Precisely timed theta oscillations are selectively required during the encoding phase of memory

Abstract

Brain oscillations have been hypothesized to support cognitive function by coordinating spike timing within and across brain regions, yet it is often not known when timing is either critical for neural computations or an epiphenomenon. The entorhinal cortex and hippocampus are necessary for learning and memory and exhibit prominent theta oscillations (6-9 Hz), which are controlled by pacemaker cells in the medial septal area. Here we show that entorhinal and hippocampal neuronal activity patterns were strongly entrained by rhythmic optical stimulation of parvalbumin-positive medial septal area neurons in mice. Despite strong entrainment, memory impairments in a spatial working memory task were not observed with pacing frequencies at or below the endogenous theta frequency and only emerged at frequencies ≥10 Hz, and specifically when pacing was targeted to maze segments where encoding occurs. Neural computations during the encoding phase were therefore selectively disrupted by perturbations of the timing of neuronal firing patterns.

Extended Data Fig. 1. LFP pacing efficiency and single unit identification.

(a) Pacing efficiency scores for recordings when each mouse explored the open field (top) or rectangular track (bottom). For every 2-s time-window, the peak LFP frequency was calculated for sessions without stimulation (gray bars) and with 12 Hz stimulation (blue bars), and the probability distribution of these peak LFP frequencies was plotted for each animal. Efficient pacing results in a narrow frequency peak at the stimulation frequency, and the pacing efficiency score was therefore defined as the maximum probability (in 0.2 Hz wide bins within 1 Hz of the stimulation frequency) in stimulation sessions. (b) The ratio of the spike waveform peak to trough amplitude (peak-valley ratio) and average firing rate (Hz) for each recorded cell was calculated to determine appropriate cutoff thresholds that separated between putative principal cells (blue circles) and putative interneurons (red circles). For cells recorded from the mEC either on the rectangular track (left) or the open field (middle), we used a rate cutoff of 15 Hz. For cells recorded from the hippocampus (right), we used a combined rate cutoff of 10 Hz and peak-valley cutoff of 1.5. (c) Example of multiple single-unit clusters recorded during the pre-stimulation baseline (baseline 1, left) and during optical stimulation (right). Defined single-unit clusters (red, green and blue) remained stable between sessions without stimulation and with stimulation. (d, top) L-ratio calculated for clusters of single units recorded in the mEC. (d, bottom) Isolation distance values calculated for clusters of single units recorded in the mEC. There was no change in L-ratio [n(B1, 8 Hz, 10 Hz, 12 Hz, B2) = 593, 476, 111, 531, 593 cells from 11 mice, H(4, 2299) = 2.17, P = 0.704, Kruskal-Wallis test] or isolation distance [n(B1, 8 Hz, 10 Hz, 12 Hz, B2) = 580, 462, 109, 518, 579 cells from 11 mice, H(4, 2243) = 7.91, P = 0.095, Kruskal-Wallis test] across stimulation conditions. n.s., not significant.

Extended Data Fig. 2. Running speed during periods with and without MSA stimulation.

(a) Running speed in either the open field (left) or on the rectangular track (right) was not altered when oscillations were paced by MSA stimulation [open field: grey and colored dots are individual data points, horizontal bars are medians, top and bottom of boxes are 25th and 75th percentile, n = 11 mice, H(4,487) = 7.2, P = 0.13, Kruskal Wallis test; linear track, grey and colored dots are individual data points, baseline vs stimulation, 8 Hz: n = 55 sessions in 6 mice, mean (±SEM), 12.08 (±0.44) and 11.51 (±0.40), t(54) = 2.31, P = 0.025 (0.074, Holm-Bonferroni corrected); 10 Hz: n = 9 sessions in 3 mice, median (25th, 75th percentile), 9.31 (8.77, 9.56) and 9.40 (9.33, 12.44), W(10) = 37, P = 0.065; 12 Hz: n = 54 sessions in 6 mice, mean (±SEM), 11.87 (±0.41) and 11.36 (±0.43), t(53) = 1.67, P = 0.10, two-sided paired t-test for normally distributed data, otherwise two-sided Wilcoxon signed rank test]. n.s., not significant. (b) There were no consistent effects on running speed in any of the maze zones during light stimulation in the spatial alternation task. During no delay trials, there was a minor increase in the delay zone with 8 Hz stimulation (note that the mice are running through the delay zone in the no delay trials) and in the reward zone with 10 Hz stimulation [delay, 8 Hz: n = 22 mice, z = −3.13, P = 0.0017 (0.027, Holm-Bonferroni corrected); reward, 10 Hz: n = 25 mice, z = −3.11, P = 0.0019 (0.028, Holm-Bonferroni corrected), two-sided Wilcoxon signed rank tests]. In 2 s delay trials, there was a minor decrease in running speed with 10 Hz stimulation on the stem [n = 25 mice, z = 3.92, P = 9.0 × 10⁻⁵ (0.0014, Holm-Bonferroni corrected), two-sided Wilcoxon signed rank test]. For all other comparisons, we do not find any differences in running speed on any of the maze segments.

Extended Data Fig. 3. The hippocampal depth profile during paced oscillations corresponded to the depth profile during endogenous theta oscillations.

