The brain has an extraordinary ability to create an internal spatial map of the external world [1]. This map-like representation of environmental surroundings is encoded through specific types of neurons, located within the hippocampus and entorhinal cortex, which exhibit spatially tuned firing patterns [2, 3]. In addition to encoding space, these neurons are believed to be related to contextual information and memory [4-7]. One class of such cells is the grid cells, which are located within the entorhinal cortex, presubiculum, and parasubiculum [3, 8]. Grid cell firing forms a hexagonal array of firing fields, a pattern that is largely thought to reflect the operation of intrinsic self-motion-related computations [9-12]. If this is the case, then fields should be relatively uniform in size, number of spikes, and peak firing rate. However, it has been suggested that this is not in fact the case [3, 13]. The possibility exists that local spatial information also influences grid cells, which-if true-would greatly change the way in which grid cells are thought to contribute to place coding. Accordingly, we asked how discriminable the individual fields of a given grid cell are by looking at the distribution of field firing rates and reproducibility of this distribution across trials. Grid fields were less uniform in intensity than expected, and the pattern of strong and weak fields was spatially stable and recurred across trials. The distribution remained unchanged even after arena rescaling, but not after remapping. This suggests that additional local information is being overlaid onto the global hexagonal pattern of grid cells.

The grid cell network in the medial entorhinal cortex (MEC) has been subject to thorough testing and analysis, and many theories for their formation have been suggested. To test some of these theories, we re-analyzed data from Bonnevie et al., 2013, in which the hippocampus was inactivated and grid cells were recorded in the rat MEC. We investigated whether the firing associations of grid cells depend on hippocampal inputs. Specifically, we examined temporal and spatial correlations in the firing times of simultaneously recorded grid cells before and during hippocampal inactivation. Our analysis revealed evidence of network coherence in grid cells even in the absence of hippocampal input to the MEC, both in regular grid cells and in those that became head-direction cells after hippocampal inactivation. This favors models, which suggest that phase relations between grid cells in the MEC are dependent on intrinsic connectivity within the MEC.

During navigation, grid cells increase their spike rates in firing fields arranged on a markedly regular triangular lattice, whereas their spike timing is often modulated by theta oscillations. Oscillatory interference models of grid cells predict theta amplitude modulations of membrane potential during firing field traversals, whereas competing attractor network models predict slow depolarizing ramps. Here, using in vivo whole-cell recordings, we tested these models by directly measuring grid cell intracellular potentials in mice running along linear tracks in virtual reality. Grid cells had large and reproducible ramps of membrane potential depolarization that were the characteristic signature tightly correlated with firing fields. Grid cells also demonstrated intracellular theta oscillations that influenced their spike timing. However, the properties of theta amplitude modulations were not consistent with the view that they determine firing field locations. Our results support cellular and network mechanisms in which grid fields are produced by slow ramps, as in attractor models, whereas theta oscillations control spike timing.

The medial entorhinal cortex is part of a neural system for mapping the position of an individual within a physical environment1. Grid cells, a key component of this system, fire in a characteristic hexagonal pattern of locations2, and are organized in modules3 that collectively form a population code for the animal's allocentric position1. The invariance of the correlation structure of this population code across environments4,5 and behavioural states6,7, independent of specific sensory inputs, has pointed to intrinsic, recurrently connected continuous attractor networks (CANs) as a possible substrate of the grid pattern1,8-11. However, whether grid cell networks show continuous attractor dynamics, and how they interface with inputs from the environment, has remained unclear owing to the small samples of cells obtained so far. Here, using simultaneous recordings from many hundreds of grid cells and subsequent topological data analysis, we show that the joint activity of grid cells from an individual module resides on a toroidal manifold, as expected in a two-dimensional CAN. Positions on the torus correspond to positions of the moving animal in the environment. Individual cells are preferentially active at singular positions on the torus. Their positions are maintained between environments and from wakefulness to sleep, as predicted by CAN models for grid cells but not by alternative feedforward models12. This demonstration of network dynamics on a toroidal manifold provides a population-level visualization of CAN dynamics in grid cells.

