Minute-scale oscillatory sequences in medial entorhinal cortex

Abstract

The medial entorhinal cortex (MEC) hosts many of the brain's circuit elements for spatial navigation and episodic memory, operations that require neural activity to be organized across long durations of experience¹. Whereas location is known to be encoded by spatially tuned cell types in this brain region^2,3, little is known about how the activity of entorhinal cells is tied together over time at behaviourally relevant time scales, in the second-to-minute regime. Here we show that MEC neuronal activity has the capacity to be organized into ultraslow oscillations, with periods ranging from tens of seconds to minutes. During these oscillations, the activity is further organized into periodic sequences. Oscillatory sequences manifested while mice ran at free pace on a rotating wheel in darkness, with no change in location or running direction and no scheduled rewards. The sequences involved nearly the entire cell population, and transcended epochs of immobility. Similar sequences were not observed in neighbouring parasubiculum or in visual cortex. Ultraslow oscillatory sequences in MEC may have the potential to couple neurons and circuits across extended time scales and serve as a template for new sequence formation during navigation and episodic memory formation.

Fig. 1. Ultraslow oscillations in MEC neurons.

a, Neural activity was recorded through a prism from GCaMP6m-expressing neurons of the MEC in head-fixed mice running in darkness on a non-motorized wheel. Cartoon of a running mouse on the right created with BioRender.com. b, Stacked z-scored autocorrelations of single-cell calcium activity for one example session (484 neurons), plotted as a function of time lag. Neurons are sorted according to the maximum power of the PSD calculated on each autocorrelation separately, in descending order. c, PSD (left) calculated on the autocorrelation (right) of one example cell’s calcium activity. The dashed red line indicates the frequency at which the PSD peaks (0.0066 Hz). d, As in c but for another example cell. The PSD peaks at 0.0066 Hz and has harmonics at 0.0132, 0.0207 and 0.0273 Hz. e,f, As in c,d but for two example cells recorded using Neuropixels probes. The PSDs peak at 0.016 Hz (e) and 0.015 Hz (f). Source Data

Fig. 2. Ultraslow oscillations are organized into oscillatory sequences.

a, Raster plot of calcium activity of all cells recorded in the example session shown in Fig. 1b (bin size = 129 ms, n = 484 cells). Time bins with calcium events are indicated with black dots; those without calcium events are indicated with white dots. Cells were sorted according to their correlation values with one arbitrary cell, in a descending manner. The example sequence indicated in red is 121 s long. b, As in a but now with neurons sorted according to the PCA method. c, Projection of neural activity of the session in a,b onto the first two principal components of PCA (left), and the first two dimensions of a Laplacian eigenmaps (LEM) analysis (right). Time is colour coded. One sequence is equivalent to one rotation along the ring-shaped manifold. d, Raster plot as in b. The phase of the oscillation, overlaid in red, was used to track the position of the population activity on the sequence. e, As in b, but showing the z-scored fluorescence calcium signals. f, Raster plot of binarized spiking activity of all units recorded in one example session using Neuropixels probes (bin size = 120 ms, n = 469 units). Neurons are sorted according to the PCA method. g, Distribution of sequence durations across 15 oscillatory sessions over 5 mice (imaging data only; one mouse did not have detectable sequences; 421 sequences in total). Each count is one sequence. h, Distribution of ISI (406 ISIs in total across 15 oscillatory sessions). Each count is an ISI. During periodic sequences the ISI is 0. Note that the y axis has a log scale. Source Data

Fig. 3. Nearly all MEC neurons are locked to the oscillatory sequences.

a, Left, locking degrees of neurons from the session shown in Fig. 2a. Black dots indicate locked neurons; red dots indicate non-locked neurons; and grey dots show the 99th percentiles of the corresponding shuffle distributions, one per cell (458 out of 484 cells were significantly locked to the phase of the oscillation). Right, similar to left, but for mutual information (MI) between phase of the oscillation and count of calcium events. Black dots indicate MI and grey dots show the estimated bias in the MI. For all cells, the MI is larger than the bias. Neurons are sorted according to ascending locking degree (left) or MI (right). b, Box plot showing percentage of locked neurons over all oscillatory sessions (median = 94%; two-sided Wilcoxon signed-rank test, n = 15 sessions, P = 6.1 × 10⁵, W = 120). Red line shows median across sessions; blue bottom and top lines delineate bottom and top quartiles, respectively; whiskers extend to 1.5 times the interquartile range; and red crosses show outliers exceeding 1.5 times the interquartile range. c, Each row shows the tuning curve (colour coded) to the phase of the oscillation of one locked neuron in Fig. 2a (n = 458) calculated on experimental (left) and shuffled (right) data. d, Distribution of participation indexes across neurons in the session in Fig. 2a (n = 484 cells, left) and across all 15 oscillatory sessions (n = 6,231 cells, right). e, Anatomical distribution of neurons in the FOV of the session in Fig. 2a. Neuronal preferred phase is colour coded. Neurons in red are not significantly locked. Dorsal MEC on top, medial on the right. f, A two-dimensional histogram of differences in preferred phase between pairs of neurons for sequence no. 19 of the session in Fig. 2a, and their distance in the FOV. In the presence of travelling waves, high values along the diagonal would be expected. Normalized frequency is colour coded. Each count is a cell pair (n = 116,886 cell pairs for 484 recorded cells). Correlation = 0.0026, cutoff for significance = 0.0099. g, Distribution of correlation values between differences in preferred phase and anatomical distance in experimental data (blue bars, n = 421 sequences across 15 oscillatory sessions) and shuffled data (orange dotted line, n = 42,100, 100 shuffled iterations per sequence) (Methods). ***P < 0.001, **P < 0.01, *P < 0.05; NS, not significant (P > 0.05). Source Data

Fig. 4. The oscillatory sequences transcend periods of running and immobility.

a, Top, raster plot of one recorded session (520 neurons). Time bins in aquamarine indicate that the mouse ran faster than 2 cm s⁻¹. Second from top, expanded view showing 160 s of neural activity. Third from top, instantaneous speed of the mouse. Bottom, position of the mouse on the wheel. b, Probability of observing the oscillatory sequences given that the mouse was either running or immobile (median probability during running and immobility was 0.93 and 0.69, respectively; two-sided two sample Wilcoxon signed-rank test, n = 10 sessions over 3 mice, P = 0.002, W = 55). c, Fraction of immobility epochs with oscillatory sequences as a function of length of the immobility epoch (data are mean ± s.d.). For each length bin, the fraction of epochs was averaged across sessions. Orange, recorded data (n = 10 per length bin); blue: shuffled data (n = 5,000 per length bin, 500 shuffled realizations per session). Recorded versus shuffled data: P ≤ 2.62 × 10⁻⁶, 4.7 ≤ Z ≤ 47.5, two-sided Wilcoxon rank-sum test. d, Number of completed laps as a function of sequence number for one mouse. Each dot indicates one sequence. Dashed lines indicate separation between recorded sessions. Source Data

