scholarly journals Modeling grid fields instead of modeling grid cells

2018 ◽  
Author(s):  
Sophie Rosay ◽  
Simon N. Weber ◽  
Marcello Mulas
Keyword(s):  
Cell Activity ◽  
Physical Space ◽  
Grid Cell ◽  
Macroscopic Model ◽  
Grid Cells ◽  
Colloidal Systems ◽  
Cell Network ◽  
Microscopic Models ◽  
The Relationship ◽  
The Brain

A neuron’s firing correlates are defined as the features of the external world to which its activity is correlated. In many parts of the brain, neurons have quite simple such firing correlates. A striking example are grid cells in the rodent medial entorhinal cortex: their activity correlates with the animal’s position in space, defining ‘grid fields’ arranged with a remarkable periodicity. Here, we show that the organization and evolution of grid fields relate very simply to physical space. To do so, we use an effective model and consider grid fields as point objects (particles) moving around in space under the influence of forces. We are able to reproduce most observations on the geometry of grid patterns. This particle-like behavior is particularly salient in a recent experiment where two separate grid patterns merge. We discuss pattern formation in the light of known results from physics of two-dimensional colloidal systems. Finally, we draw the relationship between our ‘macroscopic’ model for grid fields and existing ‘microscopic’ models of grid cell activity and discuss how a description at the level of grid fields allows to put constraints on the underlying grid cell network.

scholarly journals Correlation structure of grid cells is preserved during sleep

2017 ◽  
Author(s):  
Richard J. Gardner ◽  
Li Lu ◽  
Tanja Wernle ◽  
May-Britt Moser ◽  
Edvard I. Moser
Keyword(s):  
Cell Activity ◽  
Physical Space ◽  
Grid Cell ◽  
Correlation Structure ◽  
Head Direction ◽  
Grid Cells ◽  
Cell Network ◽  
Fixed Reference ◽  
Network States ◽  
Direction Tuning

AbstractThe network of grid cells in the medial entorhinal cortex forms a fixed reference frame for mapping physical space. The mechanistic origin of the grid representation is unknown, but continuous attractor network (CAN) models explain multiple fundamental features of grid-cell activity. An untested prediction of CAN grid models is that the grid-cell network should exhibit an activity correlation structure that transcends behavioural or brain states. By recording from MEC cell ensembles during navigation and sleep, we found that spatial phase offsets of grid cells predict arousal-state-independent spike rate correlations. Similarly, state-invariant correlations between conjunctive grid-head-direction and pure head-direction cells were predicted by their head-direction tuning offsets. Spike rates of grid cells were only weakly correlated across modules, and module scale relationships disintegrated during slow-save sleep, suggesting that modules function as independent attractor networks. Collectively, our observations suggest that network states in MEC are expressed universally across brain and behaviour states.

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.

scholarly journals Complete coverage of space favors modularity of the grid system in the brain

2016 ◽  
Author(s):  
A. Sanzeni ◽  
V. Balasubramanian ◽  
G. Tiana ◽  
M. Vergassola
Keyword(s):  
Statistical Physics ◽  
Physical Space ◽  
Grid Cell ◽  
Triangular Grid ◽  
Grid System ◽  
Grid Cells ◽  
Scaling Relation ◽  
Complete Coverage ◽  
Space Experiments ◽  
The Brain

Grid cells in the entorhinal cortex fire when animals that are exploring a certain region of space occupy the vertices of a triangular grid that spans the environment. Different neurons feature triangular grids that differ in their properties of periodicity, orientation and ellipticity. Taken together, these grids allow the animal to maintain an internal, mental representation of physical space. Experiments show that grid cells are modular, i.e. there are groups of neurons which have grids with similar periodicity, orientation and ellipticity. We use statistical physics methods to derive a relation between variability of the properties of the grids within a module and the range of space that can be covered completely (i.e. without gaps) by the grid system with high probability. Larger variability shrinks the range of representation, providing a functional rationale for the experimentally observed co-modularity of grid cell periodicity, orientation and ellipticity. We obtain a scaling relation between the number of neurons and the period of a module, given the variability and coverage range. Specifically, we predict how many more neurons are required at smaller grid scales than at larger ones.

