scholarly journals Toroidal topology of population activity in grid cells

Nature ◽  
2022 ◽  
Author(s):  
Richard J. Gardner ◽  
Erik Hermansen ◽  
Marius Pachitariu ◽  
Yoram Burak ◽  
Nils A. Baas ◽  
...  
Keyword(s):  
Grid Cell ◽  
Population Level ◽  
Neural System ◽  
Topological Data Analysis ◽  
Small Samples ◽  
Grid Cells ◽  
Population Code ◽  
Grid Pattern ◽  
Population Activity ◽  
Toroidal Manifold

AbstractThe medial entorhinal cortex is part of a neural system for mapping the position of an individual within a physical environment1. Grid cells, a key component of this system, fire in a characteristic hexagonal pattern of locations2, and are organized in modules3 that collectively form a population code for the animal’s allocentric position1. The invariance of the correlation structure of this population code across environments4,5 and behavioural states6,7, independent of specific sensory inputs, has pointed to intrinsic, recurrently connected continuous attractor networks (CANs) as a possible substrate of the grid pattern1,8–11. However, whether grid cell networks show continuous attractor dynamics, and how they interface with inputs from the environment, has remained unclear owing to the small samples of cells obtained so far. Here, using simultaneous recordings from many hundreds of grid cells and subsequent topological data analysis, we show that the joint activity of grid cells from an individual module resides on a toroidal manifold, as expected in a two-dimensional CAN. Positions on the torus correspond to positions of the moving animal in the environment. Individual cells are preferentially active at singular positions on the torus. Their positions are maintained between environments and from wakefulness to sleep, as predicted by CAN models for grid cells but not by alternative feedforward models12. This demonstration of network dynamics on a toroidal manifold provides a population-level visualization of CAN dynamics in grid cells.

scholarly journals Toroidal topology of population activity in grid cells

2021 ◽  
Author(s):  
Richard J. Gardner ◽  
Erik Hermansen ◽  
Marius Pachitariu ◽  
Yoram Burak ◽  
Nils A. Baas ◽  
...  
Keyword(s):  
Grid Cell ◽  
Population Level ◽  
Neural System ◽  
Topological Data Analysis ◽  
Small Samples ◽  
Grid Cells ◽  
Population Code ◽  
Grid Pattern ◽  
Population Activity ◽  
Toroidal Manifold

AbstractThe medial entorhinal cortex (MEC) is part of a neural system for mapping a subject’s position within a physical environment1,2. Grid cells, a key component of this system, fire in a characteristic hexagonal pattern of locations3, and are organized in modules4,5 which collectively form a population code for the animal’s allocentric position1,6–8. The invariance of the correlation structure of this population code across environments9,10 and behavioural states11,12, independently of specific sensory inputs, has pointed to intrinsic, recurrently connected continuous attractor networks (CANs) as a possible substrate of the grid pattern1,2,13–16. However, whether grid cell networks show continuous attractor dynamics, and how they interface with inputs from the environment, has remained elusive due to the small samples of cells obtained to date. Here we show, with simultaneous recordings from many hundreds of grid cells, and subsequent topological data analysis, that the joint activity of grid cells from an individual module resides on a toroidal manifold, as expected in a two-dimensional CAN. Positions on the torus correspond to the moving animal’s position in the environment. Individual cells are preferentially active at singular positions on the torus. Their positions are maintained, with minimal distortion, between environments and from wakefulness to sleep, as predicted by CAN models for grid cells but not by alternative feed-forward models where grid patterns are created from external inputs by Hebbian plasticity17–22. This demonstration of network dynamics on a toroidal manifold provides the first population-level visualization of CAN dynamics in grid cells.

scholarly journals Effect of reward on electrophysiological signatures of grid cell population activity in human spatial navigation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Wenjing Wang ◽  
Wenxu Wang
Keyword(s):  
Cell Population ◽  
Entorhinal Cortex ◽  
Grid Cell ◽  
Grid Cells ◽  
Grid Pattern ◽  
Population Activity ◽  
Spatial Measures ◽  
Moving Direction ◽  
Patients With Epilepsy ◽  
Reward Information

