A proposed rule for updating of the head direction cell reference frame following rotations in three dimensions

In the mammalian brain, allocentric (Earth-referenced) heading direction, called azimuth, is encoded by head direction (HD) cells, which fire according to the facing direction of the rat's head. If the animal is on a horizontal surface then egocentric (self-referenced) rotations of the head around the dorso-ventral axis, called yaw, correspond to changes in azimuth, and elicit appropriate updating of the HD signal. However, if the surface is sloping steeply then yaw rotations no longer map linearly to changes in azimuth. The brain could solve this problem simply by always firing according to direction on the local (sloping) surface instead; however, if the animal moves between surfaces having different compass orientations then errors would accumulate in the subsequent azimuth signal. These errors could be avoided if the HD system instead combines two updating rules: yaw rotations around the D-V axis and rotations of the D-V axis around the gravity-defined vertical axis. We show here that when rats move between vertical walls of different orientations then HD cells indeed rotate their activity by an amount corresponding to the amount of vertical-axis rotation. With modelling, we then show how this reference-frame rotation, which may be driven by inputs from the vestibular nuclei or vestibulocerebellum, allows animals to maintain a simple yaw-based updating rule while on a given plane, but also to avoid accumulation of heading errors when moving between planes.