Summary
Mammals use distances and directions from local objects to calculate trajectories during navigation but how such vectorial operations are implemented in neural representations of space has not been determined. Here we show in freely moving mice that a population of neurons in the medial entorhinal cortex (MEC) responds specifically when the animal is at a given distance and direction from a spatially confined object. These ‘object-vector cells’ are tuned similarly to a spectrum of discrete objects, irrespective of their location in the test arena. The vector relationships are expressed from the outset in novel environments with novel objects. Object-vector cells are distinct from grid cells, which use a distal reference frame, but the cells exhibit some mixed selectivity with head-direction and border cells. Collectively, these observations show that object locations are integrated in metric representations of self-location, with specific subsets of MEC neurons encoding vector relationships to individual objects.
Introduction
The hippocampus and the medial entorhinal cortex are part of a brain system for mapping of self-location that is likely recruited when animals navigate between locations in the proximal environment1–5. In the hippocampus, place cells fire specifically when the animal is at certain places6,7, and goal-vector cells encode the animal’s movement in the direction of a goal8,9. Collectively, intermixed assemblies of place cells and goal-vector cells may create maps of the animal’s present and future position in the local environment1,10. Each individual environment has a unique map11–14 that when combined with information about events in the environment15 and their temporal order16 forms the basis for location and route-based episodic memories17,18. Hippocampal place and goal representations are likely to interact with spatial maps in the adjacent medial entorhinal cortex (MEC)2,19,20. There position is encoded by multiple cell types, including grid cells, which fire at periodic locations that produce a hexagonal array across the entire available space21, border cells, which fire if and only if animals are near the geometric borders of the environment22,23, and an independently regulated class of cells with discrete but irregularly patterned spatial firing fields24. These location-coding neurons are supported by cells that by encoding head direction25,26 and speed27 may allow the representation of position to change instantaneously and dynamically in accordance with the animal’s movement in the environment, independently of environmental context28–31. As a whole, this circuit of space-coding neurons in hippocampus and entorhinal cortex is thought to form a key element of the braińs neural network for goal-directed spatial navigation1,2.
While the number of spatial circuit elements is unfolding at an accelerating rate5, insights are limited by their almost exclusive reliance on recordings from rodents foraging in empty enclosures very different from the richly populated, geometrically irregular environments of the native world3,4. Natural environments contain objects, and animals may use these for navigation. In the lateral division of the entorhinal cortex (LEC), a subset of cells fire specifically when animals encounter discrete objects in the recording environment, and firing fields at the locations of these objects are often maintained even after the objects are removed33,34. But how representations of object locations are used to navigate in the space between objects remains to be determined.
Behavioural studies have shown that rodents35–38, as well as birds39 and insects40, store information about distance and direction to discrete landmarks in the environment, and that this allocentric vector information can be used to guide navigation. Theoretical studies have further proposed that landmark-dependent vector operations give rise, in the mammalian brain, to cells with firing fields that depend on distance and direction from discrete objects41. Other theoretical work has suggested the existence of ‘boundary vector cells’ with firing fields tuned specifically to distance and direction from walls, and other extended boundaries, rather than from confined objects42–44. Evidence for vector representations of either kind is limited. One study identified a small number of hippocampal CA1 cells (less than 10) that fired at distinct directions and distances from discrete objects, consistent with a landmark-vector encoding operation45. The firing fields of these cells developed only at certain objects and mostly over a time course of multiple trials, suggesting that these cells cannot alone subserve landmark-based navigation, which should operate almost instantly. Other studies have reported cells that encode vectors to wall-shaped boundaries46,47 but the majority of these cells fire not primarily in the open space of the arena but mostly alongside the boundaries47, mirroring the firing fields of border cells in the MEC23,48. The ability of these cells to encode vectors to all possible positions is further limited by the fact that there are often few straight boundaries in the animal’s natural habitat. Vector navigation would therefore benefit a lot if cells were able to use also point-like landmarks as references. In the present study, we looked for such cells. Our search focused on the superficial layers of MEC, the very same brain network that by way of grid cells represents position on content-free planar surfaces. We report that when discrete objects are present in the environment, the animal’s direction and distance from the objects is encoded in the activity of a substantial number of MEC cells, comparable to the number of grid cells in the same brain region.
Results
Object-vector cells in the medial entorhinal cortex
We recorded neural activity from a total of 503 cells in 8 mice. Post-hoc histological analyses showed that the tetrode tracks terminated in the superficial layers of MEC (Extended Data Fig. 1). The mice foraged freely for cookie crumbs in a compartment with a floor that was either square (0.8×0.8×0.5 m or 1.0×1.0×0.5 m, 247 cells) or circular (diameter: 0.9 m or 0.65 m, height: 0.5 m, 256 cells). A typical experiment began with a trial where no object was present in the compartment. This trial was succeeded by a trial where a tower-like object was placed on the floor of the compartment before the start of the trial (Fig. 1a).
We first asked if the activity of any of the recorded MEC cells was changed by the very presence of an object. For this experiment we generally used a 5 cm wide, 20 cm tall cylinder-shaped tower (Object 7, Extended Data Fig. 2). Specifically, we looked for object-induced firing fields. Firing fields were defined by the stepwise contour surrounding areas with firing rates ranging from two times the standard deviation across bins of the rate map to the peak rate of the map. Contiguous areas within a contour of at least 16 bins and with a peak firing rate of at least 2 Hz were counted as firing fields. On trials with the object in the recording enclosure, 237 cells showed significant spatial information, exceeding the 95th percentile of a distribution of spatial information values for shuffled versions of the data (0.65 bits/spike). Among these cells, 120 had firing fields that were not present when the same cells were recorded in the absence of the object. In general, the centre of these fields was offset from the object by several centimetres, often several tens of centimetres. Only 3 of the cells (from 2 animals) had firing fields at the location of the object (< 4 cm from centre of field to centre of object). In the majority of cells that had displaced firing fields (offsets of more than 4 cm), the vector relationship (distance and direction from the object) was maintained when the object was moved to a new location on a subsequent trial (Fig. 1d), suggesting that the cell’s activity was determined by the location of the object and not the distal cues.
