Grid Cells in Cognition: Mechanisms and Function.

The activity patterns of grid cells form distinctively regular triangular lattices over the explored spatial environment and are largely invariant to visual stimuli, animal movement, and environment geometry. These neurons present numerous fascinating challenges to the curious (neuro)scientist: What are the circuit mechanisms responsible for creating spatially periodic activity patterns from the monotonic input-output responses of single neurons? How and why does the brain encode a local, nonperiodic variable-the allocentric position of the animal-with a periodic, nonlocal code? And, are grid cells truly specialized for spatial computations? Otherwise, what is their role in general cognition more broadly? We review efforts in uncovering the mechanisms and functional properties of grid cells, highlighting recent progress in the experimental validation of mechanistic grid cell models, and discuss the coding properties and functional advantages of the grid code as suggested by continuous attractor network models of grid cells.

How Do You Build a Cognitive Map? The Development of Circuits and Computations for the Representation of Space in the Brain.

In mammals, the activity of neurons in the entorhinal-hippocampal network is modulated by the animal's position and its movement through space. At multiple stages of this distributed circuit, distinct populations of neurons can represent a rich repertoire of navigation-related variables like the animal's location, the speed and direction of its movements, or the presence of borders and objects. Working together, spatially tuned neurons give rise to an internal representation of space, a cognitive map that supports an animal's ability to navigate the world and to encode and consolidate memories from experience. The mechanisms by which, during development, the brain acquires the ability to create an internal representation of space are just beginning to be elucidated. In this review, we examine recent work that has begun to investigate the ontogeny of circuitry, firing patterns, and computations underpinning the representation of space in the mammalian brain.

Converting an allocentric goal into an egocentric steering signal.

Neuronal signals that are relevant for spatial navigation have been described in many species1-10. However, a circuit-level understanding of how such signals interact to guide navigational behaviour is lacking. Here we characterize a neuronal circuit in the Drosophila central complex that compares internally generated estimates of the heading and goal angles of the fly-both of which are encoded in world-centred (allocentric) coordinates-to generate a body-centred (egocentric) steering signal. Past work has suggested that the activity of EPG neurons represents the fly's moment-to-moment angular orientation, or heading angle, during navigation2,11. An animal's moment-to-moment heading angle, however, is not always aligned with its goal angle-that is, the allocentric direction in which it wishes to progress forward. We describe FC2 cells12, a second set of neurons in the Drosophila brain with activity that correlates with the fly's goal angle. Focal optogenetic activation of FC2 neurons induces flies to orient along experimenter-defined directions as they walk forward. EPG and FC2 neurons connect monosynaptically to a third neuronal class, PFL3 cells12,13. We found that individual PFL3 cells show conjunctive, spike-rate tuning to both the heading angle and the goal angle during goal-directed navigation. Informed by the anatomy and physiology of these three cell classes, we develop a model that explains how this circuit compares allocentric heading and goal angles to build an egocentric steering signal in the PFL3 output terminals. Quantitative analyses and optogenetic manipulations of PFL3 activity support the model. Finally, using a new navigational memory task, we show that flies expressing disruptors of synaptic transmission in subsets of PFL3 cells have a reduced ability to orient along arbitrary goal directions, with an effect size in quantitative accordance with the prediction of our model. The biological circuit described here reveals how two population-level allocentric signals are compared in the brain to produce an egocentric output signal that is appropriate for motor control.

Remapping revisited: how the hippocampus represents different spaces.

The representation of distinct spaces by hippocampal place cells has been linked to changes in their place fields (the locations in the environment where the place cells discharge strongly), a phenomenon that has been termed 'remapping'. Remapping has been assumed to be accompanied by the reorganization of subsecond cofiring relationships among the place cells, potentially maximizing hippocampal information coding capacity. However, several observations challenge this standard view. For example, place cells exhibit mixed selectivity, encode non-positional variables, can have multiple place fields and exhibit unreliable discharge in fixed environments. Furthermore, recent evidence suggests that, when measured at subsecond timescales, the moment-to-moment cofiring of a pair of cells in one environment is remarkably similar in another environment, despite remapping. Here, I propose that remapping is a misnomer for the changes in place fields across environments and suggest instead that internally organized manifold representations of hippocampal activity are actively registered to different environments to enable navigation, promote memory and organize knowledge.

