Figure 4. Grid cells encode both distance and time.

(A–E) Examples of treadmill activity of grid cells (A–D) and one non-grid cell (E) whose firing patterns are more consistently explained by distance (A–B) or time (C–E). For each neuron, the same firing activity is plotted both as a function of time since the treadmill started (left panels) and distance traveled on the treadmill (right panels). Blue, brown, and green ticks (and tuning curves) represent the slowest 1/3 of runs, middle 1/3 of runs, and fastest 1/3 of runs respectively. Numbers in blue, brown, and green indicate the peak firing rate in spikes per second (Hz) of the corresponding group of runs. The rows in the raster plots represent treadmill runs sorted in order of slowest speed (on top) to fastest speed (on bottom). (F, H) Deviance of two generalized linear models comparing the effect of removing time versus removing distance. The x-axis shows the deviance of the space + distance model from the full (space + distance + time) model, effectively measuring the contribution of time to the full model. The y-axis shows the deviance of the space + time model from the full (space + distance + time) model, effectively measuring the contribution of distance to the full model. Dots indicate deviances for either grid cells (F) or non-grid cells (H). Dots above the diagonal prefer distance; below the diagonal prefer time; above the horizontal red line are significantly influenced by distance; to the right of the vertical red line are significantly influenced by time. Thresholds for significance are based on a χ² test taking into account the number of parameters removed from each model (5 degrees of freedom), and adjusted using Bonferroni correction to account for multiple comparisons. (G, I) Strength of time versus distance coding measured as the difference between time and distance deviances for the grid cells shown in panel F (G) and the non-grid cells shown in panel H (I). See also Figures S3 and S4 and Tables S2, S3, and S4.