For the 117 cells that exhibited displaced firing fields, we quantified the relationship between spatial firing and the object by constructing vector maps that expressed firing rate as a function of both direction and distance to the centre of the object (Fig. 1c). A cell was categorized as an object-vector cell if the correlation of the vector maps from the two trials with objects at different locations exceeded (i) the 99th percentile of a distribution of correlations between rate maps where spike times had been randomly jittered (99th percentile correlation value: 0.45) and (ii) the correlations between each object trial and the no-object trial. A total of 98 out of the 117 cells passed these criteria (Fig. 1e). Among these object-vector cells, as expected, the vector from object to field centre on the first object trial predicted the location of a firing field on the second trial (Fig. 1d; Extended Data Fig.3). Fifty-five of the cells (56%) had only one object-induced firing field; 42 (43%) had two fields (Fig. 1f), and 1 cell had three. Cells with two or more fields were not grid cells as they consistently had grid scores below chance levels and no firing was observed in regions defined by a hexagonal matrix extrapolated from the two or three identified fields (Extended Data Fig. 4). The presence of multiple fields was not caused by poor cluster isolation; cells with two fields were as well-separated as cells with one field (isolation distances of 44.9 ± 5.3 and 44.2 ± 4.3, respectively, means ± s.e.m.; Extended Data Fig. 5). Object-vector cells had a higher spatial information content (Wilcoxon signed rank test, W = 4024, n1 = n2 = 98, P = 1.5×10−8), a higher spatial coherence (W = 4753, n1 = n2 = 98, P = 1.6×10−16), and a higher peak firing rate (W = 4616, n1 = n2 = 98, P = 8.3×10−15), on object trials than on no-object trials (Fig. 1g).
We determined a field’s orientation and distance from the object by identifying the peak of the firing field in the object-referenced vector-map. The orientations of object-vector fields from different cells covered the entire azimuthal range (Fig. 1h). The directional preferences of the fields were similar in square and circular compartments, suggesting they were independent of the internal geometry of the box (Extended Data Fig.6). For cells with multiple fields, the mean angular difference between pairs of fields was 131.5 ± 4.3 degrees (42 cells; Extended Data Fig. 7a,b; mean ± S.E.M.). The smallest angular difference was 75 degrees. The distribution of field-distances from the object showed a skew towards proximal locations, with a mean centre-to-centre distance of 21.2 ± 0.8 cm (Fig. 1h, mean ± s.e.m.), clearly distinguishing these cells from the object-centered cells of the LEC33,34 and the very few cells with such properties in the present MEC data. The largest field distance among the object-vector cells was 52 cm. Distances between the centre of object and the contour of the field ranged from 0 cm to 33 cm (mean ± s.e.m.: 8.9 ± 0.7 cm). Field size was not significantly correlated with distance from the object (Extended Data Fig. 7c; r = 0.15, P = 0.07).
Object-vector cells are allocentric
Object-vector cells were defined as cells that fired at specific locations in space regardless of the animal’s own orientation. To test whether object-vector cells encoded vectorial information also in an egocentric reference frame, we constructed egocentric tuning curves (heading direction vs. firing rate) for each cell by counting spikes as a function of movement direction relative to the object, using procedures similar to those employed to identify egocentric goal-vector cells9 (18 bins of 20° each; time was normalized to time spent moving in each direction relative to the object). We defined 0° as moving towards the object and ± 180° as moving away from the object (Fig. 2a). In general, object-vector cells exhibited no egocentric tuning to the object (Fig. 2 b-d). Cells emitted similar numbers of spikes within allocentrically defined fields even when the heading directions relative to the object were opposite (Fig. 2b,c). To quantify the tuning to movement direction relative to the object, we defined an egocentric directionality index as the difference between the peak firing rate and the median rate of the movement-direction tuning curve, divided by the curve’s median absolute deviation. Only 3/98 object-vector cells, no more than expected by chance, had an egocentric directionality index that exceeded the 99th percentile of a distribution of directionality indices obtained from shuffled versions of the data (Fig. 2 d,e). The median value for the index was 2.25 (50th and 99th percentiles of shuffled data: 2.3 and 9.2, respectively). Object-vector cells thus encode directions and distances to landmarks independently of the animal’s heading movement towards the object, as expected if the object vectors of the recorded MEC cells are coded exclusively in an allocentric framework.
Object-vector cells generalize between objects
To determine whether object-vector cells respond to specific objects or represent directions and distances from any object, we recorded 22 of these cells from 6 mice in experiments where the number of simultaneously presented objects was increased to between 2 and 6. Objects were selected from a pool of tower-shaped objects. Some of these were fully or partly shaped like rectangular prisms, others had a more cylindrical appearance (Extended Data Fig. 2). In total, we tested 49 object-cell combinations (2-3 objects for most of the 22 cells). In 48 of the combinations, new firing fields emerged when the object was introduced in the arena (Fig. 3a). The distance and direction relationship to the object was largely retained from one object to the other, i.e. there were only small differences between object pairs in distance and direction from the nearest object (Fig. 3b; distance difference: 3.7 ± 0.5 cm; direction difference: 7.7 ± 1.0 degrees; means ± s.e.m.). These relationships were maintained even in experiments where objects were flattened to nearly two dimensions by shrinking either the width or the height of the object to less than 0.5 cm (Objects 6 and 13, respectively, in Extended Data Fig. 2; Extended Data Fig. 8a,b).
We next asked whether object-vector cells would differentiate between objects that obstructed the path of the animal and objects that were not functional barriers but still stood out from the visual background. To test this, a cylinder-shaped object was attached to one of the walls of the recording box, with the bottom of the object 15 cm above the ground level (Fig. 3c). The mice moved freely underneath the suspended object and could not reach it from an upright position. A total of 21 object-vector cells were recorded from 5 mice tested with both standing and suspended objects. In all of these cells, a new firing field was expressed in response to the lifted object (Fig. 3c). As in experiments with multiple standing objects, the vector relationship was retained across the pair of objects (Fig. 3 c,d; difference in horizontal distance: 4.0 ± 0.8 cm; difference in direction: 7.7 ± 1.3 degrees, means ± s.e.m.), suggesting that object-vector fields emerge regardless of whether the object interferes with the animal’s path or not.
The fact that also suspended objects generated object-vector fields points to visual input as one likely source of location-specific firing in these cells. We tested this further by comparing rate maps of object-vector cells in the presence of an object before and after the room lights were turned off while the animal was in the box (21 object-vector cells from 5 mice). Correlations between vector maps on light and dark trials were significantly decreased compared to correlations for pairs of light trials in the same cells (Extended Data Fig. 9ab; Wilcoxon signed rank test, W = 207, n = 21, P = 0.0015). Spatial information and spatial coherence were also reduced (Extended Data Fig. 9c). For some cells, neither of these measures were reduced to chance levels, however, possibly reflecting the continued use of path integration in darkness.
