Environmental boundaries as an error correction mechanism for grid cells

Origin and role of path integration in the cognitive representations of the hippocampus: computational insights into open questions

Path integration is a straightforward concept with varied connotations that are important to different disciplines concerned with navigation, such as ethology, cognitive science, robotics and neuroscience. In studying the hippocampal formation, it is fruitful to think of path integration as a computation that transforms a sense of motion into a sense of location, continuously integrated with landmark perception. Here, we review experimental evidence that path integration is intimately involved in fundamental properties of place cells and other spatial cells that are thought to support a cognitive abstraction of space in this brain system. We discuss hypotheses about the anatomical and computational origin of path integration in the well-characterized circuits of the rodent limbic system. We highlight how computational frameworks for map-building in robotics and cognitive science alike suggest an essential role for path integration in the creation of a new map in unfamiliar territory, and how this very role can help us make sense of differences in neurophysiological data from novel versus familiar and small versus large environments. Similar computational principles could be at work when the hippocampus builds certain non-spatial representations, such as time intervals or trajectories defined in a sensory stimulus space.

Recalibration of path integration in hippocampal place cells

Hippocampal place cells are spatially tuned neurons that serve as elements of a 'cognitive map' in the mammalian brain1. To detect the animal's location, place cells are thought to rely upon two interacting mechanisms: sensing the position of the animal relative to familiar landmarks2,3 and measuring the distance and direction that the animal has travelled from previously occupied locations4-7. The latter mechanism-known as path integration-requires a finely tuned gain factor that relates the animal's self-movement to the updating of position on the internal cognitive map, as well as external landmarks to correct the positional error that accumulates8,9. Models of hippocampal place cells and entorhinal grid cells based on path integration treat the path-integration gain as a constant9-14, but behavioural evidence in humans suggests that the gain is modifiable15. Here we show, using physiological evidence from rat hippocampal place cells, that the path-integration gain is a highly plastic variable that can be altered by persistent conflict between self-motion cues and feedback from external landmarks. In an augmented-reality system, visual landmarks were moved in proportion to the movement of a rat on a circular track, creating continuous conflict with path integration. Sustained exposure to this cue conflict resulted in predictable and prolonged recalibration of the path-integration gain, as estimated from the place cells after the landmarks were turned off. We propose that this rapid plasticity keeps the positional update in register with the movement of the rat in the external world over behavioural timescales. These results also demonstrate that visual landmarks not only provide a signal to correct cumulative error in the path-integration system4,8,16-19, but also rapidly fine-tune the integration computation itself.

Entorhinal Neurons Exhibit Cue Locking in Rodent VR

The regular firing pattern exhibited by medial entorhinal (mEC) grid cells of locomoting rodents is hypothesized to provide spatial metric information relevant for navigation. The development of virtual reality (VR) for head-fixed mice confers a number of experimental advantages and has become increasingly popular as a method for investigating spatially-selective cells. Recent experiments using 1D VR linear tracks have shown that some mEC cells have multiple fields in virtual space, analogous to grid cells on real linear tracks. We recorded from the mEC as mice traversed virtual tracks featuring regularly spaced repetitive cues and identified a population of cells with multiple firing fields, resembling the regular firing of grid cells. However, further analyses indicated that many of these were not, in fact, grid cells because: (1) when recorded in the open field they did not display discrete firing fields with six-fold symmetry; and (2) in different VR environments their firing fields were found to match the spatial frequency of repetitive environmental cues. In contrast, cells identified as grid cells based on their open field firing patterns did not exhibit cue locking. In light of these results we highlight the importance of controlling the periodicity of the visual cues in VR and the necessity of identifying grid cells from real open field environments in order to correctly characterize spatially modulated neurons in VR experiments.

Spatial synchronization codes from coupled rate-phase neurons

During spatial navigation, the frequency and timing of spikes from spatial neurons including place cells in hippocampus and grid cells in medial entorhinal cortex are temporally organized by continuous theta oscillations (6-11 Hz). The theta rhythm is regulated by subcortical structures including the medial septum, but it is unclear how spatial information from place cells may reciprocally organize subcortical theta-rhythmic activity. Here we recorded single-unit spiking from a constellation of subcortical and hippocampal sites to study spatial modulation of rhythmic spike timing in rats freely exploring an open environment. Our analysis revealed a novel class of neurons that we termed 'phaser cells,' characterized by a symmetric coupling between firing rate and spike theta-phase. Phaser cells encoded space by assigning distinct phases to allocentric isocontour levels of each cell's spatial firing pattern. In our dataset, phaser cells were predominantly located in the lateral septum, but also the hippocampus, anteroventral thalamus, lateral hypothalamus, and nucleus accumbens. Unlike the unidirectional late-to-early phase precession of place cells, bidirectional phase modulation acted to return phaser cells to the same theta-phase along a given spatial isocontour, including cells that characteristically shifted to later phases at higher firing rates. Our dynamical models of intrinsic theta-bursting neurons demonstrated that experience-independent temporal coding mechanisms can qualitatively explain (1) the spatial rate-phase relationships of phaser cells and (2) the observed temporal segregation of phaser cells according to phase-shift direction. In open-field phaser cell simulations, competitive learning embedded phase-code entrainment maps into the weights of downstream targets, including path integration networks. Bayesian phase decoding revealed error correction capable of resetting path integration at subsecond timescales. Our findings suggest that phaser cells may instantiate a subcortical theta-rhythmic loop of spatial feedback. We outline a framework in which location-dependent synchrony reconciles internal idiothetic processes with the allothetic reference points of sensory experience.

