Hippocampal place cells map terrain geometry independently of behavior

Abstract

How does the brain map uneven terrain? While spatial neurons such as hippocampal place cells and entorhinal grid cells have been extensively studied in flat, horizontal environments, the natural world is hilly and irregular. To investigate how place cells represent irregular terrain, we recorded from the hippocampus of rats foraging across either flat or ridged terrain. Place cell activity reflected terrain shape, consistent with a surface-bound cognitive map rather than a volumetric one. Place fields were elongated parallel to terrain contours, which contrasted with the movement biases of the rats, and are inconsistent with a predictive coding model. Reflecting the importance of terrain information, a third of the place cells exhibited repeating fields on each ridge. A boundary vector cell model of place cell firing replicated these results. These findings demonstrate that the cognitive map is sensitive to topography, bringing our understanding of spatial cognition closer to the real world.

Place cells map terrain geometry, not behavior, revealing a surface-based brain code for real-world navigation.

INTRODUCTION

To navigate successfully, animals construct an internal spatial representation of their surroundings, or a “cognitive map” (1). Place cells, found mainly in the hippocampus, and grid cells, found mainly in the medial entorhinal cortex, are thought to form the neural substrate of this map, with head direction cells providing a foundational orientation input (2–4). Boundary cells, found mainly in the subiculum [typically termed “boundary vector” cells (5)] and the entorhinal cortex [typically termed “border” cells (6)], also play an important role in defining both place and grid cell activity (7–10). How these spatial neurons, and thus the cognitive map, operate in flat, two-dimensional (2D) environments has been extensively investigated. However, very little is known about how these processes function when an animal has to navigate uneven terrain, despite the fact that most of the natural world is hilly and irregular (11, 12). We investigated this issue in the laboratory by testing how rats navigate a region of ridged terrain and how hippocampal place cells map its surface.

Terrain slope provides a convenient, continuously measurable gradient, enabling an animal to orient itself reliably even in the absence of visual cues. Unlike other navigation cues such as visual and olfactory stimuli, which may be obscured, kinesthetic and vestibular systems continually monitor the orientation of the head in relation to gravity and muscular exertion, keeping the body level and providing an uninterrupted navigational cue (13). Thus, encoding the slope of environmental terrain would be extremely advantageous for an animal. Evidence confirms that rats (14, 15), pigeons (16, 17), and humans (18, 19) can use the direction of terrain slope as an orienting cue. Consistent with this view, adding slopes to the arms of a radial-arm maze increases performance in rats (20). In addition to localization, minimizing energetic cost is another benefit of mapping terrain topography: Energy expenditure varies constantly across uneven terrain, and an efficient navigator must take this aspect into account when planning or comparing available routes. Elephants (21), cattle (22), and monkeys (23), for instance, all plan routes that avoid energetically costly changes in elevation.

Despite these extensive advantages, mapping uneven terrain presents a number of navigational challenges that are not encountered on flat surfaces (24), such as spatial irregularities in distance and direction. For example, routes can lead between the same spatial positions and cover the same distance in the horizontal plane but have very different path lengths due to their vertical components. In addition, directional movements across a curved surface no longer follow Euclidean geometry as the angles of a triangle can sum to more than 180° on the surface of a sphere or to less than 180° on the surface of a “saddle” (25). These movements are also noncommutative, meaning that the order in which they are made cannot be changed without affecting the destination (26–28).

As an animal traverses uneven terrain, spatial cells could overcome many of these challenges by mapping the environment in one of three ways: (i) volumetrically, mapping space with 3D firing fields that tile the environment vertically as well as horizontally (Fig. 1A, left) (29–31); (ii) earth-horizontally (planimetric), mapping space with a consistent map in the horizontal plane (relative to gravity) (Fig. 1A, middle) (32, 33); or (iii) in a surface-bound or terrain-specific way, mapping the features and distances across a physical surface (Fig. 1A, right) (34). Behavioral studies suggest that honeybees map space in a surface-bound way (35) while ants map space using an earth-horizontal representation (36). Very little is known about how mammals map hilly terrain; humans seemingly map space in a surface-bound way, even when violations of Euclidean geometry are clear (i.e., walking across the surface of a sphere) (37, 38). Evidence from rats and bats suggests that place cells map space volumetrically, with firing fields that extend in the horizontal and vertical dimensions regardless of terrain topography (29, 30). These results are consistent with functional magnetic resonance imaging results in humans navigating virtual reality environments (39). A volumetric map such as this would be advantageous for a flying or climbing animal because it allows accurate 3D distance estimation between any two points (24).

Fig. 1. Experiment hypotheses and procedure.

(A) Schematics of the different hypotheses tested. Shaded areas denote place fields. The mapping method used by an animal cannot be determined by the activity of cells on a flat environment (top) but can be revealed by changing the terrain (bottom). (B) Schematics of the Arena and Hillscape environments and example 3D trajectories in each. See fig. S1 for photos. Both environments were placed within the same 0.65-m-tall walls. Each ridge was 0.45 m tall. (C) Experiment procedure. (D) Example histological section showing electrode placement in hippocampus. See fig. S2 for all histology and a breakdown of the cells and sessions recorded per rat. (E) Example place cells, one per column, recorded in the two apparatus. The top two rows show spike and position plots; the bottom two rows show the corresponding firing rate maps. Dotted vertical lines denote the peaks of the ridges (black for trajectory plots, white for firing rate maps). A consistent color axis is used to depict each cell; bottom left text gives the max firing rate value. Cells 4 and 5 were corecorded. See fig. S3 for an additional 100 example cells.

However, when rats explore flat, planar environments, place cell activity is not consistent with a volumetric map and instead seems to be bound to the surface of the environment (40–42). This finding suggests that place cells do not map space volumetrically during navigation across surfaces—the most common situation for a surface-bound animal. In addition, while rat and bat grid cells exhibit hexagonal grid firing patterns during navigation across flat surfaces (43, 44), this pattern is lost in rat grid cells during volumetric navigation (45) and is not apparent in the medial entorhinal cortex neurons of flying bats (46). This loss of periodicity may also underlie a loss of function in 3D environments, even in mammals adapted for flying, although this issue has yet to be tested. Consistent with this, grid cell activity on sloped surfaces is also indicative of a surface-bound map, not a volumetric one (33, 34). Similarly, some studies with head direction cells indicate that they map space in a surface-bound way—within the animal’s plane of motion (47), although others have argued for a more volumetric representation in mice [(48–50) for reviews].

One possibility for the disparity in these results is that while surface-dwelling animals can develop volumetric spatial maps, these maps represent an extemporary adaptation of surface-mapping processes rather than a well-developed navigation system. This view is supported by the finding that, in a volumetric space, rat place cells map the vertical dimension using the same rules and properties as the horizontal plane, but with lower accuracy (29). In this view, place cells likely do not map terrain topography in an earth-horizontal or volumetric way but instead encode features of the terrain salient to the animal [Fig. 1A, right; (51)]. This terrain-specific (surface-bound) hypothesis makes the minimal prediction that altering the geometry of the navigable surface will induce global remapping, without making a priori predictions about specific place-field size, orientation, or repetition.

One way terrain features may be reflected in place cell activity is through subicular boundary vector cell (BVC) and entorhinal border cell inputs (5, 6) (collectively “boundary cells”). Boundary cells fire in relation to environmental boundaries, such as vertical walls, at a specific distance and allocentric direction from an animal. Computational modeling highlights boundary cells as a potentially foundational spatial input to place cells (7, 9, 52). However, if boundary cells respond more generally to terrain features, such as slopes, their inputs to place cells could also drive terrain-specific mapping. Evidence for this more general activity has been reported previously (53). Alternatively, a more recent model of place cells, the successor representation (SR) model (54, 55), posits that place cell activity reflects a predictive representation of the animal’s potential future states given its current state and past experience. Because animals generally choose paths through their environment that minimize energy expenditure (i.e., walking around rather than climbing up a cliff), changes in terrain topography often lead to changes in the transition probabilities between neighboring locations (i.e., locations at the top and bottom of a cliff become dissociated), which could also drive mapping based on terrain-specific movement statistics.

However, to date, no assessment has been made of how place cells map curved or uneven surfaces [but see (56) for a computational model]. To address this issue, we recorded the activity of hippocampal place cells as rats explored a horizontal, flat arena or a curved (quadric) surface in 3D space: a ridged terrain (“Hillscape”) that occupied the exact same room and position (Fig. 1B). This approach allowed us to differentiate volumetric from surface-bound maps and probe what information, if any, about terrain topography is incorporated into these maps. Consistent changes in the animals’ path statistics also allowed us to determine whether terrain-specific activity was the result of the physical environment, and thus boundary cell inputs, or trajectory statistics that would indicate a SR account of place cell activity.

We found that place cells completely remapped between the flat arena and Hillscape. We did not find evidence for earth-horizontal or volumetric coding. Instead, place cells mapped the Hillscape with more numerous but smaller firing fields that were consistently elongated parallel to the terrain’s contours. In contrast, animals consistently moved orthogonally to terrain contours when climbing slopes but parallel to them when moving along the ridge peaks and valleys. In addition, many place cells exhibited repeating firing fields in locations of similar terrain topography, even for locations otherwise unambiguous in 3D space. These results are inconsistent with the SR model, which would predict place cell firing biases that reflect behavioral biases. Instead, our results support a “geometric” model where place cell firing is driven not only by environmental landmarks and boundaries, such as walls and precipices, but also by terrain features such as slopes. We show that each of the observed results (place field repetition, place field elongation, and remapping) is explained by this model.

Together, these results suggest that (i) the cognitive map is highly sensitive to topographical cues, (ii) this information is encoded in the activity of hippocampal place cells, and (iii) boundary cells may be more generally sensitive to terrain shape than previously thought.

