(A) Distribution of the strength of phase precession of principal neurons in different regions/layers (Correlation between phase and position, see Supplemental Data). Only firing fields with high spatial coherence (>0.7; Hafting et al., 2008) in the linear track are included (indicated as % fields, n; total number of place fields). (B) Differences between oscillation frequencies of neuron firing and LFP theta, determined by computing the cross-correlogram of the spectra of the respective neuron and LFP (Geisler et al., 2007). Each color-coded row represents a single principal neuron, sorted by the magnitude of frequency shift (black dots) determined by the peak of cross-correlograms. Cross-correlograms were normalized by their peaks. Peak at 0 Hz indicates lack of phase precession. Only neurons with significant theta power in the linear track task are shown (expressed as % neurons, n; total number of neurons). For other behaviors, see Figures S16 and S18.

(A) Temporal relationship of principal neurons across different regions. Time zero, spike time of the reference neuron. Grey histograms: group cross-correlograms of principal neuron pairs. Counts in cross-correlograms of all the pairs in each category were summed up. Orange lines above cross-correlograms show significant peak bins (p < 0.001) for group cross-correlograms. Blue line: smoothed group cross-correlograms. Y scale (left), spike counts of the referred neuron. Black histograms: distribution of temporal offsets (cross-correlogram peaks of significantly correlated neuron pairs, see Supplemental Methods). Y scale (right), number of neuron pairs. Ninety-five % confidence intervals (yellow broken lines) are applied to smoothed distributions of temporal offsets (red lines, see Supplemental Methods). Arrows, time offsets between reference spike and peak activity of anatomically connected target neurons. (B) Same as A but referred cells are putative interneurons. Time bin; 1 msec for group cross-correlograms. 5msec for the distribution of temporal offsets.

(A) Theta phase related firing pattern of an EC2 neuron as a function of position on a linear track. Note the precession of spike phase between 5 and 40 cm on the leftward journey. Horizontal arrows above rate histograms represent the direction of travel. Spike phase autocorrelogram illustrates faster oscillatory activity of spikes relative to LFP theta (arrowheads, lines: multiples of 360°). Arrow on the phase spectrum (right; see Supplemental data; Figure S17), obtained from leftward journeys, indicates an oscillation frequency of unit firing faster than that of the theta LFP (black line). (B–D) Three further examples of phase precessing EC2 neurons and (E) a theta phase-locked EC2 neuron. (F) EC3 cell with no consistent phase-position relationship and (G) phase precessing EC5 cell. (H, I, J) Example CA1, CA3 pyramidal neurons and granule cell. (A–C) and (D–F) are from the same session. Reference theta is from EC3 for all neurons. Power spectra in the rightmost column were normalized by their peaks.

(A) Autocorrelograms and average filtered (0.8–5kHz) waveforms of a putative EC2 principal cell (light blue) and an EC3 interneuron (magenta). Right, Cross-correlogram revealed short-latency monosynaptic interactions between the neuron pair. Neuron 1 excites neuron 2 (these neurons were recorded from two different electrodes). Dashed lines indicate 1% and 99% global confidence intervals estimated by spike jittering on a uniform interval of [−5,5] msec (Fujisawa et al., 2008). (B) Same display as in A but for an EC3 interneuron-principal cell pair (also recorded from two different electrodes). Note short-latency suppression of spikes in the target neuron. (C) Putative principal cells and interneurons (empty symbols; orange, 1490 principal cells, violet, 327 interneurons) separated by waveform asymmetry and trough-to-peak latency (see inset; 0.8–5 kHz; Sirota et al., 2008) and other criteria (see Supplemental Methods). Filled orange and violet symbols correspond to excitatory (557 cells) and inhibitory (263 cells) neurons, respectively identified by monosynaptic interactions (as in A and B; see also Figure S3). Total of 2744 EC neurons. (D) Interspike intervals (mean ± SEM) of EC principal cells and interneurons. Bin size = 1msec.

(A). Top row, polar plots of group mean of preferred phase and mean resultant length as a function of instantaneous firing rate (color coded). Instantaneous rate was quantified for each spike in ten increments (1, 2,… or≥10 spikes per 250 msec (two theta cycles), corresponding to 4, 8, 12,…, ≥ 40 Hz; Harris et al., 2002). Second and third rows show preferred phase and mean resultant length for each significantly modulated principal neuron at 4 and ≥ 40 Hz. Fourth row, same but for bursting spikes (interspike interval < 6msec). Each circle is a single neuron. Black lines, group mean. Note the large and progressive shifts of preferred phase in EC2 and CA1 cells with rate increase. In each firing rate category, only neurons with significant theta modulation (at least 50 spikes in a given category and Rayleigh test, p<0.01) are shown. (B) Firing probability of principal neurons from different layers as a function of theta phase (as in Figure 3A and 3E), at different instantaneous frequencies (4 Hz, ≥40 Hz, bursting spikes, ISI<6msec). In each category, all neurons are included regardless of the significance of theta modulation. Note the large shift of active phase of EC2 and CA1 neurons between 4 Hz and ≥40 Hz of activity. Arrows in the bottom row indicate double peaks of bursting activity (ISI<6msec) in EC2 and CA1.

