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

  1. Alexander Mathis  Is a corresponding author
  2. Martin B Stemmler
  3. Andreas V M Herz
  1. Harvard University, United States
  2. Ludwig-Maximilians-Universität München, Germany

Abstract

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 a 3D 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.

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Author details

  1. Alexander Mathis

    Department of Molecular and Cellular Biology, Harvard University, Cambridge, United States
    For correspondence
    amathis@fas.harvard.edu
    Competing interests
    The authors declare that no competing interests exist.
  2. Martin B Stemmler

    Bernstein Center for Computational Neuroscience, Ludwig-Maximilians-Universität München, München, Germany
    Competing interests
    The authors declare that no competing interests exist.
  3. Andreas V M Herz

    Bernstein Center for Computational Neuroscience Munich, Ludwig-Maximilians-Universität München, München, Germany
    Competing interests
    The authors declare that no competing interests exist.

Copyright

© 2015, Mathis et al.

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.

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  1. Alexander Mathis
  2. Martin B Stemmler
  3. Andreas V M Herz
(2015)
Probable nature of higher-dimensional symmetries underlying mammalian grid-cell activity patterns
eLife 4:e05979.
https://doi.org/10.7554/eLife.05979

Share this article

https://doi.org/10.7554/eLife.05979

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