Spatial Coding Dysfunction and Network Instability in the Aging Medial Entorhinal Cortex

Across species, spatial memory declines with age, possibly reflecting altered hippocampal and medial entorhinal cortex (MEC) function. However, the integrity of cellular and network-level spatial coding in aged MEC is unknown. Here, we leveraged in vivo electrophysiology to assess MEC function in young, middle-aged, and aged mice navigating virtual environments. In aged grid cells, we observed impaired stabilization of context-specific spatial firing, correlated with spatial memory deficits. Additionally, aged grid networks shifted firing patterns often but with poor alignment to context changes. Aged spatial firing was also unstable in an unchanging environment. In these same mice, we identified 458 genes differentially expressed with age in MEC, 61 of which had expression correlated with spatial firing stability. These genes were enriched among interneurons and related to synaptic transmission. Together, these findings identify coordinated transcriptomic, cellular, and network changes in MEC implicated in impaired spatial memory in aging.

Comparison of head direction cell firing characteristics across thalamo-parahippocampal circuitry

Head direction (HD) cells, which fire persistently when an animal's head is pointed in a particular direction, are widely thought to underlie an animal's sense of spatial orientation and have been identified in several limbic brain regions. Robust HD cell firing is observed throughout the thalamo-parahippocampal system, although recent studies report that parahippocampal HD cells exhibit distinct firing properties, including conjunctive aspects with other spatial parameters, which suggest they play a specialized role in spatial processing. Few studies, however, have quantified these apparent differences. Here, we performed a comparative assessment of HD cell firing characteristics across the anterior dorsal thalamus (ADN), postsubiculum (PoS), parasubiculum (PaS), medial entorhinal (MEC), and postrhinal (POR) cortices. We report that HD cells with a high degree of directional specificity were observed in all five brain regions, but ADN HD cells display greater sharpness and stability in their preferred directions, and greater anticipation of future headings compared to parahippocampal regions. Additional analysis indicated that POR HD cells were more coarsely modulated by other spatial parameters compared to PoS, PaS, and MEC. Finally, our analyses indicated that the sharpness of HD tuning decreased as a function of laminar position and conjunctive coding within the PoS, PaS, and MEC, with cells in the superficial layers along with conjunctive firing properties showing less robust directional tuning. The results are discussed in relation to theories of functional organization of HD cell tuning in thalamo-parahippocampal circuitry.

Task-anchored grid cell firing is selectively associated with successful path integration-dependent behaviour

Grid firing fields have been proposed as a neural substrate for spatial localisation in general or for path integration in particular. To distinguish these possibilities, we investigate firing of grid and non-grid cells in the mouse medial entorhinal cortex during a location memory task. We find that grid firing can either be anchored to the task environment, or can encode distance travelled independently of the task reference frame. Anchoring varied between and within sessions, while spatial firing of non-grid cells was either coherent with the grid population, or was stably anchored to the task environment. We took advantage of the variability in task-anchoring to evaluate whether and when encoding of location by grid cells might contribute to behaviour. We find that when reward location is indicated by a visual cue, performance is similar regardless of whether grid cells are task-anchored or not, arguing against a role for grid representations when location cues are available. By contrast, in the absence of the visual cue, performance was enhanced when grid cells were anchored to the task environment. Our results suggest that anchoring of grid cells to task reference frames selectively enhances performance when path integration is required.

Spontaneous Dynamics of Hippocampal Place Fields in a Model of Combinatorial Competition among Stable Inputs

We present computer simulations illustrating how the plastic integration of spatially stable inputs could contribute to the dynamic character of hippocampal spatial representations. In novel environments of slightly larger size than typical apparatus, the emergence of well-defined place fields in real place cells seems to rely on inputs from normally functioning grid cells. Theoretically, the grid-to-place transformation is possible if a place cell is able to respond selectively to a combination of suitably aligned grids. We previously identified the functional characteristics that allow a synaptic plasticity rule to accomplish this selection by synaptic competition during rat foraging behavior. Here, we show that the synaptic competition can outlast the formation of place fields, contributing to their spatial reorganization over time, when the model is run in larger environments and the topographical/modular organization of grid inputs is taken into account. Co-simulated cells that differ only by their randomly assigned grid inputs display different degrees and kinds of spatial reorganization-ranging from place-field remapping to more subtle in-field changes or lapses in firing. The model predicts a greater number of place fields and propensity for remapping in place cells recorded from more septal regions of the hippocampus and/or in larger environments, motivating future experimental standardization across studies and animal models. In sum, spontaneous remapping could arise from rapid synaptic learning involving inputs that are functionally homogeneous, spatially stable, and minimally stochastic.

Grid cells: the missing link in understanding Parkinson's disease?

The mechanisms underlying Parkinson's disease (PD) are complex and not fully understood, and the box-and-arrow model among other current models present significant challenges. This paper explores the potential role of the allocentric brain and especially its grid cells in several PD motor symptoms, including bradykinesia, kinesia paradoxa, freezing of gait, the bottleneck phenomenon, and their dependency on cueing. It is argued that central hubs, like the locus coeruleus and the pedunculopontine nucleus, often narrowly interpreted in the context of PD, play an equally important role in governing the allocentric brain as the basal ganglia. Consequently, the motor and secondary motor (e.g., spatially related) symptoms of PD linked with dopamine depletion may be more closely tied to erroneous computation by grid cells than to the basal ganglia alone. Because grid cells and their associated central hubs introduce both spatial and temporal information to the brain influencing velocity perception they may cause bradykinesia or hyperkinesia as well. In summary, PD motor symptoms may primarily be an allocentric disturbance resulting from virtual faulty computation by grid cells revealed by dopamine depletion in PD.