Emergent elasticity in the neural code for space

Upon encountering a novel environment, an animal must construct a consistent environmental map, as well as an internal estimate of its position within that map, by combining information from two distinct sources: self-motion cues and sensory landmark cues. How do known aspects of neural circuit dynamics and synaptic plasticity conspire to accomplish this feat? Here we show analytically how a neural attractor model that combines path integration of self-motion cues with Hebbian plasticity in synaptic weights from landmark cells can self-organize a consistent map of space as the animal explores an environment. Intriguingly, the emergence of this map can be understood as an elastic relaxation process between landmark cells mediated by the attractor network. Moreover, our model makes several experimentally testable predictions, including (i) systematic path-dependent shifts in the firing fields of grid cells toward the most recently encountered landmark, even in a fully learned environment; (ii) systematic deformations in the firing fields of grid cells in irregular environments, akin to elastic deformations of solids forced into irregular containers; and (iii) the creation of topological defects in grid cell firing patterns through specific environmental manipulations. Taken together, our results conceptually link known aspects of neurons and synapses to an emergent solution of a fundamental computational problem in navigation, while providing a unified account of disparate experimental observations.

Environmental deformations dynamically shift the grid cell spatial metric

In familiar environments, the firing fields of entorhinal grid cells form regular triangular lattices. However, when the geometric shape of the environment is deformed, these time-averaged grid patterns are distorted in a grid scale-dependent and local manner. We hypothesized that this distortion in part reflects dynamic anchoring of the grid code to displaced boundaries, possibly through border cell-grid cell interactions. To test this hypothesis, we first reanalyzed two existing rodent grid rescaling datasets to identify previously unrecognized boundary-tethered shifts in grid phase that contribute to the appearance of rescaling. We then demonstrated in a computational model that boundary-tethered phase shifts, as well as scale-dependent and local distortions of the time-averaged grid pattern, could emerge from border-grid interactions without altering inherent grid scale. Together, these results demonstrate that environmental deformations induce history-dependent shifts in grid phase, and implicate border-grid interactions as a potential mechanism underlying these dynamics.

Hexadirectional Modulation of Theta Power in Human Entorhinal Cortex during Spatial Navigation

Grid cells and theta oscillations are fundamental components of the brain's navigation system. Grid cells provide animals [1, 2] and humans [3, 4] with a spatial map of the environment by exhibiting multiple firing fields arranged in a regular grid of equilateral triangles. This unique firing pattern presumably constitutes the neural basis for path integration [5-8] and may also enable navigation in visual and conceptual spaces [9-12]. Theta frequency oscillations are a prominent mesoscopic network phenomenon during navigation in both rodents and humans [13, 14] and encode movement speed [15-17], distance traveled [18], and proximity to spatial boundaries [19]. Whether theta oscillations may also carry a grid-like signal remains elusive, however. Capitalizing on previous fMRI studies revealing a macroscopic proxy of sum grid cell activity in human entorhinal cortex (EC) [20-22], we examined intracranial EEG recordings from the EC of epilepsy patients (n = 9) performing a virtual navigation task. We found that the power of theta oscillations (4-8 Hz) exhibits 6-fold rotational modulation by movement direction, reminiscent of grid cell-like representations detected using fMRI. Modulation of theta power was specific to 6-fold rotational symmetry and to the EC. Hexadirectional modulation of theta power by movement direction only emerged during fast movements, stabilized over the course of the experiment, and showed sensitivity to the environmental boundary. Our results suggest that oscillatory power in the theta frequency range carries an imprint of sum grid cell activity potentially enabled by a common grid orientation of neighboring grid cells [23].

Self-motion processing in visual and entorhinal cortices: inputs, integration, and implications for position coding

The sensory signals generated by self-motion are complex and multimodal, but the ability to integrate these signals into a unified self-motion percept to guide navigation is essential for animal survival. Here, we summarize classic and recent work on self-motion coding in the visual and entorhinal cortices of the rodent brain. We compare motion processing in rodent and primate visual cortices, highlighting the strengths of classic primate work in establishing causal links between neural activity and perception, and discuss the integration of motor and visual signals in rodent visual cortex. We then turn to the medial entorhinal cortex (MEC), where calculations using self-motion to update position estimates are thought to occur. We focus on several key sources of self-motion information to MEC: the medial septum, which provides locomotor speed information; visual cortex, whose input has been increasingly recognized as essential to both position and speed-tuned MEC cells; and the head direction system, which is a major source of directional information for self-motion estimates. These inputs create a large and diverse group of self-motion codes in MEC, and great interest remains in how these self-motion codes might be integrated by MEC grid cells to estimate position. However, which signals are used in these calculations and the mechanisms by which they are integrated remain controversial. We end by proposing future experiments that could further our understanding of the interactions between MEC cells that code for self-motion and position and clarify the relationship between the activity of these cells and spatial perception.

Integration and multiplexing of positional and contextual information by the hippocampal network

The hippocampus is known to store cognitive representations, or maps, that encode both positional and contextual information, critical for episodic memories and functional behavior. How path integration and contextual cues are dynamically combined and processed by the hippocampus to maintain these representations accurate over time remains unclear. To answer this question, we propose a two-way data analysis and modeling approach to CA3 multi-electrode recordings of a moving rat submitted to rapid changes of contextual (light) cues, triggering back-and-forth instabitilies between two cognitive representations (“teleportation” experiment of Jezek et al). We develop a dual neural activity decoder, capable of independently identifying the recalled cognitive map at high temporal resolution (comparable to theta cycle) and the position of the rodent given a map. Remarkably, position can be reconstructed at any time with an accuracy comparable to fixed-context periods, even during highly unstable periods. These findings provide evidence for the capability of the hippocampal neural activity to maintain an accurate encoding of spatial and contextual variables, while one of these variables undergoes rapid changes independently of the other. To explain this result we introduce an attractor neural network model for the hippocampal activity that process inputs from external cues and the path integrator. Our model allows us to make predictions on the frequency of the cognitive map instability, its duration, and the detailed nature of the place-cell population activity, which are validated by a further analysis of the data. Our work therefore sheds light on the mechanisms by which the hippocampal network achieves and updates multi-dimensional neural representations from various input streams.

As an animal moves in space and receives external sensory inputs, it must dynamically maintain the representations of its position and environment at all times. How the hippocampus, the brain area crucial for spatial representations, achieves this task, and manages possible conflicts between different inputs remains unclear. We propose here a comprehensive attractor neural network-based model of the hippocampus and of its multiple input streams (including self-motion). We show that this model is capable of maintaining faithful representations of positional and contextual information, and resolves conflicts by adapting internal representations to match external cues. Model predictions are confirmed by the detailed analysis of hippocampal recordings of a rat submitted to quickly varying and conflicting contextual inputs.

