Dual phase and rate coding in hippocampal place cells: theoretical significance and relationship to entorhinal grid cells

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.

The role of the hippocampus in long-term memory: is it memory store or comparator?

Several attempts have been made to reconcile a number of rival theories on the role of the hippocampus in long-term memory. Those attempts fail to explain the basic effects of the theories from the same point of view. We are reviewing the four major theories, and shall demonstrate, with the use of mathematical models of attention and memory, that only one theory is capable of reconciling all of them by explaining the basic effects of each theory in a unified fashion, without altogether sacrificing their individual contributions. The key issue here is whether or not a memory trace is ever stored in the hippocampus itself, and there is no reconciliation unless the answer to that question is that there is not. As a result of the reconciliation that we are proposing, there is a simple solution to several outstanding problems concerning the neurobiology of memory such as: consolidation and reconsolidation, persistency of long term memory, novelty detection, habituation, long-term potentiation, and the multifrequency oscillatory self-organization of the brain.

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.

The h channel mediates location dependence and plasticity of intrinsic phase response in rat hippocampal neurons

The presence of phenomenological inductances in neuronal membrane has been known for more than one-half a century. Despite this, the dramatic contributions of such inductive elements to the amplitude and, especially, phase of neuronal impedance, and their roles in modulating temporal dynamics of neuronal responses have surprisingly remained unexplored. In this study, we demonstrate that the h channel contributes a location-dependent and plastic phenomenological inductive component to the input impedance of CA1 pyramidal neurons. Specifically, we show that the h channels introduce an apparent negative delay in the local voltage response of these neurons with respect to the injected current within the theta frequency range. The frequency range and the extent of this lead expand with increases in h current either through hyperpolarization, or with increasing distance of dendritic location from the soma. We also demonstrate that a spatially widespread increase in this inductive phase component accompanies long-term potentiation. Finally, using impedance analysis, we show that both location and activity dependence of intrinsic phase response are attributable not to changes in a capacitive or a leak component, but to changes in h-channel properties. Our results suggest that certain voltage-gated ion channels can differentially regulate internal time delays within neurons, thus providing them with an independent control mechanism in temporal coding of neuronal information. Our analyses and results also establish impedance as a powerful measure of intrinsic dynamics and excitability, given that it quantifies temporal relationships among signals and excitability as functions of input frequency.

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).

Theta-mediated dynamics of spatial information in hippocampus

In rodent hippocampus, neuronal activity is organized by a 6-10 Hz theta oscillation. The spike timing of hippocampal pyramidal cells with respect to the theta rhythm correlates with an animal's position in space. This correlation has been suggested to indicate an explicit temporal code for position. Alternatively, it may be interpreted as a byproduct of theta-dependent dynamics of spatial information flow in hippocampus. Here we show that place cell activity on different phases of theta reflects positions shifted into the future or past along the animal's trajectory in a two-dimensional environment. The phases encoding future and past positions are consistent across recorded CA1 place cells, indicating a coherent representation at the network level. Consistent theta-dependent time offsets are not simply a consequence of phase-position correlation (phase precession), because they are no longer seen after data randomization that preserves the phase-position relationship. The scale of these time offsets, 100-300 ms, is similar to the latencies of hippocampal activity after sensory input and before motor output, suggesting that offset activity may maintain coherent brain activity in the face of information processing delays.

Firing rate dynamics in the hippocampus induced by trajectory learning

The hippocampus is essential for spatial navigation, which may involve sequential learning. However, how the hippocampus encodes new sequences in familiar environments is unknown. To study the impact of novel spatial sequences on the activity of hippocampal neurons, we monitored hippocampal ensembles while rats learned to switch from two familiar trajectories to a new one in a familiar environment. Here, we show that this novel spatial experience induces two types of changes in firing rates, but not locations of hippocampal place cells. First, place-cell firing rates on the two familiar trajectories start to change before the actual behavioral switch to the new trajectory. Second, repeated exposure on the new trajectory is associated with an increased dependence of place-cell firing rates on immediate past locations. The result suggests that sequence encoding in the hippocampus may involve integration of information about the recent past into current state.

Artificial synaptic conductances reduce subthreshold oscillations and periodic firing in stellate cells of the entorhinal cortex

Previous work has established that stellate cells of the medial entorhinal cortex produce prominent intrinsic subthreshold oscillations in the voltage response concentrated within the theta range (3-7 Hz). It has been speculated that these oscillations play an important role in vivo in establishing network behavior both in the entorhinal cortex and hippocampus. Consequently, it is important to investigate under what conditions theta oscillations in stellate cells can be generated and whether the spike-train power spectral density (PSD) also carries power at theta. We investigated the ability of stellate cells to generate theta oscillations in the presence of generic in vivo-like patterns of stimulation. Inputs were Poisson process-driven excitatory and inhibitory synaptic conductances or currents, introduced via dynamic clamp. We analyzed the subthreshold membrane oscillations and spike-train behavior in the presence of comparable synaptic conductance- or current-mediated membrane fluctuations. In the presence of conductance-based synapses, subthreshold oscillations are highly attenuated or entirely eliminated. Conversely, with current-based synapses stellate cells retain their ability to generate subthreshold oscillations in the theta band. These results also extend into the spiking regime, where only under current-based synapses does the PSD of the spike train show a prominent peak at theta. Furthermore, the peak in the spike-train PSD and spike clustering results from an increased probability of firing after a spike afterhyperpolarization and not directly from subthreshold oscillatory dynamics as has been previously suggested. Our results suggest that subthreshold oscillations may contribute less to in vivo response properties than has been hypothesized.

