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Research Focus
Cross-frequency coupling between neuronal oscillations Ole Jensen1 and Laura L. Colgin2 1 2
F.C. Donders Centre for Cognitive Neuroimaging, Kapittelweg 29, NL-6525 EN Nijmegen, the Netherlands Centre for the Biology of Memory, Norwegian University of Science & Technology, Trondheim NO-7489, Norway
Electrophysiological recordings in animals, including humans, are modulated by oscillatory activities in several frequency bands. Little is known about how oscillations in various frequency bands interact. Recent findings from the human neocortex show that the power of fast gamma oscillations (30–150 Hz) is modulated by the phase of slower theta oscillations (5–8 Hz). Given that this coupling reflects a specific interplay between large ensembles of neurons, it is likely to have profound implications for neuronal processing.
Introduction Oscillatory brain activity in various frequency bands is modulated by a range of cognitive tasks in humans and animals. These oscillations reflect electrophysiological signals produced by large ensembles of synchronized neuronal firing and are measured in humans and other animals using intracranial electrical recordings, electroencephalography or magnetoencephalography. Oscillations in both the theta (5–8 Hz) and gamma (30–150 Hz) bands are modulated during perception and memory tasks, but little is known about how oscillations in these frequency bands interact. Recently, Canolty et al. [1] conducted a study in which they investigated the relationship between theta and gamma oscillations. They acquired data from five human subjects who had had subdural electrodes implanted intracranially as part of neurosurgical treatment for epilepsy. The authors found that the power (or amplitude) of the fast gamma oscillations was systematically modulated during the course of a theta cycle. In other words, there was a cross-frequency coupling observed as a strong correlation between theta phase and gamma power. This was observed in time-frequency representations of power calculated from traces phase-aligned in the theta band. A full cross-frequency analysis revealed that high frequency power modulations were constrained to the 4–8 Hz theta band. The high frequency coupling was strongest in the 80–150 Hz band. Although gamma band effects above 80 Hz have not been reported in scalp EEG studies, they have been demonstrated in previous intracranial EEG studies. The observed modulations in cross-frequency interactions correlated positively with theta power over sensors. During the recordings, subjects were performing various cognitive tasks, including Corresponding author: Jensen, O. (
[email protected]). Available online 4 June 2007. www.sciencedirect.com
passive listening to tones or phonemes, verb generation and auditory working memory. Importantly, the cross-frequency coupling was modulated by these tasks and was observed in a large fraction of the subdural electrodes; it did not appear to be specific to particular neocortical brain regions. Theta phase-locking to gamma power in various species The findings of Canolty et al. add to an increasing body of evidence demonstrating cross-frequency interactions between theta phase and the power of gamma oscillations. Such interactions have been identified in in vivo recordings in anesthetized [2] and behaving rats [3]. In monkeys, theta phase to gamma power interactions have been reported in the auditory cortex both during spontaneous and stimulus driven activity [4]. Mormann et al. [5] demonstrated a similar coupling in humans implanted with depth electrodes in both the rhinal cortex and the hippocampus. The cross-frequency coupling was modulated by successful versus unsuccessful long-term memory retrieval. In short, although cross-frequency interactions between theta and gamma power so far have been little explored, it is clear that the phenomenon exists in multiple species and brain regions. How are cross-frequency interactions produced? From a theoretical point of view, there are several ways in which cross-frequency interactions might occur (Figure 1). The phase-to-power interaction reported by Canolty et al. is, in particular, sensible from a physiological perspective. Consider a network producing spontaneous gamma oscillations in which the excitability of the neurons is modulated by a theta rhythm that either is imposed by another network or emerges from the intrinsic network dynamics. Given that the excitability of the cells in the network is modulated by the phase of the slow oscillations, the resulting dynamics will produce fluctuations in the gamma oscillations that are phase locked to the theta oscillations. Consistent with this idea, a network model has recently been described in which concurrent theta and gamma oscillations are produced by slow and fast GABAergic feedback, respectively [6]. What is the computational role of theta–gamma interaction? Several theories have been proposed regarding the computational role of the interplay between oscillations
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Figure 1. Different principles of cross-frequency interactions. (a) Consider a slow oscillatory signal in the theta band (e.g. 8 Hz): although the frequency remains fairly constant, the power (amplitude; red line) of the signal fluctuates over time. The different ways in which gamma oscillations can interact with such a signal are: (b) the fluctuations in power of the faster gamma oscillations are correlated with power changes in the lower frequency band (e.g. Ref. [15]). This interaction is independent of the phases of the signals; (c) n:m phase-locking occurs between oscillations at different frequencies. In each slow cycle, there are four faster cycles and their phase relationship remains fixed. Thus, the phases of the 8 Hz and the 48 = 32 Hz oscillations are locked. Such interactions have been explored using bispectra [16] and wavelet techniques [17]; (d) the frequency of the fast oscillations is modulated by the phase of the slower oscillations; and (e) the power of the gamma oscillations is modulated by the phase of the theta oscillations [1–5].The different types of cross-frequency interaction are not mutually exclusive. For instance, the phase of theta oscillations might modulate both frequency and power of the gamma oscillations.
