Head Direction Cells and Grid Cells as the Core Components of the Core-periphery Structure

Head direction cells and grid cells are neuron types defined by their regular firing patterns in standard experimental arenas. As technology advances, we can record extensive neuronal firing activity over time using electrophysiological or calcium imaging methods. The covariance matrix is a critical measure of this neural populations discharge activity. We developed a method to identify a core-periphery structure in the covariance matrix, highlighting the central role of grid cells and head direction cells in firing correlations. This method effectively redefines these cell types in terms of firing activity correlations, with core nodes exhibiting a higher mutual information rate for spatial variables. Additionally, we developed a periodic spring network algorithm, which uses the covariance matrix alone to estimate the spatial phases of both head direction cells and grid cells due to their periodic properties. This approach offers a new perspective on utilizing the covariance matrix of the neural population to better understand and identify these specialized cell types, even when traditional firing pattern-based definitions are challenging to apply.