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Spatial periodicity in grid cell firing has been interpreted as a neural metric for space providing animals with a coordinate system in navigating physical and mental spaces. However, the specific computational problem being solved by grid cells has remained elusive. Here, we provide mathematical proof that spatial periodicity in grid cell firing is the only possible solution to a neural sequence code of 2-D trajectories and that the hexagonal firing pattern of grid cells is the most parsimonious solution to such a sequence code. We thereby provide a likely teleological cause for the existence of grid cells and reveal the underlying nature of the global geometric organization in grid maps as a direct consequence of a simple local sequence code. A sequence code by grid cells provides intuitive explanations for many previously puzzling experimental observations and may transform our thinking about grid cells. 

Understanding brain operation demands linking basic behavioral traits to cell-type specific dynamics of different brain-wide subcircuits. This requires a system to classify the basic operational modes of neurons and circuits. Single-cell phenotyping of firing behavior during ongoing oscillations in vivo has provided a large body of evidence on entorhinal–hippocampal function, but data are dispersed and diverse. Here, we mined literature to search for information regarding the phase-timing dynamics of over 100 hippocampal/entorhinal neuron types defined in Hippocampome.org . We identified missing and unresolved pieces of knowledge (e.g., the preferred theta phase for a specific neuron type) and complemented the dataset with our own new data. By confronting the effect of brain state and recording methods, we highlight the equivalences and differences across conditions and offer a number of novel observations. We show how a heuristic approach based on oscillatory features of morphologically identified neurons can aid in classifying extracellular recordings of single cells and discuss future opportunities and challenges towards integrating single-cell phenotypes with circuit function.