2014/11/08 by Alexander Mathis, Martin Stemmler, Martin B. Stemmler +1 · 72 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Neuroscience · #Biological system #Biology #Computer science #Geometry #Grid #Grid cell #Hexagonal lattice #Hexagonal tiling #Lattice (music) #Mathematics #Memory and Neural Mechanisms #Neural dynamics and brain function #Neuroscience #Photoreceptor and optogenetics research #Physics #q-bio.NC
paper · pdf · open access · doi:10.7554/elife.05979
published in eLife 4 (eLife Sciences Publications Ltd) · 12 pages, 6 figures
arxiv created 2014/11/08 · openalex publication_date 2015/04/24 · arxiv updated 2015/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.