Hippocampus-independent phase precession in entorhinal grid cells

Theta-phase precession in hippocampal place cells is one of the best-studied experimental models of temporal coding in the brain. Theta-phase precession is a change in spike timing in which the place cell fires at progressively earlier phases of the extracellular theta rhythm as the animal crosses the spatially restricted firing field of the neuron. Within individual theta cycles, this phase advance results in a compressed replication of the firing sequence of consecutively activated place cells along the animal's trajectory, at a timescale short enough to enable spike-time-dependent plasticity between neurons in different parts of the sequence. The neuronal circuitry required for phase precession has not yet been established. The fact that phase precession can be seen in hippocampal output stuctures such as the prefrontal cortex suggests either that efferent structures inherit the precession from the hippocampus or that it is generated locally in those structures. Here we show that phase precession is expressed independently of the hippocampus in spatially modulated grid cells in layer II of medial entorhinal cortex, one synapse upstream of the hippocampus. Phase precession is apparent in nearly all principal cells in layer II but only sparsely in layer III. The precession in layer II is not blocked by inactivation of the hippocampus, suggesting that the phase advance is generated in the grid cell network. The results point to possible mechanisms for grid formation and raise the possibility that hippocampal phase precession is inherited from entorhinal cortex.

A principle for learning egocentric-allocentric transformation

Numerous single-unit recording studies have found mammalian hippocampal neurons that fire selectively for the animal's location in space, independent of its orientation. The population of such neurons, commonly known as place cells, is thought to maintain an allocentric, or orientation-independent, internal representation of the animal's location in space, as well as mediating long-term storage of spatial memories. The fact that spatial information from the environment must reach the brain via sensory receptors in an inherently egocentric, or viewpoint-dependent, fashion leads to the question of how the brain learns to transform egocentric sensory representations into allocentric ones for long-term memory storage. Additionally, if these long-term memory representations of space are to be useful in guiding motor behavior, then the reverse transformation, from allocentric to egocentric coordinates, must also be learned. We propose that orientation-invariant representations can be learned by neural circuits that follow two learning principles: minimization of reconstruction error and maximization of representational temporal inertia. Two different neural network models are presented that adhere to these learning principles, the first by direct optimization through gradient descent and the second using a more biologically realistic circuit based on the restricted Boltzmann machine (Hinton, 2002; Smolensky, 1986). Both models lead to orientation-invariant representations, with the latter demonstrating place-cell-like responses when trained on a linear track environment.

Coincidence detection of place and temporal context in a network model of spiking hippocampal neurons

Recent advances in single-neuron biophysics have enhanced our understanding of information processing on the cellular level, but how the detailed properties of individual neurons give rise to large-scale behavior remains unclear. Here, we present a model of the hippocampal network based on observed biophysical properties of hippocampal and entorhinal cortical neurons. We assembled our model to simulate spatial alternation, a task that requires memory of the previous path through the environment for correct selection of the current path to a reward site. The convergence of inputs from entorhinal cortex and hippocampal region CA3 onto CA1 pyramidal cells make them potentially important for integrating information about place and temporal context on the network level. Our model shows how place and temporal context information might be combined in CA1 pyramidal neurons to give rise to splitter cells, which fire selectively based on a combination of place and temporal context. The model leads to a number of experimentally testable predictions that may lead to a better understanding of the biophysical basis of information processing in the hippocampus.

Understanding how behavior is connected to cellular and network processes is one of the most important challenges in neuroscience, and computational modeling allows one to directly formulate hypotheses regarding the interactions between these scales. We present a model of the hippocampal network, an area of the brain important for spatial navigation and episodic memory, memory of “what, when, and where.” We show how the model, which consists of neurons and connections based on biophysical properties known from experiments, can guide a virtual rat through the spatial alternation task by storing a memory of the previous path through an environment. Our model shows how neurons that fire selectively based on both the current location and past trajectory of the animal (dubbed “splitter cells”) might emerge from a newly discovered biophysical interaction in these cells. Our model is not intended to be comprehensive, but rather to contain just enough detail to achieve performance of the behavioral task. Goals of this approach are to present a scenario by which the gap between biophysics and behavior can be bridged and to provide a framework for the formulation of experimentally testable hypotheses.

Theta phase-specific codes for two-dimensional position, trajectory and heading in the hippocampus

Temporal coding is a means of representing information by the time, as opposed to the rate, at which neurons fire. Evidence of temporal coding in the hippocampus comes from place cells, whose spike times relative to theta oscillations reflect a rat's position while running along stereotyped trajectories. This arises from the backwards shift in cell firing relative to local theta oscillations (phase precession). Here we demonstrate phase precession during place-field crossings in an open-field foraging task. This produced spike sequences in each theta cycle that disambiguate the rat's trajectory through two-dimensional space and can be used to predict movement direction. Furthermore, position and movement direction were maximally predicted from firing in the early and late portions of the theta cycle, respectively. This represents the first direct evidence of a combined representation of position, trajectory and heading in the hippocampus, organized on a fine temporal scale by theta oscillations.

