scholarly journals Optimal Population Codes for Space: Grid Cells Outperform Place Cells

2012 ◽  
Vol 24 (9) ◽  
pp. 2280-2317 ◽  
Author(s):  
Alexander Mathis ◽  
Andreas V. M. Herz ◽  
Martin Stemmler
Keyword(s):  
Spatial Resolution ◽  
A Priori ◽  
Hexagonal Lattice ◽  
Grid Cell ◽  
Likelihood Estimation ◽  
Spatial Location ◽  
Neuronal Population ◽  
Place Cells ◽  
Grid Cells ◽  
Tuning Curves

Rodents use two distinct neuronal coordinate systems to estimate their position: place fields in the hippocampus and grid fields in the entorhinal cortex. Whereas place cells spike at only one particular spatial location, grid cells fire at multiple sites that correspond to the points of an imaginary hexagonal lattice. We study how to best construct place and grid codes, taking the probabilistic nature of neural spiking into account. Which spatial encoding properties of individual neurons confer the highest resolution when decoding the animal's position from the neuronal population response? A priori, estimating a spatial position from a grid code could be ambiguous, as regular periodic lattices possess translational symmetry. The solution to this problem requires lattices for grid cells with different spacings; the spatial resolution crucially depends on choosing the right ratios of these spacings across the population. We compute the expected error in estimating the position in both the asymptotic limit, using Fisher information, and for low spike counts, using maximum likelihood estimation. Achieving high spatial resolution and covering a large range of space in a grid code leads to a trade-off: the best grid code for spatial resolution is built of nested modules with different spatial periods, one inside the other, whereas maximizing the spatial range requires distinct spatial periods that are pairwisely incommensurate. Optimizing the spatial resolution predicts two grid cell properties that have been experimentally observed. First, short lattice spacings should outnumber long lattice spacings. Second, the grid code should be self-similar across different lattice spacings, so that the grid field always covers a fixed fraction of the lattice period. If these conditions are satisfied and the spatial “tuning curves” for each neuron span the same range of firing rates, then the resolution of the grid code easily exceeds that of the best possible place code with the same number of neurons.

scholarly journals Extracting grid cell characteristics from place cell inputs using non-negative principal component analysis

eLife ◽  
2016 ◽  
Vol 5 ◽  
Author(s):  
Yedidyah Dordek ◽  
Daniel Soudry ◽  
Ron Meir ◽  
Dori Derdikman
Keyword(s):  
Neural Network ◽  
Principal Component Analysis ◽  
Hexagonal Lattice ◽  
Grid Cell ◽  
Principal Component ◽  
Component Analysis ◽  
Place Cell ◽  
Place Cells ◽  
Grid Cells ◽  
Spacing Ratio

Many recent models study the downstream projection from grid cells to place cells, while recent data have pointed out the importance of the feedback projection. We thus asked how grid cells are affected by the nature of the input from the place cells. We propose a single-layer neural network with feedforward weights connecting place-like input cells to grid cell outputs. Place-to-grid weights are learned via a generalized Hebbian rule. The architecture of this network highly resembles neural networks used to perform Principal Component Analysis (PCA). Both numerical results and analytic considerations indicate that if the components of the feedforward neural network are non-negative, the output converges to a hexagonal lattice. Without the non-negativity constraint, the output converges to a square lattice. Consistent with experiments, grid spacing ratio between the first two consecutive modules is −1.4. Our results express a possible linkage between place cell to grid cell interactions and PCA.

scholarly journals Path integration in place cells of developing rats

2018 ◽  
Vol 115 (7) ◽  
pp. E1637-E1646 ◽  
Author(s):  
Tale L. Bjerknes ◽  
Nenitha C. Dagslott ◽  
Edvard I. Moser ◽  
May-Britt Moser
Keyword(s):  
Path Integration ◽  
Grid Cell ◽  
Cell System ◽  
Place Cells ◽  
Postnatal Life ◽  
Motion Information ◽  
Grid Cells ◽  
Adult Rats ◽  
Self Motion ◽  
Made In

