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, \({{\rm{\chi }}}^{2}=7.77\), 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.

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