Impaired spatial representation in CA1 after lesion of direct input from entorhinal cortex

Place-specific firing in the hippocampus is determined by path integration-based spatial representations in the grid-cell network of the medial entorhinal cortex. Output from this network is conveyed directly to CA1 of the hippocampus by projections from principal neurons in layer III, but also indirectly by axons from layer II to the dentate gyrus and CA3. The direct pathway is sufficient for spatial firing in CA1, but it is not known whether similar firing can also be supported by the input from CA3. To test this possibility, we made selective lesions in layer III of medial entorhinal cortex by local infusion of the neurotoxin gamma-acetylenic GABA. Firing fields in CA1 became larger and more dispersed after cell loss in layer III, whereas CA3 cells, which receive layer II input, still had sharp firing fields. Thus, the direct projection is necessary for precise spatial firing in the CA1 place cell population.

Dynamic ensemble odor coding in the mammalian olfactory bulb: sensory information at different timescales

Neural firing discharges are often temporally patterned, but it is often ambiguous as to whether the temporal features of these patterns constitute a useful code. Here we show in the mouse olfactory bulb that ensembles of projection neurons respond with complex odor- and concentration-specific dynamic activity sequences developing below and above sniffing frequency. Based on this activity, almost optimal discrimination of presented odors was possible during single sniffs, consistent with reported behavioral data. Within a sniff cycle, slower features of the dynamics alone (>100 ms resolution, including mean firing rate) were sufficient for maximal discrimination. A smaller amount of information was also observed in faster features down to 20-40 ms resolution. Therefore, mitral cell ensemble activity contains information at different timescales that could be separately or complementarily exploited by downstream brain centers to make odor discriminations. Our results also support suggestive analogies in the dynamics of odor representations between insects and mammals.

Long-term potentiation in rat hippocampal neurons is accompanied by spatially widespread changes in intrinsic oscillatory dynamics and excitability

Oscillations in neural activity are a prominent feature of many brain states. Individual hippocampal neurons exhibit intrinsic membrane potential oscillations and intrinsic resonance in the theta frequency range. We found that the subthreshold resonance frequency of CA1 pyramidal neurons was location dependent, varying more than 3-fold between the soma and the distal dendrites. Furthermore, activity- and NMDA-receptor-dependent long-term plasticity increased this resonance frequency through changes in h channel properties. The increase in resonance frequency and an associated reduction in excitability were nearly identical in the soma and the first 300 mum of the apical dendrites. These spatially widespread changes accompanying long-term synaptic potentiation also reduced the neuron's ability to elicit spikes evoked through a nonpotentiated synaptic pathway. Our results suggest that the frequency response of these neurons depends on the dendritic location of their inputs and that activity can regulate their response dynamics within an oscillating neural network.

A model of grid cells involving extra hippocampal path integration, and the hippocampal loop

In this paper, we present a model for the generation of grid cells and the emergence of place cells from multimodal input to the entorhinal cortex (EC). In this model, grid cell activity in the dorsocaudal medial entorhinal cortex (dMEC) [28] results from the operation of a long-distance path integration system located outside the hippocampal formation, presumably in retrosplenial and/or parietal cortex. If the connections between these structures and dMEC are organized as a modulo N operator, the resulting activity of dMEC neurons is a grid cell pattern. Furthermore, a robust high-resolution positional code can be built from a small set of different grid cells if the modulo factors are relatively prime. On the other hand, broad visual place cell activity in the MEC can result from the integration of visual information depending on the view-field of the visual input. The merging of entorhinal visual place cell information and grid cell information in the EC and/or in the dentate gyrus (DG) allows the building of precise and robust "place cells" (e.g., whose activity is maintained if light is suppressed for a short duration). Our model supports our previous proposition that hippocampal "place cell" activity code transitions between two successive states ("transition cells") rather than mere current locations. Furthermore, we discuss the possibility that the hippocampal loop participates in the emergence of grid cell activity but is not sufficient by itself. Finally, path integration at a short time scale (which is reset from one place to the next) would be merged in the subiculum with CA3/CA1 "transition cells" [22] to provide a robust feedback about current action to the deep layer of the entorhinal cortex in order to predict the recognition of the new animal location.

