Extended Data Fig. 8: Time tuning across different individual bats, and analysis of pure time-cells.

(a-d) Data for individual bats. (a) Trial durations at each of the locations in the room (balls A, B and Start), for each of the 4 observer bats which we recorded. Horizontal lines in the box-plots show the median trial duration, boxes show the 25^th to 75^th percentiles, and vertical lines show the 10^th to 90^th percentiles. n = 340, 628, 861 and 174 trials on landing ball A, for each of the bats respectively; n = 123, 624, 839 and 119 trials on landing ball B, for each of the bats respectively; n = 439, 861, 1277 and 316 trials on the Start ball, for each of the bats respectively. Mean trial durations for landing ball A: 7.9, 7.7, 7.2, 8.8 s; mean trial durations for landing ball B: 9.1, 6.3, 6.9, 7.1 s; mean trial durations for landing ball Start: 14.5, 10.5, 10.4, 14.7 s. 10^th percentile trial duration for landing ball A: 4.0, 4.3, 3.6, 3.8 s; 10^th percentile trial duration for landing ball B: 5.4, 3.5, 4.0, 3.9 s; 10^th percentile trial duration for the Start ball: 3.9, 3.9, 3.9 4.5 s; 90^th percentile trial duration for landing ball A: 12.5, 11.6, 10.9, 14.2 s; 90^th percentile trial duration for landing ball B: 14, 9.7, 10.3, 10.6 s; 90^th percentile trial duration for the Start ball: 31.7, 17.8, 17.5, 26.1 s. Minimum trial duration for landing ball A: 0.4, 0.3, 0.6, 0.6 s; minimum trial duration for landing ball B: 0.8, 0.3, 0.4, 2.4 s; minimum trial duration for the Start ball: 0.4, 0.6, 0.4, 0.5 s. Maximum trial duration for landing ball A: 23.4, 22.7, 54.2. 59.6 s; Maximum trial duration for landing ball B: 23.3, 19.4, 43.4, 31.3 s; Maximum trial duration for the Start ball: 59.3, 57.1, 56.9, 59.8 s. (b) Cumulative functions showing the cumulative fraction of cells with a particular preferred-time for each of the bats no. 1, 2, 3 (the number of cells from bat 4 was low and hence we omitted it from this panel). (c) Ensemble temporal sequences for the 3 balls (columns), depicted similarly to main Fig. 1g, but plotted here separately for the 4 bats (rows). (d) Venn diagrams showing the distributions and overlap between place-cells and time-cells, separately for each of the 4 observer bats. (e-f) Analysis of pure time cells. (e) Top panel: Scatter plot showing a significant correlation between the preferred-time on landing ball A and the preferred-time on landing ball B, for all the time-cells which were significantly tuned on both A and B in session 1 (Pure time-cells; Spearman rank correlation ρ = 0.33, P = 2.8× 10^–2; Pearson correlation r = 0.38, P = 0.011; two-sided tests; n = 44 cells; the correlation remained significant also after removing cells with short preferred-time of less than 0.5-s on both balls A and B: Pearson r = 0.32, P = 0.041). Top right inset, Venn diagram illustrating the cell population analyzed here (pink area, time-cells tuned on A and B: ‘pure time-cells’; n = 44). Bottom panel: Scatter plot for the cell-shuffling of time cells tuned on A and B (‘pure time-cells’; n = 44) – plotting all possible combinations of the preferred-time of cell i on landing-ball A and the preferred-time for cell j on landing-ball B, where i ≠ j, for all the time-cells which were significantly tuned on both A and B in session 1 (dots were slightly jittered for display purposes). The Venn diagram illustrates the cell population for the shuffle: as in the top panel. Note that for the majority of the time-cells shown in the top panel (data), the difference between the preferred-times in locations A and B was < 1 s (61.4% of the cells [27/44] were within ±1 s from the diagonal – marked by the gray shaded area). This percentage is 2–3-fold larger than expected by chance – when compared to 2 types of chance levels: (i) Only 35.2% [333/946] of the shuffles in the bottom panel were inside the gray band, showing preferred-time differences of < 1 s between locations. (ii) Only 22% of the cells are expected to show differences < 1 s, assuming uniform distribution of differences (the gray shaded area divided by the total area of the graph = 22%). (f) Pearson correlations in panel e (top), after uniform subsampling. Shown is the distribution of Pearson correlations for 1,000 subsamples, which was computed as follows: In panel e (top), we binned the preferred times on ball A (x-axis) into 12 uniform time bins, 0.5 seconds each. Then for each subsample we chose randomly one dot from each bin, to form 12 pairs of preferred times on A and B, whose times on A were uniformly-distributed (by construction). We then calculated the Pearson correlation for these 12 dots. This subsampling procedure was repeated 1,000 times; the distribution of Pearson correlations for these 1,000 subsamples is shown here. The mean Pearson correlation of this histogram was < r > = 0.31. We found that 129 