Principles governing the integration of landmark and self-motion cues in entorhinal cortical codes for navigation

To guide navigation, the nervous system integrates multisensory self-motion and landmark information. We dissected how these inputs generate spatial representations by recording entorhinal grid, border and speed cells in mice navigating virtual environments. Manipulating the gain between the animal's locomotion and the visual scene revealed that border cells responded to landmark cues while grid and speed cells responded to combinations of locomotion, optic flow and landmark cues in a context-dependent manner, with optic flow becoming more influential when it was faster than expected. A network model explained these results by revealing a phase transition between two regimes in which grid cells remain coherent with or break away from the landmark reference frame. Moreover, during path-integration-based navigation, mice estimated their position following principles predicted by our recordings. Together, these results provide a theoretical framework for understanding how landmark and self-motion cues combine during navigation to generate spatial representations and guide behavior.

How the Brain's Navigation System Shapes Our Visual Experience

We explore the environment not only by navigating, but also by viewing our surroundings with our eyes. Here we review growing evidence that the mammalian hippocampal formation, extensively studied in the context of navigation and memory, mediates a representation of visual space that is stably anchored to the external world. This visual representation puts the hippocampal formation in a central position to guide viewing behavior and to modulate visual processing beyond the medial temporal lobe (MTL). We suggest that vision and navigation share several key computational challenges that are solved by overlapping and potentially common neural systems, making vision an optimal domain to explore whether and how the MTL supports cognitive operations beyond navigation.

A unified hierarchical oscillatory network model of head direction cells, spatially periodic cells, and place cells

Spatial cells in the hippocampal complex play a pivotal role in the navigation of an animal. Exact neural principles behind these spatial cell responses have not been completely unraveled yet. Here we present two models for spatial cells, namely the Velocity Driven Oscillatory Network (VDON) and Locomotor Driven Oscillatory Network. Both models have basically three stages in common such as direction encoding stage, path integration (PI) stage, and a stage of unsupervised learning of PI values. In the first model, the following three stages are implemented: head direction layer, frequency modulation by a layer of oscillatory neurons, and an unsupervised stage that extracts the principal components from the oscillator outputs. In the second model, a refined version of the first model, the stages are extraction of velocity representation from the locomotor input, frequency modulation by a layer of oscillators, and two cascaded unsupervised stages consisting of the lateral anti-hebbian network. The principal component stage of VDON exhibits grid cell-like spatially periodic responses including hexagonal firing fields. Locomotor Driven Oscillatory Network shows the emergence of spatially periodic grid cells and periodically active border-like cells in its lower layer; place cell responses are found in its higher layer. This model shows the inheritance of phase precession from grid cell to place cell in both one- and two-dimensional spaces. It also shows a novel result on the influence of locomotion rhythms on the grid cell activity. The study thus presents a comprehensive, unifying hierarchical model for hippocampal spatial cells.

Electrophysiological Signatures of Spatial Boundaries in the Human Subiculum

Environmental boundaries play a crucial role in spatial navigation and memory across a wide range of distantly related species. In rodents, boundary representations have been identified at the single-cell level in the subiculum and entorhinal cortex of the hippocampal formation. Although studies of hippocampal function and spatial behavior suggest that similar representations might exist in humans, boundary-related neural activity has not been identified electrophysiologically in humans until now. To address this gap in the literature, we analyzed intracranial recordings from the hippocampal formation of surgical epilepsy patients (of both sexes) while they performed a virtual spatial navigation task and compared the power in three frequency bands (1-4, 4-10, and 30-90 Hz) for target locations near and far from the environmental boundaries. Our results suggest that encoding locations near boundaries elicited stronger theta oscillations than for target locations near the center of the environment and that this difference cannot be explained by variables such as trial length, speed, movement, or performance. These findings provide direct evidence of boundary-dependent neural activity localized in humans to the subiculum, the homolog of the hippocampal subregion in which most boundary cells are found in rodents, and indicate that this system can represent attended locations that rather than the position of one's own body.SIGNIFICANCE STATEMENT Spatial computations using environmental boundaries are an integral part of the brain's spatial mapping system. In rodents, border/boundary cells in the subiculum and entorhinal cortex reveal boundary coding at the single-neuron level. Although there is good reason to believe that such representations also exist in humans, the evidence has thus far been limited to functional neuroimaging studies that broadly implicate the hippocampus in boundary-based navigation. By combining intracranial recordings with high-resolution imaging of hippocampal subregions, we identified a neural marker of boundary representation in the human subiculum.

Neural mechanisms of navigation involving interactions of cortical and subcortical structures

Animals must perform spatial navigation for a range of different behaviors, including selection of trajectories toward goal locations and foraging for food sources. To serve this function, a number of different brain regions play a role in coding different dimensions of sensory input important for spatial behavior, including the entorhinal cortex, the retrosplenial cortex, the hippocampus, and the medial septum. This article will review data concerning the coding of the spatial aspects of animal behavior, including location of the animal within an environment, the speed of movement, the trajectory of movement, the direction of the head in the environment, and the position of barriers and objects both relative to the animal's head direction (egocentric) and relative to the layout of the environment (allocentric). The mechanisms for coding these important spatial representations are not yet fully understood but could involve mechanisms including integration of self-motion information or coding of location based on the angle of sensory features in the environment. We will review available data and theories about the mechanisms for coding of spatial representations. The computation of different aspects of spatial representation from available sensory input requires complex cortical processing mechanisms for transformation from egocentric to allocentric coordinates that will only be understood through a combination of neurophysiological studies and computational modeling.