Prediction of the position of an animal based on populations of grid and place cells: a comparative simulation study

The grid cells of the rodent medial entorhinal cortex (MEC) show activity patterns correlated with the animal's position. Unlike hippocampal place cells that are activated at only one specific location in the environment, MEC grid cells increase firing frequency at multiple regions in space, or subfields, that are arranged in regular triangular grids. It has been recently shown that a conjunction of MEC grid cells can lead to unique spatial representations. However, it remains unclear what the key properties of the grids are that allow for an accurate reconstruction of the position of the animal and what the comparison with hippocampal place cells is. Here we use a theoretical approach based on data from electrophysiological recordings of the MEC to simulate the neural activity of grid cells. Our simulations account for the accurate reproduction of grid cell mean firing rates, based on only three grid parameters, that is grid phase, spacing and orientation. The analysis of the key properties of the grids first reveals that for an accurate position reconstruction, it is necessary to combine cells with different grid spacings (which are found at different dorsoventral locations of the MEC) or orientations. Second, the relationship between grid spacing and subfield size observed in physiological data is optimal to predict the animal's position. Third, the regular triangular tessellating patterns of grid cells lead to the best position reconstruction results when compared with all other regular tessellations of two-dimensional space. Finally, the comparison of grid cells with place cells shows that populations of MEC grid cells can better predict the animal's position than equally-sized populations of hippocampal place cells with similar but unique spatial fields. Taken together, our results suggest that the MEC provides highly compact representations of the animal's position, which may be subsequently integrated by the place cells of the hippocampus.

Self-localization and the entorhinal-hippocampal system

Self-localization requires that information from several sensory modalities and knowledge domains be integrated in order to identify an environment and determine current location and heading. This integration occurs by the convergence of highly processed sensory information onto neural systems in entorhinal cortex and hippocampus. Entorhinal neurons combine angular and linear self-motion information to generate an oriented metric signal that is then 'attached' to each environment using information about landmarks and context. Neurons in hippocampus use this signal to determine the animal's unique position within a particular environment. Elucidating this process illuminates not only spatial processing but also, more generally, how the brain builds knowledge representations from inputs carrying heterogeneous sensory and semantic content.

Learning in a geometric model of place cell firing

Following Hartley et al. (Hartley et al. (2000) Hippocampus 10:369-379), we present a simple feed-forward model of place cell (PC) firing predicated on neocortical information regarding the environmental geometry surrounding the animal. Incorporating the idea of boundaries with distinct sensory qualities, we show that synaptic plasticity mediated by a BCM-like rule (Bienenstock et al. (1982) J Neurosci 2:32-48) produces PCs that encode position relative to specific extended landmarks. In an unchanging environment the model is shown to undergo an initial phase of learning, resulting in the formation of stable place fields. In familiar environments, perturbation of environmental cues produces graded changes in the firing rate and position of place fields. Model simulations are compared favorably with three sets of experimental data: (1) Results published by Barry et al. (Barry et al. (2006) Rev Neurosci 17:71-97) showing the slow disappearance of duplicate place fields produced when a barrier is placed into a familiar environment. (2) Rivard et al.'s (Rivard et al. (2004) J Gen Physiol 124:9-25) study showing a graded response in PC firing such that fields near to a centrally placed object encode space relative to the object, whereas more distant fields respond to the surrounding environment. (3) Fenton et al.'s (Fenton et al. (2000a) J Gen Physiol 116:191-209) observation that inconsistent rotation of cue cards produces parametric changes in place field positions. The merits of the model are discussed in terms of its extensibility and biological plausibility.

An oscillatory interference model of grid cell firing

We expand upon our proposal that the oscillatory interference mechanism proposed for the phase precession effect in place cells underlies the grid-like firing pattern of dorsomedial entorhinal grid cells (O'Keefe and Burgess (2005) Hippocampus 15:853-866). The original one-dimensional interference model is generalized to an appropriate two-dimensional mechanism. Specifically, dendritic subunits of layer II medial entorhinal stellate cells provide multiple linear interference patterns along different directions, with their product determining the firing of the cell. Connection of appropriate speed- and direction-dependent inputs onto dendritic subunits could result from an unsupervised learning rule which maximizes postsynaptic firing (e.g. competitive learning). These inputs cause the intrinsic oscillation of subunit membrane potential to increase above theta frequency by an amount proportional to the animal's speed of running in the "preferred" direction. The phase difference between this oscillation and a somatic input at theta-frequency essentially integrates velocity so that the interference of the two oscillations reflects distance traveled in the preferred direction. The overall grid pattern is maintained in environmental location by phase reset of the grid cell by place cells receiving sensory input from the environment, and environmental boundaries in particular. We also outline possible variations on the basic model, including the generation of grid-like firing via the interaction of multiple cells rather than via multiple dendritic subunits. Predictions of the interference model are given for the frequency composition of EEG power spectra and temporal autocorrelograms of grid cell firing as functions of the speed and direction of running and the novelty of the environment.

Grid cell mechanisms and function: contributions of entorhinal persistent spiking and phase resetting

This article presents a model of grid cell firing based on the intrinsic persistent firing shown experimentally in neurons of entorhinal cortex. In this model, the mechanism of persistent firing allows individual neurons to hold a stable baseline firing frequency. Depolarizing input from speed-modulated head direction cells transiently shifts the frequency of firing from baseline, resulting in a shift in spiking phase in proportion to the integral of velocity. The convergence of input from different persistent firing neurons causes spiking in a grid cell only when the persistent firing neurons are within similar phase ranges. This model effectively simulates the two-dimensional firing of grid cells in open field environments, as well as the properties of theta phase precession. This model provides an alternate implementation of oscillatory interference models. The persistent firing could also interact on a circuit level with rhythmic inhibition and neurons showing membrane potential oscillations to code position with spiking phase. These mechanisms could operate in parallel with computation of position from visual angle and distance of stimuli. In addition to simulating two-dimensional grid patterns, models of phase interference can account for context-dependent firing in other tasks. In network simulations of entorhinal cortex, hippocampus, and postsubiculum, the reset of phase effectively replicates context-dependent firing by entorhinal and hippocampal neurons during performance of a continuous spatial alternation task, a delayed spatial alternation task with running in a wheel during the delay period (Pastalkova et al., Science, 2008), and a hairpin maze task.

