Neural representations of location composed of spatially periodic bands

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.

Local origin of excitatory-inhibitory tuning equivalence in a cortical network

The interplay between excitation and inhibition determines the fidelity of cortical representations. The receptive fields of excitatory neurons are often finely tuned to encoded features, but the principles governing the tuning of inhibitory neurons remain elusive. In this study, we recorded populations of neurons in the mouse postsubiculum (PoSub), where the majority of excitatory neurons are head-direction (HD) cells. We show that the tuning of fast-spiking (FS) cells, the largest class of cortical inhibitory neurons, was broad and frequently radially symmetrical. By decomposing tuning curves using the Fourier transform, we identified an equivalence in tuning between PoSub-FS and PoSub-HD cell populations. Furthermore, recordings, optogenetic manipulations of upstream thalamic populations and computational modeling provide evidence that the tuning of PoSub-FS cells has a local origin. These findings support the notion that the equivalence of neuronal tuning between excitatory and inhibitory cell populations is an intrinsic property of local cortical networks.

Environment geometry alters subiculum boundary vector cell receptive fields in adulthood and early development

Boundaries to movement form a specific class of landmark information used for navigation: Boundary Vector Cells (BVCs) are neurons which encode an animal's location as a vector displacement from boundaries. Here we characterise the prevalence and spatial tuning of subiculum BVCs in adult and developing male rats, and investigate the relationship between BVC spatial firing and boundary geometry. BVC directional tunings align with environment walls in squares, but are uniformly distributed in circles, demonstrating that environmental geometry alters BVC receptive fields. Inserted barriers uncover both excitatory and inhibitory components to BVC receptive fields, demonstrating that inhibitory inputs contribute to BVC field formation. During post-natal development, subiculum BVCs mature slowly, contrasting with the earlier maturation of boundary-responsive cells in upstream Entorhinal Cortex. However, Subiculum and Entorhinal BVC receptive fields are altered by boundary geometry as early as tested, suggesting this is an inherent feature of the hippocampal representation of space.

Ring Attractors as the Basis of a Biomimetic Navigation System

The ability to navigate effectively in a rich and complex world is crucial for the survival of all animals. Specialist neural structures have evolved that are implicated in facilitating this ability, one such structure being the ring attractor network. In this study, we model a trio of Spiking Neural Network (SNN) ring attractors as part of a bio-inspired navigation system to maintain an internal estimate of planar translation of an artificial agent. This estimate is dynamically calibrated using a memory recall system of landmark-free allotheic multisensory experiences. We demonstrate that the SNN-based ring attractor system can accurately model motion through 2D space by integrating ideothetic velocity information and use recalled allothetic experiences as a positive corrective mechanism. This SNN based navigation system has potential for use in mobile robotics applications where power supply is limited and external sensory information is intermittent or unreliable.

Exploiting semantic information in a spiking neural SLAM system

To navigate in new environments, an animal must be able to keep track of its position while simultaneously creating and updating an internal map of features in the environment, a problem formulated as simultaneous localization and mapping (SLAM) in the field of robotics. This requires integrating information from different domains, including self-motion cues, sensory, and semantic information. Several specialized neuron classes have been identified in the mammalian brain as being involved in solving SLAM. While biology has inspired a whole class of SLAM algorithms, the use of semantic information has not been explored in such work. We present a novel, biologically plausible SLAM model called SSP-SLAM-a spiking neural network designed using tools for large scale cognitive modeling. Our model uses a vector representation of continuous spatial maps, which can be encoded via spiking neural activity and bound with other features (continuous and discrete) to create compressed structures containing semantic information from multiple domains (e.g., spatial, temporal, visual, conceptual). We demonstrate that the dynamics of these representations can be implemented with a hybrid oscillatory-interference and continuous attractor network of head direction cells. The estimated self-position from this network is used to learn an associative memory between semantically encoded landmarks and their positions, i.e., an environment map, which is used for loop closure. Our experiments demonstrate that environment maps can be learned accurately and their use greatly improves self-position estimation. Furthermore, grid cells, place cells, and object vector cells are observed by this model. We also run our path integrator network on the NengoLoihi neuromorphic emulator to demonstrate feasibility for a full neuromorphic implementation for energy efficient SLAM.

Simultaneous representation of multiple time horizons by entorhinal grid cells and CA1 place cells

Grid cells and place cells represent the spatiotemporal continuum of an animal's past, present, and future locations. However, their spatiotemporal relationship is unclear. Here, we co-record grid and place cells in freely foraging rats. We show that average time shifts in grid cells tend to be prospective and are proportional to their spatial scale, providing a nearly instantaneous readout of a spectrum of progressively increasing time horizons ranging hundreds of milliseconds. Average time shifts of place cells are generally larger compared to grid cells and also increase with place field sizes. Moreover, time horizons display nonlinear modulation by the animal's trajectories in relation to the local boundaries and locomotion cues. Finally, long and short time horizons occur at different parts of the theta cycle, which may facilitate their readout. Together, these findings suggest that population activity of grid and place cells may represent local trajectories essential for goal-directed navigation and planning.