RESULTS

Place cells were recorded as rats foraged across uneven terrain

Of 653 pyramidal neurons, we recorded 519 (79.5%) hippocampal (dCA1) place cells in five female Long-Evans rats, across 24 recording sequences. Rats initially foraged across a horizontal arena (3 m by 1.5 m with 0.65-m-high walls; Fig. 1B and figs. S1 and S2, A to D). We then switched the flat floor for an uneven surface composed of three identical sinusoidal ridges, or Hillscape (Fig. 1B and fig. S1). Intra- and extramaze cues, floor color and texture, walls, and lighting were identical between the two environments. These recordings were made in an “A–B–A” format: Rats were recorded first in the horizontal arena (“Arena 1”), followed by the Hillscape, and then a second session in the horizontal arena (“Arena 2”; Fig. 1C). Animals were tracked in three dimensions throughout the experiment (Fig. 1B). The proportion of active pyramidal cells that met our place cell criteria in Arena 1 (433 of 559; 77.5%) did not differ significantly from the Hillscape (471 of 596, 79.0%; Χ² = 0.4, P = 0.54, chi-square test). Electrodes targeted the dCA1 pyramidal cell layer (Fig. 1D and fig. S2E), and place cells exhibited firing fields in at least one of the two environments (Fig. 1E and figs. S2, C and D, and S3).

Place cells remapped when terrain topography changed

Correlations between rate maps from the first and last arena sessions were very high and differed significantly from a shuffle (Cliff’s delta = 0.94, P = 0.001, permutation test, see “Permutation tests” and “Cliff’s delta” sections; Fig. 2A) confirming that cells were recorded stably throughout the sessions. Correlations between the first half and second half of each session also confirmed that cells were spatially stable within each environment (Arena 1 versus shuffle, Cliff’s delta = 0.93, P = 0.001; Hillscape versus shuffle, Cliff’s delta = 0.98, P = 0.001; Fig. 2B), and this result did not differ between the environments (Arena 1 versus Hillscape, Cliff’s delta = −0.06, P = 0.14; Fig. 2B).

Fig. 2. Place cells formed a new map for the uneven terrain.

(A) Top: Firing rate maps for two example cells, one per row. Bottom: Probability density function (PDF) of Pearson correlation r values between the two environments, computed for all place cells. (B) Top: Firing rate maps for an example cell, in the first half and second half of the first Arena and Hillscape sessions. Bottom: PDF of Pearson correlation r values between the first half and second half for the two environments, computed for all place cells. (C) Scatter plot of the average firing rates in each environment. Firing rate 1 and 2 correspond to the environments specified by the text, respectively. Text also gives the result of Pearson’s correlations. (D) Total number of firing fields expressed per cell as a proportion of all place cells. Text gives the result of a Kolmogorov-Smirnov test. (E) Colored markers represent cells, black markers and lines denote mean ± SD, and horizontal lines denote significant post hoc comparisons. Here and throughout: ^∗P < 0.05, ^∗∗P < 0.01, ^∗∗∗P < 0.001. Total number of place fields per square meter in each environment and a representative cell exhibiting more firing fields in the Hillscape than in the Arena. “Flattened” firing rate values are calculated using maps projected onto the surface of the Hillscape rather than the xy plane. (F) Size (radius of a circle with the same surface area) of place fields in each environment. (G) An exemplar schematic of firing fields in each environment given the data in (E) and (F). (H) Surface area of each environment covered by place fields for all place cells. (I) Spatial information content (z-scored relative to 100 shuffles) of all place cells in each environment. n.s., not significant.

In an earth-horizontal model, we would expect place cells to exhibit firing fields in the same x-y locations regardless of terrain topography and thus exhibit the same fields (as seen from above) in the Arena and Hillscape (Fig. 1A, middle). However, spatial correlations between Arena 1 and the Hillscape were significantly lower than between the two arena sessions (Cliff’s delta = 0.91, P = 0.001; Fig. 2A) and were centered on zero (median r = 0.04), consistent with cells forming a distinct spatial map for the Hillscape through “remapping” (57). However, this distribution was significantly shifted to the right of a shuffled distribution (Cliff’s delta = 0.28, P = 0.001; Fig. 2A), suggesting that a subset of activity remained similar between the two environments.

The small rightward shift in the correlations between Arena 1 and the Hillscape compared with the shuffle distribution could be evidence of weak earth-horizontal coding; however, in a volumetric model, we would also expect spatial firing to remain similar when the rat occupies the same x-y-z positions (Fig. 1A, left). To test this possibility, we compared place cell activity only in regions of the Arena and Hillscape that overlapped in 3D space (fig. S4A: “volumetric overlap”). Spatial correlations remained low, consistent with remapping (fig. S4B). We also did not find evidence for a surface-bound map anchored to the environment walls or corners (fig. S4B). Together, these results suggest that cells formed a distinct spatial map for the Hillscape, even in overlapping positions, which in a few cases was more similar to the Arena than would be expected by chance (see fig. S5 for examples of cells with high interenvironment correlations).

Uneven terrain was mapped differently to a flat surface

Place cells formed a distinct spatial map in the Hillscape, indicating global remapping. While perhaps unexpected, this result is consistent with previous experiments testing sloped, planar environments (40, 41). We next asked whether place cells map uneven terrain in the same way as a flat surface by comparing the activity of place cells between Arena 1 and the Hillscape. On average, 63.6% of cells active in one environment were also active in the other environment (fig. S2, C and D), a value that is consistent with global or “complete” remapping (58–60). Cells also exhibited similar firing rates between environments (Fig. 2C). Looking at broad spatial characteristics, place cells exhibited more fields per cell on average in the Hillscape (Arena 1 mean = 1.8, Hillscape mean = 2.7 fields per cell; D = 0.362, P = 6.0 × 10⁻³⁰, Fig. 2D). To account for the increased surface area of the Hillscape, we projected the animal’s path and place cell activity onto the surface of the Hillscape and then “flattened” or “unrolled” this activity into a flat projection (“Firing rate maps” section). After flattening, the increased number of place fields was still apparent [F(2,1372) = 91.6, P = 4.5 × 10⁻³⁸, η² = 0.12; Fig. 2E; results of multiple comparisons in figure]. The effect also remained if cells with a high repetition score (described below) were excluded [Arena 1 mean ± SEM = 0.43 ± 0.01, Hillscape = 0.56 ± 0.30, fields/flattened m²; F(2,1080) = 60.2, P = 1.7 × 10⁻²⁵, η² = 0.10]. The fields exhibited in the Hillscape were also significantly smaller [F(2,1372) = 84.0, P = 3.97 × 10⁻³⁵, η² = 0.11; Fig. 2, F and G] and covered less surface area than in the flat Arena [F(2,1372) = 7.2, P = 7.4 × 10⁻⁴, η² = 0.01; Fig. 2H] although this latter effect was mild. In both environments, fields closer to physical walls were smaller than ones in the center of the environment, although this relationship was reduced in the Hillscape (fig. S6, A and B) [see also (61)]. Because fields were both smaller (which would lead to an increase in spatial information content) and more numerous (which would lead to a decrease in information content), the spatial information content of place cell activity in the Arena and Hillscape remained largely the same [Arena 1 median = 1.5 bits/s, Hillscape median = 1.3 bits/s, F(2,1372) = 2.8, P = 0.062, η² = 0.004; Fig. 2I]. Together, these results suggest that place cells not only formed distinct maps for the two environments, but their firing fields also exhibited different characteristics in the Hillscape when compared with the flat arena.

Place fields aligned to both geometry and terrain

To investigate more specifically how place cell activity is influenced by terrain shape, we compared the geometric properties of firing fields (shape and orientation) between Arena 1 and the Hillscape. Place fields in both environments were often elongated (Fig. 3A), and in the Arena, this elongation was most often parallel to the walls of the environment, especially the longest wall (Fig. 3B; orientation of 0°), an effect reported in previous studies (29, 61). Despite the unchanged geometry of the outer walls, fields in the Hillscape were more often elongated along the opposite axis, i.e., parallel to the ridge contours (Fig. 3B; orientation of ±90°). In addition, in the Arena, place fields close to physical walls (<20 cm) were more elongated than ones in the center of the environment (fig. S6C) [see also (61)]. This relationship was not observed in the Hillscape (fig. S6D).

Fig. 3. Place fields were elongated parallel to the local terrain.

See “Place field characteristics” and “Anisotropy analyses” sections. (A) Elongation of place fields in both environments. Top schematics show an ellipse with the corresponding elongation. (B) Orientation of place fields in both environments. Top schematics show an ellipse with the corresponding orientation. (C) Anisotropy of all place fields as a function of the position of their center of mass, binned and smoothed with a boxcar filter, plotted according to terrain shape. Red denotes that fields were oriented parallel to the short wall (or hill tops) on average, blue denotes elongation parallel to the long wall. (D) Behavioral anisotropy: The difference in time spent moving parallel to the y and x axes divided by their sum, averaged across all sessions. Red denotes that animals moved parallel to the short wall (or hill tops) on average, and blue denotes movement parallel to the long wall. Behavioral anisotropy matches place field anisotropy in the Arena while the pattern differs in the Hillscape. (E) Boundary anisotropy: the weighted angle of local boundaries at every location (see “Anisotropy simulations” section); this result matches very closely place field anisotropy but only in the arena. (F) Same as (E), but when ridge tops and bottoms are included as boundaries; this result matches place field anisotropy in both environments.

To quantify this effect spatially, we defined the longest wall of the two environments as the x axis and the shorter wall as the y axis. We then calculated a “field anisotropy” score for each place field as its length along the y axis minus its length along the x axis divided by the sum of these values (see “Anisotropy analyses” section). This score approaches +1.0 when a field is elongated parallel to the y axis, −1.0 when a field is elongated parallel to the x axis and 0.0 when a field is not elongated at all. Field anisotropy, averaged across all place fields in 32-mm² spatial bins, can be seen in Fig. 3C, where the relationship between field orientation, field elongation., and wall orientation is immediately apparent. Fields in the Hillscape were overwhelmingly oriented along the y axis—parallel to the ridge contours and perpendicular to their slopes.

Terrain acts as a geometric input to place cells

What is driving place field anisotropy? An increasingly popular model of place cell activity, which predicts field elongation parallel to boundaries, is the SR model (54, 55). This model posits that place cells encode a predictive representation of the animal’s potential future states given its current state. Consequently, locations that often lead to convergent future locations should be represented more similarly than ones that lead to divergent future locations. Because animals tend to move parallel to walls upon encountering them (62, 63), positions next to a wall are expected to be represented similarly, leading to the expansion of fields alongside walls (54, 55). As reported previously (29) in the Arena, rats indeed moved parallel to the walls (Fig. 3D, left, and fig. S8).

