Path integration maintains spatial periodicity of grid cell firing in a 1D circular track

Abstract

Entorhinal grid cells are thought to provide a 2D spatial metric of the environment. In this study we demonstrate that in a familiar 1D circular track (i.e., a continuous space) grid cells display a novel 1D equidistant firing pattern based on integrated distance rather than travelled distance or time. In addition, field spacing is increased compared to a 2D open field, probably due to a reduced access to the visual cue in the track. This metrical modification is accompanied by a change in LFP theta oscillations, but no change in intrinsic grid cell rhythmicity, or firing activity of entorhinal speed and head-direction cells. These results suggest that in a 1D circular space grid cell spatial selectivity is shaped by path integration processes, while grid scale relies on external information.

Fig. 1

Predictions of grid cell firing based on allocentric distance, path integrated distance or travelled distance models. a Hypothetical trajectory of a rat in the circular track; red and green represent the first and the second lap, respectively. The total length of the track (471 cm) as well as cumulative 100 cm distances are indicated. b, c Hypothetical trajectory of a rat as a function of the position in the track. The blue values indicate the cumulative travelled distance (b) or the cumulative time elapsed (c), for each lap. The trajectories corresponding to the first and second laps are indicated in red and green, respectively. d Hypothetical position of grid cell firing fields relative to the track (left diagrams) or to the travelled path (right diagrams). Top row: according to the allocentric distance model, the firing fields keep the same position in the track across different laps (left), whereas their position relative to the cumulative travelled distance is highly variable from one lap to the other (right). Middle row: according to the path integrated distance model, the distance between the firing fields across laps is constant relative to the track (left), whereas their position relative to the animal path is highly irregular (right). Bottom row: according to the travelled distance model, firing fields are irregularly distributed around the track (left) but show a constant spacing across laps relative to the path travelled (right). e According to the time model, grid cells are expected to fire regularly based on a constant time step (right), and irregularly relative to the track positions (left)

Fig. 2

Grid cell activity is linearized in the track. a, b Activity of two grid cells recorded in the arena and in the track. Top row: from left to right, rat trajectory (in grey) with spike locations (red dots), color-coded rate maps (the peak of the firing rate is indicated) and 2D autocorrelograms. ‘g’ indicates the gridness score. Bottom row: from left to right, rat trajectory with spike locations, color-coded rate maps observed in the track, and rate maps in arena in which the external area (equivalent to the track) is highlighted. Note that there is no correspondence between the maps in the track and the peripheral area of the arena. c Average firing field variability (±SD) of grid cells in the arena and in the track. Data from individual cells are shown in grey. d diagrams showing rate plots of the activity of one hypothetical grid cell linearized in relation to the track position across three laps, according to the allocentric distance model (top, i.e. the position of the firing fields is stable across laps) and the path integrated distance model (middle, i.e. the position of the firing fields is shifted from one lap to the other). Bottom: activity from one grid cell recorded in the track; note that the position of the firing fields is consistent with the path integrated distance model. e Average correlation (±SEM) of grid cell activity across laps, according to the path integrated coding (i.e. the rate plot of one lap is shifted by a constant value with respect to the previous lap) and the allocentric coding (i.e. no shift between laps). Data from individual cells are shown in grey. *p < 0.05, paired t-test. f Scatter plots showing the relation between the phase offset of 20 pairs of simultaneously recorded grid cells in the arena and in the track. The Pearson correlation coefficient ‘R’ is indicated