Grid cell disruption in a mouse model of early Alzheimer's disease reflects reduced integration of self-motion cues

Converging evidence from human and rodent studies suggests that disrupted grid cell coding in the medial entorhinal cortex (MEC) underlies path integration behavioral deficits during early Alzheimer's disease (AD). However, grid cell firing relies on both self-motion cues and environmental features, and it remains unclear whether disrupted grid coding can account for specific path integration deficits reported during early AD. Here, we report in the J20 transgenic amyloid beta (Aβ) mouse model of early AD that grid cells were spatially unstable toward the center of the arena, had qualitatively different spatial components that aligned parallel to the borders of the environment, and exhibited impaired integration of distance traveled via reduced theta phase precession. Our results suggest that disrupted early AD grid coding reflects reduced integration of self-motion cues but not environmental information via geometric boundaries, providing evidence that grid cell impairments underlie path integration deficits during early AD.

Effects of neuromodulation-inspired mechanisms on the performance of deep neural networks in a spatial learning task

In recent years, the biological underpinnings of adaptive learning have been modeled, leading to faster model convergence and various behavioral benefits in tasks including spatial navigation and cue-reward association. Furthermore, studies have investigated how the neuromodulatory system, a major driver of synaptic plasticity and state-dependent changes in the brain neuronal activities, plays a role in training deep neural networks (DNNs). In this study, we extended previous studies on neuromodulation-inspired DNNs and explored the effects of neuromodulatory components on learning and single unit activities in a spatial learning task. Under the multiscale neuromodulatory framework, plastic components, dropout probability modulation, and learning rate decay were added to the single unit, layer, and whole network levels of DNN models, respectively. We observed behavioral benefits including faster learning and smaller error of ambulation. We then concluded that neuromodulatory components can affect learning trajectories, outcomes, and single unit activities, in a component- and hyperparameter-dependent manner.

Spatial memory deficits in Alzheimer's disease and their connection to cognitive maps' formation by place cells and grid cells

Whenever we navigate through different contexts, we build a cognitive map: an internal representation of the territory. Spatial navigation is a complex skill that involves multiple types of information processing and integration. Place cells and grid cells, collectively with other hippocampal and medial entorhinal cortex neurons (MEC), form a neural network whose activity is critical for the representation of self-position and orientation along with spatial memory retrieval. Furthermore, this activity generates new representations adapting to changes in the environment. Though there is a normal decline in spatial memory related to aging, this is dramatically increased in pathological conditions such as Alzheimer's disease (AD). AD is a multi-factorial neurodegenerative disorder affecting mainly the hippocampus-entorhinal cortex (HP-EC) circuit. Consequently, the initial stages of the disease have disorientation and wandering behavior as two of its hallmarks. Recent electrophysiological studies have linked spatial memory deficits to difficulties in spatial information encoding. Here we will discuss map impairment and remapping disruption in the HP-EC network, as a possible circuit mechanism involved in the spatial memory and navigation deficits observed in AD, pointing out the benefits of virtual reality as a tool for early diagnosis and rehabilitation.

Excitatory-inhibitory recurrent dynamics produce robust visual grids and stable attractors

Spatially modulated grid cells have been recently found in the rat secondary visual cortex (V2) during active navigation. However, the computational mechanism and functional significance of V2 grid cells remain unknown. To address the knowledge gap, we train a biologically inspired excitatory-inhibitory recurrent neural network to perform a two-dimensional spatial navigation task with multisensory input. We find grid-like responses in both excitatory and inhibitory RNN units, which are robust with respect to spatial cues, dimensionality of visual input, and activation function. Population responses reveal a low-dimensional, torus-like manifold and attractor. We find a link between functional grid clusters with similar receptive fields and structured excitatory-to-excitatory connections. Additionally, multistable torus-like attractors emerged with increasing sparsity in inter- and intra-subnetwork connectivity. Finally, irregular grid patterns are found in recurrent neural network (RNN) units during a visual sequence recognition task. Together, our results suggest common computational mechanisms of V2 grid cells for spatial and non-spatial tasks.

How to build a cognitive map

Learning and interpreting the structure of the environment is an innate feature of biological systems, and is integral to guiding flexible behaviors for evolutionary viability. The concept of a cognitive map has emerged as one of the leading metaphors for these capacities, and unraveling the learning and neural representation of such a map has become a central focus of neuroscience. In recent years, many models have been developed to explain cellular responses in the hippocampus and other brain areas. Because it can be difficult to see how these models differ, how they relate and what each model can contribute, this Review aims to organize these models into a clear ontology. This ontology reveals parallels between existing empirical results, and implies new approaches to understand hippocampal-cortical interactions and beyond.

