Our study shows that place and grid cells showed less sensitivity to height than to horizontal displacement, and it thus appears that “neural odometry” was selectively impaired in the vertical dimension. Most notably, grid cells, which show periodic firing in the horizontal plane, showed no vertical periodicity. The similarity of results from environments of differing structure and which elicited different locomotor behaviour suggests that the neural representation of allocentric space has intrinsically different properties in the vertical dimension from those in the horizontal, and is therefore anisotropic.
Although both place and grid fields were vertically elongated, they were nevertheless somewhat height-modulated on both apparati, with place cells – interestingly – being more modulated than grid cells. This modulation suggests that height is
encoded by these cells, but in a different way. The difference may be merely one of scale – had we used very tall environments, we might have seen grids occurring over a very large scale, producing apparent stripes on a small apparatus but revealing periodicity on a large one (). However, it may be that the difference is qualitative rather than quantitative: the way
in which firing is modulated differs in vertical vs. horizontal dimensions. Place fields have been shown to respond to qualitative as well as quantitative variations in environmental stimuli, as evidenced by their altered firing in response to changes in “context” (reviewed in 10
). Given that changes in an animal’s height produce changes in qualitative contextual aspects of the environment, over and above mere metric changes in height, it may be that these are what modulate firing in the vertical dimension. Such contextual modulation could explain why there is a dissociation between the sensitivity of grid cells and place cells to height: possibly place cells are informed about height, via their contextual inputs, in a way that grid cells are not.
There have been earlier suggestions that encoding of the vertical dimensions may be non-metric in place cells. Initial studies of place cells on a sloping or vertically translated surface found evidence of sensitivity to vertical displacement11-13
and also to tilt13
but little evidence of true metric encoding. However, this could have been due to the strong salience of local cues conferred by the environment surfaces, causing odometry to be dominated by the floor. On our pegboard apparatus, by contrast, the wall provided the dominant (and indeed, only) surface: odometry was preserved in the horizontal dimension, despite the absence of a horizontal surface, but impaired in the vertical dimension despite the vertical surface. Thus, the impaired vertical odometry does not seem to be due to the surface structure of the environment.
The pattern of grid cell stripes on the pegboard is consistent with the stripes being cross sections through a hexagonal close-packed columnar array () which could explain the irregular inter-stripe spacing (). However, the stripes are also reminiscent of the findings of Derdikman et al. 14
of directionally dependent stripe-like activity on a hairpin maze composed of repeating segments. Instead of a continuous pattern of grid fields, the grid cell responses in the maze repeated on each successive entry into identical maze sub-compartments, introducing a discontinuity in the grid pattern that apparently indicated failure of the cells to take into account (i.e., path integrate) distance travelled in the direction orthogonal to the linear compartments. Notably, cells were highly directional in this apparatus, suggesting that the two opposing directions of travel were treated as different environments, or “contexts”. However, fields on the pegboard were not directional, and nor did rats execute such stereotyped movements that their trajectories could be broken up into compartment-like blocks. Furthermore, on the helix, unlike the discontinuous grid pattern in the hairpin maze, we observed a continuous, repeating pattern of grid bumps. The differences occurring between our experiments and that of Derdikman et al. suggests that the phenomena may be different. However, the common feature of pattern repetition seen in these environments may reflect the common feature of impaired path integration in the direction orthogonal to the main direction of travel.
The results on the helix similarly resemble those of Nitz15
who found that place field patterns repeated on successive laps of a horizontal spiral. The cells failed to encode the lateral translation that occurred with each successive lap of the spiral, in a manner analogous to how our cells failed to encode the vertical translation that occurred on each lap. This suggests a general hypothesis: that path integration does not function effectively for movement in a dimension that is perpendicular to the long axis of the animal (which usually includes, for surface-dwelling animals, the vertical dimension). An analogous finding has been reported in head direction cells, which encode directions only in the plane of locomotion 16
, apparently producing a planar compass signal, but one that can be oriented vertically if the animal – unlike on our pegboard – orients its body plane vertically.
Impaired vertical odometry might result from the fact that there is less visual information about vertical travel. We think it unlikely that vertical cues are more impoverished, as the experimental rooms possessed many features at multiple vertical levels (shelves, doors etc; Supplementary Fig. 1
), and in any case, in the horizontal plane, place and grid fields are usually well formed even when the only source of visual discontinuity is a cue card. We therefore suggest that impaired vertical path integration is the likelier explanation. Models of grid cell generation postulate a metric process by which interfield spacing is computed17-19
: like the metric models of place field generation, these models could account for the vertical elongation by presuming a deficient or absent distance-calculating process for travel in the direction perpendicular to the animal’s head/body plane.
The generality of the present findings is a question for future research. In both apparati, rats travelled on a surface and it may be that this impaired the ability of the allocentric spatial system to form a volumetric representation. Alternatively, since rats are surface-travelling it may be that the system has, in rats and other surface-travelling species, lost some of its ability to represent space volumetrically (that is, with metric information in all three dimensions), even in a volumetric environment. However, it is also possible that the planar character of the cognitive map is a general feature of animals in all settings. Representing three dimensions volumetrically is computationally highly complex, partly because it requires many more representational units (scaling as the square of the equivalent horizontal component), and also – more importantly – because it requires an integrated 3D compass having four degrees of freedom (three for heading – one in each rotational plane – plus one for orientation of the head/body around the long axis), for which there is no evidence in any animal at present. As humans, our subjective sense of 3D space feels integrated and three-dimensional. However, experiments in zero gravity where subjects can move freely in all directions find that they nevertheless tend to impose a reference “horizontal” on the environment20
. This suggests that our own internal representation of space may also be planar, and that our sense of having a complete 3D spatial map may be an illusion. This has important consequences for understanding human exploration and mapping of 3D spaces such as undersea, air, space and – more recently – virtual reality.