Researchers link patterns seen in spider silk, melodies

December 8, 2011 by Denise Brehm, Massachusetts Institute of Technology
Graphic: Christine Daniloff

Using a new mathematical methodology, researchers at MIT have created a scientifically rigorous analogy that shows the similarities between the physical structure of spider silk and the sonic structure of a melody, proving that the structure of each relates to its function in an equivalent way. 

The step-by-step comparison begins with the primary of each item — an amino acid and a sound wave — and moves up to the level of a beta sheet nanocomposite (the secondary structure of a protein consisting of repeated hierarchical patterns) and a musical riff (a repeated pattern of notes or chords). The study explains that structural patterns are directly related to the functional properties of lightweight strength in the spider silk and, in the riff, sonic tension that creates an emotional response in the listener.

While likening spider silk to musical composition may appear to be more novelty than breakthrough, the methodology behind it represents a new approach to comparing research findings from disparate scientific fields. Such analogies could help engineers develop materials that make use of the repeating patterns of simple building blocks found in many biological materials that, like spider silk, are lightweight yet extremely failure-resistant. The work also suggests that engineers may be able to gain new insights into biological systems through the study of the structure-function relationships found in music and other art forms.

The MIT researchers — David Spivak, a postdoc in the Department of Mathematics, Associate Professor Markus Buehler of the Department of Civil and Environmental Engineering (CEE) and CEE graduate student Tristan Giesa — published their findings in the December issue of BioNanoScience.

They created the analogy using ontology logs, or “ologs,” a concept introduced about a year ago by Spivak, who specializes in a branch of mathematics called category theory. Ologs provide an abstract means for categorizing the general properties of a system — be it a material, mathematical concept or phenomenon — and showing inherent relationships between function and structure.

To build the ologs, the researchers used information from Buehler’s previous studies of the nanostructure of spider silk and other biological materials.

“There is mounting evidence that similar patterns of material features at the nanoscale, such as clusters of hydrogen bonds or hierarchical structures, govern the behavior of materials in the natural environment, yet we couldn’t mathematically show the analogy between different materials,” Buehler says. “The olog lets us compile information about how materials function in a mathematically rigorous way and identify those patterns that are universal to a very broad class of materials. Its potential for engineering the built environment — in the design of new materials, structures or infrastructure — is immense.”

“This work is very exciting because it brings forth an approach founded on category theory to bridge music (and potentially other aspects of the fine arts) to a new field of materiomics,” says Associate Professor of Biomedical Engineering Joyce Wong of Boston University, a biomaterials scientist and engineer, as well as a musician. “This approach is particularly appropriate for the hierarchical design of proteins, as they show in the silk example. What is particularly exciting is the opportunity to reveal new relationships between seemingly disparate fields with the aim of improving materials engineering and design.”

At first glance, an olog may look deceptively simple, much like a corporate organizational chart that shows reporting relationships using directional arrows. But ologs demand scientific rigor to break a system down into its most basic structural building blocks, define the functional properties of the building blocks with respect to one another, show how function emerges through the building blocks’ interactions, and do this in a self-consistent manner. With this structure, two or more systems can be formally compared.

“The fact that a spider’s thread is robust enough to avoid catastrophic failure even when a defect is present can be explained by the very distinct material makeup of spider-silk fibers,” Giesa says. “It’s exciting to see that music theoreticians observed the same phenomenon in their field, probably without any knowledge of the concept of damage tolerance in materials. Deleting single chords from a harmonic sequence often has only a minor effect on the harmonic quality of the whole sequence.”

“The seemingly incredible gap between and music is no wider than the gap between the two disparate mathematical fields of geometry — think of triangles and spheres — and algebra, which uses variables and equations,” Spivak says. “Yet category theory’s first success, in the 1940s, was to express a rigorous mathematical analogy between these two domains and use it to prove new theorems about complex geometric shapes by importing existing theorems from algebra. It remains to be seen whether our olog will yield such striking results; however, the foundation for such an inquiry is now in place.”

This story is republished courtesy of MIT News (, a popular site that covers news about MIT research, innovation and teaching.

Explore further: Going nature one better: Researchers learn biology's secrets for making tough, resilient materials

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2 / 5 (1) Dec 08, 2011
Very cool research.I wonder if anybody at MIT has translated protein structures into listenable music in the human range ?

3 / 5 (2) Dec 08, 2011
vlaaing peerd
4 / 5 (1) Dec 08, 2011
mwah I do not see the "special" relationship with music at all, we just call music music because we appreciate the mathematical relationship between the tones. The reason why we universally have a 12 tone system is based on simple logarythms, the reason why we choose a number of notes within this system to call a scale is based on cultural/traditional/personal preferences.

So basically they are telling us that music and how a spider makes it's web is based on math, they could just as well make an anology between spiderwebs and calculators.

It is somewhat sad that the physics/maths behind music has come to a standstill or even to regression, the deepest research ever done on that subject were arguably works from Huygens and Euler.

Musicians usually are unaware of the mathematical relationships in music, the theory they use does not address that and neither would it be necessary, but from that corner you could expect mostly holistic answers, not analytic.
not rated yet Dec 08, 2011
X can be slightly damaged/incomplete and still be useful, so can Y. Okay. I'm still waiting for the "scientifically rigorous analogy".
1 / 5 (1) Dec 08, 2011
I wonder if there are any synesthesiacs out there who process colors or shapes as musical tones?
0.8 / 5 (51) Dec 08, 2011
Often times simply changing how you choose to view something can be revolutionary. Richard Feynman was all but laughed out of the room when he introduced his Feynman diagrams.

If it helps some engineer or researcher think about it more efficiently, it is worthwhile.
1.8 / 5 (5) Dec 08, 2011
Let's not forget Kepler's Music of the Spheres, where the movement of the solar system is represented musically, written in the year 1619!
1 / 5 (5) Dec 08, 2011
I would venture to connect the structure of DNA to a musical one, because music reverberates and resonates through our very being, a mystery that can't be explained away as logarithmic. Anyone who claims it to be simply an appreciation of the mathematical is an automaton.
1.8 / 5 (5) Dec 08, 2011
I wonder if there are any synesthesiacs out there who process colors or shapes as musical tones?

Franz Liszt was famous for his transposition of color to music. It makes complete sense- to paint with sound.
1 / 5 (4) Dec 08, 2011
Dec 09, 2011
This comment has been removed by a moderator.
not rated yet Dec 12, 2011
Vlaaing peerd, it looks like you're contradicting yourself. On one hand you're saying:
...we just call music music because we appreciate the mathematical relationship between the tones.

and then:
Musicians usually are unaware of the mathematical relationships in music

Which is exactly the point! In order to appreciate mathematics you usually need a strong cognitive effort, while appreciating music comes effortlessly. These are just different regions of the brain at work! Maybe that's why
physics/maths behind music has come to a standstill or even to regression
Yes, everything can be translated to and from mathematics, even the frequency spectrum of your morning fart. But can mathematics ever be used to create moving, emotional, touching music, or even to determine what makes music that? I seriously doubt that!
3 / 5 (2) Dec 22, 2011
To the overmoderators,
you removed a comment i made in refference to the movie called "The Last Mimzy" under an article that talks about spider webs and sounds. Since that was obviously lost on your overmoderating self ill explain. In the movie, spiders were controlled via sound to produce certain designs with their webs. The application suggested in the movie was using such a technology to have the spiders build stronger than steel type structures entirely made of spider silk.

I'm sorry such a reference was lost on you people.
not rated yet Jan 31, 2012
Ok so a new tool has been found to find similarity between something visually apparent and another acoustically detectable but what exactly is similar?!

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