Symmetries and asymmetries in the neural encoding of 3D space

The neural coding of space centres on three foundational cell types: place cells, head direction cells and grid cells. One notable characteristic of these neurons is the symmetry properties of their spatial firing patterns. In symmetric environments, firing patterns are often also symmetric: for example, place cells show translational symmetry in aligned sub-compartments of a multi-compartment environment. A single head direction cell has a mirror-symmetric firing pattern, while a sub-class of head direction cells can show multi-fold rotational symmetries in multi-compartment environments, matching the symmetry of the recently experienced environment. The entorhinal grid cells are notable for the symmetry of their firing patterns in both rotational and translational domains. However, these symmetries are broken in a variety of situations. These symmetry-making and -breaking observations shed light on the underlying computations that generate these firing patterns, and also invite speculation as to whether they may have a functional role. This article outlines these findings and speculates on the consequences of the resultant firing symmetries and asymmetries for spatial coding and cognition. This article is part of a discussion meeting issue ‘New approaches to 3D vision’

How environmental movement constraints shape the neural code for space

Study of the neural code for space in rodents has many insights to offer for how mammals, including humans, construct a mental representation of space. This code is centered on the hippocampal place cells, which are active in particular places in the environment. Place cells are informed by numerous other spatial cell types including grid cells, which provide a signal for distance and direction and are thought to help anchor the place cell signal. These neurons combine self-motion and environmental information to create and update their map-like representation. Study of their activity patterns in complex environments of varying structure has revealed that this "cognitive map" of space is not a fixed and rigid entity that permeates space, but rather is variably affected by the movement constraints of the environment. These findings are pointing toward a more flexible spatial code in which the map is adapted to the movement possibilities of the space. An as-yet-unanswered question is whether these different forms of representation have functional consequences, as suggested by an enactivist view of spatial cognition

The mosaic structure of the mammalian cognitive map

The cognitive map, proposed by Tolman in the 1940s, is a hypothetical internal representation of space constructed by the brain to enable an animal to undertake flexible spatial behaviors such as navigation. The subsequent discovery of place cells in the hippocampus of rats suggested that such a map-like representation does exist, and also provided a tool with which to explore its properties. Single-neuron studies in rodents conducted in small singular spaces have suggested that the map is founded on a metric framework, preserving distances and directions in an abstract representational format. An open question is whether this metric structure pertains over extended, often complexly structured real-world space. The data reviewed here suggest that this is not the case. The emerging picture is that instead of being a single, unified construct, the map is a mosaic of fragments that are heterogeneous, variably metric, multiply scaled, and sometimes laid on top of each other. Important organizing factors within and between fragments include boundaries, context, compass direction, and gravity. The map functions not to provide a comprehensive and precise rendering of the environment but rather to support adaptive behavior, tailored to the species and situation

Distorting the metric fabric of the cognitive map

Grid cells are neurons whose regularly spaced firing fields form apparently symmetric arrays, or grids, that are thought to collectively provide an environment-independent metric framework for the brain's cognitive map of space. However, two recent studies show that grids are naturally distorted, revealing greater local environment-specific effects than previously recognized

Grid cells on steeply sloping terrain: evidence for planar rather than volumetric encoding

Neural encoding of navigable space involves a network of structures centred on the hippocampus, whose neurons –place cells – encode current location. Input to the place cells includes afferents from the entorhinal cortex, which contains grid cells. These are neurons expressing spatially localised activity patches, or firing fields, that are evenly spaced across the floor in a hexagonal close-packed array called a grid. It is thought that grid cell grids function to enable the calculation of distances. The question arises as to whether this odometry process operates in three dimensions, and so we queried whether grids permeate three-dimensional space – that is, form a lattice – or whether they simply follow the environment surface. If grids form a three-dimensional lattice then a tilted floor should transect several layers of this lattice, resulting in interruption of the hexagonal pattern. We model this prediction with simulated grid lattices and show that on a 40-degree slope the firing of a grid cell should cover proportionally less of the surface, with smaller field size and fewer fields and reduced hexagonal symmetry. However, recording of grid cells as animals foraged on a 40-degree-tilted surface found that firing of grid cells was almost indistinguishable, in pattern or rate, from that on the horizontal surface, with if anything increased coverage and field number, and preserved field size. It thus appears unlikely that the sloping surface transected a lattice. However, grid cells on the slope displayed slightly degraded firing patterns, with reduced coherence and slightly reduced symmetry. These findings collectively suggest that the grid cell component of the metric representation of space is not fixed in absolute three-dimensional space but is influenced both by the surface the animal is on and by the relationship of this surface to the horizontal, supporting the hypothesis that the neural map of space is multi-planar rather than fully volumetric

Unpacking the navigation toolbox: insights from comparative cognition

The study of navigation is informed by ethological data from many species, laboratory investigation at behavioural and neurobiological levels, and computational modelling. However, the data are often species-specific, making it challenging to develop general models of how biology supports behaviour. Wiener et al. outlined a framework for organizing the results across taxa, called the ‘navigation toolbox’ (Wiener et al. In Animal thinking: contemporary issues in comparative cognition (eds R Menzel, J Fischer), pp. 51–76). This framework proposes that spatial cognition is a hierarchical process in which sensory inputs at the lowest level are successively combined into ever-more complex representations, culminating in a metric or quasi-metric internal model of the world (cognitive map). Some animals, notably humans, also use symbolic representations to produce an external representation, such as a verbal description, signpost or map that allows communication of spatial information or instructions between individuals. Recently, new discoveries have extended our understanding of how spatial representations are constructed, highlighting that the hierarchical relationships are bidirectional, with higher levels feeding back to influence lower levels. In the light of these new developments, we revisit the navigation toolbox, elaborate it and incorporate new findings. The toolbox provides a common framework within which the results from different taxa can be described and compared, yielding a more detailed, mechanistic and generalized understanding of navigation

