title: Probable nature of higher-dimensional symmetries underlying mammalian grid-cell activity patterns.
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 three dimensions, 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.
authors.affiliation: Department of Molecular and Cellular Biology, Harvard University, Cambridge, United States.
authors.forename: Alexander
authors.identifier: http://orcid.org/0000-0002-3777-2202
authors.initials: A
authors.lastname: Mathis
authors.affiliation: Bernstein Center for Computational Neuroscience, , , Germany.
authors.forename: Martin B
authors.initials: MB
authors.lastname: Stemmler
authors.affiliation: Bernstein Center for Computational Neuroscience, , , Germany.
authors.forename: Andreas Vm
authors.initials: AV
authors.lastname: Herz
mesh_terms: D000220:Adaptation, Biological / Q000502:physiology*; D000818:Animals; D001931:Brain Mapping / Q000379:methods; D008322:Mammals / Q000523:psychology*; D008959:Models, Neurological; D013028:Space Perception / Q000502:physiology*; D065854:Spatial Navigation / Q000502:physiology*; D013045:Species Specificity
keywords: bat; computational biology; face-centered cubic lattice; grid cell; hippocampus; human; mouse; nested grid code; neuroscience; rat; spatial representation; systems biology