(a) Sixteen-site linear silicon probes were chronically implanted in the hippocampus, and LFP recordings were performed in freely moving mice (n = 3 with one mouse excluded from analysis because of inadequate pacing; average pacing efficiency scores: 0.37 for mouse 89, 0.16 for mouse 95, and 0.04 for the excluded mouse 97). Schematic and brightfield histology images of the dorsal hippocampus for mouse 89 and 95. (b) Example raw LFP traces from all 16 recording sites during movement and rest. Ripple amplitude is known to be maximal in the pyramidal cell layer (encircled with red line), and alignment of the probe with the pyramidal layer was performed by visual inspection of sharp wave ripple amplitude and matched with the position of the probe in the histological reconstruction in (a). Scale bar is 250 ms. (c) Average current source density across hippocampal layers from recordings without stimulation (no stimulation) and with rhythmic stimulation at 8, 10, and 12 Hz. Periods from −125 to +125 ms are shown to include approximately two theta cycles (mouse 89, first and second column; mouse 95, third and fourth column). Note that there is a shortening of the theta cycle with higher stimulation frequencies, but during periods with stimulation the most pronounced current source-sink pair remained in slm, which is the termination zone of direct projections from entorhinal cortex. The distribution of less pronounced sink-source pairs across other hippocampal layers is also consistent between stimulation and no stimulation sessions. so, stratum oriens; sp, stratum pyramidale; sr, stratum radiatum; slm, stratum lacunosum moleculare.

Extended Data Fig. 4. mEC and hippocampus interneurons shifted their intrinsic firing frequencies.

(a) Example spike time autocorrelations for mEC interneurons during periods without stimulation (gray, left) and with stimulation (blue, middle) at 8 and 12 Hz. Right, FFT analysis of spike trains shows accelerated frequencies during stimulation compared to no stimulation sessions. Red vertical lines denote the peak oscillation frequency without and with light stimulation. (b) Same as in (a) but for hippocampal interneurons in the CA1 area. (c) Cumulative distribution function of the peak power (from the FFT analysis of spike trains) for mEC interneurons (left) and hippocampal interneurons (right). Interneurons generally showed high amplitude theta modulation at baseline, and a further increase compared to baseline was only observed at a subset of stimulation frequencies (mEC, 8, 10 and 12 Hz: K = 0.50, 0.30, 0.16; P = 1.7 × 10⁻⁵, 0.20, 0.44; hippocampus, 8, 10, and 12 Hz: K = 0.50, 0.80, 0.56, P = 0.014, 0.036, 0.078, two-sided KS tests). (d) Cumulative distribution function of the peak oscillation frequency of mEC interneurons (left) and hippocampal interneurons (right). Interneurons in mEC and hippocampus were similarly entrained [8, 10, and 12 Hz stimulation, mEC: n = 43, 23, 57; difference between stimulation frequency and cells’ oscillation frequency, median (±iqr) = 0.04 (±0.08), 0.10 (±0.23), 0.09 (±0.16); hippocampus: n = 18, 5, 9; median (±iqr): 0.19 (±2.64), 0.25 (±0.29), 0.11 (±1.21); mEC vs hippocampus: z = −0.14, −2.04, −0.36, P = 0.89, 0.04, 0.72, two-sided Wilcoxon rank sum tests].

Extended Data Fig. 5. Light-induced remapping was observed in the mEC of control mice on the rectangular track, but not in the open field.

(a) Rectangular track, Firing statistics of mEC cells in GFP control mice (n = 6) expressing mEmerald in the medial septal area. As described for Fig. 5, the mice ran on a rectangular track with alternating light-off and light-on laps. During light on laps, stimulation frequency was either 8 Hz or 12 Hz. The mean firing rate and peak firing rate of principal cells did not differ between no stimulation and stimulation laps for either stimulation frequency [Average firing rate, 8 and 12 Hz: n = 153 and 150 cells, two-way ANOVA, stim frequency*light-off vs on, interaction, F(1,602) = 0.037, P = 0.85, stim frequency, F(1,602) = 0.10, P = 0.76, light-off vs on, F(1,602) = 2.83, P = 0.093. Peak firing rate, 8 Hz and 12 Hz: n = 153 and 150 cells, two-way ANOVA, stim frequency*light-off vs on, interaction, F(1,602) = 0.15, P = 0.70, stim frequency, F(1,602) = 0.79, P = 0.37, light-off vs on, F(1,602) = 0.03, P = 0.86]. (b) A decrease in the number of place fields per cell as a result of light-induced remapping was observed across both stimulation frequencies in control mice [8 Hz and 12 Hz: n = 153 and 150 cells, two-way ANOVA, stim frequency*light-off vs on, interaction, F(1,602) = 0.28, P = 0.60, stim frequency, F(1,602) = 1.54, P = 0.21, light-off vs on, F(1,602) = 10.6, P = 0.0012]. Letters above columns (a, b) indicate significant differences between light-on and light-off conditions, two-sided Tukey-Kramer posthoc tests. (c) Light delivery in GFP control mice resulted in a significant decrease in place field stability within light-on trials and resulted in remapping, measured as the correlation between light-on and light-off trials. Both measures remained higher than a shuffled distribution suggesting partial light-induced remapping. There were no differences between stimulation frequencies for rate map stability condition [within light-off, within light-on, between light-on and light-off, shuffled; 8 and 12 Hz: n = 153 and 150 cells, two-way ANOVA, stim frequency*condition, interaction, F(3,1201) = 0.29, p = 0.83, stim frequency, F(1,1201) = 0.35, p = 0.56, condition, F(3,1201) = 328.2, p < 0.001]. Different letters (a-d) above columns indicate significant differences (P < 0.001) between conditions, two-sided Tukey-Kramer posthoc tests. (d) There was no change in spatial information of mEC fields on the linear track despite significant remapping [8 Hz and 12 Hz: n = 153 and 150 cells, two-way ANOVA, stim frequency*light-off vs on, interaction, F(1,602) = 0.26, P = 0.61, stim frequency, F(1,602) = 0.04, P = 0.84, light-off vs on, F(1,602) = 3.18, P =0.075]. (e) Positions of the spatial fields of mEC principal cells on the rectangular track are linearized and ordered left to right for each stimulation frequency according to the position during light-off sessions. The reorganization across light-off and light-on trials arises as a result of blue light delivery in control mice without pacing. (f) Open field, MEC cells were recorded from GFP control mice (n = 6) in a random foraging task, as described in Fig. 6. Light delivery (at either 8 Hz, 10 Hz, or 12 Hz) was performed during 1–2 sessions in-between two baseline sessions without light delivery. There was no change in the mean firing rate of principal cells and interneurons during stimulation sessions. (g) Light stimulation did not have consistent effects on irregular spatial cells as measured by the spatial information, spatial field stability (within-session correlation), and the extent of remapping (rate map correlation across sessions) [n(B1, 8Hz, 10 Hz, 12 Hz, B2) = 39, 27, 29, 21, 39 cells from 6 mice]. In (a-d), (f), and (g), grey and colored dots are individual data points, horizontal bars are medians, top and bottom of boxes are 25th and 75th percentile, see Supplementary Table 2 for detailed statistics.

