Grid Cell Percolation*

Grid cells are famous for their ability to fire near vertexes of a planar triangular lattice tiling the navigated environment, which is commonly viewed as an instrument for encoding the animal's ongoing location and constructing neuronal spatial metrics. However, direct simulations demonstrate that most grid cells' spiking is highly intermittent and hence does not convey orderliness of underlying grid field layouts to the downstream networks. Yet we argue that regular grid cell activity exists and is based on percolation phenomena. Indeed, viewing a grid cell's firing as "opening" of the corresponding grid-field vertex and a consecutive spiking over two neighboring fields as an "opening" of the lattice edge casts grid cell activity into percolation theory framework. Unlike many standard models of lattice percolation, grid cell percolation depends on multiple parameters, e.g., the animal's speed, neuronal firing rates, receptive field sizes, etc. Surprisingly, all these parameters appear to be tuned to permit percolation, which points at biological viability of the approach and suggests that the grid cell network may in fact operate in a percolative phase. The percolation perspective casts a new light on the role of grid cells in organizing spatial cognition and helps understanding several neurophysiological mechanisms of spatial information processing, such as path integration, spatial planning and establishing global spatial scales.