Medial entorhinal cortex commissural input regulates the activity of spatially and object-tuned cells contributing to episodic memory

Extensive interhemispheric projections connect many homotopic brain regions, including the hippocampal formation, but little is known as to how information transfer affects the functions supported by the target area. Here, we studied whether the commissural projections connecting the medial entorhinal cortices contribute to spatial coding, object coding, and memory. We demonstrate that input from the contralateral medial entorhinal cortex targets all major cell types in the superficial medial entorhinal cortex, modulating their firing rate. Notably, a fraction of responsive cells displayed object tuning and exhibited a reduction in their firing rate upon the inhibition of commissural input. In line with this finding are behavioral results that revealed the contribution of commissural input to episodic-like memory retrieval.

Phase coding of spatial representations in the human entorhinal cortex

The grid-like activity pattern of cells in the mammalian entorhinal cortex provides an internal reference frame for allocentric self-localization. The same neurons maintain robust phase couplings with local field oscillations. We found that neurons of the human entorhinal cortex display consistent spatial and temporal phase locking between spikes and slow gamma band local field potentials (LFPs) during virtual navigation. The phase locking maintained an environment-specific map over time. The phase tuning of spikes to the slow gamma band LFP revealed spatially periodic phase grids with environment-dependent scaling and consistent alignment with the environment. Using a Bayesian decoding model, we could predict the avatar's position with near perfect accuracy and, to a lesser extent, that of heading direction as well. These results imply that the phase of spikes relative to spatially modulated gamma oscillations encode allocentric spatial positions. We posit that a joint spatiotemporal phase code can implement the combined neural representation of space and time in the human entorhinal cortex.

Transforming Social Perspectives with Cognitive Maps

Growing evidence suggests that cognitive maps represent relations between social knowledge similar to how spatial locations are represented in an environment. Notably, the extant human medial temporal lobe literature assumes associations between social stimuli follow a linear associative mapping from an egocentric viewpoint to a cognitive map. Yet, this form of associative social memory doesn't account for a core phenomenon of social interactions in which social knowledge learned via comparisons to the self, other individuals, or social networks are assimilated within a single frame of reference. We argue that hippocampal-entorhinal coordinate transformations, known to integrate egocentric and allocentric spatial cues, inform social perspective switching between the self and others. We present evidence that the hippocampal formation helps inform social interactions by relating self versus other social attribute comparisons to society in general, which can afford rapid and flexible assimilation of knowledge about the relationship between the self and social networks of varying proximities. We conclude by discussing the ramifications of cognitive maps in aiding this social perspective transformation process in states of health and disease.

A Bionic Spatial Cognition Model and Method for Robots Based on the Hippocampus Mechanism

The hippocampus and its accessory are the main areas for spatial cognition. It can integrate paths and form environmental cognition based on motion information and then realize positioning and navigation. Learning from the hippocampus mechanism is a crucial way forward for research in robot perception, so it is crucial to building a calculation method that conforms to the biological principle. In addition, it should be easy to implement on a robot. This paper proposes a bionic cognition model and method for mobile robots, which can realize precise path integration and cognition of space. Our research can provide the basis for the cognition of the environment and autonomous navigation for bionic robots.

A Positioning Method Based on Place Cells and Head-Direction Cells for Inertial/Visual Brain-Inspired Navigation System

Mammals rely on vision and self-motion information in nature to distinguish directions and navigate accurately and stably. Inspired by the mammalian brain neurons to represent the spatial environment, the brain-inspired positioning method based on multi-sensors’ input is proposed to solve the problem of accurate navigation in the absence of satellite signals. In the research related to the application of brain-inspired engineering, it is not common to fuse various sensor information to improve positioning accuracy and decode navigation parameters from the encoded information of the brain-inspired model. Therefore, this paper establishes the head-direction cell model and the place cell model with application potential based on continuous attractor neural networks (CANNs) to encode visual and inertial input information, and then decodes the direction and position according to the population neuron firing response. The experimental results confirm that the brain-inspired navigation model integrates a variety of information, outputs more accurate and stable navigation parameters, and generates motion paths. The proposed model promotes the effective development of brain-inspired navigation research.

A Model of Spatial Cell Development in Rat Hippocampus Based on Artificial Neural Network

Physiological studies have shown that the hippocampal structure of rats develops at different stages, in which the place cells continue to develop during the whole juvenile period of rats and mature after the juvenile period. As the main information source of place cells, grid cells should mature earlier than place cells. In order to make better use of the biological information exhibited by the rat brain hippocampus in the environment, we propose a position cognition model based on the spatial cell development mechanism of rat hippocampus. The model uses a recurrent neural network with parametric bias (RNNPB) to simulate changes in the discharge characteristics during the development of a single stripe cell. The oscillatory interference mechanism is able to fuse the developing stripe waves, thus indirectly simulating the developmental process of the grid cells. The output of the grid cells is then used as the information input of the place cells, whose development process is simulated by BP neural network. After the place cells matured, the position matrix generated by the place cell group was used to realize the position cognition of rats in a given spatial region. The experimental results show that this model can simulate the development process of grid cells and place cells, and it can realize high precision positioning in the given space area. Moreover, the experimental effect of cognitive map construction using this model is basically consistent with the effect of RatSLAM, which verifies the validity and accuracy of the model.

