We performed electrophysiological recordings of neuronal activity in RSC (Figure 1A, Figure 1—figure supplement 1) of rats as they explored a squared open field arena and foraged for scattered chocolate pellets (Figure 1B). All animals were sufficiently habituated to the environment and procedures, and actively explored the entire arena (Figure 1C). The experimental setup was placed in the room with fixed landmarks to allow the animals to orient themselves relative to external features.

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We recorded the activity of 5415 RSC neurons across eight animals (n = 82 sessions) and observed a subpopulation of cells that fired consistently at the edge of the arena (Figure 1C). Across this subgroup, there was a variety of preferred firing distances from the wall, ranging from very near proximity up to a body-length (15–18 cm) away. Unlike traditional border cells found in MEC and subiculum (Solstad et al., 2008; Stewart et al., 2014), these border responses occurred throughout the environment on each of the four available walls. RSC border cells furthermore form multiple firing fields that are not necessarily directly connected to the wall. Typical border cell classification using the original border score (Solstad et al., 2008) identified only a small fraction of border cells in RSC, as this score is based on the occupancy of a single firing field along a wall and is strongly biased to connected bins (Figure 1—figure supplement 2A–C). We thus developed a new model-based approach using a template-matching procedure to classify these border cells in RSC (Figure 1D–F), based on Grossberger et al., 2018.

This method uses two-dimensional (2D) information of the firing rate maps and builds on the assumption that border cells have their spikes concentrated at the entire outer ring of the arena, incorporating geometric information into the classification procedure. The dissimilarity between a cell’s spatial firing rate map and a ‘boundary’ template (Figure 1D,E) was assessed by the algorithm based on the Earth Mover's Distance (Hitchcock, 1941; Rubner et al., 1998) (EMD; see Materials and methods), a distance metric from the mathematical theory of optimal transport. The EMD is a normalized score, calculated as the minimum cost required to match a cell’s firing rate map with the template distribution by moving firing rate units, also known as the Wasserstein distance. While this metric is sensitive to a change in the geometric shape of rate maps, it is robust to small variations of preferred firing distances or pixel-by-pixel jittering, giving a single metric that can quantitatively assess changes in the cell's spatial tuning as a function of experimental manipulations, such as reshaping of the maze or adding an object or wall.

Border cells were defined as cells with a low dissimilarity EMD score below the 1st percentile of a spike-shuffled null distribution of 0.191, and an average firing rate (FR) above 0.5 Hz. Null distributions of EMD scores were invariant to the overall FR of cells included, giving a consistent criterion across cells (Figure 1—figure supplement 2F). In total, 485 out of 5415 RSC cells (9.0%) passed this criterion (Figure 1E,F, Figure 1—figure supplement 2G), where neurons showed no relationship between their overall spiking rate and associated EMD score (Pearson’s correlation: r = 0.037, p=0.42; Figure 1—figure supplement 2D). Selected border cells had a similar distribution of average firing rates compared to other recorded cells (border cells: FR = 2.97 ± 0.20 Hz, others: FR = 3.25 ± 0.07 Hz; Wilcoxon ranksum test: z = 0.057, p=0.955; Figure 1G), but had significantly higher spatial correlations between the first and last recording sessions (border cells: r = 0.52 ± 0.008, others: r = 0.20 ± 0.003; Wilcoxon ranksum test: z = −24.50, p=1.60 × 10⁻¹³²; Figure 1H). Border cells were recorded across the granular and dysgranular regions of the RSC, and had waveform properties similar to other cells recorded on the same tetrodes (Figure 1—figure supplement 3A,B,D,E). Border cells showed activity already from the beginning of the session and did not need time for adaptation in a novel arena and experimental room (first-half familiar session, FR = 1.98 ± 0.42 Hz; first-half novel session, FR = 2.30 ± 0.53 Hz, p=0.56; second half novel session, FR = 1.71 ± 0.54 Hz, p=0.68; Wilcoxon signed-rank test; n = 14 border cells; Figure 1—figure supplement 4D–G). While firing of RSC border cells was additionally modulated by the running speed of the animal, with lower firing rates in the low-speed range (p<0.05 in the range of 0–12 cm/s; Wilcoxon ranksum test; Figure 1—figure supplement 3G), this modulation could not account for the cell’s spatial tuning, as the animal’s average speed was uniform across space and unrelated to the distance to any boundary (non-significant in the range of 5–45 cm; Wilcoxon ranksum test against overall median; Bonferroni-corrected α = 0.005; Figure 1—figure supplement 3F,H). Applying an unbiased classification approach based on linear-nonlinear models (Hardcastle et al., 2017) showed that running speed and wall-distance are two independent factors that explain the activity of RSC cells, confirming that RSC border and speed tuning are separately expressed features (Figure 1—figure supplement 3C).

To understand the generation of boundary coding in RSC, we quantified the impact of the change of environmental features on the activity of RSC border cells by using the EMD metric. We first asked if the firing of these border cells is limited to walls, or whether these cells also encode information about other features of the environment, such as local cues or objects (Høydal et al., 2019; Jacob et al., 2017). Our first manipulation was to temporarily add a wall, protruding from one side into the center of the maze (Figure 2A,B). Border cells formed new firing fields around the added walls accordingly, as their firing rate inside a region-of-interest (ROI; 15 × 5 spatial bins) around the wall increased significantly in the added wall sessions (Regular: FR = 1.19 ± 0.13 Hz; Added wall: FR = 1.58 ± 0.21 Hz; Wilcoxon signed-rank test: z = −2.67, p=0.0076; n = 42 border cells; Figure 2C). This was accompanied by a sharp drop in spatial correlations between rate maps of regular versus added wall sessions (Reg-Reg: r = 0.51 ± 0.04, Reg-Wall: r = 0.25 ± 0.04; Wilcoxon signed-rank test: z = 4.43, p=9.31 × 10⁻⁶; Bonferroni-corrected α = 0.025; Figure 2D), while correlations remained high when comparing within session types (Wall-Wall: r = 0.47 ± 0.03; Wilcoxon signed-rank test with Reg-Reg correlation: z = 0.63, p=0.53; Bonferroni-corrected α = 0.025; Figure 2D). The EMD metric furthermore showed a significant increase in dissimilarity between rate maps of these added wall sessions and the original boundary template (Normalized boundary EMD score: R1, 1.0 ± 0, W1, 1.178 ± 0.03, W2, 1.223 ± 0.03, R2, 1.016 ± 0.01; Friedman test: X²(3)=77.9, p=8.6 × 10⁻¹⁷; Post-hoc Wilcoxon signed-rank test: R1-W1, z = −5.35, p=9.0 × 10⁻⁸, R1-W2, z = −5.58, p=2.37 × 10⁻⁸, R1-R2, z = −1.27, p=0.20; Bonferroni-corrected α = 0.017; Figure 2E). In contrast, the dissimilarity between the same rate maps and an ‘added wall’ template decreased significantly (Normalized wall EMD score: R1, 1.0 ± 0, W1, 0.918 ± 0.02, W2, 0.934 ± 0.03, R2, 1.057 ± 0.02; Friedman test: X²(3)=33.7, p=2.3 × 10⁻⁷; Post-hoc Wilcoxon signed-rank test: R1-W1, z = −3.89, p=9.8 × 10⁻⁵, R1-W2, z = 2.59, p=0.0095, R1-R2, z = −2.22, p=0.027; Bonferroni-corrected α = 0.017; Figure 2E), indicating that firing fields of border cells incorporated boundary information of the added wall. Recordings performed in arenas with a hexagonal, circular, or triangular shape further confirmed the adaptation of firing fields of RSC border cells to the spatial layout of boundaries (Figure 1—figure supplement 4A–C).