Object-vector responses do not require experience
We then asked whether object-vector cells require temporally extended or repeated experience with the object or the recording environment to encode vectors from the object to locations in the open space. We recorded 19 object-vector cells in two different rooms, A and B, distributed over 6 experiments in 4 mice. Thirteen of these cells were recorded during the animal’s first exposure to room B, and the objects used during this encounter were all unfamiliar to the animal. The objects were selected from the pool of objects in Extended Data Fig. 2. All cells with object-vector properties in the familiar room (room A) had object-vector fields also in the new environment with new objects (room B), and there was no significant difference in the spatial information content of the rate maps in the two settings (Fig. 4a,b; familiar: 1.10 ± 0.05 bits/spike; novel: 0.96 ± 0.09 bits/spike, means ± s.e.m.; Wilcoxon signed rank test, W = 66, n = 13, P = 0.17), suggesting that object-vector cells were sharply tuned from the first trial when the objects were encountered. When we realigned vector maps to compensate for the reorientation that typically occurs in MEC cells when animals move from one environment to another23,28,29, correlations between vector maps in familiar and new rooms became very high (Fig. 4c; r = 0.81 ± 0.02, mean ± s.e.m.), suggesting that individual cells maintained their distance metrics.
In 5 of the 6 experiments, we recorded more than one object-vector cell, and object-vector cells were also recorded along with other spatially or directionally modulated cells. In total, there were 50 pairs of simultaneously recorded cells in experiments with two recording rooms (18 object-vector cells, 4 head-direction cells, 1 grid cell). In order to compare shifts in the directional preferences of object-vector cells and head-direction cells between rooms, we calculated circular cross-correlations between directional or spatial tuning curves for the two rooms. For each cell (object vector cell, head direction cell, or grid cell), the shift in orientation between rooms was defined as the rotation of the tuning curve or rate map from one room that maximized the correlation with the tuning curve or rate map in the other room. Then, for each pair of simultaneously recorded cells (object-vector cells or other cells), we determined the difference in angular shift between the two rooms for the two cells. The distribution of pairwise rotation differences was then compared with a distribution obtained from pairs of cells in randomly jittered versions of the tuning curves. The observed pairwise differences were significantly smaller than differences between randomly shifted tuning curves, both for pairs of simultaneously recorded object-vector cells (observed: 8.2 ± 0.8 degrees for all cell types; random: 88.8 ± 7.4 degrees, means ± s.e.m.; Wilcoxon signed rank test, W = 10, n = 50, P = 2.0×10−9) and for pairs consisting of one object-vector cell and either one head-direction or one grid cell (observed: 10.3 ± 1.3 degrees for all cell types; random: 92.8 ± 13.0 degrees, means ± s.e.m.; Wilcoxon signed rank test, W = 1, n = 16, P = 5.3×10−4) (Fig. 4 d-f). Grid cells and head-direction cells generally maintained stable orientations across object and no-object trials (Extended data 10a,b; spatial correlation of grid cells between object and no-object trials: 0.63 ± 0.04, mean ± s.e.m.; correlation of head-direction tuning curves between object and no-object trials: 0.54 ± 0.04).
These observations suggest that a fixed directional structure was maintained across all cell types from one environment to the other. The fact that object-vector cells rotated coherently with grid cells and head direction cells in the two-room experiments raises the possibility that object-vectors cells bind local cues to the global distal framework that controls head direction cells and grid cells.
Object-vector cells are distinct from grid cells and head direction cells
We next asked if object-vector cells constitute a subpopulation of previously reported spatially-modulated MEC cells, or if they represent a new and separate functional population. Out of the 503 superficial MEC cells recorded in the present study, 40 cells, or 8.0%, were identified as grid cells, 57 (11.3%) qualified as speed cells, 149 (29.6%) as head-direction cells, and 34 (6.8%) as border cells.
The majority of the 98 object-vector cells (19.5% of the 503 cells) generally did not share defining properties with any other spatially or directionally modulated cell types (Fig. 5ab). First, they were clearly distinguishable from grid cells (Fig. 5ab; Extended Data Fig. 10a). A significant object-vector response was observed only in one grid cell (1.0%), a number not significantly different from numbers expected with random selection from a shuffled distribution (binomial test with expected P0 of 0.01, P(X≥1) = 0.63; P(X≤1) = 0.74), but significantly lower than the number of cells expected to pass criteria for both grid cells and object-vector cells with the currently identified numbers of these cells, if these cell populations were independent (expected number = N(fraction of grid cells × fraction of object-vector cells) = 7.8; binomial test, P(X ≤ 1) = 0.003). Consistent with the low number of grid cells with object-vector tuning, the grid scores of the object-vector cells, assessed in the no-object condition, were significantly lower than in all other cells (Fig. 5b; Mann-Whitney U-test, U = 19949, n1 = 405, n2 = 98, P = 0.0018). Second, object-vector cells were distinct from speed-tuned cells. The number of object-vector cells that also passed the criterion for speed cells on no-object trials was 5 (5.1%) – more than expected with random selection from a shuffled distribution (binomial test with expected P0 of 0.01, P(X≥5) = 0.003), but lower than the number of object-vector cells expected to be speed-modulated based on the overall level of speed modulation in the general MEC population (expected number, calculated as for overlap with grid cells: 11.1; binomial test, P(X≤= 0.04). There was no difference in speed scores of object-vector cells compared to the other cells recorded (Fig. 5b; U = 23369, n1 = 405, n2 = 98, P = 0.29). Third, and in contrast to the limited overlap with grid cells and speed cells, as many as 38 (38.8%) of the object-vector cells passed the criterion for head-direction cells on the no-object trial (Fig. 5 a,b; Extended Data Fig. 10b). This number was larger than expected with random selection from the distribution of shuffled data (binomial test with expected P0 of 0.01, P(X≥38) = 1×10−8), but not significantly higher than the number expected to pass both head-direction criteria and object-vector cell criteria based on the number of head direction cells in the overall MEC population, if the two cell populations were independent (expected number: 29; binomial test, P(X≥38): 0.06). In the majority of object-vector cells that passed the head-direction criterion, the head-direction mean-vector-length scores were low (mean ± s.e.m.: 0.38 ± 0.02; pure head direction cells: 0.59 ± 0.02, Mann-Whitney U-test, U = 1.9×103, n1 = 38, n2 = 114, P = 1.4×10−5), yet the head-direction scores, estimated on no-object trials, were significantly higher for object-vector cells than for the remaining MEC cells (mean score ± s.e.m.: 0.24 ± 0.015; U = 29527, n1 = 405, n2 = 98, P = 2.2×10−4). Taken together, these data suggest that a fraction of the object-vector cells were weakly head direction-tuned during free running in the open arena.
