms of small molecules affectmolecules their chemical activity, the way that proteins fold affects their biological function. Incorrect protein folding, known as proteopathy, can cause disease.

protein folding example

A simplified example of the main driving force behind the folding that leads to the final conformation of a protein molecule.

Hydrophobic amino acids (blue spheres) are better shielded from the solvent environment when folded as shown on the right.

(Modified Wikimedia Commons image)

A minimally functional protein consists of about 40-50 amino acid residues, and some multi-functional proteins will contain several hundred amino acid residues. As first noticed in 1969 by American molecular biologist, Cyrus Levinthal, a chain of just a hundred residues would still have a myriad number ways in which to fold.

The number is too large to allow an exhaustive search for a lowest energy conformation, either through the physical motion of the molecules themselves, or by computer simulation, but proteins are known to fold in just milliseconds. This contradiction is called Levinthal's paradox, but it hasn't stopped attempts at computer-assisted protein structure prediction, such as the folding@home distributed computing project.

Every home has an assortment of garden hoses, extension cords, and computer cables, all of which we wouldn't want reduced to a three-dimensional tangle reminiscent of a folded protein. We're instead interested in how these might be coiled. Coiling is the folding process with a dimensional restriction.

Bacterium with flagellum

Intermediate between proteins and garden hoses are bacterial flagella. Flagella propel bacteria to better food sources. (Still image, enhanced, from an MIT YouTube Video.)

Scientists and engineers from the Department of Mechanical Engineering and Department of Civil and Environmental Engineering of the Massachusetts Institute of Technology (Cambridge, Massachusetts), and the Department of Computer Science at Columbia University (New York, NY), have experimentally examined how flexible cables coil on static and moving substrates. The results of their studies have been published in the Proceedings of the National Academy of Sciences.[2-5]

The coiling of cables may sound like a niche research area, but it's important to our Internet-connected age since it relates to the laying of submarine cables. Identifying which mechanical properties of such cables affects their deployment would prevent such things as cable breakage, or laying the cables too loosely. Any twist or tangle in a cable will cause degradation of the optical signals. Presently, there are more than 550,000 miles of undersea cables.[4] Says MIT lead researcher, Pedro Reis,
“If the boat is sailing slower than the rate of the cable, then you're putting more cable down, which generates loops, coils, and tangles... That can lead to signal attenuation. But if the boat is traveling faster, then the cable can get taut and fracture, which is really bad news. So we wanted to understand what was underlying those patterns.”[4]

The MIT laboratory experiments were done with an equivalent geometry of having a static source dropping cable onto a conveyor belt (see photograph). The apparatus allowed adjustment of the speed of deployment and the speed of the belt, and it included video capture for analysis of the results.[4] Filaments of silicone rubber were used, and three main patterns were observed; namely, meandering waves, alternating loops, and repeated coils.[4]

Cable coiling experiment

Apparatus for the coiling experiments.

A thin silicone filament (green) is layed on a black conveyor belt to form a periodic array of loops in alternating directions.

(MIT photo by John Freidah.)[4)]

To make sense of the results, the MIT engineers enlisted the aid of Eitan Grinspun and his team of computer scientists at Columbia University. As all programmers know, code-reuse is a wonderful thing, and Grinspun has developed computer algorithms for simulation of the movement of the thin filaments of hair and cloth, notably for the films, “The Hobbit” and “Tangled.” Going beyond mere visual effects, Grinspun has modeled the flow of honey. Honey, a viscous fluid, as poured from a jar, can appear as a rope or thread, forming wavelike patterns on a surface. [4]

The modeling results were initially disappointing until they added the natural curvature of the filament as a parameter. Semi-stiff filaments, when wound on a spool, retain a short-term memory of the spool's curvature. In the end, the model incorporated the speed that the filament was deployed, the speed of the conveyor belt, the stiffness and diameter of the filament, and the size of its spool.[2,4]

The research team also found that the height from which a filament is deployed didn't have an affect. Says Grinspun,
“This is important because, as a ship sails, the height of the ocean floor relative to the surface is changing all the time... We also know that how big you make the spools on the ship does matter. So we now have a map of how cables coil, and an understanding of what variables are important if you're trying to achieve certain patterns.”[4]

This research was funded, in part, by the National Science Foundation.[4]

Coiling:experiment compared with simulation

A comparison of experiment (left), and a computer model (right). It was found that the loops form in an alternating clockwise, then counter-clockwise, pattern.

(MIT photograph by the Reis research team.)[4-5)]


  1. Cyrus Levinthal, "How to Fold Graciously," in Mossbauer Spectroscopy in Biological Systems: Proceedings of a meeting held at Allerton House, Monticello, Illinois, J. T. P. DeBrunner and E. Munck, Eds., University of Illinois Press (1969), pp. 22-24 .
  2. Mohammad K. Jawed, Fang Da, Jungseock Joo, Eitan Grinspun, and Pedro M. Reis, “Coiling of elastic rods on rigid substrates,” Proc. Natl. Acad. Sci., published ahead of print, September 29, 2014, doi:10.1073/pnas.1409118111.
  3. Supplemental Information for ref. 2.
  4. Jennifer Chu, "Untangling how cables coil," MIT Press Release, October 3, 2014.
  5. Movie: Pattern of alternating loops obtained when depositing filament. See ref. 3 for details.
  6. The Wonders of Thin Structures from Failure to Functionality, MIT YouTube Video, November 12, 2013.

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