A principle of economy predicts the functional architecture of grid cells

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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: (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^1/2 for idealized neurons, and lie between 1.4-1.7 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.

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Xue-xin Wei

Department of Psychology, University of Pennsylvania, Philadelphia, United States

Competing interests
The authors declare that no competing interests exist.
Jason Prentice

Princeton Neuroscience Institute, Princeton University, Princeton, United States

Competing interests
The authors declare that no competing interests exist.
Vijay Balasubramanian

Department of Physics, University of Pennsylvania, Philadelphia, United States

For correspondence
vijay@physics.upenn.edu

Competing interests
The authors declare that no competing interests exist.

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