Oscillatory Synchrony is Energetically Cheap
Excerpt from Rhythms of the Brain (2006) by György Buzsáki (pgs. 168-170)
The paramount advantage of synchronization by oscillation is its cost-effectiveness. No other known mechanism in the physical world can bring about synchrony with so little investment. What do I mean by declaring that synchrony by oscillation is cheap? Let me illustrate the cost issue first with a few familiar examples from our everyday life. You have probably watched leisurely strolling romantic couples on a fine evening in a park or on the beach. Couples holding hands walk in perfect unison, whereas couples without such physical link walk out of step. You can do this experiment yourself. Just touching your partner’s finger will result in your walking in sync in a couple of cycles. Unless your partner is twice as tall or short as you, it costs pretty much the same effort to walk in sync as out of sync. Once you establish synchronous walking, it survives for quite some time even if physical contact is discontinued. If both of you are about the same height and have a similar step size, you will stay in sync for a long distance. In other words, synchronization by oscillation requires only an occasional update, depending on the frequency differences and precision of the oscillators. Two synchronized Patek Philippe vintage timepieces can tick together for many weeks, and quartz watches fare even better.
A much larger scale example of synchrony through oscillation is rhythmic clapping of hands, an expression of appreciation for superior theater and opera performances in some countries. Clapping always starts as a tumultuous cacophony but transforms into synchronized clapping after half a minute or so. Clapping synchrony builds up gradually and dies away after a few tens of seconds. Asynchronous and synchronous group clapping periods can alternate relatively regularly. An important observation, made by Zoltán Néda at the Babeș-Bolyai University, Romania, and his colleagues, is that synchronized clapping increases the transient noise during the duty cycle, but it actually diminishes the overall noise (Neda et al. 2000).* The explanation for the noise decrease during the synchronized clapping phase is the simple fact that everyone is clapping approximately half as fast during the synchronous compared with the nonsynchronous phase. Oscillatory entrainment nevertheless provides sharp surges of sound energy at the cost of less overall muscular effort. The waxing and waning nature of rhythmic hand clapping is reminiscent of numerous transient oscillatory events in the brain, especially in the thalamocortical system. Similar to hand clapping, the total number of spikes emitted by the participating neurons and the excitatory events leading to spiking may be fewer during these brain rhythms than during comparable nonrhythmic periods. A direct test of this hypothesis would require simultaneous recordings from large numbers of individual neurons. Indirect observations, using brain imaging methods, however, support the idea.**
Perhaps the most spectacular example of low-energy coupling, known to all physics and engineering majors, is the synchronization of Christiaan Huygen’s pendulum clocks. Huygen’s striking observation was that when two identical clocks were hung next to each other on the wall, their pendula became time-locked after some period. Synchrony did not happen when the clocks were placed on different walls in the room. Huygen’s clocks entrained because the extremely small vibrations of the wall that held both clocks were large enough that each rhythm affected the other. The physical reason for synchrony between two oscillators is relatively simple, and solid math exists to explain the phenomenon.*** However, extrapolation from two oscillators to the coupling behavior of large numbers of oscillators is not at all straightforward. Imagine that, in a cylinder-shaped room, 10 clocks are placed on the wall equidistant from one another, each started at a different time. In a second, much larger room, there are 100 clocks. Finally, in a giant arena, we hang 10,000 identical clocks on the wall. As with Huygen’s two clocks, each clock in the rooms has neighbors on each side, and these clocks influence the middle clock. Furthermore, in the new experiment, there are many distant neighbors with progressively less influence. However, the aggregate effects of more distant clocks must be significant, especially if they become synchronous. Do we expect that synchronous ticking of all clocks will develop in each room? Various things can happen, including traveling waves of synchrony or local buildup of small or large synchronous groups transiently. Only one thing cannot occur: global synchrony.
I know the answer because we did an analogous experiment with Xiao-Jing Wang and his student Caroline Geisler. We built a network of 4,000 inhibitory interneurons.**** When connectivity in the network mimicked local interneuron connections in the hippocampus, all we could see were some transient oscillations involving a small set of neurons. On the other hand, when the connections were random, a situation difficult to create in physical systems, a robust population oscillation emerged. So perfect harmony prevailed in a network with no resemblance to the brain but not with what appeared to be a copy of a local interneuronal network. The problem was the same as with the clocks on the wall: neurons could affect each other primarily locally. To reduce the synaptic path length of the network, we replaced a small subset of neurons with neurons with medium- and long-range connections. Such interneurons with medium- and long-range connections do indeed exist (see Cycle 3). The new, scale-free network ticked perfectly. Its structure shared reasonable similarities with the anatomical wiring of the hippocampus and displayed synchronized oscillations, involving each member equally, irrespective of their physical distance. The reason why our small-world-like artificial network synchronized is because it exploited two key features: few but critical long-range connections that reduced the average synaptic path length of the network and oscillatory coupling, which required very little energy. Analogously, cortical networks may achieve their efficacy by exploiting small-world-like organization at the anatomical level (Cycle 2) and oscillatory synchrony at the functional level. There is synchrony for (almost) free.
* Most of the observations were taken in the small underground Kamra (Chamber) Theater of Budapest. Global and local noise was measured by microphones above the audience and placed next to a spectator, respectively. Rhythmic group clapping emerges between 12 and 25 seconds. Average global noise intensity, integrated over 3-second time windows, indicates decreased energy spending by the audience during the rhythm despite large surges of noise.
** The BOLD signal (see Cycle 4) decreases over large cortical areas during both alpha dominance (Laufs et al., 2003) and thalamocortical spike-and-wave epilepsy (Salek-Haddadi et al., 2002), demonstrating that the metabolic cost of neuronal activity associated with increased neuronal synchrony may, in fact, be less than during nonrhythmic states.
*** For the English translation of Huygen’s original letter about the “sympathy” of clocks, see Pikovsky et al. (2001).
**** In reality, the issue we addressed was quite different from the clocks on the wall because none of the 4,000 interneurons was an oscillator. Instead, their interactions formed one single clock (Buzsáki et al., 2004). Coupling of numerous oscillators have been analyzed mathematically, but these mathematical models lack the physical constraints of axon conduction delays; therefore, they cannot be directly applied to coupling of brain oscillators (Kuramoto, 2984; Mirollo and Strogatz, 1990). For the coupling of two identical oscillators with realistic axon conduction delays, see Traub et al. (1996) and Bibbig et al. (2002).
- 5-MeO-DMT vs. N,N-DMT – Interestingly, 5-MeO-DMT seems to lead to global synchrony (and thus the melting of internal boundaries, the feeling of complete oneness with the universe) whereas N,N-DMT instead seems to give rise to powerful clusters of synchrony which are constantly competing against each other (thus creating partitions in the mind and the sense of “an other”, aka. machine elves). It would be fascinating to figure out why this difference emerges at the level of functional changes to the brain’s network topology as induced by each drug.
- Modeling Psychedelic Tracers with QRI’s Psychophysics Toolkit: The Tracer Replication Tool – makes the case that psychedelic tracers may be a window into the brain’s network topology based on the rhythms they give rise to (which the tool seeks to rigorously quantify).
- Neural Annealing – provides a model of emotional updating involving global synchronization via an annealing process.
- QC Coronavirus Edition: Preventing Pandemics by Living on Toroidal Planets and Other Cocktail Napkin Ideas – here we present the concept of “scale-specific network geometry” as a possible tool to create bottlenecks for the exponential growth of a pandemic in a social network. That said, scale-specific geometry may also be used in populations of neurons in order to prevent specific types of synchronous behavior. This seems like a very fertile area of research.