(A) First, we assigned letter identities (bold letters) to cells active on a trajectory. Spike raster of six WT and five Tau cells (same as those in Figure 3A) during a single running lap are plotted in time. Vertical lines: start and end times of the laps. (B and C) Second, we determined whether pairs of cells had stable firing relationships based on the stability of their cross-correlations (CCs). For examples, the CCs of a pair of WT (cell G and cell I in A) and a pair of Tau cells (cell A and cell H in A) are shown in (B). Each panel shows the color-coded CC for every lap and the bottom curve shows the lap-averaged CC. The color bar is shared by all panels in (B) and (C). For every lap, a CC was generated by cross-correlating the two cells' binned firing rates (bin size: 100 ms) in the lap. Note the stable peak locations of the lap CCs and the prominent peak of the lap-averaged CC for both the WT and Tau pairs in (B). For each cell pair, we computed a CC-stability, defined as the average correlation-coefficient between any two laps' CCs. To evaluate the significance of the CC-stability, we also computed a shuffled version of CCs (C) after the two cells' firing rates were circularly slid with independent, random time intervals (slide-shuffling). Note the inconsistent peaks in the lap CCs of both the WT and Tau pairs and consequently small CC-stability values in (C). For each cell pair, we generated 1000 shuffled CCs by slide-shuffling and therefore obtained 1000 chance level CC-stability values. A cell pair was considered to have a stable CC if (1) CC-stability is greater than the upper 1% of the chance level (p<0.01) and (2) there was a peak in the lap-averaged CC (the maximum value of the Z-transformed CC ≥ 1). Third, we ordered the cells in those pairs with a stable CC. For the pairs in (B), because the peak of the lap-averaged CC between cell G and I occurred at a negative time lag (*), we ordered the pair as IG. Because the peak between cell A and H occurred at a positive time lag (*), we ordered the pair as AH. If the peak of a pair occurred at exactly time lag 0, we randomly ordered the cells in the pair. (D) Finally, we constructed template sequences that agreed with all the ordered pairs (see ‘Materials and methods’). The derived template sequences for the WT (XIGQOZ) and Tau (FABHD) cells are shown. Spike raster of the cells, ordered according to the templates, are displayed in the time domain during the same five laps as in Figure 3A. Note the repeated occurrence of the template sequences across laps. This also shows that firing sequences of WT and Tau cells in the time domain were very similar to that in the space domain (Figure 3A).