Grid cells and cortical representation

The ventral hippocampus is involved in multi-goal obstacle-rich spatial navigation

A large body of evidence shows that the hippocampus is necessary for successful spatial navigation. Various studies have shown anatomical and functional differences between the dorsal (DHC) and ventral (VHC) portions of this structure. The DHC is primarily involved in spatial navigation and contains cells with small place fields. The VHC is primarily involved in context and emotional encoding contains cells with large place fields and receives major projections from the medial prefrontal cortex. In the past, spatial navigation experiments have used relatively simple tasks that may not have required a strong coordination along the dorsoventral hippocampal axis. In this study, we tested the hypothesis that the DHC and VHC may be critical for goal-directed navigation in obstacle-rich environments. We used a learning task in which animals memorize the location of a set of rewarded feeders, and recall these locations in the presence of small or large obstacles. We report that bilateral DHC or VHC inactivation impaired spatial navigation in both large and small obstacle conditions. Importantly, this impairment did not result from a deficit in the spatial memory for the set of feeders (i.e., recognition of the goal locations) because DHC or VHC inactivation did not affect recall performance when there was no obstacle on the maze. We also show that the behavioral performance of the animals was correlated with several measures of maze complexity and that these correlations were significantly affected by inactivation only in the large object condition. These results suggest that as the complexity of the environment increases, both DHC and VHC are required for spatial navigation.

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.

Vestibulo-Hippocampal Function Is Enhanced and Brain Structure Altered in Professional Ballet Dancers

Background and Objective: Life-long balance training has been shown to affect brain structure, including the hippocampus. Data are missing in this respect on professional ballet dancers of both genders. It is also unknown whether transfer effects exist on general balancing as well as spatial orientation abilities, a function mainly supported by the hippocampus. We aimed to assess differences in gray matter (GM) structure, general balancing skills, and spatial orientation skills between professional ballet dancers and non-dancers. Methods: Nineteen professional ballet dancers aged 18-35 (27.5 ± 4.1 years; 10 females) and nineteen age-matched non-dancers (26.5 ± 2.1 years; 10 females) were investigated. Main outcomes assessed were the score of a 30-item clinical balance test (CBT), the average error distance (in centimeters) on triangle completion task, and difference in GM density as seen by voxel-based morphometric analysis (VBM, SPM). Results: Ballet group performed significantly better on all conditions of the CBT and in the wheelchair (vestibular-dependent) condition of the spatial orientation test. Larger GM volumes for ballet dancers were observed in the right hippocampus, parahippocampal gyrus, insula, and cingulate motor cortex, whereas both larger and smaller volumes were detected within cerebellum bilaterally in comparison to non-dancers. Conclusion: Our results indicate that life-long ballet training could lead to better clinically relevant balancing abilities as well as vestibular-dependent spatial orientation capabilities; both of the benefits might be caused by positive influence of ballet training on the vestibular system function, and-possibly-its connectivity with temporal lobe regions responsible for vestibular-dependent orienting in space.

A hierarchical anti-Hebbian network model for the formation of spatial cells in three-dimensional space

Three-dimensional (3D) spatial cells in the mammalian hippocampal formation are believed to support the existence of 3D cognitive maps. Modeling studies are crucial to comprehend the neural principles governing the formation of these maps, yet to date very few have addressed this topic in 3D space. Here we present a hierarchical network model for the formation of 3D spatial cells using anti-Hebbian network. Built on empirical data, the model accounts for the natural emergence of 3D place, border, and grid cells, as well as a new type of previously undescribed spatial cell type which we call plane cells. It further explains the plausible reason behind the place and grid-cell anisotropic coding that has been observed in rodents and the potential discrepancy with the predicted periodic coding during 3D volumetric navigation. Lastly, it provides evidence for the importance of unsupervised learning rules in guiding the formation of higher-dimensional cognitive maps.

Neurons in the hippocampal formation encode diverse spatial properties. Here, the authors present a hierarchical network model for 3D spatial navigation that accounts for the observed neuronal representations and predict as yet unreported cell types with planar selectivity.

Space and Time: The Hippocampus as a Sequence Generator

Neural computations are often compared to instrument-measured distance or duration, and such relationships are interpreted by a human observer. However, neural circuits do not depend on human-made instruments but perform computations relative to an internally defined rate-of-change. While neuronal correlations with external measures, such as distance or duration, can be observed in spike rates or other measures of neuronal activity, what matters for the brain is how such activity patterns are utilized by downstream neural observers. We suggest that hippocampal operations can be described by the sequential activity of neuronal assemblies and their internally defined rate of change without resorting to the concept of space or time.