Fig. 5. The oscillatory sequences are not observed in PaS or VIS.

a,b, PSD (left) calculated on the autocorrelation (right) of calcium activity in one example cell recorded in PaS (a) or VIS (b). The PSDs peaked at 0.015 Hz (a) and 0.011 Hz (b). c,d, Stacked autocorrelations (as in Fig. 1b) for two example sessions recorded in PaS (c; 402 neurons) and VIS (d; 289 neurons). e,f, PCA-sorted raster plots (as in Fig. 2b) for two example sessions recorded in PaS (a,c) and VIS (b,d). Oscillation score and sequence score are indicated at the top. g, Number of sessions with and without oscillatory sequences in MEC (blue, 27 sessions), VIS (green, 19 sessions) and PaS (yellow, 25 sessions) based on oscillation scores and threshold defined from the MEC dataset (Extended Data Fig. 5d). Source Data

Extended Data Fig. 1. Histology showing imaging locations for each animal in the MEC group.

a. Left: Representative image indicating GCaMP6m expression in the superficial layers of the MEC upon local viral injection at postnatal day P1 (sagittal section). Images were acquired with a 20× objective mounted on a confocal laser scanning microscope LSM 880 (Zeiss), operated by ZEN 3 software (blue edition). Red inset, top right: 60× magnification of the most dorsal portion of the MEC. Bottom right: Fraction of MEC neurons (Nissl +) expressing GCaMP6m; data are shown for all 5 animals with MEC imaging. Data are presented as mean values, error bar indicates the S.D. calculated across multiple (n = 8) adjacent slices. Each dot represents one slice. b. Location of the ventro-lateral edge of the prism in stereotactic coordinates, and area of the FoV occupied by cells expressing GCaMP6m. Data are shown for each MEC-imaged animal. Mouse #59911 had no oscillatory sequences. c. Prism location in mice that underwent calcium imaging in MEC in the left hemisphere. Top: Maximum of 50 μm thick sagittal brain sections. For each of the 5 mice in (b), 3 sections, shown from lateral (left) to medial (right), were acquired with an LSM 880, 20×. A DiI-coated piano wire pin was inserted at the ventrolateral corner of FoV to enable identification of the FoV on histology sections. Green is GCaMP6m signal, red is DiI signal. Scale bar is 400 μm. The white stippled line encapsulates the superficial layers of MEC. The blue dot adjacent to the leftmost image of the series marks the location of the ventro-lateral corner of the prism. Bottom: estimated location of the FoV for two-photon imaging, projected onto a flat map encompassing MEC (brown outline) and parasubiculum (PaS, orange outline). The blue dot marks the location of the pin used to demarcate the most lateral-ventral border of the prism, while the green square inset is the microscope’s FoV. Inset image shows the maximum intensity projections of the FoV. Anteroposterior (AP), Mediolateral (ML), and dorso–ventral (DV) axes are indicated in panels (a) and (c). d. Micrographs of Cresylviolet stained sagittal brain sections from all 2 mice implanted with four-shank Neuropixels 2.0 silicon probes in the left hemisphere. Sections are organised from the most laterally placed shank(s) (left) to the most medially placed shank(s) (right). Mouse ID, shank number, and scale bar (1000 μm) are indicated next to each section. The brain of one mouse (#104638) was damaged during extraction, and parts of the MEC and cortex are missing from the section. Coloured arrows indicate MEC borders (dorsal, ventral) and the identified or estimated probe tip in the section. Black arrows indicate estimated dorsoventral range of the probe’s active recording sites (as indicated by the insert). For each section, inserts show the number of units recorded at each depth of the probe shank (histogram bin size = 60 μm). Note that the anatomical location of probe shanks can only be approximately estimated, and indicated unit locations are subject to measurement error, e.g., due to the shank tips exiting the cortex, the brain shrinking during perfusion and error in estimating the position of the tip of the probe. Stippled lines indicate borders between brain regions (MEC, medial entorhinal cortex; LEC, lateral entorhinal cortex; PaS, parasubiculum, HF, hippocampal formation; PoR, postrhinal cortex; VISpl, posterolateral visual area; TR, postpiriform transition area; CoA, cortical amygdalar area; PA, posterior amygdalar nucleus). D = dorsal; V = ventral; A = anterior; P = posterior. Source Data

Extended Data Fig. 2. Relationship between the oscillatory sequences and behavior.

a. Quantification of the animals’ behavior during head-fixation on the wheel. Duration of epochs of running (speed ≥ 2 cm/s, left) and immobility (speed <2 cm/s, right) for 10 oscillatory sessions over the 3 animals in which behavioral tracking was synchronized with imaging (1289 running bouts and 1286 immobility bouts in total). Each count is an epoch, and one epoch is obtained by concatenating consecutive time bins with the same behaviour (running or immobility, bin size = 129 ms). For each of the 10 sessions the smallest speed value was always 0 cm/s. The largest speed value ranged from 16.4 to 75.3 cm/s. The median calculated over the entire session ranged from 0 cm/s (in 4 out of 10 sessions) to 18.8 cm/s. Across the 10 sessions, the median of speed values was 0 cm/s (indicating that some of the animals spent much of the session time being immobile, yet those animals exhibited oscillatory sequences too, e.g. animal #60355, Extended Data Fig. 5a; see also Fig. 4a and c). The median speed during running epochs was 7.8 cm/s. The acceleration values ranged from −86.3 to 108.9 cm/s², with a median of 0 cm/s² for all the data as well as the running epochs specifically. b. Left: Schematic of the change in phase of the oscillation during immobility epochs that were longer than 25 s and that occurred during the oscillatory sequences. Right: 44 of these epochs from the same 3 mice as in (a). As in the schematic on the left, each line represents the progression of the phase of the oscillation (from –π to π rad) as a function of time. The start of each immobility epoch is aligned at t = 0, and the epoch lasts for as long as the line continues. Different epochs have different lengths, covering a range from 25 s to 258 s. For visualization purposes only the first 120 s are displayed (3 of the epochs were truncated; these had durations of 127.9 (first column, second row), 258.2 (third column, bottom row), 136.1 s (fourth column, second row)). Sudden transitions from π to –π rad reflect the periodic nature of the sequences. c. Number of completed laps on the wheel per sequence as a function of the sequence number after pooling sessions (range of completed laps on rotating wheel across 10 sessions = 10 to 1164 laps, median = 624 laps). Sessions are pooled for each animal separately (mouse #60584, 4 sessions; mouse #60585, 3 sessions; the third animal is shown in Fig. 4d). Each dot indicates one individual sequence. The dashed line indicates separation between sessions. A number of laps equal to 1 would indicate an approximate one-to-one mapping between the position on the wheel and the progression of one full sequence. d. To determine if sequences are associated with specific running speeds, we extracted all time bins participating in oscillatory sequences and calculated the distribution of observed speed values during those bins (blue bars; n = 167389 time bins concatenated across 314 sequences pooled over 10 oscillatory sessions, over 3 animals, bin size = 129 ms). This distribution was almost identical to the distribution of speed values observed during the full length of the sessions, which also included epochs without the oscillatory sequences (blue solid line, with and without oscillatory sequences; n = 238505 time bins across 10 oscillatory sessions, over 3 animals, bin size = 129 ms). e. As in (d) but for the distribution of acceleration values. There is no difference in the range of acceleration values during parts of the session with oscillatory sequences. f. Left: To determine whether the oscillatory sequences are modulated by onset of running we calculated the mean running speed during time intervals of 10 s right before and right after the sequence onset (one sample Wilcoxon signed-rank test on the difference between speed before and after sequence onset, n = 310  equence onsets over 10 sessions from 3 animals, p = 0.82, W = 25). Right: Same as left but only for sequences that were 10 s or more apart, i.e. for sequences belonging to different oscillatory epochs (one sample Wilcoxon signed-rank test on the difference between speed before and after sequence onset, n = 70 sequence onsets over 10 sessions from 3 animals, p = 0.12, W = 857). Note that there is no systematic change in speed after onset of sequences. Results remain unchanged if the analysis is repeated for 2 s windows before and after sequence onset (Analysis for all sequences: one sample Wilcoxon signed-rank test on the difference between speed before and after sequence onset, n = 310  equence onsets over 10 sessions from 3 animals, p = 0.82, W = 25; Analysis for all sequences that were 10 s or more apart, one sample Wilcoxon signed-rank test, n = 70 sequence onsets over 10 sessions from 3 animals, p = 1.0, W = 0). g–j. Examples of sections of sessions with increased speed after sequence onset (exceptions from the general pattern shown in (f)). Top of each panel: Raster plots, symbols as in Fig. 2a (bin size = 129 ms). Bottom of each panel: Instantaneous speed of the animal during the recording in the top panel. Length of the displayed section was 400, 1000, 400 and 500 s, respectively, for (g–j). Notice that while speed is higher after onset of the sequence in these examples, the increase of speed does not always occur right after sequence onset, but sometimes before (g,h), and sometimes tens of seconds after (i,j). Analyses were restricted to 10 oscillatory sessions in 3 animals, for which the behavioural tracking was synchronized to the imaging (Methods). Source Data

