Grid Cell Firing Patterns Research Articles

One-shot entorhinal maps enable flexible navigation in novel environments

Animals must navigate changing environments to find food, shelter or mates. In mammals, grid cells in the medial entorhinal cortex construct a neural spatial map of the external environment1–5. However, how grid cell firing patterns rapidly adapt to novel or changing environmental features on a timescale relevant to behaviour remains unknown. Here, by recording over 15,000 grid cells in mice navigating virtual environments, we tracked the real-time state of the grid cell network. This allowed us to observe and predict how altering environmental features influenced grid cell firing patterns on a nearly instantaneous timescale. We found evidence that visual landmarks provide inputs to fixed points in the grid cell network. This resulted in stable grid cell firing patterns in novel and altered environments after a single exposure. Fixed visual landmark inputs also influenced the grid cell network such that altering landmarks induced distortions in grid cell firing patterns. Such distortions could be predicted by a computational model with a fixed landmark to grid cell network architecture. Finally, a medial entorhinal cortex-dependent task revealed that although grid cell firing patterns are distorted by landmark changes, behaviour can adapt via a downstream region implementing behavioural timescale synaptic plasticity6. Overall, our findings reveal how the navigational system of the brain constructs spatial maps that balance rapidity and accuracy. Fixed connections between landmarks and grid cells enable the brain to quickly generate stable spatial maps, essential for navigation in novel or changing environments. Conversely, plasticity in regions downstream from grid cells allows the spatial maps of the brain to more accurately mirror the external spatial environment. More generally, these findings raise the possibility of a broader neural principle: by allocating fixed and plastic connectivity across different networks, the brain can solve problems requiring both rapidity and representational accuracy.

Neural network based successor representations to form cognitive maps of space and language

How does the mind organize thoughts? The hippocampal-entorhinal complex is thought to support domain-general representation and processing of structural knowledge of arbitrary state, feature and concept spaces. In particular, it enables the formation of cognitive maps, and navigation on these maps, thereby broadly contributing to cognition. It has been proposed that the concept of multi-scale successor representations provides an explanation of the underlying computations performed by place and grid cells. Here, we present a neural network based approach to learn such representations, and its application to different scenarios: a spatial exploration task based on supervised learning, a spatial navigation task based on reinforcement learning, and a non-spatial task where linguistic constructions have to be inferred by observing sample sentences. In all scenarios, the neural network correctly learns and approximates the underlying structure by building successor representations. Furthermore, the resulting neural firing patterns are strikingly similar to experimentally observed place and grid cell firing patterns. We conclude that cognitive maps and neural network-based successor representations of structured knowledge provide a promising way to overcome some of the short comings of deep learning towards artificial general intelligence.

Construction of the rat brain spatial cell firing model on a quadruped robot

Physiological studies have shown that rats in a dark environment rely on the limbs and vestibule for their self-motion information, which can maintain the specific firing patterns of grid cells and hippocampal CA3 place cells. In the development stage of rats, grid cells are considered to come from place cells, and place cells can be encoded by hippocampal theta cells. Based on these, the quadruped robot is used as a platform in this paper. Firstly, the sensing information of the robot's limbs and inertial measurement unit is obtained to solve its position in the environment. Then the position information is encoded by theta cells and mapped to place cells through a neural network. After obtaining the place cells with single-peak firing fields, Hebb learning is used to adjust the connection weight of the neural network between place cells and grid cells. In order to verify the model, 3-D simulation experiments are designed in this paper. The experiment results show that with the robot exploring in space, the spatial cells firing effects obtained by the model are consistent with the physiological research facts, which lay the foundation for the bionic environmental cognition model.