The storage and recall of memories in the hippocampo-cortical system

A quantitative computational theory of the operation of the hippocampus as an episodic memory system is described. The CA3 system operates as a single attractor or autoassociation network (1) to enable rapid one-trial associations between any spatial location (place in rodents or spatial view in primates) and an object or reward and (2) to provide for completion of the whole memory during recall from any part. The theory is extended to associations between time and object or reward to implement temporal order memory, which is also important in episodic memory. The dentate gyrus performs pattern separation by competitive learning to create sparse representations producing, for example, neurons with place-like fields from entorhinal cortex grid cells. The dentate granule cells generate, by the very small number of mossy fibre connections to CA3, a randomizing pattern separation effect that is important during learning but not recall and that separates out the patterns represented by CA3 firing as being very different from each other. This is optimal for an unstructured episodic memory system in which each memory must be kept distinct from other memories. The direct perforant path input to CA3 is quantitatively appropriate for providing the cue for recall in CA3 but not for learning. The CA1 recodes information from CA3 to set up associatively learned backprojections to the neocortex to allow the subsequent retrieval of information to the neocortex, giving a quantitative account of the large number of hippocampo-neocortical and neocortical-neocortical backprojections. Tests of the theory including hippocampal subregion analyses and hippocampal NMDA receptor knockouts are described and support the theory.

Hexagonal Grid Fields Optimally Encode Transitions in Spatiotemporal Sequences

Grid cells of the rodent entorhinal cortex are essential for spatial navigation. Although their function is commonly believed to be either path integration or localization, the origin or purpose of their hexagonal firing fields remains disputed. Here they are proposed to arise as an optimal encoding of transitions in sequences. First, storage requirements for transitions in general episodic sequences are examined using propositional logic and graph theory. Subsequently, transitions in complete metric spaces are considered under the assumption of an ideal sampling of an input space. It is shown that memory capacity of neurons that have to encode multiple feasible spatial transitions is maximized by a hexagonal pattern. Grid cells are proposed to encode spatial transitions in spatiotemporal sequences, with the entorhinal-hippocampal loop forming a multitransition system.

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).

Inferring circuit mechanisms from sparse neural recording and global perturbation in grid cells

A goal of systems neuroscience is to discover the circuit mechanisms underlying brain function. Despite experimental advances that enable circuit-wide neural recording, the problem remains open in part because solving the 'inverse problem' of inferring circuity and mechanism by merely observing activity is hard. In the grid cell system, we show through modeling that a technique based on global circuit perturbation and examination of a novel theoretical object called the distribution of relative phase shifts (DRPS) could reveal the mechanisms of a cortical circuit at unprecedented detail using extremely sparse neural recordings. We establish feasibility, showing that the method can discriminate between recurrent versus feedforward mechanisms and amongst various recurrent mechanisms using recordings from a handful of cells. The proposed strategy demonstrates that sparse recording coupled with simple perturbation can reveal more about circuit mechanism than can full knowledge of network activity or the synaptic connectivity matrix.

Neural Mechanisms of High-Level Vision

The last three decades have seen major strides in our understanding of neural mechanisms of high-level vision, or visual cognition of the world around us. Vision has also served as a model system for the study of brain function. Several broad insights, as yet incomplete, have recently emerged. First, visual perception is best understood not as an end unto itself, but as a sensory process that subserves the animal's behavioral goal at hand. Visual perception is likely to be simply a side effect that reflects the readout of visual information processing that leads to behavior. Second, the brain is essentially a probabilistic computational system that produces behaviors by collectively evaluating, not necessarily consciously or always optimally, the available information about the outside world received from the senses, the behavioral goals, prior knowledge about the world, and possible risks and benefits of a given behavior. Vision plays a prominent role in the overall functioning of the brain providing the lion's share of information about the outside world. Third, the visual system does not function in isolation, but rather interacts actively and reciprocally with other brain systems, including other sensory faculties. Finally, various regions of the visual system process information not in a strict hierarchical manner, but as parts of various dynamic brain-wide networks, collectively referred to as the "connectome." Thus, a full understanding of vision will ultimately entail understanding, in granular, quantitative detail, various aspects of dynamic brain networks that use visual sensory information to produce behavior under real-world conditions. © 2017 American Physiological Society. Compr Physiol 8:903-953, 2018.

Mesh electronics: a new paradigm for tissue-like brain probes

Existing implantable neurotechnologies for understanding the brain and treating neurological diseases have intrinsic properties that have limited their capability to achieve chronically-stable brain interfaces with single-neuron spatiotemporal resolution. These limitations reflect what has been dichotomy between the structure and mechanical properties of living brain tissue and non-living neural probes. To bridge the gap between neural and electronic networks, we have introduced the new concept of mesh electronics probes designed with structural and mechanical properties such that the implant begins to 'look and behave' like neural tissue. Syringe-implanted mesh electronics have led to the realization of probes that are neuro-attractive and free of the chronic immune response, as well as capable of stable long-term mapping and modulation of brain activity at the single-neuron level. This review provides a historical overview of a 10-year development of mesh electronics by highlighting the tissue-like design, syringe-assisted delivery, seamless neural tissue integration, and single-neuron level chronic recording stability of mesh electronics. We also offer insights on unique near-term opportunities and future directions for neuroscience and neurology that now are available or expected for mesh electronics neurotechnologies.

