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

A goal-directed spatial navigation model using forward trajectory planning based on grid cells

A goal-directed navigation model is proposed based on forward linear look-ahead probe of trajectories in a network of head direction cells, grid cells, place cells and prefrontal cortex (PFC) cells. The model allows selection of new goal-directed trajectories. In a novel environment, the virtual rat incrementally creates a map composed of place cells and PFC cells by random exploration. After exploration, the rat retrieves memory of the goal location, picks its next movement direction by forward linear look-ahead probe of trajectories in several candidate directions while stationary in one location, and finds the one activating PFC cells with the highest reward signal. Each probe direction involves activation of a static pattern of head direction cells to drive an interference model of grid cells to update their phases in a specific direction. The updating of grid cell spiking drives place cells along the probed look-ahead trajectory similar to the forward replay during waking seen in place cell recordings. Directions are probed until the look-ahead trajectory activates the reward signal and the corresponding direction is used to guide goal-finding behavior. We report simulation results in several mazes with and without barriers. Navigation with barriers requires a PFC map topology based on the temporal vicinity of visited place cells and a reward signal diffusion process. The interaction of the forward linear look-ahead trajectory probes with the reward diffusion allows discovery of never-before experienced shortcuts towards a goal location.

How do spatial learning and memory occur in the brain? Coordinated learning of entorhinal grid cells and hippocampal place cells

Spatial learning and memory are important for navigation and formation of episodic memories. The hippocampus and medial entorhinal cortex (MEC) are key brain areas for spatial learning and memory. Place cells in hippocampus fire whenever an animal is located in a specific region in the environment. Grid cells in the superficial layers of MEC provide inputs to place cells and exhibit remarkable regular hexagonal spatial firing patterns. They also exhibit a gradient of spatial scales along the dorsoventral axis of the MEC, with neighboring cells at a given dorsoventral location having different spatial phases. A neural model shows how a hierarchy of self-organizing maps, each obeying the same laws, responds to realistic rat trajectories by learning grid cells with hexagonal grid firing fields of multiple spatial scales and place cells with unimodal firing fields that fit neurophysiological data about their development in juvenile rats. The hippocampal place fields represent much larger spaces than the grid cells to support navigational behaviors. Both the entorhinal and hippocampal self-organizing maps amplify and learn to categorize the most energetic and frequent co-occurrences of their inputs. Top-down attentional mechanisms from hippocampus to MEC help to dynamically stabilize these spatial memories in both the model and neurophysiological data. Spatial learning through MEC to hippocampus occurs in parallel with temporal learning through lateral entorhinal cortex to hippocampus. These homologous spatial and temporal representations illustrate a kind of "neural relativity" that may provide a substrate for episodic learning and memory.

Self-organization of multiple spatial and context memories in the hippocampus

One obstacle to understanding the exact processes unfolding inside the hippocampus is that it is still difficult to clearly define what the hippocampus actually does, at the system level. Associated for a long time with the formation of episodic and semantic memories, and with their temporary storage, the hippocampus is also regarded as a structure involved in spatial navigation. These two independent perspectives on the hippocampus are not necessarily exclusive: proposals have been put forward to make them fit into the same conceptual frame. We review both approaches and argue that three critical developments need consideration: (a) recordings of neuronal activity in rodents, revealing beautiful spatial codes expressed in entorhinal cortex, upstream of the hippocampus; (b) comparative behavioral results suggesting, in an evolutionary perspective, qualitative similarity of function across homologous structures with a distinct internal organization; (c) quantitative measures of information, shifting the focus from who does what to how much each neuronal population expresses each code. These developments take the hippocampus away from philosophical discussions of all-or-none cause-effect relations, and into the quantitative mainstream of modern neural science.

