Grid Cell Firing Research Articles

Vestibular control of entorhinal cortex activity in spatial navigation.

Navigation in rodents depends on both self-motion (idiothetic) and external (allothetic) information. Idiothetic information has a predominant role when allothetic information is absent or irrelevant. The vestibular system is a major source of idiothetic information in mammals. By integrating the signals generated by angular and linear accelerations during exploration, a rat is able to generate and update a vector pointing to its starting place and to perform accurate return. This navigation strategy, called path integration, has been shown to involve a network of brain structures. Among these structures, the entorhinal cortex (EC) may play a pivotal role as suggested by lesion and electrophysiological data. In particular, it has been recently discovered that some neurons in the medial EC display multiple firing fields producing a regular grid-like pattern across the environment. Such regular activity may arise from the integration of idiothetic information. This hypothesis would be strongly strengthened if it was shown that manipulation of vestibular information interferes with grid cell activity. In the present paper we review neuroanatomical and functional evidence indicating that the vestibular system influences the activity of the brain network involved in spatial navigation. We also provide new data on the effects of reversible inactivation of the peripheral vestibular system on the EC theta rhythm. The main result is that tetrodotoxin (TTX) administration abolishes velocity-controlled theta oscillations in the EC, indicating that vestibular information is necessary for EC activity. Since recent data demonstrate that disruption of theta rhythm in the medial EC induces a disorganization of grid cell firing, our findings indicate that the integration of idiothetic information in the EC is essential to form a spatial representation of the environment.

New and distinct hippocampal place codes are generated in a new environment during septal inactivation.

The hippocampus generates distinct neural codes to disambiguate similar experiences, a process thought to underlie episodic memory function. Entorhinal grid cells provide a prominent spatial signal to hippocampus, and changes in their firing pattern could thus generate a distinct spatial code in each context. We examined whether we would preclude the emergence of new spatial representations in a novel environment during muscimol inactivation of the medial septal area, a manipulation known to disrupt theta oscillations and grid cell firing. We found that new, highly distinct configurations of place fields emerged immediately and remained stable during the septal inactivation. The new place code persisted when theta oscillations had recovered. Theta rhythmicity and feedforward input from grid cell networks were thus not required to generate new spatial representations in the hippocampus.

Are new place representations independent of theta and path integration?

Brandon et al. (2014) show that the formation of place cell representations in new environments is preserved under septal inactivation, and is thus likely independent of the hippocampal theta rhythm and, by implication, the firing of entorhinal grid cells and the process of path integration.

Controlling phase noise in oscillatory interference models of grid cell firing.

Oscillatory interference models account for the spatial firing properties of grid cells in terms of neuronal oscillators with frequencies modulated by the animal's movement velocity. The phase of such a "velocity-controlled oscillator" (VCO) relative to a baseline (theta-band) oscillation tracks displacement along a preferred direction. Input from multiple VCOs with appropriate preferred directions causes a grid cell's grid-like firing pattern. However, accumulating phase noise causes the firing pattern to drift and become corrupted. Here we show how multiple redundant VCOs can automatically compensate for phase noise. By entraining the baseline frequency to the mean VCO frequency, VCO phases remain consistent, ensuring a coherent grid pattern and reducing its spatial drift. We show how the spatial stability of grid firing depends on the variability in VCO phases, e.g., a phase SD of 3 ms per 125 ms cycle results in stable grids for 1 min. Finally, coupling N VCOs with similar preferred directions as a ring attractor, so that their relative phases remain constant, produces grid cells with consistently offset grids, and reduces VCO phase variability of the order square root of N. The results suggest a viable functional organization of the grid cell network, and highlight the benefit of integrating displacement along multiple redundant directions for the purpose of path integration.

Parvalbumin interneurons provide grid cell–driven recurrent inhibition in the medial entorhinal cortex

Grid cells in the medial entorhinal cortex (MEC) generate metric spatial representations. Recent attractor-network models suggest an essential role for GABAergic interneurons in the emergence of the grid-cell firing pattern through recurrent inhibition dependent on grid-cell phase. To test this hypothesis, we studied identified parvalbumin-expressing (PV(+)) interneurons that are the most likely candidate for providing this recurrent inhibition onto grid cells. Using optogenetics and tetrode recordings in mice, we found that PV(+) interneurons exhibited high firing rates, low spatial sparsity and no spatial periodicity. PV(+) interneurons inhibited all functionally defined cell types in the MEC and were in turn recruited preferentially by grid cells. To our surprise, we found that individual PV(+) interneurons received input from grid cells with various phases, which most likely accounts for the broadly tuned spatial firing activity of PV(+) interneurons. Our data argue against the notion that PV(+) interneurons provide phase-dependent recurrent inhibition and challenge recent attractor-network models of grid cells.

