Abstract
Grid cells have attracted broad attention because of their highly symmetric hexagonal firing patterns. Recently, research has shifted its focus from the global symmetry of grid cell activity to local distortions both in space and time, such as drifts in orientation, local defects of the hexagonal symmetry, and the decay and reappearance of grid patterns after changes in lighting condition. Here, we introduce a method that allows to visualize and quantify such local distortions, by assigning both a local grid score and a local orientation to each individual spike of a neuronal recording. The score is inspired by a standard measure from crystallography, which has been introduced to quantify local order in crystals. By averaging over spikes recorded within arbitrary regions or time periods, we can quantify local variations in symmetry and orientation of firing patterns in both space and time.
Highlights
Neurons in the entorhinal cortex are often classified based on their spatial firing patterns
Grid cells are neurons in mammals whose activity depends on the location of the animal in a striking way: grid cells fire spikes at multiple locations that form a symmetric lattice of repeating hexagons
Our method is inspired by an approach used in crystallography and we show that it reliably detects distortions in grid patterns
Summary
Neurons in the entorhinal cortex are often classified based on their spatial firing patterns. To decide whether a given cell should be classified as a grid cell or a nongrid cell [3, 3,4,5], researchers need a grid score: a number that quantifies the degree of hexagonal spatial symmetry in the firing pattern of the cell. The peaks in the spatial autocorrelogram of this rate map are used to obtain measures of the grid spacing and the grid orientation. A grid score is obtained from the resulting correlation-vs-angle function at selected angles (for details, see S1 Appendix). This procedure assumes a consistent hexagonal pattern throughout the arena and results in a single grid score for the entire firing pattern
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