Extended Data Fig. 8: The oscillatory sequences are not topographically organized.
From: Minute-scale oscillatory sequences in medial entorhinal cortex
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 95th 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 95th 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 95th 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 5th and 95th 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).
