Complete coverage of space favors modularity of the grid system in the brain

TL;DR

This paper uses statistical physics to explain how the modular organization of grid cells in the brain optimizes spatial coverage, predicting neuron requirements based on grid variability and scale.

Contribution

It introduces a theoretical framework linking grid cell modularity, variability, and spatial coverage, providing predictions on neuron numbers needed at different grid scales.

Findings

Larger variability reduces the effective coverage range of grid modules.

A scaling relation predicts neuron count increases at smaller grid scales.

The model explains the observed co-modularity of grid cell properties.

Abstract

Grid cells in the entorhinal cortex fire when animals that are exploring a certain region of space occupy the vertices of a triangular grid that spans the environment. Different neurons feature triangular grids that differ in their properties of periodicity, orientation and ellipticity. Taken together, these grids allow the animal to maintain an internal, mental representation of physical space. Experiments show that grid cells are modular, i.e. there are groups of neurons which have grids with similar periodicity, orientation and ellipticity. We use statistical physics methods to derive a relation between variability of the properties of the grids within a module and the range of space that can be covered completely (i.e. without gaps) by the grid system with high probability. Larger variability shrinks the range of representation, providing a functional rationale for the experimentally observed co-modularity of grid cell periodicity, orientation and ellipticity. We obtain a scaling relation between the number of neurons and the period of a module, given the variability and coverage range. Specifically, we predict how many more neurons are required at smaller grid scales than at larger ones.