Degeneracy in the robust expression of spectral selectivity, subthreshold oscillations, and intrinsic excitability of entorhinal stellate cells

Biological heterogeneities are ubiquitous and play critical roles in the emergence of physiology at multiple scales. Although neurons in layer II (LII) of the medial entorhinal cortex (MEC) express heterogeneities in channel properties, the impact of such heterogeneities on the robustness of their cellular-scale physiology has not been assessed. Here, we performed a 55-parameter stochastic search spanning nine voltage- or calcium-activated channels to assess the impact of channel heterogeneities on the concomitant emergence of 10 in vitro electrophysiological characteristics of LII stellate cells (SCs). We generated 150,000 models and found a heterogeneous subpopulation of 449 valid models to robustly match all electrophysiological signatures. We employed this heterogeneous population to demonstrate the emergence of cellular-scale degeneracy in SCs, whereby disparate parametric combinations expressing weak pairwise correlations resulted in similar models. We then assessed the impact of virtually knocking out each channel from all valid models and demonstrate that the mapping between channels and measurements was many-to-many, a critical requirement for the expression of degeneracy. Finally, we quantitatively predict that the spike-triggered average of SCs should be endowed with theta-frequency spectral selectivity and coincidence detection capabilities in the fast gamma-band. We postulate this fast gamma-band coincidence detection as an instance of cellular-scale-efficient coding, whereby SC response characteristics match the dominant oscillatory signals in LII MEC. The heterogeneous population of valid SC models built here unveils the robust emergence of cellular-scale physiology despite significant channel heterogeneities, and forms an efficacious substrate for evaluating the impact of biological heterogeneities on entorhinal network function.

NEW & NOTEWORTHY We assessed the impact of heterogeneities in channel properties on the robustness of cellular-scale physiology of medial entorhinal cortical stellate neurons. We demonstrate that neuronal models with disparate channel combinations were endowed with similar physiological characteristics, as a consequence of the many-to-many mapping between channel properties and the physiological characteristics that they modulate. We predict that the spike-triggered average of stellate cells should be endowed with theta-frequency spectral selectivity and fast gamma-band coincidence detection capabilities.

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

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

Space and time in the brain

Nothing is more intuitive, yet more complex, than the concepts of space and time. In contrast to spacetime in physics, space and time in neuroscience remain separate coordinates to which we attach our observations. Investigators of navigation and memory relate neuronal activity to position, distance, time point, and duration and compare these parameters to units of measuring instruments. Although spatial-temporal sequences of brain activity often correlate with distance and duration measures, these correlations may not correspond to neuronal representations of space or time. Neither instruments nor brains sense space or time. Neuronal activity can be described as a succession of events without resorting to the concepts of space or time. Instead of searching for brain representations of our preconceived ideas, we suggest investigating how brain mechanisms give rise to inferential, model-building explanations.

Gamma oscillations in the entorhinal-hippocampal circuit underlying memory and dementia

Gamma oscillations that occur within the entorhinal cortex-hippocampal circuitry play important roles in the formation and retrieval of memory in healthy brains. Recent studies report that gamma oscillations are impaired in the entorhinal-hippocampal circuit of Alzheimer's disease (AD) patients and AD animal models. Here we review the latest advancements in studies of entorhinal-hippocampal gamma oscillations in healthy memory and dementia. This review is especially salient for readers in Alzheimer's research field not familiar with in vivo electrophysiology. Recent studies have begun to show a causal link between gamma oscillations and AD pathology, suggesting that gamma oscillations may even offer a plausible future therapeutic target.

Detection of time-, frequency- and direction-resolved communication within brain networks

Electroencephalography (EEG) records fast-changing neuronal signalling and communication and thus can offer a deep understanding of cognitive processes. However, traditional data analyses which employ the Fast-Fourier Transform (FFT) have been of limited use as they do not allow time- and frequency-resolved tracking of brain activity and detection of directional connectivity. Here, we applied advanced qEEG tools using autoregressive (AR) modelling, alongside traditional approaches, to murine data sets from common research scenarios: (a) the effect of age on resting EEG; (b) drug actions on non-rapid eye movement (NREM) sleep EEG (pharmaco-EEG); and (c) dynamic EEG profiles during correct vs incorrect spontaneous alternation responses in the Y-maze. AR analyses of short data strips reliably detected age- and drug-induced spectral EEG changes, while renormalized partial directed coherence (rPDC) reported direction- and time-resolved connectivity dynamics in mice. Our approach allows for the first time inference of behaviour- and stage-dependent data in a time- and frequency-resolved manner, and offers insights into brain networks that underlie working memory processing beyond what can be achieved with traditional methods.

