Head direction cells use a head-referenced dual-axis updating rule in 3D space

Head direction (HD) cells, comprising a compass signal for the brain's spatial map, may update their firing during 3D movement by using a 'dual axis' (DA) rule that sums head rotation around a local axis and local-axis rotation around the gravity axis. To test for operation of this rule we present HD cell activity from rats exploring a hemispherical surface. We assess HD cell tuning curves in either the standard horizontal reference frame or in two reference frames governed by a DA rule, with the local axis referenced to the head (DAH) or local surface (DAS). Tuning curves are best when plotted in the DAH reference frame. This confirms that the cells use a head-referenced DA rule and indicates that the relationship of the head pose to gravity in two planes, one egocentric (head-plane) and one allocentric (earth-horizontal plane), forms a component of the inputs to the HD system.