scholarly journals Coding advantage of grid cell orientation under noisy conditions

2018 ◽  
Author(s):  
Dong Chen ◽  
Kai-Jia Sun ◽  
Liang Wang ◽  
Zhanjun Zhang ◽  
Ying-Cheng Lai ◽  
...  
Keyword(s):  
Spatial Information ◽  
Cell Activity ◽  
Grid Cell ◽  
Mammalian Brain ◽  
Grid Cells ◽  
Cell Orientation ◽  
Spatial Coding ◽  
Cell Network ◽  
Minimum Number ◽  
Universal Grid

Grid cells constitute a crucial component of the “GPS” in the mammalian brain. Recent experiments revealed that grid cell activity is anchored to environmental boundaries. More specifically, these results revealed a slight yet consistent offset of 8 degrees relative to boundaries of a square environment. The causes and possible functional roles of this orientation are still unclear. Here we propose that this phenomenon maximizes the spatial information conveyed by grid cells. Computer simulations of the grid cell network reveal that the universal grid orientation at 8 degrees optimizes spatial coding specifically in the presence of noise. Our model also predicts the minimum number of grid cells in each module. In addition, analytical results and a dynamical reinforcement learning model reveal the mechanism underlying the noise-induced orientation preference at 8 degrees. Together, these results suggest that the experimentally observed common orientation of grid cells serves to maximize spatial information in the presence of noise.

scholarly journals Probable nature of higher-dimensional symmetries underlying mammalian grid-cell activity patterns

eLife ◽  
2015 ◽  
Vol 4 ◽  
Author(s):  
Alexander Mathis ◽  
Martin B Stemmler ◽  
Andreas VM Herz
Keyword(s):  
Marine Mammals ◽  
Compound Eye ◽  
Activity Patterns ◽  
Cell Activity ◽  
Physical Space ◽  
Grid Cell ◽  
Three Dimensions ◽  
Face Centered Cubic ◽  
Higher Dimensional ◽  
The Brain

Lattices abound in nature—from the crystal structure of minerals to the honey-comb organization of ommatidia in the compound eye of insects. These arrangements provide solutions for optimal packings, efficient resource distribution, and cryptographic protocols. Do lattices also play a role in how the brain represents information? We focus on higher-dimensional stimulus domains, with particular emphasis on neural representations of physical space, and derive which neuronal lattice codes maximize spatial resolution. For mammals navigating on a surface, we show that the hexagonal activity patterns of grid cells are optimal. For species that move freely in three dimensions, a face-centered cubic lattice is best. This prediction could be tested experimentally in flying bats, arboreal monkeys, or marine mammals. More generally, our theory suggests that the brain encodes higher-dimensional sensory or cognitive variables with populations of grid-cell-like neurons whose activity patterns exhibit lattice structures at multiple, nested scales.

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 Intuitive planning: global navigation through cognitive maps based on grid-like codes

2018 ◽  
Author(s):  
Alon B. Baram ◽  
Timothy H. Muller ◽  
James C.R. Whittington ◽  
Timothy E.J. Behrens
Keyword(s):  
Spatial Information ◽  
Distance Measure ◽  
Grid Cell ◽  
Simple Algorithm ◽  
Place Cells ◽  
Grid Cells ◽  
Global Knowledge ◽  
The World ◽  
One Step ◽  
The Relationship

AbstractIt is proposed that a cognitive map encoding the relationships between objects supports the ability to flexibly navigate the world. Place cells and grid cells provide evidence for such a map in a spatial context. Emerging evidence suggests analogous cells code for non-spatial information. Further, it has been shown that grid cells resemble the eigenvectors of the relationship between place cells and can be learnt from local inputs. Here we show that these locally-learnt eigenvectors contain not only local information but also global knowledge that can provide both distributions over future states as well as a global distance measure encoding approximate distances between every object in the world. By simply changing the weights in the grid cell population, it is possible to switch between computing these different measures. We demonstrate a simple algorithm can use these measures to globally navigate arbitrary topologies without searching more than one step ahead. We refer to this as intuitive planning.

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