Extended Data Fig. 6. Peak firing rates of mEC cells during MSA stimulation.

(a) There was a minor decrease in the peak firing rate of principal cells during MSA stimulation compared to baseline (grey and colored dots are individual data points, horizontal bars are medians, top and bottom of boxes are 25th and 75th percentile). Peak rate with 8 and 12 Hz stimulation was decreased compared to both the pre- and post-stimulation baseline. Peak rate at 10 Hz was decreased only compared to the pre-stimulation baseline [n(B1, 8 Hz, 10 Hz, 12 Hz, B2) = 593, 477, 170, 589, 592 cells from 11 mice, H(4,2416) = 32.09, P = 1.8 × 10⁻⁶, Kruskal Wallis test]. (b) There was a significant decrease in the peak firing rate of interneurons during 10 Hz and 12 Hz stimulation sessions compared to the pre-stimulation baseline (grey and colored dots are individual data points, horizontal bars are medians, top and bottom of boxes are 25th and 75th percentile). The rates with 12 Hz stimulation also differed from the post-stimulation baseline [n(B1, 8 Hz, 10 Hz, 12 Hz, B2) = 58, 42, 23, 55, 58 cells from 11 mice, H(4,231) = 12.04, P = 0.017, Kruskal Wallis test]. *** P < 0.001, * P < 0.05, see Supplementary Table 2 for detailed statistics.

Extended Data Fig. 7. Pacing was efficient for all mice that were included in analysis of behavioral data.

(a) Volume of opsin expression in MSA (i.e., medial septal area and diagonal band of Broca) is plotted against the log of the ratio-based score during 10 Hz, 12 Hz, and 20 Hz stimulation (open circles). Our previously published data (Fig. 1d in ref. 19) which showed a correlation between expression volume and pacing scores, are plotted for comparison (diamonds), but with expression volume re-quantified to match the methods of the current study. The previously reported correlation between expression volume and pacing efficiency was not observed in the current dataset [ratio-based score: n(10 Hz, 12 Hz, 20 Hz) = 28, 28, 16 mice, rho = −0.016, −0.092, 0.27, P = 0.94, 0.64, 0.32; proportion-based score: n(8 Hz, 10 Hz, 12 Hz, 20 Hz) = 25, 28, 28, 16 mice; rho = 0.075, 0.064, −0.36, −0.29; P = 0.72, 0.75, 0.058, 0.28, Spearman rank correlations). In the current dataset, pacing scores were consistently high, and it is possible that the correlation is not evident without including a sufficient number of cases with low scores. (b) Some mice in (a) showed high pacing efficiency with relatively low expression volumes which may be a consequence of differences in fiber placement in the current study (open circles) compared to the previous study (ref. 19, diamonds). (c) The previously used ratio-based pacing score (power within 1 Hz of the stimulation frequency divided by power at 7–9 Hz) was not designed to capture pacing efficiency with 8 Hz stimulation. To use a score that can be applied to all frequencies, we therefore considered the observation that efficient pacing results in a narrow frequency distribution around the stimulation frequency. To quantify the frequency distribution, we first measured the predominant LFP oscillation frequency during every 2 second interval and binned these measurements with a 0.2 Hz resolution. The peak proportion (i.e., relative frequency) in bins within 1 Hz of the stimulation frequency is taken as the proportion-based pacing efficiency score. Histograms and the corresponding power spectra (inserts) show that pacing was highly efficient for scores >0.2 (examples with scores of 0.45 and 0.22 are shown). (d) Filtered (3–22 Hz, top) and raw traces (bottom) during periods with and without stimulation show efficient pacing of the hippocampal LFP. Traces are from the session for which pacing efficiency is shown to the left in (c). Light pulses are shown as a blue line. (e) For frequencies higher than 8 Hz, where both the ratio-based and the proportion-based scores can be used, the scores are highly correlated [n(10 Hz, 12 Hz, 20 Hz) = 29, 29, 17 mice, rho = 0.90, 0.78, 0.53, P = 4.7 × 10⁻⁷, 2.6 × 10⁻⁶, and 0.029; Spearman rank correlations after confirming with two-sided KS tests that scores were not normally distributed]. (f) Pacing was highly efficient for most animals and stimulation frequencies [n(8 Hz, 10 Hz, 12 Hz, 20 Hz) = 25, 29, 29, 17 ChR2 mice and 10, 10, 10, 6 GFP mice]. Dots are individual data points, open circles and bars are median ± 25th to 75th percentile. When mice with opsin expression did not reach a score of 0.2 (stippled line) at a particular stimulation frequency, the behavioral data at the frequency were excluded from the analysis (n = 1 at 8 Hz, 2 at 12 Hz, and 1 at 20 Hz). A score of 0.2 was not exceeded in any of the GFP controls except for three cases at the 8 Hz frequency. At the 8 Hz frequency, endogenous theta oscillations can result in scores up to 0.3. (g) For 10-trial blocks with the longest sustained stimulation duration (i.e., with 10 s delay, average duration for stimulation sessions, 8 Hz: 392.6 s, 10 Hz: 392.5 s; 12 Hz: 410.0 s; 20 Hz: 345.4 s), pacing efficiency did not differ between the first and the second half of the block [n(8 Hz, 10 Hz, 12 Hz, 20 Hz) = 24, 28, 27, 16 mice, dots are individual data points, open circles and bars are median ± 25th to 75th percentile, z = 0.37, −0.30, 0.82, 1.40, P = 0.71, 0.77, 0.41, 0.16, two-sided Wilcoxon signed rank tests].

