Grid Cell Firing Research Articles

Grid cell firing patterns signal environmental novelty by expansion

The hippocampal formation plays key roles in representing an animal's location and in detecting environmental novelty to create or update those representations. However, the mechanisms behind this latter function are unclear. Here, we show that environmental novelty causes the spatial firing patterns of grid cells to expand in scale and reduce in regularity, reverting to their familiar scale as the environment becomes familiar. Simultaneously recorded place cell firing fields remapped and showed a smaller, temporary expansion. Grid expansion provides a potential mechanism for novelty signaling and may enhance the formation of new hippocampal representations, whereas the subsequent slow reduction in scale provides a potential familiarity signal.

How Entorhinal Grid Cells May Learn Multiple Spatial Scales from a Dorsoventral Gradient of Cell Response Rates in a Self-organizing Map

Place cells in the hippocampus of higher mammals are critical for spatial navigation. Recent modeling clarifies how this may be achieved by how grid cells in the medial entorhinal cortex (MEC) input to place cells. Grid cells exhibit hexagonal grid firing patterns across space in multiple spatial scales along the MEC dorsoventral axis. Signals from grid cells of multiple scales combine adaptively to activate place cells that represent much larger spaces than grid cells. But how do grid cells learn to fire at multiple positions that form a hexagonal grid, and with spatial scales that increase along the dorsoventral axis? In vitro recordings of medial entorhinal layer II stellate cells have revealed subthreshold membrane potential oscillations (MPOs) whose temporal periods, and time constants of excitatory postsynaptic potentials (EPSPs), both increase along this axis. Slower (faster) subthreshold MPOs and slower (faster) EPSPs correlate with larger (smaller) grid spacings and field widths. A self-organizing map neural model explains how the anatomical gradient of grid spatial scales can be learned by cells that respond more slowly along the gradient to their inputs from stripe cells of multiple scales, which perform linear velocity path integration. The model cells also exhibit MPO frequencies that covary with their response rates. The gradient in intrinsic rhythmicity is thus not compelling evidence for oscillatory interference as a mechanism of grid cell firing. A response rate gradient combined with input stripe cells that have normalized receptive fields can reproduce all known spatial and temporal properties of grid cells along the MEC dorsoventral axis. This spatial gradient mechanism is homologous to a gradient mechanism for temporal learning in the lateral entorhinal cortex and its hippocampal projections. Spatial and temporal representations may hereby arise from homologous mechanisms, thereby embodying a mechanistic “neural relativity” that may clarify how episodic memories are learned.

Models of grid cells and theta oscillations

Arising from M. M.Yartsev, M. P. Witter & N. Ulanovsky , 103–107 (2011)10.1038/nature10583 Grid cells recorded in the medial entorhinal cortex (MEC) of freely moving rodents show a markedly regular spatial firing pattern whose underlying mechanism has been the subject of intense interest. Yartsev et al.1 report that the firing of grid cells in crawling bats does not show theta rhythmicity “causally disproving a major class of computational models” of grid cell firing that rely on oscillatory interference2,3,4,5,6,7. However, their data may be consistent with these models, with the apparent lack of theta rhythmicity reflecting slow movement speeds and low firing rates. Thus, the conclusion of Yartsev et al. is not supported by their data.

From A to Z: a potential role for grid cells in spatial navigation

Since their discovery, the strikingly regular and spatially stable firing of entorhinal grid cells has attracted the attention of experimentalists and theoreticians alike. The bulk of this work has focused either on the assumption that the principal role of grid cells is to support path integration or the extent to which their multiple firing locations can drive the sparse activity of hippocampal place cells. Here, we propose that grid cells are best understood as part of a network that combines self-motion and environmental cues to accurately track an animal’s location in space. Furthermore, that grid cells - more so than place cells - efficiently encode self-location in allocentric coordinates. Finally, that the regular structure of grid firing fields represents information about the relative structure of space and, as such, may be used to guide goal directed navigation.

Modeling the influence of optic flow on grid cell firing in the absence of other cues1

Information from the vestibular, sensorimotor, or visual systems can affect the firing of grid cells recorded in entorhinal cortex of rats. Optic flow provides information about the rat’s linear and rotational velocity and, thus, could influence the firing pattern of grid cells. To investigate this possible link, we model parts of the rat’s visual system and analyze their capability in estimating linear and rotational velocity. In our model a rat is simulated to move along trajectories recorded from rat’s foraging on a circular ground platform. Thus, we preserve the intrinsic statistics of real rats’ movements. Visual image motion is analytically computed for a spherical camera model and superimposed with noise in order to model the optic flow that would be available to the rat. This optic flow is fed into a template model to estimate the rat’s linear and rotational velocities, which in turn are fed into an oscillatory interference model of grid cell firing. Grid scores are reported while altering the flow noise, tilt angle of the optical axis with respect to the ground, the number of flow templates, and the frequency used in the oscillatory interference model. Activity patterns are compatible with those of grid cells, suggesting that optic flow can contribute to their firing.