AbstractThe regular equilateral triangular periodic firing pattern of grid cells in the entorhinal cortex is considered a regular metric for the spatial world, and the grid-like representation correlates with hexadirectional modulation of theta (4–8 Hz) power in the entorhinal cortex relative to the moving direction. However, researchers have not clearly determined whether grid cells provide only simple spatial measures in human behavior-related navigation strategies or include other factors such as goal rewards to encode information in multiple patterns. By analysing the hexadirectional modulation of EEG signals in the theta band in the entorhinal cortex of patients with epilepsy performing spatial target navigation tasks, we found that this modulation presents a grid pattern that carries target-related reward information. This grid-like representation is influenced by explicit goals and is related to the local characteristics of the environment. This study provides evidence that human grid cell population activity is influenced by reward information at the level of neural oscillations.

scholarly journals An isomorphic mapping hypothesis of the grid representation

2014 ◽  
Vol 369 (1635) ◽  
pp. 20120521 ◽  
Author(s):  
Michael Brecht ◽  
Saikat Ray ◽  
Andrea Burgalossi ◽  
Qiusong Tang ◽  
Helene Schmidt ◽  
...  
Keyword(s):  
Pyramidal Neurons ◽  
Dimensional Space ◽  
Grid Cell ◽  
Propagation Speed ◽  
Connectivity Matrix ◽  
Two Dimensional ◽  
Grid Cells ◽  
Population Activity ◽  
Medial Entorhinal Cortex ◽  
Mapping Hypothesis

We introduce a grid cell microcircuit hypothesis. We propose the ‘grid in the world’ (evident in grid cell discharges) is generated by a ‘grid in the cortex’. This cortical grid is formed by patches of calbindin-positive pyramidal neurons in layer 2 of medial entorhinal cortex (MEC). Our isomorphic mapping hypothesis assumes three types of isomorphism: (i) metric correspondence of neural space (the two-dimensional cortical sheet) and the external two-dimensional space within patches; (ii) isomorphism between cellular connectivity matrix and firing field; (iii) isomorphism between single cell and population activity. Each patch is a grid cell lattice arranged in a two-dimensional map of space with a neural : external scale of approximately 1 : 2000 in the dorsal part of rat MEC. The lattice behaves like an excitable medium with neighbouring grid cells exciting each other. Spatial scale is implemented as an intrinsic scaling factor for neural propagation speed. This factor varies along the dorsoventral cortical axis. A connectivity scheme of the grid system is described. Head direction input specifies the direction of activity propagation. We extend the theory to neurons between grid patches and predict a rare discharge pattern (inverted grid cells) and the relative location and proportion of grid cells and spatial band cells.

scholarly journals Connecting multiple spatial scales to decode the population activity of grid cells

2015 ◽  
Vol 1 (11) ◽  
pp. e1500816 ◽  
Author(s):  
Martin Stemmler ◽  
Alexander Mathis ◽  
Andreas V. M. Herz
Keyword(s):  
Large Scale ◽  
Spatial Scales ◽  
Cell Activity ◽  
Dead Reckoning ◽  
Grid Cell ◽  
Grid Cells ◽  
Population Vector ◽  
Population Activity ◽  
Multiple Spatial Scales ◽  
Scale Ratio

Mammalian grid cells fire when an animal crosses the points of an imaginary hexagonal grid tessellating the environment. We show how animals can navigate by reading out a simple population vector of grid cell activity across multiple spatial scales, even though neural activity is intrinsically stochastic. This theory of dead reckoning explains why grid cells are organized into discrete modules within which all cells have the same lattice scale and orientation. The lattice scale changes from module to module and should form a geometric progression with a scale ratio of around 3/2 to minimize the risk of making large-scale errors in spatial localization. Such errors should also occur if intermediate-scale modules are silenced, whereas knocking out the module at the smallest scale will only affect spatial precision. For goal-directed navigation, the allocentric grid cell representation can be readily transformed into the egocentric goal coordinates needed for planning movements. The goal location is set by nonlinear gain fields that act on goal vector cells. This theory predicts neural and behavioral correlates of grid cell readout that transcend the known link between grid cells of the medial entorhinal cortex and place cells of the hippocampus.