Extended Data Fig. 8. Pacing of oscillations at frequencies below 8 Hz did not result in memory impairment.

(a) Pacing was efficient with 4 Hz and 6 Hz stimulation in the majority of mice but harmonics were frequently observed. Distribution of the predominant frequency (left), power spectrum (insert), and example raw and filtered (3–22 Hz) waveforms (right) without stimulation and with 4 Hz stimulation in one mouse with weak harmonics (top) and one mouse with strong harmonics (bottom). (b) Proportion-based pacing scores at stimulation frequencies <8 Hz, and for comparison, at stimulation frequencies of 8 Hz and 12 Hz [n(4 Hz, 6 Hz, 8 Hz, 12 Hz) = 12, 12, 25, 29 mice]. Dots are individual data points, open circles and bars are median ± 25th to 75th percentile. When harmonics at 8 and 12 Hz were more pronounced the pacing efficiency score at 4 Hz was reduced [e.g., 0.16 in the bottom example in (a) is below the threshold of 0.2], such that these sessions were excluded from analysis of behavioral data (n = 3 at 4 Hz, 3 at 6 Hz). (c) Similar to the effect with 8 Hz stimulation, stimulation at 4 and 6 Hz did not result in impaired memory performance in the delayed spatial alternation task (No delay: n = 9 and 8, W = 14.0 and 6.5, P = 0.53 and 0.94; 2 s delay: W = 12.5 and 18.5, P = 0.48 and 0.59; 10 s delay: W = 25.0 and 20.5, P = 0.094 and 0.34, two-sided Wilcoxon signed rank tests). Dots are individual data points, open circles and bars are median ± 25th to 75th percentile. Data with 8 Hz and 12 Hz pacing are shown for comparison and correspond to the data shown in Fig. 8. * P < 0.05, ** P < 0.01, see Supplementary Table 3 for detailed statistics.

Extended Data Fig. 9. There was no relation between pacing efficiency and the decreased behavioral performance in the 10 s delay condition.

(a) Comparisons of the decrease in behavioral performance in the 10 s delay condition with either the pacing efficiency (left, proportion-based score; middle, ratio-based score) or the volume of viral vector expression in MSA (right) did not reveal any correlations at any stimulation frequency [ratio-based score, n(10, 12, 20 Hz) = 25, 24, 14; rho = 0.19, −0.086, −0.55; P = 0.35, 0.68, 0.033 (0.10, Holm-Bonferroni corrected); proportion-based score: n(8, 10, 12, 20 Hz) = 20, 25, 24, 14; rho = −0.12, 0.22, −0.01, −0.06; P = 0.60, 0.30, 0.96, 0.83; EYFP volume, n(8, 10, 12, 20 Hz) = 22, 26, 24, 14; rho = −0.16, 0.0096, −0.34, −0.59; P = 0.48, 0.96, 0.10, 0.027 (0.11, Holm-Bonferroni corrected), Spearman rank correlations]. (b) Behavioral data for no stimulation and stimulation sessions at each frequency. Dots are individual data points, open circles and bars are median ± 25th to 75th percentile. The experimental design included, for each of the three delay conditions on each day, blocks of 10 trials with stimulation and 10 trials without stimulation, and the difference in performance between stimulation and no-stimulation blocks was calculated to control for day-to-day variations in behavioral performance (as shown in Fig. 8c and e). Statistical analysis was thus performed on the difference in percent correct trials between blocks with and without stimulation [ChR2/oChIEF: n(8 Hz, 10 Hz, 12 Hz, 20 Hz) = 22, 27, 25, 15 mice, 2 s delay, P = 0.61, 0.021, 0.037, 0.037; 10 s delay, P = 0.86, 0.026, 0.0012, 0.0043, Holm-Bonferroni corrected, two-sided Wilcoxon signed rank tests; GFP/ChR2 green light: n = 10, 14, 14, 10 mice, all P values, n.s., two-sided Wilcoxon signed rank tests). See main text and Supplementary Table 3 for detailed statistics. (c) Behavioral data for sessions with stimulation that were targeted to maze zones [n(Reward, Delay+Stem, Delay+Stem+Reward, Return) = 12, 12, 10, 10 mice; 10 s delay/Return: P = 0.0078, Holm-Bonferroni corrected, two-sided Wilcoxon signed rank test; all other comparisons, n.s.]. Dots are individual data points, open circles and bars are median ± 25th to 75th percentile. Occupancy times in the stimulated zones were higher in the delay+stem+reward condition (medians: 8.96+1.94+6.78 s = 17.68 s) than in the return condition (median: 7.52 s) (Extended Data Fig. 10) such that time of stimulation cannot explain the selective effect of return-arm stimulation on behavioral performance. n.s., not significant, * P < 0.05, ** P < 0.01, two-sided Wilcoxon signed rank tests, see main text and Supplementary Table 3 for detailed statistics.

Extended Data Fig. 10. Length of light stimulation and magnitude of LFP power across maze segments did not explain the selective effect of return-arm stimulation on behavioral performance during 10 s delay trials.