Grid cells and theta as oscillatory interference: electrophysiological data from freely moving rats

The oscillatory interference model (Burgess et al. (2007) Hippocampus 17:801-812) explains the generation of spatially stable, regular firing patterns by medial entorhinal cortical (mEC) grid cells in terms of the interference between velocity-controlled oscillators (VCOs) with different preferred directions. This model predicts specific relationships between the intrinsic firing frequency and spatial scale of grid cell firing, the EEG theta frequency, and running speed (Burgess,2008). Here, we use spectral analyses of EEG and of spike autocorrelograms to estimate the intrinsic firing frequency of grid cells, and the concurrent theta frequency, in mEC Layer II in freely moving rats. The intrinsic firing frequency of grid cells increased with running speed and decreased with grid scale, according to the quantitative prediction of the model. Similarly, theta frequency increased with running speed, which was also predicted by the model. An alternative Moiré interference model (Blair et al.,2007) predicts a direction-dependent variation in intrinsic firing frequency, which was not found. Our results suggest that interference between VCOs generates the spatial firing patterns of entorhinal grid cells according to the oscillatory interference model. They also provide specific constraints on this model of grid cell firing and have more general implications for viewing neuronal processing in terms of interfering oscillatory processes.

A model of grid cells based on a twisted torus topology

The grid cells of the rat medial entorhinal cortex (MEC) show an increased firing frequency when the position of the animal correlates with multiple regions of the environment that are arranged in regular triangular grids. Here, we describe an artificial neural network based on a twisted torus topology, which allows for the generation of regular triangular grids. The association of the activity of pre-defined hippocampal place cells with entorhinal grid cells allows for a highly robust-to-noise calibration mechanism, suggesting a role for the hippocampal back-projections to the entorhinal cortex.

Arc length coding by interference of theta frequency oscillations may underlie context-dependent hippocampal unit data and episodic memory function

Many memory models focus on encoding of sequences by excitatory recurrent synapses in region CA3 of the hippocampus. However, data and modeling suggest an alternate mechanism for encoding of sequences in which interference between theta frequency oscillations encodes the position within a sequence based on spatial arc length or time. Arc length can be coded by an oscillatory interference model that accounts for many features of the context-dependent firing properties of hippocampal neurons observed during performance of spatial memory tasks. In continuous spatial alternation, many neurons fire selectively depending on the direction of prior or future response (left or right). In contrast, in delayed non-match to position, most neurons fire selectively for task phase (sample vs. choice), with less selectivity for left versus right. These seemingly disparate results are effectively simulated by the same model, based on mechanisms similar to a model of grid cell firing in entorhinal cortex. The model also simulates forward shifting of firing over trials. Adding effects of persistent firing with reset at reward locations addresses changes in context-dependent firing with different task designs. Arc length coding could contribute to episodic encoding of trajectories as sequences of states and actions.

Remembering the past and imagining the future: a neural model of spatial memory and imagery

The authors model the neural mechanisms underlying spatial cognition, integrating neuronal systems and behavioral data, and address the relationships between long-term memory, short-term memory, and imagery, and between egocentric and allocentric and visual and ideothetic representations. Long-term spatial memory is modeled as attractor dynamics within medial-temporal allocentric representations, and short-term memory is modeled as egocentric parietal representations driven by perception, retrieval, and imagery and modulated by directed attention. Both encoding and retrieval/imagery require translation between egocentric and allocentric representations, which are mediated by posterior parietal and retrosplenial areas and the use of head direction representations in Papez's circuit. Thus, the hippocampus effectively indexes information by real or imagined location, whereas Papez's circuit translates to imagery or from perception according to the direction of view. Modulation of this translation by motor efference allows spatial updating of representations, whereas prefrontal simulated motor efference allows mental exploration. The alternating temporal-parietal flows of information are organized by the theta rhythm. Simulations demonstrate the retrieval and updating of familiar spatial scenes, hemispatial neglect in memory, and the effects on hippocampal place cell firing of lesioned head direction representations and of conflicting visual and ideothetic inputs.

