Hippocampal remapping and grid realignment in entorhinal cortex

Continuous attractors with morphed/correlated maps

Continuous attractor networks are used to model the storage and representation of analog quantities, such as position of a visual stimulus. The storage of multiple continuous attractors in the same network has previously been studied in the context of self-position coding. Several uncorrelated maps of environments are stored in the synaptic connections, and a position in a given environment is represented by a localized pattern of neural activity in the corresponding map, driven by a spatially tuned input. Here we analyze networks storing a pair of correlated maps, or a morph sequence between two uncorrelated maps. We find a novel state in which the network activity is simultaneously localized in both maps. In this state, a fixed cue presented to the network does not determine uniquely the location of the bump, i.e. the response is unreliable, with neurons not always responding when their preferred input is present. When the tuned input varies smoothly in time, the neuronal responses become reliable and selective for the environment: the subset of neurons responsive to a moving input in one map changes almost completely in the other map. This form of remapping is a non-trivial transformation between the tuned input to the network and the resulting tuning curves of the neurons. The new state of the network could be related to the formation of direction selectivity in one-dimensional environments and hippocampal remapping. The applicability of the model is not confined to self-position representations; we show an instance of the network solving a simple delayed discrimination task.

How is your position in an environment represented in the brain, and how does the representation distinguish between multiple environments? One of the proposed answers relies on continuous attractor neural networks. Consider the web page of your campus map as a network of pixels. Every pixel is a neuron, and nearby pixels excite each other, while distant pairs are inhibited. As a result of their interactions, a bunch of close-by pixels will light up, indicating your current position as suggested by your web-cam (the sensory input). When you travel to another campus, the common assumption holds that pixels are completely scrambled and the excitatory/inhibitory pattern of connections is summed to the existing one. Now these connections and the sensory input will activate the pixels corresponding to your location in the new campus. The active pixels will look like noise in the old map. But what if the campuses are similar, i.e. the pixels are not completely scrambled? We show that the network has a novel way of distinguishing between the environments, by lighting up distinct subsets of pixels for each campus. This emergent selectivity for the environment could be a mechanism underlying hippocampal remapping and directional selectivity of place cells in 1D environments.

Grid cells in pre- and parasubiculum

Allocentric space is mapped by a widespread brain circuit of functionally specialized cell types located in interconnected subregions of the hippocampal-parahippocampal cortices. Little is known about the neural architectures required to express this variety of firing patterns. In rats, we found that one of the cell types, the grid cell, was abundant not only in medial entorhinal cortex (MEC), where it was first reported, but also in pre- and parasubiculum. The proportion of grid cells in pre- and parasubiculum was comparable to deep layers of MEC. The symmetry of the grid pattern and its relationship to the theta rhythm were weaker, especially in presubiculum. Pre- and parasubicular grid cells intermingled with head-direction cells and border cells, as in deep MEC layers. The characterization of a common pool of space-responsive cells in architecturally diverse subdivisions of parahippocampal cortex constrains the range of mechanisms that might give rise to their unique functional discharge phenotypes.

Number estimates of neuronal phenotypes in layer II of the medial entorhinal cortex of rat and mouse

Modelling entorhinal function or evaluating the consequences of neuronal losses which accompany neurodegenerative disorders requires detailed information on the quantitative cellular composition of the normal entorhinal cortex. Using design-based stereological methods, we estimated the numbers, proportions, densities and sectional areas of layer II cells in the medial entorhinal area (MEA), and its constituent caudal entorhinal (CE) and medial entorhinal (ME) fields, in the rat and mouse. We estimated layer II of the MEA to contain approximately 58,000 neurons in the rat and approximately 24,000 neurons in the mouse. Field CE accounted for more than three-quarters of the total neuron population in both species. In the rat, layer II of the MEA is comprised of 38% ovoid stellate cells, 29% polygonal stellate cells and 17% pyramidal cells. The remainder is comprised of much smaller populations of horizontal bipolar, tripolar, oblique pyramidal and small round cells. In the mouse, MEA layer II is comprised of 52% ovoid stellate cells, 22% polygonal stellate cells and 14% pyramidal cells. Significant species differences in the proportions of ovoid and polygonal stellate cells suggest differences in physiological and functional properties. The majority of MEA layer II cells contribute to the entorhinal-hippocampal pathways. The degree of divergence from MEA layer II cells to the dentate granule cells was similar in the rat and mouse. In both rat and mouse, the only dorsoventral difference we observed is a gradient in polygonal stellate cell sectional area, which may relate to the dorsoventral increase in the size and spacing of individual neuronal firing fields. In summary, we found species-specific cellular compositions of MEA layer II, while, within a species, quantitative parameters other than cell size are stable along the dorsoventral and mediolateral axis of the MEA.

Development of the spatial representation system in the rat

In the adult brain, space and orientation are represented by an elaborate hippocampal-parahippocampal circuit consisting of head-direction cells, place cells, and grid cells. We report that a rudimentary map of space is already present when 2 1/2-week-old rat pups explore an open environment outside the nest for the first time. Head-direction cells in the pre- and parasubiculum have adultlike properties from the beginning. Place and grid cells are also present but evolve more gradually. Grid cells show the slowest development. The gradual refinement of the spatial representation is accompanied by an increase in network synchrony among entorhinal stellate cells. The presence of adultlike directional signals at the onset of navigation raises the possibility that such signals are instrumental in setting up networks for place and grid representation.