Place cells in the hippocampus and grid cells in the medial entorhinal cortex rely on self-motion information and path integration for spatially confined firing. Place cells can be observed in young rats as soon as they leave their nest at around 2.5 wk of postnatal life. In contrast, the regularly spaced firing of grid cells develops only after weaning, during the fourth week. In the present study, we sought to determine whether place cells are able to integrate self-motion information before maturation of the grid-cell system. Place cells were recorded on a 200-cm linear track while preweaning, postweaning, and adult rats ran on successive trials from a start wall to a box at the end of a linear track. The position of the start wall was altered in the middle of the trial sequence. When recordings were made in complete darkness, place cells maintained fields at a fixed distance from the start wall regardless of the age of the animal. When lights were on, place fields were determined primarily by external landmarks, except at the very beginning of the track. This shift was observed in both young and adult animals. The results suggest that preweaning rats are able to calculate distances based on information from self-motion before the grid-cell system has matured to its full extent.

Grid Cells Lose Coherence in Realistic Environments

2021 ◽  
Author(s):  
Yifan Luo ◽  
Matteo Toso ◽  
Bailu Si ◽  
Federico Stella ◽  
Alessandro Treves
Keyword(s):  
Short Range ◽  
Short Range Order ◽  
Grid Cell ◽  
Place Cells ◽  
Grid Cells ◽  
Lateral Connectivity ◽  
Cell Pattern ◽  
In The Wild ◽  
Freely Moving ◽  
Adaptation Model

Spatial cognition in naturalistic environments, for freely moving animals, may pose quite different constraints from that studied in artificial laboratory settings. Hippocampal place cells indeed look quite different, but almost nothing is known about entorhinal cortex grid cells, in the wild. Simulating our self-organizing adaptation model of grid cell pattern formation, we consider a virtual rat randomly exploring a virtual burrow, with feedforward connectivity from place to grid units and recurrent connectivity between grid units. The virtual burrow was based on those observed by John B. Calhoun, including several chambers and tunnels. Our results indicate that lateral connectivity between grid units may enhance their “gridness” within a limited strength range, but the overall effect of the irregular geometry is to disable long-range and obstruct short-range order. What appears as a smooth continuous attractor in a flat box, kept rigid by recurrent connections, turns into an incoherent motley of unit clusters, flexible or outright unstable.

scholarly journals Can grid cell ensembles represent multiple spaces?

2019 ◽  
Author(s):  
Davide Spalla ◽  
Alexis Dubreuil ◽  
Sophie Rosay ◽  
Remi Monasson ◽  
Alessandro Treves
Keyword(s):  
Storage Capacity ◽  
Grid Cell ◽  
Place Cells ◽  
Dimensional Manifold ◽  
Grid Cells ◽  
Rodent Brain ◽  
Low Dimensional ◽  
Universal Grid ◽  
Low Dimensional Manifold ◽  
Spatial Maps

The way grid cells represent space in the rodent brain has been a striking discovery, with theoret-ical implications still unclear. Differently from hippocampal place cells, which are known to encode multiple, environment-dependent spatial maps, grid cells have been widely believed to encode space through a single low dimensional manifold, in which coactivity relations between different neurons are preserved when the environment is changed. Does it have to be so? Here, we compute - using two alternative mathematical models - the storage capacity of a population of grid-like units, em-bedded in a continuous attractor neural network, for multiple spatial maps. We show that distinct representations of multiple environments can coexist, as existing models for grid cells have the po-tential to express several sets of hexagonal grid patterns, challenging the view of a universal grid map. This suggests that a population of grid cells can encode multiple non-congruent metric rela-tionships, a feature that could in principle allow a grid-like code to represent environments with a variety of different geometries and possibly conceptual and cognitive spaces, which may be expected to entail such context-dependent metric relationships.

scholarly journals A Brain-Inspired Adaptive Space Representation Model Based on Grid Cells and Place Cells

