Environmental Barriers Disrupt Grid-like Representations in Humans during Navigation

SUMMARY

Environmental barriers fundamentally shape our behavior and conceptualization of space [1–5]. Evidence from rodents suggests that in contrast to an open field environment, where grid cells exhibit firing patterns with a six-fold rotational symmetry [5,6], barriers within the field abolish the six-fold symmetry and fragment the grid firing fields into compartmentalized repeating “submaps” [5]. These results suggest that barriers may exert their influence on the cognitive map through organization of the metric representation of space provided by entorhinal neurons. We directly tested this hypothesis in humans, combining functional MRI with a virtual navigation paradigm in which we manipulated the local barrier structure. When participants performed a fixed-route foraging task in an open field, functional MRI signal in right entorhinal cortex exhibited a six-fold periodic modulation by movement direction associated with conjunctive grid cell firing [7]. However, when environments were compartmentalized by barriers, the grid-like six-fold spatial metric was abolished. Instead, a four-fold modulation of entorhinal signal was observed, consistent with a vectorized organization of spatial metrics predicted by rodent models of navigation [5]. Collectively, these results provide mechanistic insight into why barriers compartmentalize our cognitive map, indicating that boundaries exert a powerful influence on the way environments are represented in human entorhinal cortex. Given that our daily environments are rarely wide open and are often segmented by barriers (e.g., the buildings of our home city), our findings have implications for applying models of cognitive mapping based on grid-like metrics [8] to naturalistic circumstances.

In Brief:

He and Brown find that entorhinal cortex represents open field environments with grid-like signals in a non-memory-based foraging task, but not in environments with hairpin barriers. Instead, entorhinal signals become aligned with the barriers. These data provide insight into how barriers compartmentalize and shape cognitive maps.

RESULTS AND DISCUSSION

Real world environments often feature local barriers, and these structural features can alter or compartmentalize cognitive mapping [4–5]. A fundamental question addressed by our data is whether human grid-like signals are disrupted and altered by environmental barriers, as predicted by rodent grid cell data [5]. We used fMRI methods that were previously developed for detecting grid-like signals in humans during an object location memory task [7] that could be modulated by conjunctive directional grid cells. They demonstrated that movement in directions aligned with the regionally-preferred grid axes can generate stronger fMRI signal than movement misaligned with the grid axes, producing a sinusoidal six-fold (60°) modulation by movement direction. While several landmark studies have demonstrated these grid cell-like signals in humans [7,9,11,12], to date, it is unclear to what extent they depend on spatially unconstrained routes and long-term spatial memory encoding or retrieval. In the rodent model on which our design and predictions were based, grid cell firing was attenuated, but nevertheless robust, when rodents navigated a spatially-constrained (non-random; experimenter directed) foraging task in an open field [5]. This demonstrated that stereotypic behavior (following a constrained route) alone cannot explain the compartmentalization of entorhinal signals associated with their barrier manipulation. Therefore, in our study we first examined whether a directed foraging task following a fixed route in an open field could generate a grid cell-like six-fold modulation in entorhinal cortex (EC). We then tested whether this periodic modulation was disrupted by barriers fragmenting the open field as predicted by rodent single-unit recording data.

Each participant (n = 20) navigated identical sequences of waypoints in virtual reality (Figure 1A), in identically-structured open field (OF) and barrier (BA) environments (see STAR Methods for extended task details). The OF and BA were implemented in both outdoor and indoor environments. Environment identities (indoor/outdoor) and the order in which OF/BA were experienced were fully counterbalanced. At each waypoint, participants were asked where one of four global landmarks were relative to their current bearing, ensuring spatial awareness (Figure 1B). Trajectories for OF and BA were matched with waypoints placed around the edges of the barriers, resulting in tighter trajectory equivalence than could be feasibly achieved in the rodent study (Figure 1C and D) [5].

Figure 1. Foraging task in virtual environments.