(a) Time in each of the maze zones did not differ between no stimulation and stimulation trials [n(no stimulation, stimulation) = [39, 36], [39, 36], [36, 39], and [36, 39] sessions for Delay, Stem, Reward, and Return, z = 0.93, 1.12, 1.12, 0.53, P = 0.35, 0.26, 0.26, 0.59, two-sided Wilcoxon rank sum test]. Data are presented as boxplots (horizontal line in box: median, bottom and top of box: 25th and 75th percentiles, whiskers: most extreme values that are not outliers). Importantly, the median time in the return arms (7.52 s) was substantially lower than in the condition when stimulation was on during the delay+stem+reward (17.68 s), which indicates that the selective effect of return-arm stimulation on memory performance (Fig. 8e and Extended Data Fig. 9c) cannot be attributed to longer stimulation durations. (b) Baseline theta power differed between maze segments [H(3) = 22.76, P = 4.5 × 10⁻⁵, Kruskal-Wallis test; delay (n = 24 sessions) vs reward (n = 22 sessions): P = 3.0 × 10⁻⁴ (0.0015, Holm-Bonferroni corrected), stem (n = 24 sessions) vs reward (n = 24 sessions): P = 3.4 × 10⁻⁵ (0.00020, Holm-Bonferroni corrected), stem (n = 24 sessions) vs return (n = 33 sessions): P = 0.0053 (0.02, Holm-Bonferroni corrected); all other comparisons, n.s., two-sided Wilcoxon rank sum tests], but oscillation power corresponded across maze segments during 12 Hz pacing [n(Delay, Return, Reward, Stem) = 20, 11, 22, 20 sessions, H(3) = 0.77, P = 0.86, Kruskal-Wallis test]. Moreover, oscillation frequency was reliably shifted to 12 Hz in each maze segment. Differences in pacing efficiency across maze segments therefore do not appear to contribute to the selective effect of return-arm stimulation on memory performance (Fig. 8e and Extended Data Fig. 9c). Dots are individual data points, open circles and bars are mean ± SEM.

Figure 1.. Rhythmic optogenetic stimulation of MSA PV neurons controlled the frequency of LFP oscillations in mEC and hippocampus of freely moving mice.

(a) Viral vectors were delivered to the MSA of PV-Cre mice to express either ChR2 or oCHIEF in PV cells. An optic fiber was placed just above the MSA and electrodes were lowered into either mEC (n = 11 mice) or hippocampus (Hpc, n = 4 mice). (b, left) Example image of the septal area shows GFP (green) that is coexpressed with opsin. Section is counterstained with DAPI (blue). (b, right) Example electrode tracks (red circles) in Hpc (top) and mEC (bottom). All scale bars are 250 μm. (c, top) Schematic of a recording sequence in the open field. (c, bottom) Schematic of the rectangular track. Arrow indicates running direction. Rhythmic stimulation was either turned on or off when the mouse crossed a boundary (blue stippled line), such that laps with and without stimulation alternated. (d, top) Example mEC LFP recording before and during a train of blue light delivery shows the higher LFP frequency during periods with light stimulation. (d, bottom) During rhythmic optical stimulation of the MSA at 8, 10, or 12 Hz, mEC and Hpc peak LFP frequency reliably shifted from the endogenous theta frequency to closely match the stimulation frequency. Each dot is a recording session (mEC: n = 41, 22, and 59 sessions; Hpc: n = 20, 6, and 20 sessions for 8, 10 and 12 Hz stimulation, respectively). (e) Example mEC recordings from an individual mouse during rhythmic optical stimulation at 8, 10, and 12 Hz on every other lap of the track. During laps with stimulation, LFP oscillations immediately and persistently shifted to match the stimulation frequency, and the optogenetically paced oscillations superseded the endogenous theta (6–9 Hz) oscillation.

Figure 2.. Pacing of MSA PV cells increased the oscillation amplitude of mEC cells, but not of hippocampal cells.

(a) Autocorrelation plots (left, middle) and FFT analysis (right) of the spike trains of two example mEC cells. Power and peak oscillation frequency in the 6–14 Hz range were calculated for each cell. (b) Cumulative density function of the power for all putative mEC principal cells during 8, 10, and 12 Hz stimulation (colored lines), and of the same cells during periods without stimulation (gray lines). (c, d) Same as in (a, b) but for putative CA1 principal cells. Septal stimulation increased the power of oscillations of mEC cells [n(8, 10, 12 Hz) = 479, 180, 591 cells in 11 mice, K = 0.32, 0.23, 0.16, P = 1.1 × 10⁻²¹, 0.00014, 1.9 × 10⁻⁷, two-sided KS tests compared to no stimulation], but not of hippocampal cells [n(8, 10, 12 Hz) = 175, 80, 138 cells, K = 0.06, 0.14, 0.14, P = 0.94, 0.34, 0.10, two-sided KS tests compared to no stimulation]. The more pronounced effect on mEC compared to hippocampal cells was observed even though pacing scores at each frequency were either comparable to or lower than hippocampal pacing scores (mean pacing score with 8, 10 and 12 Hz stimulation: mEC: 0.27, 0.40, 0.34; hippocampus: 0.38, 0.43, and 0.33).

Figure 3.. Firing of mEC cells was entrained to oscillation frequencies that closely corresponded to pacing frequencies.