A Hybrid Oscillatory Interference/Continuous Attractor Network Model of Grid Cell Firing

Grid cells in the rodent medial entorhinal cortex exhibit remarkably regular spatial firing patterns that tessellate all environments visited by the animal. Two theoretical mechanisms that could generate this spatially periodic activity pattern have been proposed: oscillatory interference and continuous attractor dynamics. Although a variety of evidence has been cited in support of each, some aspects of the two mechanisms are complementary, suggesting that a combined model may best account for experimental data. The oscillatory interference model proposes that the grid pattern is formed from linear interference patterns or "periodic bands" in which velocity-controlled oscillators integrate self-motion to code displacement along preferred directions. However, it also allows the use of symmetric recurrent connectivity between grid cells to provide relative stability and continuous attractor dynamics. Here, we present simulations of this type of hybrid model, demonstrate that it generates intracellular membrane potential profiles that closely match those observed in vivo, addresses several criticisms aimed at pure oscillatory interference and continuous attractor models, and provides testable predictions for future empirical studies.

Theta phase precession of grid and place cell firing in open environments

Place and grid cells in the rodent hippocampal formation tend to fire spikes at successively earlier phases relative to the local field potential theta rhythm as the animal runs through the cell's firing field on a linear track. However, this ‘phase precession’ effect is less well characterized during foraging in two-dimensional open field environments. Here, we mapped runs through the firing fields onto a unit circle to pool data from multiple runs. We asked which of seven behavioural and physiological variables show the best circular–linear correlation with the theta phase of spikes from place cells in hippocampal area CA1 and from grid cells from superficial layers of medial entorhinal cortex. The best correlate was the distance to the firing field peak projected onto the animal's current running direction. This was significantly stronger than other correlates, such as instantaneous firing rate and time-in-field, but similar in strength to correlates with other measures of distance travelled through the firing field. Phase precession was stronger in place cells than grid cells overall, and robust phase precession was seen in traversals through firing field peripheries (although somewhat less than in traversals through the centre), consistent with phase coding of displacement along the current direction. This type of phase coding, of place field distance ahead of or behind the animal, may be useful for allowing calculation of goal directions during navigation.

Optimal configurations of spatial scale for grid cell firing under noise and uncertainty

We examined the accuracy with which the location of an agent moving within an environment could be decoded from the simulated firing of systems of grid cells. Grid cells were modelled with Poisson spiking dynamics and organized into multiple ‘modules’ of cells, with firing patterns of similar spatial scale within modules and a wide range of spatial scales across modules. The number of grid cells per module, the spatial scaling factor between modules and the size of the environment were varied. Errors in decoded location can take two forms: small errors of precision and larger errors resulting from ambiguity in decoding periodic firing patterns. With enough cells per module (e.g. eight modules of 100 cells each) grid systems are highly robust to ambiguity errors, even over ranges much larger than the largest grid scale (e.g. over a 500 m range when the maximum grid scale is 264 cm). Results did not depend strongly on the precise organization of scales across modules (geometric, co-prime or random). However, independent spatial noise across modules, which would occur if modules receive independent spatial inputs and might increase with spatial uncertainty, dramatically degrades the performance of the grid system. This effect of spatial uncertainty can be mitigated by uniform expansion of grid scales. Thus, in the realistic regimes simulated here, the optimal overall scale for a grid system represents a trade-off between minimizing spatial uncertainty (requiring large scales) and maximizing precision (requiring small scales). Within this view, the temporary expansion of grid scales observed in novel environments may be an optimal response to increased spatial uncertainty induced by the unfamiliarity of the available spatial cues.

How to build a grid cell

Neurons in the medial entorhinal cortex fire action potentials at regular spatial intervals, creating a striking grid-like pattern of spike rates spanning the whole environment of a navigating animal. This remarkable spatial code may represent a neural map for path integration. Recent advances using patch-clamp recordings from entorhinal cortex neurons in vitro and in vivo have revealed how the microcircuitry in the medial entorhinal cortex may contribute to grid cell firing patterns, and how grid cells may transform synaptic inputs into spike output during firing field crossings. These new findings provide key insights into the ingredients necessary to build a grid cell.