(A) Example view of indoor OF and outdoor BA (environmental size and shape were same for indoor BA and outdoor OF). All landmarks could be clearly seen in both OF and BA. Participants navigated to the red waypoint in a straight line. (B) Upon reaching each waypoint, spatial awareness was probed. (C) Trajectory (pink) of one participant in OF and BA. Trajectories were very spatially-structured to sample 360° and to demonstrate that grid-like signals are eliminated by barriers and not by constrained behavior. (D) Trajectories (black) and spike locations (red) of a rat foraging in OF and BA [5]. Reproduced with permission from [5], Nature Publishing Group.

Grid-like signals in open field but not in barrier environment

In the right EC, we observed a significant grid-like signal (six-fold rotational symmetry) in OF (t₁₉ = 3.17, p = 0.005; Figure 2A). There was no evidence for five-fold or seven-fold control periodicities (ts₁₉ < 0.73, ps > 0.47; Figure 2A). As predicted by movement-sensitive conjunctive grid cells, six-fold modulation was absent in OF when participants were held stationary (spatial awareness questions) (Figure S1), replicating previous findings [9]. Critically, in BA, there was no evidence of grid-like signals (t₁₉ = 0.93, p = 0.36; Figure 2A). These results replicated findings from [5] in which rodent grid signals in OF were still present in the virtual hairpin maze (analogous to our OF foraging task) compared to free roaming, but were dramatically disrupted in BA. The lack of six-fold modulation in BA cannot be attributed to not sampling of certain movement directions (Figure 2B), differences in behavior (movement direction distributions) (OF and BA did not differ in any participant, Kuiper test for equal distributions, ps > 0.1; Figure 2C), or differences in global landmark spatial awareness (Accuracy: 91.20% in OF and 91.50% in BA, t₁₉ = 0.37, p = 0.72; Reaction time: 0.95s in OF and 0.97s in BA, t₁₉ = 0.29, p = 0.77).

Figure 2. Grid-like rotational periodicity.

(A) fMRI grid-like scores [7] (six-fold) were significant in OF, but grid-like signals were absent in BA. ** p < 0.01. (B) Movement orientation comparisons between OF and BA grouped by modulo. A comparison between open field and barrier environment in movement directions modulo by 60° (upper) and 90° (lower). There was no environment effect (OF or BA) in either 60° or 90° modulus (F_1,57 < 0.09, ps > 0.75). (C) Representative comparison of heading angle distributions for OF and BA from one participant. See also Figures S1, S2, and S4.

In rodents, grid cell firing patterns in BA develop a striking compartmentalized parallel “submap” structure [5] (Figure 3A). These firing fields cannot be measured directly with fMRI, but could give rise to a geometrically-structured rotational periodicity in signal. This would be predicted based on evidence that conjunctive grid cells preferentially fire when rodents run in various directions aligned with the principal grid system axes [7]. The data from Derdikman and colleagues [5] demonstrate a clear reorganization of the grid system axis along the hairpin barriers which, critically, produced a primary North-South firing field axis, with a secondary perpendicular (East-West) axis banded across compartments. We considered the possibility that entorhinal fMRI signals could reorganize in a similar manner, and therefore tested whether movement-dependent signals in BA were modulated by a four-fold symmetry that becomes aligned in with the hairpin structure (note, we would predict that the specific n-fold symmetry depends on the structure of environmental barriers and their impact on grid cell alignment in rodents – for example, trapezoidal environments[10] or spiral mazes could lead to different firing field reorganization which, in some cases, may not have a clear population-level rotational symmetry across 2D space. Future work could test this). In line with the rodent literature, we found significant four-fold modulation in BA (t₁₉ = 2.53, p = 0.02; Figure 3B). There was a trend towards four-fold modulation in OF (t₁₉ = 1.80, p = 0.09; Figure 3B), implying that global square symmetry could also organize human entorhinal signals [10] – note, however, that the rotational organization of this marginal signal was fundamentally statistically different from the BA condition (see Group-level distributions of preferred orientation).

Figure 3. Four-fold modulation by movement direction in BA.

(A) Rate map of a grid cell in a barrier environment, reproduced with permission from [5], Nature Publishing Group. Grid cells adopt a compartmentalized, “submap” structure that repeats across hairpin compartments. (B) Here, direction-related fMRI signals in BA exhibited a four-fold symmetry. * p < 0.05. See also Figures S1, S2, and S4.

