PMC

A) Slow gamma amplitude as a function of theta phase for one example dataset () was averaged across all the theta cycles at low (dashed) and high (solid) speeds. Further, unlike , the amplitude of gamma at each phase of theta was divided by the sum of gamma amplitudes across all phases of theta at that speed. This enabled a comparison of the depth of modulation of gamma amplitude with running speed and theta phase, independent of changes in gamma amplitude with running speed. The theta phase modulation of gamma amplitude was 158% greater and the preferred phase of theta was 63° lower at high speeds compared to low speeds B) Same data as A, but as a function of (the logarithm of) a range of running speeds. The hippocampal velo-temporal receptive field for speed (VTRF) for this example dataset shows a progressive precession of slow gamma preferred phase of theta with speed (white dotted line). C) VTRF averaged across all the data show a robust increase in the depth of modulation as well as precession (white dotted line) of slow gamma preferred phase of theta with increasing running speed. D) Same as in A, but for fast gamma showing only a small change in the depth of modulation of fast gamma amplitude (75%) and preferred theta phase (10.7°) with speed. E) Same as B showing only small changes in fast gamma VTRF with speed. F) Same as C showing minimal changes in the ensemble averaged fast gamma VTRF with speed.

A) Averaged across the ensemble of data, slow and fast gamma preferred theta phases were nearly coincident (−6.0±1.2°) at low speeds, but the slow gamma preferred phase precessed by 61±2.7° with increasing speed whereas fast gamma preferred phase precessed by only 16±1.8°. B) The slope of slow (fast) gamma preferred phase as a function of running speed is shown in red (blue). Maximal speed in each session was normalized to unity to allow comparison across data. The vast majority (95%) of slow gamma LFP showed speed-dependent phase advancement, but only 67% of fast gamma LFP showed phase advancement. C) There was only a small difference in the preferred phases of slow and fast gamma at low speeds (dashed line, −6.0±1.2°, p = 5.0e-7), but the two rhythms were separated by 37±2.1° (p = 1.3e-25) at high speeds (solid line). D) Multi-unit spike probability as a function of fast (blue) and slow (red) gamma phase was computed separately for 141 data sets and averaged across the entire ensemble (see ). E) Scatter plot of fast gamma phase vs. slow gamma modulation index of spiking for 141 data sets. Spike probability was more strongly modulated by the phase of slow gamma than fast gamma (p = 1.9e-14) F) Scatter plot of the preferred fast (81±5.7 degrees) and slow gamma phases (242±5.6 degrees) of spikes.

A) Power spectrum of a dorsal hippocampal LFP during locomotion (red) and immobility (black) in one example session. Shaded areas indicate 95% confidence intervals. B) Change in spectral power during run compared to stop as a function of frequency in the gamma band. Data are averaged across the ensemble of 214 LFP traces. Shaded regions correspond to s.e.m. here and in subsequent figures. Inset shows the change in power for the example data set from fig. 1a. The increase in power is significantly lower at 45 Hz than in the surrounding frequency band, thereby demarcating a clear border between slow (20–45 Hz) and fast (45–120 Hz) gamma bands. C) Running speed of a mouse as a function of time (black), and corresponding amplitude of slow (red) and fast (blue) gamma rhythms. Insets show slow and fast gamma amplitudes at higher temporal resolution for high (<1>) and low (<2>) speeds. Both fast and slow gamma amplitudes are larger during run than stop. D) Slow (red) and fast (blue) gamma amplitudes were 15±1.5% (p = 5.3e-24) (mean±s.e.m., Wilcoxon Ranksum test here and in subsequent figures), and 31±1.0% (p = 1.2e-65) larger during run than stop, with fast gamma amplitude showing a greater increase than slow gamma (p = 1.5e-13).

A) Each red dot depicts the amplitude of slow gamma in a window of 250 ms around each LFP theta peak as a function of running speed. The value of the slow gamma amplitude was averaged within a given speed bin (∼7 cm/s wide, with 80% overlap between neighboring bins) (red squares). Black line shows the best linear fit. B) Same as A for fast gamma (blue dots and squares) with logarithmic fit. (See for methods and , for details). C) Ensemble averaged data showing linear increases in slow gamma amplitude with speed. D) Same as C with logarithmic speed-dependence for fast gamma. E) Each vertical panel shows the cross-frequency coupling between the amplitude of a fast (15–300 Hz) signal (y-axis) and the phase of a slow (2–20 Hz) signal, whose frequency is shown on the x-axis). Separate panels show coupling at different running speeds (top) for the example data in figures 2A,B. Colorbar to the right indicates modulation index (see ). Significant cross-frequency coupling is found only between the phase of the theta (6–12 Hz) oscillation and the gamma amplitude (20–120 Hz). Fast-gamma-theta coupling is greater than slow-gamma-theta coupling (bottom panel) at all speeds. The coupling increases logarithmically and linearly with speed for fast and slow gamma respectively (see ). F) Slow gamma amplitude changes with running speed and theta phase for the example data set in figure 2A,B. G) Similarly for fast gamma. H) Slow gamma amplitude at the preferred phase (at 236±2.2°) of theta, averaged across all data, is linearly correlated with running speed (solid line, R² = 0.90±0.018, median±s.e.m.), but slow gamma amplitude around the theta trough changed minimally (dotted line). I) Similarly, fast gamma amplitude around the peak (260±1.8°) of theta increased logarithmically with speed (solid line, R² = 0.94±0.016), but fast gamma amplitude around the theta trough changed minimally (dotted line). J) Distribution of the slope of slow gamma amplitude around the theta peak as a function of running speed (solid line) across the ensemble of data, showing that it was significantly positive (0.017±0.0012, p = 1.9e-40) and far greater than the slope around the theta-trough (dotted line, 0.00067±0.00032, p = 4.3e-4). K) Similar results were true for the slope of fast gamma amplitude as a function of the logarithm of running speed around the theta peak (solid line, 0.17±0.0057, p = 4.1e-68) and the theta trough (0.013±0.0040, p = 0.0054).