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

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Cite this article as: eLife 2015;4:e05979 doi: 10.7554/eLife.05979

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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

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.
Martin B Stemmler

Bernstein Center for Computational Neuroscience, Ludwig-Maximilians-Universität München, München, Germany

Competing interests
The authors declare that no competing interests exist.
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.

Reviewing Editor

Mark S. Goldman, University of California at Davis, United States

Publication history

Received: December 9, 2014
Accepted: April 23, 2015
Accepted Manuscript published: April 24, 2015 (version 1)
Version of Record published: June 4, 2015 (version 2)

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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.