Locally ordered representation of 3D space in the entorhinal cortex

As animals navigate on a two-dimensional surface, neurons in the medial entorhinal cortex (MEC) known as grid cells are activated when the animal passes through multiple locations (firing fields) arranged in a hexagonal lattice that tiles the locomotion surface¹. However, although our world is three-dimensional, it is unclear how the MEC represents 3D space². Here we recorded from MEC cells in freely flying bats and identified several classes of spatial neurons, including 3D border cells, 3D head-direction cells, and neurons with multiple 3D firing fields. Many of these multifield neurons were 3D grid cells, whose neighbouring fields were separated by a characteristic distance-forming a local order-but lacked any global lattice arrangement of the fields. Thus, whereas 2D grid cells form a global lattice-characterized by both local and global order-3D grid cells exhibited only local order, creating a locally ordered metric for space. We modelled grid cells as emerging from pairwise interactions between fields, which yielded a hexagonal lattice in 2D and local order in 3D, thereby describing both 2D and 3D grid cells using one unifying model. Together, these data and model illuminate the fundamental differences and similarities between neural codes for 3D and 2D space in the mammalian brain.

A neural code for egocentric spatial maps in the human medial temporal lobe

Spatial navigation and memory rely on neural systems that encode places, distances, and directions in relation to the external world or relative to the navigating organism. Place, grid, and head-direction cells form key units of world-referenced, allocentric cognitive maps, but the neural basis of self-centered, egocentric representations remains poorly understood. Here, we used human single-neuron recordings during virtual spatial navigation tasks to identify neurons providing a neural code for egocentric spatial maps in the human brain. Consistent with previous observations in rodents, these neurons represented egocentric bearings toward reference points positioned throughout the environment. Egocentric bearing cells were abundant in the parahippocampal cortex and supported vectorial representations of egocentric space by also encoding distances toward reference points. Beyond navigation, the observed neurons showed activity increases during spatial and episodic memory recall, suggesting that egocentric bearing cells are not only relevant for navigation but also play a role in human memory.

A Neural Model of Intrinsic and Extrinsic Hippocampal Theta Rhythms: Anatomy, Neurophysiology, and Function

This article describes a neural model of the anatomy, neurophysiology, and functions of intrinsic and extrinsic theta rhythms in the brains of multiple species. Topics include how theta rhythms were discovered; how theta rhythms organize brain information processing into temporal series of spatial patterns; how distinct theta rhythms occur within area CA1 of the hippocampus and between the septum and area CA3 of the hippocampus; what functions theta rhythms carry out in different brain regions, notably CA1-supported functions like learning, recognition, and memory that involve visual, cognitive, and emotional processes; how spatial navigation, adaptively timed learning, and category learning interact with hippocampal theta rhythms; how parallel cortical streams through the lateral entorhinal cortex (LEC) and the medial entorhinal cortex (MEC) represent the end-points of the What cortical stream for perception and cognition and the Where cortical stream for spatial representation and action; how the neuromodulator acetylcholine interacts with the septo-hippocampal theta rhythm and modulates category learning; what functions are carried out by other brain rhythms, such as gamma and beta oscillations; and how gamma and beta oscillations interact with theta rhythms. Multiple experimental facts about theta rhythms are unified and functionally explained by this theoretical synthesis.

The Tolman-Eichenbaum Machine: Unifying Space and Relational Memory through Generalization in the Hippocampal Formation

The hippocampal-entorhinal system is important for spatial and relational memory tasks. We formally link these domains, provide a mechanistic understanding of the hippocampal role in generalization, and offer unifying principles underlying many entorhinal and hippocampal cell types. We propose medial entorhinal cells form a basis describing structural knowledge, and hippocampal cells link this basis with sensory representations. Adopting these principles, we introduce the Tolman-Eichenbaum machine (TEM). After learning, TEM entorhinal cells display diverse properties resembling apparently bespoke spatial responses, such as grid, band, border, and object-vector cells. TEM hippocampal cells include place and landmark cells that remap between environments. Crucially, TEM also aligns with empirically recorded representations in complex non-spatial tasks. TEM also generates predictions that hippocampal remapping is not random as previously believed; rather, structural knowledge is preserved across environments. We confirm this structural transfer over remapping in simultaneously recorded place and grid cells.