Democracy-independence trade-off in oscillating dendrites and its implications for grid cells

Dendritic democracy and independence have been characterized for near-instantaneous processing of synaptic inputs. However, a wide class of neuronal computations requires input integration on long timescales. As a paradigmatic example, entorhinal grid fields have been thought to be generated by the democratic summation of independent dendritic oscillations performing direction-selective path integration. We analyzed how multiple dendritic oscillators embedded in the same neuron integrate inputs separately and determine somatic membrane voltage jointly. We found that the interaction of dendritic oscillations leads to phase locking, which sets an upper limit on the timescale for independent input integration. Factors that increase this timescale also decrease the influence that the dendritic oscillations exert on somatic voltage. In entorhinal stellate cells, interdendritic coupling dominates and causes these cells to act as single oscillators. Our results suggest a fundamental trade-off between local and global processing in dendritic trees integrating ongoing signals.

Increased pattern separation in the aged fascia dentata

One prominent impairment associated with aging is a deficit in the ability of the hippocampus to form stable contextual representations. Place-specific firing in granule cells of the fascia dentata (FD) is thought to aid the formation of multiple stable memory representations by disambiguating similar experiences (a process termed pattern separation), such as when an animal repeatedly enters similar environments or contexts. Using zif268/egr1 as a marker of cellular activity, we show that aged animals, which have altered place maps in other areas of the hippocampal formation, also show altered granule cell activity during multiple visits to similar environments. That is, the FD of aged animals is more likely to recruit distinct granule cell populations, and thus show greater pattern separation, during two visits to similar (or even the same) environments. However, if two highly distinct environments are visited, this age-related increase in pattern separation is no longer apparent. Moreover, increased pattern separation in similar environments correlates with decline in the ability of aged animals to disambiguate similar contexts in a sequential spatial recognition task.

Attractor-map versus autoassociation based attractor dynamics in the hippocampal network

The autoassociative memory model of hippocampal field CA3 postulates that Hebbian associations among external input features produce attractor states embedded in a recurrent synaptic matrix. In contrast, the attractor-map model postulates that a two-dimensional continuum of attractor states is preconfigured in the network during development and that transitions among these states are governed primarily by self-motion information ("path-integration"), giving rise to the strong spatial characteristic of hippocampal activity. In this model, learned associations between "coordinates" on the attractor map and external cues can result in abrupt jumps between states, in the case of mismatches between the current input and previous associations between internal coordinates and external landmarks. Both models predict attractor dynamics, but for fundamentally different reasons; however, the two models are not a priori mutually exclusive. We contrasted these two models by comparing the dynamics of state transitions when two previously learned environmental shapes were morphed between their endpoints, in animals that had first experienced the environments either at the same location, or at two different locations, connected by a passageway through which they walked. As predicted from attractor-map theory, the latter animals expressed abrupt transitions between representations at the midpoint of the morph series. Contrary to the predictions of autoassociation theory, the former group expressed no evidence of attractor dynamics during the morph series; there was only a gradual transition between endpoints. The results of this critical test thus cast the autoassociator theory for CA3 into doubt and indicate the need for a new theory for this structure.

Hebbian analysis of the transformation of medial entorhinal grid-cell inputs to hippocampal place fields

The discovery of grid cells in the medial entorhinal cortex (MEC) permits the characterization of hippocampal computation in much greater detail than previously possible. The present study addresses how an integrate-and-fire unit driven by grid-cell spike trains may transform the multipeaked, spatial firing pattern of grid cells into the single-peaked activity that is typical of hippocampal place cells. Previous studies have shown that in the absence of network interactions, this transformation can succeed only if the place cell receives inputs from grids with overlapping vertices at the location of the place cell's firing field. In our simulations, the selection of these inputs was accomplished by fast Hebbian plasticity alone. The resulting nonlinear process was acutely sensitive to small input variations. Simulations differing only in the exact spike timing of grid cells produced different field locations for the same place cells. Place fields became concentrated in areas that correlated with the initial trajectory of the animal; the introduction of feedback inhibitory cells reduced this bias. These results suggest distinct roles for plasticity of the perforant path synapses and for competition via feedback inhibition in the formation of place fields in a novel environment. Furthermore, they imply that variability in MEC spiking patterns or in the rat's trajectory is sufficient for generating a distinct population code in a novel environment and suggest that recalling this code in a familiar environment involves additional inputs and/or a different mode of operation of the network.

A sense of direction in human entorhinal cortex

Finding our way in spatial environments is an essential part of daily life. How do we come to possess this sense of direction? Extensive research points to the hippocampus and entorhinal cortex (EC) as key neural structures underlying spatial navigation. To better understand this system, we examined recordings of single-neuron activity from neurosurgical patients playing a virtual-navigation video game. In addition to place cells, which encode the current virtual location, we describe a unique cell type, EC path cells, the activity of which indicates whether the patient is taking a clockwise or counterclockwise path around the virtual square road. We find that many EC path cells exhibit this directional activity throughout the environment, in contrast to hippocampal neurons, which primarily encode information about specific locations. More broadly, these findings support the hypothesis that EC encodes general properties of the current context (e.g., location or direction) that are used by hippocampus to build unique representations reflecting combinations of these properties.

Cellular dynamical mechanisms for encoding the time and place of events along spatiotemporal trajectories in episodic memory

Understanding the mechanisms of episodic memory requires linking behavioral data and lesion effects to data on the dynamics of cellular membrane potentials and population interactions within brain regions. Linking behavior to specific membrane channels and neurochemicals has implications for therapeutic applications. Lesions of the hippocampus, entorhinal cortex and subcortical nuclei impair episodic memory function in humans and animals, and unit recording data from these regions in behaving animals indicate episodic memory processes. Intracellular recording in these regions demonstrates specific cellular properties including resonance, membrane potential oscillations and bistable persistent spiking that could underlie the encoding and retrieval of episodic trajectories. A model presented here shows how intrinsic dynamical properties of neurons could mediate the encoding of episodic memories as complex spatiotemporal trajectories. The dynamics of neurons allow encoding and retrieval of unique episodic trajectories in multiple continuous dimensions including temporal intervals, personal location, the spatial coordinates and sensory features of perceived objects and generated actions, and associations between these elements. The model also addresses how cellular dynamics could underlie unit firing data suggesting mechanisms for coding continuous dimensions of space, time, sensation and action.

