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.

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