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To investigate generalization to other environmental features, we further added additional objects to the arena and tested the specificity of border responses to the spatial layout (Figure 2F,G). The size of the object was 10 cm in diameter, and the animal could walk around or climb on top without it impeding the animal’s movement completely. Contrary to an added wall, RSC border cells maintained tuning only to the outer walls and did not fire whenever objects were inside their receptive field (Circular ROI, eight bins in diameter; Regular: FR = 1.39 ± 0.26 Hz; Added object: FR = 1.42 ± 0.21 Hz; Wilcoxon signed-rank test: z = −0.63, p=0.53; n = 23 border cells; Figure 2H). EMD analyses however showed a significant increase in dissimilarity to the boundary template in the object sessions (Normalized boundary EMD score: R1, 1.0 ± 0, O1, 1.097 ± 0.031, O2, 1.079 ± 0.028, R2, 1.024 ± 0.021; Friedman test: X²(3)=14.7, p=0.002; Post-hoc Wilcoxon signed-rank test: R1-O1, z = −2.74, p=0.006, R1-O2, z = −2.62, p=0.009, R1-R2, z = −1.00, p=0.32; Bonferroni-corrected α = 0.017; Figure 2J), indicating changes in the rate maps by the object. This change was not due to new firing fields around the object, however, because fitting an ‘object’ template did not lead to a decrease in dissimilarity during object sessions (Normalized object EMD score: R1, 1.0 ± 0, O1, 1.026 ± 0.026, O2, 0.995 ± 0.029, R2, 0.990 ± 0.025; Friedman test: X²(3)=2.32, p=0.51; Figure 2J). The maintenance of original firing fields was further confirmed by spatial correlations across session types that did not drop when comparing rate maps between regular and object sessions, neither for the outer rows of pixels adjacent to the walls (Reg-Reg: r = 0.36 ± 0.07, Object-Object: r = 0.47 ± 0.07; z = −0.88, p=0.38; Reg-Object: r = 0.45 ± 0.07; comparing with R-R: z = −1.28, p=0.20; comparing with R-O: z = 1.16, p=0.25; Wilcoxon signed-rank test; Bonferroni-corrected α = 0.017; Figure 2I, right panel), nor the inner area surrounding the object (Reg-Reg: r = 0.29 ± 0.07, Object-Object: r = 0.49 ± 0.05: z = −1.58, p=0.11; Reg-Object: r = 0.33 ± 0.07; comparing with R-R: z = −0.49, p=0.63; comparing with R-O: z = 1.16, p=0.25; Wilcoxon signed-rank test; Bonferroni-corrected α = 0.017; Figure 2I, left panel). Taken together, these results indicate that RSC border cells encode information that is specific to boundaries of the spatial layout where cell responses differentiate between the types of added features.

One way for border cells to compute information of boundaries is through direct sensory detection of the walls, for example, by whisking or visual observation (Raudies and Hasselmo, 2012). We investigated the importance of direct sensory input on border tuning by removing either visual or somatosensory information of the boundary (Figure 3A,E). First, to assess the impact of visual information, we introduced an infrared position tracking system as opposed to regular light-emitting diodes (LED; see Materials and methods) to ensure no visible light was present in the maze for animals to identify boundaries. We recorded the activity of RSC border cells in both dim-light and darkness conditions, but observed no significant changes in EMD dissimilarity scores across the sessions (Boundary EMD score: R1, 0.183 ± 0.001, D1, 0.185 ± 0.003, D2, 0.177 ± 0.003, R2, 0.182 ± 0.002; Friedman test: X²(3)=1.23, p=0.75; n = 21 border cells; Figure 3B,D). There were also no changes across spatial correlations between different session types (Reg-Reg: r = 0.42 ± 0.03, Reg-Dark: r = 0.38 ± 0.03; Wilcoxon signed-rank test z = 0.61, p=0.54; Dark-Dark: r = 0.42 ± 0.05, Wilcoxon signed-rank test with Reg-Reg correlation, z = 1.20, p=0.23; Bonferroni-corrected α = 0.025; Figure 3C), indicating that activity is not generated through visual sensory input.

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In order to examine the role of tactile sensation on boundary representations, we next removed all four outer walls that left a drop-edge above the floor, limiting movement of the animal in the absence of direct somatosensory information of a physical barrier (Figure 3E). The EMD scores showed that the majority of border cells were unaffected by the wall removal, with no significant changes in the drop-edge session (Unaffected cells: boundary EMD score: R1, 0.183 ± 0.002, Drop, 0.186 ± 0.003, R2, 0.183 ± 0.001; Friedman test: X²(2)=4.59, p=0.10; n = 17 border cells; Figure 3G). However, a subset of cells had disrupted firing nearby the boundary edges (n = 8/25 affected cells, separated based on an increase in EMD that exceeded the 95^th-percentile of a null distribution of change, computed using the differences between first and last regular sessions; boundary EMD score: R1, 0.169 ± 0.008, Drop, 0.202 ± 0.004, R2, 0.175 ± 0.006; Friedman test: X²(2)=11.0, p=0.004; Post-hoc Wilcoxon signed-rank test: R1-Drop, z = −2.95, p=0.003, R1-R2, z = 0, p=1.0; Bonferroni-corrected α = 0.025; Figure 3G). A similar result emerged from the spatial correlations, where rate map correlations remained high when comparing regular and drop-edge sessions, but only for the unaffected cells that had stable EMD scores across session type (Unaffected cells: Reg-Reg, r = 0.50 ± 0.04, Reg-Drop, r = 0.45 ± 0.04; Wilcoxon signed-rank test: z = 1.21, p=0.23; Affected cells: Reg-Reg, r = 0.57 ± 0.05, Reg-Drop, r = 0.14 ± 0.07; Wilcoxon signed-rank test: p=0.008; Figure 3H).