Robust and efficient coding with grid cells

The neuronal code arising from the coordinated activity of grid cells in the rodent entorhinal cortex can uniquely represent space across a large range of distances, but the precise conditions for optimal coding capacity are known only for environments with finite size. Here we consider a coding scheme that is suitable for unbounded environments, and present a novel, number theoretic approach to derive the grid parameters that maximise the coding range in the presence of noise. We derive an analytic upper bound on the coding range and provide examples for grid scales that achieve this bound and hence are optimal for encoding in unbounded environments. We show that in the absence of neuronal noise, the capacity of the system is extremely sensitive to the choice of the grid periods. However, when the accuracy of the representation is limited by neuronal noise, the capacity quickly becomes more robust against the choice of grid scales as the number of modules increases. Importantly, we found that the capacity of the system is near optimal even for random scale choices already for a realistic number of grid modules. Our study demonstrates that robust and efficient coding can be achieved without parameter tuning in the case of grid cell representation and provides a solid theoretical explanation for the large diversity of the grid scales observed in experimental studies. Moreover, we suggest that having multiple grid modules in the entorhinal cortex is not only required for the exponentially large coding capacity, but is also a prerequisite for the robustness of the system.

Integration of grid maps in merged environments

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

Spatial representation in the hippocampal formation: a history

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

Volume Completion Between Contour Fragments at Discrete Depths

Building on the modal and amodal completion work of Kanizsa, Carman and Welch showed that binocular stereo viewing of two disparate images can give rise to a percept of 3D curved, nonclosed illusory contours and surfaces. Here, it is shown that binocular presentation can also give rise to the percept of closed curved surfaces or volumes that appear to vary smoothly across discrete depths in binocularly fused images, although in fact only two binocular disparities are discretely defined between corresponding contour elements of the inducing elements. Surfaces are filled in from one depth layer's visible contours to another layer's visible contours within virtual contours that are interpolated on the basis of good contour continuation between the visible portions of contour. These single depth contour segments are taken not to arise from surface edges, as in Kanizsa's or Carman and Welch's examples, but from segments of "rim" where the line of sight just grazes a surface that continues behind and beyond the rim smoothly. When there are two or more surface-propagating contour segments, the propagated surfaces can continue away from the inferred rim, merge, and then close behind the self-occluding visible surface into an everywhere differentiable closed surface or volume. Illusory surfaces can possess a depth and perceived surface curvature that is consistent with all visible contour segments, despite the absence of local disparity cues at interpolated 3D surface locations far from any visible contour. These demonstrations cannot be easily explained by existing models of visual processing. They place constraints on the surface and volume generation processes that construct our 3D world under normal viewing conditions.

A Theory of How Columns in the Neocortex Enable Learning the Structure of the World

Neocortical regions are organized into columns and layers. Connections between layers run mostly perpendicular to the surface suggesting a columnar functional organization. Some layers have long-range excitatory lateral connections suggesting interactions between columns. Similar patterns of connectivity exist in all regions but their exact role remain a mystery. In this paper, we propose a network model composed of columns and layers that performs robust object learning and recognition. Each column integrates its changing input over time to learn complete predictive models of observed objects. Excitatory lateral connections across columns allow the network to more rapidly infer objects based on the partial knowledge of adjacent columns. Because columns integrate input over time and space, the network learns models of complex objects that extend well beyond the receptive field of individual cells. Our network model introduces a new feature to cortical columns. We propose that a representation of location relative to the object being sensed is calculated within the sub-granular layers of each column. The location signal is provided as an input to the network, where it is combined with sensory data. Our model contains two layers and one or more columns. Simulations show that using Hebbian-like learning rules small single-column networks can learn to recognize hundreds of objects, with each object containing tens of features. Multi-column networks recognize objects with significantly fewer movements of the sensory receptors. Given the ubiquity of columnar and laminar connectivity patterns throughout the neocortex, we propose that columns and regions have more powerful recognition and modeling capabilities than previously assumed.

Superficial layers of the medial entorhinal cortex replay independently of the hippocampus

The hippocampus is thought to initiate systems-wide mnemonic processes through the reactivation of previously acquired spatial and episodic memory traces, which can recruit the entorhinal cortex as a first stage of memory redistribution to other brain areas. Hippocampal reactivation occurs during sharp wave-ripples, in which synchronous network firing encodes sequences of places. We investigated the coordination of this replay by recording assembly activity simultaneously in the CA1 region of the hippocampus and superficial layers of the medial entorhinal cortex. We found that entorhinal cell assemblies can replay trajectories independently of the hippocampus and sharp wave-ripples. This suggests that the hippocampus is not the sole initiator of spatial and episodic memory trace reactivation. Memory systems involved in these processes may include nonhierarchical, parallel components.