An improved bioinspired cognitive map-building system based on episodic memory recognition

Before the cognitive map is generated through the fire of the rodent hippocampal spatial cells, mammals can obtain the outside knowledge through the visual information, which comes from the eyeball to the brain. The information is encoded and transferred to the two regions of the brain based on the fact of biophysiological research, which are known as “what” loop and “where” loop. In this article, we simulate an episodic memory recognition unit consisting of the integration of two-loop information, which is applied to building the accurate bioinspired spatial cognitive map of real environments. We employ the visual bag of word algorithm based on oriented Feature from Accelerated Segment Test and rotated Binary Robust Independent Elementary Features feature to build the “what” loop and the hippocampal spatial cells cognitive model, which comes from the front-end visual information input system to build the “where” loop. At the same time, the environmental cognitive map is a topological map containing information about place cell competition firing rate, oriented Feature from Accelerated Segment Test and rotated Binary Robust Independent Elementary Features feature descriptor, similarity of image retrieval, and relative location of cognitive map nodes. The simulation experiments and physical experiments in a mobile robot platform have been done to verify the environmental adaptability and robustness of the algorithm. This proposing algorithm would provide a foundation for further research on bioinspired navigation of robots.

A computational model for grid maps in neural populations

Grid cells in the entorhinal cortex, together with head direction, place, speed and border cells, are major contributors to the organization of spatial representations in the brain. In this work we introduce a novel theoretical and algorithmic framework able to explain the optimality of hexagonal grid-like response patterns. We show that this pattern is a result of minimal variance encoding of neurons together with maximal robustness to neurons' noise and minimal number of encoding neurons. The novelty lies in the formulation of the encoding problem considering neurons as an overcomplete basis (a frame) where the position information is encoded. Through the modern Frame Theory language, specifically that of tight and equiangular frames, we provide new insights about the optimality of hexagonal grid receptive fields. The proposed model is based on the well-accepted and tested hypothesis of Hebbian learning, providing a simplified cortical-based framework that does not require the presence of velocity-driven oscillations (oscillatory model) or translational symmetries in the synaptic connections (attractor model). We moreover demonstrate that the proposed encoding mechanism naturally explains axis alignment of neighbor grid cells and maps shifts, rotations and scaling of the stimuli onto the shape of grid cells' receptive fields, giving a straightforward explanation of the experimental evidence of grid cells remapping under transformations of environmental cues.

A non-spatial account of place and grid cells based on clustering models of concept learning

One view is that conceptual knowledge is organized using the circuitry in the medial temporal lobe (MTL) that supports spatial processing and navigation. In contrast, we find that a domain-general learning algorithm explains key findings in both spatial and conceptual domains. When the clustering model is applied to spatial navigation tasks, so-called place and grid cell-like representations emerge because of the relatively uniform distribution of possible inputs in these tasks. The same mechanism applied to conceptual tasks, where the overall space can be higher-dimensional and sampling sparser, leading to representations more aligned with human conceptual knowledge. Although the types of memory supported by the MTL are superficially dissimilar, the information processing steps appear shared. Our account suggests that the MTL uses a general-purpose algorithm to learn and organize context-relevant information in a useful format, rather than relying on navigation-specific neural circuitry.

The Neurobiology of Mammalian Navigation

Mammals have evolved specialized brain systems to support efficient navigation within diverse habitats and over varied distances, but while navigational strategies and sensory mechanisms vary across species, core spatial components appear to be widely shared. This review presents common elements found in mammalian spatial mapping systems, focusing on the cells in the hippocampal formation representing orientational and locational spatial information, and 'core' mammalian hippocampal circuitry. Mammalian spatial mapping systems make use of both allothetic cues (space-defining cues in the external environment) and idiothetic cues (cues derived from self-motion). As examples of each cue type, we discuss: environmental boundaries, which control both orientational and locational neuronal activity and behaviour; and 'path integration', a process that allows the estimation of linear translation from velocity signals, thought to depend upon grid cells in the entorhinal cortex. Building cognitive maps entails sampling environments: we consider how the mapping system controls exploration to acquire spatial information, and how exploratory strategies may integrate idiothetic with allothetic information. We discuss how 'replay' may act to consolidate spatial maps, and simulate trajectories to aid navigational planning. Finally, we discuss grid cell models of vector navigation.

A geometric attractor mechanism for self-organization of entorhinal grid modules

Grid cells in the medial entorhinal cortex (MEC) respond when an animal occupies a periodic lattice of 'grid fields' in the environment. The grids are organized in modules with spatial periods, or scales, clustered around discrete values separated on average by ratios in the range 1.4-1.7. We propose a mechanism that produces this modular structure through dynamical self-organization in the MEC. In attractor network models of grid formation, the grid scale of a single module is set by the distance of recurrent inhibition between neurons. We show that the MEC forms a hierarchy of discrete modules if a smooth increase in inhibition distance along its dorso-ventral axis is accompanied by excitatory interactions along this axis. Moreover, constant scale ratios between successive modules arise through geometric relationships between triangular grids and have values that fall within the observed range. We discuss how interactions required by our model might be tested experimentally.