To quantify this effect spatially, we defined the longest wall of the two environments as the x axis, and the shorter wall as the y axis. We then calculated a “behavioral anisotropy” score as the time spent moving parallel to the y axis minus the time spent moving along the x axis divided by the sum of these values, for each 32-mm² spatial bin (“Anisotropy analyses” section). Similar to our place field anisotropy score, this value approaches +1.0 when an animal’s movements are mainly parallel to the y axis, −1.0 when they are mainly parallel to the x axis, and 0.0 when there is no movement bias. In the Arena, the resulting behavioral anisotropy map very closely approximates place field anisotropy (Fig. 3D, left versus Fig. 3C, left; Pearson’s r = 0.89). However, in the Hillscape, behavioral biases were bimodal, with rats moving parallel to the y axis along the ridge peaks and valleys and parallel to the x axis when climbing the ridge slopes (fig. S8), leading to a much weaker correspondence between behavior and place field biases (Fig. 3D, middle versus Fig. 3C, middle; Pearson’s r = 0.58). Thus, place field elongation is not comprehensively explained by behavioral biases, in disagreement with the predictive map theory.

Another model of place cell activity that predicts field elongation parallel to boundaries is the BVC model (9, 52). This model posits that place cell activity is largely informed by BVCs in the subiculum and border cells in the medial entorhinal cortex (5, 6) (collectively “boundary” cells). These boundary cells fire in relation to environmental boundaries at a specific distance and direction from an animal and thus exhibit fields that extend alongside them. Place cells modeled using these boundary cells as an input also often exhibit firing fields that are elongated parallel to environmental boundaries (9, 64). We hypothesized that anisotropy in both the Arena and Hillscape environments could be explained by a combination of geometry and terrain. As an initial test, for each position, we calculated the anisotropy of local boundaries at every position, using an approach inspired by the BVC model (see “Anisotropy simulations” section). Including only physical walls as boundary elements resulted in a boundary anisotropy map that very closely approximated place field anisotropy in the Arena but not the Hillscape (Fig. 3E versus Fig. 3C; Pearson’s r = 0.92 and 0.63, respectively). However, when the tops and bottoms of the ridges were included as additional boundary elements, boundary anisotropy more closely matched observed place field anisotropy in both the Arena and Hillscape (Fig. 3F versus Fig. 3C; Pearson’s r = 0.92 and 0.93, respectively). This result indicates that geometry and terrain inputs could explain the elongation observed in our environments, if terrain topography is processed by the brain in a similar way to vertical walls.

Place cells encode terrain topography

We next explored whether there was any additional evidence that terrain topography is interpreted similarly to geometrical information by the brain. Can other firing properties generally attributed to geometry be extended to terrain topography? One intriguing property of the cognitive map is place field repetition, whereby place fields tend to repeat their activity in locations of an environment with similar geometry (65–67). This phenomenon is well explained by a boundary-driven model of place cell activity [(9); see (68) for a review], and observations of place field repetition in the Hillscape would support our geometric interpretation of the anisotropy findings. We found that many place cells exhibited multiple, repeating firing fields at locations with similar terrain topography (Fig. 4A).

Fig. 4. Place cells repeated their activity in regions of similar terrain topography.

(A) Example cells showing repeating terrain-specific fields in the Hillscape. Top two rows: Spike plots for the Arena and Hillscape; bottom two rows: Corresponding rate maps. (B) Repetition scores (see Materials and Methods) for all place cells in each environment. Colored markers show individual cells; black markers and lines show mean ± SD; horizontal lines indicate significant post hoc comparisons (***P < 0.001). Repetition scores were higher in the Hillscape. (C) Relationship between repetition score and behavior. For each rat, the percentage of “terrain cells” (Hillscape repetition score > Arena 1 99th percentile = 0.28) was plotted against the mean ± SEM behavioral bias in the Hillscape. Text gives Spearman’s ρ; no significant correlation was found. (D) Spatial autocorrelations of all place cells linearized along the x axis for Arena 1 and the Hillscape, ranked by decreasing repetition score. Cells 1 to 150 showed pronounced repeating fields in the Hillscape. Right: Examples from different ranked positions. Bottom: Mean ± SEM correlation values across cells. (E) Z-scored activity of terrain cells, linearized along the x axis and ranked by position of maximal firing. Secondary peaks were evenly distributed along the x axis. (F) Percentage of cells with maximal firing at each x-position. Gray area indicates Hillscape topography. Many fields occurred at the arena end containing the visual cue (0 m). Text shows two-sample Kolmogorov-Smirnov (K-S) test comparing Arena 1 and Hillscape distributions. (G) Percentage of cells with maximal firing at each position relative to ridge peaks. Gray area shows Hillscape topography. Text shows two-sample K-S test comparing Arena 1 and Hillscape distributions.

To quantify this observation, we calculated the difference in spatial autocorrelations at distances that were multiples of the inter-ridge distance (1 m) and half of this distance (0.5 m; “Repetition score” section). This “repetition score” was significantly higher in the Hillscape than the Arena (Fig. 4B), confirming that many cells exhibited repetitive activity at a frequency matching the periodicity of the terrain. Next, we defined “terrain cells” as the subset of place cells with repetition scores in the Hillscape greater than Arena 1’s 99th percentile (0.28; n = 145 or 30.8% of place cells). These terrain cells were observed in four of five animals, and their prevalence was not dictated by an animal’s tendency to move parallel to the terrain (Fig. 4C).

Terrain cells do not simply encode vertical height, because their activity is always limited to one side of each ridge; a cell encoding vertical height would fire on each side of the ridge at the same elevation. By looking at the spatial autocorrelation of place cells in the Hillscape (Fig. 4D) and the position of peaks in the average autocorrelation (Fig. 4D, bottom), the peaks align with 1-m offsets and match the periodicity of the ridges. If the cells encoded elevation, additional peaks would be visible at a variety of offsets. Alternatively, repeating fields could result from conjunctive coding of elevation or head pitch and head or movement direction: for example, firing at an elevation of 0.3 m when moving from left to right along the x axis. However, place cells were rarely modulated by movement direction, and terrain cells exhibited significantly less modulation by movement direction than nonterrain place cells (fig. S9). Similarly, while some place cells were modulated by head pitch, terrain cells were, again, significantly less modulated in this way (fig. S10).

Last, we investigated whether terrain cell firing was associated with a particular terrain feature, such as the tops or bottoms of the ridges. To test this possibility, we linearized the firing rate maps of this subset of place cells, by averaging along the y axis. We then ranked these rate maps by the location of the peak firing rate; the result of this process can be seen in Fig. 4E. Other than a small overrepresentation of the end walls in Arena 1, the diagonal band in both plots confirms that cells exhibited their primary place fields throughout both environments and did not overrepresent a portion of the Hillscape. The distribution of peak firing locations along the length of the environments or relative to the individual ridges can be seen in (Fig. 4, F and G), confirming that fields did not overrepresent a specific terrain feature (Fig. 4F; D = 0.1, P = 0.15, two-sample Kolmogorov-Smirnov test) and that their distribution was not significantly different to that of the Arena (Fig. 4G; D = 0.1, P = 0.58, two-sample Kolmogorov-Smirnov test).

Field repetition and elongation are explained by the BVC model

As previously mentioned, repeating place fields are reminiscent of the place field repetition observed in environments with repeating geometric elements (66), suggesting that a common mechanism may explain both phenomena. Place field repetition has been reported in a number of experimental studies and is accurately predicted by a BVC model of place cell activity (9, 68). In addition, in the Hillscape, most place fields were elongated parallel to terrain contours. Place fields also exhibit this response to physical boundaries, such as walls (29), and this aspect is also predicted by a BVC model (52, 64), suggesting that the terrain-specific field effects we see could all be the result of boundary inputs to place cells.

To test this hypothesis, we modeled place cells in our Arena and Hillscape environments (see “Boundary vector cells” section) following previous model architectures (7, 9, 52). We showed earlier that place field anisotropy is best predicted by the shape of the terrain in addition to physical walls (Fig. 3). Thus, in addition to the walls, we included the bottom of the ridges as boundaries in our model. Place cells modeled in this way exhibited heterogeneous activity patterns in the Arena but mainly exhibited repeating firing fields in the Hillscape (Fig. 5A and fig. S13). Similar to real place cells, this repetition was prominent in the Hillscape but absent in the Arena [mean repetition score = 0.83 and −0.03, respectively, F(1,1495) = 5024.4, P < 0.0001, η² = 0.77; Fig. 5, B and C] and cells globally remapped between the two environments (mean Arena 1 × Hillscape correlation = 0.04, Fig. 5D). Therefore, this model predicts the main phenomena we described thus far: remapping and place field repetition. Note that while ~30% of real place cells exhibit strongly repeating fields, almost all modeled place cells exhibit repetition (Fig. 5, A and B), which is to be expected as biological place cells are known to integrate inputs from many sources, not only geometry [discussed in (68)].

Fig. 5. A BVC model of place cells explains the majority of observed results.

(A) Example place cell activity modeled in the arena and Hillscape using BVC inputs (Materials and Methods, in “Boundary vector cells”). Below each of these plots is a real place cell that demonstrates a high correlation to the modeled activity. See also fig. S12. (B) The plots show the Hillscape spatial autocorrelations of real place cells (left) and modeled cells (right), linearized along the x axis, ranked from top to bottom in order of decreasing repetition score. (C) Colored markers represent cells, black markers and lines denote mean ± SD, horizontal lines denote significant post hoc comparisons. Repetition score in each environment for real and modeled place cells. The BVC model predicts repeating fields. (D) Correlation between arena 1 (A1) and arena 2 (A2) or the Hillscape (Hs) for real place and modeled place cells. The A1 × A2 BVC model correlations equate to 1 because the cells exhibit identical activity. (E) Mean ± SEM. The area of place fields near to walls (<0.2 m; “wall”) or in the center of the environment (>0.2 m; “center”) for real place and modeled place cells. (F) Same as (E), but for place field elongation. (G) Same as (E), but for field-to-wall angle—the absolute angle between a field’s longest axis and the nearest wall. (H) Median distance of all place fields to the nearest boundary for real and modeled place cells. Black line and shaded area: mean, 1st and 99th percentile of 1000 uniform place field shuffles, respectively. (I) Same as (E), but for mean firing rate, averaged across place cells, one session per rat (the session with the most cells).