Combinatorial responses controlled by synaptic inhibition in the cerebellum granular layer

The granular layer of cerebellum has been long hypothesized to perform combinatorial operations on incoming signals. Although this assumption is at the basis of main computational theories of cerebellum, it has never been assessed experimentally. Here, by applying high-resolution voltage-sensitive dye imaging techniques, we show that simultaneous activation of two partially overlapping mossy fiber bundles (either with single pulses or high-frequency bursts) can cause combined excitation and combined inhibition, which are compatible with the concepts of coincidence detection and spatial pattern separation predicted by theory. Combined excitation appeared as an area in which the combination of two inputs is greater than the arithmetic sum of the individual inputs and was enhanced by gamma-aminobutyric acid type A (GABA(A)) receptor blockers. Combined inhibition was manifest as an area where two inputs combined resulted in a reduction to less than half of the activity evoked from either one of the two inputs alone and was prevented by GABA(A) receptor blockers. The combinatorial responses occupied small granular layer regions (approximately 30 microm diameter), with combined inhibition being interspersed among extended areas of combined excitation. Moreover, the combinatorial effects lasted for tens of milliseconds and combined inhibition occurred only after termination of the stimuli. These combinatorial operations, if engaged by natural input patterns in vivo, may be important to influence incoming impulses organizing spatiotemporal spike sequences to be relayed to Purkinje cells.

A phase code for memory could arise from circuit mechanisms in entorhinal cortex

Neurophysiological data reveals intrinsic cellular properties that suggest how entorhinal cortical neurons could code memory by the phase of their firing. Potential cellular mechanisms for this phase coding in models of entorhinal function are reviewed. This mechanism for phase coding provides a substrate for modeling the responses of entorhinal grid cells, as well as the replay of neural spiking activity during waking and sleep. Efforts to implement these abstract models in more detailed biophysical compartmental simulations raise specific issues that could be addressed in larger scale population models incorporating mechanisms of inhibition.

Excitability changes within transverse lamellae of dentate granule cells and their longitudinal spread following orthodromic or antidromic activation

The functional organization of the perforant path input to the dentate gyrus of the exposed hippocampus was studied in adult rabbits anesthetized with urethane and chloralose. Electrical stimulation of perforant path fibers caused excitation of granule cells along narrow, nearly transverse strips (lamellae) of tissue. Stimulation of granule cell axons (mossy fibers) in CA3 caused antidromic activation of granule cells along similar strips. Paired-pulse stimulation revealed marked changes in granule cell excitability both within a lamella (on-line) and for several mm off-line along the septo-temporal axis of the dentate gyrus. After the first pulse, granule cells were inhibited for up to about 100 ms and then facilitated for up to hundreds of ms. Feedback activity along mossy fiber collaterals exciting local inhibitory and excitatory neurons appeared to dominate in producing on- and off-line inhibition and facilitation. Neurons mediating these effects could be inhibitory basket cells and other inhibitory interneurons targeting granule cells on- and off-line. In addition, excitatory mossy cells with far reaching, longitudinally running axons could affect off-line granule cells by exciting them directly or inhibit them indirectly by exciting local inhibitory interneurons. A scheme for dentate gyrus function is proposed whereby information to the dentate gyrus becomes split into interacting transverse strips of neuronal assemblies along which temporal processing occurs. A matrix of neuronal assemblies thus arises within which fragments of events and experiences is stored through the plasticity of synapses within and between the assemblies. Similar fragments may then be recognized at later times allowing memories of the whole to be created by pattern completion at subsequent computational stages in the hippocampus.

A new touchscreen test of pattern separation: effect of hippocampal lesions

Researchers are becoming increasingly interested in the role of the hippocampus in pattern separation, a process which keeps items distinct in memory. In this study, we develop and test a new automated touchscreen-based method for studying pattern separation in rodents. Rats were trained to discriminate locations on a computer screen that varied in their similarity, that is, their distance apart on the screen. Animals with lesions of the dorsal hippocampus were impaired when the locations discriminated were close together but not when they were far apart, indicating impaired pattern separation. This test provides an automated test of pattern separation, which adds to an expanding battery of cognitive tests that can be carried out using the touchscreen testing method.

A model of episodic memory: mental time travel along encoded trajectories using grid cells

The definition of episodic memory includes the concept of mental time travel: the ability to re-experience a previously experienced trajectory through continuous dimensions of space and time, and to recall specific events or stimuli along this trajectory. Lesions of the hippocampus and entorhinal cortex impair human episodic memory function and impair rat performance in tasks that could be solved by retrieval of trajectories. Recent physiological data suggests a novel model for encoding and retrieval of trajectories, and for associating specific stimuli with specific positions along the trajectory. During encoding in the model, external input drives the activity of head direction cells. Entorhinal grid cells integrate the head direction input to update an internal representation of location, and drive hippocampal place cells. Trajectories are encoded by Hebbian modification of excitatory synaptic connections between hippocampal place cells and head direction cells driven by external action. Associations are also formed between hippocampal cells and sensory stimuli. During retrieval, a sensory input cue activates hippocampal cells that drive head direction activity via previously modified synapses. Persistent spiking of head direction cells maintains the direction and speed of the action, updating the activity of entorhinal grid cells that thereby further update place cell activity. Additional cells, termed arc length cells, provide coding of trajectory segments based on the one-dimensional arc length from the context of prior actions or states, overcoming ambiguity where the overlap of trajectory segments causes multiple head directions to be associated with one place. These mechanisms allow retrieval of complex, self-crossing trajectories as continuous curves through space and time.

