Music of the Macromolecules

To fully understand a molecule, you first need to learn what it looks like, and then, how it moves. This isn’t easy. I’ve talked before about how unusual biological molecules can be if you’re accustomed to thinking of real-world objects. They are fundamentally flexible and dynamic in a way that everyday objects aren’t. They move chaotically, at lightning speed, crashing through a molecular mosh pit on the sub-microscopic scale.

Protein and nucleic acid macromolecules are like Rube Goldberg machines of interconnected parts. These parts move independently, but in turn influence the other parts of the system as they move. There’s different levels of complexity in this motion. Slow conformational transitions that move large sections – domains – relative to each other can take milliseconds to occur. Ultra-fast bond vibrations take only picoseconds. That’s a difference of nine orders of magnitude. In the time of a single slow domain movement, a billion bond vibrations can occur. In monetary terms, this is the difference between one cent and ten million dollars.

This is what biophysicsts refer to when they talk about “timescales of molecular behaviour“. Different types of molecular motions take dramatically different lengths of time to occur. We can only measure a subset of these motions with any one experimental technique. When we try to fully understand a molecule, we need to be aware of all of its motion across all timescales. Unfortunately, we are terrible at understanding things that span such a broad range.

Our brains are trained to think about everyday objects we can see, touch, and manipulate. Microscopic molecules act in ways that make absolutely no sense on the scale of our experience. To help make sense of this strange behaviour, we need a good metaphor.

Molecular Motions are Like Musical Harmonics

What does a molecule have in common with a musical note? You might not be able to think of any way these two things are related (you also might also be wondering what I’ve been smoking). A molecule is a collection of atoms, connected by shared electrons. A note is a small part of a Bach sonata, jazz solo, or Call Me, Maybe.

Well, we’ve discussed before how the context a molecule is in is critical for understanding downstream effects. A musical note, as well, gains more meaning by the context it is placed within. The same note means different things if it’s played within a different song, or if it comes from a pan-pipe versus an electric guitar.

But even isolated molecules and isolated musical tones share something fundamental in common. They both display a complexity of vibration, with finer, more detailed vibration superimposed on top of slower, lower-frequency behaviour.

vviibbrraattiioonn
Macromolecules show motion on many scales, superimposed on each other like resonant overtones of a musical note. Structures generated from PDB 5RAS

To a first approximation, a note is just a frequency of sound. Children of the ’90s will remember that before Napster, we could download MIDI files from the internet to play as music. Many computer sound cards rendered the tones of the MIDI as pure tones, which reflects the format the note is stored as in the MIDI file. The end result is completely devoid of soul, a heartless distillation. It lacks any of the complexity of actual recorded music. The notes are there, but without details and imperfections of that come from real instruments, it seems hollow. Real musical instruments produce so much more than just pure tones.

We know that the character of an instrument changes the nature of the sound it produces. A B♭ from a trumpet and a B♭ from a clarinet sound different to us, despite both having same fundamental frequency. What makes them sound different from each other, and from a MIDI file? In one word: overtones. Every instrument layers higher-order resonances – vibrations – on top of the fundamental tone, and those resonances are dependent on the shape, material, and other properties of the instrument. Vibrational overtones add complexity and texture to an instrument’s sound. While the main pitch of the note is the same, the structure and character of the instrument produce different superimposed frequencies that make it unique.

Like the air perturbed by a musical instrument, molecules also vibrate. These vibrations and movements are central to their function. Individual atoms undergo high speed vibration. Chains of multiple atoms turn and bounce in unison. Loose loops and “floppy bits” of dozens to hundreds of atoms contort, twist, and wiggle. Whole domains can migrate back and forth between different states. Like overtones on a musical note, these motions are superimposed on each other. While large domain movements occur, loops are wiggling, within those wiggles, amino acid side chains are bouncing, and during those bounces, individual atoms vibrate across every bond in the molecule.

Harmonic Potentials

Rotation and vibration of atomic bonds follow an energy potential pretty close to sine waves. Combining the motion of those atomic vibrations and rotations across multiple atoms produces an emergent complexity where the arrangement of atoms across one bond can influence that of the nearby atoms, and by extension, the rest of the molecule. In theory, we might be able to work out how these energy potentials govern the behaviour of a single molecule.

Alas. Were it only that simple.

In the change of structure of a molecule, small transitions of single atoms can be layered on top of larger motions. The motion of an atom depends on its own vibrations, as well as that of the rest of the molecule around it, pushing and pulling it along with larger changes. This feeds both ways. While a large transition occurs, vibrations and rotations of progressively smaller components can also exert their collective effects on the entire molecule. This chicken-and-egg problem is a big part of why the behaviour of molecules is so hard to predict, even when we know its structure. It leads to a computational problem that rapidly gets too complicated for even the most powerful supercomputers to handle easily.

So just because you know the shape of a molecule doesn’t mean you can capture the full essence of its character. Like a musical note, a molecule’s shape is just the starting point to understanding the complex way it acts on itself and its environment. Static molecular structures are like notes printed on a page. Dynamics* are those notes, played aloud, containing much more richness than the printed note alone contains.