To directly test the necessity of whisker-mediated tactile sensation, we trimmed the animal’s whiskers after which they freely explored the arena (Figure 3—figure supplement 1A,B). We did not observe a significant change in the proportion of border cells in RSC after the trimming of whiskers (intact whiskers: 29/276 cells classified as border cells, boundary EMD score = 0.183 ± 0.002; trimmed whiskers: 23/285 cells classified as border cells, boundary EMD score = 0.186 ± 0.005; change in proportion of border cells: z = 1.00, p=0.32, binomial test; Figure 3—figure supplement 1B), nor did we see a change in the overall firing rates (before: FR = 1.58 ± 0.38; after: FR = 1.16 ± 0.47; Wilcoxon signed-rank test: z = 1.04, p=0.30; Figure 3—figure supplement 1C), suggesting that whisker sensation is not essential for boundary representation. We further recorded from cells located in the barrel field region of the somatosensory cortex (S1bf) in order to understand the nature of somatosensory information through whiskers (Figure 3—figure supplement 1D–F). Although we were able to identify a subpopulation of cells that fired nearby boundaries in the somatosensory cortex (n = 23/173 cells classified as border cells using the same criteria; Figure 3—figure supplement 1G), an important difference with RSC cells is that S1bf neurons fired consistently near added objects when introduced into the arena, highlighting the selective tuning of RSC border cells to boundaries but not objects (Normalized boundary EMD score: R1, 1.0 ± 0, O1, 1.067 ± 0.01, O2, 1.084 ± 0.01, R2, 0.971 ± 0.01; Friedman test: X²(3)=47.1, p=3.3 × 10⁻¹⁰; Post-hoc Wilcoxon signed-rank test: R1-O1, z = −3.65, p=2.6 × 10⁻⁴, R1-O2, z = −3.89, p=9.9 × 10⁻⁵, R1-R2, z = 2.95, p=0.003; Bonferroni-corrected α = 0.017; Normalized object EMD score: R1, 1.0 ± 0 O1, 0.977 ± 0.005, O2, 0.967 ± 0.005, R2, 1.015 ± 0.004; Friedman test: X²(3)=47.5, p=2.7 × 10⁻¹⁰; Post-hoc Wilcoxon signed-rank test: R1-O1, z = 3.50, p=4.7 × 10⁻⁴, R1-O2, z = 3.80, p=1.4 × 10⁻⁴, R1-R2, z = −3.16, p=0.002; Bonferroni-corrected α = 0.017; Figure 3—figure supplement 1H). Together, these results suggest that the activity of RSC border cells is not simply driven by the detection of boundaries through visual or tactile sensation, and their distinct firing around boundaries but not objects implies additional computations in the brain.

Our results so far suggest that RSC border cells are sensitive to the spatial layout of the environment, allowing for the distinction between boundaries and objects. However, recent reports point to the egocentric tuning of neurons in the postrhinal cortex, RSC or striatum to walls or the center of the maze, suggesting anchoring to local features of the environment (Alexander et al., 2020; Hinman et al., 2019; LaChance et al., 2019). To better clarify how border cells are anchored to the environment, we explored the impact on RSC cells of global environmental manipulations under which allocentric spatial cells shift their firing fields (Knierim and Rao, 2003).

We first confirmed that RSC border cells described here have a similar direction tuning as reported in Alexander et al., 2020, where spikes that occur near the wall are constraint by specific directions of the animal relative to the boundary (Figure 4A). Across the population of border cells identified with the EMD metric, 190 out of 485 neurons (39.2%) had significant egocentric directional tuning, with mean vector lengths above the 95th percentile of a spike-shuffled distribution in all regular sessions (Figure 4—figure supplement 1A,B). Conversely, only 190 out of 666 directionally-tuned cells (28.5%) had additional boundary-distance tuning (Figure 4—figure supplement 1A), making the population of neurons reported here considerably different from Alexander et al., 2020. Projecting trajectory data onto new body-centric axes, where coordinates indicate distance and direction of the nearest wall relative to the animal, confirmed that directionally-tuned border cells fired predominantly whenever the wall occupied proximal space at a particular angle from the animal’s viewpoint (Figure 4B,C, Figure 4—figure supplement 2).

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We then sought to establish whether this egocentric constraint was imposed by the head-direction signal through the integration with spatial or sensory cues of the environment, as RSC receives inputs from the anterior limbic system that is a major source of head-direction signals, and a subpopulation of RSC cells are tuned to allocentric head-direction (Chen et al., 1994; Mitchell et al., 2018). If the egocentric boundary representation of RSC border cells is driven by internally generated global direction signals, realignment of the head-direction cells may affect the preferred tuning direction of RSC border cells. In order to manipulate the tuning of head-direction cells, four blue landmark LEDs were placed on one side of the maze while all other sensory cues were kept invariant across the environment. The entire experimental setup was then rotated 90° clockwise in the middle sessions (Figure 4D). As a result, all allocentric head-direction (HD) cells rotated their tuning curves accordingly, although not a full 90° (A-A’: median shift = 2.6°, z = 1.23, p=0.23; B1-B2: median shift = 0.8°, z = 0.61, p=0.54; A-B1: median shift = 62.9°, z = 4.62, p=3.8 × 10⁻⁶; A-B1 rotated: median shift = −27.3°, z = −3.07, p=0.002; Wilcoxon signed-rank test; Bonferroni-corrected α = 0.013; n = 28 HD cells; Figure 4G). The preferred direction of all border cells that had significant directional tuning, in contrast, remained unchanged (two representative cells in Figure 4E,F; A-A’: median shift = 0°, z = 0.14, p=0.89; B1-B2: median shift = 0°, z = −1.21, p=0.22; A-B1: median shift = 0°, z = 2.42, p=0.015; A-B1 rotated: median shift = −68°, z = −3.74, p=1.8 × 10⁻⁴; Wilcoxon signed-rank test; Bonferroni-corrected α = 0.013; n = 31 directionally-tuned border cells; Figure 4G). This result indicates that the direction tuning of RSC border cells is generated either through the local sensation of walls independent of the head-direction signal or by the integration of allocentric boundary-position and head-direction coding that rotated together. The RSC’s ability to discriminate between boundaries and objects, together with the invariance of border tuning in the absence of visual or tactile signals, goes against the mechanism of local sensation. By contrast, in accordance with the latter possibility, we found that RSC neurons with position-selective firing, defined as cells with spatial correlations above the 99th percentile of a spike-shuffled distribution that are not border cells, rotated along with head-direction cells in RSC (two example cells in Figure 4H; spatial correlations: A-A’, r = 0.63 ± 0.018, A-B, r = 0.48 ± 0.058, Wilcoxon signed-rank test: z = 3.52, p=4.4 × 10⁻⁴; A-B rotated, r = 0.70 ± 0.033, Wilcoxon signed-rank test: z = −1.07, p=0.29; n = 32/384 spatially stable cells). RSC border cells thus maintained wall-tuning as their conjunctive coding of position and head-direction rotated together with the environment.

To further obtain the functional implications, we asked if any directional bias of egocentric tuning exists in RSC border cells by performing large-scale recordings from both hemispheres. Across the population, cells were tuned predominantly to the very near proximity (main peak at 5 cm; Figure 4J), although some cells had fields at extended distances up to 20 cm away from the wall. In order to account for a potential proximity bias of our boundary template, we simulated a set of synthetic neurons that fire at specific wall distances using all behavioral data, and found that our boundary template was able to classify cells with firing fields up to 18 cm away from the walls (Figure 4—figure supplement 1C). However, cell classification using new templates with fields at increasing distances did not yield a substantial new number of cells (Figure 4—figure supplement 1D), confirming that the majority of RSC border cells exhibit distance tuning at the proximity of walls.

