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Toroidal topology of population activity in grid cells

View ORCID ProfileRichard J. Gardner, View ORCID ProfileErik Hermansen, View ORCID ProfileMarius Pachitariu, View ORCID ProfileYoram Burak, Nils A. Baas, View ORCID ProfileBenjamin A. Dunn, View ORCID ProfileMay-Britt Moser, View ORCID ProfileEdvard I. Moser
doi: https://doi.org/10.1101/2021.02.25.432776
Richard J. Gardner
1Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology, Trondheim, Norway
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  • For correspondence: richard.gardner@ntnu.no nils.baas@ntnu.no benjamin.dunn@ntnu.no edvard.moser@ntnu.no
Erik Hermansen
2Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway
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Marius Pachitariu
3HHMI Janelia Research Campus Ashburn, VA, USA
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Yoram Burak
4Edmond and Lily Safra Center for Brain Sciences, The Hebrew University of Jerusalem, Jerusalem, Israel
5Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel
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Nils A. Baas
2Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway
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  • For correspondence: richard.gardner@ntnu.no nils.baas@ntnu.no benjamin.dunn@ntnu.no edvard.moser@ntnu.no
Benjamin A. Dunn
1Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology, Trondheim, Norway
2Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway
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  • For correspondence: richard.gardner@ntnu.no nils.baas@ntnu.no benjamin.dunn@ntnu.no edvard.moser@ntnu.no
May-Britt Moser
1Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology, Trondheim, Norway
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Edvard I. Moser
1Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology, Trondheim, Norway
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  • ORCID record for Edvard I. Moser
  • For correspondence: richard.gardner@ntnu.no nils.baas@ntnu.no benjamin.dunn@ntnu.no edvard.moser@ntnu.no
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Abstract

The medial entorhinal cortex (MEC) is part of a neural system for mapping a subject’s position within a physical environment1,2. Grid cells, a key component of this system, fire in a characteristic hexagonal pattern of locations3, and are organized in modules4,5 which collectively form a population code for the animal’s allocentric position1,6–8. The invariance of the correlation structure of this population code across environments9,10 and behavioural states11,12, independently of specific sensory inputs, has pointed to intrinsic, recurrently connected continuous attractor networks (CANs) as a possible substrate of the grid pattern1,2,13–16. However, whether grid cell networks show continuous attractor dynamics, and how they interface with inputs from the environment, has remained elusive due to the small samples of cells obtained to date. Here we show, with simultaneous recordings from many hundreds of grid cells, and subsequent topological data analysis, that the joint activity of grid cells from an individual module resides on a toroidal manifold, as expected in a two-dimensional CAN. Positions on the torus correspond to the moving animal’s position in the environment. Individual cells are preferentially active at singular positions on the torus. Their positions are maintained, with minimal distortion, between environments and from wakefulness to sleep, as predicted by CAN models for grid cells but not by alternative feed-forward models where grid patterns are created from external inputs by Hebbian plasticity17–22. This demonstration of network dynamics on a toroidal manifold provides the first population-level visualization of CAN dynamics in grid cells.

Competing Interest Statement

The authors have declared no competing interest.

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The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license.
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Toroidal topology of population activity in grid cells
Richard J. Gardner, Erik Hermansen, Marius Pachitariu, Yoram Burak, Nils A. Baas, Benjamin A. Dunn, May-Britt Moser, Edvard I. Moser
bioRxiv 2021.02.25.432776; doi: https://doi.org/10.1101/2021.02.25.432776
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Toroidal topology of population activity in grid cells
Richard J. Gardner, Erik Hermansen, Marius Pachitariu, Yoram Burak, Nils A. Baas, Benjamin A. Dunn, May-Britt Moser, Edvard I. Moser
bioRxiv 2021.02.25.432776; doi: https://doi.org/10.1101/2021.02.25.432776

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