# Figure 5. | On cross-frequency phase-phase coupling between theta and gamma oscillations in the hippocampus

# On cross-frequency phase-phase coupling between theta and gamma oscillations in the hippocampus

- Robson Scheffer-Teixeira
- Adriano BL Tort

Federal University of Rio Grande do Norte, Brazil

Download figureOpen in new tabFigure 5. Spurious detection of theta-gamma phase-phase coupling in the hippocampus.(**A**) n:m phase-locking levels for actual hippocampal LFPs. Compare with Figure 2B. (**B**) Original and surrogate distributions of R_{n:m} values for slow (R_{1:5}; left) and middle gamma (R_{1:8}; right) for different epoch lengths. The original data is significantly higher than the pooled surrogate distribution, but indistinguishable from the distribution of surrogate values computed using single runs. Similar results hold for fast gamma. *p<0.01, n = 7 animals, Friedman’s test with Nemenyi post-hoc test.

**DOI:** http://dx.doi.org/10.7554/eLife.20515.013

Download figureOpen in new tabFigure 5—figure supplement 1. Lack of evidence for cross-frequency phase-phase coupling between theta and gamma oscillations using alternative phase-locking metrics.(**A**) The left plots show the mean radial distance (R) computed for gamma phases in different theta phase bins, as described in Sauseng et al. (2009). The lines denote the mean ± SD over all channels across animals (n = 16 channels per rat x seven rats); 300 1 s long epochs were analyzed for each channel. Note that original and surrogate R values overlap. The variations of R values within a theta cycle are explained by the different number of theta phase bins (right bar plot), which leads to different number of analyzed samples; the higher the number of analyzed samples, the lower the R (see also Figure 2C). (**B**) The first column shows the mean pairwise phase consistency (PPC) between gamma and accelerated theta phases as a function of the number of $\mathrm{\Delta}{\phi}_{nm}$ samples (dashed lines denote SD over individual PPC estimates; n = 112 channels x 1000 PPC estimates per channel). Since PPC requires independent observations (Vinck et al., 2010), $\mathrm{\Delta}{\phi}_{nm}$ was randomly sampled to avoid the statistical dependence among neighboring data points imposed by the filter (Figure 2—figure supplement 1; see also Figure 5—figure supplement 7). The second column shows mean PPC as function of n:m ratio (individual PPC estimates were computed using 1000 $\mathrm{\Delta}{\phi}_{nm}$ samples); the boxplot distributions show PPC values at selected n:m ratios, as labeled. PPC values are very low for all analyzed frequency pairs and not statistically different from zero.

**DOI:** http://dx.doi.org/10.7554/eLife.20515.014

Download figureOpen in new tabFigure 5—figure supplement 2. Spurious detection of theta-gamma phase-phase coupling when theta phase is estimated by interpolation.(**A**) n:m phase-locking levels for actual hippocampal LFPs (same dataset as in Figure 5). Theta phase was estimated by the interpolation method described in Belluscio et al. (2012). (**B**) Original and surrogate distributions of R_{n:m} values. The original data are significantly higher than surrogate values obtained from pooled $\mathrm{\Delta}{\phi}_{nm}$, but indistinguishable from single run surrogates. *p<0.01, n = 7 animals, Friedman’s test with Nemenyi post-hoc test.

**DOI:** http://dx.doi.org/10.7554/eLife.20515.015

Download figureOpen in new tabFigure 5—figure supplement 3. Spurious detection of theta-gamma phase-phase coupling (second dataset).(**A**) n:m phase-locking levels for actual hippocampal LFPs. (**B**) Original and surrogate distributions of R_{n:m} values. Results obtained for three rats recorded in an independent laboratory (see Materials and methods).

**DOI:** http://dx.doi.org/10.7554/eLife.20515.016

Download figureOpen in new tabFigure 5—figure supplement 4. Lack of evidence for theta-gamma phase-phase coupling in all hippocampal layers.(Left) Example estimation of the anatomical location of a 16-channel silicon probe by the characteristic depth profile of sharp-wave ripples (inter-electrode distance = 100 μm). (Middle) Original and surrogate (*Random Permutation/Single Run*) distributions of R_{n:m} values computed between theta phase and the phase of three gamma sub-bands (1 s long epochs). Different rows show results for different layers. (Right) Distribution of original and surrogate R_{n:m} values computed for current-source density (CSD) signals (1 s long epochs) in three hippocampal layers: *s. pyramidale* (top)*, s. radiatum* (middle), and *s. lacunosum-moleculare* (bottom). Notice no difference between original and surrogate values. Similar results were found in all animals.

