Supplementary Figure 1: Recording sites and experiment setup.

Reconstructed cell location based on stereotaxic coordinates and MRI scans. Green (Animal V: n=19; Animal L: n=7), cyan (Animal V: n=12; Animal L: n=2), gray (Animal V: n=4; Animal L: n=4) symbols: G-tuned, dG-tuned and G+dG-tuned cells, respectively. White symbols: non-responsive cells (Animal V: n=28; Animal L: n=19). Blue stars: Head direction cells (n=57) recorded in a head-free setup (data from Kim, B., Dickman, J.D., Tauble, J.S. & Angelaki, D.E. Society for Neuroscience abstr. 444.11/CC2 (2015).). Ca: Tail of the Caudate Gyrus. Fo: Fornix. LV: Lateral ventricle. The dorsal, ventral and medial nuclei of the anterior thalamus are color-coded red, orange and magenta, respectively. (c) Schematic of the motion setup used in the experiments here, which includes a yaw-axis rotator (clockwise and counterclockwise yaw rotations are represented by red/blue arrows) inside a visual enclosure that has the capability of tilting (green arrows) – see also Supplementary Video 1. Note the head-stationary inner most gimbal that moves with the animal, which might have somewhat restricted the view of distant landmarks on the inside of the spherical enclosure. (d) Coordinate system used to represent small angle head tilts. Upper panel: illustration of head orientation relative to gravity in upright (UP), right ear down (RED), nose-up (NU), left ear down (LED) and nose-down (ND) orientations. Lower panel: representation of the head tilt in polar coordinates, with the radius representing the tilt angle and the angular coordinate the direction of the tilt (ND, LED, etc). The changes of head tilt associated with yaw, pitch and roll rotations (bottom right inset) are indicated. The projection of G onto the head-fixed X and Y axes, GX and GY, can be represented in Cartesian coordinates on the same plot (green). Note that this polar representation is a small tilt angle approximation of a 2D spherical topology that represents any arbitrary head orientation.