Hippocampal Sequences During Exploration: Mechanisms and Functions

Although the hippocampus plays a critical role in spatial and episodic memories, the mechanisms underlying memory formation, stabilization, and recall for adaptive behavior remain relatively unknown. During exploration, within single cycles of the ongoing theta rhythm that dominates hippocampal local field potentials, place cells form precisely ordered sequences of activity. These neural sequences result from the integration of both external inputs conveying sensory-motor information, and intrinsic network dynamics possibly related to memory processes. Their endogenous replay during subsequent sleep is critical for memory consolidation. The present review discusses possible mechanisms and functions of hippocampal theta sequences during exploration. We present several lines of evidence suggesting that these neural sequences play a key role in information processing and support the formation of initial memory traces, and discuss potential functional distinctions between neural sequences emerging during theta vs. awake sharp-wave ripples.

A local measure of symmetry and orientation for individual spikes of grid cells

Grid cells have attracted broad attention because of their highly symmetric hexagonal firing patterns. Recently, research has shifted its focus from the global symmetry of grid cell activity to local distortions both in space and time, such as drifts in orientation, local defects of the hexagonal symmetry, and the decay and reappearance of grid patterns after changes in lighting condition. Here, we introduce a method that allows to visualize and quantify such local distortions, by assigning both a local grid score and a local orientation to each individual spike of a neuronal recording. The score is inspired by a standard measure from crystallography, which has been introduced to quantify local order in crystals. By averaging over spikes recorded within arbitrary regions or time periods, we can quantify local variations in symmetry and orientation of firing patterns in both space and time.

Recent and remote retrograde memory deficit in rats with medial entorhinal cortex lesions

The hippocampus is critically involved in the acquisition and retrieval of spatial memories. Even though some memories become independent of the hippocampus over time, expression of spatial memories have consistently been found to permanently depend on the hippocampus. Recent studies have focused on the adjacent medial entorhinal cortex (MEC), as it provides major projections to the hippocampus. These studies have shown that lesions of the MEC disrupt spatial processing in the hippocampus and impair spatial memory acquisition on the watermaze task. MEC lesions acquired after learning the watermaze task also disrupt recently acquired spatial memories. However, the effect of MEC lesions on remotely acquired memories is unknown. The current study examined the effect of MEC lesions on recent and remote memory retrieval using three hippocampus-dependent tasks: the watermaze, trace fear conditioning, and novel object recognition. MEC lesions caused impaired retrieval of recently and remotely acquired memory for the watermaze. Rats with MEC lesions also showed impaired fear memory when exposed to the previously conditioned context or the associated tone, and this reduction was seen both when the lesion occurred soon after trace fear condition and when it occurred a month after conditioning. In contrast, MEC lesions did not disrupt novel object recognition. These findings indicate that even with an intact hippocampus, rats with MEC lesions cannot retrieve recent or remote spatial memories. In addition, the involvement of the MEC in memory extends beyond is role in navigation and place memory.

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.

Local transformations of the hippocampal cognitive map

Grid cells are neurons active in multiple fields arranged in a hexagonal lattice and are thought to represent the "universal metric for space." However, they become nonhomogeneously distorted in polarized enclosures, which challenges this view. We found that local changes to the configuration of the enclosure induce individual grid fields to shift in a manner inversely related to their distance from the reconfigured boundary. The grid remained primarily anchored to the unchanged stable walls and showed a nonuniform rescaling. Shifts in simultaneously recorded colocalized grid fields were strongly correlated, which suggests that the readout of the animal's position might still be intact. Similar field shifts were also observed in place and boundary cells-albeit of greater magnitude and more pronounced closer to the reconfigured boundary-which suggests that there is no simple one-to-one relationship between these three different cell types.

Structural modularity and grid activity in the medial entorhinal cortex

Following the groundbreaking discovery of grid cells, the medial entorhinal cortex (MEC) has become the focus of intense anatomical, physiological, and computational investigations. Whether and how grid activity maps onto cell types and cortical architecture is still an open question. Fundamental similarities in microcircuits, function, and connectivity suggest a homology between rodent MEC and human posteromedial entorhinal cortex. Both are specialized for spatial processing and display similar cellular organization, consisting of layer 2 pyramidal/calbindin cell patches superimposed on scattered stellate neurons. Recent data indicate the existence of a further nonoverlapping modular system (zinc patches) within the superficial MEC layers. Zinc and calbindin patches have been shown to receive largely segregated inputs from the presubiculum and parasubiculum. Grid cells are also clustered in the MEC, and we discuss possible structure-function schemes on how grid activity could map onto cortical patch systems. We hypothesize that in the superficial layers of the MEC, anatomical location can be predictive of function; thus relating functional properties and neuronal morphologies to the cortical modules will be necessary for resolving how grid activity maps onto cortical architecture. Imaging or cell identification approaches in freely moving animals will be required for testing this hypothesis.