Mechanisms Underlying the Neural Computation of Head Direction.

Many animals use an internal sense of direction to guide their movements through the world. Neurons selective to head direction are thought to support this directional sense and have been found in a diverse range of species, from insects to primates, highlighting their evolutionary importance. Across species, most head-direction networks share four key properties: a unique representation of direction at all times, persistent activity in the absence of movement, integration of angular velocity to update the representation, and the use of directional cues to correct drift. The dynamics of theorized network structures called ring attractors elegantly account for these properties, but their relationship to brain circuits is unclear. Here, we review experiments in rodents and flies that offer insights into potential neural implementations of ring attractor networks. We suggest that a theory-guided search across model systems for biological mechanisms that enable such dynamics would uncover general principles underlying head-direction circuit function.

Building an allocentric travelling direction signal via vector computation.

Many behavioural tasks require the manipulation of mathematical vectors, but, outside of computational models1-7, it is not known how brains perform vector operations. Here we show how the Drosophila central complex, a region implicated in goal-directed navigation7-10, performs vector arithmetic. First, we describe a neural signal in the fan-shaped body that explicitly tracks the allocentric travelling angle of a fly, that is, the travelling angle in reference to external cues. Past work has identified neurons in Drosophila8,11-13 and mammals14 that track the heading angle of an animal referenced to external cues (for example, head direction cells), but this new signal illuminates how the sense of space is properly updated when travelling and heading angles differ (for example, when walking sideways). We then characterize a neuronal circuit that performs an egocentric-to-allocentric (that is, body-centred to world-centred) coordinate transformation and vector addition to compute the allocentric travelling direction. This circuit operates by mapping two-dimensional vectors onto sinusoidal patterns of activity across distinct neuronal populations, with the amplitude of the sinusoid representing the length of the vector and its phase representing the angle of the vector. The principles of this circuit may generalize to other brains and to domains beyond navigation where vector operations or reference-frame transformations are required.

Transforming representations of movement from body- to world-centric space.

When an animal moves through the world, its brain receives a stream of information about the body's translational velocity from motor commands and sensory feedback signals. These incoming signals are referenced to the body, but ultimately, they must be transformed into world-centric coordinates for navigation1,2. Here we show that this computation occurs in the fan-shaped body in the brain of Drosophila melanogaster. We identify two cell types, PFNd and PFNv3-5, that conjunctively encode translational velocity and heading as a fly walks. In these cells, velocity signals are acquired from locomotor brain regions6 and are multiplied with heading signals from the compass system. PFNd neurons prefer forward-ipsilateral movement, whereas PFNv neurons prefer backward-contralateral movement, and perturbing PFNd neurons disrupts idiothetic path integration in walking flies7. Downstream, PFNd and PFNv neurons converge onto hΔB neurons, with a connectivity pattern that pools together heading and translation direction combinations corresponding to the same movement in world-centric space. This network motif effectively performs a rotation of the brain's representation of body-centric translational velocity according to the current heading direction. Consistent with our predictions, we observe that hΔB neurons form a representation of translational velocity in world-centric coordinates. By integrating this representation over time, it should be possible for the brain to form a working memory of the path travelled through the environment8-10.

Toroidal topology of population activity in grid cells.

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.

Boundary-anchored neural mechanisms of location-encoding for self and others.

Everyday tasks in social settings require humans to encode neural representations of not only their own spatial location, but also the location of other individuals within an environment. At present, the vast majority of what is known about neural representations of space for self and others stems from research in rodents and other non-human animals1-3. However, it is largely unknown how the human brain represents the location of others, and how aspects of human cognition may affect these location-encoding mechanisms. To address these questions, we examined individuals with chronically implanted electrodes while they carried out real-world spatial navigation and observation tasks. We report boundary-anchored neural representations in the medial temporal lobe that are modulated by one's own as well as another individual's spatial location. These representations depend on one's momentary cognitive state, and are strengthened when encoding of location is of higher behavioural relevance. Together, these results provide evidence for a common encoding mechanism in the human brain that represents the location of oneself and others in shared environments, and shed new light on the neural mechanisms that underlie spatial navigation and awareness of others in real-world scenarios.