A functional role for adult hippocampal neurogenesis in spatial pattern separation

The dentate gyrus (DG) of the mammalian hippocampus is hypothesized to mediate pattern separation-the formation of distinct and orthogonal representations of mnemonic information-and also undergoes neurogenesis throughout life. How neurogenesis contributes to hippocampal function is largely unknown. Using adult mice in which hippocampal neurogenesis was ablated, we found specific impairments in spatial discrimination with two behavioral assays: (i) a spatial navigation radial arm maze task and (ii) a spatial, but non-navigable, task in the mouse touch screen. Mice with ablated neurogenesis were impaired when stimuli were presented with little spatial separation, but not when stimuli were more widely separated in space. Thus, newborn neurons may be necessary for normal pattern separation function in the DG of adult mice.

Distance coding strategies based on the entorhinal grid cell system

Estimating and keeping track of the distance from salient points of the environment are important constituents of the spatial awareness and navigation. In rodents, the majority of principal cells in the hippocampus are known to be correlated with the position of the animal. However, the lack of topography in the hippocampal cognitive map does not support the assumption that connections between these cells are able to store and recall distances between coded positions. In contrast, the firing fields of the grid cells in the medial entorhinal cortex form triangular grids and are organized on metrical principles. We suggest a model in which a hypothesized 'distance cell' population is able to extract metrics from the activity of grid cells. We show that storing the momentary activity pattern of the grid cell system in a freely chosen position by one-shot learning and comparing it to the actual grid activity at other positions results in a distance dependent activity of these cells. The actual distance of the animal from the origin can be decoded directly by selecting the distance cell receiving the largest excitation or indirectly via transmission of local interneurons. We found that direct decoding works up to the longest grid spacing, but fails on smaller scales, while the indirect way provides precise distance determination up to the half of the longest grid spacing. In both cases, simulated distance cells have a multi-peaked, patchy spatial activity pattern consistent with the experimentally observed behavior of granule cells in the dentate gyrus.

Robust path integration in the entorhinal grid cell system with hippocampal feed-back

Animals are able to update their knowledge about their current position solely by integrating the speed and the direction of their movement, which is known as path integration. Recent discoveries suggest that grid cells in the medial entorhinal cortex might perform some of the essential underlying computations of path integration. However, a major concern over path integration is that as the measurement of speed and direction is inaccurate, the representation of the position will become increasingly unreliable. In this paper, we study how allothetic inputs can be used to continually correct the accumulating error in the path integrator system. We set up the model of a mobile agent equipped with the entorhinal representation of idiothetic (grid cell) and allothetic (visual cells) information and simulated its place learning in a virtual environment. Due to competitive learning, a robust hippocampal place code emerges rapidly in the model. At the same time, the hippocampo-entorhinal feed-back connections are modified via Hebbian learning in order to allow hippocampal place cells to influence the attractor dynamics in the entorhinal cortex. We show that the continuous feed-back from the integrated hippocampal place representation is able to stabilize the grid cell code.

From rapid place learning to behavioral performance: a key role for the intermediate hippocampus

Rapid place encoding by hippocampal neurons, as reflected by place-related firing, has been intensely studied, whereas the substrates that translate hippocampal place codes into behavior have received little attention. A key point relevant to this translation is that hippocampal organization is characterized by functional–anatomical gradients along the septotemporal axis: Whereas the ability of hippocampal neurons to encode accurate place information declines from the septal to temporal end, hippocampal connectivity to prefrontal and subcortical sites that might relate such place information to behavioral-control processes shows an opposite gradient. We examined in rats the impact of selective lesions to relevant parts of the hippocampus on behavioral tests requiring place learning (watermaze procedures) and on in vivo electrophysiological models of hippocampal encoding (long-term potentiation [LTP], place cells). We found that the intermediate hippocampus is necessary and largely sufficient for behavioral performance based on rapid place learning. In contrast, a residual septal pole of the hippocampus, although displaying intact electrophysiological indices of rapid information encoding (LTP, precise place-related firing, and rapid remapping), failed to sustain watermaze performance based on rapid place learning. These data highlight the important distinction between hippocampal encoding and the behavioral performance based on such encoding, and suggest that the intermediate hippocampus, where substrates of rapid accurate place encoding converge with links to behavioral control, is critical to translate rapid (one-trial) place learning into navigational performance.

The ability to remember locations in space is dependent on an area of the brain called the hippocampus. A much-studied property of neurons in the hippocampus is that they rapidly come to represent or code for specific places—i.e., the hippocampus “learns” places—as animals or humans move through an environment. Here, we identified in rats the hippocampal substrate enabling the translation of place learning into appropriate search and approach behavior (similar to the task of returning to a novel place where you parked your car). We examined the impact of selective lesions to distinct parts of the hippocampus on behavior requiring rapid place learning and on in vivo electrophysiological models of hippocampal learning such as place-related neuronal activity. We showed that translation of rapid place learning into efficient search behavior requires the “intermediate” region of the hippocampus, a region that likely combines anatomical links to visuospatial information processed by the neocortex with links to behavioral control through prefrontal cortex and subcortical sites. In contrast, the so-called “septal” region of the hippocampus, which features the relevant anatomical links to visuospatial information processing, can sustain rapid place learning (as reflected by formation of place-related neuronal firing), but not translate such learning into appropriate search and approach behavior.