Learning place cells, grid cells and invariances with excitatory and inhibitory plasticity

Neurons in the hippocampus and adjacent brain areas show a large diversity in their tuning to location and head direction, and the underlying circuit mechanisms are not yet resolved. In particular, it is unclear why certain cell types are selective to one spatial variable, but invariant to another. For example, place cells are typically invariant to head direction. We propose that all observed spatial tuning patterns - in both their selectivity and their invariance - arise from the same mechanism: Excitatory and inhibitory synaptic plasticity driven by the spatial tuning statistics of synaptic inputs. Using simulations and a mathematical analysis, we show that combined excitatory and inhibitory plasticity can lead to localized, grid-like or invariant activity. Combinations of different input statistics along different spatial dimensions reproduce all major spatial tuning patterns observed in rodents. Our proposed model is robust to changes in parameters, develops patterns on behavioral timescales and makes distinctive experimental predictions.

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.

Cell types for our sense of location: where we are and where we are going

Technological advances in profiling cells along genetic, anatomical and physiological axes have fomented interest in identifying all neuronal cell types. This goal nears completion in specialized circuits such as the retina, while remaining more elusive in higher order cortical regions. We propose that this differential success of cell type identification may not simply reflect technological gaps in co-registering genetic, anatomical and physiological features in the cortex. Rather, we hypothesize it reflects evolutionarily driven differences in the computational principles governing specialized circuits versus more general-purpose learning machines. In this framework, we consider the question of cell types in medial entorhinal cortex (MEC), a region likely to be involved in memory and navigation. While MEC contains subsets of identifiable functionally defined cell types, recent work employing unbiased statistical methods and more diverse tasks reveals unsuspected heterogeneity and adaptivity in MEC firing patterns. This suggests MEC may operate more as a generalist circuit, obeying computational design principles resembling those governing other higher cortical regions.

The hippocampus as a predictive map

A cognitive map has long been the dominant metaphor for hippocampal function, embracing the idea that place cells encode a geometric representation of space. However, evidence for predictive coding, reward sensitivity and policy dependence in place cells suggests that the representation is not purely spatial. We approach this puzzle from a reinforcement learning perspective: what kind of spatial representation is most useful for maximizing future reward? We show that the answer takes the form of a predictive representation. This representation captures many aspects of place cell responses that fall outside the traditional view of a cognitive map. Furthermore, we argue that entorhinal grid cells encode a low-dimensionality basis set for the predictive representation, useful for suppressing noise in predictions and extracting multiscale structure for hierarchical planning.

A Novel Mechanism for the Grid-to-Place Cell Transformation Revealed by Transgenic Depolarization of Medial Entorhinal Cortex Layer II

The spatial receptive fields of neurons in medial entorhinal cortex layer II (MECII) and in the hippocampus suggest general and environment-specific maps of space, respectively. However, the relationship between these receptive fields remains unclear. We reversibly manipulated the activity of MECII neurons via chemogenetic receptors and compared the changes in downstream hippocampal place cells to those of neurons in MEC. Depolarization of MECII impaired spatial memory and elicited drastic changes in CA1 place cells in a familiar environment, similar to those seen during remapping between distinct environments, while hyperpolarization did not. In contrast, both manipulations altered the firing rate of MEC neurons without changing their firing locations. Interestingly, only depolarization caused significant changes in the relative firing rates of individual grid fields, reconfiguring the spatial input from MEC. This suggests a novel mechanism of hippocampal remapping whereby rate changes in MEC neurons lead to locational changes of hippocampal place fields.

Theta sequences of grid cell populations can provide a movement-direction signal

It has been proposed that path integration in mammals is performed by the convergence of internally generated speed and directional inputs onto grid cells. Although this hypothesis has been supported by the discovery that head direction, speed, and grid cells are intermixed within entorhinal cortex and by the recent finding that head-direction inputs are necessary for grid firing, many details on how grid cells are generated have remained elusive. For example, analysis of recording data suggests that substituting head direction for movement direction accrues errors that preclude the formation of grid patterns. To address this discrepancy, we propose that the organization of grid networks makes it plausible that movement-direction signals are an output from grid cells and that temporally precise grid cell sequences provide a robust directional signal to other spatial and directional cell types.

