Grid cells are famous for the lattice-like layouts of their firing fields—a property has led many researchers to assume that these neurons readily convey spatial scales and metrics to downstream networks and thus contribute to spatial cognition and memory. In reality, this is not the case: grid cells commonly exhibit irregular spiking, reflecting how the firing fields were visited by the animal, rather than their abstracted spatial order. Yet, there exists a statistical mechanism, known in physics as “percolation,” that enforces grid cells’ contiguous firing and enables their functionality. As it turns out, one of the best studied mathematical models of percolation—percolation through triangular lattice—applies directly to the grid cell case. Analyses show that indeed, physiological spiking parameters are just right for phase-transitioning the grid cell network into a regime in which “percolating paths” that run through firing fields consecutively, without omissions, appear regularly. These paths are the ones that convey spatial regularity of field patters to the downstream networks. Viewing grid cell functionality from the perspective of percolation theory helps understanding principles of spatial information processing and sheds a new light on spatial learning, navigation, path integration and emergence of spatial metrics.

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