Regarding their preferred egocentric tuning direction, we observed a disproportionately biased distribution of preferred directions, dependent on the hemisphere where cells were recorded (Left hemisphere: mean direction = −114°, z = 3.16, p=0.041; n = 41 directionally-tuned border cells; Right hemisphere: mean direction = 41°, z = 38.8, p=9.1 × 10⁻¹⁹; n = 149 directionally-tuned border cells; Rayleigh test; comparing both distributions: two-sample Kuiper test, k = 3.1 × 10³, p=0.001; Figure 4I). The majority of border cells were tuned to the contralateral side of the recorded hemisphere, although not exclusively (Figure 4I). This hemisphere-specific tuning bias implies that boundary representations in RSC may be generated by direct sensory signals, or reflect the command of motor actions, in both of which it arises along the right-left body axis. However, a loss of tactile sensation by whisker trimming had no effect on the extent of directional tuning of border cells (before trimming: 7/49 cells had significant directional tuning, MVL = 0.538 ± 0.06; after trimming: 10/49 cells were significantly tuned, MVL = 0.502 ± 0.08; change in MVL: t(6) = 1.80, p=0.12, t-test; change in cell proportion: z = 1.05, p=0.29, binomial test; Figure 3—figure supplement 1A,B), nor did recording in complete darkness affect the directional tuning of cells (light conditions: 5/21 cells had significant directional tuning, MVL = 0.326 ± 0.07; darkness: 4/5 cells maintained their tuning, 2/16 cells were tuned only in darkness, MVL = 0.318 ± 0.05; change in MVL: t(4) = −0.51, p=0.64, t-test; change in cell proportion: z = 0.33, p=0.75, binomial test), implying that this bias is not a direct consequence of the lateralized nature of sensory input.

While our results suggest that egocentric boundary coding in RSC is likely formed by using allocentric position and head-direction signals, the exact underlying circuit mechanism has not been determined. The RSC is known to have direct, bi-directional connections with the medial entorhinal cortex (MEC) (Jones and Witter, 2007; Ohara et al., 2018), which contains several types of neurons that exhibit allocentric spatial tuning such as grid cells, head-direction cells or border cells (Boccara et al., 2010; Hafting et al., 2005; Sargolini et al., 2006; Solstad et al., 2008). Given the presence of boundary-responsive cells in both RSC and MEC, it is crucial to establish the direction and extent of functional dependence between these brain regions.

We first addressed the question of whether there is any communication between MEC and RSC in terms of encoding border information using pharmacogenetic inactivation techniques (Armbruster et al., 2007). We injected an AAV encoding the inhibitory DREADDs hM4Di into MEC, while simultaneously implanting a 28-tetrode hyperdrive into RSC (Figure 5A, Figure 5—figure supplement 1). Subcutaneous administration of agonist-21 (DREADDs agonist; Thompson et al., 2018) resulted in a drastic reduction of firing after 20 min for a group of cells in MEC that were infected with the virus (26 out of 44 cells recorded near the injection site with additional tetrodes in MEC significantly reduced their firing rates to 47.2 ± 5.5% of their baseline firing; Figure 5B, Figure 5—figure supplement 1), while not affecting the running speed of the animal (Figure 5—figure supplement 1). Inactivation of MEC led to a subsequent partial disruption of firing in a subset of RSC border cells (Figure 5C), worsening border tuning that resulted in higher EMD scores (before: EMD score = 0.181 ± 0.002, after: EMD score = 0.186 ± 0.003; Wilcoxon signed-rank test: z = −2.40, p=0.016; n = 102 border cells; Figure 5D) and lower overall firing rates after the manipulation (before: FR = 1.52 ± 0.20 Hz, after: FR = 1.12 ± 0.24 Hz, Wilcoxon signed-rank test: z = 3.15, p=0.0016; Figure 5E). Next, we performed a reversed manipulation, injecting the virus encoding DREADDs hM4Di into RSC while recording neural activity in MEC (Figure 5F, Figure 5—figure supplement 1). Administration of agonist-21 led to similar decreased activity in RSC for the infected cells (Figure 5G), but RSC inhibition had no significant effect on MEC border cell tuning (before: border score = 0.53 ± 0.013, after: border score = 0.53 ± 0.01; Wilcoxon signed-rank test: z = 0.56, p=0.57; n = 83 border cells; Figure 5H,I) or average firing rates (before: FR = 1.33 ± 0.11 Hz, after: FR = 1.27 ± 0.12 Hz; Wilcoxon signed-rank test: z = −0.31, p=0.76; Figure 5J).

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While these DREADDs-mediated manipulation experiments suggest the involvement of MEC signals for border computations in RSC, it is possible that MEC inhibition had only an indirect effect on RSC activity, for example by reducing inputs to other communication partners of RSC such as the subiculum (Roy et al., 2017). We thus performed two additional manipulation experiments that directly target the MEC-RSC pathway, using optogenetic techniques. We first injected an AAV encoding inhibitory Halorhodopsin chloride pumps (eNpHR3.0; Zhang et al., 2007) into MEC, combined with the implantation of tetrodes and an optic fiber in RSC, allowing for silencing of axon terminals of MEC neurons that project to RSC (Figure 5K, Figure 5—figure supplement 2). Our second approach was to inject a retroAAV (Tervo et al., 2016) encoding red-shifted Cruxhalorhodopsin chloride pumps (Jaws; Chuong et al., 2014) into RSC together with a silicon-probe for neural recordings, while an optic fiber was placed at the dorsal edge of MEC to allow for cell-body inhibition of RSC-projecting neurons (Figure 5M, Figure 5—figure supplement 2). This virus was expressed specifically in the deeper layers of MEC, with a gradient that decayed from dorsal to the ventral regions (Figure 5M, Figure 5—figure supplement 2). Activation of laser light during behavior of the animal led to a subsequent disruption of border coding in RSC, with cells losing specificity of firing near the edges and forming firing fields in the center of the arena (Figure 5L,N), resulting in an increase in EMD dissimilarity scores across the population, both for axon-terminal inhibition (Boundary EMD score: laser OFF₁, 0.187 ± 0.003, laser ON, 0.203 ± 0.003, laser OFF₂, 0.190 ± 0.005; Friedman test: X²(2)=6.9, p=0.032; Post-hoc Wilcoxon signed-rank test: OFF₁-ON, z = −3.45, p=5.7 × 10⁻⁴, OFF₁-OFF₂, z = −1.55, p=0.12; Bonferroni-corrected α = 0.025; n = 34 border cells; Figure 5O, Figure 5—figure supplement 3B) and cell-body inhibition (Boundary EMD score: laser OFF₁, 0.184 ± 0.002, laser ON, 0.192 ± 0.002, laser OFF₂, 0.189 ± 0.002; Friedman test: X²(2)=24.5, p=4.7 × 10⁻⁶; Post-hoc Wilcoxon signed-rank test: OFF₁-ON, z = −4.97, p=6.7 × 10⁻⁷, OFF₁-OFF₂, z = −4.11, p=4.0 × 10⁻⁵; Bonferroni-corrected α = 0.025; n = 141 border cells; Figure 5O, Figure 5—figure supplement 3B) that partially recovered after turning laser light off. Unlike our DREADD inhibition results, there were no significant changes in the overall firing rates of RSC border cells (Laser ON: normalized FR = 0.94 ± 0.04, Wilcoxon signed-rank test: z = 1.68, p=0.09; laser OFF₂: normalized FR = 0.96 ± 0.04, Wilcoxon signed-rank test: z = −1.80, p=0.07; Figure 5—figure supplement 3A), and there were no observable changes in the behavior of the animals (Figure 5—figure supplement 3D–F). Cell classification criteria allowed cells to drop their average firing rates below the rate threshold of 0.5 Hz in the manipulated session, as a reduction in spiking rate indicates disrupted coding. In order to confirm that the increased EMD scores during MEC inhibition were not driven by spurious rate maps of low-firing cells, we repeated the EMD analysis after excluding all cells with an average firing rate below 0.5 Hz in the laser ON session (axon-terminal inhibition, identical results with 34/34 cells; cell-body inhibition, Boundary EMD score: laser OFF₁, 0.183 ± 0.002, laser ON, 0.192 ± 0.002, laser OFF₂, 0.189 ± 0.002; Friedman test: X²(2)=26.9, p=1.4 × 10⁻⁶; Post-hoc Wilcoxon signed-rank test: OFF₁-ON, z = −5.26, p=1.4 × 10⁻⁷, OFF₁-OFF₂, z = −4.51, p=6.6 × 10⁻⁶; Bonferroni-corrected α = 0.025; n = 138/141 border cells), but obtained the same conclusions.