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Kun Han ◽  
Dewei Wu ◽  
Lei Lai
Keyword(s):  
Intelligent Agents ◽  
Autonomous Navigation ◽  
Spatial Representation ◽  
Information Source ◽  
Grid Cell ◽  
Place Cells ◽  
Space Representation ◽  
Generation Model ◽  
Grid Cells ◽  
Representation Model

Grid cells and place cells are important neurons in the animal brain. The information transmission between them provides the basis for the spatial representation and navigation of animals and also provides reference for the research on the autonomous navigation mechanism of intelligent agents. Grid cells are important information source of place cells. The supervised learning and unsupervised learning models can be used to simulate the generation of place cells from grid cell inputs. However, the existing models preset the firing characteristics of grid cell. In this paper, we propose a united generation model of grid cells and place cells. First, the visual place cells with nonuniform distribution generate the visual grid cells with regional firing field through feedforward network. Second, the visual grid cells and the self-motion information generate the united grid cells whose firing fields extend to the whole space through genetic algorithm. Finally, the visual place cells and the united grid cells generate the united place cells with uniform distribution through supervised fuzzy adaptive resonance theory (ART) network. Simulation results show that this model has stronger environmental adaptability and can provide reference for the research on spatial representation model and brain-inspired navigation mechanism of intelligent agents under the condition of nonuniform environmental information.

scholarly journals A theory of joint attractor dynamics in the hippocampus and the entorhinal cortex accounts for artificial remapping and grid cell field-to-field variability

eLife ◽  
2020 ◽  
Vol 9 ◽  
Author(s):  
Haggai Agmon ◽  
Yoram Burak
Keyword(s):  
Entorhinal Cortex ◽  
Activity Patterns ◽  
Grid Cell ◽  
Mechanistic Explanation ◽  
Place Cells ◽  
Mammalian Brain ◽  
Dimensional Manifold ◽  
Grid Cells ◽  
Attractor Dynamics ◽  
Low Dimensional

The representation of position in the mammalian brain is distributed across multiple neural populations. Grid cell modules in the medial entorhinal cortex (MEC) express activity patterns that span a low-dimensional manifold which remains stable across different environments. In contrast, the activity patterns of hippocampal place cells span distinct low-dimensional manifolds in different environments. It is unknown how these multiple representations of position are coordinated. Here, we develop a theory of joint attractor dynamics in the hippocampus and the MEC. We show that the system exhibits a coordinated, joint representation of position across multiple environments, consistent with global remapping in place cells and grid cells. In addition, our model accounts for recent experimental observations that lack a mechanistic explanation: variability in the firing rate of single grid cells across firing fields, and artificial remapping of place cells under depolarization, but not under hyperpolarization, of layer II stellate cells of the MEC.

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.

Learning Maps to Navigate Space

2021 ◽  
pp. 572-617
Author(s):  
Stephen Grossberg
Keyword(s):  
Entorhinal Cortex ◽  
Spatial Scales ◽  
Grid Cell ◽  
Gamma Oscillations ◽  
Place Cells ◽  
Self Organizing Map ◽  
Grid Cells ◽  
Map Learning ◽  
Neurophysiological Data ◽  
Self Organizing

This chapter explains how humans and other animals learn to learn to navigate in space. Both reaching and route-based navigation use difference vector computations. Route navigation learns a labeled graph of angles and distances moved. Spatial navigation requires neurons to learn navigable spaces that can be many meters in size. This is again accomplished by a spectrum of cells. Such spectral spacing supports learning of medial entorhinal grid cells and hippocampal place cells. The model responds to realistic rat navigational trajectories by learning grid cells with hexagonal grid firing fields of multiple spatial scales, and place cells with one or more firing fields, that match neurophysiological data about their development in juvenile rats. Both grid and place cells develop in a hierarchy of self-organizing maps by detecting, learning and remembering the most frequent and energetic co-occurrences of their inputs. Model parsimonious properties include: similar ring attractor mechanisms process linear and angular path integration inputs that drive map learning; the same self-organizing map mechanisms can learn both grid cell and place cell receptive fields; and the learning of the dorsoventral organization of multiple grid cell modules through medial entorhinal cortex to hippocampus uses a gradient of rates that is homologous to a rate gradient that drives adaptively timed learning at multiple rates through lateral entorhinal cortex to hippocampus (‘neural relativity’). The model clarifies how top-down hippocampal-to-entorhinal ART attentional mechanisms stabilize map learning, simulates how hippocampal, septal, or acetylcholine inactivation disrupts grid cells, and explains data about theta, beta and gamma oscillations.

