Extended Data Fig. 3: Theta-high gamma PAC control analyses in the hippocampus.

(a) Higher memory loads are thought to be accompanied by a wider distribution of gamma amplitudes across theta phases, thereby leading to lower PAC values⁸². To quantify the width of the distribution of gamma amplitude as a function of theta phase in load 3 than load 1, we estimated kappa. Kappa is a measure that describes the concentration (inverse of variance) of a circular variable around the mean direction. Across all PAC channels, kappa was significantly lower in load 3 compared to load 1 (n = 137 channels, t(136) = −3.7453, p = 0.0001) trials. This shows that gamma amplitudes are high for a wider range of theta phases for higher memory loads, thereby explaining why PAC decreases for higher memory loads. (b) Comparison of theta and gamma power. The significant hippocampal PAC channels showed no significant differences in theta or gamma power between the two load conditions (n = 137). (c) To determine the influence of theta waveform shape on PAC, we tested for differences in theta waveform peak-to-trough as well as rise-to-decay asymmetries between the two load conditions (see Methods). We did not find systematic differences between the conditions for both measures (n = 137). Moreover, average theta waveforms were overall symmetric as both measures were not significantly different from .5 in any of the conditions. (d) Moreover, if the differences between the load conditions observed for PAC channels in the hippocampus were explained by waveform shape differences/theta harmonics, we should also observe an effect for cross-frequency phase-phase coupling between the same frequency bands. We tested for that in all significant hippocampal PAC channels and did not observe a significant difference (n = 137). Theta-high gamma phase-phase coupling was computed as described in^73,83. (e) We determined the number of significant PAC channels that showed theta-high gamma nesting as described by Vaz et al.⁶⁹ The left upper and lower panels show two examples of significant PAC channels from the hippocampus that were determined to have nesting by the Vaz et al. method (at least three local maxima within a window of 45 ms around the preferred phase (see Methods)). 110 of the 137 significant PAC channels (80.29%) in the hippocampus showed nesting between high gamma and theta. When testing PAC between the load conditions after removing channels that did not show significant nesting, PAC was still significantly lower in load 3 than 1 (n = 110; t(109) = −4.10; p = 0.0001). (f) Comparison of theta-gamma PAC strength in the hippocampus assessed using the raw modulation index rather than the of z-transformed MI. Raw theta-gamma PAC was significantly larger in load 1 compared to load 3 (n = 137; t(136) = −4.0264, p = 0.0001). (g) Distribution of theta phases at which gamma amplitude was maximal across all significant PAC channels in the hippocampus in load 1 and 3 (upper part). In most channels, gamma amplitude was maximal at the peak or the trough of theta. Note that the local referencing scheme in our data does not allow do make statements about the polarity of theta. Red bars indicate the mean vector length across all phases. The difference in theta phase at which gamma amplitude was maximal between the two load conditions was not significantly different from zero (bottom part). (h) We further assessed whether PAC peak frequencies differed between the load conditions either within the theta or the gamma band. To do so, we recomputed PAC using a finer resolution for phase frequencies (i.e., a step size of 0.5 instead of 2 Hz) and determined the frequency bin for which PAC was maximal for the theta and the gamma band separately for all channels and both loads. We did not find significant systematic shifts in PAC peak frequencies between the load conditions in theta or gamma frequencies (n = 137). In (a-f,h), we performed two-sided permutation based-t-tests and centre values denote mean ± s.e.m. *** p < 0.001, ns = not significant.