Next, we investigated whether this model also predicts finer-scale effects observed in place fields, which may not necessarily be related to terrain shape but together would lend support to the BVC hypothesis. For example, Tanni et al. (61) reported that place fields proximal to walls (<0.2 m) tend to be smaller than those distal to walls (>0.2 m). We observed the same effect in both the Arena and Hillscape [F(1,2426) = 3862.4, P < 0.0001, n-way analysis of variance (ANOVA) with field distance, cell origin (model versus real data), and environment as factors; Fig. 5E, left, and fig. S6, A and B]. Tanni et al. (61) proposed that the wall proximity effect arises because of the greater rate of perceptual change when moving close to walls. They also proposed that this effect may be consistent with a BVC model because distal boundary responses are assumed to be more diffuse and less common than short-range tuning. To our knowledge, this prediction has not been previously tested, but we indeed observed the same relationship in our BVC modeled cells [F(1,3695) = 26.2, P < 0.0001], and the difference in field size between the environments was also statistically significant [F(1, 3695) = 1435.7, P < 0.0001; Fig. 5E, right].

To further support this view, we compared additional features of the BVC modeled place cells to our real place cell data. We found, for example, that both real and modeled cells exhibited higher rates of place field elongation closer to walls in the Arena [real data: F(1,2427) = 4051.3, P < 0.0001; modeled data: F(1,3695) = 26.2, P < 0.0001; n-way ANOVA with field elongation, cell origin, and environment as factors] (Fig. 5F), a clear prediction of the BVC model. In the Hillscape, this effect was disrupted by the more complex terrain: Real place cells tended to exhibit similar rates of elongation throughout the Hillscape, while modeled cells showed a slight decrease farther from walls (Fig. 5F and fig. S6, C and D). Related to this effect, in the Arena, real place fields exhibited smaller field-to-wall angles (the angle between the field’s long axis and the wall) when they were closer to a wall, meaning that place fields were generally elongated parallel to nearby walls [F(1,2426) = 3862.4, P < 0.0001, n-way ANOVA with field angle, cell origin, and environment as factors; Fig. 5G and fig. S7], another clear prediction of the BVC model. Again though, this relationship was disrupted in the Hillscape, where center fields exhibited higher field-to-wall angles because many fields were elongated parallel to the ridges instead of the closest wall (see fig. S7 for more detail). Modeled place fields exhibited the same relationships [F(1,3695) =1435.7, P < 0.0001; Fig. 5G], although modeled fields were more strongly influenced by the ridges, and fields elongated solely along the physical walls of the environments were very rare (fig. S13). Together, these effects support the view that boundary cells shape the properties of place fields in flat and uneven terrain.

We next looked at how boundary cell inputs might influence the overall distribution of fields in an environment. For example, a number of studies have reported that place fields tend to be more densely packed close to walls or edges than in the center of environments (61, 69–71). While our BVC-modeled results predicted increased field density around the Arena walls (Fig. 5H, red line), we found that field density instead very closely matched that expected from a uniform distribution (Fig. 5H). One explanation for the difference in these results is that studies like those of Tanni et al. (61) used a more sensitive method for detecting place fields that was more likely to split fields into sub parts; this effect will need to be studied further for a conclusive explanation. Related to the density of place fields, Tanni et al. (61) and Harland et al. (72) also reported that place cells maintain the same population-level average firing rate throughout large-scale environments, suggesting that field size, density, and firing rate are balanced at the population level. Again, although our BVC model results are consistent with these findings [F(1,2278) = 0.31, P = 0.57, n-way ANOVA with firing rate, cell origin, and environment as factors], in our real place cell data, we instead found a small but significant increase in activity toward the center of both environments, even when sampling only one session per rat—the session with the most cells—to ensure that fields are not included multiple times [F(1,436) = 8.6, P = 0.0036; Fig. 5I and fig. S6, E and F]. Thus, while a BVC model easily captures the larger-scale effects observed in our environments, many small-scale properties did not align with our model.

DISCUSSION

How does the brain map uneven terrain? Contemporary research highlights contradictions between the mapping of flat versus volumetric space, as well as between place versus grid cells. In climbing rats and flying bats, place cells map space volumetrically—with firing fields that extend in the horizontal and vertical dimensions (29, 30). In contrast, when rats explore flat, planar environments, place cells map space with fields that appear bound to the environment’s surface (40–42). Grid cells, in coherence with place cells, exhibit hexagonal grid firing patterns during navigation across flat surfaces (43, 44) but, unexpectedly, lose this periodicity during 3D navigation (45, 46) although they continue to exhibit volumetric firing fields. Why does the brain seemingly prioritize surface-based representations over volumetric ones? One explanation is that the volumetric spatial maps that can be observed in the rodent or bat hippocampus are a by-product of surface-mapping processes rather than a system fully adapted to volumetric navigation; in other words, we propose that the terrestrial mammalian brain has evolved to map surfaces rather than volumes.

To test this hypothesis, we recorded the activity of hippocampal place cells from rats exploring a large flat arena or an identically sized area of ridged terrain that occupied the exact same position in the same room (Hillscape). This approach allowed us to differentiate volumetric from surface-bound maps and probe what information, if any, about terrain features is incorporated into these maps. We found that place cells formed a distinct map when terrain topography was changed. Alone, this result would not necessarily differentiate our initial hypotheses (Fig. 1A), as sensory or contextual changes often lead to partial or global remapping in the hippocampus. However, remapping was not simply the generation of an independent map, but rather a reorganization directly driven by terrain shape. Place fields in the Hillscape exhibited different characteristics: (i) smaller and more numerous firing fields; (ii) a firing field orientation that reflected the direction of terrain slopes; and (iii) regions of specific topography were often mapped similarly. Together, these results suggest a consistent mechanism for place field formation relying on terrain-sensitive inputs. Global remapping followed by terrain-specific activity such as this is inconsistent with a volumetric or earth-horizontal map (Fig. 1A) and instead supports a terrain-specific map. A BVC model of place cell firing, incorporating walls and ridges as a proxy for continuous terrain shape, predicts almost all these characteristics. In contrast, it is unclear how a predictive coding account of place cell firing, such as the SR model (described in more detail below) could account for the divergence between behavior and firing field biases. These findings extend our knowledge of how the brain maps real-world environments with uneven terrain and demonstrate that terrain features are represented in these maps.

Different maps for different landscapes

Place cells remapped completely (58, 73) between the flat arena and the Hillscape, despite the experimental room, intra- and extramaze cues, arena walls, and lighting remaining the same between the two environments. While we changed the flooring across conditions, thereby disrupting self-deposited odor cues, the floor color and texture of the apparatus remained the same. Such global remapping is not consistent with an earth-horizontal map, where we would expect the same fields to be expressed in the same x-y locations, regardless of height. This remapping is also not consistent with a volumetric map because activity in the “valleys” of the Hillscape (same x-y-z coordinates) changed compared with the arena, despite these positions overlapping in all three dimensions.

Although perhaps unexpected, such surface-dependent remapping appears to be the typical response of place cells to changes in terrain slope. Knierim and McNaughton (40) found that when a slope was introduced in the midsection of an otherwise flat rectangular track, most CA1 place cells remapped: Only approximately one-third of the cells exhibited a high correlation between the horizontal and sloped conditions. This remapping was equally likely in portions of the track that were raised or portions that were unchanged, ruling out the possibility of a volumetric spatial map. Porter et al. (41) recorded CA1 place cells as rats shuttled between the ends of a wide linear track, which could be sloped at 0°, 15°, or 25°. In this setup, place cells were very unlikely to maintain the same firing fields between any two conditions (only 7 ± 1% of cells kept firing in the same linearized position), even though the floor was the same for all conditions, and even when the difference was just a 10° change in slope. Behavioral evidence suggests that rats use slopes as small as 1.5° to aid navigation (14). Again, how similarly the place cells mapped the track in different conditions was not related to the difference in slope between them, suggesting that these changes were not due to sampling of different slices of a volumetric map. Shelley and Nitz (74) recorded place cells in a spiral-shaped linear track that incorporated an area of increased elevation at one corner. Place cells in this environment exhibited repeating firing fields in parts of the track with similar terrain shape, again suggestive of a surface-bound, terrain-specific spatial map.

On the one hand, it should be very useful for an animal to update its spatial map when terrain topography changes. For example, if a mound of earth appears in a region of previously flat ground, the surface area of this region will be increased. Maintaining the same fields in the same x-y locations would lead to a decreased place field density, and these fields would also appear larger when projected onto the terrain surface (Fig. 1A, middle), leading to decreased spatial precision in this area. Alternatively, trying to “wrap” the existing place fields around the mound of earth while forming new fields for the newly expanded surface area would likely require extended exploration and would still lead to a highly distorted map. Forming a distinct map, through established remapping processes, might represent the most practical way to incorporate changes in terrain topography. Such remapping would be caused by the recruitment of place fields sensitive to terrain-specific properties, potentially reflected in the field orientation and repetition effects we observed, providing a terrain-enhanced spatial map.

Denser maps for complex landscapes

Not only did place cells remap in the Hillscape, but this spatial map also exhibited unexpected properties. Research in flat, 2D environments has demonstrated that the size, density, and distribution of place fields is balanced in a way that maintains the same average population activity throughout an environment (61, 72). For example, in flat environments, the number of place fields increases with environment size (29, 72, 75, 76), but this increase follows a gamma-Poisson relationship: As the scale of an environment increases, the total number of place fields increases at a lower rate, causing the number of fields per unit area (field density) to decrease (61, 76). At the same time, place field areas increase in larger environments, but the relationship between field area and environment size is less than 1:1, with fields appearing proportionally smaller in large environments [see (12) for a review, (29, 58, 61, 64, 72, 77)]. Last, place fields closer to walls also tend to be smaller and more densely packed than fields far from walls (61, 69, 72). These properties are balanced such that the population average firing rate at each position in an environment is consistent (61, 72).

Our Arena and Hillscape shared the same horizontally projected area, but the surface area of the Hillscape was 20% larger than the Arena. Thus, on the basis of the terrain-specific model, we might expect place fields to either (i) map the environments similarly on the basis of their horizontal area, (ii) map the Hillscape consistent with its increased surface area, with larger, less dense fields, or (iii) fall somewhere between these two outcomes. However, we instead found that place fields were smaller and more numerous in the Hillscape. In addition, after correcting for the surface area of the environments, and excluding cells with repeating fields, we found that the density of fields was still significantly higher in the Hillscape than the flat arena (~30% more fields per square meter), indicating a violation of the expected gamma-Poisson relationship, a result that we did not initially expect on the basis of the terrain-specific model (Fig. 1A).