scholarly journals Can Grid Cell Ensembles Represent Multiple Spaces?

2019 ◽  
Vol 31 (12) ◽  
pp. 2324-2347 ◽  
Author(s):  
Davide Spalla ◽  
Alexis Dubreuil ◽  
Sophie Rosay ◽  
Remi Monasson ◽  
Alessandro Treves
Keyword(s):  
Storage Capacity ◽  
Grid Cell ◽  
Place Cells ◽  
Dimensional Manifold ◽  
Grid Cells ◽  
Rodent Brain ◽  
Low Dimensional ◽  
Universal Grid ◽  
Low Dimensional Manifold ◽  
Spatial Maps

The way grid cells represent space in the rodent brain has been a striking discovery, with theoretical implications still unclear. Unlike hippocampal place cells, which are known to encode multiple, environment-dependent spatial maps, grid cells have been widely believed to encode space through a single low-dimensional manifold, in which coactivity relations between different neurons are preserved when the environment is changed. Does it have to be so? Here, we compute, using two alternative mathematical models, the storage capacity of a population of grid-like units, embedded in a continuous attractor neural network, for multiple spatial maps. We show that distinct representations of multiple environments can coexist, as existing models for grid cells have the potential to express several sets of hexagonal grid patterns, challenging the view of a universal grid map. This suggests that a population of grid cells can encode multiple noncongruent metric relationships, a feature that could in principle allow a grid-like code to represent environments with a variety of different geometries and possibly conceptual and cognitive spaces, which may be expected to entail such context-dependent metric relationships.

scholarly journals Hebbian Analysis of the Transformation of Medial Entorhinal Grid-Cell Inputs to Hippocampal Place Fields

2010 ◽  
Vol 103 (6) ◽  
pp. 3167-3183 ◽  
Author(s):  
Francesco Savelli ◽  
James J. Knierim
Keyword(s):  
Feedback Inhibition ◽  
Grid Cell ◽  
Nonlinear Process ◽  
Place Cells ◽  
Spike Timing ◽  
Perforant Path ◽  
Grid Cells ◽  
Novel Environment ◽  
Hebbian Plasticity ◽  
Place Fields

The discovery of grid cells in the medial entorhinal cortex (MEC) permits the characterization of hippocampal computation in much greater detail than previously possible. The present study addresses how an integrate-and-fire unit driven by grid-cell spike trains may transform the multipeaked, spatial firing pattern of grid cells into the single-peaked activity that is typical of hippocampal place cells. Previous studies have shown that in the absence of network interactions, this transformation can succeed only if the place cell receives inputs from grids with overlapping vertices at the location of the place cell's firing field. In our simulations, the selection of these inputs was accomplished by fast Hebbian plasticity alone. The resulting nonlinear process was acutely sensitive to small input variations. Simulations differing only in the exact spike timing of grid cells produced different field locations for the same place cells. Place fields became concentrated in areas that correlated with the initial trajectory of the animal; the introduction of feedback inhibitory cells reduced this bias. These results suggest distinct roles for plasticity of the perforant path synapses and for competition via feedback inhibition in the formation of place fields in a novel environment. Furthermore, they imply that variability in MEC spiking patterns or in the rat's trajectory is sufficient for generating a distinct population code in a novel environment and suggest that recalling this code in a familiar environment involves additional inputs and/or a different mode of operation of the network.

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