Grid-like modulation in OF and four-fold modulation in BA were not related to the identity of the environments (indoor/outdoor) or the OF/BA order (Fs < 0.68, ps > 0.42). Moreover, we verified their significance against null in a follow-up analysis in which we used permutation testing to establish an empirical baseline for our fMRI data and task structure (see STAR Methods; Figure S2). Grid-like and 4-fold modulations were not observed in left EC (Figure S1). Given the non-memory-based nature of our task, the fact that grid-like signals in the left EC do not reach significance may be in line with previous findings about the lateralization of entorhinal cortex and hippocampus [13, 14].

Collectively, our results showed that the non-memory-based foraging task could induce reliable grid-like signals in the right EC – only 4 of our 20 participants did not exhibit evidence for 6-fold grid-like signal modulation in OF (fMRI grid-like scores > 0). It is not clear why some people do not exhibit grid-like signals, although this has been reported and speculated on in prior studies (e.g., [11]). We directly tested whether grid-like modulation scores in OF are disrupted when barriers are introduced (in the 16 participants for whom this question could be asked). There was a significant within-subjects (repeated-measures) interaction between barrier condition (OF or BA) and n-fold scores (6-fold or 4-fold) (F_1,45 = 5.24, p = 0.04). This was indeed driven by the significant 6-fold scores in OF being significantly reduced in BA (t₁₅ = 2.68, p = 0.02). Additionally, this was driven by the 6-fold scores in OF being stronger than the marginal 4-fold scores in OF (t₁₅ = 2.21, p = 0.05). 4-fold scores in BA did not exceed the subthreshold 4-fold scores in OF (p = 0.32), but the 4-fold group-level preferred orientations rearranged from OF to become significantly clustered and dramatically aligned with the BA environment (see below).

Group-level distributions of preferred orientation.

Preferred angle distributions for n-fold modulations offer information about alignment that is distinct from the magnitude of the fMRI grid-like scores. We next examined whether the preferred orientations across our 20 participants were clustered. Individual’s grid orientations are uniformly distributed in circular environments [7,9,11,12], but are clustered in square environments [10,15], and these boundaries appear to provide error correction signals to the system [16]. In line with previous studies [10,15], the grid-like six-fold orientations in OF were not randomly distributed (Rayleigh test for non-uniformity, Z = 4.02, p = 0.02, mean angle 16.95°; Figure 4A and S3A), and they did not differ between indoor and outdoor environments (Watson-Williams test, p = 0.10). Interestingly, although grid-like 6-fold signals were significantly attenuated (and became clearly non-significant) in BA (Figure 2A), the angular distribution of these subthreshold signals remained clustered (Figure 4C and S3C), albeit at a slightly more North-aligned orientation (mean angle 9.44°, p = 0.001). This may be consistent with the subset of surviving grid-like firing fields in BA observed in the rodent work [5]. Strikingly, group-level preferred orientations of the four-fold symmetry in BA were significantly clustered around North at 3.02° (Z = 3.56, p = 0.03; Figure 4D and Figure S3D), and they did not differ between indoor and outdoor environments (Watson-Williams test, p = 0.66). In contrast, there was no clustering in orientations for the (non-significant) four-fold modulation in OF (mean angle 27.99°, Z = 0.705, p = 0.50; Figure 4B and Figure S3B) and the mean signal orientation of four-fold symmetry significantly changed from OF to the Northward orientation in BA (27.99° vs. 3.02°, Watson-Williams test, p < 0.01) (see also Figure S3 for 2D heatmaps of average grid-like scores at each preferred angle in 360° space). Therefore, whereas BA disrupts grid-like six-fold modulation, it exhibits significant four-fold entorhinal activity modulation that becomes aligned with the principal axes of the barrier geometry (Figure 1).

Figure 4. Group-level distributions of preferred orientation across environments and n-folds.