Grid and head direction codes represent cognitive spaces for navigation and memory. Pure grid cells generate grid codes that have been assumed to be independent of head direction, whereas conjunctive cells generate grid representations that are tuned to a single head direction. Here, we demonstrate that pure grid cells also encode head direction, but through distinct mechanisms. We show that individual firing fields of pure grid cells are tuned to multiple head directions, with the preferred sets of directions differing between fields. This local directional modulation is not predicted by previous continuous attractor or oscillatory interference models of grid firing but is accounted for by models in which pure grid cells integrate inputs from co-aligned conjunctive cells with firing rates that differ between their fields. We suggest that local directional signals from grid cells may contribute to downstream computations by decorrelating different points of view from the same location.

The firing patterns of grid cells in medial entorhinal cortex (mEC) and associated brain areas form triangular arrays that tessellate the environment [1, 2] and maintain constant spatial offsets to each other between environments [3, 4]. These cells are thought to provide an efficient metric for navigation in large-scale space [5-8]. However, an accurate and universal metric requires grid cell firing patterns to uniformly cover the space to be navigated, in contrast to recent demonstrations that environmental features such as boundaries can distort [9-11] and fragment [12] grid patterns. To establish whether grid firing is determined by local environmental cues, or provides a coherent global representation, we recorded mEC grid cells in rats foraging in an environment containing two perceptually identical compartments connected via a corridor. During initial exposures to the multicompartment environment, grid firing patterns were dominated by local environmental cues, replicating between the two compartments. However, with prolonged experience, grid cell firing patterns formed a single, continuous representation that spanned both compartments. Thus, we provide the first evidence that in a complex environment, grid cell firing can form the coherent global pattern necessary for them to act as a metric capable of supporting large-scale spatial navigation.

Grid cells represent an ideal candidate to investigate the allocentric determinants of the brain's cognitive map. Most studies of grid cells emphasized the roles of geometric boundaries within the navigational range of the animal. Behaviors such as novel route-taking between local environments indicate the presence of additional inputs from remote cues beyond the navigational borders. To investigate these influences, we recorded grid cells as rats explored an open-field platform in a room with salient, remote cues. The platform was rotated or translated relative to the room frame of reference. Although the local, geometric frame of reference often exerted the strongest control over the grids, the remote cues demonstrated a consistent, sometimes dominant, countervailing influence. Thus, grid cells are controlled by both local geometric boundaries and remote spatial cues, consistent with prior studies of hippocampal place cells and providing a rich representational repertoire to support complex navigational (and perhaps mnemonic) processes.

Both grid-like firing fields and theta oscillation are hallmarks of grid cells in the mammalian brain. While bump attractor dynamics have generally been recognized as the substrate for grid firing fields, how theta oscillation arises and interacts with persistent activity in a cortical circuit remains obscure. Here, we report that the theta oscillation intrinsically emerges in a continuous attractor network composed of principal neurons and interneurons. Periodic bump attractors and the theta rhythm stably coexist in both cell types due to the division of labor among interneurons via structured synaptic connectivity between principal cells and interneurons. The slow dynamics of NMDAR-mediated synaptic currents support the persistency of bump attractors and restrict the oscillation frequency in the theta band. The spikes of neurons within bump attractors are phase locked to a proxy of local field potential. The current work provides a network-level mechanism that orchestrates the bump attractor dynamics and theta rhythmicity.