Grid scale drives the scale and long-term stability of place maps

Medial entorhinal cortex (MEC) grid cells fire at regular spatial intervals and project to the hippocampus, where place cells are active in spatially restricted locations. One feature of the grid population is the increase in grid spatial scale along the dorsal-ventral MEC axis. However, the difficulty in perturbing grid scale without impacting the properties of other functionally defined MEC cell types has obscured how grid scale influences hippocampal coding and spatial memory. Here we use a targeted viral approach to knock out HCN1 channels selectively in MEC, causing the grid scale to expand while leaving other MEC spatial and velocity signals intact. Grid scale expansion resulted in place scale expansion in fields located far from environmental boundaries, reduced long-term place field stability and impaired spatial learning. These observations, combined with simulations of a grid-to-place cell model and position decoding of place cells, illuminate how grid scale impacts place coding and spatial memory.

Self-Organized Attractor Dynamics in the Developing Head Direction Circuit

Head direction (HD) cells are neurons found in an extended cortical and subcortical network that signal the orientation of an animal’s head relative to its environment [1, 2, 3]. They are a fundamental component of the wider circuit of spatially responsive hippocampal formation neurons that make up the neural cognitive map of space [4]. During post-natal development, HD cells are the first among spatially modulated neurons in the hippocampal circuit to exhibit mature firing properties [5, 6], but before eye opening, HD cell responses in rat pups have low directional information and are directionally unstable [7, 8]. Using Bayesian decoding of HD cell ensemble activity recorded in the anterodorsal thalamic nucleus (ADN), we characterize this instability and identify its source: under-signaling of angular head velocity, which incompletely shifts the directional signal in proportion to head turns. We find evidence that geometric cues (the corners of a square environment) can be used to mitigate this under-signaling and, thereby, stabilize the directional signal even before eye opening. Crucially, even when directional firing cannot be stabilized, ensembles of unstable HD cells show short-timescale (1–10 s) temporal and spatial couplings consistent with an adult-like HD network. The HD network is widely modeled as a continuous attractor whose output is one coherent activity peak, updated during movement by angular head velocity signals and anchored by landmark cues [9, 10, 11]. Our findings present strong evidence for this model, and they demonstrate that the required network circuitry is in place and functional early during development, independent of reference to landmark information.

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Non-visual cues can anchor head direction (HD) cells in pre-eye-opening rat pups

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Internal network dynamics are preserved even when the HD representation is unstable

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Angular velocity under-signaling drives instability, which is mitigated by corners

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Circuit architecture develops even before any landmarks can stabilize HD responses

Integration of grid maps in merged environments

Natural environments are represented by local maps of grid cells and place cells that are stitched together. The manner by which transitions between map fragments are generated is unknown. We recorded grid cells while rats were trained in two rectangular compartments, A and B (each 1 m × 2 m), separated by a wall. Once distinct grid maps were established in each environment, we removed the partition and allowed the rat to explore the merged environment (2 m × 2 m). The grid patterns were largely retained along the distal walls of the box. Nearer the former partition line, individual grid fields changed location, resulting almost immediately in local spatial periodicity and continuity between the two original maps. Grid cells belonging to the same grid module retained phase relationships during the transformation. Thus, when environments are merged, grid fields reorganize rapidly to establish spatial periodicity in the area where the environments meet.

Transformation of the head-direction signal into a spatial code

Animals integrate multiple sensory inputs to successfully navigate in their environments. Head direction (HD), boundary vector, grid and place cells in the entorhinal-hippocampal network form the brain’s navigational system that allows to identify the animal’s current location, but how the functions of these specialized neuron types are acquired remain to be understood. Here we report that activity of HD neurons is influenced by the ambulatory constraints imposed upon the animal by the boundaries of the explored environment, leading to spurious spatial information. However, in the post-subiculum, the main cortical stage of HD signal processing, HD neurons convey true spatial information in the form of border modulated activity through the integration of additional sensory modalities relative to egocentric position, unlike their driving thalamic inputs. These findings demonstrate how the combination of HD and egocentric information can be transduced into a spatial code.

A cognitive map of space must integrate allocentric cues such as head direction (HD) with various egocentric cues. Here the authors report that anterior thalamic (ADn) neurons encode a pure HD signal, while neurons in post-subiculum represent a conjunction of HD and egocentric cues such as body posture with respect to environment boundaries.

Spatial representation in the hippocampal formation: a history

Since the first place cell was recorded and the cognitive-map theory was subsequently formulated, investigation of spatial representation in the hippocampal formation has evolved in stages. Early studies sought to verify the spatial nature of place cell activity and determine its sensory origin. A new epoch started with the discovery of head direction cells and the realization of the importance of angular and linear movement-integration in generating spatial maps. A third epoch began when investigators turned their attention to the entorhinal cortex, which led to the discovery of grid cells and border cells. This review will show how ideas about integration of self-motion cues have shaped our understanding of spatial representation in hippocampal-entorhinal systems from the 1970s until today. It is now possible to investigate how specialized cell types of these systems work together, and spatial mapping may become one of the first cognitive functions to be understood in mechanistic detail.

Field repetition and local mapping in the hippocampus and the medial entorhinal cortex

Hippocampal place cells support spatial cognition and are thought to form the neural substrate of a global "cognitive map." A widely held view is that parts of the hippocampus also underlie the ability to separate patterns or to provide different neural codes for distinct environments. However, a number of studies have shown that in environments composed of multiple, repeating compartments, place cells and other spatially modulated neurons show the same activity in each local area. This repetition of firing fields may reflect pattern completion and may make it difficult for animals to distinguish similar local environments. In this review we 1) highlight some of the navigation difficulties encountered by humans in repetitive environments, 2) summarize literature demonstrating that place and grid cells represent local and not global space, and 3) attempt to explain the origin of these phenomena. We argue that the repetition of firing fields can be a useful tool for understanding the relationship between grid cells in the entorhinal cortex and place cells in the hippocampus, the spatial inputs shared by these cells, and the propagation of spatially related signals through these structures.