The translation of hippocampal rapid place learning into successful search behavior requires the intermediate region of the hippocampus, which integrates accurate visuo-spatial processing with behavioral control.

Prediction, sequences and the hippocampus

Recordings of rat hippocampal place cells have provided information about how the hippocampus retrieves memory sequences. One line of evidence has to do with phase precession, a process organized by theta and gamma oscillations. This precession can be interpreted as the cued prediction of the sequence of upcoming positions. In support of this interpretation, experiments in two-dimensional environments and on a cue-rich linear track demonstrate that many cells represent a position ahead of the animal and that this position is the same irrespective of which direction the rat is coming from. Other lines of investigation have demonstrated that such predictive processes also occur in the non-spatial domain and that retrieval can be internally or externally cued. The mechanism of sequence retrieval and the usefulness of this retrieval to guide behaviour are discussed.

Theta phase precession and phase selectivity: a cognitive device description of neural coding

Information in neural systems is carried by way of phase and rate codes. Neuronal signals are processed through transformative biophysical mechanisms at the cellular and network levels. Neural coding transformations can be represented mathematically in a device called the cognitive rhythm generator (CRG). Incoming signals to the CRG are parsed through a bank of neuronal modes that orchestrate proportional, integrative and derivative transformations associated with neural coding. Mode outputs are then mixed through static nonlinearities to encode (spatio) temporal phase relationships. The static nonlinear outputs feed and modulate a ring device (limit cycle) encoding output dynamics. Small coupled CRG networks were created to investigate coding functionality associated with neuronal phase preference and theta precession in the hippocampus. Phase selectivity was found to be dependent on mode shape and polarity, while phase precession was a product of modal mixing (i.e. changes in the relative contribution or amplitude of mode outputs resulted in shifting phase preference). Nonlinear system identification was implemented to help validate the model and explain response characteristics associated with modal mixing; in particular, principal dynamic modes experimentally derived from a hippocampal neuron were inserted into a CRG and the neuron's dynamic response was successfully cloned. From our results, small CRG networks possessing disynaptic feedforward inhibition in combination with feedforward excitation exhibited frequency-dependent inhibitory-to-excitatory and excitatory-to-inhibitory transitions that were similar to transitions seen in a single CRG with quadratic modal mixing. This suggests nonlinear modal mixing to be a coding manifestation of the effect of network connectivity in shaping system dynamic behavior. We hypothesize that circuits containing disynaptic feedforward inhibition in the nervous system may be candidates for interpreting upstream rate codes to guide downstream processes such as phase precession, because of their demonstrated frequency-selective properties.

The role of competitive learning in the generation of DG fields from EC inputs

We follow up on a suggestion by Rolls and co-workers, that the effects of competitive learning should be assessed on the shape and number of spatial fields that dentate gyrus (DG) granule cells may form when receiving input from medial entorhinal cortex (mEC) grid units. We consider a simple non-dynamical model where DG units are described by a threshold-linear transfer function, and receive feedforward inputs from 1,000 mEC model grid units of various spacing, orientation and spatial phase. Feedforward weights are updated according to a Hebbian rule as the virtual rodent follows a long simulated trajectory through a single environment. Dentate activity is constrained to be very sparse. We find that indeed competitive Hebbian learning tends to result in a few active DG units with a single place field each, rounded in shape and made larger by iterative weight changes. These effects are more pronounced when produced with thousands of DG units and inputs per DG unit, which the realistic system has available, than with fewer units and inputs, in which case several DG units persists with multiple fields. The emergence of single-field units with learning is in contrast, however, to recent data indicating that most active DG units do have multiple fields. We show how multiple irregularly arranged fields can be produced by the addition of non-space selective lateral entorhinal cortex (lEC) units, which are modelled as simply providing an additional effective input specific to each DG unit. The mean number of such multiple DG fields is enhanced, in particular, when lEC and mEC inputs have overall similar variance across DG units. Finally, we show that in a restricted environment the mean size of the fields is unaltered, while their mean number is scaled down with the area of the environment.

How heterogeneous place cell responding arises from homogeneous grids--a contextual gating hypothesis

How entorhinal grids generate hippocampal place fields remains unknown. The simplest hypothesis-that grids of different scales are added together-cannot explain a number of place field phenomena, such as (1) Summed grids form a repeating, dispersed activation pattern whereas place fields are focal and nonrepeating; (2) Grid cells are active in all environments but place cells only in some, and (3) Partial environmental changes cause either heterogeneous ("partial") remapping in place cells whereas they result in all-or-nothing "realignment" remapping in grid cells. We propose that this dissociation between grid cell and place cell behavior arises in the entorhinal-dentate projection. By our view, the grid-cell/place-cell projection is modulated by context, both organizationally and activationally. Organizationally, we propose that when the animal first enters a new environment, the relatively homogeneous input from the grid cells becomes spatially clustered by Hebbian processes in the dendritic tree so that inputs active in the same context and having overlapping fields come to terminate on the same sub-branches of the tree. Activationally, when the animal re-enters the now-familiar environment, active contextual inputs select (by virtue of their clustered terminations) which parts of the dendritic tree, and therefore which grid cells, drive the granule cell. Assuming this pattern of projections, our model successfully produces focal hippocampal place fields that remap appropriately to contextual changes.

Grid cells: the position code, neural network models of activity, and the problem of learning

We review progress on the modeling and theoretical fronts in the quest to unravel the computational properties of the grid cell code and to explain the mechanisms underlying grid cell dynamics. The goals of the review are to outline a coherent framework for understanding the dynamics of grid cells and their representation of space; to critically present and draw contrasts between recurrent network models of grid cells based on continuous attractor dynamics and independent-neuron models based on temporal interference; and to suggest open questions for experiment and theory.