Network and intrinsic cellular mechanisms underlying theta phase precession of hippocampal neurons

Hippocampal 'place cells' systematically shift their phase of firing in relation to the theta rhythm as an animal traverses the 'place field'. These dynamics imply that the neural ensemble begins each theta cycle at a point in its state-space that might 'represent' the current location of the rat, but that the ensemble 'looks ahead' during the rest of the cycle. Phase precession could result from intrinsic cellular dynamics involving interference of two oscillators of different frequencies, or from network interactions, similar to Hebb's 'phase sequence' concept, involving asymmetric synaptic connections. Both models have difficulties accounting for all of the available experimental data, however. A hybrid model, in which the look-ahead phenomenon implied by phase precession originates in superficial entorhinal cortex by some form of interference mechanism and is enhanced in the hippocampus proper by asymmetric synaptic plasticity during sequence encoding, seems to be consistent with available data, but as yet there is no fully satisfactory theoretical account of this phenomenon. This review is part of the INMED/TINS special issue Physiogenic and pathogenic oscillations: the beauty and the beast, based on presentations at the annual INMED/TINS symposium (http://inmednet.com).

Hippocampal place cell assemblies are speed-controlled oscillators

The phase of spikes of hippocampal pyramidal cells relative to the local field theta oscillation shifts forward ("phase precession") over a full theta cycle as the animal crosses the cell's receptive field ("place field"). The linear relationship between the phase of the spikes and the travel distance within the place field is independent of the animal's running speed. This invariance of the phase-distance relationship is likely to be important for coordinated activity of hippocampal cells and space coding, yet the mechanism responsible for it is not known. Here we show that at faster running speeds place cells are active for fewer theta cycles but oscillate at a higher frequency and emit more spikes per cycle. As a result, the phase shift of spikes from cycle to cycle (i.e., temporal precession slope) is faster, yet spatial-phase precession stays unchanged. Interneurons can also show transient-phase precession and contribute to the formation of coherently precessing assemblies. We hypothesize that the speed-correlated acceleration of place cell assembly oscillation is responsible for the phase-distance invariance of hippocampal place cells.

Experience-dependent rescaling of entorhinal grids

The firing pattern of entorhinal 'grid cells' is thought to provide an intrinsic metric for space. We report a strong experience-dependent environmental influence: the spatial scales of the grids (which are aligned and have fixed relative sizes within each animal) vary parametrically with changes to a familiar environment's size and shape. Thus grid scale reflects an interaction between intrinsic, path-integrative calculation of location and learned associations to the external environment.

Theta phase precession emerges from a hybrid computational model of a CA3 place cell

The origins and functional significance of theta phase precession in the hippocampus remain obscure, in part, because of the difficulty of reproducing hippocampal place cell firing in experimental settings where the biophysical underpinnings can be examined in detail. The present study concerns a neurobiologically based computational model of the emergence of theta phase precession in which the responses of a single model CA3 pyramidal cell are examined in the context of stimulation by realistic afferent spike trains including those of place cells in entorhinal cortex, dentate gyrus, and other CA3 pyramidal cells. Spike-timing dependent plasticity in the model CA3 pyramidal cell leads to a spatially correlated associational synaptic drive that subsequently creates a spatially asymmetric expansion of the model cell's place field. Following an initial training period, theta phase precession can be seen in the firing patterns of the model CA3 pyramidal cell. Through selective manipulations of the model it is possible to decompose theta phase precession in CA3 into the separate contributing factors of inheritance from upstream afferents in the dentate gyrus and entorhinal cortex, the interaction of synaptically controlled increasing afferent drive with phasic inhibition, and the theta phase difference between dentate gyrus granule cell and CA3 pyramidal cell activity. In the context of a single CA3 pyramidal cell, the model shows that each of these factors plays a role in theta phase precession within CA3 and suggests that no one single factor offers a complete explanation of the phenomenon. The model also shows parallels between theta phase encoding and pattern completion within the CA3 autoassociative network.

Scale-invariant memory representations emerge from moiré interference between grid fields that produce theta oscillations: a computational model

The dorsomedial entorhinal cortex (dMEC) of the rat brain contains a remarkable population of spatially tuned neurons called grid cells (Hafting et al., 2005). Each grid cell fires selectively at multiple spatial locations, which are geometrically arranged to form a hexagonal lattice that tiles the surface of the rat's environment. Here, we show that grid fields can combine with one another to form moiré interference patterns, referred to as "moiré grids," that replicate the hexagonal lattice over an infinite range of spatial scales. We propose that dMEC grids are actually moiré grids formed by interference between much smaller "theta grids," which are hypothesized to be the primary source of movement-related theta rhythm in the rat brain. The formation of moiré grids from theta grids obeys two scaling laws, referred to as the length and rotational scaling rules. The length scaling rule appears to account for firing properties of grid cells in layer II of dMEC, whereas the rotational scaling rule can better explain properties of layer III grid cells. Moiré grids built from theta grids can be combined to form yet larger grids and can also be used as basis functions to construct memory representations of spatial locations (place cells) or visual images. Memory representations built from moiré grids are automatically endowed with size invariance by the scaling properties of the moiré grids. We therefore propose that moiré interference between grid fields may constitute an important principle of neural computation underlying the construction of scale-invariant memory representations.

Temporal frequency of subthreshold oscillations scales with entorhinal grid cell field spacing

Grid cells in layer II of rat entorhinal cortex fire to spatial locations in a repeating hexagonal grid, with smaller spacing between grid fields for neurons in more dorsal anatomical locations. Data from in vitro whole-cell patch recordings showed differences in frequency of subthreshold membrane potential oscillations in entorhinal neurons that correspond to different positions along the dorsal-to-ventral axis, supporting a model of physiological mechanisms for grid cell responses.