What is driving the increased density of place fields in the Hillscape? If the brain scales its spatial map based on an environment’s surface area, then an overestimation of this area in the Hillscape could have led to the increased density of place fields there. Behavioral experiments in humans provide evidence for this kind of perceptual bias: Humans consistently overestimate distances across hilly terrain when judging static images (78) or when asked to estimate physical distances traveled (79, 80). Consistent with these findings, when Hayman et al. (33) recorded the activity of grid cells on a 40° slope, they found a significant increase in the number of grid fields when compared with a flat environment of the same size, suggesting that animals may have overestimated the size of the sloped surface. In contrast, when Porter et al. (41) recorded place cells on a linear track, which was then sloped at different angles (0°, 15°, or 25°), the density of place fields and the number of active place cells did not change significantly between conditions, suggesting that the rats consistently estimated the environment’s size despite the slope. At this point, it is still unclear how distances across uneven terrain are incorporated into the hippocampal cognitive map or if perceptual biases explain our findings. Future behavioral experiments will be necessary to explore this issue.

Another explanation behind the increased field density is that the smaller and more numerous place fields in the Hillscape reflect the increased sensory information available to the animal for self-localization. Animals navigating in darkness (81, 82), without tactile input from their whiskers (83) or without odor cues (84), exhibit larger and less stable firing fields. In head-fixed mice navigating a virtual linear track, thus without vestibular information, fewer place cells were active than in a real environment (85). Similarly, place cells are less stable in darkness (84) but exhibit more numerous and smaller place fields in object-rich environments (86, 87). Burke et al. (86) proposed that this increase reflects the incorporation of additional sensory and feature information into the hippocampal spatial map, which we might also expect to occur if the complexity of the terrain is increased. In support of this interpretation, we found that place fields in both environments were smaller close to physical walls and larger toward the center of the environment. This effect has previously been attributed to the increased sensory information and rate of perceptual change associated with navigation close to walls and the visual cues they provide (61). Unlike other navigation cues, which may be obscured, kinesthetic and vestibular systems continually monitor the orientation of the head in relation to gravity and muscular exertion keeping the body level, providing a continuous sensory input and navigational cue (13). Thus, uneven terrain would increase the rate of perceptual change throughout an environment and could drive the formation of smaller, more densely packed place fields in a similar way to physical walls. This hypothesis will need to be tested in future work. In support of this possibility, in the Hillscape, we found that the relationship between place field size and the distance to the nearest wall was significantly weaker, with place cells exhibiting smaller fields throughout the Hillscape, consistent with terrain topography itself providing a continuous sensory, and perhaps also localization, input. These results are inconsistent with place cell models based on the integration of a thresholded random Gaussian process (88) that do not take into account local landmarks and features.

While our analyses demonstrate that terrain shape exerts a strong influence on hippocampal spatial coding, we did not attempt to decode the animal’s position from population activity. Reliable 2D decoding in large environments typically requires substantially larger populations of simultaneously recorded neurons [e.g., 103 to 250 cells (89); 100 to 383 cells, (90)], whereas our recordings yielded at most ~50 active place cells per session. Moreover, the repeating topography of the Hillscape, in which we observed terrain-dependent field repetition, precludes an unbiased comparison of decoding accuracy across environments. Nevertheless, the observed reduction in field size, increased field number, and alignment of fields with terrain contours already imply that terrain information contributes to the structure of the spatial map. Future work using higher-density recordings across terrains with varied shapes and slopes will be required to directly test whether terrain geometry enhances the spatial resolution of the hippocampal map.

Maps reflect terrain and geometry

In addition to general differences in firing field properties, place cells also encoded terrain features in two primary ways: (i) Most place fields were oriented and elongated perpendicular to the slopes of the ridges and (ii) about one-third of place cells exhibited repeating firing fields in regions of similar terrain topography.

In flat, 2D environments, previous studies have shown that place fields are typically elongated parallel to physical walls (29, 61, 64), although there is no comprehensive explanation for why this effect occurs. Field elongation parallel to boundaries is predicted by the SR model of place cells (54, 55), which has gained recent popularity. This model posits that place cells encode a predictive representation of the animal’s potential future states given its current state and that locations that lead to similar future locations are represented more similarly than ones that lead to different locations (91). Because animals tend to move parallel to walls (62, 63), the SR model would predict that positions next to a wall will be represented similarly, leading to the expansion of fields alongside it (54, 55). In a 2D apparatus, this explanation is entirely reasonable, and indeed, in our Arena the anisotropy (elongation and orientation) of place fields is consistent with behavioral biases as predicted by the SR model. However, in the Hillscape, place fields were almost exclusively elongated parallel to terrain contours, even in places where the animals almost exclusively moved perpendicular to terrain contours. This observation challenges the validity of the SR model explanation for place field elongation. For similar reasons, it is unclear whether the clone-structured causal graph (CSCG) model proposed by Raju et al. (92) would predict place field elongation throughout our Hillscape. Because animals tend to move perpendicular to the terrain contours while moving up or down the slopes of the ridges, a graph model would not have sufficient opportunity to merge neighboring slope positions, and elongation will likely be limited to the ridge peaks and valleys of the Hillscape. However, this model remains to be tested in our environment.

An alternative model that accounts for the elongation of place fields is the BVC model (7, 9, 52). This model posits that place cell activity is largely informed by boundary cells (BVCs or border cells), found in the subiculum and medial entorhinal cortex, both of which project to the hippocampus (5, 6). These boundary cells fire when an environmental boundary is at a specific distance and direction from an animal; they tend to exhibit fields active all along their preferred boundary. Because of this property, place cells modeled using boundary cell inputs also often exhibit firing fields that are elongated parallel to environmental boundaries [(9, 64); see (93) for a combined SR-BVC model]. When we modeled place cell firing based on BVC inputs, we replicated virtually every main result observed in our real place cells, such as elongation, repeating fields and remapping between the environments. Here, in addition to the outer walls, we incorporated the valleys between ridges as boundaries, to act as a simple proxy for terrain shape, but more sophisticated models will be required to describe more complex environments. Previous research has found that a number of place field characteristics, such as their size, elongation, and orientation, vary according to the animal’s distance from the nearest boundary (61). We assessed these characteristics in a BVC model of place cells and found a strong correspondence between the model and real data.

The second form of terrain coding we observed, place field repetition, has been extensively characterized in multicompartment environments [see (68) for a review]. When animals explore geometrically and visually identical compartments, connected and arranged parallel to one another, place cells form “repeating” maps that are nearly identical across compartments rather than a single continuous global map of the whole environment (65, 66, 94). A global map does eventually emerge in entorhinal grid cells, which initially show corresponding “fragmentation” across compartments (95). The presence of a similar phenomenon in both hippocampal and entorhinal populations is notable, as these cell types often exhibit distinct spatial coding properties. In hippocampal place cells, field repetition can be parsimoniously explained by a BVC model (9). In this view, because boundary cells respond similarly to the walls of geometrically identical compartments, their inputs drive repeated firing fields in place cells. This mechanism could also account for grid cell fragmentation, if boundary inputs “reset” grid activity in sub compartments (8, 96). In contrast, the SR model cannot easily account for place field repetition, as it would require identical behavioral statistics across compartments, a condition that fails to explain why repetition disappears by simply orienting visually and geometrically identical compartments differently, while maintaining similar within-compartment behavior (66, 97).

A more recent model, the dynamic entorhinal-hippocampal loop model of Li et al. (98), predicts both place field repetition and grid fragmentation, as well as their gradual consolidation into a global map. In this framework, place field repetition is driven by identical local visual inputs (combined with allocentric heading direction), and the long-term integration of self-motion signals leads to the eventual formation of a global map. It remains unclear whether this elegant model would also predict field repetition in the Hillscape because in our environment, repetition was associated with terrain geometry rather than discrete walls, and thus, the visual scene differed substantially from one ridge to the next. For the same reason, it is unclear whether the CSCG model proposed by Raju et al. (92) would predict place field repetition under these circumstances, because the visual scene associated with each ridge would differ. Despite these visual differences, a substantial proportion of cells (~33%) exhibited repeating fields in the Hillscape. This finding contrasts with some multicompartment environments, where repetition is typically observed in the majority of cells [>80% in (68), but see (99)]. This reduction may suggest a more flexible mechanism, such as that proposed by Li et al. (98), or that boundary-related inputs exhibit a graded sensitivity to environmental features, with stronger responses to vertical walls and weaker responses to continuous slopes. Future experiments and computational models will be needed to distinguish between these possibilities and determine how boundary and terrain information are integrated in the hippocampal-entorhinal system.

In spatial cognition, environmental geometry is typically defined as the physical walls or barriers to movement in an environment (100), and for this reason, boundary cells are almost always investigated in relation to these types of barriers (5, 6). However, Poulter et al. (53) showed that boundary cells also respond to low walls, such as a line of bricks, that the animal could climb over [see also (101)]. It was previously unknown how place cells respond to “soft” boundaries such as uneven terrain. However, the place field elongation, repetition, and alignment with terrain contours we observed are fully consistent with effects previously attributed to walls and compartmentalization (68). We would predict similar field structure in an environment subdivided by parallel walls as in one composed of repeating terrain features. This suggests that the same geometric inputs that drive place field repetition in multicompartment environments (e.g., boundary cells) are sensitive not only to discrete barriers such as walls but also to continuous terrain features such as ridges or valleys and that boundary cells may respond to terrain features more generally than just physical barriers. In this view, physical walls simply represent a form of impassable terrain and a subset of their broader sensitivity. Naturalistically, this idea makes sense because walls are a primarily human construction, and animals in natural environments are concerned with terrain, not walls (102). Thus, one implication of our findings is that surface geometry (terrain) that can be traveled over physically may be sufficient to evoke boundary-like modulation of hippocampal spatial representations. Future research will be needed to investigate how boundary cells respond to general terrain features such as those in our Hillscape, to conclusively determine whether the brain’s “cognitive map” interprets terrain similarly to vertical walls and drop-offs.

