Phase-amplitude Coupling: An Interaction of Brain Vibes

By Dhruv Mehrotra

Imagine you’re at a party. The DJ is playing music, and the lights are dazzling. The chorus is about to come on, and the beat drops. As soon as it does, the lights start flashing more intensely. And during the more mellow parts of the song, the lights remain on, albeit dimly.

In the scenario above, the beat seems to influence the brightness of the lights. In other words, the beat is coupled to the brightness. A similar process occurs in the brain: the phase of low-frequency brain oscillations coordinates the amplitude of high-frequency oscillations. This phenomenon is known as phase-amplitude coupling (PAC) and is thought to mediate processes such as attention or even remembering your friend’s birthday.

Figure 1: Left: This figure denotes the coordination between the sound wave and the lights, while illustrating the terminology used to understand oscillations. The amplitude of the oscillation is given by the height of the peak. The frequency of the oscillation denotes how many full cycles (peak + trough) occur in 1 second. Finally, the phase of the oscillation denotes the timing during an oscillatory cycle. Right: Two oscillations are said to be “in phase” when the timing of their peaks and troughs is matched, and “out of phase” when it isn’t. In the left figure, when the “beat drops” (i.e. during the peak of the oscillation), the lights are more intense, showing how the phase of the beat is coupled to the amplitude of the lights. Figure adapted from (Tune & Obleser, 2022)

Brain Oscillations

But first, what exactly are these brain oscillations? Oscillations in the brain are thought to arise due to the coordinated electrical activity of large populations of neurons. Brain oscillations have different characteristic frequencies, often reflecting a behavioral state. The frequency of the oscillation depends on the type of neurons involved and the mechanism underlying the coordinated activity. state. For example, delta oscillations (1-4 Hz) are observed when we are in the deep stages of non-REM sleep (Amzica & Steriade, 1998), and alpha oscillations (8-12 Hz) are observed when we close our eyes (Berger, 1929). In humans, these oscillations are typically detected using electroencephalography (EEG).

Interestingly, brain oscillations are largely conserved across species (Buzsáki, Logothetis, & Singer, 2013). This means that a phenomenon like PAC is observed across species as well. Indeed, in addition to humans, PAC has been observed in rats (Bragin et al., 1995), mice, (Buzsáki et al., 2003), monkeys (Lakatos et al., 2005), and even sheep! (Kendrick et al., 2011). However, PAC may play slightly different roles in each species.

Functional Role of Phase-Amplitude Coupling

The most well-described PAC is observed between the theta oscillation (4-8 Hz) and the gamma oscillation (30-150 Hz). In theta-gamma PAC, the phase of theta modulates the amplitude of gamma. Theta oscillations are strongly observed during locomotion or during REM sleep (Vanderwolf, 1969). On the other hand, gamma oscillations are implicated in a variety of phenomena and their exact roles remain a matter of active debate. In the context of theta-gamma PAC, theta phase is  thought to reflect the excitability of the local population, while gamma amplitude is well-correlated with the activation of specific sub-networks of neurons (Canolty & Knight, 2010). In fact, the frequency of hippocampal gamma oscillations differs based on which upstream structure is being engaged (Fernandez-Ruiz et al., 2023). In this manner, theta-gamma PAC could potentially facilitate inter-region communication of different brain networks. 

One of the most researched topics within theta-gamma PAC is its role in memory. This coupling has been  observed in a variety of brain regions during working memory tasks (Axmacher et al., 2010; Canolty et al., 2006). One model hypothesizes that different memory items are repeatedly activated in each gamma cycle. This leads to the separation of distinct items from each other. The span of the working memory is thus given by the number of gamma cycles per theta oscillation (Lisman & Idiart, 1995, also see Figure 2). In fact, researchers were able to slow down theta oscillations using a brain stimulation protocol. By doing so, they found that they were able to improve working memory! (Vosskuhl, Huster, & Herrmann, 2015; Wolinski, Cooper, Sauseng, & Romei, 2018)

Figure 2: Depiction of theta-gamma PAC. The phase of the theta oscillation (blue) modulates the amplitude of the gamma oscillation (red) such that during theta peaks, gamma amplitude is large. In addition, each gamma cycle is thought to represent a distinct memory item, denoted by the alphabets. Repetitive activation of memory items during each theta cycle is thought to underlie working memory. Moreover, the number of memory items per theta cycle is thought to determine the span of working memory. Figure adapted from (Jensen & Colgin, 2007).

PAC has also been shown to be involved in other aspects of cognition such as language (Doesburg, Green, McDonald, & Ward, 2012; Wang, Hagoort, & Jensen, 2018) and attention (Schroeder & Lakatos, 2009). PAC thus has potential value as a neural biomarker for neuropsychiatric conditions. One study showed that PAC was reduced in individuals with ADHD during an arithmetic task (Kim et al., 2016). In another study, PAC has also been shown to have better discriminating ability between individuals with schizophrenia and healthy individuals, compared to other contemporary EEG-based methods. (Won et al., 2018). In addition, PAC can lend itself well to longitudinal research, to unravel the development of mental disorders. For instance, adolescence is a critical period for the development of mental health issues. However, it is also a life stage marked with brain-wide structural changes. Therefore, research focusing on the progression of PAC throughout adolescence and beyond may provide a clearer picture of the progression of mental disorders through this period, and more generally, throughout the lifespan (Sacks, Schwenn, McLoughlin, Lagopoulos, & Hermens, 2021).

Limitations and Challenges

PAC is, no doubt, a phenomenon that is crucial to gaining insight into brain function. An understanding of PAC holds the key to elucidating how different brain regions communicate and work together as a whole. However, in this pursuit, there remain some technical challenges to accurately characterizing PAC.

One major challenge is understanding the role of different types of oscillatory coupling. In addition to PAC, we have other types of coupling between oscillations: 1) Amplitude-amplitude coupling, where, thinking back to our analogy, the volume of the music modulates the brightness of the lights. 2) Phase-phase coupling, where the beat of the music influences the on-off patterns of the lights, and 3) Phase-frequency coupling, where the beat would cause the lights to change their rate of flickering. Given how complex the brain is, these phenomena are not mutually exclusive of each other. This makes it difficult to pinpoint the exact type of coupling and attribute it to a specific function.

The second major challenge is in the detection of PAC itself. PAC detection remains a technical hurdle and is quite sensitive to the selection of frequency ranges over which we detect the oscillatory activity, which can vary across different research labs or studies. PAC also needs an especially “clean” EEG signal (see Aru et al., 2015, for a summary of caveats in current PAC detection methods). Thus, current methods may sometimes result in spurious PAC. Hence, there remains no “gold standard” for PAC detection to date. Better methods to detect PAC are the need of future research efforts in this field. 

In conclusion, PAC has emerged as a key phenomenon to understand information processing in the brain during health and disease. To truly link oscillatory coupling to functional roles and potential clinical applications, we need to improve our current methodologies for studying PAC. This will enhance our understanding of PAC, paving the way for novel discoveries in the field.

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Written by Dhruv Mehrotra

Illustrated by Gopal Khodve

Edited by Paige Nicklas, Johanna Popp, and Chris Gabriel

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