Backward shift of head direction tuning curves of the anterior thalamus: comparison with CA1 place fields

The head direction cell system is composed of multiple regions associated with the hippocampal formation. The dynamics of head direction tuning curves (HDTCs) were compared with those of hippocampal place fields. In both familiar and cue-altered environments, as a rat ran an increasing number of laps on a track, the center of mass (COM) of the HDTC tended to shift backward, similar to shifting observed in place cells. However, important differences existed between these cells in terms of the shift patterns relative to the cue-altered conditions, the proportion of backward versus forward shifts, and the time course of shift resetting. The demonstration of backward COM shifts in head direction cells and place cells suggests that similar plasticity mechanisms (such as temporally asymmetric LTP induction or spike timing-dependent plasticity) may be at work in both brain systems, and these processes may reflect a general mechanism for storing learned sequences of neural activity patterns.

From grid cells to place cells: a mathematical model

Anatomical connectivity and recent neurophysiological results imply that grid cells in the medial entorhinal cortex are the principal cortical inputs to place cells in the hippocampus. The authors propose a model in which place fields of hippocampal pyramidal cells are formed by linear summation of appropriately weighted inputs from entorhinal grid cells. Single confined place fields could be formed by summing input from a modest number (10-50) of grid cells with relatively similar grid phases, diverse grid orientations, and a biologically plausible range of grid spacings. When the spatial phase variation in the grid-cell input was higher, multiple, and irregularly spaced firing fields were formed. These observations point to a number of possible constraints in the organization of functional connections between grid cells and place cells.

Grid cell firing may arise from interference of theta frequency membrane potential oscillations in single neurons

Intracellular recording and computational modelling suggest that interactions of subthreshold membrane potential oscillation frequency in different dendritic branches of entorhinal cortex stellate cells could underlie the functional coding of continuous dimensions of space and time. Among other things, these interactions could underlie properties of grid cell field spacing. The relationship between experimental data on membrane potential oscillation frequency (f) and grid cell field spacing (G) indicates a constant scaling factor H = fG. This constant scaling factor between temporal oscillation frequency and spatial periodicity provides a starting constraint that is used to derive the model of Burgess et al. (Hippocampus, 2007). This model provides a consistent quantitative link between single cell physiological properties and properties of spiking units in awake behaving animals. Further properties and predictions of this model about single cell and network physiological properties are analyzed. In particular, the model makes quantitative predictions about the change in membrane potential, single cell oscillation frequency, and network oscillation frequency associated with speed of movement, about the independence of single cell properties from network theta rhythm oscillations, and about the effect of variations in initial oscillatory phase on the pattern of grid cell firing fields. These same mechanisms of subthreshold oscillations may play a more general role in memory function, by providing a method for learning arbitrary time intervals in memory sequences.

Entorhinal cortex grid cells can map to hippocampal place cells by competitive learning

'Grid cells' in the dorsocaudal medial entorhinal cortex (dMEC) are activated when a rat is located at any of the vertices of a grid of equilateral triangles covering the environment. dMEC grid cells have different frequencies and phase offsets. However, cells in the dentate gyrus (DG) and hippocampal area CA3 of the rodent typically display place fields, where individual cells are active over only a single portion of the space. In a model of the hippocampus, we have shown that the connectivity from the entorhinal cortex to the dentate granule cells could allow the dentate granule cells to operate as a competitive network to recode their inputs to produce sparse orthogonal representations, and this includes spatial pattern separation. In this paper we show that the same computational hypothesis can account for the mapping of EC grid cells to dentate place cells. We show that the learning in the competitive network is an important part of the way in which the mapping can be achieved. We further show that incorporation of a short term memory trace into the associative learning can help to produce the relatively broad place fields found in the hippocampus.

Theta phase coding in a network model of the entorhinal cortex layer II with entorhinal-hippocampal loop connections

We investigated successive firing of the stellate cells within a theta cycle, which replicates the phase coding of place information, using a network model of the entorhinal cortex layer II with loop connections. Layer II of the entorhinal cortex (ECII) sends signals to the hippocampus, and the hippocampus sends signals back to layer V of the entorhinal cortex (ECV). In addition to this major pathway, projection from ECV to ECII also exists. It is, therefore, inferred that reverberation activity readily appears if projections from ECV to ECII are potentiated. The frequency of the reverberation would be in a gamma range because it takes signals 20-30 ms to go around the entorhinal-hippocampal loop circuits. On the other hand, it has been suggested that ECII is a theta rhythm generator. If the reverberation activity appears in the entorhinal-hippocampal loop circuits, gamma oscillation would be superimposed on a theta rhythm in ECII like a gamma-theta oscillation. This is a reminiscence of the theta phase coding of place information. In this paper, first, a network model of ECII will be developed in order to reproduce a theta rhythm. Secondly, we will show that loop connections from one stellate cell to the other one are selectively potentiated by afferent signals to ECII. Frequencies of those afferent signals are different, and transmission delay of the loop connections is 20 ms. As a result, stellate cells fire successively within one cycle of the theta rhythm. This resembles gamma-theta oscillation underlying the phase coding. Our model also replicates the phase precession of stellate cell firing within a cycle of subthreshold oscillation (theta rhythm).