Dynamic spatial representation of self and others' actions in the macaque frontal cortex.

Modulation of neuronal firing rates by the spatial locations of physical objects is a widespread phenomenon in the brain. However, little is known about how neuronal responses to the actions of biological entities are spatially tuned and whether such spatially tuned responses are affected by social contexts. These issues are of key importance for understanding the neural basis of embodied social cognition, such as imitation and perspective-taking. Here, we show that spatial representation of actions can be dynamically changed depending on others' social relevance and agents of action. Monkeys performed a turn-taking choice task with a real monkey partner sitting face-to-face or a filmed partner in prerecorded videos. Three rectangular buttons (left, center, and right) were positioned in front of the subject and partner as their choice targets. We recorded from single neurons in two frontal nodes in the social brain, the ventral premotor cortex (PMv) and the medial prefrontal cortex (MPFC). When the partner was filmed rather than real, spatial preference for partner-actions was markedly diminished in MPFC, but not PMv, neurons. This social context-dependent modulation in the MPFC was also evident for self-actions. Strikingly, a subset of neurons in both areas switched their spatial preference between self-actions and partner-actions in a diametrically opposite manner. This observation suggests that these cortical areas are associated with coordinate transformation in ways consistent with an actor-centered perspective-taking coding scheme. The PMv may subserve such functions in context-independent manners, whereas the MPFC may do so primarily in social contexts.

The grid code for ordered experience.

Entorhinal cortical grid cells fire in a periodic pattern that tiles space, which is suggestive of a spatial coordinate system. However, irregularities in the grid pattern as well as responses of grid cells in contexts other than spatial navigation have presented a challenge to existing models of entorhinal function. In this Perspective, we propose that hippocampal input provides a key informative drive to the grid network in both spatial and non-spatial circumstances, particularly around salient events. We build on previous models in which neural activity propagates through the entorhinal-hippocampal network in time. This temporal contiguity in network activity points to temporal order as a necessary characteristic of representations generated by the hippocampal formation. We advocate that interactions in the entorhinal-hippocampal loop build a topological representation that is rooted in the temporal order of experience. In this way, the structure of grid cell firing supports a learned topology rather than a rigid coordinate frame that is bound to measurements of the physical world.

Boundary vector cells in the goldfish central telencephalon encode spatial information.

Navigation is one of the most fundamental cognitive skills for the survival of fish, the largest vertebrate class, and almost all other animal classes. Space encoding in single neurons is a critical component of the neural basis of navigation. To study this fundamental cognitive component in fish, we recorded the activity of neurons in the central area of the goldfish telencephalon while the fish were freely navigating in a quasi-2D water tank embedded in a 3D environment. We found spatially modulated neurons with firing patterns that gradually decreased with the distance of the fish from a boundary in each cell's preferred direction, resembling the boundary vector cells found in the mammalian subiculum. Many of these cells exhibited beta rhythm oscillations. This type of spatial representation in fish brains is unique among space-encoding cells in vertebrates and provides insights into spatial cognition in this lineage.

A map of object space in primate inferotemporal cortex.

The inferotemporal (IT) cortex is responsible for object recognition, but it is unclear how the representation of visual objects is organized in this part of the brain. Areas that are selective for categories such as faces, bodies, and scenes have been found1-5, but large parts of IT cortex lack any known specialization, raising the question of what general principle governs IT organization. Here we used functional MRI, microstimulation, electrophysiology, and deep networks to investigate the organization of macaque IT cortex. We built a low-dimensional object space to describe general objects using a feedforward deep neural network trained on object classification6. Responses of IT cells to a large set of objects revealed that single IT cells project incoming objects onto specific axes of this space. Anatomically, cells were clustered into four networks according to the first two components of their preferred axes, forming a map of object space. This map was repeated across three hierarchical stages of increasing view invariance, and cells that comprised these maps collectively harboured sufficient coding capacity to approximately reconstruct objects. These results provide a unified picture of IT organization in which category-selective regions are part of a coarse map of object space whose dimensions can be extracted from a deep network.