Beyond correlation: optimal transport metrics for characterizing representational stability and remapping in neurons encoding spatial memory

Introduction

Spatial representations in the entorhinal cortex (EC) and hippocampus (HPC) are fundamental to cognitive functions like navigation and memory. These representations, embodied in spatial field maps, dynamically remap in response to environmental changes. However, current methods, such as Pearson's correlation coefficient, struggle to capture the complexity of these remapping events, especially when fields do not overlap, or transformations are non-linear. This limitation hinders our understanding and quantification of remapping, a key aspect of spatial memory function.

Methods

We propose a family of metrics based on the Earth Mover's Distance (EMD) as a versatile framework for characterizing remapping.

Results

The EMD provides a granular, noise-resistant, and rate-robust description of remapping. This approach enables the identification of specific cell types and the characterization of remapping in various scenarios, including disease models. Furthermore, the EMD's properties can be manipulated to identify spatially tuned cell types and to explore remapping as it relates to alternate information forms such as spatiotemporal coding.

Discussion

We present a feasible, lightweight approach that complements traditional methods. Our findings underscore the potential of the EMD as a powerful tool for enhancing our understanding of remapping in the brain and its implications for spatial navigation, memory studies and beyond.

Beyond Correlation: Optimal Transport Metrics For Characterizing Representational Stability and Remapping in Neurons Encoding Spatial Memory

Spatial representations in the entorhinal cortex (EC) and hippocampus (HPC) are fundamental to cognitive functions like navigation and memory. These representations, embodied in spatial field maps, dynamically remap in response to environmental changes. However, current methods, such as Pearson's correlation coefficient, struggle to capture the complexity of these remapping events, especially when fields do not overlap, or transformations are non-linear. This limitation hinders our understanding and quantification of remapping, a key aspect of spatial memory function. To address this, we propose a family of metrics based on the Earth Mover's Distance (EMD) as a versatile framework for characterizing remapping. Applied to both normalized and unnormalized distributions, the EMD provides a granular, noise-resistant, and rate-robust description of remapping. This approach enables the identification of specific cell types and the characterization of remapping in various scenarios, including disease models. Furthermore, the EMD's properties can be manipulated to identify spatially tuned cell types and to explore remapping as it relates to alternate information forms such as spatiotemporal coding. By employing approximations of the EMD, we present a feasible, lightweight approach that complements traditional methods. Our findings underscore the potential of the EMD as a powerful tool for enhancing our understanding of remapping in the brain and its implications for spatial navigation, memory studies and beyond.

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.

Empirically validated theoretical analysis of visual-spatial perception under change of nervous system arousal

Introduction

Visual-spatial perception is a process for extracting the spatial relationship between objects in the environment. The changes in visual-spatial perception due to factors such as the activity of the sympathetic nervous system (hyperactivation) or parasympathetic nervous system (hypoactivation) can affect the internal representation of the external visual-spatial world. We formulated a quantitative model of the modulation of visual-perceptual space under action by hyperactivation or hypoactivation-inducing neuromodulating agents. We showed a Hill equation based relationship between neuromodulator agent concentration and alteration of visual-spatial perception utilizing the metric tensor to quantify the visual space.

Methods

We computed the dynamics of the psilocybin (hyperactivation-inducing agent) and chlorpromazine (hypoactivation-inducing agent) in brain tissue. Then, we validated our quantitative model by analyzing the findings of different independent behavioral studies where subjects were assessed for alterations in visual-spatial perception under the action of psilocybin and under chlorpromazine. To validate the neuronal correlates, we simulated the effect of the neuromodulating agent on the computational model of the grid-cell network, and also performed diffusion MRI-based tractography to find the neural tracts between the cortical areas involved: V2 and the entorhinal cortex.

Results

We applied our computational model to an experiment (where perceptual alterations were measured under psilocybin) and found that for n (Hill-coefficient) = 14.8 and k = 1.39, the theoretical prediction followed experimental observations very well (χ2 test robustly satisfied, p > 0.99). We predicted the outcome of another psilocybin-based experiment using these values (n = 14.8 and k = 1.39), whereby our prediction and experimental outcomes were well corroborated. Furthermore, we found that also under hypoactivation (chlorpromazine), the modulation of the visual-spatial perception follows our model. Moreover, we found neural tracts between the area V2 and entorhinal cortex, thus providing a possible brain network responsible for encoding visual-spatial perception. Thence, we simulated the altered grid-cell network activity, which was also found to follow the Hill equation.

Conclusion

We developed a computational model of visuospatial perceptual alterations under altered neural sympathetic/parasympathetic tone. We validated our model using analysis of behavioral studies, neuroimaging assessment, and neurocomputational evaluation. Our quantitative approach may be probed as a potential behavioral screening and monitoring methodology in neuropsychology to analyze perceptual misjudgment and mishaps by highly stressed workers.