Functional network topography of the medial entorhinal cortex

The medial entorhinal cortex (MEC) creates a map of local space, based on the firing patterns of grid, head-direction (HD), border, and object-vector (OV) cells. How these cell types are organized anatomically is debated. In-depth analysis of this question requires collection of precise anatomical and activity data across large populations of neurons during unrestrained behavior, which neither electrophysiological nor previous imaging methods fully afford. Here, we examined the topographic arrangement of spatially modulated neurons in the superficial layers of MEC and adjacent parasubiculum using miniaturized, portable two-photon microscopes, which allow mice to roam freely in open fields. Grid cells exhibited low levels of co-occurrence with OV cells and clustered anatomically, while border, HD, and OV cells tended to intermingle. These data suggest that grid cell networks might be largely distinct from those of border, HD, and OV cells and that grid cells exhibit strong coupling among themselves but weaker links to other cell types.

Effect of reward on electrophysiological signatures of grid cell population activity in human spatial navigation

The regular equilateral triangular periodic firing pattern of grid cells in the entorhinal cortex is considered a regular metric for the spatial world, and the grid-like representation correlates with hexadirectional modulation of theta (4–8 Hz) power in the entorhinal cortex relative to the moving direction. However, researchers have not clearly determined whether grid cells provide only simple spatial measures in human behavior-related navigation strategies or include other factors such as goal rewards to encode information in multiple patterns. By analysing the hexadirectional modulation of EEG signals in the theta band in the entorhinal cortex of patients with epilepsy performing spatial target navigation tasks, we found that this modulation presents a grid pattern that carries target-related reward information. This grid-like representation is influenced by explicit goals and is related to the local characteristics of the environment. This study provides evidence that human grid cell population activity is influenced by reward information at the level of neural oscillations.

Computational model of grid cells based on back‐propagation neural network

To simulate the firing pattern of biological Grid cells (GCs), an efficient computational model based on back-propagation neural network (BPNN), which allows for the generation of regular hexagonal grids, is described. For each GC, it is associated with the output of a learned BPNN. The firing characteristics of GCs can be controlled by the adjustment factors (AFs) flexibly. During the vehicle's space exploration, GCs can exhibit hexagonal firing patterns with different characteristics according to the settings of the AFs. Simulation results validate the proposed model's accuracy as they are in agreement with GCs' biological experimental electroencephalogram results. Meanwhile, the application of the three-layer BPNN can greatly reduce the computational complexity, which lay a foundation for its application in realistic bio-inspired autonomous navigation systems.

The broadband power shifts in entorhinal EEG are related to the firing of grid cells

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

Impaired speed encoding and grid cell periodicity in a mouse model of tauopathy.

Dementia is associated with severe spatial memory deficits which arise from dysfunction in hippocampal and parahippocampal circuits. For spatially sensitive neurons, such as grid cells, to faithfully represent the environment these circuits require precise encoding of direction and velocity information. Here, we have probed the firing rate coding properties of neurons in medial entorhinal cortex (MEC) in a mouse model of tauopathy. We find that grid cell firing patterns are largely absent in rTg4510 mice, while head-direction tuning remains largely intact. Conversely, neural representation of running speed information was significantly disturbed, with smaller proportions of MEC cells having firing rates correlated with locomotion in rTg4510 mice. Additionally, the power of local field potential oscillations in the theta and gamma frequency bands, which in wild-type mice are tightly linked to running speed, was invariant in rTg4510 mice during locomotion. These deficits in locomotor speed encoding likely severely impact path integration systems in dementia.

Advantages and detection of phase coding in the absence of rhythmicity.