The medial entorhinal cortex (MEC) is part of the brain's network for dynamic representation of location. The most abundant class of neurons in this circuit is the grid cell, characterized by its periodic, hexagonally patterned firing fields. While in developing animals some MEC cell types express adult-like firing patterns already on the first exposure to an open spatial environment, only days after eye opening, grid cells mature more slowly, over a 1-to-2-wk period after the animals leave their nest. Whether the later emergence of a periodic grid pattern reflects a need for experience with spatial environments has not been determined. We here show that grid-like firing patterns continue to appear during exploration of open square environments in rats that are raised for the first months of their life in opaque spherical environments, in the absence of stable reference boundaries to guide spatial orientation. While strictly periodic firing fields were initially absent in these animals, clear grid patterns developed after only a few trials of training. In rats that were tested in the same open environment but raised for the first months of life in opaque cubes, with sharp vertical boundaries, grid-like firing was from the beginning indistinguishable from that of nondeprived control animals growing up in large enriched cages. Thus, although a minimum of experience with peripheral geometric boundaries is required for expression of regular grid patterns in a new environment, the effect of restricted spatial experience is overcome with short training, consistent with a preconfigured experience-independent basis for the grid pattern.

Grid cells in the brain respond when an animal occupies a periodic lattice of 'grid fields' during navigation. Grids are organized in modules with different periodicity. We propose that the grid system implements a hierarchical code for space that economizes the number of neurons required to encode location with a given resolution across a range equal to the largest period. This theory predicts that (i) grid fields should lie on a triangular lattice, (ii) grid scales should follow a geometric progression, (iii) the ratio between adjacent grid scales should be √e for idealized neurons, and lie between 1.4 and 1.7 for realistic neurons, (iv) the scale ratio should vary modestly within and between animals. These results explain the measured grid structure in rodents. We also predict optimal organization in one and three dimensions, the number of modules, and, with added assumptions, the ratio between grid periods and field widths.

At rest, hippocampal "place cells," neurons with receptive fields corresponding to specific spatial locations, reactivate in a manner that reflects recently traveled trajectories. These "replay" events have been proposed as a mechanism underlying memory consolidation, or the transfer of a memory representation from the hippocampus to neocortical regions associated with the original sensory experience. Accordingly, it has been hypothesized that hippocampal replay of a particular experience should be accompanied by simultaneous reactivation of corresponding representations in the neocortex and in the entorhinal cortex, the primary interface between the hippocampus and the neocortex. Recent studies have reported that coordinated replay may occur between hippocampal place cells and medial entorhinal cortex grid cells, cells with multiple spatial receptive fields. Assessing replay in grid cells is problematic, however, as the cells exhibit regularly spaced spatial receptive fields in all environments and, therefore, coordinated replay between place cells and grid cells may be detected by chance. In the present report, we adapted analytical approaches utilized in recent studies of grid cell and place cell replay to determine the extent to which coordinated replay is spuriously detected between grid cells and place cells recorded from separate rats. For a subset of the employed analytical methods, coordinated replay was detected spuriously in a significant proportion of cases in which place cell replay events were randomly matched with grid cell firing epochs of equal duration. More rigorous replay evaluation procedures and minimum spike count requirements greatly reduced the amount of spurious findings. These results provide insights into aspects of place cell and grid cell activity during rest that contribute to false detection of coordinated replay. The results further emphasize the need for careful controls and rigorous methods when testing the hypothesis that place cells and grid cells exhibit coordinated replay.

Neural encoding of navigable space involves a network of structures centered 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 localized 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 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 (3D) space - that is, form a lattice - or whether they simply follow the environment surface. If grids form a 3D lattice then this lattice would ordinarily be aligned horizontally (to explain the usual hexagonal pattern observed). A tilted floor would transect several layers of this putative lattice, resulting in interruption of the hexagonal pattern. We model this prediction with simulated grid lattices, and show that the firing of a grid cell on a 40°-tilted surface should cover proportionally less of the surface, with smaller field size, fewer fields, and reduced hexagonal symmetry. However, recording of real grid cells as animals foraged on a 40°-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 3D 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.