Improved Visual Recognition Memory Model Based on Grid Cells for Face Recognition

Traditional facial recognition methods depend on a large number of training samples due to the massive turning of synaptic weights for low-level feature extractions. In prior work, a brain-inspired model of visual recognition memory suggested that grid cells encode translation saccadic eye movement vectors between salient stimulus features. With a small training set for each recognition type, the relative positions among the selected features for each image were represented using grid and feature label cells in Hebbian learning. However, this model is suitable only for the recognition of familiar faces, objects, and scenes. The model's performance for a given face with unfamiliar facial expressions was unsatisfactory. In this study, an improved computational model via grid cells for facial recognition was proposed. Here, the initial hypothesis about stimulus identity was obtained using the histograms of oriented gradients (HOG) algorithm. The HOG descriptors effectively captured the sample edge or gradient structure features. Thus, most test samples were successfully recognized within three saccades. Moreover, the probability of a false hypothesis and the average fixations for successful recognition were reduced. Compared with other neural network models, such as convolutional neural networks and deep belief networks, the proposed method shows the best performance with only one training sample for each face. Moreover, it is robust against image occlusion and size variance or scaling. Our results may give insight for efficient recognition with small training samples based on neural networks.

A Plane-Dependent Model of 3D Grid Cells for Representing Both 2D and 3D Spaces Under Various Navigation Modes

Grid cells are crucial in path integration and representation of the external world. The spikes of grid cells spatially form clusters called grid fields, which encode important information about allocentric positions. To decode the information, studying the spatial structures of grid fields is a key task for both experimenters and theorists. Experiments reveal that grid fields form hexagonal lattice during planar navigation, and are anisotropic beyond planar navigation. During volumetric navigation, they lose global order but possess local order. How grid cells form different field structures behind these different navigation modes remains an open theoretical question. However, to date, few models connect to the latest discoveries and explain the formation of various grid field structures. To fill in this gap, we propose an interpretive plane-dependent model of three-dimensional (3D) grid cells for representing both two-dimensional (2D) and 3D space. The model first evaluates motion with respect to planes, such as the planes animals stand on and the tangent planes of the motion manifold. Projection of the motion onto the planes leads to anisotropy, and error in the perception of planes degrades grid field regularity. A training-free recurrent neural network (RNN) then maps the processed motion information to grid fields. We verify that our model can generate regular and anisotropic grid fields, as well as grid fields with merely local order; our model is also compatible with mode switching. Furthermore, simulations predict that the degradation of grid field regularity is inversely proportional to the interval between two consecutive perceptions of planes. In conclusion, our model is one of the few pioneers that address grid field structures in a general case. Compared to the other pioneer models, our theory argues that the anisotropy and loss of global order result from the uncertain perception of planes rather than insufficient training.

Burst activity plays no role in the field-to-field variability and rate remapping of grid cells

Grid cells in rodent medial entorhinal cortex are thought to play a key role for spatial navigation. When the animal is freely moving in an open arena the firing fields of each grid cell tend to form a highly regular, hexagonal lattice spanning the environment. However, firing rates vary from field to field and change under contextual modifications, whereas the field locations shift at most by a small amount under such "rate remapping." The observed differences in firing rate could reflect overall activity changes or changes in the detailed spike-train statistics. As these two alternatives imply distinct neural coding schemes, we investigated whether temporal firing patterns vary from field to field and whether they change under rate remapping. Focusing on short time scales, we found that the proportion of bursts compared to all discharge events is similar in all firing fields of a given grid cell and does not change under rate remapping. For each cell, mean firing rates with bursts are proportional to mean firing rates without bursts. However, this ratio varies across cells. Additionally, we looked at how rate remapping relates to entorhinal theta-frequency oscillations. Theta-phase coding was preserved despite firing-rate changes from rate remapping but we did not observe differences between the first and second half of the theta cycle, as had been reported for CA1. Our results indicate that both, the heterogeneity between firing fields and rate remapping, are not due to altered firing patterns on short time scales but reflect location-specific changes at the firing-rate level.

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.

Multi-Scale Extension in an Entorhinal-Hippocampal Model for Cognitive Map Building

Neuroscience research shows that, by relying on internal spatial representations provided by the hippocampus and entorhinal cortex, mammals are able to build topological maps of environments and navigate. Taking inspiration from mammals' spatial cognition mechanism, entorhinal-hippocampal cognitive systems have been proposed for robots to build cognitive maps. However, path integration and vision processing are time-consuming, and the existing model of grid cells is hard to achieve in terms of adaptive multi-scale extension for different environments, resulting in the lack of viability for real environments. In this work, an optimized dynamical model of grid cells is built for path integration in which recurrent weight connections between grid cells are parameterized in a more optimized way and the non-linearity of sigmoidal neural transfer function is utilized to enhance grid cell activity packets. Grid firing patterns with specific spatial scales can thus be accurately achieved for the multi-scale extension of grid cells. In addition, a hierarchical vision processing mechanism is proposed for speeding up loop closure detection. Experiment results on the robotic platform demonstrate that our proposed entorhinal-hippocampal model can successfully build cognitive maps, reflecting the robot's spatial experience and environmental topological structures.

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.