In order to control for non-specific effects of laser application, we performed an additional control experiment in two animals (Figure 5—figure supplement 4). Recording of RSC neurons in the absence of inhibitory opsin expression showed stable firing patterns for border cells near all boundaries of the environment, before, during and after the application of laser light, with no changes for the neurons in their EMD scores (Boundary EMD score: laser OFF₁, 0.173 ± 0.002, laser ON₁, 0.176 ± 0.003, laser ON₂, 0.174 ± 0.004, laser OFF₂, 0.170 ± 0.001; Friedman test: X²(3)=5.44, p=0.14; n = 33 border cells; Figure 5—figure supplement 4D) or overall firing rates (FR: laser OFF₁, 2.95 ± 0.72, laser ON₁, 2.43 ± 0.75, laser ON₂, 2.39 ± 0.88, laser OFF₂, 2.78 ± 0.68; Friedman test: X²(3)=2.64, p=0.45; Figure 5—figure supplement 4C), confirming that the impairment of boundary tuning in RSC during laser application is specific to the silencing of MEC inputs.

In contrast to border cells, our optogenetic manipulations did not affect allocentric head-direction tuning in RSC, with no changes in firing rate (Average FR: laser OFF₁, 1.86 ± 0.53, laser ON, 1.68 ± 0.61, laser OFF₂, 1.91 ± 0.62; Friedman test: X²(2)=0.17, p=0.92; n = 47 HD cells; Figure 5—figure supplement 3G), mean vector length (MVL: laser OFF₁, 0.29 ± 0.03, laser ON, 0.26 ± 0.03, laser OFF₂, 0.28 ± 0.03; Friedman test: X²(2)=6.64, p=0.036; Post-hoc Wilcoxon signed-rank test: OFF₁-ON, z = 2.17, p=0.030, OFF₁-OFF₂, z = 1.92, p=0.055; Bonferroni-corrected α = 0.025; Figure 5—figure supplement 3H), nor a shift in the preferred direction (Shift in preferred direction: laser OFF₁-ON, 0.056 ± 0.06; Wilcoxon signed-rank test: z = 0.95, p=0.34; laser OFF₁-OFF₂, −0.005 ± 0.07; Wilcoxon ranksum test: z = 0.20, p=0.84; Bonferroni-corrected α = 0.025; Figure 5—figure supplement 3I) for allocentric head-direction cells, indicating that the head-direction signal in RSC is likely provided by brain regions other than MEC, for example, the anterodorsal thalamic nucleus (Mitchell et al., 2018). Further analysis on spatially-stable cells, classified based on high spatial correlations across sessions (see Figure 4H), shows that inhibition of MEC did affect firing of spatial cells in RSC, as spatial correlations significantly dropped during laser on sessions (spatial correlations: laser OFF1-OFF2, r = 0.59 ± 0.02, laser OFF1-ON, r = 0.44 ± 0.03; Wilcoxon signed-rank test: z = 5.87, p=4.5 × 10⁻⁹; n = 83 spatial cells; Figure 5—figure supplement 3C), suggesting that spatial firing beyond border cording is contingent on spatial information coming from MEC. Altogether our manipulation results confirm that both RSC and MEC are involved in a broader border coding network, where border representations in RSC are dependent on direct inputs from MEC but not vice versa.

We have shown that MEC input is necessary to maintain sharp border tuning in RSC. However, border cells in both regions differ in their respective firing properties, for example, MEC border cells have firing fields consistently attached to only one or two walls rather than all, indicating allocentric representations of boundaries (two examples shown in Figure 6A; variance between average FR near each wall: RSC, CV = 0.103 ± 0.004, MEC, CV = 0.458 ± 0.02; Wilcoxon ranksum test: z = −13.25, p=4.6 × 10⁻⁴⁰; Figure 6—figure supplement 1C). This raises the question of how spatial information in MEC converges and maps onto RSC border cells. We thus compared the nature and content of information present in spikes of border cells between both regions with respect to the animal’s behavior.

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We first quantified the spatial information carried by spikes of border cells in RSC and MEC at a population level. The peak firing rates of border cells in RSC were lower than in MEC (RSC: FR = 4.02 ± 0.53 Hz, MEC: FR = 5.30 ± 0.47 Hz, Wilcoxon ranksum test: z = 2.79, p=0.0053; Figure 6—figure supplement 1D), but both populations had a similar distribution of peak distance tuning (Figure 4J, Figure 6—figure supplement 1E). Regarding directional tuning properties, we observed that nearly all directionally-selective border cells in RSC have egocentric directional tuning, while MEC border cells show a high degree of conjunctive selectivity to allocentric head-direction (Figure 6B). A decoder based on support vector machines estimated the animal's distance away from the wall using population spiking activity, and performed with high accuracy for both MEC and RSC in the lower distance range (p<0.05 for 0–20 cm, compared with a chance level of 20%; Figure 6C), whereas the animal’s running speed was not significantly different across distance bins (Kruskal-Wallis test: X²(4)=3.24, p=0.519). However, decoding performance from RSC activity dropped to chance level in the higher distance range (p>0.05 for 30–50 cm; Figure 6C), suggesting RSC border cells mainly encode local information. This matches the firing properties of RSC cells which have preferred distance tuning up to 20 cm away from the wall (Figure 4J). Conversely, MEC computes distance information that extends toward the center of the arena, with decoding performance above chance-level until the maximum range of 50 cm (p<0.05 for 0–50 cm; Figure 6C). Even though MEC border cells fire maximally at the edge of the arena, population vector correlations along neighboring bins decay faster for MEC than RSC, particularly when the animals are more than 20 cm away from the wall (Figure 6—figure supplement 1A,B), which allows for MEC cells to distinguish wall distance to a larger extent.