Alternating predictive and short‐term memory modes of entorhinal grid cells

Several lines of evidence indicate that the entorhinal cortex has memory functions, but such functions have not been previously found in grid cells, a cell type that provides major input to the hippocampus. We examined the firing of grid cells as rats crossed (runs) through grid cell vertices. We found that on some runs, firing tended to occur mostly inbound as the rat approached a vertex center while on other runs firing occurred mainly outbound. These results suggest that cells have a predictive mode (inbound firing) in which they represent a position ahead of the animal and a short term memory (STM) mode (outbound firing) in which they represent positions just passed through. Analysis of cell pairs showed that when vertex crossings were less than 1 second apart, the two cells tended to have the same mode. This indicates that modes are a network property. The tendency to have the same mode disappeared if crossings were separated by 2-3 seconds, suggesting that modes alternate on the time scale of seconds. There was a small but statistically significant behavioral correlate of modes: velocity was slightly less in the STM mode. Both modes were organized by theta and gamma oscillations. The results suggest that the dual requirement for hippocampal storage and recall is met by rapidly alternating modes appropriate for predicting the future and storing the recent past.

Grid cells in rat entorhinal cortex encode physical space with independent firing fields and phase precession at the single-trial level

When a rat moves, grid cells in its entorhinal cortex become active in multiple regions of the external world that form a hexagonal lattice. As the animal traverses one such "firing field," spikes tend to occur at successively earlier theta phases of the local field potential. This phenomenon is called phase precession. Here, we show that spike phases provide 80% more spatial information than spike counts and that they improve position estimates from single neurons down to a few centimeters. To understand what limits the resolution and how variable spike phases are across different field traversals, we analyze spike trains run by run. We find that the multiple firing fields of a grid cell operate as independent elements for encoding physical space. In addition, phase precession is significantly stronger than the pooled-run data suggest. Despite the inherent stochasticity of grid-cell firing, phase precession is therefore a robust phenomenon at the single-trial level, making a theta-phase code for spatial navigation feasible.

Voltage dependence of subthreshold resonance frequency in layer II of medial entorhinal cortex.

The resonance properties of individual neurons in entorhinal cortex (EC) may contribute to their functional properties in awake, behaving rats. Models propose that entorhinal grid cells could arise from shifts in the intrinsic frequency of neurons caused by changes in membrane potential owing to depolarizing input from neurons coding velocity. To test for potential changes in intrinsic frequency, we measured the resonance properties of neurons at different membrane potentials in neurons in medial and lateral EC. In medial entorhinal neurons, the resonant frequency of individual neurons decreased in a linear manner as the membrane potential was depolarized between -70 and -55 mV. At more hyperpolarized membrane potentials, cells asymptotically approached a maximum resonance frequency. Consistent with the previous studies, near resting potential, the cells of the medial EC possessed a decreasing gradient of resonance frequency along the dorsal to ventral axis, and cells of the lateral EC lacked resonant properties, regardless of membrane potential or position along the medial to lateral axis within lateral EC. Application of 10 μM ZD7288, the H-channel blocker, abolished all resonant properties in MEC cells, and resulted in physiological properties very similar to lateral EC cells. These results on resonant properties show a clear change in frequency response with depolarization that could contribute to the generation of grid cell firing properties in the medial EC.

A Model Combining Oscillations and Attractor Dynamics for Generation of Grid Cell Firing

Different models have been able to account for different features of the data on grid cell firing properties, including the relationship of grid cells to cellular properties and network oscillations. This paper describes a model that combines elements of two major classes of models of grid cells: models using interactions of oscillations and models using attractor dynamics. This model includes a population of units with oscillatory input representing input from the medial septum. These units are termed heading angle cells because their connectivity depends upon heading angle in the environment as well as the spatial phase coded by the cell. These cells project to a population of grid cells. The sum of the heading angle input results in standing waves of circularly symmetric input to the grid cell population. Feedback from the grid cell population increases the activity of subsets of the heading angle cells, resulting in the network settling into activity patterns that resemble the patterns of firing fields in a population of grid cells. The properties of heading angle cells firing as conjunctive grid-by-head-direction cells can shift the grid cell firing according to movement velocity. The pattern of interaction of oscillations requires use of separate populations that fire on alternate cycles of the net theta rhythmic input to grid cells.