We then asked how tuning by head direction was influenced by introduction of an object on the floor of the arena. In general, the object decreased the tuning to head direction (Fig. 5b-d; Extended Data Fig. 10b). The number of cells passing the criterion for head direction cells on the object trial was reduced to 20 (20.4% of the cells). While this was still more than expected with random selection from shuffled data (binomial test with expected P0 of 0.01, P(X≥20) = 1×10−8), it was significantly lower than the number of cells expected to share head-direction and object-vector properties in the entire population of recorded cells if these two cell types were independent (binomial test, expected number: 29, P(X≤20) = 0.04). Similarly, head direction scores for object-vector cells were significantly reduced on object trials compared to no-object trials (W = 3555, n = 98, P = 6.3×10−5; head direction scores for object-vector cells vs. remaining cell population on the object trial: U = 25827, n1 = 405, n2 = 98, P = 0.40). There was no difference in the distribution of time spent across the spectrum of head directions on object and no-object trials (Fig. 5c; Extended Data Fig. 10b; mean vector lengths of head-direction occupancy, Wilcoxon signed rank test, W = 1967, n = 98, P = 0.10). The loss of head-direction tuning on object trials could be taken to imply that head direction inputs exert a strong influence on firing in object-vector cells when objects are not present, whereas upon object insertion they combine with inputs from cells that signal object location33,34 or the animal’s egocentric orientation to the object9,49,50 to form an allocentric object-vector representation, much in the same way as head direction inputs dominate firing in grid cells when hexagonally patterned firing breaks down after blockade of hippocampal excitatory feedback51. Taken together, these observations and those from the two-room experiment suggest that object-vector cells are modulated by head direction inputs, but this modulation may be secondary to influences from object-informative cells and does not account for the presence of a distinct population of cells expressing vectorial relationships to local objects.
Object-vector cells are distinguishable from border cells
Next, we asked to what extent object-vector cells overlap with border cells, since objects and borders can be seen as overlapping and potentially continuous stimulus populations. The data suggest that object-vector cells and border cells exhibit only partial overlap. Most object-vector cells lacked firing fields along the peripheral walls of the recording enclosure (Fig. 5a), and border scores on the no-object-trial were lower for object-vector cells than for cells that were not object-vector cells (Fig. 5b; Mann-Whitney U-test, U = 20680, n1 = 405, n2 = 98, P = 0.0017). Yet, among the 98 object-vector cells recorded on the no-object trial, as many as 12 passed the criterion for border cells (35.3% of the border cells; 12.2% of the object-vector cells; Fig. 6 a,b). The number of object-vector cells that also passed the border cell criteria was larger than expected with random selection from a shuffled distribution (binomial test with expected P0 of 0.01, P(X≥11) = 1×10−8), and larger than the number expected if the properties of border cells and object-vector cells were independently distributed in the MEC population (expected number: 6.6; binomial test, P(X≥12) = 0.04).
Most of the object-induced fields in border cells had properties similar to those of object-vector fields with no border activity. The fields were confined and distributed across a wide spectrum of angles, not deviating significantly from a uniform distribution (Fig. 6c; Rayleigh test, Z = 1.1, n = 13, P = 0.35). Their orientation with respect to the object could not be predicted by the orientation of the border field (Fig. 6d; circular correlation r = −0.39, n = 14 object-vector fields from 12 cells, P = 0.13), and there was no significant correlation between the distance between border field and border and the distance between object-vector field and object (Fig. 6d; distance from border to centre of border field vs. distance from object centre to object-vector field centre: r = 0.04, n = 14, P = 0.89). There was a significant correlation between the difference in orientation to wall and object and the difference in distance (Fig. 6e; r = 0.56, n = 14, P = 0.04), i.e. cells that differed with respect to orientation also tended to differ with respect to distance. The distance between the object and the centre of the object-vector field in the 12 cells ranged from 9 to 39 cm (Fig. 6c; mean ± s.e.m.: 21.9 ± 2.6 cm), whereas the distance from the object to the field boundary ranged from 0 to 27 cm (9.6 ± 2.1 cm). These ranges contrasted with the distance from the wall to the centre of the border field, which ranged only from 6 to 14 cm (Fig. 6c; mean ± s.e.m, 8.8 ± 0.2 cm). Altogether, the analyses suggest that a small fraction of the object-vector cells overlapped with the border-cell population. In those cells, there was no consistent vectorial relationship from firing field to border and object.
Finally, we asked if cells with responses to both borders and objects could be differentiated with regard to how they respond to elevated objects. Five of the 12 border cells that also passed the object-vector cell criteria were tested with suspended objects in addition to standing objects (Fig. 6 f,g). We quantified, for these cells, the difference in response to standing and suspended objects using the object-vector field at the standing object to define a template area with a given distance and orientation from the object, and then applying the same vector-defined area with reference to the suspended object (Fig. 6f). Corresponding areas were next identified for the no-object trial. The response to standing and suspended objects was then taken as the difference in firing rate on no-object and object trials in the template area defined by the suspended object, normalized to the firing rate in the template area for the standing object on the object trial. For the 21 non-border object-vector cells tested with suspended objects, the score was always positive (Fig. 6h; mean ± s.e.m., 1.1 ± 0.17), suggesting that firing rates increased reliably in the template area near the suspended object, whereas for the 5 border cells, the score was only −0.24 ± 0.09 (non-border vs. border: U = 334, n1 = 21, n2 = 5, P = 7.2×10−4, Mann-Whitney U-test), indicating no increase in firing compared to no-object trials in the vicinity of suspended objects. These observations raise the possibility that object-vector cells and border cells respond differentially not only to the extension of object dimensions but also to their vertical location and the degree to which they constrain the animal’s path.
