Neuronal oscillations of different frequencies can interact in several ways. There has been particular interest in the modulation of the amplitude of high-frequency oscillations by the phase of low-frequency oscillations, since recent evidence suggests a functional role for this type of cross-frequency coupling (CFC). Phase-amplitude coupling has been reported in continuous electrophysiological signals obtained from the brain at both local and macroscopic levels. In the present work, we present a new measure for assessing phase-amplitude CFC. This measure is defined as an adaptation of the Kullback-Leibler distance-a function that is used to infer the distance between two distributions-and calculates how much an empirical amplitude distribution-like function over phase bins deviates from the uniform distribution. We show that a CFC measure defined this way is well suited for assessing the intensity of phase-amplitude coupling. We also review seven other CFC measures; we show that, by some performance benchmarks, our measure is especially attractive for this task. We also discuss some technical aspects related to the measure, such as the length of the epochs used for these analyses and the utility of surrogate control analyses. Finally, we apply the measure and a related CFC tool to actual hippocampal recordings obtained from freely moving rats and show, for the first time, that the CA3 and CA1 regions present different CFC characteristics.

Phase-amplitude cross-frequency coupling (CFC) between theta (4 -12 Hz) and gamma (30 -100 Hz) oscillations occurs frequently in the hippocampus. However, it still remains unclear whether thetagamma coupling has any functional significance. To address this issue, we studied CFC in local field potential oscillations recorded from the CA3 region of the dorsal hippocampus of rats as they learned to associate items with their spatial context. During the course of learning, the amplitude of the low gamma subband (30 -60 Hz) became more strongly modulated by theta phase in CA3, and higher levels of theta-gamma modulation were maintained throughout overtraining sessions. Furthermore, the strength of theta-gamma coupling was directly correlated with the increase in performance accuracy during learning sessions. These findings suggest a role for hippocampal theta-gamma coupling in memory recall.associative memory ͉ brain rhythms ͉ local field potential B rain oscillations have been classically divided into specific frequency ranges associated with multiple cognitive processes (1, 2). Oscillations in these frequency bands may occur simultaneously and can interact with each other (3, 4), suggesting that this coupling may reflect a higher-order representation (5, 6). In one type of interaction, the phase of low-frequency rhythms modulates the amplitude of higher-frequency oscillations (3). This type of cross-frequency coupling (CFC) is called phase-amplitude modulation, and its best known example occurs in the rodent hippocampus between the theta (4-12 Hz) phase and the amplitude of gamma (30-100 Hz) oscillations (6-9). Based on this finding, theoretical work has suggested that gamma and theta oscillations coordinate in support of a neural code (10-15). According to this view, events are represented by distinct neuronal ensembles, each contained within a distinct gamma cycle, and entire episodes are encoded by a succession of event-specific gamma cycles embedded into each theta cycle (12-15). These theories are elegant and appealing, but there is a paucity of evidence linking the existence of theta-gamma coupling to behavior (but see ref. 16). Therefore, it remains unclear whether the hippocampal theta-gamma coupling possesses any functional role (13).Here, we investigated coupling between theta and gamma rhythms as rats learned which of two stimuli was rewarded depending on the environmental context in which the stimuli were presented. Learning in this type of conditional discrimination task depends on hippocampal function (17, 18). On each trial, a rat initially explored one of two environmental contexts, then the two stimuli were placed into different corners of the environment and the rat was required to choose the correct stimulus for that context to receive a reward (Fig. 1A). In our preliminary studies, we found that the initial context exploration period is essential for learning the context-dependent choice. Therefore, we focused on the prominent theta and gamma activity that is prevalent during this period. We fou...