Grid cells anticipate the animal's future movement

Grid cells in the rodent medial entorhinal cortex preferentially fire spikes when the animal is within certain regions of space. When experimental data are averaged over time, spatial firing fields become apparent. If these firing fields represented only the current position of the animal, a grid cells firing should not depend on whether the animal is running into or out of a firing field. Yet many grid cells are sensitive to the animals direction of motion relative to the firing-field center. Such apparent egocentric "inbound-outbound tuning" could be a sign of prospective encoding of future position, but it is unclear whether grid cells code ahead in space or in time. To investigate this question, we decided to undo the inbound-outbound modulation by shifting all spikes within a given firing field by a fixed distance in space or in time. For grid-cell data recorded in mice, optimizing in space requires a forward shift of around 2.5 cm, whereas optimizing in time yielded a forward shift of about 170 ms. In either case the firing-field sizes decrease. Minimizing just the field size yields somewhat smaller shifts (roughly 1.8 cm and around 115 ms ahead). Jointly optimizing along the temporal and spatial dimension reveals a continuum of flat inbound-outbound tuning curves and a shallow minimum for field sizes, located at about 2.3 cm and 35 ms. These findings call into question a purely spatial or purely temporal interpretation of grid-cell firing fields and inbound-outbound tuning.