When we combine multiple musical notes, the complexity grows even greater. Multiple notes from a single instrument like a guitar or piano interact with each other to form chords. Different instruments in a band or orchestra combine together to further increase the complexity. All of these interactions combine together to make a symphony much greater than the sum of its parts.

Likewise, combination of motions within molecules also adds to a complex whole, where the collective motion of thousands or millions of atoms can lead to much more nuanced patterns of behaviour than we might otherwise expect. Two macromolecules, playing their own melodies, can come into contact (bind) with each other, and if so, they join together in harmony. These molecules become a single, resonating entity, sometimes for a brief exchange, other times for much longer.

Just like in a symphony, the complexity grows even more as we scale up interactions of molecules to complexes, signalling pathways, cells, and even whole organisms. This intricate opera underlies all biological processes.

Fine Tuning

So, if molecules are so complex, how can we make any sense of their messy behaviour? In science, we don’t aim to simply appreciate nature, but to understand it and make predictions about the future, and to generate changes that help us innovate on existing phenomena. Our metaphor of a molecule as a musical note becomes useful to help us move from thinking about how a molecule is to how it might change.

Ask any manufacturer of a musical instrument: changes to small details of a musical instrument can dramatically influence the quality of sound you get. This is the same with molecules – changes that alter the dynamics change the character of the molecule. For example, in a protein, biological activity frequently requires large movements between domains of a protein, as well as finer motions of hinge regions, short loops, and amino acid side chains. Changes to a molecule, by post-translational modification, mutation, binding to another protein, or allosteric regulation can distort or modulate the dynamics of a protein. They change the tune of the molecule, by altering its resonances.

This resonance-tuning feature of proteins has led to many mysteries in the literature about macromolecules. With surprising frequency, mutations are found that disrupt the activity of a protein, despite being far away from the business end (the “active site”) of the protein molecule. These reductionism-breaking proteins have caused many a biochemist to throw up their hands in dismay at the apparent lack of connection between a mutant protein they identify and their observed change in molecular function. Happily, though, we’re starting to track down the culprit: dynamics.

Changes to a molecule that have very little structural change can still alter the molecule’s vibrational frequencies. A protein with an amino acid important for dynamics changed is like a band whose bass player is hung over and can’t keep time.

A paper from earlier this year demonstrates this effect very well. It came from Dorothee Kern‘s group at Brandeis. Looking at two well-known protein kinases(PMC) and reconstituting the evolutionary and biochemical pathway between the enzymes, the group found that there’s a small set of amino acids that drive the change in behaviour between the enzymes. Almost none of these amino acids are directly involved in the chemical behaviour of the protein. Like making alterations to an instrument, these mutations tune and refine the dynamic properties of the enzyme, and direct it toward different behaviour.

Molecular and structural biologists are just starting to get a good understanding of the role of mutation and chemical change to altered dynamics and function of proteins. I’ll be watching this field closely for future developments.

From Chaos, Order

The analogy of molecules as musical notes with harmonics isn’t perfect. Music depends on perfectly repeatable, precise tones (that’s not to say innovation and improvisation aren’t important, but they use the same, standard notes). Molecules have an intrinsic chaotic nature that is not really predictable at all. But while the molecule is unpredictable on the microscopic level when you look closely, take a step back and the molecule starts to average out into predictable, regular rules. From a stochastic and random process on the microscopic level, step back farther and farther, and a kind of predictable order emerges.

There’s also a difference in scale. The first overtone of a note is merely twice the frequency. Proteins have motions at least 9 orders of magnitude different. However, we could compare it to the difference in loudness our ears can perceive, the difference between a bond vibration and large macromolecular rearrangement is about the same difference in magnitude as a pin dropping when compared to a loud rock concert. The musical analogy isn’t perfect, but it helps understand a hugely complex system with thousands or millions of moving parts in a more intuitive way.

Symphonies in the Molecular World

Molecules are alien entities, very different than anything we interact with in our everyday lives. Their actions are determined first by their structures, then by their dynamics – how those structures move and vibrate. The structure and movement of these molecules results in a complex molecular symphony going on at the microscopic level. And from the single complex note that one molecule makes, it can be tuned by others, harmonize with partners, and join in with the grand symphony that goes on in the complex molecular opera of life.

Dynamics are a frontier of structural biochemistry research (a Grand Challenge, if you will). Moving forward, we continue to chip away at the mysteries of how molecules work and learn how to better predict molecular behaviour. Every time we do so, we get a little bit better at listening to the complex arias and beautiful harmonies these molecules play. Our ear gets a little bit more refined, our appreciation of this molecular orchestra more acute. The symphony goes on all around us, can you hear it?

* I’m using the definition of dynamics as it relates to molecules here, as in the field of molecular dynamics modelling. The term dynamics as it relates to music is a slightly different concept than anything we’re discussing here, so I’ll skip over it.

Citation:
C. Wilson, R. V. Agafonov, M. Hoemberger, S. Kutter, A. Zorba, J. Halpin, V. Buosi, R. Otten, D. Waterman, D. L. Theobald, D. Kern (2015). Using ancient protein kinases to unravel a modern cancer drug’s mechanism Science, 347, 882-886 : 10.1126/science.aaa1823

Advertisements