To further explore if the activity of border cells has behavioral correlates, we finally examined the relationship between cell firing and the animal’s self-motion, computing rate maps for movement directions (Figure 6D). Shifting spike times in respect to the animal’s motion revealed that spikes of RSC border cells tend to precede a particular movement of the animal, as the amount of information present in motion maps is maximal when shifting spikes earlier in time (p<0.05 for the time lag range of −300 to −50 ms compared to shuffled data; Figure 6E,F). This shift was not observed in motion rate maps of MEC border cells, which peaks at zero time lag (Figure 6G), showing that spike correlations of RSC border cells with prospective motion are not simply due to behavioral restrictions near walls. Next, we aligned the animal’s changes in movement direction using the cell’s spike timings, which revealed consistent turning behavior of the animal 200 ms after cell firing (Figure 6H). The direction of turning was opposite for cells recorded in different hemispheres, where border cells in right RSC fired prospective to right turns, while spikes in left RSC preceded left turns (Figure 6H). Such prospective correlates were not observed in MEC border cells (Figure 6I), nor in simulated cells with egocentric border tuning (Figure 6—figure supplement 1F,G), confirming the relationship between RSC border cell firing and the animal’s next motion. These results together support the idea that RSC and MEC encode different aspects of border representations, playing distinct roles in navigation behavior.

All experiments were approved by the local authorities (RP Darmstadt, protocol F126/1009) in concordance with the European Convention for the Protection of Vertebrate Animals used for Experimental and Other Scientific Purposes. Subjects were 19 male Long-Evans rats weighing 400 to 550 g (aged 3–5 months) at the start of the experiment. Rats were housed individually in Plexiglass cages (45 × 35 × 40 cm; Tecniplast GR1800) and maintained a reversed 12 hr light-dark cycle, with behavioral experiments performed during the dark phase. Animals were mildly food-restricted with unlimited access to water and kept at 85–90% of their free-feeding body-weight throughout the experiment. For recording experiments, eight rats had tetrodes located unilaterally in RSC, either in the left (four rats) or right (four rats) hemisphere. One rat had a 64-channel silicon probe (Buzsaki64-sp; Neuronexus) implanted directly into the barrel field of the right primary somatosensory cortex (S1bf). Four rats were injected with an AAV encoding inhibitory DREADDs bilaterally in either MEC or RSC, combined with a tetrode drive in MEC or RSC in the right hemisphere. For optogenetic inactivation experiments, two rats were injected with a retroAAV (Tervo et al., 2016) expressing inhibitory Cruxhalorhodopsin chloride pumps (Jaws; Chuong et al., 2014) in the right RSC together with the implantation of a 64-channel silicon probe (Buzsaki64-sp), while an optic fiber was positioned above MEC. Finally, two more rats were injected with an AAV expressing inhibitory Halorhdopsin chloride pumps (eNpHR3.0; Zhang et al., 2007) in the right MEC, while eight tetrodes and an optic fiber were implanted together in the right RSC. No statistical method was used to predetermine sample size, although the number of animals used here is similar to previous work.

Anesthesia was induced by isoflurane (5% induction concentration, 0.5–2% maintenance adjusted according to physiological monitoring). For analgesia, Buprenovet (Buprenorphine, 0.06 mg/mL; WdT) was administered by subcutaneous injection, followed by local intracutaneous application of either Bupivacain (Bupivacain hydrochloride, 0.5 mg/mL; Jenapharm) or Ropivacain (Ropivacain hydrochloride, 2 mg/mL; Fresenius Kabi) into the scalp. Rats were subsequently placed in a Kopf stereotaxic frame, and an incision was made in the scalp to expose the skull. After horizontal alignment, several holes were drilled into the skull to place anchor screws, and craniotomies were made for microdrive implantation. The microdrive was fixed to the anchor screws with dental cement, while two screws above the cerebellum were connected to the electrode's ground. All tetrodes were then positioned at 920 μm depth from the cortical surface. All animals received analgesics (Metacam, 2 mg/mL Meloxicam; Boehringer Ingelheim) and antibiotics (Baytril, 25 mg/mL Enrofloxacin; Bayer) for at least 5 d post-surgery.

For tetrode recordings, rats were unilaterally implanted with a hyperdrive that contained 28 individually adjustable tetrodes made from 17 μm polyimide-coated platinum-iridium (90–10%; California Fine Wire; plated with gold to impedances below 150 kΩ at 1 kHz). The tetrode bundle consisted of 30-gauge stainless steel cannulae, soldered together in a 14 × 2 rectangular shape for recordings of the entire RSC, 7 × 4 for anterior RSC, or two squared bundles for bilateral MEC. For RSC, tetrodes were implanted alongside the anteroposterior axis, starting at (AP) −2.5 mm posterior from bregma until −4 mm to −6.5 mm, (ML) 0.8 mm lateral from the midline, (DV) 1.0 mm below the dura, and at a 25° angle in a coronal plane pointing to the midline in order the get underneath the superior sagittal sinus. For MEC, tetrodes were implanted at 4.5 mm lateral of the midline, 0.2 mm anterior to the transverse sinus, at an angle of 15 degrees in a sagittal plane with the tips pointing to the anterior direction. Experiments began at least 1 week post-surgery to allow the animals to recover.

For DREADDs experiments, an AAV8-hSyn-hM4Di-mCherry (a gift from Bryan Roth; Addgene viral prep # 44362-AAV8) was injected with an infusion rate of 100 nL/min using a 10 μL NanoFil syringe and a 33-gauge beveled metal needle (World Precision Instruments). After injection was completed the needle was left in place for 10 min. The virus was injected at two sites for each bilateral MEC (500 nL each at the depth of 2.5 mm and 3.5 mm from the cortical surface, 4.5 mm lateral to the midline, 0.2 mm anterior to the transverse sinus at an angle of 20° in a sagittal plane with the needle pointing to the anterior direction), or four sites along the anteroposterior axis for each bilateral RSC (500 nL each at AP 2.5, 3.5, 4.5, 5.5 mm, 0.8 mm lateral to the midline, at an angle of 25° in a coronal plane pointing to the midline). The flow was controlled with a Micro4 microsyringe pump controller. A small microdrive (Axona Ltd) connected to four-wire tetrodes was additionally implanted nearby the injection site to evaluate the effects of the manipulation. Virus injection was performed in the same surgery as electrode implantation, and recordings began at least 3 weeks post-surgery to allow time for the virus to express.