[A grid field calculation model based on perceived speed and perceived angle]

The method of directly using speed information and angle information to drive attractors model of grid cells to encode environment has poor anti-interference ability and is not bionic. In response to the problem, this paper proposes a grid field calculation model based on perceived speed and perceived angle. The model has the following characteristics. Firstly, visual stream is decoded to obtain visual speed, and speed cell is modeled and decoded to obtain body speed. Visual speed and body speed are integrated to obtain perceived speed information. Secondly, a one-dimensional circularly connected cell model with excitatory connection is used to simulate the firing mechanism of head direction cells, so that the robot obtains current perception angle information in a biomimetic manner. Finally, the two kinds of perceptual information of speed and angle are combined to realize the driving of grid cell attractors model. The proposed model was experimentally verified. The results showed that this model could realize periodic hexagonal firing field mode of grid cells and precise path integration function. The proposed algorithm may provide a foundation for the research on construction method of robot cognitive map based on hippocampal cognition mechanism.

A Generalized Linear Model of a Navigation Network

Navigation by mammals is believed to rely on a network of neurons in the hippocampal formation, which includes the hippocampus, the medial entorhinal cortex (MEC), and additional nearby regions. Neurons in these regions represent spatial information by tuning to the position, orientation, and speed of the animal in the form of head direction cells, speed cells, grid cells, border cells, and unclassified spatially modulated cells. While the properties of single cells are well studied, little is known about the functional structure of the network in the MEC. Here, we use a generalized linear model to study the network of spatially modulated cells in the MEC. We found connectivity patterns between all spatially encoding cells and not only grid cells. In addition, the neurons’ past activity contributed to the overall activity patterns. Finally, position-modulated cells and head direction cells differed in the dependence of the activity on the history. Our results indicate that MEC neurons form a local interacting network to support spatial information representations and suggest an explanation for their complex temporal properties.

Home, head direction stability, and grid cell distortion

The home is a unique location in the life of humans and animals. In rats, home presents itself as a multicompartmental space that involves integrating navigation through subspaces. Here we embedded the laboratory rat’s home cage in the arena, while recording neurons in the animal’s parasubiculum and medial entorhinal cortex, two brain areas encoding the animal’s location and head direction. We found that head direction signals were unaffected by home cage presence or translocation. Head direction cells remain globally stable and have similar properties inside and outside the embedded home. We did not observe egocentric bearing encoding of the home cage. However, grid cells were distorted in the presence of the home cage. While they did not globally remap, single firing fields were translocated toward the home. These effects appeared to be geometrical in nature rather than a home-specific distortion and were not dependent on explicit behavioral use of the home cage during a hoarding task. Our work suggests that medial entorhinal cortex and parasubiculum do not remap after embedding the home, but local changes in grid cell activity overrepresent the embedded space location and might contribute to navigation in complex environments.

NEW & NOTEWORTHY Neural findings in the field of spatial navigation come mostly from an abstract approach that separates the animal from even a minimally biological context. In this article we embed the home cage of the rat in the environment to address some of the complexities of natural navigation. We find no explicit home cage representation. While both head direction cells and grid cells remain globally stable, we find that embedded spaces locally distort grid cells.

Untethered firing fields and intermittent silences: Why grid-cell discharge is so variable

Grid cells in medial entorhinal cortex are notoriously variable in their responses, despite the striking hexagonal arrangement of their spatial firing fields. Indeed, when the animal moves through a firing field, grid cells often fire much more vigorously than predicted or do not fire at all. The source of this trial-to-trial variability is not completely understood. By analyzing grid-cell spike trains from mice running in open arenas and on linear tracks, we characterize the phenomenon of "missed" firing fields using the statistical theory of zero inflation. We find that one major cause of grid-cell variability lies in the spatial representation itself: firing fields are not as strongly anchored to spatial location as the averaged grid suggests. In addition, grid fields from different cells drift together from trial to trial, regardless of whether the environment is real or virtual, or whether the animal moves in light or darkness. Spatial realignment across trials sharpens the grid representation, yielding firing fields that are more pronounced and significantly narrower. These findings indicate that ensembles of grid cells encode relative position more reliably than absolute position.

Identifying Core Regions for Path Integration on Medial Entorhinal Cortex of Hippocampal Formation

Path integration is one of the functions that support the self-localization ability of animals. Path integration outputs position information after an animal’s movement when initial-position and movement information is input. The core region responsible for this function has been identified as the medial entorhinal cortex (MEC), which is part of the hippocampal formation that constitutes the limbic system. However, a more specific core region has not yet been identified. This research aims to clarify the detailed structure at the cell-firing level in the core region responsible for path integration from fragmentarily accumulated experimental and theoretical findings by reviewing 77 papers. This research draws a novel diagram that describes the MEC, the hippocampus, and their surrounding regions by focusing on the MEC’s input/output (I/O) information. The diagram was created by summarizing the results of exhaustively scrutinizing the papers that are relative to the I/O relationship, the connection relationship, and cell position and firing pattern. From additional investigations, we show function information related to path integration, such as I/O information and the relationship between multiple functions. Furthermore, we constructed an algorithmic hypothesis on I/O information and path-integration calculation method from the diagram and the information of functions related to path integration. The algorithmic hypothesis is composed of regions related to path integration, the I/O relations between them, the calculation performed there, and the information representations (cell-firing pattern) in them. Results of examining the hypothesis confirmed that the core region responsible for path integration was either stellate cells in layer II or pyramidal cells in layer III of the MEC.