Grid cells in rats deprived of geometric experience during development.

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.

The temporal and contextual stability of activity levels in hippocampal CA1 cells.

Recent long-term optical imaging studies have demonstrated that the activity levels of hippocampal neurons in a familiar environment change on a daily to weekly basis. However, it is unclear whether there is any time-invariant property in the cells' neural representations. In this study, using miniature fluorescence microscopy, we measured the neural activity of the mouse hippocampus in four different environments every 3 d. Although the activity level of hippocampal neurons fluctuated greatly in each environment across days, we found a significant correlation between the activity levels for different days, and the correlation was higher for averaged activity levels across multiple environments. When the number of environments used for averaging was increased, a higher activity correlation was observed. Furthermore, the number of environments in which a cell showed activity was preserved. Cells that showed place cell activity in many environments had greater spatial information content and more stable spatial representation, and thus carried more abundant and stable information about the current position. In contrast, cells that were active only in a small number of environments provided sparse representation for the environment. These results suggest that each cell has not only an inherent activity level but also play a characteristic role in the coding of space.

The Anterior Thalamus Preferentially Drives Allocentric But Not Egocentric Orientation Tuning in Postrhinal Cortex.

Navigating a complex world requires integration of multiple spatial reference frames, including information about one's orientation in both allocentric and egocentric coordinates. Combining these two information sources can provide additional information about one's spatial location. Previous studies have demonstrated that both egocentric and allocentric spatial signals are reflected by the firing of neurons in the rat postrhinal cortex (POR), an area that may serve as a hub for integrating allocentric head direction (HD) cell information with egocentric information from center-bearing and center-distance cells. However, we have also demonstrated that POR HD cells are uniquely influenced by the visual properties and locations of visual landmarks, bringing into question whether the POR HD signal is truly allocentric as opposed to simply being a response to visual stimuli. To investigate this issue, we recorded HD cells from the POR of female rats while bilaterally inactivating the anterior thalamus (ATN), a region critical for expression of the "classic" HD signal in cortical areas. We found that ATN inactivation led to a significant decrease in both firing rate and tuning strength for POR HD cells, as well as a disruption in the encoding of allocentric location by conjunctive HD/egocentric cells. In contrast, POR egocentric cells without HD tuning were largely unaffected in a consistent manner by ATN inactivation. These results indicate that the POR HD signal originates at least partially from projections from the ATN and supports the view that the POR acts as a hub for the integration of egocentric and allocentric spatial representations.

Decoding Remapped Spatial Information in the Peri-Saccadic Period.

It has been suggested that, prior to a saccade, visual neurons predictively respond to stimuli that will fall in their receptive fields after completion of the saccade. This saccadic remapping process is thought to compensate for the shift of the visual world across the retina caused by eye movements. To map the timing of this predictive process in the brain, we recorded neural activity using electroencephalography during a saccade task. Human participants (male and female) made saccades between two fixation points while covertly attending to oriented gratings briefly presented at various locations on the screen. Data recorded during trials in which participants maintained fixation were used to train classifiers on stimuli in different positions. Subsequently, data collected during saccade trials were used to test for the presence of remapped stimulus information at the post-saccadic retinotopic location in the peri-saccadic period, providing unique insight into when remapped information becomes available. We found that the stimulus could be decoded at the remapped location ∼180 ms post-stimulus onset, but only when the stimulus was presented 100-200 ms before saccade onset. Within this range, we found that the timing of remapping was dictated by stimulus onset rather than saccade onset. We conclude that presenting the stimulus immediately before the saccade allows for optimal integration of the corollary discharge signal with the incoming peripheral visual information, resulting in a remapping of activation to the relevant post-saccadic retinotopic neurons.