Influence of boundary removal on the spatial representations of the medial entorhinal cortex

The medial entorhinal cortex (MEC) is thought to create and update a dynamical representation of the animal's spatial location. Most suggestive of this process are grid cells, whose firing locations occur periodically in space. Prior studies in small environments were ambiguous as to whether all spatially modulated cells in MEC were variants of grid cells or whether a subset resembled classic place cells of the hippocampus. Recordings from the dorsal and ventral MEC were performed as four rats foraged in a small square box centered inside a larger one. After 6 min, without removing the rat from the enclosure, the walls of the small box were quickly removed, leaving the rat free to continue foraging in the whole area enclosed by the larger box. The rate-responses of most recorded cells (70 out of 93 cells, including 15 of 16 putative interneurons) were considered spatially modulated based on information-theoretic analysis. A number of cells that resembled classic hippocampal place cells in the small box were revealed to be grid cells in the larger box. In contrast, other cells that fired along the boundaries or corners of the small box did not show grid-cell firing in the large box, but instead fired along the corresponding locations of the large box. Remapping of the spatial response in the area corresponding to the small box after the removal of its walls was prominent in most spatially modulated cells. These results show that manipulation of local boundaries can exert a powerful influence on the spatial firing patterns of MEC cells even when the manipulations leave global cues unchanged and allow uninterrupted, self-motion-based localization. Further, they suggest the presence of landmark-related information in MEC, which might prevent cumulative drift of the spatial representation or might reset it to a previously learned configuration in a familiar environment.

A metric for space

Not all areas of neuronal systems investigation have matured to the stage where computation can be understood at the microcircuit level. In mammals, insights into cortical circuit functions have been obtained for the early stages of sensory systems, where signals can be followed through networks of increasing complexity from the receptors to the primary sensory cortices. These studies have suggested how neurons and neuronal networks extract features from the external world, but how the brain generates its own codes, in the higher-order nonsensory parts of the cortex, has remained deeply mysterious. In this terra incognita, a path was opened by the discovery of grid cells, place-modulated entorhinal neurons whose firing locations define a periodic triangular or hexagonal array covering the entirety of the animal's available environment. This array of firing is maintained in spite of ongoing changes in the animal's speed and direction, suggesting that grid cells are part of the brain's metric for representation of space. Because the crystal-like structure of the firing fields is created within the nervous system itself, grid cells may provide scientists with direct access to some of the most basic operational principles of cortical circuits.

The emergence of grid cells: Intelligent design or just adaptation?

Individual medial entorhinal cortex (mEC) 'grid' cells provide a representation of space that appears to be essentially invariant across environments, modulo simple transformations, in contrast to multiple, rapidly acquired hippocampal maps; it may therefore be established gradually during rodent development. We explore with a simplified mathematical model the possibility that the self-organization of multiple grid fields into a triangular grid pattern may be a single-cell process, driven by firing rate adaptation and slowly varying spatial inputs. A simple analytical derivation indicates that triangular grids are favored asymptotic states of the self-organizing system, and computer simulations confirm that such states are indeed reached during a model learning process, provided it is sufficiently slow to effectively average out fluctuations. The interactions among local ensembles of grid units serve solely to stabilize a common grid orientation. Spatial information, in the real mEC network, may be provided by any combination of feedforward cortical afferents and feedback hippocampal projections from place cells, since either input alone is likely sufficient to yield grid fields.

Grid cells and theta as oscillatory interference: theory and predictions

The oscillatory interference model [Burgess et al. (2007) Hippocampus 17:801-802] of grid cell firing is reviewed as an algorithmic level description of path integration and as an implementation level description of grid cells and their inputs. New analyses concern the relationships between the variables in the model and the theta rhythm, running speed, and the intrinsic firing frequencies of grid cells. New simulations concern the implementation of velocity-controlled oscillators (VCOs) with different preferred directions in different neurons. To summarize the model, the distance traveled along a specific direction is encoded by the phase of a VCO relative to a baseline frequency. Each VCO is an intrinsic membrane potential oscillation whose frequency increases from baseline as a result of depolarization by synaptic input from speed modulated head-direction cells. Grid cell firing is driven by the VCOs whose preferred directions match the current direction of motion. VCOs are phase-reset by location-specific input from place cells to prevent accumulation of error. The baseline frequency is identified with the local average of VCO frequencies, while EEG theta frequency is identified with the global average VCO frequency and comprises two components: the frequency at zero speed and a linear response to running speed. Quantitative predictions are given for the inter-relationships between a grid cell's intrinsic firing frequency and grid scale, the two components of theta frequency, and the running speed of the animal. Qualitative predictions are given for the properties of the VCOs, and the relationship between environmental novelty, the two components of theta, grid scale and place cell remapping.

Accurate path integration in continuous attractor network models of grid cells

Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat's velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of ∼10–100 meters and ∼1–10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other.

Even in the absence of external sensory cues, foraging rodents maintain an estimate of their position, allowing them to return home in a roughly straight line. This computation is known as dead reckoning or path integration. A discovery made three years ago in rats focused attention on the dorsolateral medial entorhinal cortex (dMEC) as a location in the rat's brain where this computation might be performed. In this area, so-called grid cells fire whenever the rat is on any vertex of a triangular grid that tiles the plane. Here we propose a model that could generate grid-cell-like responses in a neural network. The inputs to the model network convey information about the rat's velocity and heading, consistent with known inputs projecting into the dMEC. The network effectively integrates these inputs to produce a response that depends on the rat's absolute position. We show that such a neural network can integrate position accurately and can reproduce grid-cell-like responses similar to those observed experimentally. We then suggest a set of experiments that could help identify whether our suggested mechanism is responsible for the emergence of grid cells and for path integration in the rat's brain.