The encoding of information in spike phase relative to local field potential (LFP) oscillations offers several theoretical advantages over equivalent firing rate codes. One notable example is provided by place and grid cells in the rodent hippocampal formation, which exhibit phase precession—firing at progressively earlier phases of the 6–12 Hz movement‐related theta rhythm as their spatial firing fields are traversed. It is often assumed that such phase coding relies on a high amplitude baseline oscillation with relatively constant frequency. However, sustained oscillations with fixed frequency are generally absent in LFP and spike train recordings from the human brain. Hence, we examine phase coding relative to LFP signals with broadband low‐frequency (2–20 Hz) power but without regular rhythmicity. We simulate a population of grid cells that exhibit phase precession against a baseline oscillation recorded from depth electrodes in human hippocampus. We show that this allows grid cell firing patterns to multiplex information about location, running speed and movement direction, alongside an arbitrary fourth variable encoded in LFP frequency. This is of particular importance given recent demonstrations that movement direction, which is essential for path integration, cannot be recovered from head direction cell firing rates. In addition, we investigate how firing phase might reduce errors in decoded location, including those arising from differences in firing rate across grid fields. Finally, we describe analytical methods that can identify phase coding in the absence of high amplitude LFP oscillations with approximately constant frequency, as in single unit recordings from the human brain and consistent with recent data from the flying bat. We note that these methods could also be used to detect phase coding outside of the spatial domain, and that multi‐unit activity can substitute for the LFP signal. In summary, we demonstrate that the computational advantages offered by phase coding are not contingent on, and can be detected without, regular rhythmicity in neural activity.

GNM: GridCell navigational model

It has been shown that grid cell firing patterns in the medial entorhinal cortex, can be used as a mapping reference for spatial navigation in mice and other mammalian species. In this paper, we propose a novel computational model for patterns of grid cells and combine it with a mechanism to tune the weights of cells, which we use to create a decision-making process for robot navigation. The method is used as an unsupervised method for uninformed online search with unknown goal positions and unknown environments, such as finding the exit out of a maze or help a robot to find its way in a jungle where there is no clue about the exit. The results of this approach in simulated and real environments show superior algorithmic steps over current search methods. In addition, the typical size of the memory can be reduced without compromising completeness of the method. Our results show that the number of steps is stable in terms of variations in memory allocations.

Deforming the metric of cognitive maps distorts memory.

Environmental boundaries anchor cognitive maps that support memory. However, trapezoidal boundary geometry distorts the regular firing patterns of entorhinal grid cells, proposedly providing a metric for cognitive maps. Here we test the impact of trapezoidal boundary geometry on human spatial memory using immersive virtual reality. Consistent with reduced regularity of grid patterns in rodents and a grid-cell model based on the eigenvectors of the successor representation, human positional memory was degraded in a trapezoid environment compared with a square environment-an effect that was particularly pronounced in the narrow part of the trapezoid. Congruent with changes in the spatial frequency of eigenvector grid patterns, distance estimates between remembered positions were persistently biased, revealing distorted memory maps that explained behaviour better than the objective maps. Our findings demonstrate that environmental geometry affects human spatial memory in a similar manner to rodent grid-cell activity and, therefore, strengthen the putative link between grid cells and behaviour along with their cognitive functions beyond navigation.

IMPAIRED NEURAL CODE OF SPATIAL INFORMATION IN A MOUSE MODEL OF TAU PATHOLOGY

Dementias are associated with severe spatial memory deficits which likely arises due to dysfunction in hippocampal and parahippocampal circuits. These circuits rely on precise encoding of directional and velocity information for spatially-sensitive neurons, such as grid cells in the medial entorhinal cortex (mEC), to faithfully represent the environment. In this study we examined the impact of tau pathology on the spatial coding properties of neurons in the mEC, using a well-studied transgenic mouse model of tauopathy, the rTg4510 mouse. We have used high density silicon probe electrode arrays to examine the local field potential (LFP) and firing rate coding properties of mEC neurons in male rTg4510 mice (7-8 month old), a mouse model of tauopathy which displays severe spatial memory deficits. Grid cell firing patterns were largely absent in rTg4510 mice, suggesting deficiencies in some, or all, of the information required for path integration. Interestingly, we find that head-direction cells, a key component of any path integration system, are largely intact. In contrast, representation of running speed is significantly disturbed in several ways. A significantly smaller proportion of mEC cells from rTg4510 mice display firing rates correlated with locomotion. Of those cells, a much greater proportion are negatively modulated. Finally, we show large scale changes to neuronal oscillations in rTg4510 mice, which in wildtype animals are tightly linked to running speed. Deficits in locomotor speed encoding are likely to severely impact the ability of animals to continuously update positional information and thus disrupt path integration systems in these mice and in dementia patients.