Extended Data Fig. 3. Examples of ultraslow oscillations in single cell calcium activity.

a. Autocorrelation of 15 example cells’ calcium activity (one per oscillatory session). b. PSD calculated on the autocorrelation of the example cell shown in (a). The dashed line indicates the frequency at which the PSD peaks. Note that the peak is at a frequency <0.1 Hz. c. As in (a) but for the signal obtained after the calcium activity was circularly shuffled (blue) or shuffled by destroying the inter calcium event intervals (red). Note that circularly shuffling the calcium activity preserves its periodicity. d. PSD calculated on the autocorrelations in (c). Blue indicates circularly shuffled data. Red indicates data that was shuffled by destroying the inter calcium event intervals. e. Mean z-scored autocorrelation calculated over all recorded cells in the session. Error bars indicate S.E.M. Black: Experimental data. Red: Shuffled data (obtained by destroying the inter calcium event intervals). f. Mean z-scored PSD calculated over all recorded cells in the session. For each cell the PSD was calculated on the autocorrelation of the cell’s calcium activity. Error bars indicate S.E.M. Color convention as in (e). Each row shows data from one oscillatory session (15 rows in total, each row corresponds to one oscillatory session). Animal number and session number are indicated at the top. Source Data

Extended Data Fig. 4. Oscillatory sequences shown by cell sorting based on correlation or dimensionality reduction.

a. Left: Because neural activity progresses sequentially, the time lag that maximizes the correlation between the calcium activity of pairs of cells increases with their distance in the correlation sorting. Sorting is performed as in Fig. 2a. Time lag is expressed in seconds, distance is expressed as the number of cells between the two cells in the sorting. Notice that for large distances (e.g. > 300 cells), the time lag to peak correlation is either larger than 60 s or close to zero. This bimodality is due to the periodicity of the MEC sequences. The dashed line indicates a linear regression (n = 301 cell pairs, $R^2=0.17$, $p=2\times {10}^{-14}$, two-sided t-test. The line was fitted to the intermediate samples to avoid the effect of the periodic boundary conditions). Right: The cross correlation between the calcium activity of pairs of cells is oscillatory and temporally shifted. Examples are shown for 3 cell pairs with different distances in the sorting based on correlation values. Orange: cells are 5 cells apart; purple: cells are 199 cells apart; green: cells are 401 cells apart. The dotted line indicates the time lag at which the cross correlation peaks within the first peak. Note that the larger the distance between the cells in the sorting, the larger the time lag that maximizes the cross correlation. b. Schematic representation of the “PCA method”. Principal component analysis (PCA) was applied to the binarized matrix of deconvolved calcium activity (“matrix of calcium activity”) of individual sessions by considering every neuron as a variable, and every time point as an observation. The first two principal components (PC1, PC2) were identified. In the plane defined by PC1 and PC2 (left), the loadings of each neuron defines a vector, which has an associated angle θ $\in [-\mathrm{\pi },\mathrm{\pi })$ rad with respect to the axis of PC1 (in the schematic, neuron N_i (orange) is characterized by an angle θ_i). Neurons were sorted according to their angles θ in a descending order (right). Cyan: neuron sorting before application of the PCA method. Orange: neuron sorting after the application of the PCA method. c. Projection of neural activity during the oscillatory sequences onto a low-dimensional embedding generated by the first two principal components obtained by applying PCA to the matrix of calcium activity of each session. Each plot shows one session; all 15 oscillatory sessions from the calcium imaging data set are presented. Time is color-coded and shown in minutes, and the temporal range corresponds to all concatenated epochs with oscillatory sequences in the session. Neural trajectories are often circular, with population activity propagating along a ring-shaped manifold. The ring-shaped manifold became even more salient when we applied a non-linear dimensionality reduction method (Laplacian Eigenmaps, LEM) instead of PCA to the data (Fig. 2c, right), suggesting that at least some of the data might lie on a curved surface. d. Oscillatory sequences are not revealed with a random sorting of the cells (first row) or when the PCA sorting method is applied to circularly shuffled data (second row). Oscillatory sequences similar to those of Fig. 2a,b (with correlation sorting or PCA method) are recovered when neurons are sorted according to non-linear dimensionality reduction techniques (UMAP, Isomap, LEM, t-SNE, third to sixth row). Each row of each raster plot is a neuron, whose calcium activity is plotted as a function of time (as in Fig. 2a). Every black dot represents a time bin where a neuron was active (bin size = 129 ms). e. Raster plot of calcium activity of the session presented in Fig. 2a. Neurons are sorted according to the PCA method. For calculating the sorting, only the first (top), second (middle) and third (bottom) third of the data was used. The portion of the data used for calculating the sorting is indicated in red. Otherwise, conventions are as in Fig. 2a. This visualization was extended to a quantification for all sessions. For each session we calculated the sortings using (i) all data, (ii) the first half of the data, (iii) the second half of the data. Next we calculated the correlation between the distances in the different sortings. If sortings obtained with different chunks of data preserve the ordering of the neurons, we would expect high correlation values. We compared the obtained correlation values with the 95^th percentile of a shuffled distribution obtained by shuffling the position of the cells in the sortings. When comparing sorting (i) vs. sorting (ii), (i) vs. (iii), and (ii) vs. (iii), all oscillatory sessions (15 of 15) were above the cutoff of significance (see Methods). The high correlation values obtained in these distance estimates provide support to the fact that using different chunks of data for sorting the cells unveils the same dynamics. f. Neuropixels recording showing ultraslow sequences without prior smoothing of the data. Same data as in Fig. 2f. While in Fig. 2f spike trains were first convolved with a Gaussian kernel of width equal to 5 s and next binarized according to the mean plus one standard deviation (Methods), here the spike trains are not convolved with a Gaussian kernel. The bin size is 120 ms. The threshold for binarization of the spike trains is equal to the mean + 1.5 standard deviations. Sorting and conventions as in Fig. 2f. Example session from animal #104638. Sequences are still visible. This session had an oscillation score of 1.0. In this session we identified 12 sequences of durations spanning 18–43 s. g. Oscillatory sequences from a Neuropixels recording in a different mouse than in (f) (and Fig. 2f). Top: Similar to Fig. 2f, but from mouse #102335 (n = 410 units). Bottom: Similar to (f), but for the same session as presented in the top panel, without prior smoothing of the data. This session had an oscillation score of 0.91 (see Methods). See comparable example sessions for calcium data in Extended Data Fig. 5a. In this session 9 sequences were identified, with durations ranging from 14 to 69 s. Source Data