Discussion
We have shown that a distinct population of MEC cells encodes direction and distance from discrete objects, independently of the identity or location of the object in the environment. These cells differ from the object-encoding cells of the LEC, which fire only at the object location and not in the space between the objects. Object-vector firing fields are expressed instantly when new objects are encountered in new environments. The vector representation is allocentric, i.e. the firing fields are fixed in room coordinates, irrespective of the animal’s direction of movement, distinguishing them from the egocentrically tuned goal-vector cells of the hippocampus8,9. Object-vector cells are part of a broader MEC representation, with which it remains aligned even when grid and head-direction cells undergo changes in spatial and directional tuning, such as after relocation from one room to another. Taken together, these results identify an object-centered entorhinal metric of navigational space tightly integrated with the more distantly anchored framework enabled by grid cells and head-direction cells.
Object-vector cells provide a possible cellular basis for spatial mapping where objects rather than surrounding geometry serve as the reference frame. Unlike laboratory environments, real worlds are cluttered with objects. When objects maintain stable positions relative to a goal, animals have been observed to use them as references for navigation35–40. Based on this finding, theoretical studies have proposed the existence, in cortical networks, of allocentric vectorial representations where trajectories are derived from differences between vectors from the animal to perceived objects and vectors between such objects and goals stored in memory41. The present study shows that vectors to perceived objects are represented in a dedicated neural population in the superficial layers of MEC. This neural population interweaves with the network of grid cells and head direction cells that encodes position for space in a more distal geometric framework21,26,52, independently of the location of the objects. The continued alignment of these networks across environments suggests that the networks are strongly interconnected. Although their mode of interaction remains to be determined, one possibility is that object-vector cells receive distally anchored positional and directional input from grid cells53 and head direction cells41, and that this metric is anchored to landmarks by association with visual or other sensory signals, or signals from object-informative cells in LEC33,34 or elsewhere54,55. The strong reciprocal connections of MEC and LEC56–58 might enable such interactions.
Previous studies have identified object-responsive cells across a wide network of brain regions that include both LEC33,34 and areas connected with the LEC, such as the perirhinal54 and anterior cingulate55 cortices. These ‘object cells’ differ from the object-vector cells of the MEC in that they respond only when the animal is at the object, not when it perceives it from a distance. The cells also lack directional tuning. Thus, they cannot alone account for navigation in the space between objects. More direct evidence for cells with object-vector properties comes from a study of CA1 cells in which place cells were found to intermix with a sparse population of cells that fired repeatedly at specific distances and directions from a subset of objects placed in the recording compartment45. Earlier work has similarly shown that firing fields of some CA1 cells follow the location of an array of landmarks when the array is moved in a test arena59, and more recent work has identified subsets of CA1 place cells that fire consistently at or before mobile visual-tactile landmarks on a linear treadmill, regardless of the location of the landmarks on the belt60. While allocentric directional relationships were either not investigated or not quantified in these studies, the cells do seem to have properties in common with the object-vector cells of the MEC. But there are also likely to be important differences. Hippocampal cells often responded only to a subset of the objects, unlike their entorhinal counterparts, which developed fields unconditionally at every single object the mouse encountered. Moreover, hippocampal cells fired at a single location relative to each object, while the entorhinal object-vector cells frequently expressed firing fields in more than one direction from it. Finally, during foraging in the box, the firing fields of the hippocampal cells in many cases developed over multiple trials45, distinguishing them from entorhinal object-vector cells, which emerged instantly, not requiring any extended experience with the environment or the object. The apparently slow appearance of object-vector representations in the hippocampal population points to instantly-appearing object-vector cells in MEC as a possible source for training hippocampal cells secondarily to form vectors between often-visited goals and stable landmarks for subsequent storage in memory41. Such a training process would be reminiscent of how odour-selective cells in the LEC can, over many trials, entrain odour-selective cells in the CA1 61.
We have characterized a population of object-vector cells in MEC that responds to a wide variety of spatially confined, tower-like objects. The exact range of objects and object shapes that elicit vectorial representations in this cell population remains to be determined but our study shows that the majority of object-vector cells fail to respond to spatially extended objects in the distal background, such as the walls of the recording box, whereas instead they respond to discrete objects that stand out from the monotonous planar surfaces of the environment. Obstruction of the animal’s upcoming path was not a condition for object-vector cells to respond, as these cells, unlike border cells, fired vigorously also to suspended objects that the mice could not reach. The distinction between confined objects and walls was not absolute, however, because approximately one-third of the border cells with firing fields alongside the wall of the box had additional circular fields at specific distances and directions from more point-like objects on the arena floor. This proportion is larger than expected if object-vector cells and border cells were independent populations and raises the possibility that object-vector and border cells are activated by a continuum of shapes and sizes, from point-like bodies to lengthy surfaces. The fact that border cells with responses to discrete objects did not develop additional fields when the discrete objects were out of reach may imply that object-vector cells and border cells are categories of a broader class varying along multiple axes and dimensions. Such a breadth of response profiles would enable MEC networks to perform positional vector calculations across a wide variety of naturalistic environments, where discrete landmarks often are more common than the long walls or edges of test boxes in the laboratory.
Because object-vector cells define a range of distances and directions from restricted locations, they are reminiscent of ‘boundary-vector cells’ predicted by theoretical models of spatial coding42–44. In these models, each boundary-vector cell fires at a specific distance and direction from an extensive boundary in the local environment. Inputs from such boundary-vector cells were proposed by the models to give rise to place cells in the hippocampus. Cells with properties similar to boundary vector cells have been reported in the subiculum46,47 but most of these cells fire preferentially along the boundaries of the environment and not primarily out in open arena space47. Furthermore, cells with boundary-related activity in the subiculum do not project to place cells in the hippocampus. Instead, place cells receive abundant inputs from the superficial layers of MEC, where boundary-vector cells with fields offset from the arena walls are not common22,23,48. Our study shows that the MEC instead has a high density of object-vector cells, which define positions anywhere in the local space based on vectors from discrete objects, including vertical surfaces. This representation is versatile not only because it operates universally across environments and covers positions all across the environment, but also because it is independent of the presence of lengthy monotonous boundaries in the environment.
Author Contributions
Ø.A.H., M.-B.M. and E.I.M. designed experiments and analytic approaches; Ø.A.H. and E.R.S. collected data; Ø.A.H. performed analyses; M.-B.M. and E.I.M. supervised the project; Ø.A.H. and E.I.M. wrote the paper with input from all authors.
Author Information
Reprints and permissions information is available at www.nature.com/reprints.
Competing interests statement
The authors declare that they have no competing financial interests.
