A principle of economy predicts the functional architecture of grid cells

Xue-Xin Wei,Jason Prentice,Vijay Balasubramanian

doi:10.7554/elife.08362

Abstract

Grid cells in the brain respond when an animal occupies a periodic lattice of 'grid fields' during navigation. Grids are organized in modules with different periodicity. We propose that the grid system implements a hierarchical code for space that economizes the number of neurons required to encode location with a given resolution across a range equal to the largest period. This theory predicts that (i) grid fields should lie on a triangular lattice, (ii) grid scales should follow a geometric progression, (iii) the ratio between adjacent grid scales should be √e for idealized neurons, and lie between 1.4 and 1.7 for realistic neurons, (iv) the scale ratio should vary modestly within and between animals. These results explain the measured grid structure in rodents. We also predict optimal organization in one and three dimensions, the number of modules, and, with added assumptions, the ratio between grid periods and field widths.

Highlights

How does the brain represent space? Tolman (1948) suggested that the brain must have an explicit neural representation of physical space, a cognitive map, that supports higher brain functions such as navigation and path planning
Place cells have spatially localized firing fields which reorganize dramatically when the environment changes (Leutgeb et al, 2005). Another potential locus for the cognitive map of space has been uncovered in the main input to hippocampus, a structure known as the medial entorhinal cortex (MEC) (Figure 1, Fyhn et al, 2004; Hafting et al, 2005)
How does the grid system represent spatial location and what function does the modular variation in grid scale serve? Here, we propose that the grid system provides a hierarchical representation of space where fine grids provide precise location and coarse grids resolve ambiguity, and that the grids are organized to minimize the number of neurons required to achieve the behaviorally necessary spatial resolution across a spatial range equal in size to the period of the largest grid module

Summary

Introduction

How does the brain represent space? Tolman (1948) suggested that the brain must have an explicit neural representation of physical space, a cognitive map, that supports higher brain functions such as navigation and path planning. The discovery of place cells in the rat hippocampus (O’Keefe, 1976; O’Keefe and Nadel, 1978) suggested one potential locus for this map. Place cells have spatially localized firing fields which reorganize dramatically when the environment changes (Leutgeb et al, 2005). Another potential locus for the cognitive map of space has been uncovered in the main input to hippocampus, a structure known as the medial entorhinal cortex (MEC) (Figure 1, Fyhn et al, 2004; Hafting et al, 2005). When rats freely explore a two-dimensional open environment, individual ‘grid cells’ in the MEC display spatial firing fields that form a periodic triangular grid which tiles space (Figure 1A). It was shown that grid cells are organized in discrete modules within which cells share the same orientation and periodicity but vary randomly in phase (Barry et al, 2007; Stensola et al, 2012)

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