Extended Data Fig. 5. Sorted raster plots for the complete MEC calcium imaging dataset.

a. PCA-sorted raster plots (as in Fig. 2b) for all analysed sessions across the 5 animals in which MEC population activity was recorded, sorted by animals and day of recording. Session numbering starts the first day of habituation on the wheel, with either 5 or 15 habituation sessions. One session was recorded per day, and recordings were conducted on consecutive days. Note that sessions had lengths of approximately 1800 s or 3600 s. Oscillation score and sequence score were calculated for each session separately and are indicated at the top right corner of every plot. Scores colored in green correspond to sessions with oscillatory sequences (see panel d), scores colored in red to sessions without oscillatory sequences. b. Left: Distance d between two neurons in the PCA sorting is calculated as the difference between the angles of the vectors defined by the loadings of each neuron on PC1 and PC2 with respect to PC1. The schematic shows the distance between two neurons, one in orange and the other in green. The length of the vectors is disregarded in this quantification. Right: Joint distribution of the time lag τ that maximizes the cross-correlation between the calcium activity of any given pair of neurons and their distance d in the PCA sorting. Color code: normalized frequency, each count is a cell pair. The increasing relationship between τ and d indicates sequential organization of neural activity. c. Example sessions with (top) and without (bottom) oscillatory sequences. These sessions were recorded in the same area of the MEC in the same animal, but on different days (Mouse #60355 in panel a). Left: Raster plots of the matrices of calcium activity. Right: Joint distributions of the time lag τ that maximizes the correlation between the calcium activity of any given pair of neurons and their distance d in the PCA sorting (as in panel b). Color code: normalized frequency, each count is a cell pair. Notice the lack of linear pattern in the session without oscillatory sequences. d. Left: Distribution of oscillation scores for calcium-imaging sessions recorded in MEC (27 sessions in total over 5 animals). Each count is a session. The oscillation score quantifies the extent to which single cell calcium activity is periodic, and ranges from 0 (no oscillations) to 1 (oscillations). Dashed line: Threshold used for classifying sessions as oscillatory (oscillation score ≥ 0.72) or non-oscillatory sessions (oscillation score <0.72). The threshold was chosen based on the bimodal nature of the distribution (no values between 0.27 and 0.72). 12/27 sessions exhibited scores between 0 and 0.27 (no oscillatory sequences), and 15/27 sessions exhibited scores between 0.72 and 1 (‘oscillatory sessions’). Right: List of sessions sorted by animal and number of sessions the animals experienced on the wheel. Session numbering as in (a). Red, sessions classified as not oscillatory; green, session classified as oscillatory. Source Data

Extended Data Fig. 6. Identification of individual sequences and characterization of the oscillatory sequences.

a. Top: Raster plot of the PCA-sorted matrix of calcium activity of the example session in Fig. 2a. Bottom: Phase of the oscillation calculated on the session presented in the top panel is shown in black, and phase of individual sequences is colored in cyan (bin size = 129 ms). During one sequence the phase of the oscillation traversed smoothly $\left[-\mathrm{\pi },\mathrm{\pi }\right)$ rad. We identified individual sequences by extracting the subset of adjacent time bins where the phase of the oscillation increased smoothly within the range $[-\mathrm{\pi },\mathrm{\pi })$ rad. First the phase of the oscillation was calculated across the entire session, second discontinuities in the succession of such phases were identified and used to extract putative sequences and third, putative sequences were classified as sequences if the phase of the oscillation progressed smoothly and in an ascending manner, allowing for the exception of small fluctuations (lower than 10% of 2π, e.g. as in the sequence at 500 s). Points of sustained activity were ignored. Fractions of sequences in which the phase of the oscillation traversed 50% or more of the range $\left[-\mathrm{\pi },\mathrm{\pi }\right)$ rad were also analysed (for example at the beginning of this session). b. Total number of individual sequences per session, across 15 oscillatory sessions. Animal number is color-coded. Note that 4 of 5 MEC calcium imaging animals had identifiable oscillatory sequences. c. Box plot showing mean event rate as a function of sequence segment for all 15 oscillatory sessions. Each sequence was divided into 10 segments of equal length, and for each sequence segment the mean event rate was calculated as the total number of calcium events across cells divided by the length of the segment and the number of recorded cells. Red lines indicate median across sessions, the bottom and top lines in blue (bounds of box) indicate lower and upper quartiles, respectively. The length of the whiskers indicates 1.5 times the interquartile range. Red crosses show outliers that lie more than 1.5 times outside the interquartile range. The mean event rate remained approximately constant across the length of the sequence. While a non-parametric analysis revealed an overall difference (n = 15 oscillatory sessions per segment, p = 0.0052, ${\mathrm{\chi }}^2=23.5$, Friedman test), the rate change from the segment with minimum to maximum event rate was no more than 18% and there were no significant differences in the event rate between pairs of segments (Wilcoxon rank-sum test with Bonferroni correction, p > 0.05 for all pairs). *** p < 0.001, ** p < 0.01, * p < 0.05, n.s. p > 0.05. d. Box plot of sequence duration, for the 15 oscillatory sessions. Note the relatively fixed duration of sequences in individual sessions. Box plot symbols as in (c). e. Sequence durations shown separately for each animal with oscillatory sequences (421 sequences in total over 5 animals, only 4 presented sequences). For each animal all oscillatory sessions were pooled. Sequence duration was heterogenous across sessions and animals. f. Left: Box plot of the standard deviation of sequence duration within a session, in experimental and shuffled data. The standard deviation of sequence duration is smaller in the experimental data (n = 15 oscillatory sessions, 7500 shuffle realizations where sequences were randomly reassigned to the 15 sessions, preserving the original number of sequences per session, $p=1.8\times {10}^{-7}$, Z = 5.08, one-tailed Wilcoxon rank-sum test). Right: Box plot of the ratio between the shortest sequence duration and the longest sequence duration for all pairs of sequences within and between sessions. This fraction is larger for sequence pairs in the within-session group (n = 15 oscillatory sessions, the mean fraction per session and group was calculated separately, $p=1.7\times {10}^{-6}$, Z = 4.64, one-tailed Wilcoxon rank-sum test). Notice that for each sequence pair, the larger this ratio, the more similar the length of the sequences are. Symbols as in (c). g. Sequence duration is not correlated with the number of recorded cells in the session (n = 421 sequences across 15 oscillatory sessions, ρ = 0.02, p = 0.64, Spearman correlation, two-sided t-test). Each dot is a sequence. Animal number is color-coded as in (b). h. Fraction of the session in which the MEC population engaged in the oscillatory sequences. Session length was 30 min for mice 59914 and 60355, and 60 min for mice 60584 and 60585. The fraction of session time with oscillatory sequences varied within and across animals. i. Duration of the longest epoch with uninterrupted oscillatory sequences. Only epochs that met the strict criterion of no separation between sequences were considered. Sequences could progress uninterruptedly for minutes in each of the animals and span up to 23 consecutive sequences. Source Data