Grid cells, place cells, and geodesic generalization for spatial reinforcement learning

Reinforcement learning (RL) provides an influential characterization of the brain's mechanisms for learning to make advantageous choices. An important problem, though, is how complex tasks can be represented in a way that enables efficient learning. We consider this problem through the lens of spatial navigation, examining how two of the brain's location representations--hippocampal place cells and entorhinal grid cells--are adapted to serve as basis functions for approximating value over space for RL. Although much previous work has focused on these systems' roles in combining upstream sensory cues to track location, revisiting these representations with a focus on how they support this downstream decision function offers complementary insights into their characteristics. Rather than localization, the key problem in learning is generalization between past and present situations, which may not match perfectly. Accordingly, although neural populations collectively offer a precise representation of position, our simulations of navigational tasks verify the suggestion that RL gains efficiency from the more diffuse tuning of individual neurons, which allows learning about rewards to generalize over longer distances given fewer training experiences. However, work on generalization in RL suggests the underlying representation should respect the environment's layout. In particular, although it is often assumed that neurons track location in Euclidean coordinates (that a place cell's activity declines "as the crow flies" away from its peak), the relevant metric for value is geodesic: the distance along a path, around any obstacles. We formalize this intuition and present simulations showing how Euclidean, but not geodesic, representations can interfere with RL by generalizing inappropriately across barriers. Our proposal that place and grid responses should be modulated by geodesic distances suggests novel predictions about how obstacles should affect spatial firing fields, which provides a new viewpoint on data concerning both spatial codes.

Computational models of grid cells

Grid cells are space-modulated neurons with periodic firing fields. In moving animals, the multiple firing fields of an individual grid cell form a triangular pattern tiling the entire space available to the animal. Collectively, grid cells are thought to provide a context-independent metric representation of the local environment. Since the discovery of grid cells in 2005, a number of models have been proposed to explain the formation of spatially repetitive firing patterns as well as the conversion of these signals to place signals one synapse downstream in the hippocampus. The present article reviews the most recent developments in our understanding of how grid patterns are generated, maintained, and transformed, with particular emphasis on second-generation computational models that have emerged during the past 2-3 years in response to criticism and new data.

Chemosensory learning in the cortex

Taste is a primary reinforcer. Olfactory–taste and visual–taste association learning takes place in the primate including human orbitofrontal cortex to build representations of flavor. Rapid reversal of this learning can occur using a rule-based learning system that can be reset when an expected taste or flavor reward is not obtained, that is by negative reward prediction error, to which a population of neurons in the orbitofrontal cortex responds. The representation in the orbitofrontal cortex but not the primary taste or olfactory cortex is of the reward value of the visual/olfactory/taste input as shown by devaluation experiments in which food is fed to satiety, and by correlations of the activations with subjective pleasantness ratings in humans. Sensory-specific satiety for taste, olfactory, visual, and oral somatosensory inputs produced by feeding a particular food to satiety is implemented it is proposed by medium-term synaptic adaptation in the orbitofrontal cortex. Cognitive factors, including word-level descriptions, modulate the representation of the reward value of food in the orbitofrontal cortex, and this effect is learned it is proposed by associative modification of top-down synapses onto neurons activated by bottom-up taste and olfactory inputs when both are active in the orbitofrontal cortex. A similar associative synaptic learning process is proposed to be part of the mechanism for the top-down attentional control to the reward value vs. the sensory properties such as intensity of taste and olfactory inputs in the orbitofrontal cortex, as part of a biased activation theory of selective attention.

The structure of networks that produce the transformation from grid cells to place cells

Since grid cells were discovered in the medial entorhinal cortex, several models have been proposed for the transformation from periodic grids to the punctate place fields of hippocampal place cells. These prior studies have each focused primarily on a particular model structure. By contrast, the goal of this study is to understand the general nature of the solutions that generate the grids-to-places transformation, and to exploit this insight to solve problems that were previously unsolved. First, we derive a family of feedforward networks that generate the grids-to-places transformations. These networks have in common an inverse relationship between the synaptic weights and a grid property that we call the normalized offset. Second, we analyze the solutions of prior models in terms of this novel measure and found to our surprise that almost all prior models yield solutions that can be described by this family of networks. The one exception is a model that is unrealistically sensitive to noise. Third, with this insight into the structure of the solutions, we then construct explicitly solutions for the grids-to-places transformation with multiple spatial maps, that is, with place fields in arbitrary locations either within the same (multiple place fields) or in different (global remapping) enclosures. These multiple maps are possible because the weights are learned or assigned in such a way that a group of weights contributes to spatial specificity in one context but remains spatially unstructured in another context. Fourth, we find parameters such that global remapping solutions can be found by synaptic learning in spiking neurons, despite previous suggestions that this might not be possible. In conclusion, our results demonstrate the power of understanding the structure of the solutions and suggest that we may have identified the structure that is common to all robust solutions of the grids-to-places transformation.

