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

  1. Robson Scheffer-Teixeira
  2. Adriano BL Tort  Is a corresponding author
  1. Federal University of Rio Grande do Norte, Brazil
11 figures

Figures

Figure 1 with 1 supplement
Measuring cross-frequency phase-phase coupling.

(A) Traces show 500 ms of the instantaneous phase time series of two Kuramoto oscillators (see Materials and methods). When uncoupled (top panels), the mean natural frequencies of the ‘theta’ and …

https://doi.org/10.7554/eLife.20515.003
Figure 1—figure supplement 1
Uncoupled oscillators display uniform Δφnm distribution.

(A,B) Panels show the same as in Figure 1B,C, but for the uncoupled oscillators. Notice roughly uniform Δφnm distributions.

https://doi.org/10.7554/eLife.20515.004
Figure 2 with 3 supplements
Detection of spurious n:m phase-locking in white-noise signals due to inappropriate surrogate-based statistical testing.

(A) Example white-noise signal (black) along with its theta- (blue) and gamma- (red) filtered components. The corresponding instantaneous phases are also shown. (B) n:m phase-locking levels for 1- …

https://doi.org/10.7554/eLife.20515.005
Figure 2—figure supplement 1
Filtering induces quasi-linear phase shifts in white-noise signals.

(A) Distribution of the phase difference between two consecutive samples for white noise band-pass filtered at theta (4–12 Hz, top) and slow gamma (30–50 Hz, bottom). Epoch length = 100 s; sampling …

https://doi.org/10.7554/eLife.20515.006
Figure 2—figure supplement 2
Filter bandwidth influences n:m phase-locking levels in white-noise signals.

(A) Mean Rn:m curves computed for 1 s long white-noise signals filtered into different bands (same color labels as in B; n = 2100). Notice that the narrower the filter bandwidth, the higher the Rn:m

https://doi.org/10.7554/eLife.20515.007
Figure 2—figure supplement 3
Uniform p-value distributions upon multiple testing of Original Rn:m values against Single Run Rn:m surrogates.

The histograms show the distribution of p-values (bin width = 0.02) for 10000 t-tests of Original Rn:m vs Single Run surrogate values (n = 30 samples per group; epoch length = 1 s). The red dashed …

https://doi.org/10.7554/eLife.20515.008
True n:m phase-locking leads to significant Rn:m values.

(A) The left panels show mean Rn:m curves and distributions of R1:5 values for original and surrogate (Random Permutation/Single Run) data obtained from the simulation of two coupled Kuramoto …

https://doi.org/10.7554/eLife.20515.009
Figure 4 with 2 supplements
Waveform asymmetry may lead to artifactual n:m phase-locking.

(A) The top traces show a theta sawtooth wave along with its decomposition into a sum of sinusoids at the fundamental (7 Hz) and harmonic (14 Hz, 21 Hz, 28 Hz, 35 Hz, etc) frequencies. The bottom …

https://doi.org/10.7554/eLife.20515.010
Figure 4—figure supplement 1
Waveform asymmetry may lead to spurious phase-amplitude coupling.

(A) A theta sawtooth wave along with its theta- (7 Hz) and gamma-filtered (35 Hz) components. Notice that no gamma oscillations exist in the original sawtooth wave, but they spuriously appear when …

https://doi.org/10.7554/eLife.20515.011
Figure 4—figure supplement 2
The statistical significance of artifactual n:m phase-locking levels induced by waveform asymmetry depends on epoch length and peak frequency variability.

