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

Mathis, Alexander; Stemmler, Martin B. and Herz, Andreas V. M. (2015): Probable nature of higher-dimensional symmetries underlying mammalian grid-cell activity patterns. In: eLife, Vol. 4, e05979

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.

• Item Type: Journal article
• Faculties: Biology > Department Biology II > Neurobiology
• Subjects: 500 Science > 570 Life sciences; biology
• ISSN: 2050-084X
• Language: English