Modular realignment of entorhinal grid cell activity as a basis for hippocampal remapping

Hippocampal place fields, the local regions of activity recorded from place cells in exploring rodents, can undergo large changes in relative location during remapping. This process would appear to require some form of modulated global input. Grid-cell responses recorded from layer II of medial entorhinal cortex in rats have been observed to realign concurrently with hippocampal remapping, making them a candidate input source. However, this realignment occurs coherently across colocalized ensembles of grid cells (Fyhn et al., 2007). The hypothesized entorhinal contribution to remapping depends on whether this coherence extends to all grid cells, which is currently unknown. We study whether dividing grid cells into small numbers of independently realigning modules can both account for this localized coherence and allow for hippocampal remapping. To do this, we construct a model in which place-cell responses arise from network competition mediated by global inhibition. We show that these simulated responses approximate the sparsity and spatial specificity of hippocampal activity while fully representing a virtual environment without learning. Place-field locations and the set of active place cells in one environment can be independently rearranged by changes to the underlying grid-cell inputs. We introduce new measures of remapping to assess the effectiveness of grid-cell modularity and to compare shift realignments with other geometric transformations of grid-cell responses. Complete hippocampal remapping is possible with a small number of shifting grid modules, indicating that entorhinal realignment may be able to generate place-field randomization despite substantial coherence.

Cortical attractor network dynamics with diluted connectivity

The connectivity of the cerebral cortex is diluted, with the probability of excitatory connections between even nearby pyramidal cells rarely more than 0.1, and in the hippocampus 0.04. To investigate the extent to which this diluted connectivity affects the dynamics of attractor networks in the cerebral cortex, we simulated an integrate-and-fire attractor network taking decisions between competing inputs with diluted connectivity of 0.25 or 0.1, and with the same number of synaptic connections per neuron for the recurrent collateral synapses within an attractor population as for full connectivity. The results indicated that there was less spiking-related noise with the diluted connectivity in that the stability of the network when in the spontaneous state of firing increased, and the accuracy of the correct decisions increased. The decision times were a little slower with diluted than with complete connectivity. Given that the capacity of the network is set by the number of recurrent collateral synaptic connections per neuron, on which there is a biological limit, the findings indicate that the stability of cortical networks, and the accuracy of their correct decisions or memory recall operations, can be increased by utilizing diluted connectivity and correspondingly increasing the number of neurons in the network, with little impact on the speed of processing of the cortex. Thus diluted connectivity can decrease cortical spiking-related noise. In addition, we show that the Fano factor for the trial-to-trial variability of the neuronal firing decreases from the spontaneous firing state value when the attractor network makes a decision. This article is part of a Special Issue entitled "Neural Coding".

Head direction cells in the postsubiculum do not show replay of prior waking sequences during sleep

During slow-wave sleep (SWS) and rapid eye movement (REM) sleep, hippocampal place cells in the rat show replay of sequences previously observed during waking. We tested the hypothesis from computational modeling that the temporal structure of REM sleep replay could arise from an interplay of place cells with head direction cells in the postsubiculum. Physiological single-unit recording was performed simultaneously from five or more head direction or place by head direction cells in the postsubiculum during running on a circular track allowing sampling of a full range of head directions, and during sleep periods before and after running on the circular track. Data analysis compared the spiking activity during individual REM periods with waking as in previous analysis procedures for REM sleep. We also used a new procedure comparing groups of similar runs during waking with REM sleep periods. There was no consistent evidence for a statistically significant correlation of the temporal structure of spiking during REM sleep with spiking during waking running periods. Thus, the spiking activity of head direction cells during REM sleep does not show replay of head direction cell activity occurring during a previous waking period of running on the task. In addition, we compared the spiking of postsubiculum neurons during hippocampal sharp wave ripple events. We show that head direction cells are not activated during sharp wave ripples, whereas neurons responsive to place in the postsubiculum show reliable spiking at ripple events.

