A Two-Dimensional Grid-Cell Code for Three-Dimensional Navigation in Freely Flying Bats

Animals have evolved to navigate environments with diverse geometries and dimensionalities, yet how neural circuits for spatial navigation support behavior across such varied demands remains unresolved. In two-dimensional environments, grid cells in the medial entorhinal cortex provide a periodic signal for self-location that is thought to arise from underlying toroidal attractor dynamics at the ensemble level. However, during movement in three-dimensional environments, studies have reported a loss of global grid-cell periodicity. Furthermore, it remains unknown whether, at the ensemble level, a toroidal attractor is preserved across species and, if so, how such a two-dimensional code could support navigation in three-dimensional space. Here we performed large-scale, wireless neural recordings from the medial entorhinal cortex of freely flying bats engaged in spontaneous aerial foraging. We find that grid cells exhibit robust periodic firing during structured flight trajectories, and that co-modular grid-cell ensembles show topological signatures consistent with a two-dimensional toroidal manifold. Behavioral analyses of bats navigating in the wild and in the laboratory revealed that individual flight paths are organized along two-dimensional planes of motion, providing a natural substrate for a two-dimensional code. Accordingly, toroidal phase along flights was consistent with plane-wave patterns on the plane of motion, and single-cell firing was well described by a hexagonal lattice on the same plane. Together, these findings reveal a parsimonious solution whereby a two-dimensional neural code aligns with behaviorally relevant subspaces to support navigation in a three-dimensional world.