Replay as wavefronts and theta sequences as bump oscillations in a grid cell attractor network

Grid cells fire in sequences that represent rapid trajectories in space. During locomotion, theta sequences encode sweeps in position starting slightly behind the animal and ending ahead of it. During quiescence and slow wave sleep, bouts of synchronized activity represent long trajectories called replays, which are well-established in place cells and have been recently reported in grid cells. Theta sequences and replay are hypothesized to facilitate many cognitive functions, but their underlying mechanisms are unknown. One mechanism proposed for grid cell formation is the continuous attractor network. We demonstrate that this established architecture naturally produces theta sequences and replay as distinct consequences of modulating external input. Driving inhibitory interneurons at the theta frequency causes attractor bumps to oscillate in speed and size, which gives rise to theta sequences and phase precession, respectively. Decreasing input drive to all neurons produces traveling wavefronts of activity that are decoded as replays.

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.

Environmental Barriers Disrupt Grid-like Representations in Humans during Navigation

Environmental barriers fundamentally shape our behavior and conceptualization of space [1-5]. Evidence from rodents suggests that, in contrast to an open-field environment, where grid cells exhibit firing patterns with a 6-fold rotational symmetry [5, 6], barriers within the field abolish the 6-fold symmetry and fragment the grid firing fields into compartmentalized repeating "submaps" [5]. These results suggest that barriers may exert their influence on the cognitive map through organization of the metric representation of space provided by entorhinal neurons. We directly tested this hypothesis in humans, combining functional MRI with a virtual navigation paradigm in which we manipulated the local barrier structure. When participants performed a fixed-route foraging task in an open field, the functional MRI signal in right entorhinal cortex exhibited a 6-fold periodic modulation by movement direction associated with conjunctive grid cell firing [7]. However, when environments were compartmentalized by barriers, the grid-like 6-fold spatial metric was abolished. Instead, a 4-fold modulation of the entorhinal signal was observed, consistent with a vectorized organization of spatial metrics predicted by rodent models of navigation [5]. Collectively, these results provide mechanistic insight into why barriers compartmentalize our cognitive map, indicating that boundaries exert a powerful influence on the way environments are represented in human entorhinal cortex. Given that our daily environments are rarely wide open and are often segmented by barriers (e.g., the buildings of our home city), our findings have implications for applying models of cognitive mapping based on grid-like metrics [8] to naturalistic circumstances.

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.

A Framework for Intelligence and Cortical Function Based on Grid Cells in the Neocortex

How the neocortex works is a mystery. In this paper we propose a novel framework for understanding its function. Grid cells are neurons in the entorhinal cortex that represent the location of an animal in its environment. Recent evidence suggests that grid cell-like neurons may also be present in the neocortex. We propose that grid cells exist throughout the neocortex, in every region and in every cortical column. They define a location-based framework for how the neocortex functions. Whereas grid cells in the entorhinal cortex represent the location of one thing, the body relative to its environment, we propose that cortical grid cells simultaneously represent the location of many things. Cortical columns in somatosensory cortex track the location of tactile features relative to the object being touched and cortical columns in visual cortex track the location of visual features relative to the object being viewed. We propose that mechanisms in the entorhinal cortex and hippocampus that evolved for learning the structure of environments are now used by the neocortex to learn the structure of objects. Having a representation of location in each cortical column suggests mechanisms for how the neocortex represents object compositionality and object behaviors. It leads to the hypothesis that every part of the neocortex learns complete models of objects and that there are many models of each object distributed throughout the neocortex. The similarity of circuitry observed in all cortical regions is strong evidence that even high-level cognitive tasks are learned and represented in a location-based framework.

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.

A Map-like Micro-Organization of Grid Cells in the Medial Entorhinal Cortex

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

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].

Stability of medial entorhinal cortex representations over time

Distinct functional cell types in the medial entorhinal cortex (mEC) have been shown to represent different aspects of experiences. To further characterize mEC cell populations, we examined whether spatial representations of neurons in mEC superficial layers depended on the scale of the environment and changed over extended time periods. Accordingly, mEC cells were recorded while rats repeatedly foraged in a small or a large environment in sessions that were separated by time intervals from minutes to hours. Comparing between large and small environments, we found that the overall precision of grid and non-grid cell spatial maps was higher in smaller environments. When examining the stability of spatial firing patterns over time, differences and similarities were observed across cell types. Within-session stability was higher for grid cells than for non-grid cell populations. Despite differences in baseline stability between cell types, stability levels remained consistent over time between sessions, up to 1 hr. Even for sessions separated by 6 hrs, activity patterns of grid cells and of most non-grid cells lacked any systematic decrease in spatial similarity over time. However, a subset of ~15% of mEC non-grid cells recorded preferentially from layer III exhibited dramatic, time dependent changes in firing patterns across 6 hrs, reminiscent of previous characterizations of the hippocampal CA2 subregion. Collectively, our data suggest that mEC grid cell input to hippocampus in conjunction with many time invariant non-grid cells may aid in stabilizing hippocampal spatial maps, while a subset of time varying non-grid cells could provide complementary temporal information.