Neuronal rebound spiking, resonance frequency and theta cycle skipping may contribute to grid cell firing in medial entorhinal cortex

Data show a relationship of cellular resonance and network oscillations in the entorhinal cortex to the spatial periodicity of grid cells. This paper presents a model that simulates the resonance and rebound spiking properties of entorhinal neurons to generate spatial periodicity dependent upon phasic input from medial septum. The model shows that a difference in spatial periodicity can result from a difference in neuronal resonance frequency that replicates data from several experiments. The model also demonstrates a functional role for the phenomenon of theta cycle skipping in the medial entorhinal cortex.

PLACE CELL FORMATION BY GRID CELL CONVERGENCE IN THE DENDRITES OF A CA1 MODEL NEURON

Event Abstract Back to Event PLACE CELL FORMATION BY GRID CELL CONVERGENCE IN THE DENDRITES OF A CA1 MODEL NEURON Evangelia Pollali1, George I. Kastellakis2 and Panayiota Poirazi2* 1 University of Crete, School of Medicine, Greece 2 IMBB/FORTH, Greece Place cells are pyramidal neurons in CA1 and CA3 regions of hippocampus which fire selectively when the animal is located in a particular place in space. CA1 place cells receive synaptic input from CA3 via the Schaffer collateral fibers to their proximal apical and basal dendrites and from the third layer of medial entorhinal cortex to their apical tuft dendrites. Both of these input pathways encode spatial information. Grid cells, which form the entorhinal input to CA1 cells, have a spatial firing field with multiple peaks which displays a regularly spaced, triangular grid pattern that covers the entire space of a given environment. Both grid and place cells are phase-modulated by theta rhythm and this modulation may be important for their spatial properties. Studying the formation of place cells is an important step in understanding how representation of the external environment is coded in neural networks that constitute spatial maps. It is not currently known how place fields emerge in CA1 neurons. An influential model of place cell formation predicts the convergence of various grid field inputs which combine linearly to create the place field output of CA1 cells. In this study, we constructed a model of CA1 place cell formation through the convergence of grid field inputs to the distal dendrites of our model neuron. We created a model of grid cell activity which represents the firing of grid cells modulated be the theta rhythm. We varied the number of different grid fields used as synaptic inputs to stimulate the distal dendrites of a biophysically constrained, detailed compartmental CA1 pyramidal cell model. In addition, inhibition was placed in both the distal and proximal dendrites. These inhibitory pathways are known to be active in different phases of the theta rhythm. We used this model to study the properties of CA1 place cell formation and to assess the output of the CA1 model cell during place cell activity. Additionally, we examined the effects of local dendritic integration by altering the dendritic distribution of grid cell inputs. Finally, we examined the effect of theta modulation on the spatial extent, the coherence and the information content of CA1 place cells. Acknowledgements This project is funded by the European Research Council grant ‘dEMORY’ (GA 311435). Keywords: Place Cells, grid cells, computational model, Dendrites, Theta Rhythm, Hippocampus Conference: 4th NAMASEN Training Workshop - Dendrites 2014, Heraklion, Greece, 1 Jul - 4 Jul, 2014. Presentation Type: Poster presentation Topic: the role of dendrites in complex processes, including learning/memory and neural computations Citation: Pollali E, Kastellakis GI and Poirazi P (2014). PLACE CELL FORMATION BY GRID CELL CONVERGENCE IN THE DENDRITES OF A CA1 MODEL NEURON. Front. Syst. Neurosci. Conference Abstract: 4th NAMASEN Training Workshop - Dendrites 2014. doi: 10.3389/conf.fnsys.2014.05.00007 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 11 Apr 2014; Published Online: 12 Jun 2014. * Correspondence: Dr. Panayiota Poirazi, IMBB/FORTH, Heraklion, Greece, poirazi@imbb.forth.gr Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Evangelia Pollali George I Kastellakis Panayiota Poirazi Google Evangelia Pollali George I Kastellakis Panayiota Poirazi Google Scholar Evangelia Pollali George I Kastellakis Panayiota Poirazi PubMed Evangelia Pollali George I Kastellakis Panayiota Poirazi Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

DC-shifts in amplitude in-field generated by an oscillatory interference model of grid cell firing

