Grid and head direction codes represent cognitive spaces for navigation and memory. Pure grid cells generate grid codes that have been assumed to be independent of head direction, whereas conjunctive cells generate grid representations that are tuned to a single head direction. Here, we demonstrate that pure grid cells also encode head direction, but through distinct mechanisms. We show that individual firing fields of pure grid cells are tuned to multiple head directions, with the preferred sets of directions differing between fields. This local directional modulation is not predicted by previous continuous attractor or oscillatory interference models of grid firing but is accounted for by models in which pure grid cells integrate inputs from co-aligned conjunctive cells with firing rates that differ between their fields. We suggest that local directional signals from grid cells may contribute to downstream computations by decorrelating different points of view from the same location.

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Grid and head direction codes in the medial entorhinal cortex represent cognitive spaces for navigation and memory 1,2 . In grid cells the expression of the grid code is thought to be independent of head direction, whereas in conjunctive cells the grid code is tuned to a single head direction 3 . This distinction between non-directional grid cells and unidirectional conjunctive cells is also present in models and proposed functions for grid codes 4-11 . However, while grid cells are not tuned to a single direction, whether their firing is independent of direction is less clear. Here we demonstrate location-dependent modulation of grid cell firing by head direction. Individual firing fields recorded from mouse and rat grid cells have multiple and different preferred directions. This local directionality of grid firing is accounted for by models in which grid cells integrate inputs from conjunctive cells with co-aligned, spatially non-uniform firing fields. Thus, the firing of grid cells is consistent with their integration of upstream grid codes. For downstream neurons in the dentate gyrus that receive input from grid cells, integration of rich directional information within the grid code may contribute to pattern separation computations by decorrelating different points of view from the same spatial location [12][13][14] .Grid codes are thought to provide a metric for spatial and conceptual representations used for navigation, learning and memory 1,15,16 . In the spatial domain grid codes have six-fold rotational symmetry, with individual fields appearing as the vertices of tessellating triangles that tile the floor of an environment 15 . Grid codes are generated by two functionally defined cell types found in the medial entorhinal cortex (MEC). Grid cells have grid firing fields that are thought to lack selectivity for head direction or other navigational variables 3,17 . In contrast, conjunctive cells have grid fields that manifest only when an animal moves in a particular direction 3 . Established models for grid firing assume that neurons with grid fields have either an absence of directional