Parvalbumin and Somatostatin Interneurons Control Different Space-Coding Networks in the Medial Entorhinal Cortex

The medial entorhinal cortex (MEC) contains several discrete classes of GABAergic interneurons, but their specific contributions to spatial pattern formation in this area remain elusive. We employed a pharmacogenetic approach to silence either parvalbumin (PV)- or somatostatin (SOM)-expressing interneurons while MEC cells were recorded in freely moving mice. PV-cell silencing antagonized the hexagonally patterned spatial selectivity of grid cells, especially in layer II of MEC. The impairment was accompanied by reduced speed modulation in colocalized speed cells. Silencing SOM cells, in contrast, had no impact on grid cells or speed cells but instead decreased the spatial selectivity of cells with discrete aperiodic firing fields. Border cells and head direction cells were not affected by either intervention. The findings point to distinct roles for PV and SOM interneurons in the local dynamics underlying periodic and aperiodic firing in spatially modulated cells of the MEC.

Video Abstract

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Parvalbumin (PV) interneurons maintain spatially periodic firing in grid cells

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PV interneurons are necessary for speed tuning in entorhinal speed cells

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Somatostatin (SOM) interneurons maintain selectivity of aperiodic spatial cells

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PV and SOM cells regulate discrete subsets of spatially tuned entorhinal cell types

Mapping of a non-spatial dimension by the hippocampal-entorhinal circuit

During spatial navigation, neural activity in the hippocampus and the medial entorhinal cortex (MEC) is correlated to navigational variables like location^1,2, head direction³, speed⁴, and proximity to boundaries⁵. These activity patterns are thought to provide a map-like representation of physical space. However, the hippocampal/entorhinal circuit is involved not only in spatial navigation, but in a variety of memory-guided behaviors⁶. The relationship between this general function and the specialized spatial activity patterns is unclear. A conceptual framework reconciling these views is that spatial representation is just one example of a more general mechanism for encoding continuous, task-relevant variables^7–10. We tested this idea by recording hippocampal and entorhinal neurons in a task that required rats to use a joystick to manipulate sound along a continuous frequency axis. We found neural representation of the entire behavioral task, including activity that formed discrete firing fields at particular sound frequencies. Neurons involved in this representation overlapped with the known spatial cell types in the circuit like place cells and grid cells. These results suggest that common circuit mechanisms in the hippocampal/entorhinal system are used for representations of diverse behavioral tasks, possibly supporting cognitive processes beyond spatial navigation.

Size Matters: How Scaling Affects the Interaction between Grid and Border Cells

Many hippocampal cell types are characterized by a progressive increase in scale along the dorsal-to-ventral axis, such as in the cases of head-direction, grid and place cells. Also located in the medial entorhinal cortex (MEC), border cells would be expected to benefit from such scale modulations. However, this phenomenon has not been experimentally observed. Grid cells in the MEC of mammals integrate velocity related signals to map the environment with characteristic hexagonal tessellation patterns. Due to the noisy nature of these input signals, path integration processes tend to accumulate errors as animals explore the environment, leading to a loss of grid-like activity. It has been suggested that border-to-grid cells' associations minimize the accumulated grid cells' error when rodents explore enclosures. Thus, the border-grid interaction for error minimization is a suitable scenario to study the effects of border cell scaling within the context of spatial representation. In this study, we computationally address the question of (i) border cells' scale from the perspective of their role in maintaining the regularity of grid cells' firing fields, as well as (ii) what are the underlying mechanisms of grid-border associations relative to the scales of both grid and border cells. Our results suggest that for optimal contribution to grid cells' error minimization, border cells should express smaller firing fields relative to those of the associated grid cells, which is consistent with the hypothesis of border cells functioning as spatial anchoring signals.

Models of spatial and temporal dimensions of memory

Episodic memory involves coding of the spatial location and time of individual events. Coding of space and time is also relevant to working memory, spatial navigation, and the disambiguation of overlapping memory representations. Neurophysiological data demonstrate that neuronal activity codes the current, past and future location of an animal as well as temporal intervals within a task. Models have addressed how neural coding of space and time for memory function could arise, with both dimensions coded by the same neurons. Neural coding could depend upon network oscillatory and attractor dynamics as well as modulation of neuronal intrinsic properties. These models are relevant to the coding of space and time involving structures including the hippocampus, entorhinal cortex, retrosplenial cortex, striatum and parahippocampal gyrus, which have been implicated in both animal and human studies.

The Head-Direction Signal Plays a Functional Role as a Neural Compass during Navigation

The rat limbic system contains head direction (HD) cells that fire according to heading in the horizontal plane, and these cells are thought to provide animals with an internal compass. Previous work has found that HD cell tuning correlates with behavior on navigational tasks, but a direct, causal link between HD cells and navigation has not been demonstrated. Here, we show that pathway-specific optogenetic inhibition of the nucleus prepositus caused HD cells to become directionally unstable under dark conditions without affecting the animals' locomotion. Then, using the same technique, we found that this decoupling of the HD signal in the absence of visual cues caused the animals to make directional homing errors and that the magnitude and direction of these errors were in a range that corresponded to the degree of instability observed in the HD signal. These results provide evidence that the HD signal plays a causal role as a neural compass in navigation.

Framing of grid cells within and beyond navigation boundaries

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.

Complete coverage of space favors modularity of the grid system in the brain

Grid cells in the entorhinal cortex fire when animals that are exploring a certain region of space occupy the vertices of a triangular grid that spans the environment. Different neurons feature triangular grids that differ in their properties of periodicity, orientation, and ellipticity. Taken together, these grids allow the animal to maintain an internal, mental representation of physical space. Experiments show that grid cells are modular, i.e., there are groups of neurons which have grids with similar periodicity, orientation, and ellipticity. We use statistical physics methods to derive a relation between variability of the properties of the grids within a module and the range of space that can be covered completely (i.e., without gaps) by the grid system with high probability. Larger variability shrinks the range of representation, providing a functional rationale for the experimentally observed comodularity of grid cell periodicity, orientation, and ellipticity. We obtain a scaling relation between the number of neurons and the period of a module, given the variability and coverage range. Specifically, we predict how many more neurons are required at smaller grid scales than at larger ones.