Oscillatory interference models propose a mechanism by which the spatial firing pattern of grid cells can arise from the interaction of multiple oscillators that shift in relative phase. These models produce aspects of the physiological data such as the phase precession dynamics observed in grid cells. However, existing oscillatory interference models did not predict the in-field DC shifts in the membrane potential of grid cells that have been observed during intracellular recordings in navigating animals. Here, we demonstrate that DC shifts can be generated in an oscillatory interference model when half-wave rectified oscillatory inputs are summed by a leaky integrate-and-fire neuron with a long membrane decay constant (100 ms). The non-linear mean of the half-wave rectified input signal is reproduced in the grid cell's membrane potential trace producing the DC shift within field. For shorter values of the decay constant integration is more effective if the input signal, comprising input from 6 head direction selective populations, is temporally spread during in-field epochs; this requires that the head direction selective populations act as velocity controlled oscillators with baseline oscillations that are phase offset from one another. The resulting simulated membrane potential matches several properties of the empirical intracellular recordings, including: in-field DC-shifts, theta-band oscillations, phase precession of both membrane potential oscillations and grid cell spiking activity relative to network theta and a stronger correlation between DC-shift amplitude and firing-rate than between theta-band oscillation amplitude and firing-rate. This work serves to demonstrate that oscillatory interference models can account for the DC shifts in the membrane potential observed during intracellular recordings of grid cells without the need to appeal to attractor dynamics.

Comparison of Properties of Medial Entorhinal Cortex Layer II Neurons in Two Anatomical Dimensions with and without Cholinergic Activation

Mechanisms underlying grid cell firing in the medial entorhinal cortex (MEC) still remain unknown. Computational modeling studies have suggested that cellular properties such as spike frequency adaptation and persistent firing might underlie the grid cell firing. Recent in vivo studies also suggest that cholinergic activation influences grid cell firing. Here we investigated the anatomical distribution of firing frequency adaptation, the medium spike after hyperpolarization potential (mAHP), subthreshold membrane potential oscillations, sag potential, input resistance and persistent firing, in MEC layer II principal cells using in vitro whole-cell patch clamp recordings in rats. Anatomical distributions of these properties were compared along both the dorso-ventral and medio-lateral axes, both with and without the cholinergic receptor agonist carbachol. We found that spike frequency adaptation is significantly stronger in ventral than in dorsal neurons both with and without carbachol. Spike frequency adaptation was significantly correlated with the duration of the mAHP, which also showed a gradient along the dorso-ventral axis. In carbachol, we found that about 50% of MEC layer II neurons show persistent firing which lasted more than 30 seconds. Persistent firing of MEC layer II neurons might contribute to grid cell firing by providing the excitatory drive. Dorso-ventral differences in spike frequency adaptation we report here are opposite from previous predictions by a computational model. We discuss an alternative mechanism as to how dorso-ventral differences in spike frequency adaptation could contribute to different scales of grid spacing.

A model for greed cells in 3-D environments

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. lf this is the case, then the topology of the environment in which the development takes place should affect the way the grid final configuration appears. Until now, models of grid cells have dealt only with planar, two-dimensional topologies. We extend our single-cell adaptation model [1] to include the third dimension in the environment. We study two non-planar topologies: the sphere surface [2] the fully three-dimensional space. What grid cell firing maps would we expect to observe? In the first condition the model predicts a sequence of spherical harmonics, each of which is the optimal asymptotic solution for the self-organizing adaptation process, within a certain range of the world radius. In the second, it predicts that the grid fields should assume a configuration analogous to an hexagonal close-packing lattice. New experiments that make use of virtual reality on a revolving sphere, or in which rats are reared inside a spherical cage, will likely be a direct test for our model on the sphere, while experiments with flying bats will provide evidence on the feasibility of a genuine 3-dimensional representation of space in terms of grid units.

Segregation of cortical head direction cell assemblies on alternating theta cycles

High-level cortical systems for spatial navigation, including entorhinal grid cells, critically depend on input from the head direction system. We examined spiking rhythms and modes of synchrony between neurons participating in head direction networks for evidence of internal processing, independent of direct sensory drive, which may be important for grid cell function. We demonstrate that head direction networks of rats are segregated into at least two populations of neurons firing on alternate theta cycles (theta cycle skipping) with fixed synchronous or anti-synchronous relationships. Pairs of anti-synchronous theta cycle skipping neurons exhibited larger differences in head direction tuning with a minimum difference of 40 degrees of head direction. Septal inactivation preserved the head direction signal but eliminated theta cycle skipping of head direction cells and grid cell spatial periodicity. We propose that internal mechanisms underlying cycle skipping in head direction networks may be critical for downstream spatial computation by grid cells.