Shown are the median R1:5 computed between theta and slow gamma for sawtooth waves simulated as in Figure 4C, but of different epoch lengths and peak frequency variability. Dashed area corresponds …

https://doi.org/10.7554/eLife.20515.012
Figure 5 with 8 supplements
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 Rn:m values for slow (R1:5; left) and middle gamma (R1:8; right) for …

https://doi.org/10.7554/eLife.20515.013
Figure 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 …

https://doi.org/10.7554/eLife.20515.014
Figure 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 …

https://doi.org/10.7554/eLife.20515.015
Figure 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 Rn:m values. Results obtained for three rats recorded in an independent laboratory (see …

https://doi.org/10.7554/eLife.20515.016
Figure 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 …

https://doi.org/10.7554/eLife.20515.017
Figure 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 …

https://doi.org/10.7554/eLife.20515.018
Figure 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 …

https://doi.org/10.7554/eLife.20515.019
Figure 5—figure supplement 7
The bump in the Rn:m curve of hippocampal LFPs highly depends on analyzing contiguous phase time series data.

Average Rn: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 …

https://doi.org/10.7554/eLife.20515.020
Figure 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 …

https://doi.org/10.7554/eLife.20515.021
Phase-phase plots of hippocampal LFPs display diagonal stripes.

Phase-phase plot for theta and slow gamma (average over animals; n = 7 rats). Notice diagonal stripes suggesting phase-phase coupling.

https://doi.org/10.7554/eLife.20515.022
Figure 7 with 1 supplement
Phase–phase coupling between theta and gamma oscillations may be confounded by theta harmonics.

(A) Top, representative LFP epoch exhibiting prominent theta activity (~7 Hz) during REM sleep. Bottom, power spectral density. The inset shows power in dB scale. (B) Phase–phase plots for theta and …

https://doi.org/10.7554/eLife.20515.023
Figure 7—figure supplement 1
Histogram counts leading to diagonal stripes in phase-phase plots are statistically significant when compared to the distribution of surrogate counts.

Panels show the significance of the phase-phase plots in Figure 7 when compared to the mean and standard deviation of pooled surrogate counts.

https://doi.org/10.7554/eLife.20515.024
Figure 8 with 1 supplement
The number of stripes in phase-phase plots is determined by the frequency of the first theta harmonic within the filtered gamma range.

(A) Representative example in which theta has peak frequency of 7.1 Hz. The phase-phase plot between theta and slow gamma (30–50 Hz) exhibits five stripes, since the fourth theta harmonic (35.5 Hz) …

https://doi.org/10.7554/eLife.20515.025
Figure 8—figure supplement 1
Individual time-shifted surrogate runs exhibit diagonal stripes in phase-phase plots.

(A) The middle panels show phase-phase plots for theta and slow gamma computed for different time shifts of the example epoch analyzed in Figure 8A. Notice diagonal stripes in individual surrogate …

https://doi.org/10.7554/eLife.20515.026
Phase-phase plots of white-noise signals display diagonal stripes.

(A) Representative phase-phase plots computed for white-noise signals. Notice the presence of diagonal stripes for both 100 s (left) and 1200 s (right) epochs. The colormaps underneath show the …

https://doi.org/10.7554/eLife.20515.027
Figure 10 with 2 supplements
Weak but statistically significant n:m phase-locking can be detected when analyzing long LFP epochs (>100 s).

(A) Panels show the same as in Figure 9A but for a representative hippocampal LFP. Notice that several bin counts of the 1200 s epoch remain statistically significant after correction for multiple …

https://doi.org/10.7554/eLife.20515.028
Figure 10—figure supplement 1
Random Permutation leads to less visible diagonal stripes than Time Shift in phase-phase plots of long LFP epochs.

Examples of phase-phase plots computed for single Time Shift (top) and Random Permutation (bottom) surrogate runs of 100 (left) and 1200 s (right) for the same hippocampal LFP as in Figure 10A. …

https://doi.org/10.7554/eLife.20515.029
Figure 10—figure supplement 2
Diagonal stripes in phase-phase plots depend on analyzing contiguous phase time series data.

Phase-phase plots of a white noise (left) and an actual LFP (right) computed using 100 s of total data, but subsampled at 83.3 Hz (we used a subsampling period of 12 ms because the total data length …

https://doi.org/10.7554/eLife.20515.030

Download links