Probabilistic Learning by Rodent Grid Cells

Mounting evidence shows mammalian brains are probabilistic computers, but the specific cells involved remain elusive. Parallel research suggests that grid cells of the mammalian hippocampal formation are fundamental to spatial cognition but their diverse response properties still defy explanation. No plausible model exists which explains stable grids in darkness for twenty minutes or longer, despite being one of the first results ever published on grid cells. Similarly, no current explanation can tie together grid fragmentation and grid rescaling, which show very different forms of flexibility in grid responses when the environment is varied. Other properties such as attractor dynamics and grid anisotropy seem to be at odds with one another unless additional properties are assumed such as a varying velocity gain. Modelling efforts have largely ignored the breadth of response patterns, while also failing to account for the disastrous effects of sensory noise during spatial learning and recall, especially in darkness. Here, published electrophysiological evidence from a range of experiments are reinterpreted using a novel probabilistic learning model, which shows that grid cell responses are accurately predicted by a probabilistic learning process. Diverse response properties of probabilistic grid cells are statistically indistinguishable from rat grid cells across key manipulations. A simple coherent set of probabilistic computations explains stable grid fields in darkness, partial grid rescaling in resized arenas, low-dimensional attractor grid cell dynamics, and grid fragmentation in hairpin mazes. The same computations also reconcile oscillatory dynamics at the single cell level with attractor dynamics at the cell ensemble level. Additionally, a clear functional role for boundary cells is proposed for spatial learning. These findings provide a parsimonious and unified explanation of grid cell function, and implicate grid cells as an accessible neuronal population readout of a set of probabilistic spatial computations.

Cells in the mammalian hippocampal formation are thought to be central for spatial learning and stable spatial representations. Of the known spatial cells, grid cells form strikingly regular and stable patterns of activity, even in darkness. Hence, grid cells may provide the universal metric upon which spatial cognition is based. However, a more fundamental problem is how grids themselves may form and stabilise, since sensory information is noisy and can vary tremendously with environmental conditions. Furthermore, the same grid cell can display substantially different yet stable patterns of activity in different environments. Currently, no model explains how vastly different sensory cues can give rise to the diverse but stable grid patterns. Here, a new probabilistic model is proposed which combines information encoded by grid cells and boundary cells. This noise-tolerant model performs robust spatial learning, under a variety of conditions, and produces varied yet stable grid cell response patterns like rodent grid cells. Across numerous experimental manipulations, rodent and probabilistic grid cell responses are similar or even statistically indistinguishable. These results complement a growing body of evidence suggesting that mammalian brains are inherently probabilistic, and suggest for the first time that grid cells may be involved.

Spatial Cognition: Grid Cell Firing Depends on Self-Motion Cues

A recent study has found that the periodic spatial activity of grid cells is completely degraded when animals are moved passively around an enclosure, strengthening the view that grid-firing is generated on the basis of self-motion information.

Visual landmarks sharpen grid cell metric and confer context specificity to neurons of the medial entorhinal cortex

Neurons of the medial entorhinal cortex (MEC) provide spatial representations critical for navigation. In this network, the periodic firing fields of grid cells act as a metric element for position. The location of the grid firing fields depends on interactions between self-motion information, geometrical properties of the environment and nonmetric contextual cues. Here, we test whether visual information, including nonmetric contextual cues, also regulates the firing rate of MEC neurons. Removal of visual landmarks caused a profound impairment in grid cell periodicity. Moreover, the speed code of MEC neurons changed in darkness and the activity of border cells became less confined to environmental boundaries. Half of the MEC neurons changed their firing rate in darkness. Manipulations of nonmetric visual cues that left the boundaries of a 1D environment in place caused rate changes in grid cells. These findings reveal context specificity in the rate code of MEC neurons.

DOI:http://dx.doi.org/10.7554/eLife.16937.001

Modelling effects on grid cells of sensory input during self-motion

The neural coding of spatial location for memory function may involve grid cells in the medial entorhinal cortex, but the mechanism of generating the spatial responses of grid cells remains unclear. This review describes some current theories and experimental data concerning the role of sensory input in generating the regular spatial firing patterns of grid cells, and changes in grid cell firing fields with movement of environmental barriers. As described here, the influence of visual features on spatial firing could involve either computations of self-motion based on optic flow, or computations of absolute position based on the angle and distance of static visual cues. Due to anatomical selectivity of retinotopic processing, the sensory features on the walls of an environment may have a stronger effect on ventral grid cells that have wider spaced firing fields, whereas the sensory features on the ground plane may influence the firing of dorsal grid cells with narrower spacing between firing fields. These sensory influences could contribute to the potential functional role of grid cells in guiding goal-directed navigation.

Functional Architecture of the Rat Parasubiculum

The parasubiculum is a major input structure of layer 2 of medial entorhinal cortex, where most grid cells are found. Here we investigated parasubicular circuits of the rat by anatomical analysis combined with juxtacellular recording/labeling and tetrode recordings during spatial exploration. In tangential sections, the parasubiculum appears as a linear structure flanking the medial entorhinal cortex mediodorsally. With a length of ∼5.2 mm and a width of only ∼0.3 mm (approximately one dendritic tree diameter), the parasubiculum is both one of the longest and narrowest cortical structures. Parasubicular neurons span the height of cortical layers 2 and 3, and we observed no obvious association of deep layers to this structure. The "superficial parasubiculum" (layers 2 and 1) divides into ∼15 patches, whereas deeper parasubicular sections (layer 3) form a continuous band of neurons. Anterograde tracing experiments show that parasubicular neurons extend long "circumcurrent" axons establishing a "global" internal connectivity. The parasubiculum is a prime target of GABAergic and cholinergic medial septal inputs. Other input structures include the subiculum, presubiculum, and anterior thalamus. Functional analysis of identified and unidentified parasubicular neurons shows strong theta rhythmicity of spiking, a large fraction of head-direction selectivity (50%, 34 of 68), and spatial responses (grid, border and irregular spatial cells, 57%, 39 of 68). Parasubicular output preferentially targets patches of calbindin-positive pyramidal neurons in layer 2 of medial entorhinal cortex, which might be relevant for grid cell function. These findings suggest the parasubiculum might shape entorhinal theta rhythmicity and the (dorsoventral) integration of information across grid scales.