Grid cell hexagonal patterns formed by fast self-organized learning within entorhinal cortex

Grid cells in the dorsal segment of the medial entorhinal cortex (dMEC) show remarkable hexagonal activity patterns, at multiple spatial scales, during spatial navigation. It has previously been shown how a self-organizing map can convert firing patterns across entorhinal grid cells into hippocampal place cells that are capable of representing much larger spatial scales. Can grid cell firing fields also arise during navigation through learning within a self-organizing map? This article describes a simple and general mathematical property of the trigonometry of spatial navigation which favors hexagonal patterns. The article also develops a neural model that can learn to exploit this trigonometric relationship. This GRIDSmap self-organizing map model converts path integration signals into hexagonal grid cell patterns of multiple scales. GRIDSmap creates only grid cell firing patterns with the observed hexagonal structure, predicts how these hexagonal patterns can be learned from experience, and can process biologically plausible neural input and output signals during navigation. These results support an emerging unified computational framework based on a hierarchy of self-organizing maps for explaining how entorhinal-hippocampal interactions support spatial navigation.

A Kalman filtering approach to the representation of kinematic quantities by the hippocampal-entorhinal complex

Several regions of the brain which represent kinematic quantities are grouped under a single state-estimator framework. A theoretic effort is made to predict the activity of each cell population as a function of time using a simple state estimator (the Kalman filter). Three brain regions are considered in detail: the parietal cortex (reaching cells), the hippocampus (place cells and head-direction cells), and the entorhinal cortex (grid cells). For the reaching cell and place cell examples, we compute the perceived probability distributions of objects in the environment as a function of the observations. For the grid cell example, we show that the elastic behavior of the grids observed in experiments arises naturally from the Kalman filter. To our knowledge, the application of a tensor Kalman filter to grid cells is completely novel.

A manifold of spatial maps in the brain

Two neural systems are known to encode self-location in the brain: Place cells in the hippocampus encode unique locations in unique environments, whereas grid cells, border cells and head-direction cells in the parahippocampal cortex provide a universal metric for mapping positions and directions in all environments. These systems have traditionally been studied in very simple environments; however, natural environments are compartmentalized, nested and variable in time. Recent studies indicate that hippocampal and entorhinal spatial maps reflect this complexity. The maps fragment into interconnected, rapidly changing and tightly coordinated submaps. Plurality, fast dynamics and dynamic grouping are optimal for a brain system thought to exploit large pools of stored information to guide behavior on a second-by-second time frame in the animal's natural habitat.

The single place fields of CA3 cells: a two-stage transformation from grid cells

Granule cells of the dentate gyrus (DG) generally have multiple place fields, whereas CA3 cells, which are second order, have only a single place field. Here, we explore the mechanisms by which the high selectivity of CA3 cells is achieved. Previous work showed that the multiple place fields of DG neurons could be quantitatively accounted for by a model based on the number and strength of grid cell inputs and a competitive network interaction in the DG that is mediated by gamma frequency feedback inhibition. We have now built a model of CA3 based on similar principles. CA3 cells receive input from an average of one active DG cell and from 1,400 cortical grid cells. Based on experimental findings, we have assumed a linear interaction of the two pathways. The results show that simulated CA3 cells generally have a single place field, as observed experimentally. Thus, a two-step process based on simple rules (and that can occur without learning) is able to explain how grid cell inputs to the hippocampus give rise to cells having ultimate spatial selectivity. The CA3 processes that produce a single place depend critically on the competitive network processes and do not require the direct cortical inputs to CA3, which are therefore likely to perform some other unknown function.

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.

Continuous transformation learning of translation invariant representations

We show that spatial continuity can enable a network to learn translation invariant representations of objects by self-organization in a hierarchical model of cortical processing in the ventral visual system. During 'continuous transformation learning', the active synapses from each overlapping transform are associatively modified onto the set of postsynaptic neurons. Because other transforms of the same object overlap with previously learned exemplars, a common set of postsynaptic neurons is activated by the new transforms, and learning of the new active inputs onto the same postsynaptic neurons is facilitated. We show that the transforms must be close for this to occur; that the temporal order of presentation of each transformed image during training is not crucial for learning to occur; that relatively large numbers of transforms can be learned; and that such continuous transformation learning can be usefully combined with temporal trace training.

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 computational theory of episodic memory formation in the hippocampus

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

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.

