Extended Data Fig. 9: Sweeps extend into never-visited space and persist in novel environments and during darkness.

a, Left: histogram of decoded directions (green bars) and head-direction occupancy (solid line) during an example linear-track session (top) and wagon-wheel session (bottom). Although the occupancy on the linear track is biased to the axes of the track (visible as peaks), the sampling of other directions was sufficient for subsequent decoding of the direction to either side of the track. Right: circular histogram of decoded directions in head-centered coordinates. Note that the internal direction signal is bimodally distributed around the head axis also in 1D environments. b, Theta cycle skipping during linear-track running. Heat maps show firing-rate temporal autocorrelograms (±500 ms) from all internal direction cells, grid cells and hippocampal cells (left to right). Each row corresponds to one cell; cells are sorted by theta-skipping index. Cells above the red arrowhead have positive scores and are thus classified as ‘skipping’ cells. One example autocorrelogram from a skipping cell is shown above each plot. The presence of cycle skipping in this task indicates representation of alternating directions and locations, incompatible with coding for the running path, but compatible with representation of unvisited space on either side of the track. c, Alternating internal direction and sweeps during linear-track running extracted from fitted latent variables. Left: raster plot showing spike times of internal direction cells (sorted by preferred internal direction) during a lap on the linear track. Right: decoded sweeps (lines) and internal direction (arrows) during four successive theta cycles during the lap (indicated by red square in left panel). Note that sweep and direction signals point to the same side of the track in an alternating pattern. d, Decoded direction and sweeps from consecutive theta cycles during a period of running along one of the open-field walls (white square). Sweeps and decoded direction are plotted as in Fig. 4d, with colour indicating time within sweep. Note that sweeps travel through the opaque walls of the arena, in alignment with the internal direction signal. e, Sweeps span a 2D map even when navigation is confined to 1D paths. Scatter plot of sweep terminal positions during two recording sessions on the WW maze (left panel: rat 25843; right panel: rat 25691). Note that density of sweep terminal positions is similar for visited and unvisited locations. f, More examples of grid-cell tuning to unvisited locations in the three environments (top to bottom: open field, wagon wheel, linear track). Each column corresponds to one cell and shows the position of the rat at the time of each spike (left) or the latent position from the LMT model at the time of each spike (right). g, Because the LMT model, like other dimensionality-reduction methods, finds dense representations of the input data, in principle, grid-like tuning could emerge as a close-packing artifact during fitting. As a control, an alternative single-cell model was used to infer out-of-bounds tuning for each cell independently. The activity of each cell was fitted by a GLM-based model in which the animal’s recorded position (black dot) was shifted along the axis parallel to internal direction (‘ID’) as a function of theta phase, according to a ‘shift curve’ which was fitted separately for each cell (see Methods for details). h, Firing-rate maps for a grid cell with respect to tracked 2D position (left), inferred by the LMT model (middle) and by the GLM-based single-cell model described in g (right) during an open field experiment (top row) and on the wagon wheel track (middle row). Each plot in the bottom row shows the positions of spatial receptive fields (coloured patches) of three co-recorded cells on the wagon wheel track. Spikes from each cell is plotted with different colours. Note that the latent fields identified by the LMT and GLM models preserve similar phase offsets between the grid cells, as expected based on extrapolation of their grid patterns. i, Hippocampal sweeps extend into never-visited locations. Left: heatmap of sweep end positions as inferred by the LMT model when fitted to hippocampal data from one example session. Note that many sweeps terminate outside the confines of the open field arena (red box). A total of 17.6 ± 1.3% (mean ± s.e.m.) of hippocampal sweeps in 5 rats terminated outside the open arena (red box). Right: hippocampal sweep endpoints (black dots) during theta cycles where sweeps from co-recorded MEC-parasubiculum cells terminated outside the open field arena (red box). Out-of-bounds hippocampal sweeps were detected in the majority (65.7 ± 6.4%, mean ± s.e.m.) of theta cycles in which simultaneously decoded MEC sweeps terminated outside the open field arena, significantly more often than during the preceding or following theta cycle (difference in fraction of outside sweeps: 11.6 ± 2.7%, p = 0.031, two-tailed Wilcoxon signed-rank test). j, Place-cell maps include never-visited space. Plots show firing-rate maps for three hippocampal place cells during an open-field session based on (left) original tracked position, (middle) latent position extracted from hippocampal activity, and (right) latent position extracted from co-recorded MEC-parasubiculum cells. Note that the two LMT models infer similar place fields outside the walls of the arena. k, Left-right-alternating sweeps during the first traversal through a novel environment. Top: decoded sweeps and internal direction during four consecutive theta cycles after 7 s of exploration of a novel circular open field (in complete darkness). Tuning curves from a succeeding recording session with room lights on (same arena) were used to decode position and direction in the novel, dark condition. The rat’s current position (white arrowhead) and running trajectory from the beginning of the session (grey line) is also shown. Note substantial spatial offset between the rat’s position and the left-right-alternating sweeps, which may reflect inaccuracies in the animal’s self-location estimate due to the novel and sensory-deprived conditions. Bottom: spikes from internal direction cells (black ticks), decoded internal direction (green) and tracked head direction (blue) during a 2-second epoch after 6 s of exploration. Note that left-right-alternating internal direction signals are expressed during the first traversal of the novel environment. l, Sweeps extracted from the LMT position latent variable during the novel open field session shown in k), during a 2.5-second epoch after 140 s of exploration (still in complete darkness). Alternating sweeps are visible, although the decoded position still deviates substantially from the rat’s actual running trajectory (in black), as in k. Credit: rat, scidraw.io/Gil Costa.