Individual preferred headings projected into n-fold sinusoidal repetition across 360° space. Amplitudes at each angle (repeating every 60°/90°) aggregate the number of participants (if any) sharing that preferred signal orientation (single-participant = repeating 0-1 amplitude wave, trough-peak; additional participants add amplitude at their preferred angle) (see STAR Methods). (A) 6-fold angles were clustered in OF, resulting in a plot with clear 6-fold periodicity. (B) The 4-fold angular distribution was uniform OF. (C) In BA, (non-significant) six-fold signals retained a clustering in preferred orientations across participants. (D) four-fold signals in BA rearranged to become most-frequently aligned with the barrier axis. Note, these plots communicate preferred modulation orientations, not modulation strength/significance (Figures 2 and S3).

Signal modulations in retrosplenial cortex (RSC)

Although our high-resolution fMRI field of view was restricted primarily to the medial temporal lobes, the posterior extent of our bounding box encompassed anatomical RSC (Figures S4A–B). This was an interesting opportunity to test for grid-like signals in RSC and signal modulation related to the BA manipulation, given that this region has been shown to also exhibit grid-like signals in some prior work [7] and is thought to mediate the transition between egocentric and allocentric representations [17]. This exploratory analysis revealed bilateral RSC grid-like signals in OF (right RSC, p = 0.044), albeit marginal in the left hemisphere (p = 0.052). On the other hand, bilateral RSC consistently exhibited significant four-fold modulations in BA (right p = 0.001; left p = 0.011; Figure S4 for visualization and additional statistics), mirroring right EC.

Conclusions

Collectively, we provide, to the best of our knowledge, the first evidence for grid-like signals in human EC during guided (non-memory-based), and spatially-constrained, foraging route navigation. These grid-like signals were observed in right EC during translation periods. Critically, grid-like signals were abolished in a hairpin barrier environment, despite identical trajectory structure. The movement-related EC signals in these compartmentalized environments were modulated with a non-grid-like four-fold symmetry that became organized by the barriers. These findings demonstrate cross-species similarities in how grid-like signals are affected by environmental barriers [5], with broad implications for models of cognitive mapping based on grid-like metrics [8]. There has been great interest in investigating the interaction between environmental geometry and barriers on grid cells [10,16,18,19]. Here, our four-fold modulation in BA may be suggestive of a vectorization of conjunctive spatial metrics in humans along local boundaries. Human behavioral studies consistently demonstrate impacts of barriers in spatial memory [1–3], and the current study provides the first neural evidence that grid-like representations of space are fragmented by such barriers in humans. Considering that our daily environments are often compartmentalized by boundaries and barriers, the findings from our barrier condition indicate how grid-like signals in humans respond to space in naturalistic circumstances such as traversing our home city streets.

STAR★Methods

LEAD CONTACT AND MATERIALS AVAILABILITY

Further information and requests for resources should be directed to and will be fulfilled by the Lead Contact, Thackery Brown (thackery.brown@psych.gatech.edu). This study did not generate new unique reagents.

EXPERIMENTAL MODEL AND SUBJECT DETAILS

Because the task structure, environmental geometry and scanning parameters are the most similar between Stangl et al. [12] and our study, we conducted the power analysis based on Stangl et al.’s effect size (d = 0.83). As a result, eighteen participants were needed to reach a power of 0.8. All participants (n = 20, 9 female, age 18 - 22) gave written consent and were either paid or received course credits, in compliance with procedures approved by the Georgia Institute of Technology Institutional Review Board. All had normal or corrected-to-normal vision and reported that they were in good health with no history of neurological disease. All participants reported right-handedness. Data of one scan run from one participant was not recorded due to technical failure. Before scanning, each participant completed the Santa Barbara Sense of Direction questionnaire and Questionnaire on Spatial Representation, which provide a standardized measure of self-reported navigational ability and preferences on spatial strategy. Results of these two questionnaires are not discussed in this paper.

METHOD DETAILS

Foraging task

The foraging task was implemented in Unity3D (Unity Technologies, http://www.unity3d.com). Each participant performed the foraging task in two virtual environments (Figures 1A and C): One open field (OF) and the other one the same outer structure but with hairpin barriers [5] (BA). The OF/BA presentation order was counterbalanced across participants. Participants’ position and facing orientation in the virtual environments were sampled every 100 ms. The sizes (200 X 200 virtual meters [vm]), shapes (square) and movement speed (8 vm/second) in the two environments were identical. The virtual eye-height for each participant was set to 1.8 vm and the height of the barriers was 5 vm. All landmarks could be clearly seen in both OF and BA environments (Figure 1A).