scholarly journals Altered neural odometry in the vertical dimension

2019 ◽  
Vol 116 (10) ◽  
pp. 4631-4636 ◽  
Author(s):  
Giulio Casali ◽  
Daniel Bush ◽  
Kate Jeffery
Keyword(s):  
Vertical Plane ◽  
Grid Cell ◽  
Vertical Surface ◽  
The Body ◽  
Grid Cells ◽  
Grid Pattern ◽  
3D Space ◽  
Cell Firing ◽  
Circular Grid ◽  
Self Motion

Entorhinal grid cells integrate sensory and self-motion inputs to provide a spatial metric of a characteristic scale. One function of this metric may be to help localize the firing fields of hippocampal place cells during formation and use of the hippocampal spatial representation (“cognitive map”). Of theoretical importance is the question of how this metric, and the resulting map, is configured in 3D space. We find here that when the body plane is vertical as rats climb a wall, grid cells produce stable, almost-circular grid-cell firing fields. This contrasts with previous findings when the body was aligned horizontally during vertical exploration, suggesting a role for the body plane in orienting the plane of the grid cell map. However, in the present experiment, the fields on the wall were fewer and larger, suggesting an altered or absent odometric (distance-measuring) process. Several physiological indices of running speed in the entorhinal cortex showed reduced gain, which may explain the enlarged grid pattern. Hippocampal place fields were found to be sparser but unchanged in size/shape. Together, these observations suggest that the orientation and scale of the grid cell map, at least on a surface, are determined by an interaction between egocentric information (the body plane) and allocentric information (the gravity axis). This may be mediated by the different sensory or locomotor information available on a vertical surface and means that the resulting map has different properties on a vertical plane than a horizontal plane (i.e., is anisotropic).

scholarly journals Environmental deformations dynamically shift the grid cell spatial metric

eLife ◽  
2018 ◽  
Vol 7 ◽  
Author(s):  
Alexandra T Keinath ◽  
Russell A Epstein ◽  
Vijay Balasubramanian
Keyword(s):  
Computational Model ◽  
Grid Cell ◽  
Phase Shifts ◽  
Cell Interactions ◽  
Geometric Shape ◽  
Grid Cells ◽  
Potential Mechanism ◽  
Grid Pattern ◽  
Border Cell ◽  
Local Distortions

In familiar environments, the firing fields of entorhinal grid cells form regular triangular lattices. However, when the geometric shape of the environment is deformed, these time-averaged grid patterns are distorted in a grid scale-dependent and local manner. We hypothesized that this distortion in part reflects dynamic anchoring of the grid code to displaced boundaries, possibly through border cell-grid cell interactions. To test this hypothesis, we first reanalyzed two existing rodent grid rescaling datasets to identify previously unrecognized boundary-tethered shifts in grid phase that contribute to the appearance of rescaling. We then demonstrated in a computational model that boundary-tethered phase shifts, as well as scale-dependent and local distortions of the time-averaged grid pattern, could emerge from border-grid interactions without altering inherent grid scale. Together, these results demonstrate that environmental deformations induce history-dependent shifts in grid phase, and implicate border-grid interactions as a potential mechanism underlying these dynamics.

scholarly journals Decoding the Population Activity of Grid Cells for Spatial Localization and Goal-Directed Navigation

2015 ◽  
Author(s):  
Martin Stemmler ◽  
Alexander Mathis ◽  
Andreas VM Herz
Keyword(s):  
Multiple Scales ◽  
Cell Activity ◽  
Dead Reckoning ◽  
Grid Cell ◽  
Spatial Localization ◽  
Grid Cells ◽  
Population Vector ◽  
Nonlinear Gain ◽  
Population Activity ◽  
Homing Vector

Mammalian grid cells fire whenever an animal crosses the points of an imaginary, hexagonal grid tessellating the environment. Here, we show how animals can localize themselves and navigate by reading-out a simple population vector of grid cell activity across multiple scales, even though this activity is intrinsically stochastic. This theory of dead reckoning explains why grid cells are organized into modules with equal lattice scale and orientation. Computing the homing vector is least error-prone when the ratio of successive grid scales is around 3/2. Silencing intermediate-scale modules should cause systematic errors in navigation, while knocking out the module at the smallest scale will only affect navigational precision. Read-out neurons should behave like goal-vector cells subject to nonlinear gain fields.