Summary

We investigated the neural mapping of uneven terrain by recording hippocampal place cell activity in rats foraging on ridged, hilly terrain. Place cells exhibited global remapping and formed a distinct map in this Hillscape compared to a flat environment, demonstrating terrain-specific activity that is surface bound and neither 3D nor volumetric. Place fields were smaller and more numerous across uneven terrain, which we propose results from increased sensory information (tactile, proprioceptive, vestibular, visual, effort-based, etc.) available to the animal for spatial localization. Place fields tended to be elongated parallel to terrain contours, which could be a mechanism for encoding terrain topography more generally. A subset of place cells, the terrain cells, exhibited identical activity in regions of similar topography, and we propose that these repeating responses are the result of repeating inputs from topography-sensitive boundary cells. Last, we show that a BVC model of place cell firing accounts for these results. These findings extend our knowledge of how the brain maps real-world environments with uneven terrain, suggesting that the brain is adapted to mapping surfaces as opposed to volumes. Future research will look to systematically test how place, grid, and boundary cells represent terrains with differing slopes, orientations, and curvatures, to determine whether the terrain-based coding principles identified in this study generalize across a wider range of surface geometries.

MATERIALS AND METHODS

Ethics statement

We followed approved guidelines and ethical standards for animal care throughout our experiments. This included compliance with the American Physiological Society’s principles, approval from the Institutional Animal Care and Use Committee (Dartmouth College IACUC protocol number: 00002133), and adherence to the National Institutes of Health Guide for the Care and Use of Laboratory Animals and the Society for Neuroscience standards. All experiments were performed at Dartmouth College. We chose Long-Evans rats because of their similarities to humans in anatomy and physiology. To minimize stress, animals were familiarized with their surroundings well before surgery. The surgery, conducted under aseptic conditions and monitored anesthesia, aimed for a quick and safe procedure to reduce recovery time. Postsurgery, pain relief, and antibiotics were administered to support the animals’ recovery. Our approach prioritized the well-being and comfort of the animals throughout the entire process.

Animals

Five female Long-Evans rats (Envigo, US), weighing between 250 and 350 g, were used for single-unit electrophysiological recording. Animals were dual housed before surgery and exposed to the experimental environments (Arena and Hillscape) in groups (typically 5 sessions, 20 min each). Thus, animals experienced both environments for ~100 min before surgery. After implantation surgery, animals were regularly reexposed to the arena and the Hillscape for at least 20 min every week until the recording tetrodes were advanced into the targeted area (usually 2 to 3 weeks on average). Environments explored for this duration are typically considered familiar (103), and we therefore expect that animals had sufficient prior exposure for any potential predictive representation (e.g., SR) to develop. Animals were housed individually after surgery and were given access to a climbable nest box in their home cage and group exposure to a 3D “playpen” (~1 hour per day) for continued climbing experience.

Electrodes and surgery

A combination of Axona (MDR-xx, Axona, UK) and custom-built microdrives were used for recording. Drives supported four tetrodes, driven in a single moveable bundle, each of which was composed of four HML-coated (heavy polyimide enamel), 17-μm-diameter, 90% platinum, 10% iridium wires (California Fine Wire, Grover Beach, CA). Wires were gold plated (Non-Cyanide Gold Plating Solution, NeuraLynx, MT) to reduce the impedance of the wire to a range of 180 to 250 kΩ. Microdrives were implanted using standard stereotaxic procedures under isoflurane anesthesia (29). Electrodes were lowered to just above the CA1 cell layer of the hippocampus (−3.5 mm anterior-posterior from bregma, ±2.4 mm medial-lateral from the midline, and ~1.5 mm dorsal-ventral from dura surface). During recording, electrodes were advanced between sessions by at least 12.5 to 25 μm to sample additional neurons. However, given the spatial extent over which extracellular spikes can be detected and potential effects of tissue movement, this approach cannot guarantee that successive sessions yield fully nonoverlapping neuronal populations, and it is likely that some neurons were recorded across multiple sessions. Neuron identity across sessions was not explicitly tracked or quantified. To assess whether potential repeated sampling influenced our results, we replicated the main analyses using only a single session per animal: These analyses yielded results consistent with those that included all sessions (fig. S14).

Apparatus

All experiments were conducted in the same room (3 m by 3.2 m by 2.7 m) under moderately dimmed light conditions. Stable landmarks in the room included the following: One room wall was covered with black material, the second wall included a 1.2 m–by–1.2 m blue cue card, the third wall included a 1.5 m–by–0.7 m black cue card, and the fourth wall included a doorway. We used two pieces of experimental apparatus: a square open-field environment (“Arena”) and an uneven surface composed of three undulating ridges (“Hillscape”). See fig. S1 for photographs and schematics.

The Arena was a 3 m–by–1.2 m rectangular enclosure, with 0.65-m-high, matte light blue–painted wooden walls. The floor of the Arena was covered with white matte antislip linoleum flooring. One 0.3 m–by–0.65 m matte black wooden cue serving as landmark was affixed to the end wall nearest the doorway. Rats were recorded while freely foraging in the Arena for randomly dispersed, flavored puffed rice (CocoPops, Kelloggs).

The Hillscape was constructed from the same matte white antislip linoleum flooring that was found in the Arena, but this was affixed to a wire frame and stabilized with polyurethane foam. This surface was placed within the same 0.65-m-high, matte blue–painted wooden walls that formed the Arena, so that the two environments occupied the exact same x-y-z locations. Each ridge had a footprint of 1 m by 1.2 m and a Gaussian cross section with a 0.45-m peak, so that the entire Hillscape surface had a footprint of 3 m by 1.2 m (the same as the Arena) but a surface area of 3.6 m by 1.2 m (1.2× larger along the long axis). To encourage homogeneous exploration, food reward (malt paste, GimCat Malt-Soft Paste, H. von Gimborn) was manually affixed onto the surface with a stick and regularly reapplied, evenly throughout the environment, but flavored puffed rice was also used.

Recording procedure

After a postsurgery recovery period of at least 7 days, rats were transported from a holding room to the recording room in their home cage and screened for single-unit activity together with theta oscillations once or twice per day, 5 days a week. Screening was performed in a 1.5 m–by–1.5 m arena within the experimental setup. Single-unit activity was observed and recorded using a 64-channel recording system (Digital Lynx SX, Neuralynx, Bozeman, MT). For experimental sessions, rats were recorded for a minimum of 25 min in the Arena, followed by a minimum of 45 min in the Hillscape and a further minimum 20 min in the Arena. Between these sessions, rats were allowed to rest and drink in their home cage, while remaining connected to the recording system, for ~5 min.

Spike-sorting

Single-unit data were first processed using an automated spike-sorting algorithm [Klustakwik v3.0 (104)] using the first three principal components and peak waveform amplitude as parameters. Manual refinement of the classification was then performed using the TINT spike-sorting software (Axona, St Albans, UK). Only well-isolated putative neurons were kept (pyramidal or interneuron-like waveforms). Only the subset of pyramidal cells matching place cell detection criteria was analyzed.

Place cell criteria

A putative cluster was classified as a place cell if it satisfied the following criteria in the session with the greatest number of spikes:

1) the peak-to-trough width of the waveform with the highest amplitude was >250 μs;

2) the mean firing rate was >0.1 spikes/s; and

3) the z-scored bootstrapped spatial information content exceeded a shuffle by 2 SDs (see the “Spatial information content” section).

In combination with these parameters, we also manually updated the resulting place cell classification as needed to resolve false positives and negatives.

Position tracking

The terms “position” and “location” are used interchangeably throughout, to mean location in space irrespective of orientation. Five cameras (MOKOSE 4k) were used to track the animal’s location and orientation. Online tracking was performed using Bonsai [bonsai-rx.org (105)]. Three light-emitting diodes (LEDs) (red, green, and blue omnidirectional LEDs, Super Bright LEDs Inc., MI) were attached to the headstage; these LEDs were arranged in a triangular array to allow estimation of head orientation in three dimensions. The animal’s position was estimated as

$$P=m-\mid (P_{\mathrm{r}}-P_{\mathrm{b}})\times (P_{\mathrm{r}}-P_{\mathrm{g}})\mid h$$

where m is the average location of the three LEDs, P_r, P_b, and P_g are the locations of the red, blue, and green LEDs, respectively (LEDs were arranged in this order, counterclockwise starting with red at the front), and h is the height of the drive above the animal’s skull; × is the cross-product, and || is the L₂ or Euclidean norm. Descriptively, this formula gives the animals’ location as a point on the animal’s skull directly below the recording implant. The animal’s head azimuth, or “head direction,” was calculated as

$$x,y,z=\mid P_{\mathrm{r}}-m\mid$$

$$\text{Azimuth}={\text{tan}}^{-1}(x,y)$$

Descriptively, this formula gives the animals’ head direction as the counterclockwise angle in the xy plane, from the positive x axis, of the vector between the center of the LED array and the red (front) LED. The animals head tilt was similarly calculated as

$$\text{Tilt}={\text{tan}}^{-1}(z,\sqrt{x^2+y^2})$$

Descriptively, this formula gives the animals’ head tilt as the angle between the xy plane and the vector from the center of the LED array to the red (front) LED. The animal’s head roll was calculated as

$$x,y,z=\left|(P_{\mathrm{r}}-m)\times [P_{\mathrm{r}}-m+(P_{\mathrm{r}}-P_{\mathrm{b}})\times (P_{\mathrm{r}}-P_{\mathrm{g}})]\right|$$

$$\text{Roll}={\text{tan}}^{-1}(z,\sqrt{x^2+y^2})$$

Descriptively, this formula gives the animals’ head roll as the angle between the xy plane and the surface normal of the LED array.

