TY - JOUR TI - Probable nature of higher-dimensional symmetries underlying mammalian grid-cell activity patterns AU - Mathis, Alexander AU - Stemmler, Martin B AU - Herz, Andreas VM A2 - Goldman, Mark S VL - 4 PY - 2015 DA - 2015/04/24 SP - e05979 C1 - eLife 2015;4:e05979 DO - 10.7554/eLife.05979 UR - https://doi.org/10.7554/eLife.05979 AB - 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. KW - bat KW - spatial representation KW - grid cell KW - hippocampus KW - face-centered cubic lattice KW - nested grid code JF - eLife SN - 2050-084X PB - eLife Sciences Publications, Ltd ER -