Grid Cells Encode Local Positional Information

The brain has an extraordinary ability to create an internal spatial map of the external world [1]. This map-like representation of environmental surroundings is encoded through specific types of neurons, located within the hippocampus and entorhinal cortex, which exhibit spatially tuned firing patterns [2, 3]. In addition to encoding space, these neurons are believed to be related to contextual information and memory [4, 5, 6, 7]. One class of such cells is the grid cells, which are located within the entorhinal cortex, presubiculum, and parasubiculum [3, 8]. Grid cell firing forms a hexagonal array of firing fields, a pattern that is largely thought to reflect the operation of intrinsic self-motion-related computations [9, 10, 11, 12]. If this is the case, then fields should be relatively uniform in size, number of spikes, and peak firing rate. However, it has been suggested that this is not in fact the case [3, 13]. The possibility exists that local spatial information also influences grid cells, which—if true—would greatly change the way in which grid cells are thought to contribute to place coding. Accordingly, we asked how discriminable the individual fields of a given grid cell are by looking at the distribution of field firing rates and reproducibility of this distribution across trials. Grid fields were less uniform in intensity than expected, and the pattern of strong and weak fields was spatially stable and recurred across trials. The distribution remained unchanged even after arena rescaling, but not after remapping. This suggests that additional local information is being overlaid onto the global hexagonal pattern of grid cells.

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Individual grid cell fields exhibit large variability in firing rates

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The fields firing rate ratios tend to remain stable within and across sessions

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The fields' firing rate ratios are stable even during rescaling of the arena

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The firing profile of different fields is retained until remapping occurs

A Multiplexed, Heterogeneous, and Adaptive Code for Navigation in Medial Entorhinal Cortex

Medial entorhinal grid cells display strikingly symmetric spatial firing patterns. The clarity of these patterns motivated the use of specific activity pattern shapes to classify entorhinal cell types. While this approach successfully revealed cells that encode boundaries, head direction, and running speed, it left a majority of cells unclassified, and its pre-defined nature may have missed unconventional, yet important coding properties. Here, we apply an unbiased statistical approach to search for cells that encode navigationally relevant variables. This approach successfully classifies the majority of entorhinal cells and reveals unsuspected entorhinal coding principles. First, we find a high degree of mixed selectivity and heterogeneity in superficial entorhinal neurons. Second, we discover a dynamic and remarkably adaptive code for space that enables entorhinal cells to rapidly encode navigational information accurately at high running speeds. Combined, these observations advance our current understanding of the mechanistic origins and functional implications of the entorhinal code for navigation. VIDEO ABSTRACT.

Context-dependent spatially periodic activity in the human entorhinal cortex

The spatially periodic activity of grid cells in the entorhinal cortex (EC) of the rodent, primate, and human provides a coordinate system that, together with the hippocampus, informs an individual of its location relative to the environment and encodes the memory of that location. Among the most defining features of grid-cell activity are the 60° rotational symmetry of grids and preservation of grid scale across environments. Grid cells, however, do display a limited degree of adaptation to environments. It remains unclear if this level of environment invariance generalizes to human grid-cell analogs, where the relative contribution of visual input to the multimodal sensory input of the EC is significantly larger than in rodents. Patients diagnosed with nontractable epilepsy who were implanted with entorhinal cortical electrodes performing virtual navigation tasks to memorized locations enabled us to investigate associations between grid-like patterns and environment. Here, we report that the activity of human entorhinal cortical neurons exhibits adaptive scaling in grid period, grid orientation, and rotational symmetry in close association with changes in environment size, shape, and visual cues, suggesting scale invariance of the frequency, rather than the wavelength, of spatially periodic activity. Our results demonstrate that neurons in the human EC represent space with an enhanced flexibility relative to neurons in rodents because they are endowed with adaptive scalability and context dependency.

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.

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.

The Art of Grid Fields: Geometry of Neuronal Time

The discovery of grid cells in the entorhinal cortex has both elucidated our understanding of spatial representations in the brain, and germinated a large number of theoretical models regarding the mechanisms of these cells' striking spatial firing characteristics. These models cross multiple neurobiological levels that include intrinsic membrane resonance, dendritic integration, after hyperpolarization characteristics and attractor dynamics. Despite the breadth of the models, to our knowledge, parallels can be drawn between grid fields and other temporal dynamics observed in nature, much of which was described by Art Winfree and colleagues long before the initial description of grid fields. Using theoretical and mathematical investigations of oscillators, in a wide array of mediums far from the neurobiology of grid cells, Art Winfree has provided a substantial amount of research with significant and profound similarities. These theories provide specific inferences into the biological mechanisms and extraordinary resemblances across phenomenon. Therefore, this manuscript provides a novel interpretation on the phenomenon of grid fields, from the perspective of coupled oscillators, postulating that grid fields are the spatial representation of phase resetting curves in the brain. In contrast to prior models of gird cells, the current manuscript provides a sketch by which a small network of neurons, each with oscillatory components can operate to form grid cells, perhaps providing a unique hybrid between the competing attractor neural network and oscillatory interference models. The intention of this new interpretation of the data is to encourage novel testable hypotheses.