**DOI:** http://dx.doi.org/10.7554/eLife.20515.017

Download figureOpen in new tabFigure 5—figure supplement 5. Lack of theta-gamma phase-phase coupling in independent components of gamma activity.(Left) Average phase-amplitude comodulograms for three independent components (IC) that maximize coupling between theta phase and the amplitude of slow gamma (top row), middle gamma (middle row) and fast gamma (bottom row) oscillations (n = 4 animals). Each IC is a weighted sum of LFPs recorded in different hippocampal layers (see Schomburg et al., 2014). (Middle) n:m phase-locking levels for theta phase and the phase of ICs filtered at the gamma band maximally coupled to theta in the phase-amplitude comodulogram. (Right) Original and surrogate distributions of R_{n:m} values. R_{n:m} values were computed for 1 s long epochs (n = 4 animals); surrogate gamma phases were obtained by *Random Permutation/Single Run*.

**DOI:** http://dx.doi.org/10.7554/eLife.20515.018

Download figureOpen in new tabFigure 5—figure supplement 6. Lack of theta-gamma phase-phase coupling during transient gamma bursts.(**A**) Examples of slow-gamma bursts. Top panels show raw LFPs, along with theta- (thick blue line) and slow gamma-filtered (thin red line) signals. The amplitude envelope of slow gamma is also shown (thick red line). The bottom rows show gamma and accelerated theta phases (m = 5), along with their instantaneous phase difference ($\mathrm{\Delta}{\phi}_{1:5}$). For each gamma sub-band, a ‘gamma burst’ was defined to occur when the gamma amplitude envelope was 2SD above the mean. In these examples, periods identified as slow-gamma bursts are marked with yellow in the amplitude envelope and phase difference time series. Notice variable $\ufffd{\phi}_{1:5}$ across different burst events. (**B**) The left panel shows n:m phase-locking levels for theta phase and the phase of different gamma sub-bands (1 s epochs); for each gamma sub-band, R_{n:m} values were computed using only theta and gamma phases during periods of gamma bursts. The right panels show original and surrogate (*Random Permutation/Single Run*) distributions of R_{n:m} values (n = 4 animals).

**DOI:** http://dx.doi.org/10.7554/eLife.20515.019

Download figureOpen in new tabFigure 5—figure supplement 7. The bump in the R_{n:m} curve of hippocampal LFPs highly depends on analyzing contiguous phase time series data.Average R_{n:m} curves computed for theta- and gamma-filtered hippocampal LFPs. The green curves were obtained using 1 s (top) or 10 s (bottom) continuous epochs of the phase time series, sampled at 1000 Hz (same analysis as in Figure 5A). The blue curves were obtained by analyzing 1000 data points subsampled from the phase time series at 20 Hz (i.e., 50 ms sampling period, longer than a gamma cycle). The red curves were obtained by analyzing 1000 (top) or 10000 (bottom) data points randomly sampled from the phase time series. These plots show that the prominent bump in the R_{n:m} curve of actual LFPs only occurs for continuously sampled data (1000 Hz sampling rate), and therefore probably reflects the ‘sinusoidality’ imposed by the filter (see also Figure 2—figure supplement 1). But notice that a small R_{n:m} bump remains for θ−γ_{S} (see Figure 10—figure supplement 2). Due to limitation of total epoch length, we could not perform the 20 Hz subsampling analysis for 10000 points, but notice that the blue and red curves coincide for 1000 points.

**DOI:** http://dx.doi.org/10.7554/eLife.20515.020

Download figureOpen in new tabFigure 5—figure supplement 8. Different filter types give rise to similar results.(**A**) Original (green) and surrogate (red) n:m phase-locking levels for actual hippocampal LFPs (same dataset as in Figure 5) filtered at theta and slow gamma (1 s epochs). Different rows show results for different types of filters. FIR corresponds to the same finite impulse response filter employed in all other figures. For the infinite impulse response filters (Butterworth and Bessel), the digit on the right denotes the filter order. Wavelet filtering was achieved by convolution with a complex Morlet wavelet with a center frequency of 7 Hz. (**B**) Original and surrogate distributions of R_{1:5} values. For each filter type, the original data is significantly higher than surrogate values obtained from pooled $\mathrm{\Delta}{\phi}_{nm}$, but indistinguishable from single run surrogates. *p<0.01, n = 7 animals, Friedman’s test with Nemenyi post-hoc test.

**DOI:** http://dx.doi.org/10.7554/eLife.20515.021