SIGNIFICANCE STATEMENT

Grid cells in medial entorhinal cortex (MEC) are crucial components of an internal navigation system of the mammalian brain. The parasubiculum is a major input structure of layer 2 of MEC, where most grid cells are found. Here we provide a functional and anatomical characterization of the parasubiculum and show that parasubicular neurons display unique features (i.e., strong theta rhythmicity of firing, prominent head-direction selectivity, and output selectively targeted to layer 2 pyramidal cell patches of MEC). These features could contribute to shaping the temporal and spatial code of downstream grid cells in entorhinal cortex.

Activity-dependent plasticity of hippocampal place maps

Hippocampal neurons encode a cognitive map of space. These maps are thought to be updated during learning and in response to changes in the environment through activity-dependent synaptic plasticity. Here we examine how changes in activity influence spatial coding in rats using halorhodopsin-mediated, spatially selective optogenetic silencing. Halorhoposin stimulation leads to light-induced suppression in many place cells and interneurons; some place cells increase their firing through disinhibition, whereas some show no effect. We find that place fields of the unaffected subpopulation remain stable. On the other hand, place fields of suppressed place cells were unstable, showing remapping across sessions before and after optogenetic inhibition. Disinhibited place cells had stable maps but sustained an elevated firing rate. These findings suggest that place representation in the hippocampus is constantly governed by activity-dependent processes, and that disinhibition may provide a mechanism for rate remapping.

Place cells in hippocampus encode a map of space, however the role of activity in place map stability is not known. Schoenenberger and colleagues optogenetically manipulate hippocampal firing rates within place fields and show lasting changes in spatial firing patterns through two separate mechanisms.

Framing the grid: effect of boundaries on grid cells and navigation

Cells in the mammalian hippocampal formation subserve neuronal representations of environmental location and support navigation in familiar environments. Grid cells constitute one of the main cell types in the hippocampal formation and are widely believed to represent a universal metric of space independent of external stimuli. Recent evidence showing that grid symmetry is distorted in non-symmetrical environments suggests that a re-examination of this hypothesis is warranted. In this review we will discuss behavioural and physiological evidence for how environmental shape and in particular enclosure boundaries influence grid cell firing properties. We propose that grid cells encode the geometric layout of enclosures.

Spatial Cognition: Entorhinal Cortex and the Hippocampal Place-Cell Map

Hippocampal place cells form a spatial 'map' which is modifiable by environmental change. A new study suggests that one route for the modification, or 'remapping', signal might be through medial entorhinal cortex, perhaps via the grid cells.

Continuous attractor network models of grid cell firing based on excitatory-inhibitory interactions

Neurons in the medial entorhinal cortex encode location through spatial firing fields that have a grid‐like organisation. The challenge of identifying mechanisms for grid firing has been addressed through experimental and theoretical investigations of medial entorhinal circuits. Here, we discuss evidence for continuous attractor network models that account for grid firing by synaptic interactions between excitatory and inhibitory cells. These models assume that grid‐like firing patterns are the result of computation of location from velocity inputs, with additional spatial input required to oppose drift in the attractor state. We focus on properties of continuous attractor networks that are revealed by explicitly considering excitatory and inhibitory neurons, their connectivity and their membrane potential dynamics. Models at this level of detail can account for theta‐nested gamma oscillations as well as grid firing, predict spatial firing of interneurons as well as excitatory cells, show how gamma oscillations can be modulated independently from spatial computations, reveal critical roles for neuronal noise, and demonstrate that only a subset of excitatory cells in a network need have grid‐like firing fields. Evaluating experimental data against predictions from detailed network models will be important for establishing the mechanisms mediating grid firing.

Hebbian Plasticity Realigns Grid Cell Activity with External Sensory Cues in Continuous Attractor Models

After the discovery of grid cells, which are an essential component to understand how the mammalian brain encodes spatial information, three main classes of computational models were proposed in order to explain their working principles. Amongst them, the one based on continuous attractor networks (CAN), is promising in terms of biological plausibility and suitable for robotic applications. However, in its current formulation, it is unable to reproduce important electrophysiological findings and cannot be used to perform path integration for long periods of time. In fact, in absence of an appropriate resetting mechanism, the accumulation of errors over time due to the noise intrinsic in velocity estimation and neural computation prevents CAN models to reproduce stable spatial grid patterns. In this paper, we propose an extension of the CAN model using Hebbian plasticity to anchor grid cell activity to environmental landmarks. To validate our approach we used as input to the neural simulations both artificial data and real data recorded from a robotic setup. The additional neural mechanism can not only anchor grid patterns to external sensory cues but also recall grid patterns generated in previously explored environments. These results might be instrumental for next generation bio-inspired robotic navigation algorithms that take advantage of neural computation in order to cope with complex and dynamic environments.

The Cognitive Architecture of Spatial Navigation: Hippocampal and Striatal Contributions

Spatial navigation can serve as a model system in cognitive neuroscience, in which specific neural representations, learning rules, and control strategies can be inferred from the vast experimental literature that exists across many species, including humans. Here, we review this literature, focusing on the contributions of hippocampal and striatal systems, and attempt to outline a minimal cognitive architecture that is consistent with the experimental literature and that synthesizes previous related computational modeling. The resulting architecture includes striatal reinforcement learning based on egocentric representations of sensory states and actions, incidental Hebbian association of sensory information with allocentric state representations in the hippocampus, and arbitration of the outputs of both systems based on confidence/uncertainty in medial prefrontal cortex. We discuss the relationship between this architecture and learning in model-free and model-based systems, episodic memory, imagery, and planning, including some open questions and directions for further experiments.

