Hexagons all the way down: grid cells as a conformal isometric map of space.
Grid cells in the entorhinal cortex are known for their hexagonal spatial activity patterns and are thought to provide a neural metric for space, and support path integration. In this study, we further investigate grid cells as a metric of space by optimising them for a conformal isometric (CI) map...
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| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2025-02-01
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| Series: | PLoS Computational Biology |
| Online Access: | https://doi.org/10.1371/journal.pcbi.1012804 |
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| author | Vemund Sigmundson Schøyen Kosio Beshkov Markus Borud Pettersen Erik Hermansen Konstantin Holzhausen Anders Malthe-Sørenssen Marianne Fyhn Mikkel Elle Lepperød |
| author_facet | Vemund Sigmundson Schøyen Kosio Beshkov Markus Borud Pettersen Erik Hermansen Konstantin Holzhausen Anders Malthe-Sørenssen Marianne Fyhn Mikkel Elle Lepperød |
| author_sort | Vemund Sigmundson Schøyen |
| collection | DOAJ |
| description | Grid cells in the entorhinal cortex are known for their hexagonal spatial activity patterns and are thought to provide a neural metric for space, and support path integration. In this study, we further investigate grid cells as a metric of space by optimising them for a conformal isometric (CI) map of space using a model based on a superposition of plane waves. By optimising the phases within a single grid cell module, we find that the module can form a CI of two-dimensional flat space with phases arranging into a regular hexagonal pattern, supporting an accurate spatial metric. Additionally, we find that experimentally recorded grid cells exhibit CI properties, with one example module showing a phase arrangement similar to the hexagonal pattern observed in our model. These findings provide computational and preliminary experimental support for grid cells as a CI-based spatial representation. We also examine other properties that emerge in CI-optimised modules, including consistent energy expenditure across space and the minimal cell count required to support unique representation of space and maximally topologically persistent toroidal population activity. Altogether, our results suggest that grid cells are well-suited to form a CI map, with several beneficial properties arising from this organisation. |
| format | Article |
| id | doaj-art-a0ad5e96e54e4b3aad0cf198e699d1e2 |
| institution | OA Journals |
| issn | 1553-734X 1553-7358 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS Computational Biology |
| spelling | doaj-art-a0ad5e96e54e4b3aad0cf198e699d1e22025-08-20T02:16:09ZengPublic Library of Science (PLoS)PLoS Computational Biology1553-734X1553-73582025-02-01212e101280410.1371/journal.pcbi.1012804Hexagons all the way down: grid cells as a conformal isometric map of space.Vemund Sigmundson SchøyenKosio BeshkovMarkus Borud PettersenErik HermansenKonstantin HolzhausenAnders Malthe-SørenssenMarianne FyhnMikkel Elle LepperødGrid cells in the entorhinal cortex are known for their hexagonal spatial activity patterns and are thought to provide a neural metric for space, and support path integration. In this study, we further investigate grid cells as a metric of space by optimising them for a conformal isometric (CI) map of space using a model based on a superposition of plane waves. By optimising the phases within a single grid cell module, we find that the module can form a CI of two-dimensional flat space with phases arranging into a regular hexagonal pattern, supporting an accurate spatial metric. Additionally, we find that experimentally recorded grid cells exhibit CI properties, with one example module showing a phase arrangement similar to the hexagonal pattern observed in our model. These findings provide computational and preliminary experimental support for grid cells as a CI-based spatial representation. We also examine other properties that emerge in CI-optimised modules, including consistent energy expenditure across space and the minimal cell count required to support unique representation of space and maximally topologically persistent toroidal population activity. Altogether, our results suggest that grid cells are well-suited to form a CI map, with several beneficial properties arising from this organisation.https://doi.org/10.1371/journal.pcbi.1012804 |
| spellingShingle | Vemund Sigmundson Schøyen Kosio Beshkov Markus Borud Pettersen Erik Hermansen Konstantin Holzhausen Anders Malthe-Sørenssen Marianne Fyhn Mikkel Elle Lepperød Hexagons all the way down: grid cells as a conformal isometric map of space. PLoS Computational Biology |
| title | Hexagons all the way down: grid cells as a conformal isometric map of space. |
| title_full | Hexagons all the way down: grid cells as a conformal isometric map of space. |
| title_fullStr | Hexagons all the way down: grid cells as a conformal isometric map of space. |
| title_full_unstemmed | Hexagons all the way down: grid cells as a conformal isometric map of space. |
| title_short | Hexagons all the way down: grid cells as a conformal isometric map of space. |
| title_sort | hexagons all the way down grid cells as a conformal isometric map of space |
| url | https://doi.org/10.1371/journal.pcbi.1012804 |
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