Fig. 4: Modeling 3D responses.
From: A gravity-based three-dimensional compass in the mouse brain
a Modeling tilt tuning. Top: Gravity is a 3D vector (green) sensed in egocentric Cartesian coordinates by the otolith organs. Middle: to model tilt tuning, we first assume a 3D Gaussian function (orange ellipsoid) in this Cartesian space. Bottom: on earth, the magnitude of gravity is constant. Therefore, we restrict the tilt tuning curve to a 2D sphere surrounding the head, which corresponds to the egocentric gravity vector experienced when tilting on earth. b Modeling azimuth tuning. Azimuth is expressed in a TA frame (top), and tuning is modeled as a von Mises distribution combined with a tilt-dependent gain factor (Fig. 3g). c 3D tuning defined by the product of these two curves. d Distribution of the model’s coefficient of correlation (ρ) across areas. e, f Experimentally measured 3D tuning curves (top) from two conjunctive cells that maintain their azimuth tuning in the rotator and fitted tuning curves (bottom), represented as color maps in 3D space (animated in Supplementary Movies 8, 9). The cell is e is the same as in a, b. Source data are provided as a Source Data file.