Sensory feedback in a bump attractor model of path integration

Mammalian spatial navigation systems utilize several different sensory information channels. This information is converted into a neural code that represents the animal's current position in space by engaging place cell, grid cell, and head direction cell networks. In particular, sensory landmark (allothetic) cues can be utilized in concert with an animal's knowledge of its own velocity (idiothetic) cues to generate a more accurate representation of position than path integration provides on its own (Battaglia et al. The Journal of Neuroscience 24(19):4541-4550 (2004)). We develop a computational model that merges path integration with feedback from external sensory cues that provide a reliable representation of spatial position along an annular track. Starting with a continuous bump attractor model, we explore the impact of synaptic spatial asymmetry and heterogeneity, which disrupt the position code of the path integration process. We use asymptotic analysis to reduce the bump attractor model to a single scalar equation whose potential represents the impact of asymmetry and heterogeneity. Such imperfections cause errors to build up when the network performs path integration, but these errors can be corrected by an external control signal representing the effects of sensory cues. We demonstrate that there is an optimal strength and decay rate of the control signal when cues appear either periodically or randomly. A similar analysis is performed when errors in path integration arise from dynamic noise fluctuations. Again, there is an optimal strength and decay of discrete control that minimizes the path integration error.

How environment and self-motion combine in neural representations of space

Estimates of location or orientation can be constructed solely from sensory information representing environmental cues. In unfamiliar or sensory-poor environments, these estimates can also be maintained and updated by integrating self-motion information. However, the accumulation of error dictates that updated representations of heading direction and location become progressively less reliable over time, and must be corrected by environmental sensory inputs when available. Anatomical, electrophysiological and behavioural evidence indicates that angular and translational path integration contributes to the firing of head direction cells and grid cells. We discuss how sensory inputs may be combined with self-motion information in the firing patterns of these cells. For head direction cells, direct projections from egocentric sensory representations of distal cues can help to correct cumulative errors. Grid cells may benefit from sensory inputs via boundary vector cells and place cells. However, the allocentric code of boundary vector cells and place cells requires consistent head-direction information in order to translate the sensory signal of egocentric boundary distance into allocentric boundary vector cell firing, suggesting that the different spatial representations found in and around the hippocampal formation are interdependent. We conclude that, rather than representing pure path integration, the firing of head-direction cells and grid cells reflects the interface between self-motion and environmental sensory information. Together with place cells and boundary vector cells they can support a coherent unitary representation of space based on both environmental sensory inputs and path integration signals.

Environmental boundaries as a mechanism for correcting and anchoring spatial maps

Ubiquitous throughout the animal kingdom, path integration-based navigation allows an animal to take a circuitous route out from a home base and using only self-motion cues, calculate a direct vector back. Despite variation in an animal's running speed and direction, medial entorhinal grid cells fire in repeating place-specific locations, pointing to the medial entorhinal circuit as a potential neural substrate for path integration-based spatial navigation. Supporting this idea, grid cells appear to provide an environment-independent metric representation of the animal's location in space and preserve their periodic firing structure even in complete darkness. However, a series of recent experiments indicate that spatially responsive medial entorhinal neurons depend on environmental cues in a more complex manner than previously proposed. While multiple types of landmarks may influence entorhinal spatial codes, environmental boundaries have emerged as salient landmarks that both correct error in entorhinal grid cells and bind internal spatial representations to the geometry of the external spatial world. The influence of boundaries on error correction and grid symmetry points to medial entorhinal border cells, which fire at a high rate only near environmental boundaries, as a potential neural substrate for landmark-driven control of spatial codes. The influence of border cells on other entorhinal cell populations, such as grid cells, could depend on plasticity, raising the possibility that experience plays a critical role in determining how external cues influence internal spatial representations.

Grid Cells and Place Cells: An Integrated View of their Navigational and Memory Function

Much has been learned about the hippocampal/entorhinal system, but an overview of how its parts work in an integrated way is lacking. One question regards the function of entorhinal grid cells. We propose here that their fundamental function is to provide a coordinate system for producing mind-travel in the hippocampus, a process that accesses associations with upcoming positions. We further propose that mind-travel occurs during the second half of each theta cycle. By contrast, the first half of each theta cycle is devoted to computing current position using sensory information from the lateral entorhinal cortex (LEC) and path integration information from the medial entorhinal cortex (MEC). This model explains why MEC lesions can abolish hippocampal phase precession but not place fields.

Interspike Intervals Reveal Functionally Distinct Cell Populations in the Medial Entorhinal Cortex

The superficial layers of the medial entorhinal cortex (MEC) contain spatially selective neurons that are crucial for spatial navigation and memory. These highly specialized neurons include grid cells, border cells, head-direction cells, and irregular spatially selective cells. In addition, MEC neurons display a large variability in their spike patterns at a millisecond time scale. In this study, we analyzed spike trains of neurons in the MEC superficial layers of mice and found that these neurons can be classified into two groups based on their propensity to fire spike doublets at 125-250 Hz. The two groups, labeled "bursty" and "non-bursty" neurons, differed in their spike waveforms and interspike interval adaptation but displayed a similar mean firing rate. Grid cell spatial periodicity was more commonly observed in bursty than in non-bursty neurons. In contrast, most neurons with head-direction selectivity or those that fired at the border of the environment were non-bursty neurons. During theta oscillations, both bursty and non-bursty neurons fired preferentially near the end of the descending phase of the cycle, but the spikes of bursty neurons occurred at an earlier phase than those of non-bursty neurons. Finally, analysis of spike-time crosscorrelations between simultaneously recorded neurons suggested that the two cell classes are differentially coupled to fast-spiking interneurons: bursty neurons were twice as likely to have excitatory interactions with putative interneurons as non-bursty neurons. These results demonstrate that bursty and non-bursty neurons are differentially integrated in the MEC network and preferentially encode distinct spatial signals.

SIGNIFICANCE STATEMENT

We report that neurons in the superficial layers of the medial entorhinal cortex can be classified based on their tendency to fire bursts of action potentials at 125-250 Hz. The relevance of this classification is demonstrated by the types of spatial information preferentially encoded by bursty and non-bursty neurons. Grid-like spatial periodicity is more commonly observed in bursty neurons, whereas most cells with head-direction selectivity or those that are firing at the border of the environment are non-bursty neurons. This work indicates that the spatial firing patterns of neurons in the medial entorhinal cortex can be predicted by electrophysiological features reflecting the synaptic inputs and/or integrating properties of the neurons.