(a) Oscillatory firing of the spike trains of all putative principal cells in mEC. Each line in color-coded panels is the normalized power of the oscillations of spike trains at frequencies between 6 and 14 Hz. Within each panel, cells are ordered by their peak oscillation frequency. Cells with power <0.1 were excluded because frequency could not be accurately estimated. Vertical white lines indicate stimulation frequency. (b, left) Cumulative density function of the entrainment of the cells’ spike trains to 8, 10, and 12 Hz pacing frequencies (colored lines), and of the same cells’ spike train oscillations during periods without stimulation (gray lines). (b, bottom) The spiking of most mEC cells became entrained to the stimulation frequency, irrespective of their preferred spiking frequency at baseline. (b, right) Cumulative density function of the difference between the spike train’s oscillation frequency and the stimulation frequency. For 8, 10, and 12 Hz stimulation (n = 395, 158, 483 cells), the median difference (±iqr) to the stimulation frequency is 0.11 Hz(±0.18), 0.16 Hz(±0.20), and 0.10 Hz(±0.21), respectively. (c, d) Same as in (a, b) but for hippocampal principal cells. Hippocampal cells showed differences from the stimulation frequency [n(8, 10, 12 Hz) = 89, 46, 71 cells, median difference (±iqr) = 0.59 (±0.54), 0.46 (±0.34), 0.21 (±0.35)], which were larger than for mEC (Z = −8.92, −6.17, −2.10, P = 4.6 × 10⁻¹⁹, 6.9 × 10⁻¹⁰, 0.035, two-sided Wilcoxon rank sum tests).

Figure 4.. Medial entorhinal cells were more strongly entrained to septal stimulation than hippocampal cells.

(a) Peri-stimulus time histograms show the normalized rate of each mEC cell (top, color coded with the same color scheme as in Fig. 3) and the average over all normalized rates (bottom). Red vertical line is the light onset, and 250 ms are plotted to show approximately two cycles. (b) Same as (a), but for hippocampus. The relative increase in firing rate in the 30 ms following the onset of the optical stimulation was higher in mEC principal cells than in hippocampal CA1 principal neurons [mEC: n(8, 10, 12 Hz)= 480, 180, 591 cells; median (±iqr) = 1.62 (±1.90), 1.59 (±1.54), 1.42 (±0.92); hippocampus: n(8, 10, 12 Hz) = 181, 85, 152 cells; median (±iqr) = 1.46 (±1.03), 1.29 (±0.61), 1.23 (±0.78); mEC vs. hippocampus: z = 2.08, 3.26, 3.22, P = 0.037, 0.0011, 0.0013, two-sided Wilcoxon rank sum tests) (c) Phase locking between spiking and LFP oscillations in the 6–14 Hz range is obtained by first determining the phase of each spike and by then calculating the mean resultant length from all spike phases during periods with and without stimulation. Violin plots show the distribution of all cells’ resultant lengths for each stimulation condition [n(8, 10, 12 Hz) = 436, 193, 639 cells, baseline vs. stimulation: z = −15.92, −5.55, −1.07, P = 4.8 × 10⁻⁵⁵, 1.4 × e⁻⁵, 0.29, two-sided Wilcoxon paired signed-rank tests]. (d) Same as (c), but for hippocampus [n(8, 10, 12 Hz) = 181, 84, 152 cells, baseline vs. stimulation: z = −0.31, −1.71, −6.07, P = 0.76, = 0.088, 1.3 × 10⁻⁹, two-sided Wilcoxon paired signed-rank tests]. *** P < 0.001, n.s., not significant.

Figure 5.. Effects on spatial firing patterns were corresponding across stimulation frequencies.

(a) Example spatial firing patterns of mEC cells recorded during sessions with 8 Hz (left) and 12 Hz pacing (right). The entire session is shown by plotting spike position (red dots) on the trajectory and the firing rates relative to the peak rate as a heat map. Firing rates are also shown in a linearized heat map, and individual trials with and without stimulation are plotted as heat maps. Spatial firing was observed during trials with and without optical stimulation. (b) Spatial correlations across laps differed between all 4 types of comparisons [within light-off, within light-on, between light-off/on, with cell identify shuffled, 8 Hz and 12 Hz: n = 98 and 86 cells in 2 mice, χ²(3) = 129.3 and 121.4, P = 7.3 × 10⁻³⁰ and 6.5 × 10⁻²⁸, Friedman tests followed by two-sided Dunn Bonferroni rank sum difference, P values for all pairwise differences < 0.01]. Individual data points are shown as dots, the median as a horizontal line, and the 25^th to 75^th percentile interval as a box. Different letters above columns indicate significant differences. The pattern of results indicates that remapping was partial (i.e., between light-off/on value is higher than for shuffle but lower than within light off and within light on values). Similar remapping also occurs in response to light stimulation in GFP control mice (Extended Data Fig. 5). In addition, the higher values for within light-off stability and within light-on stability indicates stable spatial organization within each condition. (c) Spatial information even showed an increase during light-on compared to light-off (8 and 12 Hz: n = 98 and 86 cells, z = −3.57 and −2.38, P = 0.00022 and 0.017, two-sided Wilcoxon signed rank tests). (d) The number of fields per cell decreased (8 and 12 Hz: n = 98 and 86 cells, z = 1.96 and 4.34, P = 0.049 and 0.00025, two-sided Wilcoxon signed-rank tests) consistent with a sharpening of the spatial firing patterns. (e) Mean and peak firing rate were not altered by light stimulation (average and peak rate, 8 Hz: n = 98 cells, z = −0.25 and −1.36, P = 0.80 and 0.17; 12 Hz: n = 86 cells, z = 0.81 and −0.79, P = 0.42 and 0.43, two-sided Wilcoxon signed-rank tests). (f) Positions of the spatial fields of mEC principal cells on the rectangular track are linearized and ordered left to right according to the position during light-off sessions. The reorganization across no stimulation and stimulation laps reflects remapping. (g-l) Same as (a-f) but for hippocampal principal cells. (h) Spatial correlations differed between all 4 comparisons [within light-off, within light on, between light-off/on, with cell identify shuffled, 8 and 12 Hz: n = 127 and 104 cells in 4 mice, χ2(3) = 245.3 and 207.8, P = 1.4 × 10⁻⁵⁴ and 8.5 × 10⁻⁴⁷; Friedman tests followed by Dunn Bonferroni rank sum difference, P values for all pairwise differences <0.05]. Similar remapping was previously shown to be a consequence of light stimulation alone in GFP control mice and is thus unrelated to the pacing of oscillations. (i-k) Spatial information did not differ between light-off and light-on, while other firing properties showed a decrease during light-off compared to light-on, but to a similar extent for the 8 Hz and 12 Hz stimulation (spatial information, number of fields per cell, mean firing rate, peak firing rate, 8 Hz: n = 127 cells, z = −0.23, 4.99, 4.01, 4.62, P = 0.82, 6.1 × 10⁻⁷, 6.1 × 10⁻⁵, 3.9 × 10⁻⁶; 12 Hz: n = 104 cells; z = −0.54, 4.29, 2.46, 3.97, P = 0.59, 1.8 × 10⁻⁵, 0.014, 7.2 × 10⁻⁵, two-sided Wilcoxon signed-rank tests). The matching effects on spatial firing for 8 Hz compared to 12 Hz stimulation were also confirmed with a two-way ANOVA (see Supplementary Table 1 for detailed statistics). Individual data points are shown as dots, the median as a horizontal line, and the 25^th to 75^th percentile interval as a box.