Extended Data Fig. 7. Characterization of locking degree and participation index.

a. Consistency between two measures of phase locking for individual neurons. The locking degree was calculated for each cell as the length of the mean vector over the distribution of oscillation phases ([−π,π) rad) at which the calcium events occurred (bin size = 129 ms). The locking degree was consistent with the mutual information between the calcium event counts and the phase of the oscillation (bin size = 0.52 s). Scatter plots show the relation between the two measures, with each dot representing one neuron. Left: Data from the example session in Fig. 2a (n = 484 cells). Right: All neurons from all 15 oscillatory sessions are pooled (n = 6231 cells over 5 animals). Red dots indicate neurons that did not meet criteria for locking. The consistency between the two measures strengthens the conclusion that the vast majority of the neurons in MEC are locked to the oscillatory sequences. b. Distribution of preferred phases (the mean phase at which the calcium events occurred) in the population of locked neurons for all 15 oscillatory sessions. Black line indicates the preferred phases; red intervals indicate one standard deviation (calculated over the oscillation phases at which the calcium events of an individual cell occurred). Neurons are sorted according to their preferred phase in an ascending manner. Across the 15 oscillatory sessions, the smallest preferred phases ranged from −3.14 to −3.11 rad, and the largest preferred phase ranged from 3.08 to 3.14 rad, suggesting that the entire range of phases was covered. c. Phase preferences are distributed evenly across the MEC cell population. Left: The nearly-flat nature of the phase distribution is illustrated by comparing the entropy of the distribution of preferred phases in recorded (y axis) and shuffled data (x axis). H_ratio is the entropy of the distribution of preferred phases (calculated as in (b)) estimated from the data and divided by the entropy of a flat distribution (H_ratio = 1 if the distribution of preferred phases is perfectly flat, H_ratio = 0 if all neurons have the same preferred phase). Each point in the scatterplot indicates one session (15 sessions). Horizontal error bars indicate one S.D. across shuffled realizations, and are centered around the mean across shuffled realizations. The black dashed line indicates identical values for recorded and shuffled data. Animal number if color-coded. Notice the discontinuity in the y axis between 0 and 0.85. H_ratio is substantially larger for recorded data than for shuffled data. Right: Box plot of H_ratio for recorded and shuffled data. For each session the 1000 shuffled realizations were averaged (n = 15 oscillatory sessions, $p=6\times {10}^{-6}$, Z = 4.52, two-sided Wilcoxon rank-sum test). Red lines indicate median across sessions, the bottom and top lines in blue (bounds of box) indicate lower and upper quartiles, respectively. The length of the whiskers indicates 1.5 times the interquartile range. Red crosses show outliers that lie more than 1.5 times outside the interquartile range. d. Left: Box plot comparing locking degree for cells with an oscillatory frequency that was similar (relative frequency ~ 1) or different (relative frequency ≠ 1) from the sequence frequency in the example session in Fig. 2a (n = 48 cells in each group from a total of 484 cells in the recorded session, $p=3.4\times {10}^{-11}$, Z = 6.63, two-sided Wilcoxon rank-sum test). Right: As left panel but for the locking degree across all 15 oscillatory sessions, including the example in the left panel (n = 15 sessions over 5 animals, $p=2.8\times {10}^{-5}$, Z = 4.19, two-sided Wilcoxon rank-sum test). Ten per cent of the total number of cells was used to define each of the groups with similar (relative frequency ~ 1) and different (relative frequency ≠ 1) oscillatory frequency as compared to the sequence frequency. Relative frequency was calculated for each cell as the oscillatory frequency of the cell’s calcium activity divided by the sequence frequency in the session. Box plot symbols as in (c). Note that cells with relative frequency similar to 1 are more locked to the phase of the oscillation. For all percentages considered to define similar and different groups (5, 10, 20, 30, 40, and 50%) the p-values were significant. e. Histogram showing the distribution of single-cell oscillatory frequency divided by the sequence frequency of the session (n = 6231 cells pooled across 15 oscillatory sessions). A value of 1.0 indicates that single-cell and sequence frequency coincide. The left and right dashed lines indicate 25^th (0.52) and 75^th (1.08) percentiles respectively. Note that for approximately half of the data the oscillatory frequency is very similar at single-cell and population level. f. The oscillatory sequences remain visible after excluding increasing fractions of neurons and keeping only those with the lowest locking degree. Each row shows a PCA-sorted raster plot (left, rasterplot conventions as in Fig. 2b) and the corresponding joint distributions of the time lag τ that maximizes the correlation between the calcium activity of neuron pairs and their distance d in the PCA sorting (right, symbols as in Extended Data Fig. 5b). The fraction of included neurons is indicated on top of the raster plot. For building the raster plots, neurons were sorted according to their locking degree value and neurons with the highest locking degrees were removed. g. Examples of different participation degrees in 3 example neurons from the session in Fig. 2a. Top: PCA sorted raster plot of the calcium matrix shown in Fig. 2a. Calcium events from the neuron with high participation index (PI, 0.72) are highlighted in light blue, from the neuron with intermediate PI (0.56) in purple, and from the neuron with low PI (0.36) in orange. Bottom three panels: Z-scored fluorescence calcium signals as a function of time from the above neurons with high (top), intermediate (middle), and low (bottom) PIs. Colored arrows represent the time points at which the oscillatory sequences are at the neuron’s preferred phase. Notice how the neuron with high PI tends to exhibit a peak in the calcium signal for most of the sequences. Neurons with intermediate and low PIs demonstrate the same but to a lesser extent, with the calcium signal not peaking in each sequence. h. Similar to (d), but for the participation index. Box plot symbols as in (c). Left: Data from the example session shown in Fig. 2a (n = 48 cells in each group, p = 0.51, Z = 0.66, two-sided Wilcoxon rank-sum test). Right: As left panel but for data pooled across 15 oscillatory sessions. The mean participation index was calculated for each group (“relative frequency ~ 1” and “relative frequency ≠ 1”) and each session separately and the data was then pooled across sessions (n = 15 sessions, p = 0.56, Z = 0.58, two-sided Wilcoxon rank-sum test). For all percentages considered to define the similar and different groups (5, 10, 20, 30, 40, and 50%) the p-values were non-significant. *** p < 0.001, n.s. p > 0.05. Source Data