Human spatial representation: what we cannot learn from the studies of rodent navigation

Studies of human and rodent navigation often reveal a remarkable cross-species similarity between the cognitive and neural mechanisms of navigation. Such cross-species resemblance often overshadows some critical differences between how humans and nonhuman animals navigate. In this review, I propose that a navigation system requires both a storage system (i.e., representing spatial information) and a positioning system (i.e., sensing spatial information) to operate. I then argue that the way humans represent spatial information is different from that inferred from the cellular activity observed during rodent navigation. Such difference spans the whole hierarchy of spatial representation, from representing the structure of an environment to the representation of subregions of an environment, routes and paths, and the distance and direction relative to a goal location. These cross-species inconsistencies suggest that what we learn from rodent navigation does not always transfer to human navigation. Finally, I argue for closing the loop for the dominant, unidirectional animal-to-human approach in navigation research so that insights from behavioral studies of human navigation may also flow back to shed light on the cellular mechanisms of navigation for both humans and other mammals (i.e., a human-to-animal approach).

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.

Neurons in Primate Entorhinal Cortex Represent Gaze Position in Multiple Spatial Reference Frames

Primates rely predominantly on vision to gather information from the environment and neurons representing visual space and gaze position are found in many brain areas. Within the medial temporal lobe, a brain region critical for memory, neurons in the entorhinal cortex of macaque monkeys exhibit spatial selectivity for gaze position. Specifically, the firing rate of single neurons reflects fixation location within a visual image (Killian et al., 2012). In the rodents, entorhinal cells such as grid cells, border cells, and head direction cells show spatial representations aligned to visual environmental features instead of the body (Hafting et al., 2005; Sargolini et al., 2006; Solstad et al., 2008; Diehl et al., 2017). However, it is not known whether similar allocentric representations exist in primate entorhinal cortex. Here, we recorded neural activity in the entorhinal cortex in two male rhesus monkeys during a naturalistic, free-viewing task. Our data reveal that a majority of entorhinal neurons represent gaze position and that simultaneously recorded neurons represent gaze position relative to distinct spatial reference frames, with some neurons aligned to the visual image and others aligned to the monkey's head position. Our results also show that entorhinal neural activity can be used to predict gaze position with a high degree of accuracy. These findings demonstrate that visuospatial representation is a fundamental property of entorhinal neurons in primates and suggest that entorhinal cortex may support relational memory and motor planning by coding attentional locus in distinct, behaviorally relevant frames of reference.SIGNIFICANCE STATEMENT The entorhinal cortex, a brain area important for memory, shows striking spatial activity in rodents through grid cells, border cells, head direction cells, and nongrid spatial cells. The majority of entorhinal neurons signal the location of a rodent relative to visual environmental cues, representing the location of the animal relative to space in the world instead of the body. Recently, we found that entorhinal neurons can signal location of gaze while a monkey explores images visually. Here, we report that spatial entorhinal neurons are widespread in the monkey and these neurons are capable of showing a world-based spatial reference frame locked to the bounds of explored images. These results help connect the extensive findings in rodents to the primate.

Hippocampal Remapping and Its Entorhinal Origin

The activity of hippocampal cell ensembles is an accurate predictor of the position of an animal in its surrounding space. One key property of hippocampal cell ensembles is their ability to change in response to alterations in the surrounding environment, a phenomenon called remapping. In this review article, we present evidence for the distinct types of hippocampal remapping. The progressive divergence over time of cell ensembles active in different environments and the transition dynamics between pre-established maps are discussed. Finally, we review recent work demonstrating that hippocampal remapping can be triggered by neurons located in the entorhinal cortex.

Task Demands Predict a Dynamic Switch in the Content of Awake Hippocampal Replay

Reactivation of hippocampal place cell sequences during behavioral immobility and rest has been linked with both memory consolidation and navigational planning. Yet it remains to be investigated whether these functions are temporally segregated, occurring during different behavioral states. During a self-paced spatial task, awake hippocampal replay occurring either immediately before movement toward a reward location or just after arrival at a reward location preferentially involved cells consistent with the current trajectory. In contrast, during periods of extended immobility, no such biases were evident. Notably, the occurrence of task-focused reactivations predicted the accuracy of subsequent spatial decisions. Additionally, during immobility, but not periods preceding or succeeding movement, grid cells in deep layers of the entorhinal cortex replayed coherently with the hippocampus. Thus, hippocampal reactivations dynamically and abruptly switch between operational modes in response to task demands, plausibly moving from a state favoring navigational planning to one geared toward memory consolidation.

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.

Place and Grid Cells in a Loop: Implications for Memory Function and Spatial Coding

Place cells in the hippocampus and grid cells in the medial entorhinal cortex have different codes for space. However, how one code relates to the other is ill understood. Based on the anatomy of the entorhinal-hippocampal circuitry, we constructed a model of place and grid cells organized in a loop to investigate their mutual influence in the establishment of their codes for space. Using computer simulations, we first replicated experiments in rats that measured place and grid cell activity in different environments, and then assessed which features of the model account for different phenomena observed in neurophysiological data, such as pattern completion and pattern separation, global and rate remapping of place cells, and realignment of grid cells. We found that (1) the interaction between grid and place cells converges quickly; (2) the spatial code of place cells does not require, but is altered by, grid cell input; (3) plasticity in sensory inputs to place cells is key for pattern completion but not pattern separation; (4) grid realignment can be explained in terms of place cell remapping as opposed to the other way around; (5) the switch between global and rate remapping is self-organized; and (6) grid cell input to place cells helps stabilize their code under noisy and/or inconsistent sensory input. We conclude that the hippocampus-entorhinal circuit uses the mutual interaction of place and grid cells to encode the surrounding environment and propose a theory on how such interdependence underlies the formation and use of the cognitive map.SIGNIFICANCE STATEMENT The mammalian brain implements a positional system with two key pieces: place and grid cells. To gain insight into the dynamics of place and grid cell interaction, we built a computational model with the two cell types organized in a loop. The proposed model accounts for differences in how place and grid cells represent different environments and provides a new interpretation in which place and grid cells mutually interact to form a coupled code for space.