The up and down of localization

Neuroscience![Figure][1] Moving through the 3D world (in this case a brown rat climbing a bird feeder) requires constant readjustment in the brain. CREDIT: ALAN KEITH BEASTALL/ALAMY STOCK PHOTO Grid cells in the entorhinal cortex interact with place cells in the hippocampus to represent the current location of an animal. In the past, experiments were largely performed on rats running across horizontal surfaces. The real world, however, is three-dimensional. It is not known whether the reference plane for the grid cells is horizontal or an animal's locomotor plane. Casali et al. recorded from place and grid cells while rats moved across a flat surface or climbed up walls. The firing patterns of grid and place cells changed and constantly readjusted when the rat was climbing. Proc. Natl. Acad. Sci. U.S.A. 116 , 4631 (2019). [1]: pending:yes

Differential influences of environment and self-motion on place and grid cell firing

Place and grid cells in the hippocampal formation provide foundational representations of environmental location, and potentially of locations within conceptual spaces. Some accounts predict that environmental sensory information and self-motion are encoded in complementary representations, while other models suggest that both features combine to produce a single coherent representation. Here, we use virtual reality to dissociate visual environmental from physical motion inputs, while recording place and grid cells in mice navigating virtual open arenas. Place cell firing patterns predominantly reflect visual inputs, while grid cell activity reflects a greater influence of physical motion. Thus, even when recorded simultaneously, place and grid cell firing patterns differentially reflect environmental information (or ‘states’) and physical self-motion (or ‘transitions’), and need not be mutually coherent.

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.

Inhibitory Connectivity Dominates the Fan Cell Network in Layer II of Lateral Entorhinal Cortex.

Fan cells in layer II of the lateral entorhinal cortex (LEC) form a main component of the projection to the dentate gyrus, CA3 and CA2 of the hippocampal formation. This projection has a counterpart originating from stellate cells in layer II of the medial entorhinal cortex (MEC). Available evidence suggests that the two pathways carry different information, exemplified by a difference in spatial tuning of cells in LEC and MEC. The grid cell, a prominent position-modulated cell type present in MEC, has been postulated to derive its characteristic hexagonal firing pattern from dominant disynaptic inhibitory connections between hippocampal-projecting stellate cells. Given that grid cells have not been described in LEC, we aim to describe the local synaptic connectivity of fan cells, to explore whether the network architecture is similar to that of the MEC stellate cell. Using a combination of in vitro multicell electrophysiological and optogenetic approaches in acute slices from rodents of either sex, we show that excitatory connectivity between fan cells is very sparse. Fan cells connect preferentially with two distinct types of inhibitory interneurons, suggesting disynaptic inhibitory coupling as the main form of communication among fan cells. These principles are similar to those reported for stellate cells in MEC, indicating an overall comparable local circuit architecture of the main hippocampal-projecting cell types in the lateral and medial entorhinal cortex.SIGNIFICANCE STATEMENT Our data provide the first description of the synaptic microcircuit of hippocampal-projecting layer II cells in the lateral entorhinal cortex. We show that these cells make infrequent monosynaptic connections with each other, and that they preferentially communicate through a disynaptic inhibitory network. This is similar to the microcircuit of hippocampal-projecting stellate cells in layer II of the medial entorhinal cortex, but dissimilar to the connectivity observed in layer 2 of neocortex. In medial entorhinal cortex, the observed network structure has been proposed to underlie the firing pattern of grid cells. This opens the possibility that layer II cells in lateral entorhinal cortex exhibit regular firing patterns in an unexplored domain.