For optogenetic silencing of MEC terminals in RSC, an AAV1-hSyn-eNpHR3.0-EYFP (a gift from Karl Deisseroth; Addgene viral prep # 26972-AAV1) was injected into right MEC with the same procedure as the DREADDs experiments; injection location was 4.0 mm lateral to the midline, 0.2 mm anterior to the transverse sinus pointing 20° in the anterior direction, with two sites at 2.5 mm and 3.5 mm depths from the cortical surface (500 nL volume each). For optogenetic inhibition of MEC cells projecting to RSC, an AAV-retro-hSyn-Jaws-GFP (a gift from Edward Boyden; Addgene viral prep # 65014-AAVrg) was injected into right RSC at four sites (AP 2.5, 3.5, 4.5, and 5.5 mm, 0.8 mm lateral of the midline and pointing 25° to the midline; 500 nL volume each). Electrode and optic fiber implantation were performed 1 week following virus injection, and experiments began at least 3 weeks post-surgery.

All main analyses and data processing steps were performed in MatLab (MathWorks). Neural signals were acquired and amplified using two 64-channel RHD2164 headstages (Intan technologies), combined with an OpenEphys acquisition system, sampling data at 15 kHz. Neuronal spikes were detected by passing a digitally band-pass filtered LFP (0.6–6 kHz) through the 'Kilosort' algorithm to isolate individual spikes and assign them to separate clusters based on waveform properties (https://github.com/cortex-lab/KiloSort; Pachitariu et al., 2016). Clusters were manually checked and adjusted in autocorrelograms and for waveform characteristics in principal component space to obtain well-isolated single units, discarding any multi-unit or noise clusters. Tetrodes were moved a minimum distance of 80 µm between recording days to find a new set of neurons for the next recording session.

We applied a novel template-matching procedure to classify RSC neurons as border cells using the Earth Mover's Distance (EMD), a distance metric from the mathematical theory of optimal transport (Hitchcock, 1941; Rubner et al., 1998). First, the animal's spatial position occupancy was divided into 4 × 4 cm spatial bins, and the firing rate in each position bin was calculated by dividing the number of spikes with the amount of time spent there. The resulting rate map was smoothed by applying a 2D Gaussian filter (width of 1 bin), and converted to a probability distribution by taking unit weight. We then calculated the Earth Mover's Distance relative to a ‘boundary template’ using a MatLab implementation of the fastEMD algorithm (https://github.com/dkoslicki/EMDeBruijn, Koslicki, 2015; Pele et al., 2008; Pele and Werman, 2009). This boundary template consisted of a 25 × 25 matrix with each bin's value set to 0, except the outer ring bins with a value of 1, smoothed with the same Gaussian kernel and converted to unit weight. Several additional templates were constructed to assess the effects of behavioral manipulation, adding additional weight in the location of placed objects/walls (Figure 2E,J). The EMD distance between a rate map and a template represents the minimal cost that must be paid to transform one distribution into another, with values ranging between zero (identical maps) and one (maximal difference), and is thus a normalized metric of dissimilarity (Grossberger et al., 2018).

To assess whether a cell's rate map was significantly similar to the boundary template, we computed a null distribution to compare against using Monte Carlo simulations. We performed 32.000 permutations of a shuffling procedure, and for each iteration we randomly sampled a spike-train from the data, time-shifted this vector along the animal's recorded trajectory by a random interval of at least 4 s and less than the total trial length, wrapping any excess at the and back to the beginning. We then used this shifted data to compute a rate map and calculated the EMD distance relative to the boundary template. Criteria for border cell classification was an EMD dissimilarity score below the 1st percentile of this null distribution in all regular sessions, and an average firing rate of at least 0.5 Hz (Figure 1D,E). These cell classification criteria were applied only for the regular sessions of the manipulation experiments.

To compare classification results with a related metric, we computed the original border score for each cell (Solstad et al., 2008). We first estimated a cell's firing field by isolating a continuous region of at least 200 cm² and a maximum of 70% of the arena surface where the firing rate was above 30% of the peak firing rate. This was an iterative search until all fields with the above criteria were identified. We next computed the border score, b, for each wall separately:

where c_m was defined as the maximum coverage of any single field over the wall and d_m the mean firing distance, calculated as the average distance to the nearest wall over all bins covered by the field. This was done separately for each of the four walls out of which the maximum score was selected. Cells recorded in MEC were classified as border cells whenever their border score was above the threshold of 0.5 (corresponding to the 99.3th percentile of scores generated from randomly time-shifted spikes) for either of the two recorded sessions, and had an average firing rate of at least 0.5 Hz.

The rat's head-direction was calculated based on the relative x/y-position of two light-emitting diodes (LEDs), corrected for an offset in the placement of the LEDs relative to the animal's true head-direction. For each cell, the mean vector length (MVL) and direction (MVD) was calculated by computing the circular mean and direction from a vector that contained the head-direction of the animal at spike timings in unit space. A cell was classified as a head-direction cell when its MVL was greater than the 95th percentile of a null distribution obtained by thousand-fold Monte Carlo simulations with randomly time-shifted spike trains.

Locations of walls were estimated based on the most extreme values of the position of the animal. The animal's distance to the wall was computed for each of the four walls separately by taking the difference between the wall's location and the animal's position in the respective x or y-dimension, and selecting the lowest value at each time point. The direction of this wall relative to the animal's direction was computed by calculating the angle difference between the animal's true heading direction and a vector pointing directly toward the wall (e.g., relative to an angle of 0° for the east wall, 90° for the north wall). Because 0° corresponds with the 'east' side in angular polar plots, this data was further shifted by 90° to align the front of the animal with the 'north' part in border maps (see Figure 4C) to improve visual interpretation of the results.

Firing rate in body-centric border coordinates was calculated by dividing the animal's occupancy in these coordinates into 4 cm distance bins and 20° angle bins. The number of spikes in each bin was then divided by the time spent there, further smoothed using a 2-D Gaussian kernel (one bin width), similar to how spatial rate maps are computed. A cell's preferred direction and distance was obtained by finding the bin with maximal firing rate and selecting the bin's corresponding distance and angle values. For visualization purposes only, this matrix was transformed into a circular diagram shown in Figure 4.

To establish the directional tuning of a cell, the wall-direction angle at the time of each spike was taken whenever the animal was located within 20 cm distance of a wall, from which a mean vector length was calculated. This MVL was then compared to a thousand-fold shuffled distribution, where each iteration produced an MVL value using randomly time-shifted spike timings (similar to head-direction cell classification). If the real MVL exceeded the 95th percentile of this shuffled distribution in all regular sessions, it was considered significantly tuned to wall direction.