correlations out of the total 1,000 correlations showed P-value < 0.05, which amounts to 12.9% of the total subsamples. This fraction of P-values is significantly higher than the fraction of 5% that is expected by chance (one-sided Binomial test: P < 10^–300). These results further support the notion that pure time-cells preserved their preferred-time between balls A and B. (g) Analysis of contextual time-cells. Solid purple: distribution (kernel density plot) of the differences in preferred time for contextual time-cells in both experimental sessions 1 and 2, with differences computed within-ball – for both landing-balls A and B; that is, pooling ΔT preferred times for A₁ – A₂ and B₁ – B₂ (n = 39 cells × positions). Dashed purple: distribution (kernel density plot) of the shuffled ΔT preferred times between different landing-balls from different sessions: A₁ – B₂ and B₁ – A₂. These distributions were very significantly different (two-sided nonparametric F-test [Ansari-Bradley test]: P = 4.0 × 10^–17), indicating that contextual time-cells showed stability across sessions, and were more similar between different sessions of the same kind (landing on the same ball) than between different sessions of different kind (landing on different balls). (h-i) Comparing pure time-cells across the two sessions. (h) Distributions (kernel density plots) of the differences in preferred time for the group of 14 cells which were pure time-cells in both session 1 and session 2. Green, distribution of ΔT between preferred times on ball A versus ball B, for session 1 (A₁ – B₁; n = 14 cells; two-sided nonparametric F-test [Ansari-Bradley test] compared to cell-shuffling [dotted line]: P = 6.5 × 10^–2). Yellow, distribution of ΔT between preferred times on ball A versus ball B, for session 2 (A₂ – B₂; n = 14 cells; two-sided nonparametric F-test compared to cell-shuffling: P = 4.6 × 10^–2). The cell shuffling distributions (dotted lines) were calculated as the difference between the preferred times for cells i and j, where i ≠ j. (i) Distributions (kernel density plots) of the differences in preferred time for the group of 14 cells which were significant pure time-cells in both session 1 and session 2. Dark green, distribution of ΔT between preferred times in session 1 versus session 2, for ball A (A₁ – A₂; n = 14; two-sided nonparametric F-test [Ansari-Bradley test] compared to cell-shuffling [dotted line]: P = 8.0 × 10^–4). Light green, distribution of ΔT between preferred times in session 1 versus session 2, for ball B (B₁ – B₂; n = 14; two-sided nonparametric F-test: P = 2.9 × 10^–3). Note that ΔT is strongly and significantly concentrated around ΔT = 0 – suggesting high stability of the pure-time-cell tuning across the two sessions. (j-k) Matching the sample size between sets of neural data or between neural data and shuffles. (j) Distribution of P-values over 1,000 independent two-sided nonparametric F-tests [Ansari-Bradley tests], where each test was done between the distribution of real ΔT differences (ball A – B, in session 1) of the preferred-times for pure-time cells (n = 44) and randomly chosen 44 samples (neurons), taken from the distribution of ΔT of contextual time-cells. In each of the 1,000 tests the sample size of the pure time-cells and the contextual time-cells was thus identical (matched): n = 44. This distribution shows the percentage (y-axis) of the P-values for each of the 1,000 tests (x-axis); red line indicates the P = 0.05 cutoff. The y-axis was clipped at 10% for display purposes only. Note that 96.3% of the tests yielded P-values smaller then 0.05, indicating that the variance of the distribution of ΔT in pure time-cells was significantly smaller than the variance of the distribution in contextual time-cells – consistent with main Fig. 4c. (k) Similar to panel j, but here showing the distribution of P-values between the pure time-cells (n = 44) and 1,000 randomly chosen 44 samples taken from the cells-shuffling distribution of all cells. Note that 96.6% of the tests yielded P-values smaller than 0.05, indicating that the variance of the distribution of ΔT in pure time-cells was significantly smaller than the variance of the distribution for the cells-shuffling – again consistent with main Fig. 4c. (l) Distribution of ∆T for pure time cells on balls A and B, compared to a null distribution of shuffles for ∆T using the preferred times on ball A for even trials minus preferred times on ball A for odd trials (and likewise for ball B); plotted for all the pure time cells which exhibited a difference in preferred time of < 1 sec (n = 27 cells). The shuffle (null) distribution was significantly different from the data (two-sided nonparametric F-test [Ansari-Bradley test]: P = 1.4 × 10^–4); but nevertheless, the distributions of data (black) and shuffles (red) were clearly highly similar.