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

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

Video Abstract

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

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PV interneurons are necessary for speed tuning in entorhinal speed cells

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Somatostatin (SOM) interneurons maintain selectivity of aperiodic spatial cells

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

Laminar Organization of Encoding and Memory Reactivation in the Parietal Cortex

Egocentric neural coding has been observed in parietal cortex (PC), but its topographical and laminar organization is not well characterized. We used multi-site recording to look for evidence of local clustering and laminar consistency of linear and angular velocity encoding in multi-neuronal spiking activity (MUA) and in the high-frequency (300-900 Hz) component of the local field potential (HF-LFP), believed to reflect local spiking activity. Rats were trained to run many trials on a large circular platform, either to LED-cued goal locations or as a spatial sequence from memory. Tuning to specific self-motion states was observed and exhibited distinct cortical depth-invariant coding properties. These patterns of collective local and laminar activation during behavior were reactivated in compressed form during post-experience sleep and temporally coupled to cortical delta waves and hippocampal sharp-wave ripples. Thus, PC neuron motion encoding is consistent across cortical laminae, and this consistency is maintained during memory reactivation.

Distinct Neural Circuits for the Formation and Retrieval of Episodic Memories

The formation and retrieval of a memory is thought to be accomplished by activation and reactivation, respectively, of the memory-holding cells (engram cells) by a common set of neural circuits, but this hypothesis has not been established. The medial temporal-lobe system is essential for the formation and retrieval of episodic memory for which individual hippocampal subfields and entorhinal cortex layers contribute by carrying out specific functions. One subfield whose function is poorly known is the subiculum. Here, we show that dorsal subiculum and the circuit, CA1 to dorsal subiculum to medial entorhinal cortex layer 5, play a crucial role selectively in the retrieval of episodic memories. Conversely, the direct CA1 to medial entorhinal cortex layer 5 circuit is essential specifically for memory formation. Our data suggest that the subiculum-containing detour loop is dedicated to meet the requirements associated with recall such as rapid memory updating and retrieval-driven instinctive fear responses.

Selforganization of modular activity of grid cells

A unique topographical representation of space is found in the concerted activity of grid cells in the rodent medial entorhinal cortex. Many among the principal cells in this region exhibit a hexagonal firing pattern, in which each cell expresses its own set of place fields (spatial phases) at the vertices of a triangular grid, the spacing and orientation of which are typically shared with neighboring cells. Grid spacing, in particular, has been found to increase along the dorso‐ventral axis of the entorhinal cortex but in discrete steps, that is, with a modular structure. In this study, we show that such a modular activity may result from the self‐organization of interacting units, which individually would not show discrete but rather continuously varying grid spacing. Within our “adaptation” network model, the effect of a continuously varying time constant, which determines grid spacing in the isolated cell model, is modulated by recurrent collateral connections, which tend to produce a few subnetworks, akin to magnetic domains, each with its own grid spacing. In agreement with experimental evidence, the modular structure is tightly defined by grid spacing, but also involves grid orientation and distortion, due to interactions across modules. Thus, our study sheds light onto a possible mechanism, other than simply assuming separate networks a priori, underlying the formation of modular grid representations.

Impaired In Vivo Gamma Oscillations in the Medial Entorhinal Cortex of Knock-in Alzheimer Model

The entorhinal cortex (EC) has bidirectional connections with the hippocampus and plays a critical role in memory formation and retrieval. EC is one of the most vulnerable regions in the brain in early stages of Alzheimer’s disease (AD), a neurodegenerative disease with progressive memory impairments. Accumulating evidence from healthy behaving animals indicates gamma oscillations (30–100 Hz) as critical for mediating interactions in the circuit between EC and hippocampus. However, it is still unclear whether gamma oscillations have causal relationship with memory impairment in AD. Here we provide the first evidence that in vivo gamma oscillations in the EC are impaired in an AD mouse model. Cross-frequency coupling of gamma (30–100 Hz) oscillations to theta oscillations was reduced in the medial EC of anesthetized amyloid precursor protein knock-in (APP-KI) mice. Phase locking of spiking activity of layer II/III pyramidal cells to the gamma oscillations was significantly impaired. These data indicate that the neural circuit activities organized by gamma oscillations were disrupted in the medial EC of AD mouse model, and point to gamma oscillations as one of possible mechanisms for cognitive dysfunction in AD patients.

Architecture of the Entorhinal Cortex A Review of Entorhinal Anatomy in Rodents with Some Comparative Notes