A Physiologically Inspired Model for Global Remapping in the Hippocampus

Event Abstract Back to Event A Physiologically Inspired Model for Global Remapping in the Hippocampus Axel J. Kammerer1, 2*, Alexander Mathis1, 2, 3, Martin Stemmler1, 3, Andreas V. Herz1, 3 and Christian Leibold1, 3 1 Ludwigs Maximilians Universitaet Muenchen, Division of Neurobiology, Germany 2 Graduate School of Systemic Neuroscience Munich, Germany 3 BCCN Munich, Germany Population activity patterns (place maps) in the hippocampus change dramatically if the animal is exposed to the same maze in different lab environments (global remapping) [Leutgeb et al. 2007, Science]. Such decorrelated patterns are essential for many models of associative memory: they sustain flexibility and allow many patterns to be stored. This remapping could have its root in an observed shift of grid cell firing patterns: During hippocampal remapping the spatial activity pattern of grid cells undergoes locally coherent rotations and translations [Fyhn et al. 2007, Nature], but it is not known whether this coherence extends over different spatial modules, which are anatomically separated within entorhinal cortex [Witter, Moser 2006, Trends in Neurosciences]. Also, the environment's size and shape are of importance for the remapping. We studied the influence of these realignments of grid cells on the formation of place cell firing patterns in the hippocampus and find that global remapping can indeed be caused by realigning a realistic number of grid cell modules. Also the size of the environment (relative to the grid field's period length) has influence on the remapping. To support these hypothesis, we employed a model with physiologically plausible connections in which grid cells give rise to place cells for a single environment [de Almeida et al. 2010, Hippocampus]. We investigate the behavior of the place cell output layer in response to incoherent rotations and translations of the spatial patterns in the grid cell modules in different sized environments, while leaving the synaptic weights from the grid to place layer unaltered. Simulations of the full model with noise create rate remapping for small shifts, leaving strong spatial correlations, while larger shifts produce strong rate fluctuations as well as spatial decorrelation of place fields. This recreates the findings in experiments by Fyhn et al. [Fyhn et al. 2007, Nature]. Furthermore the population vector decorrelation depends on the size of the environment, such that smaller shifts suffice to achieve the same decorrelation in larger environments. Keywords: grid cells, remapping Conference: Bernstein Conference 2012, Munich, Germany, 12 Sep - 14 Sep, 2012. Presentation Type: Poster Topic: Motor control, movement, navigation Citation: Kammerer AJ, Mathis A, Stemmler M, Herz AV and Leibold C (2012). A Physiologically Inspired Model for Global Remapping in the Hippocampus. Front. Comput. Neurosci. Conference Abstract: Bernstein Conference 2012. doi: 10.3389/conf.fncom.2012.55.00181 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 May 2012; Published Online: 12 Sep 2012. * Correspondence: Mr. Axel J Kammerer, Ludwigs Maximilians Universitaet Muenchen, Division of Neurobiology, Munich, 82152, Germany, axel.kammerer@gmail.com 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 Axel J Kammerer Alexander Mathis Martin Stemmler Andreas V Herz Christian Leibold Google Axel J Kammerer Alexander Mathis Martin Stemmler Andreas V Herz Christian Leibold Google Scholar Axel J Kammerer Alexander Mathis Martin Stemmler Andreas V Herz Christian Leibold PubMed Axel J Kammerer Alexander Mathis Martin Stemmler Andreas V Herz Christian Leibold 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.

Linear Look-Ahead in Conjunctive Cells: An Entorhinal Mechanism for Vector-Based Navigation

The crisp organization of the “firing bumps” of entorhinal grid cells and conjunctive cells leads to the notion that the entorhinal cortex may compute linear navigation routes. Specifically, we propose a process, termed “linear look-ahead,” by which a stationary animal could compute a series of locations in the direction it is facing. We speculate that this computation could be achieved through learned patterns of connection strengths among entorhinal neurons. This paper has three sections. First, we describe the minimal grid cell properties that will be built into our network. Specifically, the network relies on “rigid modules” of neurons, where all members have identical grid scale and orientation, but differ in spatial phase. Additionally, these neurons must be densely interconnected with synapses that are modifiable early in the animal’s life. Second, we investigate whether plasticity during short bouts of locomotion could induce patterns of connections amongst grid cells or conjunctive cells. Finally, we run a simulation to test whether the learned connection patterns can exhibit linear look-ahead. Our results are straightforward. A simulated 30-min walk produces weak strengthening of synapses between grid cells that do not support linear look-ahead. Similar training in a conjunctive cell module produces a small subset of very strong connections between cells. These strong pairs have three properties: the pre- and post-synaptic cells have similar heading direction. The cell pairs have neighboring grid bumps. Finally, the spatial offset of firing bumps of the cell pair is in the direction of the common heading preference. Such a module can produce strong and accurate linear look-ahead starting in any location and extending in any direction. We speculate that this process may: (1) compute linear paths to goals; (2) update grid cell firing during navigation; and (3) stabilize the rigid modules of grid cells and conjunctive cells.

