# Figure 2. | 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 2. 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- (left) and 10 s (right) epochs, computed for noise filtered at theta (θ; 4–12 Hz) and at three gamma bands: slow gamma (γ_{S}; 30–50 Hz), middle gamma (γ_{M}; 50–90 Hz) and fast gamma (γ_{F}; 90–150 Hz). Notice R_{n:m} peaks in each case. (**C**) Boxplot distributions of θ−γ_{S} R_{1:5} values for different epoch lengths (n = 2100 simulations per epoch length). The inset shows representative $\mathrm{\Delta}{\phi}_{nm}$ distributions for 0.3- and 100 s epochs. (**D**) Overview of surrogate techniques. See text for details. (**E**) Top panels show representative $\mathrm{\Delta}{\phi}_{nm}$ distributions for single surrogate runs (*Time Shift*; 10 runs of 1 s epochs), along with the corresponding R_{n:m} values. The bottom panel shows the pooled $\mathrm{\Delta}{\phi}_{nm}$ distribution; the R_{n:m} of the pooled distribution is lower than the R_{n:m} of single runs (compare with values for 1- and 10 s epochs in panel **C**). (**F**) Top, n:m phase-locking levels computed for 1- (left) or 10 s (right) epochs using either the *Original* or five surrogate methods (insets are a zoomed view of R_{n:m} peaks). Bottom, R_{1:5} values for white noise filtered at θ and γ_{S}. Original R_{n:m} values are not different from R_{n:m} values obtained from single surrogate runs of *Random Permutation* and *Time Shift* procedures. Less conservative surrogate techniques provide lower R_{n:m} values and lead to the spurious detection of θ−γ_{S} phase-phase coupling in white noise. *p<0.01, n = 2100 per distribution, one-way ANOVA with Bonferroni post-hoc test.

**DOI:** http://dx.doi.org/10.7554/eLife.20515.005

Download figureOpen in new tabFigure 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 rate = 1000 Hz (dt = 0.001 s). Notice that the top histogram peaks at ~0.05, which corresponds to 2*3.14*8*0.001 (i.e., 2*π*f_{c}*dt, where f_{c} is the center frequency), and the bottom histogram peaks at ~0.25 =2*3.14*40*0.001. (**B**) R_{n:m} curves computed for theta- and slow gamma-filtered white-noise signals. The black curve was obtained using continuous 1 s long time series sampled at 1000 Hz. The red curve was obtained by also analyzing 1000 data points, but which were subsampled at 20 Hz (subsampling was performed after filtering). Notice R_{n:m} peak at n:m = 1:5 only for the former case. See also Figure 5—figure supplement 7 for similar results in hippocampal LFPs.

**DOI:** http://dx.doi.org/10.7554/eLife.20515.006

Download figureOpen in new tabFigure 2—figure supplement 2. Filter bandwidth influences n:m phase-locking levels in white-noise signals.(**A**) Mean R_{n: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 R_{n:m} peak. (**B**) Mean R_{n:m} peak values for different filter bandwidths and epoch lengths (n = 2100 simulations per filter setting and epoch length).

**DOI:** http://dx.doi.org/10.7554/eLife.20515.007

Download figureOpen in new tabFigure 2—figure supplement 3. Uniform p-value distributions upon multiple testing of *Original* R_{n:m} values against *Single Run* R_{n:m} surrogates.The histograms show the distribution of p-values (bin width = 0.02) for 10000 t-tests of *Original* R_{n:m} vs *Single Run* surrogate values (n = 30 samples per group; epoch length = 1 s). The red dashed line marks p=0.05. The p-value distributions do not statistically differ from the uniform distribution (Kolmogorov-Smirnov test).

**DOI:** http://dx.doi.org/10.7554/eLife.20515.008