Methods summary
Methods, along with any additional Extended Data display items, are available in the online version of the paper; references unique to this section appear only in the online paper.
Online Methods
Subjects
Data were obtained from 8 male wild type black 6 mice at the age of 4-11 months. All mice were kept on a 12 hr light/12 hr dark schedule in a humidity and temperature-controlled environment. The mice were housed in single animal cages after implantation. Testing occurred in the dark phase. The animals were not deprived of food or water. Experiments were performed in accordance with the Norwegian Animal Welfare Act and the European Convention for the Protection of Vertebrate Animals used for Experimental and Other Scientific Purposes.
Surgery and electrode implantation
The mice were anesthetized with 5% isoflurane (air flow: 1.2 l/min) in an induction chamber. Upon induction of anesthesia, they received subcutaneous injections of buprenorphine (Temgesic) and Meloxicam (Metacam). The mice were then fixed in a Kopf stereotaxic frame for implantation. Local anesthetic Bupivacaine (Marcaine) was injected subcutaneously before making the incision. During surgery, isoflurane was gradually reduced from 3% to 1% according to physiological condition. The depth of anesthesia was monitored by testing tail and pinch reflexes as well as breathing.
Anesthetized mice were implanted with a single bundle of 4 tetrodes attached to a microdrive fastened to the skull of the animal. The tetrodes were targeted to MEC at an angle of 3-4 degrees relative to the bregma/lambda horizontal reference plane, with the tips pointing in the posterior direction. The tetrodes were inserted 3.1-3.3 mm lateral to the midline and 0.3-0.4 mm anterior to the transverse sinus edge, with an initial depth of 800 μm. The implant was secured to the skull with histoacryl and dental cement. One screw was connected to the drive ground.
Tetrodes were constructed from four twisted 17 μm polyimide-coated platinum-iridium (90%–10%) wires (California Fine Wire, CA). The electrode tips were plated with platinum to reduce electrode impedances to between 120 and 220 kΩ at 1 kHz.
Behavioral procedures
The mice were trained to forage for cookie crumbs in an 80 cm × 80 cm square and a 90 cm diameter circular compartment, both enclosed by 50 cm high walls. Thick dark blue curtains surrounded the recording arena, except for a slit to one side (Fig. 1a). Before testing, the mouse rested outside the curtain on a flowerpot on a pedestal covered with towels. Testing was performed at low light levels to encourage exploration. Between trial sequences, the mat covering the floor of the recording box was cleaned.
A typical trial sequence started with a trial where no object was present in the arena, followed by one in which a tower-shaped object was placed at a semi-randomly varied location, with a bias towards the box centre on the first trial (to capture fields with large offsets from the object). The object used for standard trials (Fig. 1 and Fig. 2) was usually Object 7 in Extended Data Fig. 2, a 5-cm wide, 20-cm tall cylinder-shaped object. For subsequent experiments, objects were selected from a pool of tower-like modified rectangular prisms or cylinders ranging in size between 3 and 7 cm in width and 9 and 20 cm in height for the prisms and between 3 and 8 cm in diameter and 20 and 35 cm in height for the cylinders. All of these objects were substantially taller than the mouse. In addition, on selected trials we used a flattened cylinder (11 cm in diameter, height of 0.5 cm; Object 13 in Extended Data Fig. 2), or a block that had the shape of a wall (Object 6 in Extended Data Fig. 2; 50 cm long, 0.5 cm wide, 50 cm high).
In order to verify that any observed change in neural activity between the first and the second trial was tied to the location of the object, the object was displaced in a pseudo-random fashion on a third trial in the sequence (only in those experiments where object-responsive cells were present on the preceding trial). In a few cases, not only the location but also the identity of the object was changed on the third trial (see below for tests with different object identities). The average object displacement on the third trial was 19.4 ± 1.1 cm (mean ± s.e.m.). Each trial lasted approximately 15 minutes. Trials were typically spaced by a few minutes, during which the experimenter clustered and inspected recorded cells and placed the object in a new location. The mouse was in most circumstances not removed from the arena between the trials.
In most experiments, only one object was placed in the arena, although tests with multiple simultaneously presented objects (2-6, mostly 2 or 3) were also conducted. In a subset of tests, cells were recorded in two rooms – one familiar and one new to the mouse. A few cells were recorded in both rooms also after the initial test in the second room. Only novel objects were presented in the novel room. Both novel and familiar objects were chosen from the pool of objects shown in Extended Data Fig. 2. Tests in familiar and novel rooms were consecutive, with an interval of 10-15 min for transport and preparation. During preparation for recording, the mouse rested in a flowerpot on a pedestal outside the curtains.
In a subset of the experiments, the mouse was tested with a suspended object, out of reach to the animal (Object 9 in Extended Data Fig. 2). On these tests, a blue plastic tube with a diameter of 7 cm was taped to the wall, with the lower end approximately 15 cm above the floor level. In each individual experiment, the mouse was observed to make sure that the elevation was sufficient to not obstruct the animal’s movement in any way. The suspended object was presented at the same time as a standing object elsewhere in the arena.
Finally, while the majority of experiments were performed with lights on, objects were also presented in darkness in a few instances. The mice first explored the arena with an object present and curtains fully enclosing the arena. Subsequently, the lights were turned off and the mouse explored the arena and the object in darkness. The mouse was not taken out of the arena between the light and dark trials. Each trial lasted approximately 15 minutes.
Recording procedure
Data collection started 1-2 weeks after implantation of the tetrodes. During recording, the animal was connected to an Axona data acquisition system (Axona Ltd., Herts, U.K.) via an AC-coupled unity-gain operational amplifier close to the animal’s head, using a light-weight counterbalanced multiwire cable from both implants to an amplifier. Unit activity was amplified 3000-14,000 times and band-pass filtered between 0.8 and 6.7 kHz. Triggered spikes were stored to disk at 48 kHz with a 32-bit time stamp. An overhead camera recorded the position of two light-emitting diodes (LEDs) on the head stage, each at a sampling rate of 50 Hz. The diodes were separated by 3 cm and aligned with the body axis of the mouse. To sample activity at multiple dorso-ventral MEC positions, the tetrodes were lowered in steps of 25-50 μm between trial sequences after all relevant tests had been completed. Recordings started as soon as the tetrodes were judged to be in MEC, using theta modulation and presence of spatially or directionally modulated cells as criteria in addition to tetrode depth.
