Grid cell populations maintain their hexagonal firing patterns on a circular track

In an open 2D environment, grid cells in the medial entorhinal cortex are known to be active in multiple locations, displaying a striking periodic hexagonal firing pattern covering the space. According to attractor network theory, grid cell activity in any stable 1D environment is a slice through an underlying 2D hexagonal pattern, but this underlying pattern has not been observed in some experimental studies on a circular track. Grid cells are believed to play a fundamental role in path integration, and understanding their behavior in various environments is crucial for understanding the flow of information through the entorhinal-hippocampal system. We analyzed the activity of grid cells when rats traversed a circular track. A previous study involving this data set analyzed individual grid cell activity patterns separately, but we found that individual grid cells provide insufficient data for determining the underlying spatial activity pattern. To circumvent this, we compute the population autocorrelation, which pools together population responses from grid cells within the same module. This novel approach recovers the underlying six-peak hexagonal pattern that was not observable in the individual autocorrelations. We also use the population autocorrelation to infer the population lattice properties, revealing how the lattice differs across environments. Furthermore, the population autocorrelation of the linearized track reveals that at the population level, grid cells have an allocentric code for space. These results are strong support for the attractor network theory for grid cells, and our novel approach can be used to analyze grid cell activity in undersampled environments.