The Postsubiculum and Spatial Learning: The Role of Postsubicular Synaptic Activity and Synaptic Plasticity in Hippocampal Place Cell, Object, and Object-Location Memory

Visual landmarks exert stimulus control over spatial behavior and the spatially tuned firing of place, head-direction, and grid cells in the rodent. However, the neural site of convergence for representations of landmarks and representations of space has yet to be identified. A potential site of plasticity underlying associations with landmarks is the postsubiculum. To test this, we blocked glutamatergic transmission in the rat postsubiculum with CNQX, or NMDA receptor-dependent plasticity with d-AP5. These infusions were sufficient to block evoked potentials from the lateral dorsal thalamus and long-term depression following tetanization of this input to the postsubiculum, respectively. In a second experiment, CNQX disrupted the stability of rat hippocampal place cell fields in a familiar environment. In a novel environment, blockade of plasticity with d-AP5 in the postsubiculum did not block the formation of a stable place field map following a 6 h delay. In a final behavioral experiment, postsubicular infusions of both compounds blocked object-location memory in the rat, but did not affect object recognition memory. These results suggest that the postsubiculum is necessary for the recognition of familiar environments, and that NMDA receptor-dependent plasticity in the postsubiculum is required for the formation of new object-place associations that support recognition memory. However, plasticity in the postsubiculum is not necessary for the formation of new spatial maps.

Circuits supporting the grid

Two studies show that local inhibitory connectivity and hippocampal excitatory input support the spatial firing patterns of entorhinal grid cells, providing support for continuous attractor model of grid cell firing.

Cellular mechanisms of spatial navigation in the medial entorhinal cortex

Neurons in the medial entorhinal cortex exhibit a grid-like spatial pattern of spike rates that has been proposed to represent a neural code for path integration. To understand how grid cell firing arises from the combination of intrinsic conductances and synaptic input in medial entorhinal stellate cells, we performed patch-clamp recordings in mice navigating in a virtual-reality environment. We found that the membrane potential signature of stellate cells during firing field crossings consisted of a slow depolarization driving spike output. This was best predicted by network models in which neurons receive sustained depolarizing synaptic input during a field crossing, such as continuous attractor network models of grid cell firing. Another key feature of the data, phase precession of intracellular theta oscillations and spiking with respect to extracellular theta oscillations, was best captured by an oscillatory interference model. Thus, these findings provide crucial new information for a quantitative understanding of the cellular basis of spatial navigation in the entorhinal cortex.

Recurrent inhibitory circuitry as a mechanism for grid formation

Grid cells in layer II of the medial entorhinal cortex form a principal component of the mammalian neural representation of space. The firing pattern of a single grid cell has been hypothesized to be generated through attractor dynamics in a network with a specific local connectivity including both excitatory and inhibitory connections. However, experimental evidence supporting the presence of such connectivity among grid cells in layer II is limited. Here we report recordings from more than 600 neuron pairs in rat entorhinal slices, demonstrating that stellate cells, the principal cell type in the layer II grid network, are mainly interconnected via inhibitory interneurons. Using a model attractor network, we demonstrate that stable grid firing can emerge from a simple recurrent inhibitory network. Our findings thus suggest that the observed inhibitory microcircuitry between stellate cells is sufficient to generate grid-cell firing patterns in layer II of the medial entorhinal cortex.

How reduction of theta rhythm by medial septum inactivation may covary with disruption of entorhinal grid cell responses due to reduced cholinergic transmission

Oscillations in the coordinated firing of brain neurons have been proposed to play important roles in perception, cognition, attention, learning, navigation, and sensory-motor control. The network theta rhythm has been associated with properties of spatial navigation, as has the firing of entorhinal grid cells and hippocampal place cells. Two recent studies reduced the theta rhythm by inactivating the medial septum (MS) and demonstrated a correlated reduction in the characteristic hexagonal spatial firing patterns of grid cells. These results, along with properties of intrinsic membrane potential oscillations (MPOs) in slice preparations of medial entorhinal cortex (MEC), have been interpreted to support oscillatory interference models of grid cell firing. The current article shows that an alternative self-organizing map (SOM) model of grid cells can explain these data about intrinsic and network oscillations without invoking oscillatory interference. In particular, the adverse effects of MS inactivation on grid cells can be understood in terms of how the concomitant reduction in cholinergic inputs may increase the conductances of leak potassium (K+) and slow and medium after-hyperpolarization (sAHP and mAHP) channels. This alternative model can also explain data that are problematic for oscillatory interference models, including how knockout of the HCN1 gene in mice, which flattens the dorsoventral gradient in MPO frequency and resonance frequency, does not affect the development of the grid cell dorsoventral gradient of spatial scales, and how hexagonal grid firing fields in bats can occur even in the absence of theta band modulation. These results demonstrate how models of grid cell self-organization can provide new insights into the relationship between brain learning and oscillatory dynamics.