Spike sorting and cell classification
Spike sorting was performed offline using graphical cluster-cutting software (tint; Neil Burgess and Axona Ltd.). Spikes were clustered manually in two-dimensional projections of the multidimensional parameter space (consisting of waveform amplitudes), using autocorrelation and cross-correlation functions as additional separation tools and separation criteria. Cluster separation was determined by calculating distances between spikes of different cells in Mahalonobis space (Extended Data Fig. 5). Noise in the vicinity of clusters was expressed as the L ratio (Extended Data Fig. 5). Clusters on successive recording trials were identified as the same unit if the locations of the spike clusters in cluster space were stable.
Firing-rate maps and head-direction tuning curves
Position estimates were convolved with a 35-point Gaussian window and x,y-coordinates were sorted into 2 cm × 2 cm bins. Spike timestamps were matched with position timestamps. Only spikes collected at instantaneous running speeds above 3 cm/s were included. Firing rate distributions were determined by counting the number of spikes and assessing time spent in 2 cm × 2 cm bins of the firing rate maps and in directional bins of 5 degrees in tuning curves for head direction. The distributions were smoothed with a two-dimensional Gaussian Kernel with standard deviation of 2.5 bins (5 cm) in both the x and the y direction for the rate maps and with a Gaussian filter with a standard deviation of 2 bins (10 degrees) for the head-direction maps.
Definition of object-vector cells
We detected firing fields in the rate map by iteratively applying the Matlab “contour” function (Mathworks.inc), starting from the cell’s peak firing rate until reaching two times the standard deviation of the firing rates of all bins in the rate map. Firing fields were defined as contiguous areas within a contour of at least 16 bins and with a peak firing rate of at least 2 Hz. Cells that after insertion of the object expressed firing fields that were not present on the no-object trial, were selected for further analysis. We distinguished between cells that fired at the object (object cells; 0-4 cm from the centre of the object) and cells whose firing fields were offset by more than 4 cm from the object. The focus of the analyses was on the latter category, which accounted for nearly all object-responsive cells.
For cells with fields that were offset by more than 4 cm from the object centre, the vector-relationship between the cell’s spatial firing and the object was expressed in a “vector-map” in which firing rate was measured as a function of distance and direction from the object location. With the centre of the object as the reference, the arena was divided into directional bins of 5 degrees’ width, and for each directional bin, the time-normalized firing rate was measured in distance bins of 2 cm (Fig. 1c). The resulting distance-by-direction matrix was smoothed with a two-dimensional Gaussian kernel using a standard deviation of 2 bins (10 degrees, 4 cm). In the vector map, 0 degrees was defined as east of the object in the room frame (Fig. 1 a,c). The vector map on the object trial was then compared with that of subsequent trial where the object was moved to a new location. Object-vector cells were defined as cells that had a correlation between vector maps on object and displaced-object trials that exceeded chance levels determined by repeated shuffling of the experimental data (see below). In addition, for a cell to be accepted as an object-vector cell, the vector-map correlation between object and displaced-object trials was required to be higher than between the no-object trial and either of the object trials, spatial information on the object trial had to exceed the 95th percentile of the shuffled data, and the peak firing rate had to be at least 2 Hz. Vector maps for the no-object trial were made using the respective object locations on the object trials as references.
Shuffling was conducted with 100 permutations for each of the object trials. For each permutation, the entire sequence of spikes fired by the cell was time-shifted along the animal’s path by a random interval between on one side 20 s and on the other side 20 s less than the length of the session, with the end of the session wrapped to the beginning. Time shifts varied randomly between permutations and between cells. Vector maps were constructed for each permutation, with the object location of the experimental data as the reference in all permutations. Surrogate vector maps from the object trial were next correlated with surrogate vector maps from the displaced-object trial. The 99th percentile correlation of the distribution of all vector-map correlations from all 120 cells was taken to be the chance level.
Vector maps were also used to determine the similarity of responses to different objects in experiments where multiple objects were present in the arena. For each cell, a vector-map was constructed around each object and fields were detected in the vector maps in the same way as for the firing rate maps. In these analyses, each vector map would contain multiple fields – at least one per object. We compared vector maps for different pairs of objects and defined the difference in orientation and distance of vectors to the two objects as the difference in orientation and distance of the two fields in the pair of maps that had the nearest peak-to-peak distance.
Egocentric directional tuning
Egocentric directional tuning curves were constructed according to the procedure described in Sarel et al.9. Briefly, tuning curves were constructed with movement (heading) direction bins of 20 degrees relative to the object location, and with zero degrees defined as moving toward the object and ±180 degrees moving away from the object. Curves were smoothed over 1.5 bins (30 degrees) with a Gaussian filter. We defined the egocentric directionality index as: where p is the peak of the curve, m is the median of the curve, and m.a.d. is the median absolute deviation. Again we defined a 99th percentile threshold by time-shifting the spikes 100 times for each cell and subsequently calculating egocentric directionality for each of these data.
Definition of grid cells
The spatial periodicity of each rate map – the cell’s grid score – was determined by calculating a spatial autocorrelogram26. For each cell, a grid score was determined by taking a central circular sample of the autocorrelogram, with the central peak excluded (the central peak was defined as 100 or more contiguous pixels of 1.5 × 1.5 cm2 above a fixed threshold of r > 0.1), and comparing rotated versions of this sample26,62. The Pearson correlation of the circular sample with its rotation in α degrees was obtained separately for angles of 60 and 120 on one hand and 30, 90 and 150 on the other. The cell’s grid score was defined as the minimum difference between any of the elements in the first group (60 and 120 degrees) and any of the elements in the second.
A cell was defined as a grid cell if its grid score exceeded a chance level determined by repeated shuffling of the experimental data (100 permutations per cell). For each permutation, the entire sequence of spikes fired by the cell was time-shifted along the animal’s path by a random interval between on one side 20 s and on the other side 20 s less than the length of the session, with the end of the session wrapped to the beginning. Time shifts varied randomly between permutations and between cells. If the grid score from the recorded data was larger than the 99th percentile of grid scores in the distribution of shuffled data from all cells, the cell was defined as a grid cell. As an additional criterion we required the cell to have a peak firing rate of at least 2 Hz.
Template grid patterns from object-vector cells with multiple fields
For cells with two or more object-vector fields, we constructed a regular grid lattice extrapolated from the positions of the two object-vector fields. Template fields were modelled as circular areas centred at vertices in the grid lattice, and with size equal to the mean area of the two object-vector fields. A Z-score was calculated by first determining the difference between the mean firing rate inside the extrapolated template areas and the mean firing rate outside all projected and real firing fields, and then dividing this difference by the standard deviation of the firing rate of all bins in the rate map.