To create the impression that these two virtual environments had different identities and minimize interference between representations, one environment was textured with an indoor theme and the other one was textured with an outdoor theme (Figure 1A and C). Each environment had four landmarks: The indoor environment had color patches of blue, yellow, back, green on the east, south, west and north walls, respectively; the outdoor environment had a tower, rock, tree and cactus outside the east, south, west and north walls, respectively. The indoor and outdoor environments were used equally for OF and BA environments across participants.

One day prior to the scanning in MRI, participants were trained on how to perform the foraging task. Participants were told that there were numerous waypoints scattered around the environment, appearing one by one. Participants were instructed to look around to find the waypoint first, aim it correctly so that they could reach the waypoint in a straight-line, and then hold the forward key until they reached the waypoint. In the circumstance that they could not reach the waypoint after pressing the forward key (i.e., their heading angle was wide), participants were instructed to keep going until they went past the waypoint, and then went back to the waypoint. Because the placement of waypoints was designed in a way that the duration to navigate from one waypoint to another was almost always longer than 1.5 secs (>= 1 TR), the said instructions were to ensure that participants kept moving in a certain direction for more than 1.5 secs. The experiment program could only register one key input at a time so that participants could not rotate and translate at the same time.

One possible reason that the grid-like signals were disrupted in BA was that participants’ spatial awareness was obstructed by the barriers. To examine whether spatial awareness was worse in BA than open field, upon reaching each waypoint (Figure 1B), participants were given a spatial awareness test. Here, they were asked where one of the landmarks was with respective to their current bearing and feedback was provided (correct or incorrect). The duration of the feedback was contingent on the response time: If the response time was less than 2.5 secs, then the duration of the feedback would be (2.5 secs – response time); if the response time was more than 2.5 secs, then the duration of the feedback would be 0.5 sec. Each question and feedback period was combined and categorized as stationary event in our fMRI model (see below).

Three different trajectories were created using waypoints for use in both OF and BA. One trajectory zigzagged North-South in a virtual hairpin eastward-bound (i.e., starting from the West wall and head to the East wall), one headed westward (i.e., starting from the East and head to the West) and one began in the geographic center and headed eastward. See Figure 1C for example eastward path, and 2b for the 15° increment samples of translation achieved across these East-West-bound trajectories. The same trajectories were used in each environment type (indoor and outdoor; open field and barrier). On the second day, during fMRI scanning, each trajectory consisted of one scan run and participants finished six scan runs (eastward-> westward -> center-eastward, and then repeated) in each environment (OF or BA) for a total of 12 runs. The total scan time for each participant was approximately 135 minutes.

fMRI acquisition

Scanning was performed at the GSU/GT Center for Advanced Brain Imaging using a 3 T Siemens Prisma scanner equipped with a 32-channel head coil. High-resolution T1-weighted structural images were acquired using generalized autocalibrating partially parallel acquisitions (GRAPPA) (TR = 2530 ms; TE = 3.55 ms; flip angle = 7°; field-of-view = 256 mm; slices = 176; voxel size = 1 mm isotropic). High-resolution T2*-weighted functional images sensitive to blood oxygenation level-dependent (BOLD) contrasts were acquired using a gradient-echo echoplanar pulse sequence (TR = 1500 ms; TE = 32 ms; flip angle = 56°; field-of-view = 192 mm; slices = 20; voxel size = 2 mm isotropic). The T2*-weighted images were acquired as a partial volume encompassing the medial temporal lobe, with slices oriented parallel to the long axis of the hippocampus.

fMRI preprocessing

Imaging analysis was conducted using SPM12 (Wellcome Department of Cognitive Neurology, London, UK) [20] for MATLAB R2018a [21]. BOLD images were slice-time corrected to the first slice acquired. Motion correction was conducted, including realigning the BOLD images to the first functional image acquired and unwarping the BOLD images to correct for movement-by-susceptibility artifact interactions. BOLD images were spatially smoothed using an 8mm full-width at half-maximum Gaussian kernel.

