Grid Cell Firing Patterns Maintain their Hexagonal Firing Patterns on a Circular Track

In an open two-dimensional 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 entire space. Both modeling and experimental data suggest that such periodic spatial representations may emerge from a continuous attractor network. According to this theory, grid cell activity in any stable 1D environment is a slice through an underlying 2D hexagonal pattern, which is supported by some experimental studies but challenged by others. Grid cells are believed to play a fundamental role in path integration, and so understanding their behavior in various environments is crucial for understanding the flow of information through the entorhinal-hippocampal system. To this end, 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 do not provide sufficient data for determining the underlying spatial activity pattern. To circumvent this, we compute the population autocorrelation, which pools together population responses from all 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 spacing and orientation of the population lattice, revealing how the lattice differs across environments. Furthermore, the population autocorrelation of the linearized track reveals that at the level of the population, 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 any undersampled environment.