Figure 6.. Spatial firing patterns in mEC matched across pacing frequencies, and grid coding was not altered by pacing in the open field.

(a) mEC cells were recorded while mice (n = 11) performed a random foraging task for 3–5 sessions per day. No stimulation was delivered during the first and last session, and continuous rhythmic stimulation at either 8, 10, or 12 Hz was delivered during each of the intervening stimulation sessions. (b) The average firing rate of mEC principal cells [n(B1, 8 Hz, 10 Hz, 12 Hz, B2) = 593, 477, 170, 589, 592 in 11 mice] and interneurons [n(B1, 8 Hz, 10 Hz, 12 Hz, B2) = 25, 17, 17, 14, 25 in 11 mice] showed minor differences between conditions with and without light stimulation (H(4, 2416) = 16.24, P = 0.0027; interneurons: n = 58, 42, 23, and 55; mean rate: H(4,231) = 14.05, P = 0.0071, Kruskal-Wallis tests), but for principal cells at the 10 Hz and 12 Hz stimulation only compared to the pre-stimulation and not the post-stimulation baseline. Columns marked with a differ from b, and those marked with c differ from d (two-sided Wilcoxon rank-sum tests, Holm-Bonferroni corrected). See Extended Data Fig. 6 for peak rate. (c) Cells were classified as irregular spatial cells when their spatial information exceeded the 95^th percentile of values from shuffled patterns in at least two recording sessions. Rate map correlations between the pre-stimulation baseline and session with either 8 Hz or 12 Hz pacing showed a decrease compared to rate map correlations between the pre-stimulation and the post-stimulation baseline [n(B1 vs B2, B1 vs 8 Hz, B1 vs 10 Hz, B1 vs 12 Hz) = 152, 125, 44, 152 spatial cells from 11 mice, H(4,231) = 14.05, P = 0.0071, Kruskal-Wallis test]. (d, left) Two example irregular spatial cells (spatial non-grid cells) are shown. Firing patterns in each of the four recording sessions are depicted by plotting spike locations (red dots) on top of the trajectory (gray lines) and by plotting the average firing rates at each location as a heat map. (d, right) Spatial information of irregular spatial cells showed a small decrease between sessions with and without light stimulation, but did not differ between any of the light stimulation frequencies [n(B1, 8 Hz, 10 Hz, 12 Hz, B2) = 152, 125, 44, 152, 152 spatial cells from 11 mice, H(4,620) = 27.84, P = 1.35 × 10⁻⁵, Kruskal-Wallis test]. The consistency of spatial firing patterns (within-session correlation) of irregular spatial cells was decreased at the 8 Hz and 12 Hz frequency compared to the pre-stimulation baseline but only at the 12 Hz frequency compared to the post-stimulation baseline (H(4,620) = 20.07, P = 0.00048, Kruskal-Wallis test). (e, left) Two example grid cells are plotted as in (d). (e, right) Grid cells were identified by gridness scores above the 95^th percentile of scores from shuffled data in at least two recording sessions. Values below criterion can thus be observed in a subset of sessions, including baseline sessions with no light stimulation. The precision (spatial information) and regularity (gridness score) of grid cells did not differ between any of the stimulation conditions [n(B1, 8 Hz, 10 Hz, 12 Hz, B2) = 18, 18, 6, 18, 18 grid cells in 11 mice, spatial information: H(4,73) = 2.151, P = 0.71; gridness score: H(4,73) = 2.42, P = 0.66, Kruskal-Wallis tests]. (f) Panels to the left are the firing maps of grid cells in a series of 4 recording sessions (B1, 8 Hz, 12 Hz, B2; color scale is from zero in blue to maximum rate in red, grid scores are indicated on top). Panels to the right are the spatial crosscorrelation between sessions (B1 vs B2, B1 vs 8 Hz, B1 vs 12 Hz, color scale is from minimum in blue to maximum in red, offset of the central peak from the origin is indicated on top). Grid patterns did not shift during light stimulation sessions compared to sessions without stimulation, as measured by the offset of the central peak from the origin in the spatial crosscorrelograms (n = 18 grid cells, χ²(2) = 0.90, P = 0.64, Friedman test; Friedman test). (g) Grid spacing was not altered by light stimulation [n(B1, 8 Hz, 10 Hz, 12 Hz, B2) = 18, 18, 6, 18, 18 grid cells in 11 mice, H(4,73) = 5.62, P = 0.23, Kruskal-Wallis test). Individual data points are shown as dots, the median as a horizontal line, and the 25^th to 75^th percentile interval as a box. ** P < 0.01, *** P < 0.001. See Supplementary Table 2 for detailed statistics.