scholarly journals Grid-cell modules remain coordinated when neural activity is dissociated from external sensory cues

2021 ◽  
Author(s):  
Torgeir Waaga ◽  
Haggai Agmon ◽  
Velentin A. Normand ◽  
Anne Nagelhus ◽  
Richard J. Gardner ◽  
...  
Keyword(s):  
Neural Activity ◽  
Activity Patterns ◽  
Internal Representation ◽  
Grid Cell ◽  
Grid Cells ◽  
Sensory Cues ◽  
Population Activity ◽  
Medial Entorhinal Cortex ◽  
True Position ◽  
Cell Modules

The representation of an animal's position in the medial entorhinal cortex (MEC) is distributed across several modules of grid cells, each characterized by a distinct spatial scale. The population activity within each module is tightly coordinated and preserved across environments and behavioral states. Little is known, however, about the coordination of activity patterns across modules. We analyzed the joint activity patterns of hundreds of grid cells simultaneously recorded in animals that were foraging either in the light, when sensory cues could stabilize the representation, or in darkness, when such stabilization was disrupted. We found that the states of different grid modules are tightly coordinated, even in darkness, when the internal representation of position within the MEC deviates substantially from the true position of the animal. These findings suggest that internal brain mechanisms dynamically coordinate the representation of position in different modules, to ensure that grid cells jointly encode a coherent and smooth trajectory of the animal.

scholarly journals During hippocampal inactivation, grid cells maintain their synchrony, even when the grid pattern is lost

2019 ◽  
Author(s):  
Noam Almog ◽  
Gilad Tocker ◽  
Tora Bonnevie ◽  
Edvard Moser ◽  
May-Britt Moser ◽  
...  
Keyword(s):  
Grid Cell ◽  
Phase Relations ◽  
Head Direction ◽  
Grid Cells ◽  
Regular Grid ◽  
Spatial Correlations ◽  
Grid Pattern ◽  
Cell Network ◽  
Intrinsic Connectivity ◽  
Temporal And Spatial

AbstractThe grid cell network in the MEC has been subject to thorough testing and analysis, and many theories for their formation have been suggested. To test some of these theories we re-analyzed data from Bonnevie et al. (2013), in which the hippocampus was inactivated and grid cells were recorded in the MEC, to investigate whether the firing associations of grid cells depend on hippocampal inputs. Specifically, we examined temporal and spatial correlations in the firing times of simultaneously recorded grid cells before and during hippocampal inactivation. Our analysis revealed evidence of network coherence in grid cells even in the absence of hippocampal input to the MEC, both in regular grid cells and in those that became head-direction cells after hippocampal inactivation. This favors models which suggest that phase relations between grid cells in the MEC are dependent on intrinsic connectivity within the MEC.

scholarly journals During hippocampal inactivation, grid cells maintain synchrony, even when the grid pattern is lost

eLife ◽  
2019 ◽  
Vol 8 ◽  
Author(s):  
Noam Almog ◽  
Gilad Tocker ◽  
Tora Bonnevie ◽  
Edvard I Moser ◽  
May-Britt Moser ◽  
...  
Keyword(s):  
Grid Cell ◽  
Head Direction ◽  
Grid Cells ◽  
Regular Grid ◽  
Spatial Correlations ◽  
Grid Pattern ◽  
Medial Entorhinal Cortex ◽  
Cell Network ◽  
Intrinsic Connectivity ◽  
Temporal And Spatial

The grid cell network in the medial entorhinal cortex (MEC) has been subject to thorough testing and analysis, and many theories for their formation have been suggested. To test some of these theories, we re-analyzed data from Bonnevie et al., 2013, in which the hippocampus was inactivated and grid cells were recorded in the rat MEC. We investigated whether the firing associations of grid cells depend on hippocampal inputs. Specifically, we examined temporal and spatial correlations in the firing times of simultaneously recorded grid cells before and during hippocampal inactivation. Our analysis revealed evidence of network coherence in grid cells even in the absence of hippocampal input to the MEC, both in regular grid cells and in those that became head-direction cells after hippocampal inactivation. This favors models, which suggest that phase relations between grid cells in the MEC are dependent on intrinsic connectivity within the MEC.

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