To be a Grid Cell: Shuffling procedures for determining “Gridness”

Grid cells in freely behaving mammals are defined by the strikingly regular periodic spatial distribution of their firing. The standard method of identification calculates the \"Gridness\" of the spatial firing pattern, with significance being defined relative to the 95th percentile of a null distribution of the Gridness values found after randomly permuting spike times relative to behaviour. We determined the false-positive rate by applying the method to simulated firing with irregular spatially inhomogeneity (i.e. randomly distributed Gaussian patches). We found surprisingly high false positive rates (potentially approaching 20%), which were strongly dependent on the type of Gridness measure used and the number of spatial fields in the synthetic data. This likely reflects the spatial homogeneity of the distributions of spikes after shuffling compared to the inhomogeneous synthetic data. However, false positive rates were reduced (generally below 8%), and less dependent on other factors, when an alternative spatial field shuffling method was used to generate the null Gridness distribution. For comparison, we analysed single unit recordings made using tetrodes implanted into rat medial entorhinal cortex for the purpose of finding grid cells. We found 24% of active neurons were classified as grid cells via spike shuffling and 22% via field shuffling. These results, and the potentially high false-positive rate when classifying cells with patchy but irregular firing as grid cells, indicate that the proportion of cells with regular grid-like firing patterns can be over-estimated by standard methods.