Spatial cell firing during virtual navigation of open arenas by head-restrained mice

We present a mouse virtual reality (VR) system which restrains head-movements to horizontal rotations, compatible with multi-photon imaging. This system allows expression of the spatial navigation and neuronal firing patterns characteristic of real open arenas (R). Comparing VR to R: place and grid, but not head-direction, cell firing had broader spatial tuning; place, but not grid, cell firing was more directional; theta frequency increased less with running speed, whereas increases in firing rates with running speed and place and grid cells' theta phase precession were similar. These results suggest that the omni-directional place cell firing in R may require local-cues unavailable in VR, and that the scale of grid and place cell firing patterns, and theta frequency, reflect translational motion inferred from both virtual (visual and proprioceptive) and real (vestibular translation and extra-maze) cues. By contrast, firing rates and theta phase precession appear to reflect visual and proprioceptive cues alone.

Modulating medial septal cholinergic activity reduces medial entorhinal theta frequency without affecting speed or grid coding

Medial septal inputs to the hippocampal system are crucial for aspects of temporal and spatial processing, such as theta oscillations and grid cell firing. However, the precise contributions of the medial septum’s cholinergic neurones to these functions remain unknown. Here, we recorded neuronal firing and local field potentials from the medial entorhinal cortex of freely foraging mice, while modulating the excitability of medial septal cholinergic neurones. Alteration of cholinergic activity produced a reduction in the frequency of theta oscillations, without affecting the slope of the non-linear theta frequency vs running speed relationship observed. Modifying septal cholinergic tone in this way also led mice to exhibit behaviours associated with novelty or anxiety. However, grid cell firing patterns were unaffected, concordant with an absence of change in the slopes of the theta frequency and firing rate speed signals thought to be used by grid cells.

An Analysis of Waves Underlying Grid Cell Firing in the Medial Enthorinal Cortex

Layer II stellate cells in the medial enthorinal cortex (MEC) express hyperpolarisation-activated cyclic-nucleotide-gated (HCN) channels that allow for rebound spiking via an I_{text{h}} current in response to hyperpolarising synaptic input. A computational modelling study by Hasselmo (Philos. Trans. R. Soc. Lond. B, Biol. Sci. 369:20120523, 2013) showed that an inhibitory network of such cells can support periodic travelling waves with a period that is controlled by the dynamics of the I_{text{h}} current. Hasselmo has suggested that these waves can underlie the generation of grid cells, and that the known difference in I_{text{h}} resonance frequency along the dorsal to ventral axis can explain the observed size and spacing between grid cell firing fields. Here we develop a biophysical spiking model within a framework that allows for analytical tractability. We combine the simplicity of integrate-and-fire neurons with a piecewise linear caricature of the gating dynamics for HCN channels to develop a spiking neural field model of MEC. Using techniques primarily drawn from the field of nonsmooth dynamical systems we show how to construct periodic travelling waves, and in particular the dispersion curve that determines how wave speed varies as a function of period. This exhibits a wide range of long wavelength solutions, reinforcing the idea that rebound spiking is a candidate mechanism for generating grid cell firing patterns. Importantly we develop a wave stability analysis to show how the maximum allowed period is controlled by the dynamical properties of the I_{text{h}} current. Our theoretical work is validated by numerical simulations of the spiking model in both one and two dimensions.

Excitatory Microcircuits within Superficial Layers of the Medial Entorhinal Cortex

The distinctive firing pattern of grid cells in the medial entorhinal cortex (MEC) supports its role in the representation of space. It is widely believed that the hexagonal firing field of grid cells emerges from neural dynamics that depend on the local microcircuitry. However, local networks within the MEC are still not sufficiently characterized. Here, applying up to eight simultaneous whole-cell recordings in acute brain slices, we demonstrate the existence of unitary excitatory connections between principal neurons in the superficial layers of the MEC. In particular, we find prevalent feed-forward excitation from pyramidal neurons in layer III and layer II onto stellate cells in layer II, which might contribute to the generation or the inheritance of grid cell patterns.