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.

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.

Physiological Properties of Neurons in Bat Entorhinal Cortex Exhibit an Inverse Gradient along the Dorsal-Ventral Axis Compared to Entorhinal Neurons in Rat

Medial entorhinal cortex (MEC) grid cells exhibit firing fields spread across the environment on the vertices of a regular tessellating triangular grid. In rodents, the size of the firing fields and the spacing between the firing fields are topographically organized such that grid cells located more ventrally in MEC exhibit larger grid fields and larger grid-field spacing compared with grid cells located more dorsally. Previous experiments in brain slices from rodents have shown that several intrinsic cellular electrophysiological properties of stellate cells in layer II of MEC change systematically in neurons positioned along the dorsal-ventral axis of MEC, suggesting that these intrinsic cellular properties might control grid-field spacing. In the bat, grid cells in MEC display a functional topography in terms of grid-field spacing, similar to what has been reported in rodents. However, it is unclear whether neurons in bat MEC exhibit similar gradients of cellular physiological properties, which may serve as a conserved mechanism underlying grid-field spacing in mammals. To test whether entorhinal cortex (EC) neurons in rats and bats exhibit similar electrophysiological gradients, we performed whole-cell patch recordings along the dorsal-ventral axis of EC in bats. Surprisingly, our data demonstrate that the sag response properties and the resonance properties recorded in layer II neurons of entorhinal cortex in the Egyptian fruit bat demonstrate an inverse relationship along the dorsal-ventral axis compared with the rat.

SIGNIFICANCE STATEMENT

As animals navigate, neurons in medial entorhinal cortex (MEC), termed grid cells, discharge at regular spatial intervals. In bats and rats, the spacing between the firing fields of grid cells changes systematically along the dorsal-ventral axis of MEC. It has been proposed that these changes could be generated by systematic differences in the intrinsic cellular physiology of neurons distributed along the dorsal-ventral axis of MEC. The results from our study show that key intrinsic physiological properties of neurons in entorhinal cortex of the bat and rat change in the opposite direction along the dorsal-ventral axis of entorhinal cortex, suggesting that these intrinsic physiological properties cannot account in the same way across species for the change in grid-field spacing shown along the dorsal-ventral axis.

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

Multiple Running Speed Signals in Medial Entorhinal Cortex

Grid cells in medial entorhinal cortex (MEC) can be modeled using oscillatory interference or attractor dynamic mechanisms that perform path integration, a computation requiring information about running direction and speed. The two classes of computational models often use either an oscillatory frequency or a firing rate that increases as a function of running speed. Yet it is currently not known whether these are two manifestations of the same speed signal or dissociable signals with potentially different anatomical substrates. We examined coding of running speed in MEC and identified these two speed signals to be independent of each other within individual neurons. The medial septum (MS) is strongly linked to locomotor behavior, and removal of MS input resulted in strengthening of the firing rate speed signal, while decreasing the strength of the oscillatory speed signal. Thus, two speed signals are present in MEC that are differentially affected by disrupted MS input.

Extracting grid cell characteristics from place cell inputs using non-negative principal component analysis

Many recent models study the downstream projection from grid cells to place cells, while recent data have pointed out the importance of the feedback projection. We thus asked how grid cells are affected by the nature of the input from the place cells. We propose a single-layer neural network with feedforward weights connecting place-like input cells to grid cell outputs. Place-to-grid weights are learned via a generalized Hebbian rule. The architecture of this network highly resembles neural networks used to perform Principal Component Analysis (PCA). Both numerical results and analytic considerations indicate that if the components of the feedforward neural network are non-negative, the output converges to a hexagonal lattice. Without the non-negativity constraint, the output converges to a square lattice. Consistent with experiments, grid spacing ratio between the first two consecutive modules is -1.4. Our results express a possible linkage between place cell to grid cell interactions and PCA.

Saccade direction encoding in the primate entorhinal cortex during visual exploration

We recently demonstrated that position in visual space is represented by grid cells in the primate entorhinal cortex (EC), suggesting that visual exploration of complex scenes in primates may employ signaling mechanisms similar to those used during exploration of physical space via movement in rodents. Here, we describe a group of saccade direction (SD) cells that encode eye movement information in the monkey EC during free-viewing of complex images. Significant saccade direction encoding was found in 20% of the cells recorded in the posterior EC. SD cells were generally broadly tuned and two largely separate populations of SD cells encoded future and previous saccade direction. Some properties of these cells resemble those of head-direction cells in rodent EC, suggesting that the same neural circuitry may be capable of performing homologous spatial computations under different exploratory contexts.