The ventral basal ganglia, a selection mechanism at the crossroads of space, strategy, and reward

The basal ganglia are often conceptualised as three parallel domains that include all the constituent nuclei. The 'ventral domain' appears to be critical for learning flexible behaviours for exploration and foraging, as it is the recipient of converging inputs from amygdala, hippocampal formation and prefrontal cortex, putatively centres for stimulus evaluation, spatial navigation, and planning/contingency, respectively. However, compared to work on the dorsal domains, the rich potential for quantitative theories and models of the ventral domain remains largely untapped, and the purpose of this review is to provide the stimulus for this work. We systematically review the ventral domain's structures and internal organisation, and propose a functional architecture as the basis for computational models. Using a full schematic of the structure of inputs to the ventral striatum (nucleus accumbens core and shell), we argue for the existence of many identifiable processing channels on the basis of unique combinations of afferent inputs. We then identify the potential information represented in these channels by reconciling a broad range of studies from the hippocampal, amygdala and prefrontal cortex literatures with known properties of the ventral striatum from lesion, pharmacological, and electrophysiological studies. Dopamine's key role in learning is reviewed within the three current major computational frameworks; we also show that the shell-based basal ganglia sub-circuits are well placed to generate the phasic burst and dip responses of dopaminergic neurons. We detail dopamine's modulation of ventral basal ganglia's inputs by its actions on pre-synaptic terminals and post-synaptic membranes in the striatum, arguing that the complexity of these effects hint at computational roles for dopamine beyond current ideas. The ventral basal ganglia are revealed as a constellation of multiple functional systems for the learning and selection of flexible behaviours and of behavioural strategies, sharing the common operations of selection-by-disinhibition and of dopaminergic modulation.

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.

Parallel computational subunits in dentate granule cells generate multiple place fields

A fundamental question in understanding neuronal computations is how dendritic events influence the output of the neuron. Different forms of integration of neighbouring and distributed synaptic inputs, isolated dendritic spikes and local regulation of synaptic efficacy suggest that individual dendritic branches may function as independent computational subunits. In the present paper, we study how these local computations influence the output of the neuron. Using a simple cascade model, we demonstrate that triggering somatic firing by a relatively small dendritic branch requires the amplification of local events by dendritic spiking and synaptic plasticity. The moderately branching dendritic tree of granule cells seems optimal for this computation since larger dendritic trees favor local plasticity by isolating dendritic compartments, while reliable detection of individual dendritic spikes in the soma requires a low branch number. Finally, we demonstrate that these parallel dendritic computations could contribute to the generation of multiple independent place fields of hippocampal granule cells.

Neurons were originally divided into three morphologically distinct compartments: the dendrites receive the synaptic input, the soma integrates it and communicates the output of the cell to other neurons via the axon. Although several lines of evidence challenged this oversimplified view, neurons are still considered to be the basic information processing units of the nervous system as their output reflects the computations performed by the entire dendritic tree. In the present study, the authors build a simplified computational model and calculate that, in certain neurons, relatively small dendritic branches are able to independently trigger somatic firing. Therefore, in these cells, an action potential mirrors the activity of a small dendritic subunit rather than the input arriving to the whole dendritic tree. These neurons can be regarded as a network of a few independent integrator units connected to a common output unit. The authors demonstrate that a moderately branched dendritic tree of hippocampal granule cells may be optimized for these parallel computations. Finally the authors show that these parallel dendritic computations could explain some aspects of the location dependent activity of hippocampal granule cells.

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.

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.

A second function of gamma frequency oscillations: an E%-max winner-take-all mechanism selects which cells fire

The role of gamma oscillations in producing synchronized firing of groups of principal cells is well known. Here, we argue that gamma oscillations have a second function: they select which principal cells fire. This selection process occurs through the interaction of excitation with gamma frequency feedback inhibition. We sought to understand the rules that govern this process. One possibility is that a constant fraction of cells fire. Our analysis shows, however, that the fraction is not robust because it depends on the distribution of excitation to different cells. A robust description is termed E%-max: cells fire if they have suprathreshold excitation (E) within E% of the cell that has maximum excitation. The value of E%-max is approximated by the ratio of the delay of feedback inhibition to the membrane time constant. From measured values, we estimate that E%-max is 5-15%. Thus, an E%-max winner-take-all process can discriminate between groups of cells that have only small differences in excitation. To test the utility of this framework, we analyzed the role of oscillations in V1, one of the few systems in which both spiking and intracellular excitation have been directly measured. We show that an E%-max winner-take-all process provides a simple explanation for why the orientation tuning of firing is narrower than that of the excitatory input and why this difference is not affected by increasing excitation. Because gamma oscillations occur in many brain regions, the framework we have developed for understanding the second function of gamma is likely to have wide applicability.

