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

2014 ◽  
Vol 369 (1635) ◽  
pp. 20130290 ◽  
Author(s):  
Benjamin W. Towse ◽  
Caswell Barry ◽  
Daniel Bush ◽  
Neil Burgess
Keyword(s):  
Spatial Scale ◽  
Spatial Scales ◽  
Grid Cell ◽  
Spatial Uncertainty ◽  
Grid System ◽  
Grid Cells ◽  
Spatial Cues ◽  
Firing Patterns ◽  
Wide Range ◽  
Spatial Noise

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.

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 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 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 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 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 co-activity patterns during sleep reflect spatial overlap of grid fields during active behaviors

2017 ◽  
Author(s):  
Sean G. Trettel ◽  
John B. Trimper ◽  
Ernie Hwaun ◽  
Ila R. Fiete ◽  
Laura Lee Colgin
Keyword(s):  
Activity Patterns ◽  
Cell Activity ◽  
Grid Cell ◽  
Network Models ◽  
Grid Cells ◽  
Tuning Curves ◽  
Sensory Inputs ◽  
Cell Network ◽  
Spatial Tuning ◽  
Cell Cell

ABSTRACTContinuous attractor network models of grid formation posit that recurrent connectivity between grid cells controls their patterns of co-activation. Grid cells from a common module exhibit stable offsets in their periodic spatial tuning curves across environments, which may reflect recurrent connectivity or correlated sensory inputs. Here we explore whether cell-cell relationships predicted by attractor models persist during sleep states in which spatially informative sensory inputs are absent. We recorded ensembles of grid cells in superficial layers of medial entorhinal cortex during active exploratory behaviors and overnight sleep. Per pair and collectively, we found preserved patterns of spike-time correlations across waking, REM, and non-REM sleep, which reflected the spatial tuning offsets between these cells during active exploration. The preservation of cell-cell relationships across states was not explained by theta oscillations or CA1 activity. These results suggest that recurrent connectivity within the grid cell network drives grid cell activity across behavioral states.

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