The entorhinal cortex (EC) is the major input and output structure of the hippocampal formation, forming the nodal point in cortico-hippocampal circuits. Different division schemes including two or many more subdivisions have been proposed, but here we will argue that subdividing EC into two components, the lateral EC (LEC) and medial EC (MEC) might suffice to describe the functional architecture of EC. This subdivision then leads to an anatomical interpretation of the different phenotypes of LEC and MEC. First, we will briefly summarize the cytoarchitectonic differences and differences in hippocampal projection patterns on which the subdivision between LEC and MEC traditionally is based and provide a short comparative perspective. Second, we focus on main differences in cortical connectivity, leading to the conclusion that the apparent differences may well correlate with the functional differences. Cortical connectivity of MEC is features interactions with areas such as the presubiculum, parasubiculum, retrosplenial cortex (RSC) and postrhinal cortex, all areas that are considered to belong to the "spatial processing domain" of the cortex. In contrast, LEC is strongly connected with olfactory areas, insular, medial- and orbitofrontal areas and perirhinal cortex. These areas are likely more involved in processing of object information, attention and motivation. Third, we will compare the intrinsic networks involving principal- and inter-neurons in LEC and MEC. Together, these observations suggest that the different phenotypes of both EC subdivisions likely depend on the combination of intrinsic organization and specific sets of inputs. We further suggest a reappraisal of the notion of EC as a layered input-output structure for the hippocampal formation.

Anterolateral Entorhinal Cortex Volume Predicted by Altered Intra-Item Configural Processing

Recent functional imaging studies have proposed that the human entorhinal cortex (ERC) is subdivided into functionally distinct anterolateral (alERC) and posteromedial (pmERC) subregions. The alERC overlaps with regions that are affected earliest by Alzheimer's disease pathology, yet its cognitive function remains poorly understood. Previous human fMRI studies have focused on its role in object memory, but rodent studies on the putatively homologous lateral entorhinal cortex suggest that it also plays an important role in representing spatial properties of objects. To investigate the cognitive effects of human alERC volume differences, we developed an eye-tracking-based task to evaluate intra-item configural processing (i.e., processing the arrangement of an object's features) and used manual segmentation based on a recently developed protocol to delineate the alERC/pmERC and other medial temporal lobe (MTL) subregions. In a group of older adult men and women at varying stages of brain atrophy and cognitive decline, we found that intra-item configural processing, regardless of an object's novelty, was strongly predicted by alERC volume, but not by the volume of any other MTL subregion. These results provide the first evidence that the human alERC plays a role in supporting a distinct aspect of object processing, namely attending to the arrangement of an object's component features.SIGNIFICANCE STATEMENT Alzheimer's disease pathology appears earliest in brain regions that overlap with the anterolateral entorhinal cortex (alERC). However, the cognitive role of the alERC is poorly understood. Previous human studies treat the alERC as an extension of the neighboring perirhinal cortex, supporting object memory. Animal studies suggest that the alERC may support the spatial properties of objects. In a group of older adult humans at the earliest stages of cognitive decline, we show here that alERC volume selectively predicted configural processing (attention to the spatial arrangement of an object's parts). This is the first study to demonstrate a cognitive role related to alERC volume in humans. This task can be adapted to serve as an early detection method for Alzheimer's disease pathology.

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.

Semi-Supervised Learning of Cartesian Factors: A Top-Down Model of the Entorhinal Hippocampal Complex

The existence of place cells (PCs), grid cells (GCs), border cells (BCs), and head direction cells (HCs) as well as the dependencies between them have been enigmatic. We make an effort to explain their nature by introducing the concept of Cartesian Factors. These factors have specific properties: (i) they assume and complement each other, like direction and position and (ii) they have localized discrete representations with predictive attractors enabling implicit metric-like computations. In our model, HCs make the distributed and local representation of direction. Predictive attractor dynamics on that network forms the Cartesian Factor "direction." We embed these HCs and idiothetic visual information into a semi-supervised sparse autoencoding comparator structure that compresses its inputs and learns PCs, the distributed local and direction independent (allothetic) representation of the Cartesian Factor of global space. We use a supervised, information compressing predictive algorithm and form direction sensitive (oriented) GCs from the learned PCs by means of an attractor-like algorithm. Since the algorithm can continue the grid structure beyond the region of the PCs, i.e., beyond its learning domain, thus the GCs and the PCs together form our metric-like Cartesian Factors of space. We also stipulate that the same algorithm can produce BCs. Our algorithm applies (a) a bag representation that models the "what system" and (b) magnitude ordered place cell activities that model either the integrate-and-fire mechanism, or theta phase precession, or both. We relate the components of the algorithm to the entorhinal-hippocampal complex and to its working. The algorithm requires both spatial and lifetime sparsification that may gain support from the two-stage memory formation of this complex.

Stellate cells drive maturation of the entorhinal-hippocampal circuit

The neural representation of space relies on a network of entorhinal-hippocampal cell types with firing patterns tuned to different abstract features of the environment. To determine how this network is set up during early postnatal development, we monitored markers of structural maturation in developing mice, both in naïve animals and after temporally restricted pharmacogenetic silencing of specific cell populations. We found that entorhinal stellate cells provide an activity-dependent instructive signal that drives maturation sequentially and unidirectionally through the intrinsic circuits of the entorhinal-hippocampal network. The findings raise the possibility that a small number of autonomously developing neuronal populations operate as intrinsic drivers of maturation across widespread regions of the cortex.