The input-output transformation of the hippocampal granule cells: from grid cells to place fields

Grid cells in the rat medial entorhinal cortex fire (periodically) over the entire environment. These cells provide input to hippocampal granule cells whose output is characterized by one or more small place fields. We sought to understand how this input-output transformation occurs. Available information allows simulation of this process with no freely adjustable parameters. We first examined the spatial distribution of excitation in granule cells produced by the convergence of excitatory inputs from randomly chosen grid cells. Because the resulting summation depends on the number of inputs, it is necessary to use a realistic number (approximately 1200) and to take into consideration their 20-fold variation in strength. The resulting excitation maps have only modest peaks and valleys. To analyze how this excitation interacts with inhibition, we used an E%-max (percentage of maximal suprathreshold excitation) winner-take-all rule that describes how gamma-frequency inhibition affects firing. We found that simulated granule cells have firing maps that have one or more place fields whose size and number approximates those observed experimentally. A substantial fraction of granule cells have no place fields, as observed experimentally. Because the input firing rates and synaptic properties are known, the excitatory charge into granule cells could be calculated (2-3 pC) and was found to be only somewhat larger than required to fire granule cells (1 pC). We conclude that the input-output transformation of dentate granule does not depend strongly on synaptic modification; place field formation can be understood in terms of simple summation of randomly chosen excitatory inputs, in conjunction with a winner-take-all network mechanism.

A role for hilar cells in pattern separation in the dentate gyrus: a computational approach

We present a simple computational model of the dentate gyrus to evaluate the hypothesis that pattern separation, defined as the ability to transform a set of similar input patterns into a less-similar set of output patterns, is dynamically regulated by hilar neurons. Prior models of the dentate gyrus have generally fallen into two categories: simplified models that have focused on a single granule cell layer and its ability to perform pattern separation, and large-scale and biophysically realistic models of dentate gyrus, which include hilar cells, but which have not specifically addressed pattern separation. The present model begins to bridge this gap. The model includes two of the major subtypes of hilar cells: excitatory hilar mossy cells and inhibitory hilar interneurons that receive input from and project to the perforant path terminal zone (HIPP cells). In the model, mossy cells and HIPP cells provide a mechanism for dynamic regulation of pattern separation, allowing the system to upregulate and downregulate pattern separation in response to environmental and task demands. Specifically, pattern separation in the model can be strongly decreased by decreasing mossy cell function and/or by increasing HIPP cell function; pattern separation can be increased by the opposite manipulations. We propose that hilar cells may similarly mediate dynamic regulation of pattern separation in the dentate gyrus in vivo, not only because of their connectivity within the dentate gyrus, but also because of their modulation by brainstem inputs and by the axons that "backproject" from area CA3 pyramidal cells.

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.

Technical integration of hippocampus, Basal Ganglia and physical models for spatial navigation

Computational neuroscience is increasingly moving beyond modeling individual neurons or neural systems to consider the integration of multiple models, often constructed by different research groups. We report on our preliminary technical integration of recent hippocampal formation, basal ganglia and physical environment models, together with visualisation tools, as a case study in the use of Python across the modelling tool-chain. We do not present new modeling results here. The architecture incorporates leaky-integrator and rate-coded neurons, a 3D environment with collision detection and tactile sensors, 3D graphics and 2D plots. We found Python to be a flexible platform, offering a significant reduction in development time, without a corresponding significant increase in execution time. We illustrate this by implementing a part of the model in various alternative languages and coding styles, and comparing their execution times. For very large-scale system integration, communication with other languages and parallel execution may be required, which we demonstrate using the BRAHMS framework's Python bindings.

Spatial scene representations formed by self-organizing learning in a hippocampal extension of the ventral visual system

We show in a unifying computational approach that representations of spatial scenes can be formed by adding an additional self-organizing layer of processing beyond the inferior temporal visual cortex in the ventral visual stream without the introduction of new computational principles. The invariant representations of objects by neurons in the inferior temporal visual cortex can be modelled by a multilayer feature hierarchy network with feedforward convergence from stage to stage, and an associative learning rule with a short-term memory trace to capture the invariant statistical properties of objects as they transform over short time periods in the world. If an additional layer is added to this architecture, training now with whole scenes that consist of a set of objects in a given fixed spatial relation to each other results in neurons in the added layer that respond to one of the trained whole scenes but do not respond if the objects in the scene are rearranged to make a new scene from the same objects. The formation of these scene-specific representations in the added layer is related to the fact that in the inferior temporal cortex and, we show, in the VisNet model, the receptive fields of inferior temporal cortex neurons shrink and become asymmetric when multiple objects are present simultaneously in a natural scene. This reduced size and asymmetry of the receptive fields of inferior temporal cortex neurons also provides a solution to the representation of multiple objects, and their relative spatial positions, in complex natural scenes.