To avoid spatial distortions or interpolation errors during normalization to a template, BOLD images were analyzed in each participant’s native space. Anatomical masks of the entorhinal cortex were traced manually on each participant’s structural image using ITK-SNAP (http://www.itksnap.org/) based on the guidelines from [22]. Region of interest (ROI) mask images were created using ITK-SNAP. For each participant, the high-resolution structural image was coregistered and resliced with the mean BOLD image obtained during motion correction. ROI mask images were then coregistered with the mean functional image along with the processed structural image. We also conducted an exploratory analysis of grid-like signals in retrosplenial cortex (RSC), which has been previously shown to exhibit these effects in some studies [7]. Because there are no standardized anatomical boundaries for manual segmentation of RSC for fMRI analyses, we generated a probabilistic mask of BA29+BA30 in MNI space using the WFU PickAtlas [23–26], warped the combined ROI into individual participant native space using DARTEL, and manually trimmed the resulting masks in ITK-SNAP to ensure they were restricted to the dorsal side of the parietooccipital sulcus (Figures S4A and B).

Analysis of grid-like representations

We used the Grid Code Analysis Toolbox [27] (GridCAT) for analysis of grid-like representations, which follows procedures used previously to identify grid-like signals with fMRI [7,9,11,12]. Within each environment (OF/BA), we used the first 3 scan runs to estimate the putative grid axes relative to the environment in each participant’s entorhinal cortex, and this estimated orientation was then used to predict a grid signal in the other half of the runs. We note that it cannot be definitively known that hexadirectional fMRI signals measured with these techniques reflect grid cells, and not a (potentially related) spatial code in human EC.

To estimate the putative grid axes, the first half of the data was modeled with a first general linear model (GLM) including four parametric modulators (PM), two for movement time points and two for the stationary (combined question and feedback period) time points. The six motion parameters calculated during motion correction were added to the model as additional covariates of no interest. The two PMs for each event type (movement and stationary) were cos[6 * a(t)] and sin[6 * a(t)], where a(t) is the direction (either the movement direction or the facing direction during stationary events) at time t. Next, the beta estimates of the two PMs were extracted from the entorhinal cortex to calculate its putative mean grid orientation using this formula: arctan[mean(beta1)/mean(beta2)]/6. The remaining data of three runs were then modeled in a second GLM, with regressors for aligned (within ± 15° of the nearest axis of the grid estimated from the first three runs) and misaligned (more than ± 15° from a grid axis). Contrast values (“fMRI grid-like scores”; Beta _aligned – Beta _misaligned) were extracted from the ROI and averaged across voxels within participants. Positive values indicate grid-like representations. Negative grid-like scores would reflect grid-like modulation that is unstable and has shifted orientation across sessions. This analysis was conducted independently in each environment (OF or BA) for each participant.

Visualization of n-fold rotational periodicity

Our visualizations are based on code for generating 3D polar plots (https://www.mathworks.com/matlabcentral/fileexchange/13200-3d-polar-plot). These plots represent an alternative to the 2D polar histograms commonly used in studies of grid-like signals using fMRI (Figure S3). Reflecting the underling fMRI modeling approach, cosine functions (ranging 0 to 1, trough to peak, for visualization/aggregation across participants) are visualized with a desired 360° periodicity (e.g. four-fold) centered over a given participant’s preferred orientation for that modulation. Shared orientations were binned between participants by 7.5° increments for 4-fold and 5° increments for 6-fold symmetries. When multiple participants shared a preferred orientation, the cosine function amplitude at that orientation was scaled up in 1-unit increments per participant. Participant clusters representing a different preferred orientation produce a second (or third, etc) set of peaks with the respective participant cluster size amplitude (or, if the added peak was highly overlapping with the first cluster’s wave envelope, the plot would broaden the width of the current wave envelope at the appropriate angle to the appropriate cluster size height). The primary benefits of this plot type are twofold: 1) these illustrations project polar histogram data into 360° space as sinusoidal wave functions. This offers explicit visualization of the repeating (e.g. four-fold, six-fold, etc) nature of the signals modeled with sine/cosine functions (that is, not a discretized neural response to one angle/360° in the environment). 2) by aggregating participant frequencies at different preferred orientations, the plot offers a smoothed visualization of group level trends (e.g., approaching uniform distribution (Figure 4B); one dominant clustering (Figure 4D); multiple dominant clusters) in the 3D space of the task environment. Because of this, our 3D plots offer a visualization of the group trend somewhat analogous to a rotational error bar, since the width (and distortions) in the wave envelop reflect rotational dispersion in the clustering of preferred orientations. The primary drawback of these plots relative to 2D polar histograms is the sinusoidal wave function displays subject-level differences in preferred grid orientations in a rotationally-smoothed manner. For completeness, we have also provided these 2D polar histograms (Figure S3).