Neural representations of location outside the hippocampus

Place cells of the rat hippocampus are a dominant model system for understanding the role of the hippocampus in learning and memory at the level of single-unit and neural ensemble responses. A complete understanding of the information processing and computations performed by the hippocampus requires detailed knowledge about the properties of the representations that are present in hippocampal afferents and efferents in order to decipher the transformations that occur to these representations in the hippocampal circuitry. Neural recordings in behaving rats have revealed a number of brain areas that contain place-related firing properties in the parahippocampal regions and in other brain regions that are thought to interact with the hippocampus in certain behavioral tasks. Although investigators have just begun to scratch the surface in terms of understanding these properties, differences in the precise nature of the spatial firing between the hippocampus and these other regions promise to reveal important clues regarding the exact role of the hippocampus in learning and memory and the nature of its interactions with other brain systems to support adaptive behavior.

Interleaving brain systems for episodic and recognition memory

Conflicting models persist over the nature of long-term memory. Crucial issues are whether episodic memory and recognition memory reflect the same underlying processes, and the extent to which various brain structures work as a single unit to support these processes. New findings that have resulted from improved resolution of functional brain imaging, together with recent studies of amnesia and developments in animal testing, reinforce the view that recognition memory comprises at least two independent processes: one recollective and the other using familiarity detection. Only recollective recognition appears to depend on episodic memory. Attempts to map brain areas supporting these two putative components of recognition memory indicate that they depend on separate, but interlinked, structures.

Conjunctive representation of position, direction, and velocity in entorhinal cortex

Grid cells in the medial entorhinal cortex (MEC) are part of an environment-independent spatial coordinate system. To determine how information about location, direction, and distance is integrated in the grid-cell network, we recorded from each principal cell layer of MEC in rats that explored two-dimensional environments. Whereas layer II was predominated by grid cells, grid cells colocalized with head-direction cells and conjunctive grid x head-direction cells in the deeper layers. All cell types were modulated by running speed. The conjunction of positional, directional, and translational information in a single MEC cell type may enable grid coordinates to be updated during self-motion-based navigation.

A spin glass model of path integration in rat medial entorhinal cortex

Electrophysiological recording studies in the dorsocaudal region of medial entorhinal cortex (dMEC) of the rat reveal cells whose spatial firing fields show a remarkably regular hexagonal grid pattern (Fyhn et al., 2004; Hafting et al., 2005). We describe a symmetric, locally connected neural network, or spin glass model, that spontaneously produces a hexagonal grid of activity bumps on a two-dimensional sheet of units. The spatial firing fields of the simulated cells closely resemble those of dMEC cells. A collection of grids with different scales and/or orientations forms a basis set for encoding position. Simulations show that the animal's location can easily be determined from the population activity pattern. Introducing an asymmetry in the model allows the activity bumps to be shifted in any direction, at a rate proportional to velocity, to achieve path integration. Furthermore, information about the structure of the environment can be superimposed on the spatial position signal by modulation of the bump activity levels without significantly interfering with the hexagonal periodicity of firing fields. Our results support the conjecture of Hafting et al. (2005) that an attractor network in dMEC may be the source of path integration information afferent to hippocampus.

Head direction cell representations maintain internal coherence during conflicting proximal and distal cue rotations: comparison with hippocampal place cells

Place cells of the hippocampal formation encode a spatial representation of the environment, and the orientation of this representation is apparently governed by the head direction cell system. The representation of a well explored environment by CA1 place cells can be split when there is conflicting information from salient proximal and distal cues, because some place fields rotate to follow the distal cues, whereas others rotate to follow the proximal cues (Knierim, 2002a). In contrast, the CA3 representation is more coherent than CA1, because the place fields in CA3 tend to rotate in the same direction (Lee et al., 2004). The present study tests whether the head direction cell network produces a split representation or remains coherent under these conditions by simultaneously recording both CA1 place cells and head direction cells from the thalamus. In agreement with previous studies, split representations of the environment were observed in ensembles of CA1 place cells in approximately 75% of the mismatch sessions, in which some fields followed the counterclockwise rotation of proximal cues and other fields followed the clockwise rotation of distal cues. However, of 225 recording sessions, there was not a single instance of the head direction cell ensembles revealing a split representation of head direction. Instead, in most of the mismatch sessions, the head direction cell tuning curves rotated as an ensemble clockwise (94%) and in a few sessions rotated counterclockwise (6%). The findings support the notion that the head direction cells may be part of an attractor network bound more strongly to distal landmarks than proximal landmarks, even under conditions in which the CA1 place representation loses its coherence.

A metric for the cognitive map: found at last?

A network of brain areas collectively represent location, but the underlying nature of this "cognitive map" has remained elusive. A recent study reports that the activity patterns of some entorhinal cortical neurons form a remarkably regular array of evenly spaced peaks across the surface of the environment. These "grid cells" might be the basis of a metric used for calculating position, and their discovery could greatly advance our understanding of how navigational computations are performed.