Physiological roles of Kv2 channels in entorhinal cortex layer II stellate cells revealed by Guangxitoxin-1E

KEY POINTS

Kv2 channels underlie delayed-rectifier potassium currents in various neurons, although their physiological roles often remain elusive. Almost nothing is known about Kv2 channel functions in medial entorhinal cortex (mEC) neurons, which are involved in representing space, memory formation, epilepsy and dementia. Stellate cells in layer II of the mEC project to the hippocampus and are considered to be space-representing grid cells. We used the new Kv2 blocker Guangxitoxin-1E (GTx) to study Kv2 functions in these neurons. Voltage clamp recordings from mEC stellate cells in rat brain slices showed that GTx inhibited delayed-rectifier K+ current but not transient A-type current. In current clamp, GTx had multiple effects: (i) increasing excitability and bursting at moderate spike rates but reducing firing at high rates; (ii) enhancing after-depolarizations; (iii) reducing the fast and medium after-hyperpolarizations; (iv) broadening action potentials; and (v) reducing spike clustering. GTx is a useful tool for studying Kv2 channels and their functions in neurons.

ABSTRACT

The medial entorhinal cortex (mEC) is strongly involved in spatial navigation, memory, dementia and epilepsy. Although potassium channels shape neuronal activity, their roles in mEC are largely unknown. We used the new Kv2 blocker Guangxitoxin-1E (GTx; 10-100 nm) in rat brain slices to investigate Kv2 channel functions in mEC layer II stellate cells (SCs). These neurons project to the hippocampus and are considered to be grid cells representing space. Voltage clamp recordings from SCs nucleated patches showed that GTx inhibited a delayed rectifier K+ current activating beyond -30 mV but not transient A-type current. In current clamp, GTx (i) had almost no effect on the first action potential but markedly slowed repolarization of late spikes during repetitive firing; (ii) enhanced the after-depolarization (ADP); (iii) reduced fast and medium after-hyperpolarizations (AHPs); (iv) strongly enhanced burst firing and increased excitability at moderate spike rates but reduced spiking at high rates; and (v) reduced spike clustering and rebound potentials. The changes in bursting and excitability were related to the altered ADPs and AHPs. Kv2 channels strongly shape the activity of mEC SCs by affecting spike repolarization, after-potentials, excitability and spike patterns. GTx is a useful tool and may serve to further clarify Kv2 channel functions in neurons. We conclude that Kv2 channels in mEC SCs are important determinants of intrinsic properties that allow these neurons to produce spatial representation. The results of the present study may also be important for the accurate modelling of grid cells.

ARM-Cortex M3-Based Two-Wheel Robot for Assessing Grid Cell Model of Medial Entorhinal Cortex: Progress towards Building Robots with Biologically Inspired Navigation-Cognitive Maps

This article presents the implementation and use of a two-wheel autonomous robot and its effectiveness as a tool for studying the recently discovered use of grid cells as part of mammalian’s brains space-mapping circuitry (specifically the medial entorhinal cortex). A proposed discrete-time algorithm that emulates the medial entorhinal cortex is programed into the robot. The robot freely explores a limited laboratory area in the manner of a rat or mouse and reports information to a PC, thus enabling research without the use of live individuals. Position coordinate neural maps are achieved as mathematically predicted although for a reduced number of implemented neurons (i.e., 200 neurons). However, this type of computational embedded system (robot’s microcontroller) is found to be insufficient for simulating huge numbers of neurons in real time (as in the medial entorhinal cortex). It is considered that the results of this work provide an insight into achieving an enhanced embedded systems design for emulating and understanding mathematical neural network models to be used as biologically inspired navigation system for robots.

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

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

Brain Computation Is Organized via Power-of-Two-Based Permutation Logic

There is considerable scientific interest in understanding how cell assemblies—the long-presumed computational motif—are organized so that the brain can generate intelligent cognition and flexible behavior. The Theory of Connectivity proposes that the origin of intelligence is rooted in a power-of-two-based permutation logic (N = 2ⁱ–1), producing specific-to-general cell-assembly architecture capable of generating specific perceptions and memories, as well as generalized knowledge and flexible actions. We show that this power-of-two-based permutation logic is widely used in cortical and subcortical circuits across animal species and is conserved for the processing of a variety of cognitive modalities including appetitive, emotional and social information. However, modulatory neurons, such as dopaminergic (DA) neurons, use a simpler logic despite their distinct subtypes. Interestingly, this specific-to-general permutation logic remained largely intact although NMDA receptors—the synaptic switch for learning and memory—were deleted throughout adulthood, suggesting that the logic is developmentally pre-configured. Moreover, this computational logic is implemented in the cortex via combining a random-connectivity strategy in superficial layers 2/3 with nonrandom organizations in deep layers 5/6. This randomness of layers 2/3 cliques—which preferentially encode specific and low-combinatorial features and project inter-cortically—is ideal for maximizing cross-modality novel pattern-extraction, pattern-discrimination and pattern-categorization using sparse code, consequently explaining why it requires hippocampal offline-consolidation. In contrast, the nonrandomness in layers 5/6—which consists of few specific cliques but a higher portion of more general cliques projecting mostly to subcortical systems—is ideal for feedback-control of motivation, emotion, consciousness and behaviors. These observations suggest that the brain’s basic computational algorithm is indeed organized by the power-of-two-based permutation logic. This simple mathematical logic can account for brain computation across the entire evolutionary spectrum, ranging from the simplest neural networks to the most complex.