The preferred angle distribution information above is distinct from the magnitude of the fMRI grid-like scores at that angle. Indeed, as Figure 4C shows, significantly reduced (and statistically non-significant) 6-fold signal modulation in BA still exhibits a preferred angle distribution across subjects similar to that from OF. To illustrate the angular distributions of average grid-like scores, we generated 2D heatmaps of the average grid-like score at each angle (within 60° and 90° for 6-fold and 4-fold, respectively), and visualized these as repeating signals in 360° space as with the 3D preferred angle plots described above (consistent with the underlying fMRI modeling procedure). Angles which were not a preferred signal orientation for any participant are displayed as NaN, rather than zero.

QUANTIFICATION AND STATISTICAL ANALYSES

Error bars in Figures indicate standard-errors of the mean (SEM). Statistical analyses were performed using a significance threshold of p < 0.05.

We used one-sample t-tests to test whether n-fold scores were significantly different from zero (Figures 2, 3, S1 and S4). We used permutation tests to establish an empirical baseline and test whether the six-fold modulations in OF and four-fold modulations in BA were significant given our unique scan and task parameters (Figure S2). Here, we circularly shifted the vector of the movement orientation labels by a random amount in the testing data 1000 times for each participant (importantly, this procedure preserves the temporal task structure in the model) [28] and refit the GLM for each shift to recompute the aligned-misaligned grid-like scores. For group-level statistics, we then calculated the mean of these 1000 betas (Beta _aligned – Beta _misaligned) as subject-wise empirical baselines for each participant, and used paired samples t-tests for group comparisons. This computationally intensive analysis validated the assumption that zero is baseline for our scan parameters and task structure (see empirical baseline in Figure S3).

We used Rayleigh test to test whether preferred headings were uniformly distributed across participants (Figures 4 and S3). We used Kuiper test to test whether the heading angle distribution in the open field were significantly different from that in the barrier environment for each participant (Figure 2).

DATA AND CODE AVAILABILITY STATEMENT

The dataset generated during this study is available in the Open Science Framework at https://osf.io/swav5/. No custom code was generated from this study.

KEY RESOURCES TABLE

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Antibodies
N/A
Bacterial and Virus Strains
N/A
Biological Samples
N/A
Chemicals, Peptides, and Recombinant Proteins
N/A
Critical Commercial Assays
N/A
Deposited Data
Raw data	This paper	https://osf.io/swav5/
Experimental Models: Cell Lines
N/A
Experimental Models: Organisms/Strains
N/A
Oligonucleotides
N/A
Recombinant DNA
N/A
Software and Algorithms
MATLAB R2018a	[21]	https://www.mathworks.com/
Statistical Parametrical Mapping Toolbox (SPM12)	[20]	http://www.fi.ion.ucl.ac.uk/spm/software/spm12/
The Grid Code Analysis Toolbox (GridCAT) v1.04	[27]	https://www.nitrc.org/projects/gridcat
Other
N/A

Highlights.

• Human participants engaged in a non-memory-based VR foraging task.

• Grid-cell-like representations are observed in open field environments.

• Grid-cell-like representations are disrupted in environments with hairpin barriers.

• Entorhinal signals develop a four-fold periodicity in barrier environments.