Extended Data Fig. 8. The oscillatory sequences are not topographically organized.

a. 2D histograms of differences in preferred phase between pairs of neurons and their anatomical distance in the FoV for all 15 oscillatory sessions (5 animals, of which 4 had oscillatory sequences). Preferred phases were calculated as the mean oscillation phase at which the calcium events occurred (after pooling all sequences in a session and not on each sequence separately; see Fig. 3f, g for one individual sequence). Each histogram was built using N*(N-1)/2 samples, where N is the total number of recorded cells in the session. One count is a cell pair, the color bar indicates normalized frequency. The absolute Pearson correlation values were calculated for each session, and ranged from 8.5 x 10⁻⁵ to 0.015. Only session 6 from animal #60585 (first row, fourth column) had a correlation value above the 95^th percentile of a shuffled distribution built by shuffling the preferred phases in the FoV (1/15, probability = 0.37, binomial probability distribution; not statistically significant at a chance level of 5%). For the participation index (not shown) the correlation values were also very small and ranged from 9.3 x 10⁻⁴ to 0.040. Out of 15 oscillatory sessions, 2 sessions (sessions 6 and 8 from animal #60584, correlation = 0.033 and 0.040 respectively) were classified as significant (2/15 sessions, probability = 0.13, binomial distribution, not statistically significant at a chance level of 5%). b. Analysis of similarity of preferred phases within spatial bins for one single example sequence (number 19) of the session presented in Fig. 2a. Similarity was calculated as the mean vector length (MVL) of the distribution of preferred phases in the spatial bin. In the presence of travelling waves, large MVL values in every bin are expected. Top: The FoV is binned into 6×6 bins, each of size 100 um x 100 um. The heat map shows the number of cells located within each spatial bin. Counts are color coded. Bottom: Each panel indicates a spatial bin in the FoV, and shows the shuffled distribution of MVL values obtained after shuffling the preferred phases in the FoV (histogram), the 95^th percentile of the shuffled distribution (dotted blue line), and the MVL calculated on experimental data (dotted red line). To have good statistics only spatial bins that had more than 10 neurons were included in the quantifications. The plots that are missing are for bins with 10 or fewer cells, as indicated in the heat map. When using 100 μm x 100 μm bins, only 17 bins had more than 10 cells. From the 17 bins, one was classified as having similar phases (1/17, probability = 0.37, binomial distribution, not statistically significant at a chance level of 5%); when using 200 μm x 200 μm, only one bin out of eight with more than 10 cells was classified as having cells with similar phases (1/8, probability = 0.28, binomial distribution, not statistically significant at a chance level of 5%). When all sequences across all calcium imaging sessions are considered (n = 421, 15 oscillatory sessions over 5 animals), the MVL values calculated on experimental data ranged from 0.0082 to 0.98 (the 95^th percentile MVL value was 0.3399, i.e. small), and were larger than the cutoff for significance in 121 out of 2448 spatial bins (121/2448, smaller than expected at a chance level of 0.05: 122/2448). This analysis was focused on the degree of similarity between preferred phases in spatial bins. In order to avoid small cell sample effects, we performed a second analysis based on the difference in preferred phases for all pairs of cells that were located within small neighborhoods in the FoV (Methods). We expected that in the presence of travelling waves the mean and median of the distributions of differences in preferred phases of cell pairs within small neighborhoods would be smaller than expected by chance. For neighborhoods of 50 μm, only 16 out of 421 sequences had a mean below the cutoff for significance (16/421, smaller than expected at a chance level of 0.05: 21/421), and 16 out of 421 sequences a median below the cutoff for significance (16/421, smaller than expected at a chance level of 0.05: 21/421). For neighborhoods of 100 μm, 16 and 19 sequences (out of 421) were below the cutoff for the mean and median, respectively (16/421 and 19/451, both below a chance level of 0.05: 21/421). For neighborhoods of 200 μm, 25 sequences were slightly above the cutoff for the mean and 18 were below the cutoff for the median (chance level of 0.05: 21/421). c. Similar to (b), but with spatial bins of 200 μm x 200 μm. For all sequences, the MVL values calculated on experimental data ranged from 0.0037 to 0.975 (the median of MVL values was 0.3105, i.e. small), and were larger than the cutoff for significance in 115 spatial bins out of 2392 (115/2392, smaller than expected at a chance level of 0.05: 120/2392). The lack of similarity in preferred phases within spatial bins is inconsistent with a coherent oscillation in that spatial bin, and therefore inconsistent with the presence of travelling waves. d. Top: Rasterplots showing one example sequence from the session in Fig. 2a (sequence #19). Y axis: Neuron #. X axis: Time (s). Each panel shows the same sequence, and a total of 150 s (the length of the illustrated sequence). Neurons that were active in one particular time bin are indicated in red. The visualized time bin is indicated at the top of each panel (bin size = 1 s). Middle: Anatomical distribution of the population activity in each of the time bins in the top panel (bin size is now 5 s). The FoV (600 μm x 600 μm) was divided into 50×50 square spatial bins. The total number of calcium events across cells in one spatial bin is color coded (yellow indicates high activity, purple no activity). The big red dots indicate the position of the center-of-mass (COM) of the population activity in that time bin. Bottom: Similar to the middle panel, but for one shuffle realization in which the position of the cells was randomly shuffled within the FoV. e. Quantification of the flow of the COM for the example sequence shown in (d). Cumulative distance travelled, quantified as the sum of the distances travelled by the COM between consecutive time points (bin size = 5 s), in experimental data (dotted red line), in shuffled data (blue histogram, built by shuffling the positions of the cells in the FoV 500 times), and the 5^th and 95^th percentile of the shuffled distribution (dotted blue and green lines, respectively). The data shows no significant difference from cumulative distances expected by chance. f. Quantification of the flow of the COM for all sequences. Cumulative normalized frequency of the cumulative distance travelled in experimental data (n = 421 sequences, orange) and the median of the shuffled distributions (n = 421 sequences, blue). Out of 421 sequences, 21 were below the cutoff for significance (21/421, at the chance level of 0.05: 21/421, bin size = 5 s). The results are similar when changing the temporal bin size used for the quantifications (23/421 for bin size = 1 s, 23/421 for bin size = 2 s, chance level of 0.05: 21/421). Source Data