First, the animal’s movement direction was computed at each time point, using position changes in a 100 ms segment of the preceding and succeeding 50 ms, and calculating the angle of movement by taking the arctangent of the difference in x/y-position. The movement directions were then aligned with the animal’s forward head-direction, giving moment-to-moment changes in the animal’s movement directions from a self-centered perspective (Ito et al., 2015; Whitlock et al., 2012). The distance traveled in this time bin captures the distance from the origin in self-motion maps, while clockwise or counter-clockwise movements are reflected in shifts over the x-axis. Self-motion data was binned into 3 cm/s bins, and rate maps were computed by dividing the number of spikes by time spent in each bin (Figure 6E). For time-lagged analyses, shifted self-motion maps were generated by shifting spike-timing step-wise between −1000 and +1000 ms earlier or later relative to self-motion data. For each time lag, an additional shuffled distribution was computed by shifting the spike-timings a random amount of time, at least 4 s forward, with the excess wrapped around to the beginning, and taking the average over 10 iterations.

From these self-motion rate maps, the total amount of self-motion information could be calculated as:

with i = 1, …, N motion bins, p_i the probability of occupancy in bin i, λ_i the mean firing rate for bin i, and λ the overall mean firing rate of the neuron (Skaggs et al., 1996).

For decoding of wall distance from the activity of border cells in RSC and MEC, the optimal wall with maximum coverage by firing fields was chosen for individual cells (the same procedure as used in border score calculations; Solstad et al., 2008). To determine the optimal head-direction to the selected wall for individual border cells, we searched for a range of head-directions (360-degree range in 5-degree steps) that gave the maximum mean firing rate of the cell when the animal was within 20 cm of the wall. We then focused on neural activity when the animal was at this optimal head-direction and in the range of wall distances from 0 to 50 cm at 10 cm steps (five ranges in total), but excluding timepoints where the animal was within 25 cm of other walls to avoid their potential influence. All of the incidents when the animal was in each of the five wall-distance ranges were equally divided into 20 segments in time, and mean firing rates of individual border cells in the 20 segments were assembled across recording sessions. To implement a decoding analysis, 20 cells were randomly chosen, and the order of 20 segments was randomly shuffled for each cell, such that the data in each segment is a collection of firing rates from 20 border cells across various time points of behaviors when the animal was in a particular distance range to the wall. Ensemble firing rates of border cells in one of the segments were selected as a test dataset, and the rest of the data were used to train a support vector machine (using a MATLAB package LibSVM with a linear function; Chang and Lin, 2011). Trained weights were then applied to the activity of border cells in the test dataset to estimate the animal’s distance to the wall, which was repeated for all segments to be tested (leave-one-out cross-validation), giving a representative decoding performance for the selected population of cells. This procedure was repeated for different cell pairs for 1000 times to estimate a statistical distribution of decoding performance (bootstrap resampling method).

Data was collected over a total of 30–120 min per day while rats foraged for food (chocolate cereal) in a squared open field arena, either 50 × 50 cm, 100 × 100 cm, or 120 × 120 cm in size. Each session consisted of 10–15 min of free exploration in the arena, separated by 5 min of resting time on a pedestal. No curtains surrounded the recording arena, with the exception of the rotation and darkness experiments where all distal cues were blocked completely. The surface of the arena was elevated 50 cm above the ground, and was enclosed by three black and one white wall with a 50 cm height that were positioned with consistent orientation in the room for all animals. The experimental set-up was extensively cleaned with a 70% ethanol solution in between every recording session to eliminate any odors.

Behavioral manipulation experiments always followed the same protocol of A-B-B-A', where A is a regular session, and the manipulation was performed in B. This allowed for a recovery phase after the manipulation in the final session A'. The only exception was the drop-edge experiment (Figure 3E) where the animal had limited motivation; so to ensure good coverage of the arena we reduced the protocol to A-B-A'. All changes to the maze were made in between the first and second session while the animal was resting on a pedestal. For the added wall manipulation (Figure 2A), an additional black wall (50 cm length × 50 cm height × 1 cm width) was placed in the maze, protruding from one outer wall at half-length toward the center. For the added object manipulation (Figure 2F) either a circular, non-climbable aluminum object (10 cm diameter × 50 cm height) or circular climbable object (10 cm diameter × 10 cm height) was placed in the center, or off-center 40 cm away from the north and west walls.

For the DREADDs-mediated manipulation experiments, animals were injected with agonist-21 (DREADDs agonist 21 dihydrochloride, 3.52 mg/mL [10 mM]; Hellobio) subcutaneously after the first recording session, followed by at least 30 min waiting time to allow the drug to reach the brain and take effect before starting the next recording session. For the experiments using optogenetic methods, laser light was turned on continuously for the duration of the middle session (5 min, with laser power of 20 mW at the fiber tip), after which the animals had at least 5 min of recovery time on the pedestal before starting the final behavioral session. A green laser (532 nm; Shanghai Laser and Optics Century, China) was used to activate eNpHR3.0, while a red laser (632 nm; Shanghai Laser and Optics Century, China) was used to activate red-shifted opsins.

The animal's position and head-direction were obtained by tracking two LEDs on the headstage at 25 Hz and recording under dim light conditions. For darkness sessions, we switched to an infra-red OptiTrack camera system (Natural Points Inc) under the assumption that rats have limited vision in the higher wavelengths, with cone sensitivity tapering off rapidly above 600–650 nm (Jacobs et al., 2001). Six Flex three cameras were positioned 2 m above the arena surface on a ceiling mount, at a 45–60° angle pointing downwards, that used infra-red illumination (peak spectral emission at 850 nm) to track the location of three reflective markers in an asymmetric frame attached to the headstage. Position and direction data were acquired and processed using Motive 2.0 software. To ensure no visible light was present for the animals, all lights were turned off and small light sources in the room such as computer and sensor lights were taped off, while the arena was enclosed by a thick, black curtain. A room lamp was turned on for dimly light conditions until 10 s before the start of the recording, and turned on again during the inter-trial interval duration of 5 min. During recording, the experimenter remained stationary and silent near the arena throughout the recording while scattering food pellets.

Once the experiment was completed, animals were deeply anesthetized by sodium pentobarbital and perfused intracardially with saline, followed by 10% formalin solution. Brains were extracted and fixed in formalin for at least 72 hr at 6° C temperature. Frozen coronal sections were cut (50 μm) and stained using cresyl violet and mounted on glass slides. Electrode tips were identified by comparison across adjacent sections, with the location of recorded cells estimated by backward measurement from the most ventral tip of the tetrode tracks.

All statistical tests were two-sided and non-parametric unless stated otherwise. Error bars in all figures represent the standard error of the mean (SEM). All values mentioned in the text are medians ± SEM.

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

We thank Martin Vinck for suggesting the approach with the Earth Mover Distance (EMD) and providing initial software for analysis; Diogo Santos-Pata for discussion and comments related to the manuscript; N Vogt, S Zeissler, E Northrup and G Wexel for animal care; F Bayer and A Umminger for building the behavioral mazes; Robert Gebauer for technical support; and all members of the Ito laboratory for discussions.

Animal experimentation: The experiments were approved by the local authorities (RP Darmstadt, protocol F126/1009) in concordance with the European Convention for the Protection of Vertebrate Animals used for Experimental and Other Scientific Purposes.

© 2020, van Wijngaarden et al.

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