A dual-axis rotation rule for updating the head direction cell reference frame during movement in three dimensions

In the mammalian brain, allocentric (Earth-referenced) head direction, called azimuth, is encoded by head direction (HD) cells, which fire according to the facing direction of the animal's head. On a horizontal surface, rotations of the head around the dorso-ventral (D-V) axis, called yaw, correspond to changes in azimuth, and elicit appropriate updating of the HD 'compass' signal to enable large-scale navigation. However, if the animal moves through three-dimensional (3D) space then there is no longer a simple relationship between yaw rotations and azimuth changes, and so processing of three-dimensional rotations is needed. Construction of a global 3D compass would require complex integration of 3D rotations, and also a large neuronal population, most neurons of which would be silent most of the time since animals rarely sample all available 3D orientations. We propose that instead, the HD system treats the 3D space as a set of interrelated 2D surfaces. It could do this by updating activity according to both yaw rotations around the D-V axis and rotations of the D-V axis around the gravity-defined vertical axis. We present preliminary data to suggest that this rule operates when rats move between walls of opposing orientations. This dual-axis rule, which we show is straightforward to implement using the classic one-dimensional 'attractor' architecture, allows consistent representation of azimuth even in volumetric space, and thus may be a general feature of mammalian directional computations even for animals that swim or fly.

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