For thousands of years, sound has been an integral part of the human experience, and in many ways, it forms the bedrock of our social and cultural experiences. Indeed, humans have developed a taste for artistic expression through the generation of music. Music has become a powerful art form – both in performance and the creative process. When it comes to western classical music in particular, much of it is based on and developed through mathematical concepts – quite evident, for instance, in the detailed analyses of the compositions of the eminent musician Johann Sebastian Bach.

At the very foundation of many musical styles in classical music is the concept of “harmony” – the sound of two or more notes played at the same time – and then the more dissonant chords. Taken together, they can form opposing poles in musical creation. Interestingly, these concepts are deeply rooted in the physics of vibrations of macroscopic objects such as strings or membranes, and have evolved through the interaction of humans with physical objects.

Lend an ear

Whether it’s a piano, violin or guitar, many of our contemporary musical instruments are built and tuned such that notes played together sound pleasing to variant degrees. In order to achieve this result, musicians have developed the so-called “equal temperament” or tuning system, wherein a fundamental structure called an “octave” (or some other interval) is divided into equal steps, usually such that the musical pitch doubles its frequency. Following the definition of the harmonic series, the octave is uniformly divided into 12 tones whose frequencies are integer multiples of a fundamental vibrational frequency. This makes the equal temperament-octave system a near-perfect organization for musical composition and interpretation, and it has been at the core of classical western music.

Music, and its harmonic structure of sounds, is perceived by humans and animals through a complex auditory system, whereby an organ – such as the ear – collects pressure waves, applies a filter to prevent damages, and transmits (after an amplification and mechano-electrical conversion) sensory signals to the brain. This fascinating mechanism allows humans to interact with the surrounding environment. But the interaction of sound waves and other physical phenomena is also an engaging avenue of research (iScience 10.1016/j.isci.2021.102873). Such studies may lead to a different sensorial interpretation of sounds, providing a distinct stimulus perceived by eyes instead of ears, while also creating visual representations that can be subjects of new forms of art.

Molecular motions and even much smaller scales can be used to generate sound

Furthermore, recent research suggests that there is much to be explored when it comes to vibrational patterns as a fundamental, universal language of all living systems. In fact, it’s not just macroscopic objects that can serve as the source for sound. Molecular motions and even much smaller scales (such as wave phenomena at the quantum level) can also, if properly processed, be used to generate sound, thereby expanding our artistic palette based on advances in physics.

Protein sonification

A remarkable example of translating music into molecular structure, and vice-versa, lies in a key chemical constituent of life – namely the 20 amino acids that link up in chains to form all proteins. Generally speaking, proteins are the building blocks of all life, creating materials as diverse as human cells, hair and spider silk. Proteins are also key in countless other functions, including enzymes, drugs and viruses – each with unique physical properties that often link closely to their role as a biological agency. But protein structures, including the way they fold themselves into the shapes that often determine their functions, are exceedingly complicated.

With this in mind, we developed a systematic way of translating a protein’s sequence of amino acids into a musical sequence, using the physical properties of the molecules to determine the sounds (ACS Nano 13 7471). The system translates the 20 types of amino acids (figure 1) into a 20-tone scale. Any protein’s long sequence of amino acids then becomes a sequence of notes. The sounds are transposed in order to bring them within the audible range for humans (20 Hz–20 kHz), without affecting the structural features by following the concept of transpositional equivalence. Indeed, the tones and their relationships are based on the actual vibrational frequencies of each amino acid molecule itself, providing a physical basis for protein sonification.

To underscore this concept, think of a song that can be sung or played at different frequencies. As long as the ratios of the frequencies played are consistent, the human brain can properly recognize specific musical information. For example,  you can listen below to Beethoven’s “Fur Elise” which can be played at different transpositions – early on it is inaudible, but as the frequency ranges reach the audible spectrum, we can clearly recognize the piece through its salient musical structures that clearly identify it.

