Framing the grid: effect of boundaries on grid cells and navigation

Krupic, Julija; Bauža, Marius; Burton, Stephen; O’Keefe, John

doi:10.1113/jp270607

Cited by 37 publications

(36 citation statements)

References 104 publications

(142 reference statements)

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“…Existing datasets [2,4] have a confoundanimals are tested in square and rectangular enclosures which have distinguishable orientations marked by the corners. Grid orientations can anchor to such features [29], either through the integration of visual and external cues [30,31], or through interaction with boundaries [19,[32][33][34][35][36][37]. Experiments in circular or other nonrectangular environments may help disambiguate the effects of such anchoring.…”

Section: Discussionmentioning

confidence: 99%

A geometric attractor mechanism for self-organization of entorhinal grid modules

Kang

Balasubramanian

2018

Preprint

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Grid cells in the medial entorhinal cortex (MEC) respond when an animal occupies a periodic lattice of "grid fields" in the environment. The grids are organized in modules with spatial periods, or scales, clustered around discrete values separated by ratios in the range 1.2-2.0. We propose a mechanism that produces this modular structure through dynamical self-organization in the MEC. In attractor network models of grid formation, the grid scale of a single module is set by the distance of recurrent inhibition between neurons. We show that the MEC forms a hierarchy of discrete modules if a smooth increase in inhibition distance along its dorso-ventral axis is accompanied by excitatory interactions along this axis. Moreover, constant scale ratios between successive modules arise through geometric relationships between triangular grids and have values that fall within the observed range. We discuss how interactions required by our model might be tested experimentally.

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Section: Discussionmentioning

confidence: 99%

A geometric attractor mechanism for self-organization of entorhinal grid modules

Kang

Balasubramanian

2018

Preprint

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“…For our current considerations, one important property of SR for a circular or square environment is that some of the eigenvectors (vectors that explain the most variance) have a similar spatial pattern to that of grid cells (Stachenfeld et al, 2017). These grid-like eigenvectors have also been shown to be warped in triangular environments, similar to grid cells recorded in the rodent (Krupic et al, 2016). In this way, the eigenvector (basis function) of a grid cell representation is a form of information reduction and state prediction rather than a structure isomorphic to behavior.…”

Section: Successor Representation Modelsmentioning

confidence: 85%

“…Additional evidence suggests that neural coding in the entorhinal cortex, rather than read out in a static fashion, is dynamically influenced by the environment and behavioral demands. For example, deformations (i.e., changes from the typical sixfold hexagonal symmetry) of grid cells have been observed in trapezoidal and irregular environments (Krupic, Bauza, Burton, Barry, & O'keefe, 2015;Krupic, Bauza, Burton, & O'keefe, 2018), suggesting that the medial entorhinal cortex is sensitive to the local shape of the environment (Krupic, Bauza, Burton, & O(keefe, 2016). Additionally, while many studies have investigated grid coding during free foraging tasks, a recent study found that introducing reward locations altered the structure of grid cells in medial entorhinal cortex to preferentially represent the reward location (Butler, Hardcastle, & Giocomo, 2019).…”

Section: What About Situations Involving Neural Recordings Of Grid mentioning

confidence: 99%

Grid coding, spatial representation, and navigation: Should we assume an isomorphism?

2019

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Grid cells provide a compelling example of a link between cellular activity and an abstract and difficult to define concept like space. Accordingly, a representational perspective on grid coding argues that neural grid coding underlies a fundamentally spatial metric. Recently, some theoretical proposals have suggested extending such a framework to nonspatial cognition as well, such as category learning. Here, we provide a critique of the frequently employed assumption of an isomorphism between patterns of neural activity (e.g., grid cells), mental representation, and behavior (e.g., navigation). Specifically, we question the strict isomorphism between these three levels and suggest that human spatial navigation is perhaps best characterized by a wide variety of both metric and nonmetric strategies. We offer an alternative perspective on how grid coding might relate to human spatial navigation, arguing that grid coding is part of a much larger conglomeration of neural activity patterns that dynamically tune to accomplish specific behavioral outputs.

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“… θ : Grid cells have a discrete organization into grid modules in MEC, where up to 10 grid modules, each with a single orientation, θ , are estimated to exist in the rat MEC (Stensola et al, ). Border cells (Barry et al, ; Krupic, Bauza, Burton, & O'Keefe, ; Lever, Burton, Jeewajee, O'Keefe, & Burgess, ; Solstad, Boccara, Kropff, Moser, & Moser, ) in MEC are active when the rat is at the boundary of an enclosure. Along with evidence that grid cells can show different orientations in a single environment if there are distorted boundaries (Krupic, Bauza, Burton, Barry, & O'Keefe, ), this suggests boundary cells may orient grid cells.…”

Section: Methodsmentioning

confidence: 99%

A hexagonal Fourier model of grid cells

Rodríguez-Domínguez

Caplan

2018

Hippocampus

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Grid cells in rat medial entorhinal cortex are widely thought to play a major role in spatial behavior. However, the exact computational role of the population of grid cells is not known. Here we provide a descriptive model, which nonetheless considers biologically feasible mechanisms, whereby the grid cells are viewed as a two-dimensional Fourier basis set, in hexagonal coordinates, with restricted availability of basis functions. With known properties imposed in the model parameters, we demonstrate how various empirical benchmark findings are straight-forward to understand in this model. We also explain how complex computations, inherent in a Fourier model, are feasible in the medial entorhinal cortex with simple mechanisms. We further suggest, based on model experiments, that grid cells may support a form of lossy compression of contextual information, enabling its representation in an efficient manner. In sum, this hexagonal Fourier model suggests how the entire population of grid cells may be modeled in a principled way, incorporates biologically feasible mechanisms and provides a potentially powerful interpretation of the relationship between grid-cell activity and contextual information beyond spatial knowledge. This enables various phenomena to be modeled with relatively simple mechanisms, and leads to novel and testable predictions.

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Framing the grid: effect of boundaries on grid cells and navigation

Cited by 37 publications

References 104 publications

A geometric attractor mechanism for self-organization of entorhinal grid modules

A geometric attractor mechanism for self-organization of entorhinal grid modules

Grid coding, spatial representation, and navigation: Should we assume an isomorphism?

A hexagonal Fourier model of grid cells

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