The mathematical patterns in the physical structure of spider silk show similarities to those in classical music composition, according to a new U.S. study.
Researchers at Massachusetts Institute of Technology (MIT) have revealed a structure-function relationship in two seemingly disparate fields—the composition of proteins and musical riffs—that may help engineers design new materials and even infrastructures.
The team used a branch of mathematics called category theory to create ontology logs or “ologs” by looking at the items’ primary building blocks: amino acids and sound waves. Ologs allow a system’s properties to be categorized abstractly, and reveal the inherent relationships between structure and function.
“The seemingly incredible gap between spider silk 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,” said study co-author David Spivak in a press release.
“Yet category theory’s first success—in the 1940s—was to express a rigorous mathematical analogy between these two domains and to use it to prove new theorems about complex geometric shapes by importing existing theorems from algebra.”
The olog allows scientists to compile information about how materials function in a mathematically rigorous way, and pinpoint patterns that are found universally in a broad variety of 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,” said Markus J. Buehler of the Department of Civil and Environmental Engineering (CEE) in the release.
Interestingly, even when mistakes occur in the patterns, the overall harmonic sequence and function is generally unaffected.
“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,” said study co-author Tristan Giesa in the release.
“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,” he continued.
“Deleting single chords from a harmonic sequence often has only a minor effect on the harmonic quality of the whole sequence.”
The findings were published in the December issue of the journal BioNanoScience.