Place cells in the hippocampus and grid cells in the entorhinal cortex are elements of a neural map of self position1–5. For these cells to benefit navigation, their representation must be dynamically related to the surrounding locations2. A candidate mechanism for linking places along an animal’s path has been described for place cells, in which the sequence of spikes in each cycle of the hippocampal theta oscillation encodes a trajectory from the animal’s current location towards upcoming locations6–8. In mazes that bifurcate, such trajectories alternately traverse the two upcoming arms when the animal approaches the choice point9,10, raising the possibility that the trajectories express available forward paths encoded on previous trials10. However, to bridge the animal’s path with the wider environment, beyond places previously or subsequently visited, an experience-independent spatial sampling mechanism might be required. Here we show in freely moving rats that in individual theta cycles, ensembles of grid cells and place cells encode a position signal that sweeps linearly outwards from the animal’s location into the ambient environment, with sweep direction alternating stereotypically between left and right across successive theta cycles. These sweeps are accompanied by, and aligned with, a similarly alternating directional signal in a discrete population of parasubiculum cells that have putative connections to grid cells via conjunctive grid × direction cells. Sweeps extend into never-visited locations that are inaccessible to the animal. Sweeps persist during REM sleep. The sweep directions can be explained by an algorithm that maximizes the cumulative coverage of the surrounding manifold space. The sustained and unconditional expression of theta-patterned left–right-alternating sweeps in the entorhinal–hippocampal positioning system provides an efficient ‘look around’ mechanism for sampling locations beyond the travelled path.
