Hippocampal place cell assemblies are speed-controlled oscillators

Abstract

The phase of spikes of hippocampal pyramidal cells relative to the local field theta oscillation shifts forward ("phase precession") over a full theta cycle as the animal crosses the cell's receptive field ("place field"). The linear relationship between the phase of the spikes and the travel distance within the place field is independent of the animal's running speed. This invariance of the phase-distance relationship is likely to be important for coordinated activity of hippocampal cells and space coding, yet the mechanism responsible for it is not known. Here we show that at faster running speeds place cells are active for fewer theta cycles but oscillate at a higher frequency and emit more spikes per cycle. As a result, the phase shift of spikes from cycle to cycle (i.e., temporal precession slope) is faster, yet spatial-phase precession stays unchanged. Interneurons can also show transient-phase precession and contribute to the formation of coherently precessing assemblies. We hypothesize that the speed-correlated acceleration of place cell assembly oscillation is responsible for the phase-distance invariance of hippocampal place cells.

Fig. 1.

Speed affects oscillation frequency of place cells. (A) Trajectories of the rat through a place field on two trials with different speeds [Top: green, slow trial (mean speed 31 cm/sec); blue, fast trial (mean speed 55 cm/sec)]. (Middle and Bottom) Spikes of one place cell and the corresponding LFP of the same two trials. The black arrows indicate the time it takes for the rat to cross the place field. (B) Smoothed firing rates (tuning curves) and position vs. spike phase of θ (spatial-phase precession) of the neuron (phases are plotted twice for better visibility). Trials were sorted by speed and divided into fast (upper 20%, 11 trials) and slow (lower 20%, 11 trials) trials. (C) Autocorrelograms of spike phases during slow (Upper) and fast (Lower) trials. (D) Autocorrelograms of spike times and above spike-triggered average of the LFP using all spikes in the 20% fastest and 20% slowest trials, respectively. Note the larger phase advance of place cells during fast runs.

Fig. 2.

Speed modulates oscillation frequency of place cells. (A) (Left) The power spectra of fast (upper 50%) and slow (lower 50%) runs of a single place cell and the LFP segments during the place field crossing. The frequency shift between these spectra was determined by computing the maximum of their cross-correlograms. (Right) Most place cells show a positive frequency shift between fast and slow runs. The cross-correlograms for all place cells are normalized by their SD, and their amplitude is color-coded. The black dots mark the maxima of the cross-correlograms, and the dashed line marks zero frequency lag. The place fields are sorted by the speed difference between the fast and slow trials (ranging from Δf = 5 cm/sec to Δf = 25 cm/sec). Note the larger frequency shift for a larger speed difference (n = 84 place fields from 48 CA1 pyramidal cells). (B) Same as in A, but for interneurons. Speed difference between the fast and slow trials ranges from Δf = 4 cm/sec to Δf = 19 cm/sec (n = 20 CA1 interneurons; the two running directions were treated separately). (C) Frequency difference between neuronal and LFP oscillations as a function of speed (dots, mean of five trials). Note the positive correlation between speed and the frequency shift. (D) Frequency shifts of units as a function of the associated shifts in LFP θ. Values above the dashed line indicate a larger frequency increase due to speed for units than for the corresponding LFP. Note that most of the pyramidal cells lie above the diagonal.

Fig. 3.

Sequence compression of place cells varies as a function of speed. (A) Tuning curves of two place cells (P1, P2) with overlapping fields and a distance d between field centers. (B) Cross-correlograms between the two neurons for slow (Left, lower 50%) and fast (Right, upper 50%) trials, low-pass filtered at 1.5 Hz (time scale of travel time between place fields) and 40 Hz (time scale of θ). The peak of the cross-correlogram filtered at 1.5 Hz indicates the travel time between the centers of two place fields. (C) The cross-correlograms filtered at 1.5 Hz from B for fast and slow trials. (Left) It takes Δτ longer to cross between the place fields in slow runs than in fast runs. (Right) This travel time difference Δτ is linearly correlated with the distance d between the place fields, as shown for all cell pairs. (D) (Left) The cross-correlograms filtered at 40 Hz from B for fast and slow trials. (Right) The time difference Δτ_θ between the fast and slow trials within one θ cycle does not depend on the distance d, as shown for all cell pairs. For all group plots, n = 96 place fields of 55 CA1 pyramidal cells were used, corresponding to 801 pairs.

Fig. 4.

Interneurons segregate place cell assemblies. (A) Firing rates of two pyramidal cells (red, P1; magenta, P2) and an interneuron (black, IN) as a function of distance on the running track. (B) Phase precession of interneuron spikes. The interneuron's color-coded smoothed density of firing is plotted as a function of θ phase and the rat's position on the track. Phase distributions are shown twice for better visibility. Stars and dots indicate the running mean phase of P1 and P2, respectively. Note the similar phase slope of P1 and the interneuron. (C) Temporal cross-correlation between P1 and interneuron IN and P2 and the same interneuron IN. Note the opposite phase relationship of P1 and P2. The dashed lines indicate the 95% confidence interval (C.I.) for shuffled spike trains such that the phase is conserved. Distribution that exceeds the C.I. is significantly more correlated or anticorrelated than could be expected simply by common phase locking. (D) Autocorrelogram, θ-spike cross-correlogram, and ripple-spike cross-correlogram of the interneuron. (E) Autocorrelogram of the interneuron's spike phases during 10% slowest (five trials, average speed 19 cm/sec) and 10% fastest (five trials, average speed 40 cm/sec) runs across the field marked by black arrows in B. (F) Superimposed autocorrelograms of spike times of the same trials as in E and the spike-triggered average (using all spikes from the slow and fast trials, respectively) of the related θ oscillation from the CA1 pyramidal layer during slow and fast runs across the field marked by black arrows in B. Note the steeper phase advancement of the interneuron spikes during faster speed.

Fig. 5.

Oscillation frequency of phase-precessing interneurons is speed-dependent. The power spectra are calculated only for spikes and LFP during segments when the rat crosses the interneuron's place field (compare with Fig. 2B). Interneurons increase their oscillation frequency significantly more with faster running speed than the LFP [interneurons, mean (Δf) = 0.8 ± 0.7; LFP, mean(Δf) = 1.5 ± 0.9; P < 0.01]. Fields were sorted according to the speed difference between fast and slow trials (speed differences ranged from 5 to 25 cm/sec). Spectra were computed for 12 place fields of eight interneurons.

Fig. 6.

Nonphase-precessing interneuron. (A) Firing rates of two pyramidal cells (red, P1; magenta, P2) and an interneuron (black, IN) as a function of distance on the running track. (B) The spikes of the interneuron are locked to a small phase range (compare Fig. 4). The circular mean phases of the two simultaneously recorded pyramidal cells are marked with red dots and magenta stars, respectively. (C) Temporal cross-correlograms between P1 and interneuron IN and P2 and the same interneuron IN. Note that both pyramidal cells are anticorrelated to the activity on the interneuron. The dashed lines give the 95% C.I. for phase locking; cross-correlograms exceeding this C.I. have a significant correlation beyond phase locking. (D) Autocorrelogram, θ-spike cross-correlogram, and ripple–spike cross-correlogram of the interneuron.