Temporally structured replay of neural activity in a model of entorhinal cortex, hippocampus and postsubiculum

The spiking activity of hippocampal neurons during rapid eye movement (REM) sleep exhibits temporally structured replay of spiking occurring during previously experienced trajectories. Here, temporally structured replay of place cell activity during REM sleep is modeled in a large-scale network simulation of grid cells, place cells and head direction cells. During simulated waking behavior, the movement of the simulated rat drives activity of a population of head direction cells that updates the activity of a population of entorhinal grid cells. The population of grid cells drives the activity of place cells coding individual locations. Associations between location and movement direction are encoded by modification of excitatory synaptic connections from place cells to speed modulated head direction cells. During simulated REM sleep, the population of place cells coding an experienced location activates the head direction cells coding the associated movement direction. Spiking of head direction cells then causes frequency shifts within the population of entorhinal grid cells to update a phase representation of location. Spiking grid cells then activate new place cells that drive new head direction activity. In contrast to models that perform temporally compressed sequence retrieval similar to sharp wave activity, this model can simulate data on temporally structured replay of hippocampal place cell activity during REM sleep at time scales similar to those observed during waking. These mechanisms could be important for episodic memory of trajectories.

Dopamine D1 receptor modulates hippocampal representation plasticity to spatial novelty

The human hippocampus is critical for learning and memory. In rodents, hippocampal pyramidal neurons fire in a location-specific manner, forming relational representations of environmental cues. The importance of glutamatergic systems in learning and in hippocampal neural synaptic plasticity has been shown. However, the role of dopaminergic systems in the response of hippocampal neural plasticity to novel and familiar spatial stimuli remains unclear. To clarify this important issue, we recorded hippocampal neurons from dopamine D(1) receptor knock-out (D1R-KO) mice and their wild-type (WT) littermates under the manipulation of distinct spatial cues in a familiar and a novel environment. Here we report that in WT mice, the majority of place cells quickly responded to the manipulations of distal and proximal cues in both familiar and novel environments. In contrast, the influence of distal cues on spatial firing in D1R-KO mice was abolished. In the D1R-KO mice, the influence of proximal cues was facilitated in a familiar environment, and in a novel environment most of the place cells were less likely to respond to changes of spatial cues. Our results demonstrate that hippocampal neurons in mice can rapidly and flexibly encode information about space from both distal and proximal cues to cipher a novel environment. This ability is necessary for many types of learning, and lacking D1R can radically alter this learning-related neural activity. We propose that D1R is crucially implicated in encoding spatial information in novel environments, and influences the plasticity of hippocampal representations, which is important in spatial learning and memory.

Sources of the spatial code within the hippocampus

Neurons in the hippocampus are thought to provide information on an animal's location within its environment. Input to the hippocampus comes via afferents from the entorhinal cortex, which are separated into several major pathways serving different hippocampal regions. Recent studies show the significance of individual afferent pathways in location perception, enhancing our understanding of hippocampal function.

Representation of Geometric Borders in the Entorhinal Cortex

We report the existence of an entorhinal cell type that fires when an animal is close to the borders of the proximal environment. The orientation-specific edge-apposing activity of these “border cells” is maintained when the environment is stretched and during testing in enclosures of different size and shape in different rooms. Border cells are relatively sparse, making up less than 10% of the local cell population, but can be found in all layers of the medial entorhinal cortex as well as the adjacent parasubiculum, often intermingled with head-direction cells and grid cells. Border cells may be instrumental in planning trajectories and anchoring grid fields and place fields to a geometric reference frame.

All my circuits: using multiple electrodes to understand functioning neural networks

Much of the work in systems neuroscience thus far has focused on the brain's parts studied individually. The past 20 years has seen the advent, rise, and application of multiple-electrode technology. This allows the study of the activity of many neurons simultaneously, which in turn has provided insight into how different neuron populations interact and collaborate to produce thought and action.

Unmasking the CA1 ensemble place code by exposures to small and large environments: more place cells and multiple, irregularly arranged, and expanded place fields in the larger space

In standard experimental environments, a constant proportion of CA1 principal cells are place cells, each with a spatial receptive field called a place field. Although the properties of place cells are a basis for understanding the mammalian representation of spatial knowledge, there is no consensus on which of the two fundamental neural-coding hypotheses correctly accounts for how place cells encode spatial information. Within the dedicated-coding hypothesis, the current activity of each cell is an independent estimate of the location with respect to its place field. The average of the location estimates from many cells represents current location, so a dedicated place code would degrade if single cells had multiple place fields. Within the alternative, ensemble-coding hypothesis, the concurrent discharge of many place cells is a vector that represents current location. An ensemble place code is not degraded if single cells have multiple place fields as long as the discharge vector at each location is unique. Place cells with multiple place fields might be required to represent the substantially larger space in more natural environments. To distinguish between the dedicated-coding and ensemble-coding hypotheses, we compared the characteristics of CA1 place fields in a standard cylinder and an approximately six times larger chamber. Compared with the cylinder, in the chamber, more CA1 neurons were place cells, each with multiple, irregularly arranged, and enlarged place fields. The results indicate that multiple place fields is a fundamental feature of CA1 place cell activity and that, consequently, an ensemble place code is required for CA1 discharge to accurately signal location.