Firing rate maps

Firing rate maps were generated using the rate_mapper function described by Grieves (106). The maps were calculated as bivariate histograms where each bin denotes the number of spikes falling within that bin divided by the amount of time the animal spent in the bin, smoothed with a Gaussian kernel. In more detail: Where x0,y0 is the origin of the histogram and h is the side length of a square bin (which we set to 32 mm), the ij^th bin of the histogram is defined as the left-closed right-open interval

$$B_{\mathit{ij}}=[x_0+\mathit{ih},x_0+(i+1) h]\&[y_0+\mathit{jh},y_0+(j+1)h]$$

If the number of spikes falling into B_ij is denoted by S_ij and the number of position samples as P_ij, then a firing rate map would be defined as

$$r(x,y)=\frac{S_{\mathit{ij}}}{P_{\mathit{ij}}\left({f\mathrm{s}}^{-1}\right)}$$

where $f_{\mathrm{s}}$ is the sampling rate of the position data (in our case resampled at 50 Hz). For smoothing, we implemented a Gaussian smoothing kernel defined as

$$g(x,y)=e^{-\frac{x^2+y^2}{2{\mathrm{\sigma }}^2}}$$

where x and y denote the bin position relative to the one being smoothed and σ is the SD of the distribution (set to 64 mm). Throughout our analyses, the kernel size was always set to

$$\text{kernel width}=2\lceil \left(2\mathrm{\sigma }\right)\rceil +1$$

ensuring that the kernel was always an odd number of pixels and at least 4 SDs in width. Smoothing was performed before the division of spikes and position samples. Maps were padded with zero values before smoothing to accommodate the smoothing kernel and reduce edge effects. In addition, bins that were visited for <0.01 s were treated as unvisited.

The Arena and Hillscape environments share the same horizontal footprint (i.e., the same size when viewed from above); however, the Hillscape has a much larger surface area (i.e., when the ridges are “unrolled”). Thus, we tracked the animals in three dimensions as they foraged in both environments, which allowed us to “unroll” the animal’s path in the Hillscape. This procedure was achieved by projecting the animal’s trajectory onto the surface of the environment and then expressing the x-coordinate as the distance from one end of the Hillscape. Thus, we generated top-down or earth-horizontal firing rate maps for both environments but also a projected or unrolled (“flattened”) surface map for the Hillscape. All analyses were performed on the top-down maps unless specified otherwise.

Spatial information content

Spatial information content (107) was calculated in bits per second from firing rate maps ( “Firing rate maps” section) as

$${\displaystyle \sum _{i=1}^N}{P}_i\left(\frac{R_i}{R}\right){\text{log}}_2\left(\frac{R_i}{R}\right)$$

where i is the spatial bin, P_i is the probability for occupancy of bin i, R_i is the mean firing rate for bin i, and R is the overall average firing rate.

To determine whether a cell’s spatial information content was greater than could be expected by chance, for each session, we used a bootstrap-versus-shuffle approach (108). First, the cell’s spatial information content was calculated by resampling the cell’s spikes using a bootstrap with replacement procedure (100 iterations). At each iteration, we recreated a firing rate map and calculated spatial information content; the final value was the median of the collected bootstrapped values.

Next, we repeated the same procedure (100 iterations), but instead of resampling spikes, we circularly shifted the spike train of the cell by a random time increment (a random multiple of 200 ms, greater than or equal to 20 s, and less than the total duration of the session). Last, we expressed the observed spatial information values in SDs from the shuffle

$$\text{Standardized value}=\frac{({\text{median}}_{\text{bootstrap}}-{\mathrm{\mu }}_{\text{shuffle}})}{{\mathrm{\sigma }}_{\text{shuffle}}}$$

This formula essentially z-scores the bootstrap value relative to the shuffle distribution. If the median parameter value obtained from bootstrapping exceeded the 95th percentile (1.96 SDs) of the shuffle distribution, the cell was considered to be more spatially modulated than expected by chance.

In our analyses, we chose to use these normalized information scores because the Arena and Hillscape environments differed substantially in behavioral sampling (e.g., coverage, trajectory biases, and session duration) as well as in surface area. These differences mean that the raw spatial information values are not directly comparable across environments, because the expected baseline information content varies with both environment size and sampling statistics. By expressing spatial information as a z-score relative to a shuffle-derived null distribution, we control for these confounds and obtain a measure that is directly comparable across conditions.

Autocorrelations

The spatial autocorrelation, $r$, of a cell’s firing rate map was defined as

$$r({\mathrm{\tau }}_x,{\mathrm{\tau }}_y,{\mathrm{\tau }}_z)$$

$$=\frac{M\sum _{x,y,z}\mathrm{\lambda }(x,y,z)\mathrm{\lambda }(x-{\mathrm{\tau }}_x,y-{\mathrm{\tau }}_y,z-{\mathrm{\tau }}_z)-\sum _{x,y,z}\mathrm{\lambda }(x,y,z)\sum _{x,y,z}\mathrm{\lambda }(x-{\mathrm{\tau }}_x,y-{\mathrm{\tau }}_y,z-{\mathrm{\tau }}_z)}{\sqrt{\left\{M\sum _{x,y,z}\mathrm{\lambda }{(x,y,z)}^2-{\left[\sum _{x,y,z}\mathrm{\lambda }(x,y,z)\right]}^2\right\}\left\{M\sum _{x,y,z}\mathrm{\lambda }{(x-{\mathrm{\tau }}_x,y-{\mathrm{\tau }}_y,z-{\mathrm{\tau }}_z)}^2-{\left[\mathrm{\lambda }(x-{\mathrm{\tau }}_x,y-{\mathrm{\tau }}_y,z-{\mathrm{\tau }}_z)\right]}^2\right\}}}$$

where $\mathrm{\lambda }(x,y,z)$ is the firing rate at the location $(x,y,z)$ in the firing rate map, $M$ is the total number of voxels in the rate map, and ${\mathrm{\tau }}_x$, ${\mathrm{\tau }}_y$, and ${\mathrm{\tau }}_z$ correspond to x, y, and z coordinate spatial lags (109). In this study, the third z dimension was omitted when correlating 2D maps.

Repetition score

To quantify the level of slope-related repetition exhibited by a cell, spatial autocorrelations were generated as above (“Firing rate maps” section) but for the x-coordinate spatial lags only. We then calculated a repetition score as

$$\text{Repetition score}=\frac{1}{n}{\displaystyle \sum _{i=1}^n}{a}_i-\frac{1}{n}{\displaystyle \sum _{i=1}^n}{b}_i$$

where a_i are all the autocorrelation bin values at spatial lags equal to the inter-ridge distance ±120 mm and b_i are all the autocorrelation bin values at spatial lags equal to half the inter-ridge distance ±120 mm. The repetition score can range from −2 to +2, with positive scores indicating that the firing rate map exhibits periodicity matching the periodicity of the ridges.

Place field detection

Firing rate maps were constructed as above (“Firing rate maps” section). Then, using an analysis adapted for large-scale environments (72), we z-scored the firing rate maps and thresholded them at 1.2 SDs. Among these thresholded values, we then defined place fields as contiguous regions larger than 400 cm² that also contained a peak firing rate greater than 1 spike/s.

Place field characteristics

Place fields were detected as described in the “Place field detection” section. For each field, we then calculated its weighted centroid (average pixel position weighted by pixel values) and length along each Cartesian axis (side lengths of minimum enclosing rectangle; MATLAB regionprops). We also counted the total number of fields exhibited by each place cell. Place field elongation was calculated as

$$\text{Elongation}=\sqrt{1-\left(\frac{\mathrm{\alpha }}{\mathrm{\beta }}\right)}$$

where α is the minor-axis length and β is the major-axis length of an ellipse with the same normalized second central moments as the place field (MATLAB regionprops). Field orientation was defined as the angle between the longest axis of an ellipse with the same normalized second central moments as the place field (MATLAB regionprops) and the x axis.

Many place field characteristics can be estimated using the spatial autocorrelation (see “Autocorrelations” section) of a cell’s firing rate map, because the central peak of the autocorrelogram represents an average of the cell’s spatial firing field characteristics. For each place cell, we estimated its average firing field radius by thresholding the spatial autocorrelation at 0.5 and calculating the radius of a circle with the same surface area as the autocorrelation’s central peak.

Anisotropy analyses

Field anisotropy: For each place field, we calculated its anisotropy as

$$\text{Anisotropy}=\frac{y-x}{y+x}$$

where y is the height or y-axis length and x is the width or x-axis length of the of the smallest rectangle containing the place field. To visualize anisotropy across all place cells and fields, we pooled data for all place fields, binned their anisotropy values into a bivariate histogram with the same pixel size (32 mm²) and dimensions as the firing rate maps (“Firing rate maps” section) based on their weighted centroid, and then smoothed this histogram with a 5-pixel boxcar kernel.

Behavioral anisotropy was calculated as

$$\text{Anisotropy}=\frac{y-x}{y+x}$$

where y is the time spent moving parallel to the y axis (±45° in either direction) and x is the time spent moving parallel to the x axis (±45° in either direction). Given the positional change across dimensions ∆x and ∆y, azimuthal movement direction θ was estimated as

$$\mathrm{\theta }\left(t\right)={\text{tan}}^{-1}\left[\frac{{∆}_y\left(t\right)}{{∆}_x\left(t\right)}\right]$$

For this analysis, only movement directions calculated when the animal’s running speed was >5 cm/s were included. To average anisotropy across all animals and sessions, for each session we binned the x-y trajectory positions into a bivariate histogram with the same pixel size (32 mm²) and dimensions as the firing rate maps (see “Firing rate maps” section) and then calculated the anisotropy of movement direction, as above, for each bin. We then averaged across these session maps to calculate the average spatial anisotropy.

Anisotropy simulations

To estimate the contribution of boundaries to the anisotropy of place fields, we calculated a “boundary anisotropy” score using a simplified BVC–inspired simulation. For each position within an environment, we calculated the predicted local boundary anisotropy as a function of both the angle and distance to the surrounding walls.

Briefly, the environment perimeter was represented as a closed polygon with boundary segments associated with an allocentric orientation relative to the x axis. For every position (x, y) within the environment, the Euclidean distance from that position to every point along all boundaries was computed. Similarly to the BVC model, two Gaussian weighting functions were then applied: one weighting the angular influence of each wall as a function of its distance and another weighting the distance-dependent contribution to anisotropy.

For each position, the weighted mean wall angle (i.e., the orientation of the wall relative to the x axis) and weighted mean wall distance were obtained as

$$\overline{\mathrm{\theta }}(x,y)=\frac{\sum _i{w}_i {\mathrm{\theta }}_i}{\sum _i{w}_i},\overline{ d}(x,y)=\frac{\sum _i{w}_i d_i}{\sum _i{w}_i}$$

where w_i is the Gaussian weight applied to each boundary sample $i$ (MATLAB normpdf, σ = 10). Boundary anisotropy was then defined as the product of these two weighted components, capturing the combined angular and distance-dependent influence of the surrounding boundaries

$$A(x,y)=f_{\text{angle}}\left(\overline{\mathrm{\theta }}\right)\times f_{\text{dist}}\left(\overline{d}\right)$$

where $f_{\text{angle}}\left(\overline{\mathrm{\theta }}\right)=(\overline{\mathrm{\theta }}/45)-1$ normalizes the angular component and $f_{\text{dist}}\left(\overline{d}\right)$ represents the distance weighting (MATLAB normpdf, σ = 16). The resulting 2D anisotropy map A(x, y) therefore provides an estimate of local boundary anisotropy at every position. To probe the influence of terrain shape, we repeated the above analysis for the Hillscape but included boundaries corresponding to the locations of the ridge tops and bottoms as a rough proxy for terrain shape, which is a continuous input. Future modeling work should look to improve on this approach.