Figure 7.. Head direction and speed coding were not disrupted when pacing oscillations at frequencies between 8–12 Hz.

(a) The directional tuning of two example head direction cells is shown in circular plots of firing rates by head direction. (b) The sharpness (i.e., HD vector length) of either sharply or broadly tuned HD cells did not differ across stimulus conditions [n(B1, 8 Hz, 10 Hz, 12 Hz, B2) = 58, 55, 5, 58, 58 sharply tuned HD cells in 11 mice, H(4, 229) = 1.41, P = 0.84; n(B1, 8 Hz, 10 Hz, 12 Hz, B2) = 47, 42, 10, 47, 47 broadly tuned HD cells in 11 mice, H(4,188) = 4.51, P = 0.34, Kruskal-Wallis tests]. (c and d) The head direction angle during the pre-stimulation baseline (B1) is compared to the angle in post-stimulation baseline (B2), 8 Hz, 10 Hz and 12 Hz stimulation sessions. The tuning angle of HD cells was not altered by MSA stimulation [n(B1, 8 Hz, 10 Hz, 12 Hz) = 105, 97, 15, 105 cells in 11 mice, H(3, 318) = 2.98, P = 0.40, Kruskal-Wallis test]. (e) Speed is plotted against instantaneous firing rate (Instant. rate), and regression lines are shown in black. (f) Average speed scores (r values of the regression lines) of neither speed-modulated principal cells [n(B1, 8 Hz, 10 Hz, 12 Hz, B2) = 97, 72, 31, 97, 96, H(4, 388) = 5.38, P = 0.25, Kruskal-Wallis test] nor of speed-modulated interneurons [n(B1, 8 Hz, 10 Hz, 12 Hz, B2) = 18, 11, 8, 17, 18, H(4, 67) = 2.81, P = 0.59, Kruskal-Wallis test] differed between any of the stimulation conditions. Individual data points are shown as dots, the median as a horizontal line, and the 25^th to 75^th percentile interval as a box. n.s., not significant, see Supplementary Table 2 for detailed statistics.

Figure 8.. Spatial memory deficits emerged at pacing frequencies of 10, 12, and 20 Hz.

(a) Mice that expressed either opsins (ChR2 or oCHIEF) or GFP were trained in a spatial alternation task with no delay, 2 s delay and 10 s delay. (b) Once mice performed the task with high accuracy, they were tested in alternating blocks with and without light stimulation of the MSA. One stimulation frequency per day was selected, and different stimulation frequencies (i.e., 8, 10, 12, and 20 Hz) were used across days. An example session with 12 Hz stimulation is shown, along with a time-frequency spectrogram of the LFP. During stimulation periods, LFP oscillation frequency consistently matched the stimulation frequency and replaced endogenous theta oscillations. For comparison, an example 12 Hz session in a GFP-expressing control mouse is shown, where blue light stimulation did not alter ongoing LFP. (c, top) In mice with opsin expression, blue light stimulation did not have any effect on behavior at the 8 Hz frequency (n = 22, no delay: W = 47.5, P = 0.09; 2 s delay: W = 74.0, P = 0.61; 10 s delay: W = 89.5, P = 0.86, two-sided Wilcoxon paired signed-rank tests), but impaired performance in trials with 2 s and 10 s delays for stimulation at 10, 12, or 20 Hz (n = 27, 25, and 15, no delay: W = 98.5, 94.0, 36.0, P = 0.14, 0.97 and 0.54; 2 s delay: W = 42.5, 41.0, 9.0, P = 0.021, 0.037 and 0.037, Holm-Bonferroni corrected; 10 s delay: W = 43.0, 16.0, 7.0, P = 0.026, 0.0012, and 0.0043, Holm Bonferroni corrected, two-sided Wilcoxon paired signed-rank tests). (c, bottom) There was no effect of stimulation in mice with GFP expression and in ChR2 mice with green light stimulation [n(8, 10, 12, 20 Hz) = 10, 14, 14, 10; no delay: W = 3, 37, 31, 29, P = 0.092 (Holm-Bonferroni corrected), 0.60, 0.77, 0.92; 2-s delay: W = 15.5, 11.5, 50.0, 6, P = 0.46, 0.25, 0.42, 0.10; 10 s delay: W = 26.5, 64.5, 46.0, 21.5, P = 0.28, 0.20, 0.70, 0.99, two-sided Wilcoxon paired signed-rank tests). (d) Optogenetic stimulation at 12 Hz was restricted to various zones of the maze, including (1) arm segments with reward, (2) stem+delay zone, (3) delay+stem+reward segments, and (4) return arms. One zone per day was selected, and different zones were tested across days. (e) There was no effect on memory performance during stimulation in zones 1–3 (n = 12, 12, 10; no delay: W = 24.5, 30.5, 15.0, P = 0.91, 0.82, 0.94; 2 s delay: W = 19.5, 33.5, 2.5, P = 0.45, 1, 0.25; 10 s delay: W = 22.5, 44.0, 32.0, P = 0.21, 0.090, 0.25). Stimulation on the return arms resulted in a decreased performance during 10 s delay trials (n = 10, W = 0, P = 0.0078, Holm-Bonferroni corrected, two-sided Wilcoxon paired signed-rank test) and a trend towards a decrease during 2-s delay trials (n = 10, W = 6.5, P = 0.067, two-sided Wilcoxon paired signed-rank tests). No effect was found without delay (W = 11, P = 0.94, two-sided Wilcoxon signed rank tests). Individual data points are shown as dots, the median as an open circle, and the 25^th to 75^th percentile interval as error bars. * P < 0.05, ** P < 0.01, n.s., not significant, see Supplementary Table 3 for detailed statistics.