title: An isomorphic mapping hypothesis of the grid representation.
abstract: We introduce a grid cell microcircuit hypothesis. We propose the 'grid in the world' (evident in grid cell discharges) is generated by a 'grid in the cortex'. This cortical grid is formed by patches of calbindin-positive pyramidal neurons in layer 2 of medial entorhinal cortex (MEC). Our isomorphic mapping hypothesis assumes three types of isomorphism: (i) metric correspondence of neural space (the two-dimensional cortical sheet) and the external two-dimensional space within patches; (ii) isomorphism between cellular connectivity matrix and firing field; (iii) isomorphism between single cell and population activity. Each patch is a grid cell lattice arranged in a two-dimensional map of space with a neural : external scale of approximately 1 : 2000 in the dorsal part of rat MEC. The lattice behaves like an excitable medium with neighbouring grid cells exciting each other. Spatial scale is implemented as an intrinsic scaling factor for neural propagation speed. This factor varies along the dorsoventral cortical axis. A connectivity scheme of the grid system is described. Head direction input specifies the direction of activity propagation. We extend the theory to neurons between grid patches and predict a rare discharge pattern (inverted grid cells) and the relative location and proportion of grid cells and spatial band cells.
authors.affiliation: Bernstein Center for Computational Neuroscience, Humboldt University of Berlin, , Philippstrasse 13 Haus 6, 10115 Berlin, Germany.
authors.forename: Michael
authors.initials: M
authors.lastname: Brecht
authors.forename: Saikat
authors.initials: S
authors.lastname: Ray
authors.forename: Andrea
authors.initials: A
authors.lastname: Burgalossi
authors.forename: Qiusong
authors.initials: Q
authors.lastname: Tang
authors.forename: Helene
authors.initials: H
authors.lastname: Schmidt
authors.forename: Robert
authors.initials: R
authors.lastname: Naumann
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D064026:Calbindins / Q000502:physiology; D003198:Computer Simulation; D018728:Entorhinal Cortex / Q000033:anatomy & histology* / Q000166:cytology / Q000502:physiology; D008959:Models, Neurological; D009415:Nerve Net / Q000033:anatomy & histology* / Q000166:cytology / Q000502:physiology; D017966:Pyramidal Cells / Q000166:cytology / Q000502:physiology*; D051381:Rats; D013028:Space Perception / Q000502:physiology*
chemical_list: D064026:Calbindins
keywords: attractor model; border cell; grid cell; interference model; spatial representation