Local transformations of the hippocampal cognitive map

Abstract

Grid cells are neurons active in multiple fields arranged in a hexagonal lattice and are thought to represent the "universal metric for space." However, they become nonhomogeneously distorted in polarized enclosures, which challenges this view. We found that local changes to the configuration of the enclosure induce individual grid fields to shift in a manner inversely related to their distance from the reconfigured boundary. The grid remained primarily anchored to the unchanged stable walls and showed a nonuniform rescaling. Shifts in simultaneously recorded colocalized grid fields were strongly correlated, which suggests that the readout of the animal's position might still be intact. Similar field shifts were also observed in place and boundary cells-albeit of greater magnitude and more pronounced closer to the reconfigured boundary-which suggests that there is no simple one-to-one relationship between these three different cell types.

Fig. 1. Local grid deformations.

(A) A representative grid cell (R2338) where a single field adjacent to the slanting wall shifts, with lesser displacements in some farther fields and none in distant fields. (Top left) Peak firing rates. Blue arrows indicate moving fields, * indicates a newly emerged field, and red arc, the slanting angle. Dashed line outlines grid structure in the rectangle. (B) Mean vector fields of all the recorded grid cells indicating average field shifts between pairs of successive (but not necessarily immediately following each other) geometrical enclosures; the vector tail specifies field position in the first enclosure. The first and the second enclosures are shown in dashed and solid lines, respectively. (C) (Top and left) Mean field shift across all transformations was inversely correlated with the distance to the slanting wall in x (top) and y (left) directions (ρ_x = 0.93, P < 10⁻⁵; ρ_y = 0.88, P = 0.004); color-coded maps show the mean range of grid field shifts in poly 129° to rectangle (top) and rectangle to poly 129° transformations (bottom). (Top left) Peak shift in cm. (D) Directional changes of fields in expanding (exp) and contracting (cont) enclosures. (Top) Black solid and dashed lines represent transformations to poly 160° and rectangular enclosures, respectively. (Bottom) Black solid and dashed lines represent transformations to poly 129° and poly 145°, respectively. Dashed red lines show directions perpendicular to the slanting walls, as well as vertical and horizontal walls.

Fig. 2. Uniform versus nonuniform grid rescaling.

(A) A typical grid cell with larger changes close to the slanting wall. Dashed lines indicate matched successive increments from right to left in exposed areas for homogeneity analysis. (B) Average grid rescaling in different transformations. Different colors represent different transformations specified in (C). (C) Average grid rescaling in x direction. (D and E) Simulated grid rescaling with nonuniform (D) and uniform (E) grid rescaling.

Fig. 3. Simultaneous changes in grid field positions.

(A) Twenty-four corecorded grid cells (R2405) from two different modules (ratio ~1.6). (Top left) Peak firing rate. (B) Maximum average field shifts versus grid scale of six different grid modules (five rats). Individual animals are shown with different colors (green, R2405). (C) Vector fields of cells in (A). (Top and bottom) Smaller and larger modules, respectively. Different colors correspond to different cells. Diamonds and open circles indicate fields that disappeared in poly 129°. (D) Similarity matrices of field shift directions (left) and magnitudes (right) between corecorded grid cells from five rats combined (R2405, R2383, R2338, R2375, and R2298). All transformations from poly 129° to a rectangle (and vice versa) and poly 145° to a rectangle (and vice versa) were included. GC-GC direction and magnitude similarity thresholds: 0.20 and 0.16, respectively. (E) Position decoding error decreases with the number of cells and is smaller in grids nonuniformly transformed in register (blue) compared with uncoupled ones (red). Black indicates decoding in the absence of any transformation; + indicates decoding accuracy of our largest data set (50 simultaneously recorded grid cells). (F) Systematic position decoding error is larger in nonuniformly (violet) compared with uniformly (brown) transformed grid cells close to the slanting wall. The tendency reverses close to the stable east wall.

Fig. 4. Local changes in place fields.

(A) Representative place cell with one of its fields shifting with the slanting wall while a second more distant field remains stable. (Top left) Peak firing rate. (B) Mean vector fields indicating the average place-field shifts between successive pairs of different geometrical enclosures. (C) Color-coded map showing the range of vector magnitudes. First and second enclosures are shown in dashed and solid lines, respectively. (Top left) Peak shift in cm. (D) Mean field shifts in all transformations (place cells, blue; grid cells, black) in x (top) and y (bottom) directions were more pronounced in place cells compared to grid cells, with the difference larger close to the slanting wall. (E) Color-coded map showing the range of vector directions.