The abrupt development of adult-like grid cell firing in the medial entorhinal cortex

Understanding the development of the neural circuits subserving specific cognitive functions such as navigation remains a central problem in neuroscience. Here, we characterize the development of grid cells in the medial entorhinal cortex, which, by nature of their regularly spaced firing fields, are thought to provide a distance metric to the hippocampal neural representation of space. Grid cells emerge at the time of weaning in the rat, at around 3 weeks of age. We investigated whether grid cells in young rats are functionally equivalent to those observed in the adult as soon as they appear, or if instead they follow a gradual developmental trajectory. We find that, from the very youngest ages at which reproducible grid firing is observed (postnatal day 19): grid cells display adult-like firing fields that tessellate to form a coherent map of the local environment; that this map is universal, maintaining its internal structure across different environments; and that grid cells in young rats, as in adults, also encode a representation of direction and speed. To further investigate the developmental processes leading up to the appearance of grid cells, we present data from individual medial entorhinal cortex cells recorded across more than 1 day, spanning the period before and after the grid firing pattern emerged. We find that increasing spatial stability of firing was correlated with increasing gridness.

Head direction maps remain stable despite grid map fragmentation

Areas encoding space in the brain contain both representations of position (place cells and grid cells) and representations of azimuth (head direction cells). Previous studies have already suggested that although grid cells and head direction cells reside in the same brain areas, the calculation of head direction is not dependent on the calculation of position. Here we demonstrate that realignment of grid cells does not affect head direction tuning. We analyzed head direction cell data collected while rats performed a foraging task in a multi-compartment environment (the hairpin maze) vs. an open-field environment, demonstrating that the tuning of head direction cells did not change when the environment was divided into multiple sub-compartments, in the hairpin maze. On the other hand, as we have shown previously (Derdikman et al., 2009), the hexagonal firing pattern expressed by grid cells in the open-field broke down into repeating patterns in similar alleys when rats traversed the multi-compartment hairpin maze. The grid-like firing of conjunctive cells, which express both grid properties and head direction properties in the open-field, showed a selective fragmentation of grid-like firing properties in the hairpin maze, while the head directionality property of the same cells remained unaltered. These findings demonstrate that head direction is not affected during the restructuring of grid cell firing fields as a rat actively moves between compartments, thus strengthening the claim that the head direction system is upstream from or parallel to the grid-place system.

Intrinsic electrophysiological properties of entorhinal cortex stellate cells and their contribution to grid cell firing fields

The medial entorhinal cortex (MEC) is an increasingly important focus for investigation of mechanisms for spatial representation. Grid cells found in layer II of the MEC are likely to be stellate cells, which form a major projection to the dentate gyrus. Entorhinal stellate cells are distinguished by distinct intrinsic electrophysiological properties, but how these properties contribute to representation of space is not yet clear. Here, we review the ionic conductances, synaptic, and excitable properties of stellate cells, and examine their implications for models of grid firing fields. We discuss why existing data are inconsistent with models of grid fields that require stellate cells to generate periodic oscillations. An alternative possibility is that the intrinsic electrophysiological properties of stellate cells are tuned specifically to control integration of synaptic input. We highlight recent evidence that the dorsal-ventral organization of synaptic integration by stellate cells, through differences in currents mediated by HCN and leak potassium channels, influences the corresponding organization of grid fields. Because accurate cellular data will be important for distinguishing mechanisms for generation of grid fields, we introduce new data comparing properties measured with whole-cell and perforated patch-clamp recordings. We find that clustered patterns of action potential firing and the action potential after-hyperpolarization (AHP) are particularly sensitive to recording condition. Nevertheless, with both methods, these properties, resting membrane properties and resonance follow a dorsal-ventral organization. Further investigation of the molecular basis for synaptic integration by stellate cells will be important for understanding mechanisms for generation of grid fields.

