On its own, each of our neurons is a dumb oscillator. But when they fire together in their billions, something incredible begins to happen.
I don’t remember why we were clapping.
I was six years old, I think, perhaps seven, sitting with my classmates towards the back of the school hall. Our applause began as normal — the white noise of 300 children putting their hands together and apart, each with his or her own idiosyncratic rhythm. But then from this noise, a pulse emerged. A slow drum beat, quiet at first but growing ever louder as it picked us off one by one. Within a few moments, the whole school was clapping in time.
I remember a strange exhilaration, the feeling of being out of control, subsumed by the crowd, slave to the collective rhythm. And then, as abruptly as it had begun, the spell was broken, the waves of sound subsided, and we were each released to our individual rhythms and, finally, silence. I remember looking at my friend, cross-legged next to me, looking wide-eyed back. “What just happened?”
We weren’t to know, of course, but this profound episode was far from unusual. Emergent synchrony is found throughout nature, bringing order to chaos, creating signals out of noise. It’s there in the coordinated flashing of fireflies, in the chirping of crickets, and the syncopated burping of frogs on a warm summer evening. You find it, too, in the firing of the heart’s pacemaker cells. And it’s there in our brains, where 86 billion neurons pulsate in complex electrical harmony.
This idea has held for me an enduring fascination. Neurons come in assorted shapes and dimensions — pyramidal, Purkinje, basket, spindle. But their core programs are in essence the same: accumulate electrical charge, and, when it reaches a certain level, fire an electrical impulse. On its own, each neuron is inconsequential, a dumb oscillator, cycling endlessly through the same program. Fire and recharge. Fire, recharge. But through feedback loops and dense interconnections, neurons gently nudge one another towards synchrony, forming and breaking alliances signalled by their common rhythm. And it is through these rhythms, through the dappled waves of electricity rippling through the brain, that our experience of this universe arises.
The study of brainwaves has a curious origin story. In 1892, Hans Berger, a young officer in the Prussian Army, fell from his horse and narrowly avoided being crushed by a cannon. Shortly thereafter, he received a letter from his father describing the accident as witnessed by his sister in a dream. “It was,” Berger wrote, “a case of spontaneous telepathy in which at a time of mortal danger, and as I contemplated certain death, I transmitted my thoughts, while my sister, who was particularly close to me, acted as the receiver.”
On completing his military service, Berger returned to work as a psychiatrist but devoted his research efforts to understanding this “psychic energy”. He experimented by measuring electrical activity from his own scalp and from patients in his clinic. The pursuit of telepathy, of course, never amounted to anything. But Berger’s years of painstaking and carefully controlled experiments allowed him to conclude, in 1929, that the waves of electrical activity picked up by his electroencephalogram were generated in the brain.
Berger’s research was met at first with understandable scepticism. Even when other scientists confirmed that electroencephalography (EEG) does, indeed, measure neural activity, brainwaves were dismissed as nothing more than an idling rhythm, neurons ticking over, waiting for a call to action. Berger’s own data showed that so-called alpha waves recorded over the visual cortex were strongest when the subject’s eyes were closed. The largest waves of all — long, slow delta waves — are found in the deep stages of sleep.
There is, however, more to brainwaves than meets the eye. In 1822, French mathematician Joseph Fourier showed that any repeating signal can be broken down into a collection of sine waves of different amplitudes and frequencies. Applied to sound waves, the Fourier transform can pull apart the notes and instruments in a piece of music. Applied to EEG data, it reveals the subtle shifts in brain activity related to ongoing mental events. Looking at simple black and white stripes, for example, affects high frequency ‘gamma’ oscillations recorded by electrodes over the visual cortex. Performing a memory task affects low frequency ‘theta’ oscillations.
The exact significance of these oscillations remains an open question. One idea is that, by oscillating in synchrony, neurons are indicating the fact that they are responding to different aspects of the same entity, such as the colour and shape of an object. A related suggestion is that oscillations are the brain’s routing mechanism. Different parts of the brain can “tune in” to one another by synchronising their oscillations, allowing flexible transfer of information.
However, as Hungarian neuroscientist György Buzsáki notes in his book, Rhythms of the Brain, the evidence concerning the role of oscillations is mostly correlational. Changes in brain rhythms accompany changes in mental activity, but do they cause them? Are oscillations really an essential component of brain ‘design’? Or are they just a meaningless or even unwanted by-product of neural activity — like the resonant sway of a bridge or tall building. Perhaps the brain works in spite of oscillations, not because of them.