Connecting multiple spatial scales to decode the population activity of grid cells

Mammalian grid cells fire when an animal crosses the points of an imaginary hexagonal grid tessellating the environment. We show how animals can navigate by reading out a simple population vector of grid cell activity across multiple spatial scales, even though neural activity is intrinsically stochastic. This theory of dead reckoning explains why grid cells are organized into discrete modules within which all cells have the same lattice scale and orientation. The lattice scale changes from module to module and should form a geometric progression with a scale ratio of around 3/2 to minimize the risk of making large-scale errors in spatial localization. Such errors should also occur if intermediate-scale modules are silenced, whereas knocking out the module at the smallest scale will only affect spatial precision. For goal-directed navigation, the allocentric grid cell representation can be readily transformed into the egocentric goal coordinates needed for planning movements. The goal location is set by nonlinear gain fields that act on goal vector cells. This theory predicts neural and behavioral correlates of grid cell readout that transcend the known link between grid cells of the medial entorhinal cortex and place cells of the hippocampus.

Passive Transport Disrupts Grid Signals in the Parahippocampal Cortex

Navigation is usually thought of relative to landmarks, but neural signals representing space also use information generated by an animal's movements. These signals include grid cells, which fire at multiple locations, forming a repeating grid pattern. Grid cell generation depends upon theta rhythm, a 6-10 Hz electroencephalogram (EEG) oscillation that is modulated by the animals' movement velocity. We passively moved rats in a clear cart to eliminate motor related self-movement cues that drive moment-to-moment changes in theta rhythmicity. We found that passive movement maintained theta power and frequency at levels equivalent to low active movement velocity, spared overall head-direction (HD) cell characteristics, but abolished both velocity modulation of theta rhythmicity and grid cell firing patterns. These results indicate that self-movement motor cues are necessary for generating grid-specific firing patterns, possibly by driving velocity modulation of theta rhythmicity, which may be used as a speed signal to generate the repeating pattern of grid cells.

Distinct speed dependence of entorhinal island and ocean cells, including respective grid cells

Entorhinal-hippocampal circuits in the mammalian brain are crucial for an animal's spatial and episodic experience, but the neural basis for different spatial computations remain unknown. Medial entorhinal cortex layer II contains pyramidal island and stellate ocean cells. Here, we performed cell type-specific Ca(2+) imaging in freely exploring mice using cellular markers and a miniature head-mounted fluorescence microscope. We found that both oceans and islands contain grid cells in similar proportions, but island cell activity, including activity in a proportion of grid cells, is significantly more speed modulated than ocean cell activity. We speculate that this differential property reflects island cells' and ocean cells' contribution to different downstream functions: island cells may contribute more to spatial path integration, whereas ocean cells may facilitate contextual representation in downstream circuits.

Probable nature of higher-dimensional symmetries underlying mammalian grid-cell activity patterns

Lattices abound in nature-from the crystal structure of minerals to the honey-comb organization of ommatidia in the compound eye of insects. These arrangements provide solutions for optimal packings, efficient resource distribution, and cryptographic protocols. Do lattices also play a role in how the brain represents information? We focus on higher-dimensional stimulus domains, with particular emphasis on neural representations of physical space, and derive which neuronal lattice codes maximize spatial resolution. For mammals navigating on a surface, we show that the hexagonal activity patterns of grid cells are optimal. For species that move freely in three dimensions, a face-centered cubic lattice is best. This prediction could be tested experimentally in flying bats, arboreal monkeys, or marine mammals. More generally, our theory suggests that the brain encodes higher-dimensional sensory or cognitive variables with populations of grid-cell-like neurons whose activity patterns exhibit lattice structures at multiple, nested scales.

Coordinating with the "Inner GPS"

The 2014 Nobel Prize for Physiology or Medicine was awarded for the discoveries that have elucidated the components of the internal positioning system that is centered on the hippocampus and entorhinal cortex. Here I provide a less than objective discussion of the importance of these accomplishments to systems neuroscience. By identifying positioning components like place, direction, distance, borders and the like, the field is given the opportunity to have a shot at piecing together how these components are integrated into the synthetic positioning sense. We are also given what is in my view, the most experimentally accessible and therefore potentially understandable, cognitive representation. Lest we feel too confident in the completeness of our understanding, and to inspire redoubled curiosity, I briefly describe a preliminary observation from our work with the psychosis-inducing drug phencyclidine (PCP). While PCP does not disturb where individual place cells fire, it dramatically discoordinates how these cells discharge together in time. Trying to understand how the positioning component cells are coordinated to provide useful knowledge is an exciting and tenable problem to be working on.

Cellular resolution optical access to brain regions in fissures: imaging medial prefrontal cortex and grid cells in entorhinal cortex

In vivo two-photon microscopy provides the foundation for an array of powerful techniques for optically measuring and perturbing neural circuits. However, challenging tissue properties and geometry have prevented high-resolution optical access to regions situated within deep fissures. These regions include the medial prefrontal and medial entorhinal cortex (mPFC and MEC), which are of broad scientific and clinical interest. Here, we present a method for in vivo, subcellular resolution optical access to the mPFC and MEC using microprisms inserted into the fissures. We chronically imaged the mPFC and MEC in mice running on a spherical treadmill, using two-photon laser-scanning microscopy and genetically encoded calcium indicators to measure network activity. In the MEC, we imaged grid cells, a widely studied cell type essential to memory and spatial information processing. These cells exhibited spatially modulated activity during navigation in a virtual reality environment. This method should be extendable to other brain regions situated within deep fissures, and opens up these regions for study at cellular resolution in behaving animals using a rapidly expanding palette of optical tools for perturbing and measuring network structure and function.