Navigation often requires movement in three-dimensional (3D) space. Recent studies have postulated two different models for how head direction (HD) cells encode 3D space: the rotational plane hypothesis and the dual-axis model. To distinguish these models, we recorded HD cells in female rats while they traveled different routes along both horizontal and vertical surfaces from an elevated platform to the top of a cuboidal apparatus. We compared HD cell preferred firing directions (PFDs) in different planes and addressed the issue of whether HD cell firing is commutative-does the order of the animal's route affect the final outcome of the cell's PFD? Rats locomoted a direct or indirect route from the floor to the cube top via one, two, or three vertical walls. Whereas the rotational plane hypothesis accounted for PFD shifts when the animal traversed horizontal corners, the cell's PFD was better explained by the dual-axis model when the animal traversed vertical corners. Responses also followed the dual-axis model (1) under dark conditions, (2) for passive movement of the rat, (3) following apparatus rotation, (4) for movement around inside vertical corners, and (5) across a 45°outside vertical corner. The order in which the animal traversed the different planes did not affect the outcome of the cell's PFD, indicating that responses were commutative. HD cell peak firing rates were generally equivalent along each surface. These findings indicate that the animal's orientation with respect to gravity plays an important role in determining a cell's PFD, and that vestibular and proprioceptive cues drive these computations.

Specialized circuitry in the brain processes spatial information to provide a sense of direction used for navigation. The dorsal tegmental nucleus (DTN) is a core component of this circuitry and utilizes vestibular inputs to generate neural activity encoding the animal's directional heading. Projections arising from the nucleus prepositus hypoglossi (NPH) and the medial vestibular nucleus (MVe) are thought to transmit critical vestibular signals to the DTN and other brain areas, including the abducens nucleus (ABN), a component of eye movement circuitry. Here, we utilized a dual retrograde tracer approach in rats to investigate whether overlapping or distinct populations of neurons project from the NPH or MVe to the DTN and ABN. We report that individual MVe neurons project to both the DTN and ABN. In contrast, we observed individual NPH neurons that project to either the DTN or ABN, but rarely to both structures simultaneously. We also examined labeling patterns in other structures located in the brainstem and posterior cortex and observed (1) complex patterns of interhemispheric connectivity between the left and right DTN, (2) projections from the supragenual nucleus, interpeduncular nucleus, and retrosplenial cortex to the DTN, (3) projections from the lateral superior olive to the ABN, and (4) a unique population of cerebrospinal fluid‐contacting neurons in the dorsal raphe nucleus. Collectively, our experiments provide valuable new information that extends our understanding of the anatomical organization of the brain's spatial processing circuitry.

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