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 Environmental deformations dynamically shift the grid cell spatial metric

2017 ◽  
Author(s):  
Alexandra T Keinath ◽  
Russell A Epstein ◽  
Vijay Balasubramanian
Keyword(s):  
Computational Model ◽  
Direct Evidence ◽  
Grid Cell ◽  
Place Cells ◽  
Grid Cells ◽  
Border Cell ◽  
Spatial Phase ◽  
Specific Experience ◽  
Place Fields ◽  
Local Distortions

AbstractEnvironmental deformations induce stereotyped distortions in the time-averaged activity of grid and place cells. We hypothesized that these effects are partly driven by border cell inputs which reset the spatial phase of grid cells, maintaining learned relationships between grid phase and environmental boundaries without altering inherent grid scale. A computational model of this mechanism reproduced diverse distortions during deformations, including scale-dependent and local distortions of grid fields, and stretched, duplicated, and fractured place fields. This model predicted a striking new effect: dynamic, history-dependent, boundary-tethered ‘shifts’ in grid phase during deformations. We reanalyzed two rodent grid cell rescaling datasets and found direct evidence of these shifts, which have not been previously reported and contribute to the appearance of rescaling. These results demonstrate that the grid representation of geometrically deformed environments is not fixed, but rather dynamically changes with the specific experience of the navigator.

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 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 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 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 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 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 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.

scholarly journals Description and Analysis of a 20-Year (1960-79) Digital Ice-Concentration Database for the Great Lakes of North America

1983 ◽  
Vol 4 ◽  
pp. 14-18 ◽  
Author(s):  
Raymond A. Assel
Keyword(s):  
North America ◽  
Great Lakes ◽  
Surface Area ◽  
Information Service ◽  
Grid Cell ◽  
Ice Cover ◽  
Unit Surface Area ◽  
Grid Cells ◽  
Data Set ◽  
Ice Concentration

A digital ice-concentration database spanning 20 years (1960 to 1979) was established for the Great Lakes of North America. Data on ice concentration, i.e. the percentage of a unit surface area of the lake that is ice-covered, were abstracted from over 2 800 historic ice charts produced by United States and Canadian government agencies. The database consists of ice concentrations ranging from zero to 100% in 10% increments for individual grid cells of size 5 × 5 km constituting the surface area of each Great Lake. The data set for each of the Great Lakes was divided into half-month periods for statistical analysis. Maxinium, minimum, median, mode, and average ice-concentrations statistics were calculated for each grid cell and half-month period. A lakewide average value was then calculated for each of the half-month ice-concentration statistics for all grid cells for a given lake. Ice-cover variability and the normal extent and progression of the ice cover is discussed within the context of the lakewide averaged value of the minimum and maximum ice concentrations and the lakewide averaged value of the median ice concentrations, respectively. Differences in ice-cover variability among the five Great Lakes are related to mean lake depth and accumulated freezing degree-days. A Great Lakes ice atlas presenting a series of ice charts which depict the maximum, minimum, and median icecover concentrations for each of the Great Lakes for nine half-monthly periods, starting the last half of December and continuing through the last half of April will be published in 1983 by the National Oceanic and Atmospheric Administration (NOAA). The database will be archived at the National Snow and Ice Data Center of the National Environmental Satellite Data and Information Service (NESDIS) in Boulder, Colorado, USA, also in 1983.

scholarly journals A new discrete multiplicative random cascade model for downscaling intermittent rainfall fields

2019 ◽  
Author(s):  
Marc Schleiss
Keyword(s):  
Classical Method ◽  
Mathematical Problem ◽  
Grid Cell ◽  
Cascade Model ◽  
Small Scale ◽  
Grid Cells ◽  
Cascade Generator ◽  
Cascade Models ◽  
First Results ◽  
Original Amount

Abstract. Spatial downscaling of rainfall fields is a challenging mathematical problem for which many different types of methods have been proposed. One popular solution consists in redistributing rainfall amounts over smaller and smaller scales by means of a discrete multiplicative random cascade (DMRC). This works well for slowly varying, homogeneous rainfall fields but often fails in the presence of intermittency (i.e., large amounts of zero rainfall values). The most common workaround in this case is to use two separate cascade models, one for the occurrence and another for the intensity. In this paper, a new and simpler approach based on the notion of equal-volume areas (EVAs) is proposed. Unlike classical cascades where rainfall amounts are redistributed over grid cells of equal size, the EVA cascade splits grid cells into areas of different sizes, each of them containing exactly half of the original amount of water. The relative areas of the sub-grid cells are determined by drawing random values from a logit-normal cascade generator model with scale and intensity dependent standard deviation. The process ends when the amount of water in each sub-grid cell is smaller than a fixed bucket capacity, at which point the output of the cascade can be re-sampled over a regular Cartesian mesh. The present paper describes the implementation of the EVA cascade model and gives some first results for 100 selected events in the Netherlands. Performance is assessed by comparing the outputs of the EVA model to bilinear interpolation and to a classical DMRC model based on fixed grid cell sizes. Results show that on average, the EVA cascade outperforms the classical method, producing fields with more realistic distributions, small-scale extremes and spatial structures. Improvements are mostly credited to the higher robustness of the EVA model to the presence of intermittency and to the lower variance of its generator. However, improvements are not systematic and both approaches have their advantages and weaknesses. For example, while the classical cascade tends to overestimate small-scale extremes and variability, the EVA model tends to produce fields that are slightly too smooth and blocky compared with observations.

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