Fig. 1: Three-dimensional response of two example cells.

a Proposed framework for 3D orientation. Top: tilt is measured by sensing the gravity vector (green pendulum) in egocentric coordinates, resulting in a 2D spherical topology. Bottom: azimuth has a circular topology, and is measured by rotating an earth-horizontal compass in alignment with the head-horizontal plane (TA frame). b Schematic of the arena used to identify azimuth-tuned cells in the horizontal plane. c, d Example azimuth tuning of a traditional HD cell, i.e. tuned to azimuth (Az-tuned) in the ADN (c) and another cell not tuned to azimuth (non-Az-tuned cell) in the cingulum (d), as the mouse walks freely in light (red) and darkness (black) in a horizontal arena (shown in b), on a platform oriented horizontally (shown in e, left; broken pink lines) and in the rotator (shown in h; gray lines). The azimuth-tuned cell showed significant tuning with different preferred directions (PD) in all setups, although response was strongly attenuated in the rotator (compare gray with red/pink lines). e Schematic of a 3D orientable platform used to measure 3D tuning. f, g Tuning curves for the two cells in c and d, obtained from responses as the mouse foraged on the orientable platform (shown in e). Firing rate is shown as a heat map in 3D space (Supplementary Movies 1, 2). The peak and trough of the average tilt response (across all azimuths) are indicated with arrows on the color scale; NTA = (peak-trough)/peak. Note that tuning curves are restricted to 60° tilt (Methods). h Schematic of a rotator used to measure full 3D tuning curves. i, j Tuning curves for the two cells in c, f and d, g as the mouse was passively re-oriented uniformly throughout the full 3D space using the rotator (Supplementary Movies 3–5).