While studying lysozyme – a naturally occurring, anti-microbial enzyme found in bodily secretions such as tears, saliva and milk – we developed a new type of “amino acid music scale” (figure 2). It provides a sonified reflection of each of the enzyme’s amino-acid building blocks, uniquely characterizing their chemical makeup. An example for a protein mapped into this scale is provided for lysozyme, which you can listen to below. As with music, the structure of proteins is hierarchical, with different levels of structure at different scales of length or time. So in addition to the sounds generated by each amino acid, the expression of rhythm and note volume can be derived from the secondary and higher-order structure of the protein molecules.

Key COVID vibrations

Whether it’s birds singing or humans talking, the vibration of macroscopic objects is critical to communication. But vibrations as a mode of communication also works at the nanoscale, where molecular vibrations mediate inter-protein interactions and docking. In a recent work, for instance, we demonstrated that the vibrational signature of coronavirus proteins in the virus structure can be directly correlated to epidemiological data of virus lethality and transmission rates (Matter 10.1016/j.matt.2020.10.032).

A crucial step in how a virus causes an infection is when its protein spikes attach to the ACE2 human cell receptor. Once these spikes bind with the receptor, it unlocks a channel that allows the virus to penetrate the cell. Previously, researchers looked at biochemical mechanisms when studying how spike proteins, which give coronaviruses their distinct crown-like appearance, interact with human cells. Instead, we used atomistic simulations and AI to study the mechanical aspects of how the spike proteins move, change shape and vibrate.

The vibrations matter because the protein spikes are not static. Instead, they continuously change shape slightly, as they morph and attempt to break into the cell. This means that vibrations play a key role in the strategy adopted by the virus, as it attempts to trick the locking mechanism on the cell’s surface into letting it in, and then hijacking the cell’s reproductive mechanisms.

By modelling the atoms as point masses connected to each other by springs that represent the various forces acting between them, we were able to study how the vibrations develop and propagate. We found that differences in vibrational characteristics correlate strongly with the different rates of infectivity and lethality of different kinds of coronaviruses, taken from a global database of confirmed case numbers and case fatality rates. The viruses studied included SARS-CoV, MERS-CoV, SARS-CoV-2 and one of the mutations of the SARS-CoV-2 virus.

In all the cases we looked at, we observed key fluctuations in an upward swing of one branch of the protein molecule, which helps make it accessible to bind to the receptor. Another important indicator was the observed ratio between two different vibrational motions in the molecule. Together, these two factors show a direct relationship to the epidemiological data, including how infectious and lethal the virus may be.

As our method is based on understanding the detailed molecular structure of these proteins, it could be used to screen emerging coronaviruses or new mutations of the virus that causes COVID-19, to quickly assess their potential risk. Our work could also potentially point towards new ways to treat coronaviruses, by perhaps finding a molecule that can bind to the spike proteins such that their vibrations are limited or cancelled out altogether.

This work, together with the importance of complex vibrational signals in spider webs, for instance, points to a universality of vibrations and waves as elementary descriptors of materials.

Bach and proteins

If one had to name a classical composer who has influenced virtually all genres of music, from classical to pop, one would immediately think of Bach himself. A key concept on which he and many other composers designed their compositions is the so-called “circle of fifths” – a specific arrangement of the 12 tones of the chromatic scale, their corresponding key signatures, and the associated major and minor keys – as a sequence of perfect fifths.

A fifth is the interval from the first to the last of five consecutive notes in a diatonic scale, and musical theory defines a perfect fifth as the interval corresponding to a pair of pitches with a frequency ratio of 3:2. The perfect fifth spans seven semitones. Although this organization may appear complicated, it is worth noting that composers and musicians have used it to make distinctions between pitches, and to make composition and melody harmonization easier to perform in different scales. The cycle of fifths is, in fact, the most natural sequence of pitches recognizable and familiar to the human ear.

One of the cornerstones of Bach’s compositional approach is the use of a method called counterpoint – the relationship between two or more musical lines (or voices) that are harmonically interdependent, yet independent in rhythm and melodic contour. The idea is to play “note against note” (hence: counter-point), making it a simple and, yet, deeply foundational concept in music.