Probabilistic Learning by Rodent Grid Cells

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

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

Asymmetry of Neuronal Combinatorial Codes Arises from Minimizing Synaptic Weight Change

Synaptic change is a costly resource, particularly for brain structures that have a high demand of synaptic plasticity. For example, building memories of object positions requires efficient use of plasticity resources since objects can easily change their location in space and yet we can memorize object locations. But how should a neural circuit ideally be set up to integrate two input streams (object location and identity) in case the overall synaptic changes should be minimized during ongoing learning? This letter provides a theoretical framework on how the two input pathways should ideally be specified. Generally the model predicts that the information-rich pathway should be plastic and encoded sparsely, whereas the pathway conveying less information should be encoded densely and undergo learning only if a neuronal representation of a novel object has to be established. As an example, we consider hippocampal area CA1, which combines place and object information. The model thereby provides a normative account of hippocampal rate remapping, that is, modulations of place field activity by changes of local cues. It may as well be applicable to other brain areas (such as neocortical layer V) that learn combinatorial codes from multiple input streams.

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

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

Distinct dendritic morphology across the blades of the rodent dentate gyrus

The dentate gyrus (DG) is a hippocampal region that has long been characterized as a critical mediator of enduring memory formation and retrieval. As such, there is a wealth of studies investigating this area. Most of these studies have either treated the DG as a homogeneous structure, or examined differences in neurons along the septal-temporal axis. Recent data, however, have indicated that a functional distinction exists between the suprapyramidal and infrapyramidal blades of the DG, with the former showing more robust responses during spatial tasks. To date, few anatomical studies have addressed this functional gradient in rats, and no study has done so in the mouse. To address this, we investigated dendritic morphology and spine density in hippocampal granule cells of rats and mice using the Golgi-Cox technique. We find that granule cells from the suprapyramidal blade of the DG contain greater dendritic material in the region receiving spatial information from the medial perforant path. This provides a potential anatomical substrate for the asymmetric response of the DG to spatial input. Synapse 70:277-282, 2016. © 2016 Wiley Periodicals, Inc.

Excitatory Postrhinal Projections to Principal Cells in the Medial Entorhinal Cortex

The postrhinal cortex (POR) provides substantial input to the entorhinal cortex, mainly targeting superficial layers of the medial entorhinal cortex (MEC). Major inputs to POR originate in the visual and parietal cortex, thus providing neurons in MEC with a subset of cortical information relevant to their spatial firing properties. The POR takes a position that is comparable with that of the perirhinal cortex (PER) with regard to the lateral entorhinal cortex (LEC). Neurons in LEC and MEC show different functional properties likely reflecting differences in their respective inputs. Projections from PER to LEC exert a main inhibitory influence, which may relate to the sparse object-selective firing in LEC. In view of the continuous, spatially modulated firing properties of principal neurons in MEC, we tested in rats the hypothesis that projections from POR to MEC are functionally different from the PER-to-LEC counterpart in providing an excitatory drive to MEC. Our combined confocal and quantitative electron-microscopic observations indicated that POR projections target mainly principal cells in MEC, including neurons that project to the hippocampus. The ultrastructure of the majority of the synapses indicated that they are excitatory. Voltage-sensitive dye imaging in sagittal slices confirmed this morphologically derived conclusion, showing that the MEC network always responded with an overall depolarization, indicative for net excitatory transmission. In vitro single-cell recordings from principal cells showed only excitatory responses upon POR stimulation. These results show that POR provides an excitatory projection to MEC, differing fundamentally from the inhibitory projection of PER to LEC.

Locating and navigation mechanism based on place-cell and grid-cell models

Extensive experiments on rats have shown that environmental cues play an important role in goal locating and navigation. Major studies about locating and navigation are carried out based only on place cells. Nevertheless, it is known that navigation may also rely on grid cells. Therefore, we model locating and navigation based on both, thus developing a novel grid-cell model, from which firing fields of grid cells can be obtained. We found a continuous-time dynamic system to describe learning and direction selection. In our simulation experiment, according to the results from physiology experiments, we successfully rebuild place fields of place cells and firing fields of grid cells. We analyzed the factors affecting the locating accuracy. Results show that the learning rate, firing threshold and cell number can influence the outcomes from various tasks. We used our system model to perform a goal navigation task and showed that paths that are changed for every run in one experiment converged to a stable one after several runs.