Environment symmetry drives a multidirectional code in rat retrosplenial cortex

We investigated how environment symmetry shapes the neural processing of direction, by recording directionally tuned retrosplenial neurons in male Lister-hooded rats exploring multi-compartment environments that had different levels of global rotational symmetry. Our hypothesis built on prior observations of twofold symmetry in the directional tuning curves of rats in a globally twofold-symmetric environment. To test whether environment symmetry was the relevant factor shaping the directional responses, here we deployed the same apparatus (two connected rectangular boxes) plus one with fourfold symmetry (a 2x2 array of connected square boxes) and one with onefold symmetry (a circular open-field arena). Consistent with our hypothesis we found many neurons with tuning curve symmetries that mirrored these environment symmetries, having twofold, fourfold or onefold-symmetric tuning respectively. Some cells expressed this pattern only globally (across the whole environment), maintaining singular tuning curves in each subcompartment. However, others also expressed it locally, within each subcompartment. Since multidirectionality has not been reported in naïve rats in single environmental compartments, this suggests an experience-dependent effect of global environment symmetry on local firing symmetry. An intermingled population of directional neurons were “classic” head direction cells, with globally referenced directional tuning: these cells were electrophysiologically distinct, with narrower tuning curves and a burstier firing pattern. Thus, retrosplenial directional neurons can simultaneously encode overall head direction and local head direction (relative to compartment layout). Furthermore, they can learn about global environment symmetry and express this locally: this may be important for the encoding of environment structure beyond immediate perceptual reach

A dual-axis rotation rule for updating the head direction cell reference frame during movement in three dimensions

In the mammalian brain, allocentric (Earth-referenced) head direction, called azimuth, is encoded by head direction (HD) cells, which fire according to the facing direction of the animal’s head. On a horizontal surface, rotations of the head around the dorsoventral (D-V) axis, called yaw, correspond to changes in azimuth and elicit appropriate updating of the HD “compass” signal to enable large-scale navigation. However, if the animal moves through three-dimensional (3D) space then there is no longer a simple relationship between yaw rotations and azimuth changes, and so processing of 3D rotations is needed. Construction of a global 3D compass would require complex integration of 3D rotations, and also a large neuronal population, most neurons of which would be silent most of the time since animals rarely sample all available 3D orientations. We propose that, instead, the HD system treats the 3D space as a set of interrelated 2D surfaces. It could do this by updating activity according to both yaw rotations around the D-V axis and rotations of the D-V axis around the gravity-defined vertical axis. We present preliminary data to suggest that this rule operates when rats move between walls of opposing orientations. This dual-axis rule, which we show is straightforward to implement using the classic one-dimensional “attractor” architecture, allows consistent representation of azimuth even in volumetric space and thus may be a general feature of mammalian directional computations even for animals that swim or fly

Multivoxel pattern analysis reveals 3D place information in the human hippocampus

The spatial world is three dimensional (3D) and humans and other animals move both horizontally and vertically within it. Extant neuroscientific studies have typically investigated spatial navigation on a horizontal 2D plane, leaving much unknown about how 3D spatial information is represented in the brain. Specifically, horizontal and vertical information may be encoded in the same or different neural structures with equal or unequal sensitivity. Here, we investigated these possibilities using fMRI while participants were passively moved within a 3D lattice structure as if riding a rollercoaster. Multivoxel pattern analysis was used to test for the existence of information relating to where and in which direction participants were heading in this virtual environment. Behaviorally, participants had similarly accurate memory for vertical and horizontal locations and the right anterior hippocampus (HC) expressed place information that was sensitive to changes along both horizontal and vertical axes. This is suggestive of isotropic 3D place encoding. In contrast, participants indicated their heading direction faster and more accurately when they were heading in a tilted-up or tilted-down direction. This direction information was expressed in the right retrosplenial cortex and posterior HC and was only sensitive to vertical pitch, which could reflect the importance of the vertical (gravity) axis as a reference frame. Overall, our findings extend previous knowledge of how we represent the spatial world and navigate within it by taking into account the important third dimension

Neural encoding of large-scale three-dimensional space-properties and constraints

How the brain represents represent large-scale, navigable space has been the topic of intensive investigation for several decades, resulting in the discovery that neurons in a complex network of cortical and subcortical brain regions co-operatively encode distance, direction, place, movement etc. using a variety of different sensory inputs. However, such studies have mainly been conducted in simple laboratory settings in which animals explore small, two-dimensional (i.e., flat) arenas. The real world, by contrast, is complex and three dimensional with hills, valleys, tunnels, branches, and—for species that can swim or fly—large volumetric spaces. Adding an additional dimension to space adds coding challenges, a primary reason for which is that several basic geometric properties are different in three dimensions. This article will explore the consequences of these challenges for the establishment of a functional three-dimensional metric map of space, one of which is that the brains of some species might have evolved to reduce the dimensionality of the representational space and thus sidestep some of these problems