Grid cells of the rodent entorhinal cortex are essential for spatial navigation. Although their function is commonly believed to be either path integration or localization, the origin or purpose of their hexagonal firing fields remains disputed. Here they are proposed to arise as an optimal encoding of transitions in sequences. First, storage requirements for transitions in general episodic sequences are examined using propositional logic and graph theory. Subsequently, transitions in complete metric spaces are considered under the assumption of an ideal sampling of an input space. It is shown that memory capacity of neurons that have to encode multiple feasible spatial transitions is maximized by a hexagonal pattern. Grid cells are proposed to encode spatial transitions in spatiotemporal sequences, with the entorhinal-hippocampal loop forming a multitransition system.

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