We have found that the observation of the structural properties in living materials leads to a “materialization” of the counterpoint concept, when proteins fold. Folding is encoded structurally by the alignment of multiple sequences, which can be used to glean information on how they are spatially organized. Counterpoint can be a way to code structural information, to define where in a structure a specific type of connections is made, thereby defining its topology in 3D. We developed a method to represent folded protein nanostructures as musical compositions. The physical closeness of two amino-acid sequences, for example, can be reflected using a structure-score mapping by an overlay of notes for that feature, and vice versa, leading to webs of melodies (figure 2) (Nano Futures 5 12501).

We developed a method to represent folded protein nanostructures as musical compositions

The interplay between Bach and proteins to study counterpoint can be better understood if we consider the “Goldberg Variations” (BWV 988) – you can listen to an extract below. This piece is, undoubtedly, one of the most intriguing of Bach’s compositions, consisting of an aria with 30 variations for harpsichord, published between 1741 and 1745. Each variation provides a different counterpoint style that helps the composer to continuously change tempos and melody, from slow harmonies to fugues, which can be beautifully interpreted by musicians (Bioinspir. Biomim. 17 015001).

To underscore the similarities between music and protein design, we mapped the first 16 measures of the main aria to a unique tonal scale, and then reverse-mapped notes to amino acids in the protein domain. The result was the sequence shown in figure 3, which can be folded using homology methods or deep learning approaches. The ordering of the amino acids is dictated by the scaling and mapped to the equal temperament scale, with notes from low to high pitch. The result from folding using a deep learning method (figure 3c) reveals the structure of a completely new protein that does not yet exist in nature, but rather was invented through Bach’s musical creativity. Through this mapping, we are learning new things about Bach, as well as exploiting specific features of the proteins to extract new musical compositions as one way to represent nature’s concept of hierarchy as a paradigm to create function from universal building blocks.

Strings and things, from a web to a harp

Another intersection between music and materials lies in the spider web. A commonplace architecture in nature, it nevertheless exhibits complex geometry and an extremely resilient building material. We can think of a spider as an “autonomous 3D printer”, as it builds its web using signals via vibrations, in which the silk exhibits properties comparable to various forms of music, in terms of hierarchical structure and function. In fact, we have recently developed a thousand-string harp out of a spider web – a natural structure with “strings” tuned to endow spiders with an exquisite sensor to detect the environment, that becomes an extension of their bodies. We can exploit this system to extract structural information as the basis for a new musical instrument (figure 4).

Through the use of virtual reality to map out a web that is traversable by humans, for instance, we can enter a world of new design methods for such systems where large-scale and small-scale relationships interplay. In 2014 our lab, with special efforts from postdoc Zhao Qin and graduate student Bogda Demian, created a computer model and simulation of the data generated via 3D scans of spider webs, made by artist Tomàs Saraceno in 2012. For the first time, not only could we accurately visualize the web, but also replicate its internal structure, gaining precise information about every single silk thread – the thickness, tension and length – and how threads interacted to create such an elaborate architecture.

The structure of the spider web also inspired many new musical pieces (listen to the clip below) and we also developed a granular synthesis technique that mimics the biochemical process of silk production (Computer Music Journal 44 4). More recently, we combined this kind of web sonification with our molecular music, overlaying frequencies and melodies extracted from the proteins that make up silk, as well as other key features of spiders, such as its venom molecules. 

This work can be useful for understanding not only spider webs but also the complex hierarchical arrangement of neurons in the brain – and even the web-like large scale structure of our universe.

From amorphous nature to structure

A special feature of music is its abstraction, as it is devoid of direct image-bound meaning. Unlike words which are associated with a subject matter, sounds are abstractions that provide a foundation to ask the question of how hierarchical systems, building block by building block, generate more than the sum of their parts. The outcome of musical expression can be purely mathematical or logical, or physics driven (such as to generate perfect harmony by invoking certain cadences or chord progressions), or it can be based on an emotional objective. We now propose an alternative outcome in showing that it is possible to derive music from a living structure – such as a protein – that can be sonified.

In doing so, it can be heard, understood and experienced by our conscious brain in terms of its 3D-folded structure for the first time. So can music be a measure of consciousness? At the very core of the question of our personal experience as a human being, the universality of vibrations and resonances may be a key in the emergence of conscience. Such discussions may provide exciting opportunities for further research at the interface of neuroscience, physics, biology and music theory – and to explore new dualities of reality in this way.