How the topography of neural circuits relates to their function remains unclear. Although topographic maps exist for sensory and motor variables, they are rarely observed for cognitive variables. Using calcium imaging during virtual navigation, we investigated the relationship between the anatomical organization and functional properties of grid cells, which represent a cognitive code for location during navigation. We found a substantial degree of grid cell micro-organization in mouse medial entorhinal cortex: grid cells and modules all clustered anatomically. Within a module, the layout of grid cells was a noisy two-dimensional lattice in which the anatomical distribution of grid cells largely matched their spatial tuning phases. This micro-arrangement of phases demonstrates the existence of a topographical map encoding a cognitive variable in rodents. It contributes to a foundation for evaluating circuit models of the grid cell network and is consistent with continuous attractor models as the mechanism of grid formation.

Dendritic democracy and independence have been characterized for near-instantaneous processing of synaptic inputs. However, a wide class of neuronal computations requires input integration on long timescales. As a paradigmatic example, entorhinal grid fields have been thought to be generated by the democratic summation of independent dendritic oscillations performing direction-selective path integration. We analyzed how multiple dendritic oscillators embedded in the same neuron integrate inputs separately and determine somatic membrane voltage jointly. We found that the interaction of dendritic oscillations leads to phase locking, which sets an upper limit on the timescale for independent input integration. Factors that increase this timescale also decrease the influence that the dendritic oscillations exert on somatic voltage. In entorhinal stellate cells, interdendritic coupling dominates and causes these cells to act as single oscillators. Our results suggest a fundamental trade-off between local and global processing in dendritic trees integrating ongoing signals.

Anticipating the future is a key motif of the brain, possibly supported by mental simulation of upcoming events. Rodent single-cell recordings suggest the ability of spatially tuned cells to represent subsequent locations. Grid-like representations have been observed in the human entorhinal cortex during virtual and imagined navigation. However, hitherto it remains unknown if grid-like representations contribute to mental simulation in the absence of imagined movement. Participants imagined directions between building locations in a large-scale virtual-reality city while undergoing fMRI without re-exposure to the environment. Using multi-voxel pattern analysis, we provide evidence for representations of absolute imagined direction at a resolution of 30° in the parahippocampal gyrus, consistent with the head-direction system. Furthermore, we capitalize on the six-fold rotational symmetry of grid-cell firing to demonstrate a 60° periodic pattern-similarity structure in the entorhinal cortex. Our findings imply a role of the entorhinal grid-system in mental simulation and future thinking beyond spatial navigation.

Grid cells in the entorhinal cortex (EC) of rodents [1] and humans [2] fire in a hexagonally distributed spatially periodic manner. In concert with other spatial cells in the medial temporal lobe (MTL) [3-6], they provide a representation of our location within an environment [7, 8] and are specifically thought to allow the represented location to be updated by self-motion [9]. Grid-like signals have been seen throughout the autobiographical memory system [10], suggesting a much more general role in memory [11, 12]. Grid cells may allow us to move our viewpoint in imagination [13], a useful function for goal-directed navigation and planning [12, 14-16], and episodic future thinking more generally [17, 18]. We used fMRI to provide evidence for similar grid-like signals in human entorhinal cortex during both virtual navigation and imagined navigation of the same paths. We show that this signal is present in periods of active navigation and imagination, with a similar orientation in both and with the specifically 6-fold rotational symmetry characteristic of grid cell firing. We therefore provide the first evidence suggesting that grid cells are utilized during movement of viewpoint within imagery, potentially underpinning our more general ability to mentally traverse possible routes in the service of planning and episodic future thinking.