Session stability

The spatial stability between sessions, such as Arena 1 and Arena 2, was defined as the Pearson pairwise linear correlation coefficient (MATLAB corr) between the firing rate maps (“Firing rate maps” section) for the two sessions. Correlations were only calculated when at least one map had a peak firing rate value >1 spike/s. To determine the likelihood of observing correlation values by chance, we repeated this process 1000 times but compared maps from two place cells randomly selected without replacement from among all place cells pooled together (i.e., Arena 1 from cell A and Arena 2 from cell B).

Similarly, within session stability was defined as the Pearson pairwise linear correlation coefficient (MATLAB corr) between firing rate maps for the first and second halves of the session. These firing rate maps were generated as described above (“Firing rate maps” section), but data were partitioned into spikes and position data falling before versus after the median time sample. Again, correlations were only calculated when at least one map had a peak firing rate value >1 spike/s. To determine the likelihood of observing correlation values by chance, we repeated this process 1000 times but compared half-session maps from two place cells randomly selected without replacement from among all place cells pooled together (i.e., Arena 1 first half from cell A and Arena 1 second half from cell B).

To test various hypotheses, the correlations described above and their shuffles were also repeated using masked spatial maps, as follows. To test whether stability was greater in the corners of the environments, correlations were performed only on spatial bins with a Euclidean distance <15 bins from a corner. To test the same for the boundaries, correlations were performed only on spatial bins with a Euclidean distance <5 bins from a wall. For the central portion of the environments, correlations were performed only on spatial bins with a Euclidean distance >10 bins from a wall. Last, to test whether place cells maintained the same map for both the Arena and Hillscape, for the between-session correlations only, we correlated the Arena earth-horizontal map with the projected Hillscape map (“Firing rate maps” section) after aligning the two maps on the left or right edge. We then took the maximum of these two values.

Cliff’s delta

We used Cliff’s delta as a nonparametric measure of effect size to quantify the degree of overlap between two distributions. The statistic measures the degree to which one sample overlaps another (110). The function was defined as

$$\mathrm{\delta }(i,j)=\{\begin{array}{c}+1, x_i>y_j\\ -1, x_i<y_j\\ 0, x_i=y_j\end{array}$$

Cliff’s delta effect size was then defined as

$$\mathrm{\delta }=\frac{1}{\mathit{mn}}{\displaystyle \sum _{i=1}^m}{\displaystyle \sum _{j=1}^n}\mathrm{\delta }(i,j)$$

Values near ±1 indicate minimal overlap between distributions, while values near 0 indicate substantial overlap. Unlike tests based solely on means or medians, Cliff’s delta leverages the full distribution, allowing us to assess similarity beyond a binary “different/not different” outcome. This approach was critical for our hypotheses because subtle shifts in distributions can reveal partial similarity between conditions. For example, in Fig. 2A, correlations between Arena 1 and the Hillscape were significantly lower than correlations between the two Arena sessions, a difference that a shuffle-of-means test would also detect. However, we also observed that the Arena-Hillscape correlation distribution was shifted to the right relative to a shuffle distribution, indicating residual similarity between environments. This nuance is highly relevant for distinguishing between competing models and would not be captured by a mean-based approach.

Permutation tests

For hypothesis testing, we used nonparametric permutation tests. These tests were most often used in conjunction with the Cliff’s delta measure of effect size (“Cliff’s delta” section). For each comparison, we calculated the observed test statistic (e.g., Cliff’s delta) and then generated a null distribution by randomly permuting the pooled data and recomputing the statistic (n = 1000 permutations). The P value was estimated by counting the fraction of permuted statistics at least as extreme as the observed statistic and applying the standard small-sample correction: P = (k + 1) / (n + 1), where k is the number of permutations exceeding the observed value. Two-sided tests were used unless otherwise stated.

Boundary vector cells

As in Hartley et al. (52), Barry et al. (7), and Grieves et al. (9), the spatially receptive tuning curves of BVCs were modeled as the product of two Gaussians. One Gaussian varies as a function of the rat’s distance from a boundary, and the other Gaussian varies as a function of the angle this boundary presents at the rat. We simulated our 3 m–by–1.5 m Arena and 3 m–by–1.5 m Hillscape as binary matrices such that each pixel was equivalent to 1 cm². Then, for each pixel, we calculated the distance (r) from the pixel to the nearest boundary segment at a direction (θ) and the angle (δθ) that segment subtended to the pixel. Then, for a given BVC that is optimally responsive to boundaries at a distance d_i and at an angle α_i relative to the rat, the receptive field was defined as

$$F_{\text{bvc}}=g_i(r,\mathrm{\theta })\mathrm{\delta \theta }$$

where δθ is the subtending angle of the wall segment at angle α_i and

$$g_i(r,\mathrm{\theta })=\frac{e^{-{(r-d_i)}^2/2{\mathrm{\sigma }}_{\text{rad}}^2\left(d_i\right)}}{\sqrt{2\mathrm{\pi }{\mathrm{\sigma }}_{\text{rad}}^2\left(d_i\right)}}\times \frac{e^{-{(\mathrm{\theta }-{\mathrm{\alpha }}_i)}^2/2{\mathrm{\sigma }}_{\text{ang}}^2}}{\sqrt{2\mathrm{\pi }{\mathrm{\sigma }}_{\text{ang}}^2}}$$

Here, the tuning width σ_ang was constant and was set to 0.2, but radial tuning width σ_rad increased linearly with preferred tuning distance such that boundary fields closer to walls were smaller and more precise while fields away from walls were more diffuse, consistent with neural data (7, 9, 52)

$${\mathrm{\sigma }}_{\text{rad}}^2\left(d_i\right)=a(\frac{d_i}{b}+1)$$

Here, a and b were constants determining, respectively, the radial extent of fields at zero distance and the rate of tuning width increase with distance. We set these values to 20 and 100 cm, respectively. For each location x in the environment, the contribution to the firing of a BVC of all boundaries visible to the rat by direct line of sight (determined using a modified Bresenham’s line algorithm) was estimated by integrating the first equation over values of θ. The firing of a place cell pc at a location F_pc(x) is then proportional to the thresholded linear sum of N BVCs according to

$$F_{\text{pc}}\left(x\right)=H[\sum _{i=1}^N{f}_{\text{bvc}}\left(x\right)-T]A$$

where the threshold T and coefficient A are constants. We set A to 1000, and for each place cell, the value for T was drawn from a truncated Gaussian distribution (MATLAB normrnd) on the range [5 × 10⁻³, 7 × 10⁻³] with a mean of 6 × 10⁻³ and SD of 5 × 10⁻⁴. This distribution of values aimed to simulate the varying excitability of different hippocampal pyramidal cells. H was the Heaviside step function

$$H\left(x\right)≔\{\begin{array}{c}1,x\ge 0\\ 0,x<0\end{array}$$

Following this procedure, we modeled the activity of 512 BVCs. The preferred distances d_i of these cells were drawn from a bounded Gamma distribution (MATLAB gamrnd) with range [16, 256 cm] with a shape parameter equal to 1 and a scale parameter equal to 128. The preferred directions α_i of these cells were randomly drawn from a uniform distribution with range [1, 360°] at a resolution of 1° (MATLAB randi). Using these BVCs, we then modeled the activity of 1024 place cells; the number of BVCs projecting to a place cell was determined by a truncated Poisson distribution (MATLAB poissrnd) with range [4, 10 cells] and a lambda value of 10. We then analyzed these modeled place cells using the same approaches described above for real place cells. The MATLAB code used to model these cells is freely available (see Data and Materials Availability).

Generalized linear model

To assess which factors best explained the degree of terrain modulation observed across hippocampal place cells, we performed a generalized linear model analysis. The dependent variable was repetition score (see “Repetition score” section). Briefly, this measure was defined as the difference in spatial correlation between each cell’s 2D firing rate map and itself at a spatial lag equal to one ridge spacing versus a lag equal to half a ridge spacing. This measure quantifies the extent to which a cell exhibited repeating place fields aligned with the terrain’s periodic structure.

Predictor variables included several behavioral and spatial coding measures: speed score [the correlation between firing rate and running speed; (111)], directionality [spatial information content of firing rate × head direction in the horizontal plane; (107)], tilt directionality (spatial information content of firing rate × head tilt), directional stability (correlation between firing rate maps filtered to include left or right movements only), tilt stability (correlation between firing rate maps filtered to include head tilt up or down movements only), and terrain score (correlation between each cell’s firing rate map and a map of absolute terrain slope). The model was fit using ordinary least-squares regression (MATLAB fitglm) with the form: repetition score ∼ speed score + directionality + tilt directionality + directional stability + tilt stability + terrain score (this notation means that the model will seek to explain the repetition score variable as a function of these other parameters).

Partial R² values were used to estimate the unique contribution of each predictor. The full model explained R² = 0.232, indicating that ~23% of the variance in repetition score was accounted for by the included factors. Terrain score remained highly significant when all other predictors were included, indicating that terrain geometry uniquely explains a large proportion of the variance in repetition score beyond behavioral or directional confounds.

Histology

At the end of the experiment animals were anesthetized, given an overdose of pentobarbital intraperitoneally (Euthasol, Virbac, TX), and perfused with 0.9% saline solution followed by a 4% formalin solution. The brain was extracted and stored in 4% formalin for at least 4 days before any histological analyses. Brains were sliced coronally in 30-μm sections on a freezing microtome at −20°C. These sections were stained with a 0.125% thionin (Sigma-Aldrich, MA, no. 861340) solution, and the slice that best represented the electrode track was then imaged. Histology results for every animal are shown in fig. S2E.

Supplementary Materials

This PDF file includes:

Figs. S1 to S14