Tracking the Misallocation and Reallocation of Spatial Attention toward Auditory Stimuli.

Completely ignoring a salient distractor presented concurrently with a target is difficult, and sometimes attention is involuntarily attracted to the distractor's location (attentional capture). Employing the N2ac component as a marker of attention allocation toward sounds, in this study we investigate the spatiotemporal dynamics of auditory attention across two experiments. Human participants (male and female) performed an auditory search task, where the target was accompanied by a distractor in two-third of the trials. For a distractor more salient than the target (Experiment 1), we observe not only a distractor N2ac (indicating attentional capture) but the full chain of attentional dynamics implied by the notion of attentional capture, namely, (1) the distractor captures attention before the target is attended, (2) allocation of attention to the target is delayed by distractor presence, and (3) the target is attended after the distractor. Conversely, for a distractor less salient than the target (Experiment 2), although responses were delayed, no attentional capture was observed. Together, these findings reveal two types of spatial attentional dynamics in the auditory modality (distraction with and without attentional capture).

Complexity Matters: Normalization to Prototypical Viewpoint Induces Memory Distortion along the Vertical Axis of Scenes.

Scene memory is prone to systematic distortions potentially arising from experience with the external world. Boundary transformation, a well-known memory distortion effect along the near-far axis of the three-dimensional space, represents the observer's erroneous recall of scenes' viewing distance. Researchers argued that normalization to the prototypical viewpoint with the high-probability viewing distance influenced this phenomenon. Herein, we hypothesized that the prototypical viewpoint also exists in the vertical angle of view (AOV) dimension and could cause memory distortion along scenes' vertical axis. Human subjects of both sexes were recruited to test this hypothesis, and two behavioral experiments were conducted, revealing a systematic memory distortion in the vertical AOV in both the forced choice (n = 79) and free adjustment (n = 30) tasks. Furthermore, the regression analysis implied that the complexity information asymmetry in scenes' vertical axis and the independent subjective AOV ratings from a large set of online participants (n = 1,208) could jointly predict AOV biases. Furthermore, in a functional magnetic resonance imaging experiment (n = 24), we demonstrated the involvement of areas in the ventral visual pathway (V3/V4, PPA, and OPA) in AOV bias judgment. Additionally, in a magnetoencephalography experiment (n = 20), we could significantly decode the subjects' AOV bias judgments ∼140 ms after scene onset and the low-level visual complexity information around the similar temporal interval. These findings suggest that AOV bias is driven by the normalization process and associated with the neural activities in the early stage of scene processing.

Conflicting Sensory Information Sharpens the Neural Representations of Early Selective Visuospatial Attention.

Adaptive behaviors require the ability to resolve conflicting information caused by the processing of incompatible sensory inputs. Prominent theories of attention have posited that early selective attention helps mitigate cognitive interference caused by conflicting sensory information by facilitating the processing of task-relevant sensory inputs and filtering out behaviorally irrelevant information. Surprisingly, many recent studies that investigated the role of early selective attention on conflict mitigation have failed to provide positive evidence. Here, we examined changes in the selectivity of early visuospatial attention in male and female human subjects performing an attention-cueing Eriksen flanker task, where they discriminated the shape of a visual target surrounded by congruent or incongruent distractors. We used the inverted encoding model to reconstruct spatial representations of visual selective attention from the topographical patterns of amplitude modulations in alpha band oscillations in scalp EEG (∼8-12 Hz). We found that the fidelity of the alpha-based spatial reconstruction was significantly higher in the incongruent compared with the congruent condition. Importantly, these conflict-related modulations in the reconstruction fidelity occurred at a much earlier time window than those of the lateralized posterior event-related potentials associated with target selection and distractor suppression processes, as well as conflict-related modulations in the frontocentral negative-going wave and midline-frontal theta oscillations (∼3-7 Hz), thought to track executive control functions. Taken together, our data suggest that conflict resolution is supported by the cascade of neural processes underlying early selective visuospatial attention and frontal executive functions that unfold over time.