(A) Population discharge probability of principal neurons from different subregions as a function of EC3 theta phase (top dotted magenta traces in A and B, idealized reference theta cycle in EC3). Spikes from all principal neurons were included, independent of whether or not the neuron was significantly modulated by theta phase. Two theta cycles are shown to facilitate visual comparison. DG, dentate gyrus cells. Bin size = 10°. Note the deviation of most histograms from an idealized sinusoidal pattern. (B) Distribution of preferred phase of single neurons. Note that the majority of EC3 neurons occupy a phase space (ascending phase of EC3 theta), in which the discharge probability of all other neurons groups is at minimum (shaded columns in A, B, E and F). Bin size = 20°. (C) Polar plots of preferred phase and modulation depth (mean resultant length) of single neurons (circles) and group mean (lines). Only neurons with significant theta modulation (with at least 50 spikes and firing rate > 0.1 Hz; Rayleigh test, p<0.01) are included in (B) and (C). Note the largest mean resultant length in EC2 and in a small subset of EC3 principal cells with a phase preference opposite to the majority of the EC3 population. (D) Magnitude of modulation depth by the theta cycle (mean resultant rength ± standard deviation; only significantly theta-modulated neurons are included) and the percentage of neurons significantly modulated by the theta cycle. **; p < 0.05, *; p < 10⁻⁴, red *; p < 10⁻¹¹, Wilcoxon rank sum test (mean resultant length) and chi-square independence test (proportion of significantly modulated cells). (E to H) Same display for interneurons.

(A) Top. Nissl-stained EC sagittal section with reconstructed tracks of the 4-shank silicon probe (200 μm inter-shank distance). Bottom. The same section with DiI fluorescence labeling. Recording locations in each session were estimated from the magnitude of probe movement by the experimenter and from physiological parameters, shown in B and C. Brown; EC1, light blue; EC2, magenta; EC3, gray; EC5 recording sites. Scale bar = 1mm. AB, angular bundle. (B) Left 2 top traces (red); mean ripple power from the CA1 pyramidal cell layer (normalized by standard deviation) and averaged ripple trace at a higher temporal resolution. Left bottom 4 traces, CA1 ripple power-centered average traces (n=1656–2590) of EC sharp waves across different layers. Traces from 3 different sessions in progressively deeper sites (corresponding to circles in A) are superimposed. Note the polarity reversal of EC sharp waves between EC2 and lower layers. Right, averaged theta waves, centered on the peak of the CA1 pyramidal layer theta from the same sessions. (C) As in B but with the tip of the rightmost shank in EC1 (last recording session). Note the phase-reversed theta signals between EC1 and lower layers. (D) Polar plots of principal neurons in CA1 and different layers of EC (EC2, EC3 and EC5) referenced to theta oscillation in CA1 pyramidal layer. Each circle represents preferred phase (peak of theta = 0,360°, trough = 180°in all figures) and modulation depth (mean resultant length or R̄, 0–1, represented by the distance from the center of the plot) of a single neuron. All data (A–D) are from the same rat (ec14). Layer and region-specific color-coding apply to all figures. Positive polarity is up in all figures.

Top: Distribution of preferred theta phase. The height of the histograms reflects the proportion of principal neurons significantly modulated in each firing rate category (as in Figure 5A, reference = EC3 theta). Black dashed line, population mean (as in Figure 3B). Instantaneous rate (color coded) was quantified for each spike in ten increments (1, 2, … or ≥10 spikes per 250 msec [~two theta cycles], corresponding to 4, 8, 12,…, ≥ 40 Hz; as in Figure 5). In each region and layer, most principal neurons are silent or fire at low rates, with only a minority of neurons discharging at high frequency at a given time (Figure S19). Bottom: Current-source density (CSD) theta traces, taken from Montgomery et al. (2009), are superimposed on a histological section in the CA1-dentate gyrus axis, with highlighted pyramidal cell and granule cell. Note phase-reversed sinks in CA1 str. lacunosum-moleculare (lm) and dentate molecular layers (ml), and phase-shifted sink (relative to lm sink) in str. radiatum (rad). pyr, pyramidal layer. Arrows indicate the temporal (phase) offsets between the peak of population firing in upstream layers and the theta sinks in the target layers with the expected delays (based on axonal conduction velocity; 30° or ~ 10 msec). Note that while the population peak of an upstream layer correctly predicts the timing of the dendritic sink in its target layer, spiking activity in the downstream target population is substantially delayed.