Extended Data Fig. 9. Analysis of ensemble activation during the oscillatory sequences.

a. Schematic of calcium activity merging steps (data are not included in this panel). We began by sorting the neurons according to the PCA method. Next, in successive iterations, or merging steps, we added up the calcium activity of pairs of consecutive neurons (merging step = 1) or consecutive ensembles (merging step > 1). b. Participation index (PI) as a function of merging step (mean ± S.D.). Black trace, example session in Fig. 2a; red trace, all 15 oscillatory sessions. The more neurons per ensemble, the higher the participation index of the ensemble. Note that the participation index plateaus after 5 merging steps, which corresponds to approximately 10 ensembles in most of the sessions (two-sided Wilcoxon rank-sum test to compare the participation indexes in merging steps 5 and 6; Black trace: n = 30 PIs in merging step 5, n = 15 PIs in merging step 6, p = 0.23, Z = 1.20; Red trace: n = 15 PIs in merging step 5 and 6, PIs of each merging step were averaged for each session separately, p = 0.14, Z = 1.49). c. Schematic of the process for splitting neurons into ensembles of co-active cells. Neurons sorted according to the PCA method are allocated to 10 equally sized ensembles (color-coded). Note that the participation index plateaued after 5 merging iterations, consisting of approximately 10 ensembles depending on the session (panel b). d. To quantify the temporal progression of the population activity at the time scale at which the oscillatory sequences evolved, we calculated, for each session, an oscillation bin size. This bin size is proportional to the inverse of the peak frequency of the PSD calculated on the phase of the oscillation, and hence captures the time scale at which the sequences progress. The oscillation bin size is shown for each of the 15 oscillatory sessions (4 out of 5 animals, those that had oscillatory sequences). e. Schematic of the method used for quantifying temporal dynamics of ensemble activity. For each session and each ensemble we calculated the mean ensemble activity at each time bin (oscillation bin size). Only the ensemble with the highest activity within each time bin (red rectangle) was considered. The number of transitions between ensembles in adjacent time bins divided by the total number of transitions was used to calculate the transition matrices in (g). f. The ensemble with the highest activity in each time bin, indicated in yellow and calculated as in (e), plotted as a function of time for the example session in Fig. 2a. All other ensembles are indicated in purple. Notice that the transformation in (e) preserves the oscillatory sequences. g. Left: Matrix of transition probabilities between pairs of ensembles at consecutive time points. Rows indicate the ensemble at time point t, columns indicate the ensemble at time point t + 1. Data are from the example session in Fig. 2a (bin size = 15.12 s). Right: Same as left panel but for one shuffle realization. Transition probabilities are color coded. In the left diagram, note the higher probability of transitions between consecutive ensembles (increased probabilities near the diagonal), the directionality of transitions (increased probabilities above diagonal) and the periodic boundary conditions in ensemble activation (presence of transitions from ensemble 10 to ensemble 1). h. Box plot showing transition probabilities between consecutive ensembles for all 15 oscillatory sessions. The probabilities remain approximately constant across transitions between ensemble pairs (n = 15 oscillatory sessions per transition, p = 0.56, ${\mathrm{\chi }}^2=7.77$, Friedman test), and there were no significant differences between pairs of transitions (two-sided Wilcoxon rank-sum test with Bonferroni correction, p > 0.05 for all transitions). Transitions from ensemble 10 to ensemble 1 were equally frequent as transitions between consecutive ensembles, as expected from the periodic nature of the sequences. Red lines indicate median across sessions, the bottom and top lines in blue (bounds of box) indicate lower and upper quartiles, respectively. The length of the whiskers indicates 1.5 times the interquartile range. Red crosses show outliers that lie more than 1.5 times outside the interquartile range. i. Probability of sequential ensemble activation as a function of the number of ensembles that are sequentially activated (mean ± S.D.; For 3–9 ensembles: n = 15 oscillatory sessions over 5 animals, 7500 shuffle realizations; $p=5.4\times {10}^{-11}$, $1.0\times {10}^{-11}$, $5.9\times {10}^{-13}$, $4.5\times {10}^{-49}$, $0,0,9.0\times {10}^{-220}$ respectively, range of Z values: 6.45 to 59.18, one-tailed Wilcoxon rank-sum test). Orange, recorded data; blue, shuffled data. For each session, the probability of sequential ensemble activation was calculated over 500 shuffled realizations, and shuffled realizations were pooled across sessions. The recorded data contained significantly longer sequences than the shuffled control. Probability of sequential activation of ≥ 3 ensembles in recorded data = 0.62; probability of sequential activation of ≥ 3 ensembles in shuffled data = 0.27. j. Percentage of sessions with significant sequence score in sessions classified as oscillatory vs non-oscillatory. In MEC sessions with oscillatory sequences, 100% (15 of 15) of the sessions showed significant sequence scores, while in MEC sessions without oscillations, 41% (5 of 12) of the sessions demonstrated significant sequence scores. For corresponding raster plots, see Extended Data Fig. 5a. ***p < 0.01, ns p > 0.05. Source Data

Extended Data Fig. 10. Histology showing imaging location in animals with FoVs in parasubiculum and visual cortex.

a. Histological determination of prism location in mice that were implanted more medially, touching parasubiculum more than MEC. Top: Maximum intensity projection of 50 μm thick sagittal brain sections (sections acquired with an LSM 880, 20x). Three consecutive sections from the same mouse are shown, from the most lateral (left) to the most medial (right). Green is GCaMP6m signal, while red is DiI signal (used to demarcate ventrolateral corner of the prism, as in Extended Data Fig. 1). Scale bar is 400 μm. The white stippled line encapsulates the superficial layers of the parasubiculum (PaS). Dorsal PaS on top, layer 1 on the left. Bottom: Estimated location of the field of view (FoV) on a flat map encompassing MEC (brown outline) and PaS (yellow outline). The blue dot marks the location of the pin used to demarcate the most lateral-ventral border of the prism, while the green square inset shows the microscope FoV. Inset images show maximum intensity projections of the FoV. Dorsoventral (DV), and mediolateral (ML) axes are indicated. b. Location of the ventro-lateral edge of the prism in stereotactic coordinates, and area of the FoV occupied by cells expressing GCaMP6m for each PaS-imaged animal. c. Histological determination of imaging location in the visual cortex (VIS) of three mice that underwent calcium imaging. Green is GCaMP6m signal. Images are taken from coronal slices, and zoomed in on visual cortex (Scale bar is 100 μm; L1 at the top, L6 at the bottom). Dorsal pole of the brain is on top. Maximum intensity projection, LSM 880, 20x.