The relationship between the firing of the grid cell and mesoscopic neural oscillations is one of the key issues to understand the neural mechanism of grid cells. Previous studies have focused more on the correspondence between neuronal firing and phases of oscillations, such as phase precession. There are also some conclusions about the relationship between the activity of grid cells and the intensity of neural oscillations, such as the disappearance of grid pattern caused by the blocking of theta rhythm, but the correlation between the firing rates of grid cells and the narrowband power of neural oscillations or the broadband LFP power is still scarce. Through analyzing the records of spike times of grid cells and local entorhinal EEG obtained by Hafting et al., in the spatial navigation experiment, we find that grid cells are, to a large proportion, a kind of broadband-shift neurons, and the positive correlation between grid cell activity and power of low theta and gamma bands was observed. These results have well verified, promoted, and connected many scattered research conclusions, such as the broadband shift phenomenon of hippocampal neurons, the influence of low theta activity on the firing pattern of grid cells, and the positive correlation between single-cell activity and gamma-band activity. This work is of great significance for the study of the neural mechanism of grid cells at the micro and mesoscopic levels, and may also inspire the use of indicators such as broadband power as markers for grid cell activity.

Grid cells are part of a widespread network which supports navigation and spatial memory. Stable grid patterns appear late in development, in concert with extracellular matrix aggregates termed perineuronal nets (PNNs) that condense around inhibitory neurons. It has been suggested that PNNs stabilize synaptic connections and long-term memories, but their role in the grid cell network remains elusive. We show that removal of PNNs leads to lower inhibitory spiking activity, and reduces grid cells' ability to create stable representations of a novel environment. Furthermore, in animals with disrupted PNNs, exposure to a novel arena corrupted the spatiotemporal relationships within grid cell modules, and the stored representations of a familiar arena. Finally, we show that PNN removal in entorhinal cortex distorted spatial representations in downstream hippocampal neurons. Together this work suggests that PNNs provide a key stabilizing element for the grid cell network.

Patients with Alzheimer's disease (AD) suffer from spatial memory impairment and wandering behavior, but the brain circuit mechanisms causing such symptoms remain largely unclear. In healthy brains, spatially tuned hippocampal place cells and entorhinal grid cells exhibit distinct spike patterns in different environments, a circuit function called "remapping." We tested remapping in amyloid precursor protein knockin (APP-KI) mice with impaired spatial memory. CA1 neurons, including place cells, showed disrupted remapping, although their spatial tuning was only mildly diminished. Medial entorhinal cortex (MEC) neurons severely lost their spatial tuning and grid cells were almost absent. Fast gamma oscillatory coupling between the MEC and CA1 was also impaired. Mild disruption of MEC grid cells emerged in younger APP-KI mice, although the spatial memory and CA1 remapping of the animals remained intact. These results point to remapping impairment in the hippocampus, possibly linked to grid cell disruption, as circuit mechanisms underlying spatial memory impairment in AD.

The medial entorhinal cortex (MEC) is an increasingly important focus for investigation of mechanisms for spatial representation. Grid cells found in layer II of the MEC are likely to be stellate cells, which form a major projection to the dentate gyrus. Entorhinal stellate cells are distinguished by distinct intrinsic electrophysiological properties, but how these properties contribute to representation of space is not yet clear. Here, we review the ionic conductances, synaptic, and excitable properties of stellate cells, and examine their implications for models of grid firing fields. We discuss why existing data are inconsistent with models of grid fields that require stellate cells to generate periodic oscillations. An alternative possibility is that the intrinsic electrophysiological properties of stellate cells are tuned specifically to control integration of synaptic input. We highlight recent evidence that the dorsal-ventral organization of synaptic integration by stellate cells, through differences in currents mediated by HCN and leak potassium channels, influences the corresponding organization of grid fields. Because accurate cellular data will be important for distinguishing mechanisms for generation of grid fields, we introduce new data comparing properties measured with whole-cell and perforated patch-clamp recordings. We find that clustered patterns of action potential firing and the action potential after-hyperpolarization (AHP) are particularly sensitive to recording condition. Nevertheless, with both methods, these properties, resting membrane properties and resonance follow a dorsal-ventral organization. Further investigation of the molecular basis for synaptic integration by stellate cells will be important for understanding mechanisms for generation of grid fields.