Complementary roles of hippocampus and medial entorhinal cortex in episodic memory

Spatial mapping and navigation are figured prominently in the extant literature that describes hippocampal function. The medial entorhinal cortex is likewise attracting increasing interest, insofar as evidence accumulates that this area also contributes to spatial information processing. Here, we discuss recent electrophysiological findings that offer an alternate view of hippocampal and medial entorhinal function. These findings suggest complementary contributions of the hippocampus and medial entorhinal cortex in support of episodic memory, wherein hippocampal networks encode sequences of events that compose temporally and spatially extended episodes, whereas medial entorhinal networks disambiguate overlapping episodes by binding sequential events into distinct memories.

Linking cellular mechanisms to behavior: entorhinal persistent spiking and membrane potential oscillations may underlie path integration, grid cell firing, and episodic memory

The entorhinal cortex plays an important role in spatial memory and episodic memory functions. These functions may result from cellular mechanisms for integration of the afferent input to entorhinal cortex. This article reviews physiological data on persistent spiking and membrane potential oscillations in entorhinal cortex then presents models showing how both these cellular mechanisms could contribute to properties observed during unit recording, including grid cell firing, and how they could underlie behavioural functions including path integration. The interaction of oscillations and persistent firing could contribute to encoding and retrieval of trajectories through space and time as a mechanism relevant to episodic memory.

Navigating from hippocampus to parietal cortex

The navigational system of the mammalian cortex comprises a number of interacting brain regions. Grid cells in the medial entorhinal cortex and place cells in the hippocampus are thought to participate in the formation of a dynamic representation of the animal's current location, and these cells are presumably critical for storing the representation in memory. To traverse the environment, animals must be able to translate coordinate information from spatial maps in the entorhinal cortex and hippocampus into body-centered representations that can be used to direct locomotion. How this is done remains an enigma. We propose that the posterior parietal cortex is critical for this transformation.

Place cells, grid cells, and the brain's spatial representation system

More than three decades of research have demonstrated a role for hippocampal place cells in representation of the spatial environment in the brain. New studies have shown that place cells are part of a broader circuit for dynamic representation of self-location. A key component of this network is the entorhinal grid cells, which, by virtue of their tessellating firing fields, may provide the elements of a path integration-based neural map. Here we review how place cells and grid cells may form the basis for quantitative spatiotemporal representation of places, routes, and associated experiences during behavior and in memory. Because these cell types have some of the most conspicuous behavioral correlates among neurons in nonsensory cortical systems, and because their spatial firing structure reflects computations internally in the system, studies of entorhinal-hippocampal representations may offer considerable insight into general principles of cortical network dynamics.

Time constants of h current in layer ii stellate cells differ along the dorsal to ventral axis of medial entorhinal cortex

Chronic recordings in the medial entorhinal cortex of behaving rats have found grid cells, neurons that fire when the rat is in a hexagonal array of locations. Grid cells recorded at different dorsal-ventral anatomical positions show systematic changes in size and spacing of firing fields. To test possible mechanisms underlying these differences, we analyzed properties of the hyperpolarization-activated cation current I(h) in voltage-clamp recordings from stellate cells in entorhinal slices from different dorsal-ventral locations. The time constant of h current was significantly different between dorsal and ventral neurons. The time constant of h current correlated with membrane potential oscillation frequency and the time constant of the sag potential in the same neurons. Differences in h current could underlie differences in membrane potential oscillation properties and contribute to grid cell periodicity along the dorsal-ventral axis of medial entorhinal cortex.

What grid cells convey about rat location

We characterize the relationship between the simultaneously recorded quantities of rodent grid cell firing and the position of the rat. The formalization reveals various properties of grid cell activity when considered as a neural code for representing and updating estimates of the rat's location. We show that, although the spatially periodic response of grid cells appears wasteful, the code is fully combinatorial in capacity. The resulting range for unambiguous position representation is vastly greater than the approximately 1-10 m periods of individual lattices, allowing for unique high-resolution position specification over the behavioral foraging ranges of rats, with excess capacity that could be used for error correction. Next, we show that the merits of the grid cell code for position representation extend well beyond capacity and include arithmetic properties that facilitate position updating. We conclude by considering the numerous implications, for downstream readouts and experimental tests, of the properties of the grid cell code.

Understanding memory through hippocampal remapping

Memory interference is a common cause of forgetting. Interference is a byproduct of the need to balance the formation of well-differentiated representations against the ability to retrieve memories from cues that are not identical to the original experience. How the brain accomplishes this has remained elusive. Here we review how insights can be gained from studies of an apparently unrelated phenomenon in the rodent brain--remapping in hippocampal place cells. Remapping refers to the formation of distinct representations in populations of place cells after minor changes in inputs to the hippocampus. Remapping might reflect processes involved generally in decorrelation of overlapping signals. These processes might be crucial for storing large numbers of similar experiences with only minimal interference.

Spatial cognition and the brain

Recent advances in the understanding of spatial cognition are reviewed, focusing on memory for locations in large-scale space and on those advances inspired by single-unit recording and lesion studies in animals. Spatial memory appears to be supported by multiple parallel representations, including egocentric and allocentric representations, and those updated to accommodate self-motion. The effects of these representations can be dissociated behaviorally, developmentally, and in terms of their neural bases. It is now becoming possible to construct a mechanistic neural-level model of at least some aspects of spatial memory and imagery, with the hippocampus and medial temporal lobe providing allocentric environmental representations, the parietal lobe egocentric representations, and the retrosplenial cortex and parieto-occipital sulcus allowing both types of representation to interact. Insights from this model include a common mechanism for the construction of spatial scenes in the service of both imagery and episodic retrieval and a role for the remainder of Papez's circuit in orienting the viewpoint used. In addition, it appears that hippocampal and striatal systems process different aspects of environmental layout (boundaries and local landmarks, respectively) and do so using different learning rules (incidental learning and associative reinforcement, respectively).