Extended Data Fig. 11. Lack of oscillatory sequences in parasubiculum and visual cortex.

a. Alternative sorting methods, as in Extended Data Fig. 4d, but applied to sessions recorded in the PaS (left) or VIS (right). The PCA sorting method applied to temporally shuffled data did not unveil oscillatory sequences (first row). No oscillatory sequences were recovered when neurons were sorted according to their correlation values (second row), or according to different dimensionality reduction techniques (UMAP, Isomap, LEM, t-SNE). Each row of each raster plot shows the calcium activity of a single neuron, with activity plotted as a function of time, as in Fig 2a. Every dot indicates that one neuron was active at one specific time bin (bin size = 129 ms). Sequence scores and oscillation scores are presented in Fig. 5e,f. b,c. Joint distributions of time lag τ that maximizes the cross-correlation between any given pair of neurons and their distance d in the PCA sorting (as in Extended Data Fig. 5b), applied to the recordings in Fig. 5e (PaS) and Fig. 5f (VIS). Normalized frequency is color-coded. Notice lack of linear relationship between d and τ, in contrast to Extended Data Fig. 5b. d,e. Projection of the neural activity onto the low-dimensional embedding defined by the first two principal components obtained from applying PCA to the matrix of calcium activity of the PaS session (d) and the VIS session (e) shown in Fig. 5e, f. Bin size = 8.5 s. Note lack of obvious ring topology. Time is color-coded. f. Transition probabilities between ensembles across consecutive time bins (bin size ~ 8.5 s, Methods) for the PaS example session in Fig. 5e (left) and the VIS example session in Fig. 5f (right). g. Probability of sequential ensemble activation as a function of the number of ensembles that are sequentially activated in PaS (left) and VIS (right) (mean ± S.D.). Orange, recorded data (25 PaS sessions; 19 VIS sessions); blue, shuffled data. For each session, the probability of sequential ensemble activation was calculated over 500 shuffled realizations, and shuffled realizations were pooled across sessions for each brain area separately. Probability is shown on a log-scale. In PaS the probability of long sequences was significantly larger in experimental data than in shuffled data (n = 25 PaS sessions, 12500 shuffled realizations; For 2 ensembles: p = 0.998, Z = −2.90; For 3–7 ensembles: range of p values: ${5.7\times 10}^{-4}$ to 0.036, range of Z values: 1.80 to 3.25, one-tailed Wilcoxon rank-sum test). This was not the case in VIS (n = 19 VIS sessions, 9500 shuffled realizations; For 2 ensembles: p = 0.106, Z = 1.25; For 3–6 ensembles: range of p values: 0.087 to 0.999, range of Z values: −3.34 to 1.36, one-tailed Wilcoxon rank-sum test). h. Percentage of sessions with significant sequence score (MEC oscillatory sessions: 15 of 15, PaS: 7 of 25; VIS: 1 of 19). The sequence score quantifies the probability of observing sequential activation of 3 or more ensembles. i. Distribution of oscillation scores for the entire calcium imaging data set, as in Extended Data Fig. 5d (19 VIS sessions over 3 animals, 25 PaS sessions over 4 animals, 27 MEC sessions of which 15 were classified as oscillatory, over 5 animals). Dashed line indicates threshold for classifying sessions as oscillatory with reference to the MEC data. Note that the bars for different brain regions sometimes overlap, and that bars are colored with transparency for visualization purposes (e.g. for sessions in PaS with oscillation score 0, the count is 24). j. Normalized distribution of the Pearson correlation values (absolute value) between the activity of cell pairs in VIS (green) and in PaS (yellow). Each dot indicates the mean across sessions (25 PaS sessions, 19 VIS sessions; all sessions in the data set were used, not only those with behavioural tracking synchronized to imaging), error bars indicate S.E.M. Probability is shown on a log-scale. k. Same as (j) but for the distribution of values of coactivity for all sessions recorded in PaS (yellow) and VIS (green). Coactivity was estimated for each session separately as the fraction of the recorded cells that was simultaneously active in 129 ms bins. Probability is shown on a log-scale. l. Cumulative probability of correlation values calculated between the calcium activity of one cell and the speed of the animal in that session for MEC (n = 4595 cells from 10 sessions, 3 animals), PaS (n = 6851 cells from 18 sessions, 3 animals), VIS (n = 6037 cells from 19 sessions, 3 animals). Only sessions for which the imaging data was synchronized to behavioural data were used (VIS-PaS: $p=3.15\times {10}^{-169}$, Z = 27.7; VIS-MEC: $p=1.05\times {10}^{-85}$, Z = 19.6, MEC-PaS: $p=5.16\times {10}^{-12}$, Z = 6.80, one tailed Wilcoxon rank-sum test). Calcium activity was more correlated with the speed of the animal in visual cortex than in MEC and PaS. Source Data

Extended Data Fig. 12. Ultraslow oscillatory sequences might serve as template for generating new activity patterns.

a. Schematic of the model. 500 input units (depicted in purple, on the left) are connected to an output unit (blue dot, on the right). Each arrow represents a connection, and there are 500 connections in total. The activity of each input unit is represented by a periodic Gaussian bump. The means of the Gaussians are temporally displaced such that, all together, input units fire in a sequence (the ‘template’). b. The weights between the input units and the output unit were trained such that the output unit reproduced a target activity. Two targets were considered: a ramp of activity, which is deterministic (left), and an Ornstein-Uhlenbeck process, which is stochastic (right). Both targets had a characteristic time scale of 100 s. c. Input (left) and output (right) activity for three different sequence lengths: sequences are very slow (top row), slow (middle) or fast (bottom) as compared to the targets. Left: Heat map of the activity of the input units as a function of time, in seconds. Blue indicates no activity, yellow indicates maximal activity. Top: Sequences are 400 s long. Middle: Sequences are 120 s long. Bottom: Sequences are 30 s long. Right: Output response corresponding to the three sequences regimes: very slow, slow and fast sequences. Target response is shown in blue, obtained response after training the networks using the sequences as input is shown in orange. Note that when the sequences have a time scale that is similar (middle) or slower (top) than the targets, the output unit can reproduce the desired target. d. Mean total error, calculated as the difference between the target and the obtained response after training, as a function of the input sequence length. Top: Target is the ramp of activity. Bottom: Target is the Ornstein-Uhlenbeck process. Source Data