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.

Conversion of a phase- to a rate-coded position signal by a three-stage model of theta cells, grid cells, and place cells

As a rat navigates through a familiar environment, its position in space is encoded by firing rates of place cells and grid cells. Oscillatory interference models propose that this positional firing rate code is derived from a phase code, which stores the rat's position as a pattern of phase angles between velocity-modulated theta oscillations. Here we describe a three-stage network model, which formalizes the computational steps that are necessary for converting phase-coded position signals (represented by theta oscillations) into rate-coded position signals (represented by grid cells and place cells). The first stage of the model proposes that the phase-coded position signal is stored and updated by a bank of ring attractors, like those that have previously been hypothesized to perform angular path integration in the head-direction cell system. We show analytically how ring attractors can serve as central pattern generators for producing velocity-modulated theta oscillations, and we propose that such ring attractors may reside in subcortical areas where hippocampal theta rhythm is known to originate. In the second stage of the model, grid fields are formed by oscillatory interference between theta cells residing in different (but not the same) ring attractors. The model's third stage assumes that hippocampal neurons generate Gaussian place fields by computing weighted sums of inputs from a basis set of many grid fields. Here we show that under this assumption, the spatial frequency spectrum of the Gaussian place field defines the vertex spacings of grid cells that must provide input to the place cell. This analysis generates a testable prediction that grid cells with large vertex spacings should send projections to the entire hippocampus, whereas grid cells with smaller vertex spacings may project more selectively to the dorsal hippocampus, where place fields are smallest.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

What is the mammalian dentate gyrus good for?

In the mammalian hippocampus, the dentate gyrus (DG) is characterized by sparse and powerful unidirectional projections to CA3 pyramidal cells, the so-called mossy fibers (MF). The MF form a distinct type of synapses, rich in zinc, that appear to duplicate, in terms of the information they convey, what CA3 cells already receive from entorhinal cortex layer II cells, which project both to the DG and to CA3. Computational models have hypothesized that the function of the MF is to enforce a new, well-separated pattern of activity onto CA3 cells, to represent a new memory, prevailing over the interference produced by the traces of older memories already stored on CA3 recurrent collateral connections. Although behavioral observations support the notion that the MF are crucial for decorrelating new memory representations from previous ones, a number of findings require that this view be reassessed and articulated more precisely in the spatial and temporal domains. First, neurophysiological recordings indicate that the very sparse dentate activity is concentrated on cells that display multiple but disorderly place fields, unlike both the single fields typical of CA3 and the multiple regular grid-aligned fields of medial entorhinal cortex. Second, neurogenesis is found to occur in the adult DG, leading to new cells that are functionally added to the existing circuitry, and may account for much of its ongoing activity. Third, a comparative analysis suggests that only mammals have evolved a DG, despite some of its features being present also in reptiles, whereas the avian hippocampus seems to have taken a different evolutionary path. Thus, we need to understand both how the mammalian dentate operates, in space and time, and whether evolution, in other vertebrate lineages, has offered alternative solutions to the same computational problems.

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.

Impact of temporal coding of presynaptic entorhinal cortex grid cells on the formation of hippocampal place fields

Many behavioural experiments have pointed out the important role played by the hippocampus in spatial navigation. This role was enlightened by the discovery of hippocampal cells in rodents firing only at very specific locations in an environment, the so-called 'place field'. Recently, it has been observed that one synapse upstream of the hippocampus, entorhinal cells fire when the rat is located at any of the vertices of grid fields covering the environment. Furthermore, it was reported that both hippocampal and entorhinal cells have firing activity modulated by the theta local field potential in term of theta phase precession. In a previous report, the authors suggested that the temporal code driven by theta phase precession should play an important role in the building of hippocampal place cells from entorhinal grid cells. Here, with the help of a simpler computational model, we further investigate the implications of our hypothesis. We demonstrate that the nonlinear nature of the shape of the phase precession predicts that place field location are slightly backward shifted according to the direction of the rat.

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.