To push the case for oscillations, Buzsáki relies on a thought experiment. “What makes the brain so special and fundamentally different from all other living tissue,” he argues, “is its organized action in time.” It’s possible for a nervous system to have evolved without rhythm, without oscillations, but it would have required an alternative timing mechanism to coordinate its activity. Evolution, after all, is nature’s great up-cycler, fashioning ears out of jaw bones and flippers from forelimbs. The male firefly isn’t trying to synchronise with his compatriots, but a coordinated signal is more salient to potential mates. If synchronisation confers an advantage, natural selection favours the subtle tweaks of body and brain that allow it to emerge. The same applies to heart cells and, presumably, brain cells.
Perhaps, then, these analogies are more than a poetic metaphor.
Writing in 1908, the French mathematician and physicist Henri Poincaré described mathematics as “the art of giving the same name to different things”. In turning the concrete into the abstract, it reveals similarities between phenomena that may appear on the surface to be quite different. To the mathematician, an oscillator — whether a neuron, firefly, or child clapping — can be thought of as a point moving around a circular path, like the Moon orbiting the Earth, or the hand of a clock, coming back repeatedly to the same point.
Interest in emergent synchronisation dates to the 17th century, when Dutch watchmaker Christiaan van Huygens observed two pendulum clocks hanging in his workshop, swinging together in lockstep. But it wasn’t until 1975 that Japanese physicist Yoshiki Kuramoto provided a tractable mathematical model. Kuramoto’s model determines the speed of a given oscillator around the circle. This depends in part on its own natural speed, and in part on its interaction or coupling with all the other oscillators. To simplify the mathematical problem, Kuramoto assumed that all couplings are of equal strength. Rather than working out, for example, how the clapping of one child is affected by each of the other children individually, we can look instead at how he or she is affected by the combined sound of the whole school.
With weak coupling, the oscillators remain unsynchronised, each circulating independently at their own speed. But, as coupling increases in strength, a sudden change occurs. The oscillators start clumping together as they move around. The more that join the circulating pack, the stronger the effect on the remaining oscillators, and the more likely they, too, will be subsumed by the collective. As in that school hall years ago, once the rhythm starts, it’s hard to resist.
Kuramoto’s initial interest was in oscillations in chemical systems. But his model has found wide application in the study of physical and biological synchrony, from laser arrays and superconducting devices through to fireflies in South Asia and rhythmic applause in Romanian theatres. The question, however, is can we really apply it to the brain?
Michael Breakspear, a computational neuroscientist at the QIMR Berghofer Medical Research Institute in Brisbane, argues that Kuramoto’s model oversimplifies the problem, assuming not only that all oscillators coupled equally to one another, but that coupling between oscillators happens instantaneously. In reality, neurons tend to be more closely connected to their neighbours than to distant neurons, and signals take time to travel through the brain.
In a 2010 study, Breakspear and his colleagues built a computer simulation with oscillators arranged in a two-dimensional sheet, programmed to obey a more neurobiologically plausible version of the Kuramoto model. Instead of the oscillators all falling into lockstep, bouncing up and down as one, the simulation revealed patterns of travelling waves rippling across the surface of the simulated brain.
Breakspear points out that, while conventional analysis of EEG data reveals changes in oscillations at different locations, it’s blind to waves moving across the brain. To detect travelling waves, more advanced analyses are required that combine information about space and time to look at wave trajectories. This, Breakspear says, illustrates one advantage of mathematical modelling: “We can make new predictions, measure new things, and think of different ways of looking at data.”
Even with added bells and whistles, Kuramoto’s model is far too simple to begin describing the human brain. For a start, it only considers oscillations at a particular frequency and misses out on the complex interplay of higher and lower frequencies. Breakspear and his lab have moved on to what they consider more realistic modelling approaches.
Yet in its elegant failure, the Kuramoto model provides an important lesson. We boast of the human brain as the most complex entity in the known universe, but it’s still a part of the universe. It still obeys the same principles of physics and mathematics and has evolved in the same way as everything else. And so, it would seem, our best handle on the brain may be to apply what we already know about the natural and physical world, to take these analogies and metaphors and run with them as far as we can.
There is a beauty, I think, in this notion. This marvellous organ that gives us memories and language, ideas and emotion — it’s more than neurons and neurotransmitters, synapses and axons. It’s music and rhythm, the ebb and flow of electric waves. Fireflies in the dark.
Edited by Andrew Katsis