The Sense of Place: Grid Cells in the Brain and the Transcendental Number e

Abstract

Grid cells in the brain respond when an animal occupies a periodic lattice of "grid fields" during spatial navigation. The grid scale varies along the dorso-ventral axis of the entorhinal cortex. We propose that the grid system minimizes the number of neurons required to encode location with a given resolution. We derive several predictions that match recent experiments: (i) grid scales follow a geometric progression, (ii) the ratio between adjacent grid scales is the square root of e for idealized neurons, and robustly lies in the range 1.4-1.7 for realistic neurons, (iii) the scale ratio varies modestly within and between animals, (iv) the ratio between grid scale and individual grid field widths at that scale also lies in this range, (v) grid fields lie on a triangular lattice. The theory also predicts the optimal grids in one and three dimensions, and the total number of discrete scales.

20 pages, 5 figures

References in corpus (3)

• Accurate path integration in continuous attractor network models of grid cells
• Correlations and functional connections in a population of grid cells
• Multi-Scale Codes in the Nervous System: The Problem of Noise Correlations and the Ambiguity of Periodic Scales

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• Complete coverage of space favors modularity of the grid system in the brain
• Neural tuning and representational geometry
• A framework for philosophical biology
• Physical networks become what they learn
• On Path Integration of Grid Cells: Group Representation and Isotropic Scaling
• Disentangling Fact from Grid Cell Fiction in Trained Deep Path Integrators
• Extracting grid characteristics from spatially distributed place cell inputs using non-negative PCA
• Localization Algorithm with Circular Representation in 2D and its Similarity to Mammalian Brains
• Neural Coding as a Statistical Testing Problem