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 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 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 Home, head direction stability, and grid cell distortion

2020 ◽  
Vol 123 (4) ◽  
pp. 1392-1406 ◽  
Author(s):  
Juan Ignacio Sanguinetti-Scheck ◽  
Michael Brecht
Keyword(s):  
Entorhinal Cortex ◽  
Home Cage ◽  
Cell Activity ◽  
Grid Cell ◽  
Head Direction ◽  
Grid Cells ◽  
Head Direction Cells ◽  
Medial Entorhinal Cortex ◽  
Abstract Approach ◽  
Globally Stable

The home is a unique location in the life of humans and animals. In rats, home presents itself as a multicompartmental space that involves integrating navigation through subspaces. Here we embedded the laboratory rat’s home cage in the arena, while recording neurons in the animal’s parasubiculum and medial entorhinal cortex, two brain areas encoding the animal’s location and head direction. We found that head direction signals were unaffected by home cage presence or translocation. Head direction cells remain globally stable and have similar properties inside and outside the embedded home. We did not observe egocentric bearing encoding of the home cage. However, grid cells were distorted in the presence of the home cage. While they did not globally remap, single firing fields were translocated toward the home. These effects appeared to be geometrical in nature rather than a home-specific distortion and were not dependent on explicit behavioral use of the home cage during a hoarding task. Our work suggests that medial entorhinal cortex and parasubiculum do not remap after embedding the home, but local changes in grid cell activity overrepresent the embedded space location and might contribute to navigation in complex environments. NEW & NOTEWORTHY Neural findings in the field of spatial navigation come mostly from an abstract approach that separates the animal from even a minimally biological context. In this article we embed the home cage of the rat in the environment to address some of the complexities of natural navigation. We find no explicit home cage representation. While both head direction cells and grid cells remain globally stable, we find that embedded spaces locally distort grid cells.

scholarly journals Entorhinal cortex receptive fields are modulated by spatial attention, even without movement

eLife ◽  
2018 ◽  
Vol 7 ◽  
Author(s):  
Niklas Wilming ◽  
Peter König ◽  
Seth König ◽  
Elizabeth A Buffalo
Keyword(s):  
Entorhinal Cortex ◽  
Cell Activity ◽  
Receptive Fields ◽  
Grid Cell ◽  
Covert Attention ◽  
Grid Cells ◽  
Physical Movement ◽  
Mental Operations ◽  
Triangular Tiling ◽  
Central Fixation

Grid cells in the entorhinal cortex allow for the precise decoding of position in space. Along with potentially playing an important role in navigation, grid cells have recently been hypothesized to make a general contribution to mental operations. A prerequisite for this hypothesis is that grid cell activity does not critically depend on physical movement. Here, we show that movement of covert attention, without any physical movement, also elicits spatial receptive fields with a triangular tiling of space. In monkeys trained to maintain central fixation while covertly attending to a stimulus moving in the periphery we identified a significant population (20/141, 14% neurons at a FDR <5%) of entorhinal cells with spatially structured receptive fields. This contrasts with recordings obtained in the hippocampus, where grid-like representations were not observed. Our results provide evidence that neurons in macaque entorhinal cortex do not rely on physical movement.

scholarly journals A Local Measure of Symmetry and Orientation for Individual Spikes of Grid Cells

2018 ◽  
Author(s):  
Simon N. Weber ◽  
Henning Sprekeler
Keyword(s):  
Cell Activity ◽  
Grid Cell ◽  
Local Order ◽  
Global Symmetry ◽  
Grid Cells ◽  
Lighting Condition ◽  
Firing Patterns ◽  
Space And Time ◽  
Local Defects ◽  
Local Distortions

ABSTRACTGrid cells have attracted broad attention because of their highly symmetric hexagonal firing patterns. Recently, research has shifted its focus from the global symmetry of grid cell activity to local distortions both in space and time, such as drifts in orientation, local defects of the hexagonal symmetry, and the decay and reappearance of grid patterns after changes in lighting condition. Here, we introduce a method that allows to visualize and quantify such local distortions, by assigning both a local grid score and a local orientation to each individual spike of a neuronal recording. The score is inspired by a standard measure from crystallography, which has been introduced to quantify local order in crystals. By averaging over spikes recorded within arbitrary regions or time periods, we can quantify local variations in symmetry and orientation of firing patterns in both space and time.

scholarly journals Deforming the metric of cognitive maps distorts memory

2018 ◽  
Author(s):  
Jacob L. S. Bellmund ◽  
William de Cothi ◽  
Tom A. Ruiter ◽  
Matthias Nau ◽  
Caswell Barry ◽  
...  
Keyword(s):  
Spatial Memory ◽  
Cell Model ◽  
Cell Activity ◽  
Grid Cell ◽  
Cognitive Maps ◽  
Grid Cells ◽  
Boundary Geometry ◽  
Frequency Changes ◽  
Environmental Geometry ◽  
The Impact

AbstractEnvironmental boundaries anchor cognitive maps that support memory. However, trapezoidal boundary geometry distorts the regular firing patterns of entorhinal grid cells proposedly providing a metric for cognitive maps. Here, we test the impact of trapezoidal boundary geometry on human spatial memory using immersive virtual reality. Consistent with reduced regularity of grid patterns in rodents and a grid-cell model based on the eigenvectors of the successor representation, human positional memory was degraded in a trapezoid compared to a square environment; an effect particularly pronounced in the trapezoid’s narrow part. Congruent with spatial frequency changes of eigenvector grid patterns, distance estimates between remembered positions were persistently biased; revealing distorted memory maps that explained behavior better than the objective maps. Our findings demonstrate that environmental geometry affects human spatial memory similarly to rodent grid cell activity — thus strengthening the putative link between grid cells and behavior along with their cognitive functions beyond navigation.

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 A computational model that explores the effect of environmental geometries on grid cell representations

2017 ◽  
Author(s):  
Samyukta Jayakumar ◽  
Rukhmani Narayanamurthy ◽  
Reshma Ramesh ◽  
Karthik Soman ◽  
Vignesh Muralidharan ◽  
...  
Keyword(s):  
Cell Activity ◽  
Grid Cell ◽  
Point Of View ◽  
Experimental Results ◽  
Grid Cells ◽  
Computational Point ◽  
Model Code ◽  
Wide Range ◽  
Environmental Geometry ◽  
Geometry Analysis

AbstractGrid cells are a special class of spatial cells found in the medial entorhinal cortex (MEC) characterized by their strikingly regular hexagonal firing fields. This spatially periodic firing pattern was originally considered to be invariant to the geometric properties of the environment. However, this notion was contested by examining the grid cell periodicity in environments with different polarity (Krupic et al 2015) and in connected environments (Carpenter et al 2015). Aforementioned experimental results demonstrated the dependence of grid cell activity on environmental geometry. Analysis of grid cell periodicity on practically infinite variations of environmental geometry imposes a limitation on the experimental study. Hence we analyze the grid cell periodicity from a computational point of view using a model that was successful in generating a wide range of spatial cells, including grid cells, place cells, head direction cells and border cells. We simulated the model in four types of environmental geometries such as: 1) connected environments, 2) convex shapes, 3) concave shapes and 4) regular polygons with varying number of sides. Simulation results point to a greater function for grid cells than what was believed hitherto. Grid cells in the model code not just for local position but also for more global information like the shape of the environment. The proposed model is interesting not only because it was able to capture the aforementioned experimental results but, more importantly, it was able to make many important predictions on the effect of the environmental geometry on the grid cell periodicity.

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 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.

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