Fig. 3

Grid cell regularity is based on path integrated distance—autocorrelation analysis. a Activity of one grid cell recorded in the arena (top) and in the circular track (bottom), with peak firing rate and gridness score (‘g’). b First row: activity of the grid cell (from panel a—track) linearized according to the path integrated distance (first column), the travelled distance (second column) and the time (third column). Second row: autocorrelation. Third row: Toeplitz matrix of the first 500 centimeters (corresponding to a complete lap). The color-coded matrix reveals regularity only for the path integrated distance. c Distribution of the average value of the first two peaks in the autocorrelation for all grid cells (Observed), as well as shuffled distribution obtained by resampling spike times from the same cells with a jitter procedure (Jitter; 400 permutations). Red lines indicate the ninety-ninth percentile for the shuffled data. d, e Distribution of the average value of the first two peaks in the autocorrelation of the linearized grid cell activity according to travelled distance (d) or time (e). Red lines indicate the ninety-ninth percentile for the shuffled data. Only one grid cell showed autocorrelation value above the statistical threshold, exclusively for the travel distance. f–h Example of one grid cell showing allocentric coding. f Activity of the cell in the arena (top) and the track (bottom). g Linearized firing activity (first row) of the cell according to the three distance models, autocorrelation (second row) and Toeplitz matrix. h Color-coded rate map of the cell activity linearized in relation to the track position (top row), and rate plots of the firing activity across four laps; note that the position of the firing fields is consistent with the allocentric firing model. i Average correlation (±SD) of grid cell activity across laps, according to the allocentric distance model (i.e. no shift between laps) for the 16 grid cells which do not show a path integrated distance firing and the 48 grid cells which show a path integrated distance firing. Data from individual cells are shown in grey. ***p < 0.005, paired t-test

Fig. 4

Grid cell regularity is based on path integrated distance-model fitting. a Average value (±SEM) of the fitting score (i.e. the sum of squared differences of the best fitting) for the path integrated distance, travelled distance and time model. ^§§§p < 0.001, repeated measure ANOVA. b Activity of one grid cell in the track from the real data (left) and reconstructed with best-fit parameters for each model (right ‘MODEL’). Real (left) or reconstructed (right ‘MODEL’) trajectory of the animal with spike locations. c Average spatial correlation (±SEM) between the reconstructed maps from each model and the observed maps. Dots represent values from individual grid cells. ^§§§p < 0.001, repeated measure ANOVA. d Scatterplot showing the relation between the distance (i.e. path integrated distance) calculated with two different methods (i.e. autocorrelations and model fitting); the Pearson correlation coefficient ‘R’ is indicated

Fig. 5

Environmental features influence grid cell activity. a Example of the activity of one grid cell linearized according to the path integrated distance model, in both light and dark conditions. Top row: firing rate; middle row: autocorrelation; bottom row: Toeplitz matrix. Note that the regularity is altered in darkness. b Average spatial correlation (±SEM) between the rate plots from all grid cells recorded in the two light sessions (light vs light) and in light vs dark sessions. Data from individual cells are shown in grey. ***p < 0.001, paired t-test. c Left: Diagram showing the two regions of the track in which the cue is visible (yellow) or not (grey). Note that an ambiguous zone (white) was excluded from the analysis, so that the areas of the visible-cue and non-visible-cue region are equivalent. Right: Correlation (±SD) between the integrated distance firing activity in the visible-cue and non-visible-cue region of the track. Data from individual cells are shown in grey. ***p < 0.001 paired t-test. d Ratio (±SEM) between grid cell field distance in the arena and the track; the distance in the track is calculated based on the path integrated distance model. Dashed line indicates a ratio of 1 (i.e. same field distance in the two environments). ^§§§p < 0.001, repeated measure ANOVA. Note that grid cell field distance is unchanged between large and small arenas, whereas it significantly increases in the large track compared to all other environments

Fig. 6

Theta rhythm in the track. a Autocorrelograms of the firing activity from one grid cell recorded in the arena and the track. Top row: trajectory with spikes locations. Bottom row: autocorrelogram of firing in 500 millisecond lags. b Average peak frequency (±SD) in the theta band (4–12 Hz) of the grid cell autocorrelogram. c Example of raw (top row) and filtered (4–12 Hz, bottom row) LFP recorded in the arena and the track. d Average peak frequency (±SD) in the theta band of LFPs recorded in the arena and the track. ***p < 0.001, paired t-test. e Average animal speed (±SEM) in the arena and the track. ***p < 0.001, paired t-test. f Scatterplot showing the relation between the arena/track speed ratio and the arena/track LFP theta peak ratio; the Pearson correlation coefficient ‘R’ is indicated with its significance (n.s.)