Analysis of head direction cells
The animal’s head direction was determined for each tracked sample by plotting the relative positions of the two LEDs onto the horizontal plane. The directional tuning function for each cell was obtained by plotting the firing rate as a function of the animal’s heading direction, divided into bins of 5 degrees and smoothed with a Gaussian moving average of 2 bins on each side. Directional tuning was estimated by computing the length of the mean resultant vector (mean vector length) for the circular distribution of firing rates. For a cell to be included as a head direction cell, its mean vector length needed to pass the 99th percentile threshold of the mean vector length in the shuffled version of the same data. Shuffling was performed by shifting spike times at random intervals along the path in the same way as for grid cells.
Analysis of border cells
Border cells were identified by computing a border score for each cell23. Firing fields were defined as areas corresponding to a minimum of 9 neighboring bins (1 bin = 2 cm) of the smoothed rate map where firing rates were higher than 20% of the cell’s peak firing rate. The cell’s border score was expressed as the difference between the maximal length of a wall touching on any single firing field of the cell and the average distance of the field from the nearest wall, divided by the sum of those values. Border scores ranged from - 1 for cells with infinitely small central fields to +1 for cells with infinitely narrow fields that lined up perfectly along the entire wall. For circular arenas, the rate map was first transformed into a square image using a polar transform with the centre of the box as the reference. The resulting polar image represented distance from the wall (in cm) on one axis and distance along the perimeter or the wall (in angles) on the other. The border score was then computed as for square arenas. Since border cells often cover half of the arena in a circular environment, a border score of +1 would be assigned to cells with infinitely narrow fields lining up along the wall of half the box, or covering 180 degrees in the polar-image. After border scores were computed for each cell, border cells were identified as cells in which the border score exceeded the 99th percentile of the distribution of border scores in shuffled versions of the same data. Shuffling was performed by shifting spike times at randomly chosen intervals along the path in the same way as for grid cells. In addition, for a cell to be defined as a border cell, we required the cell to have a peak rate of at least 2 Hz and a spatial information content that exceeded the 95th percentile for spatial information on the no-object trial.
Spatial information content and spatial coherence
Information content was determined for each rate map by computing the spatial information rate as where λi the mean firing rate in the i-th bin, λ the overall mean firing rate and pi the probability of the animal being in the i-th bin (occupancy in the i-th bin/total recording time). Spatial information in bits/spike was obtained by dividing the information rate with the mean firing rate of the cell. Spatial coherence was calculated for each cell as the z-transform of the correlation between the firing rates of each bin and the averaged firing rates of the 8 nearest neighbours of that bin.
Coherence between directional or spatial rate distributions
We quantified the degree to which orientation of different cell types shifted coherently between trials in different rooms by performing circular cross-correlations on their directional or spatial rate distributions. For each head-direction cell, we cross-correlated the directional tuning curves obtained from the two recording rooms, using a bin size of 5 degrees. For object-vector cells, we cross-correlated the object-centered allocentric directional tuning curves - where firing rate was expressed as a function of orientation relative to object - across trials in the same two rooms, also using a bin size of 5 degrees. For grid cells, we rotated the rate map in the first room in steps of 5 degrees and correlated this map with the rate map of the other room for each step. For all cell types, we identified the shift between the two pairs of distributions or maps that gave the peak correlation. Two of the object-vector cells with two firing fields had symmetrically arranged fields, one on each side of the object, yielding two clear peaks in the cross-correlation. In these two cases we determined the shift of the maps by taking advantage of consistent differences in field sizes and distances between the two fields and the object. For each pair of concurrently recorded cells, we noted the difference in the angles that resulted in peak correlation. We compared the distribution of these differences with the distribution of pairwise differences obtained by randomly shifting the tuning curves in a circular manner while maintaining the shapes of the tuning curves.
Response to suspended object
Border cell and object-vector cell response to suspended objects was compared by first identifying firing fields in the vicinity of a standing object, as described above. The field area and vector from object to field-center was then transferred to the projection of the suspended object on the floor surface to act as a template for an expected field (Fig. 6f). Mean firing rates were measured in both of these areas in the presence of the objects and on no-object trials. This procedure was also used to compare how well the vector between a firing field of an object-vector cell and the object in one object trial predicted the position of a field in a trial where the object was displaced (Extended Data Fig. 3a). We defined a suspended-object response score as: where Rsuspended+ is the mean firing rate in the template area associated with the suspended object, Rsuspended− is the mean firing rate in the template area when the suspended object is absent, and Rstanding is the mean firing rate of the original field in the vicinity of the standing object.
Histology and Reconstruction of Recording Positions
The tetrodes were not moved after the final recording session. The mouse received an overdose of Pentobarbital and was perfused intracardially with 9% saline and 4% formaldehyde. The brain was extracted and stored in 4% formaldehyde. Frozen, 30mm sagittal sections were cut, mounted on glass, and stained with cresyl violet (Nissl). The final position of the tip of each tetrode was identified on photomicrographs obtained with Axio Scan.Z1 microscope and Axio Vision software (Carl Zeiss, Germany) (Extended data Fig. 1).
Statistical tests
All statistical tests were two-sided. We used Mann-Whitney U tests for independent group comparisons and Wilcoxon signed rank tests for paired tests. Correlations were determined using Pearson’s product-moment correlation coefficients. P-values for Pearson’s correlations were computed using a Student’s t distribution for a transformation of the correlation (Matlabs ‘corr’ function). Binomial tests were used to determine expected probabilities of observing reported counts. No statistical methods were used to pre-determine sample sizes but our sample sizes are similar to those reported in previous publications.
Acknowledgments
We thank A.M. Amundsgård, K. Haugen, K. Jenssen, E. Kråkvik, and H. Waade for technical assistance. The work was supported by two Advanced Investigator Grants from the European Research Council (GRIDCODE’, Grant Agreement N°338865; ENSEMBLE’ – Grant Agreement N°268598), a NEVRONOR grant from the Research Council of Norway (grant no. 226003), the Centre of Excellence scheme and the National Infrastructure Scheme of the Research Council of Norway (Centre for Neural Computation, grant number 223262; NORBRAIN1, grant number 197467), the Louis Jeantet Prize, the Körber Prize, and the Kavli Foundation.