Frequency of Subthreshold Oscillations at Different Membrane Potential Voltages in Neurons at Different Anatomical Positions on the Dorsoventral Axis in the Rat Medial Entorhinal Cortex

Neurons from layer II of the medial entorhinal cortex show subthreshold membrane potential oscillations (SMPOs) which could contribute to theta-rhythm generation in the entorhinal cortex and to generation of grid cell firing patterns. However, it is unclear whether single neurons have a fixed unique oscillation frequency or whether their frequency varies depending on the mean membrane potential in a cell. We therefore examined the frequency of SMPOs at different membrane potentials in layer II stellate-like cells of the rat medial entorhinal cortex in vitro. Using whole-cell patch recordings, we found that the fluctuations in membrane potential show a broad band of low power frequencies near resting potential that transition to more narrowband oscillation frequencies with depolarization. The transition from broadband to narrowband frequencies depends on the location of the neuron along the dorsoventral axis in the entorhinal cortex, with dorsal neurons transitioning to higher-frequency oscillations relative to ventral neurons transitioning to lower-frequency oscillations. Once SMPOs showed a narrowband frequency, systematic frequency changes were not observed with further depolarization. Using a Hodgkin-Huxley-style model of membrane currents, we show that differences in the influence of depolarization on the frequency of SMPOs at different dorsal to ventral positions could arise from differences in the properties of the h current. The properties of frequency changes in this data are important for evaluating models of the generation of grid cell firing fields with different spacings along the dorsal-to-ventral axis of medial entorhinal cortex.

Anisotropic encoding of three-dimensional space by place cells and grid cells

The subjective sense of space may result in part from the combined activity of place cells, in the hippocampus, and grid cells in posterior cortical regions such as entorhinal cortex and pre/parasubiculum. In horizontal planar environments, place cells provide focal positional information while grid cells supply odometric (distance-measuring) information. How these cells operate in three dimensions is unknown, even though the real world is three–dimensional. The present study explored this issue in rats exploring two different kinds of apparatus, a climbing wall (the “pegboard”) and a helix. Place and grid cell firing fields had normal horizontal characteristics but were elongated vertically, with grid fields forming stripes. It appears that grid cell odometry (and by implication path integration) is impaired/absent in the vertical domain, at least when the animal itself remains horizontal. These findings suggest that the mammalian encoding of three-dimensional space is anisotropic.

The Spatial Periodicity of Grid Cells Is Not Sustained During Reduced Theta Oscillations

Grid cells in parahippocampal cortices fire at vertices of a periodic triangular grid that spans the entire recording environment. Such precise neural computations in space have been proposed to emerge from equally precise temporal oscillations within cells or within the local neural circuitry. We found that grid-like firing patterns in the entorhinal cortex vanished when theta oscillations were reduced after intraseptal lidocaine infusions in rats. Other spatially modulated cells in the same cortical region and place cells in the hippocampus retained their spatial firing patterns to a larger extent during these periods without well-organized oscillatory neuronal activity. Precisely timed neural activity within single cells or local networks is thus required for periodic spatial firing but not for single place fields.

Does Optic Flow Explain the Firing of Grid Cells?

Abstract*Problem.* Various cues such as vestibular, sensorimotor, or visual information can lead to the firing of grid cells recorded in entorhinal cortex of rats. A recent model uses boundary vector cells to provide information about the 2D spatial position (Barry et al., Review Neuroscience, 17, 2006). However, boundary vector cells need to know the angle and distance of the boundary wall. In contrast we study the estimation of 2D velocity and change of heading of the rat from optic flow and if this information can lead to grid cell firing.*Approach.* A simple circular cage is modeled as a 3D world and trajectories of a rat’s movement are simulated. Optic flow for a spherical camera model is calculated for regularly sampled locations on the ground of the cage. This flow information is used in a template model to estimate the rat’s 2D linear velocity and yaw rotational velocity. 2D linear velocities are integrated into the velocity controlled oscillator (VCO) model (Burgess, Hippocampus, 18, 2008) while spatial locations are taken from the original trajectory. Result and Conclusion. If velocity estimates are temporally integrated over ~20min the error summation by path integration prevents generation of a clear grid cell firing pattern by the VCO model. However, for short durations velocity estimates and path integration are accurate. If we assume a reset mechanism that recalibrates the spatial location of the rat grid cell firing can be achieved. Different reset intervals were simulated and the grid score for the firing pattern was calculated. For a reset interval longer than one minute this grid score decreases rapidly. We conclude that grid cell firing is not generated only by optic flow, but that a recalibration of the spatial position using cues other than optic flow occurs at least every minute.Supported by CELEST (NSF SMA-0835976).

Does Optic Flow Explain the Firing of Grid Cells?

Does Optic Flow Explain the Firing of Grid Cells?

A Handbook for Modeling Hippocampal Circuits

A Handbook for Modeling Hippocampal Circuits