in various frequency bands. For instance, it has been suggested that slow oscillations serve to synchronize networks over long distances. Because of conduction delays, low frequency oscillations, such as the theta rhythm, are particularly suited for this purpose [7,8]. Fast oscillations, such as the gamma rhythm, are thought to synchronize cell assemblies over relatively short spatial scales. Spatial integration from a local to a global scale requires longer integration times and, thus, a slower ‘clock’. Gamma oscillations might emerge at a particular phase of the theta cycle and thereby recruit assemblies of cells involved in processing at that time. Theta could then serve to integrate
several functional networks, each associated with a particular gamma episode, across longer periods of time. Another theoretical framework for cross-frequency interactions builds on the notion of phase coding, namely that different information is encoded at different phases of the theta cycle [9]. By this scheme, the gamma oscillations divide the theta cycle into ‘time slots’, which segment several active representations in time. A theory based on this principle was proposed by Lisman and Idiart [10], who suggested a physiologically inspired model in which 7 2 memory items are represented in separate gamma cycles within one theta cycle (Figure 2a). The set of items are
Figure 2. Models proposing computational roles for cross-frequency interactions between theta and gamma oscillations by means of phase coding. (a) In a model for working memory, individual memory representations are activated repeatedly in every theta cycle [10] (reviewed in Ref. [11]). Each memory representation is represented by a subset of neurons in the network firing synchronously. Because different representations are activated in different gamma cycles, the gamma rhythm serves to keep the individual memories segmented in time. The number of gamma cycles per theta cycle determines the span of the working memory. (b) A model accounting for theta phase precession in rats. As a rat advances through an environment, positional information is passed to the hippocampus. This activates the respective place cell representations, which provokes the prospective recall of upcoming positions. In each theta cycle, time-compressed sequences are recalled: one representation per gamma cycle. Consider the firing of a cell participating in representation E. As the rat advances, this cell fires earlier in the theta cycle, thus accounting for phase precession. According to this scheme, the number of gamma cycles per theta cycle is related quantitatively to the phase precession [13]. www.sciencedirect.com
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reactivated in each theta cycle at a rate of one item per gamma cycle. The number of gamma cycles per theta cycle was hypothesized to determine the span of the working memory. Furthermore, the rate of item retrieval, as measured in the Sternberg paradigm, is consistent with the period of a gamma cycle. This model has received some experimental support given that theta and gamma activity have both been reported to be modulated in working memory tasks (reviewed in Ref. [11]). The findings of Canolty et al., demonstrating cross-frequency interaction between theta and gamma oscillations during working memory operations, are in line with the predictions of the model of Lisman and Idiart [10]. Coupling between theta and gamma oscillations has also been proposed to account for the phenomenon of theta phase-precession observed in the rat hippocampus. Hippocampal ’place cells’ are activated when a rat moves through a specific location, known as the ‘place field’ of that cell. When the firing of place cells is compared with the phase of the ongoing theta rhythm, a specific relationship emerges. As a rat enters a place field, the corresponding place cell fires late in the theta cycle. As the rat moves through the place field, the place cell fires at progressively earlier phases of the theta cycles [12]. This finding is consistent with the notion of phase coding. One model accounting for phase precession predicts that time-compressed sequences of space representations repeatedly are read out in each theta cycle [13] (Figure 2b). A crucial element of the model is that phase precession advances one gamma cycle per theta cycle. This suggests that the number of gamma cycles per theta cycle corresponds to the number of theta cycles that a given place cell is active. Indeed a place field is active for 5–10 theta cycles [14], consistent with a gamma frequency of 40–80 Hz. This relationship between phase precession and hippocampal gamma activity has not yet been demonstrated experimentally. Further research exploring cross-frequency interactions between theta and gamma oscillations will facilitate empirical testing of such a model. Conclusion The experimental findings thus far on cross-frequency interactions raise many interesting questions. During which tasks and in which brain areas do such interactions occur? What is the computational purpose of theta–gamma coupling? It might facilitate the transient coordination of local networks on short time scales and integrate multiple networks in disparate locations across longer time scales. Gamma activity might divide theta cycles into discrete temporal segments supporting phase coding. Whatever
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the case might be, further investigations of theta–gamma cross frequency interactions are needed to find the answers. Acknowledgements This work was supported by the Volkswagen Foundation Grant I/79876 and Netherlands Organization for Scientific Research Innovative Research Incentive Schemes 864.03.007.
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