Spatial symmetries in vestibular projections to the uvula-nodulus

The discharge of secondary vestibular neurons relays the activity of the vestibular endorgans, occasioned by movements in three-dimensional physical space. At a slightly higher level of analysis, the discharge of each secondary vestibular neuron participates in a multifiber projection or pathway from primary afferents via the secondary neurons to another neuronal population. The logical organization of this projection determines whether characteristics of physical space are retained or lost. The logical structure of physical space is standardly expressed in terms of the mathematics of group theory. The logical organization of a projection can be compared to that of physical space by evaluating its symmetry group. The direct projection from the semicircular canal nerves via the vestibular nuclei to neck motor neurons has a full three-dimensional symmetry group, allowing it to maintain a three-dimensional coordinate frame. However, a projection may embed only a subgroup of the symmetry group of physical space, which incompletely mirrors the properties of physical space. The major visual and vestibular projections in the rabbit via the inferior olive to the uvula-nodulus carry three degrees of freedom-rotations about one vertical and two horizontal axes-but do not have full three dimensional symmetry. Instead, the vestibulo-olivo-nodular projection has symmetries corresponding to a product of two-dimensional vestibular and one-dimensional optokinetic spaces. This combination of projection symmetries provides the foundation for distinguishing horizontal from vertical rotations within a three dimensional space. In this study, we evaluate the symmetry group given by the physiological organization of the vestibulo-olivo-nodular projection. Although it acts on the same sets of elements and mirrors the rotations that occur in physical space, the physiological transformation group is distinct from the spatial group. We identify symmetries as products of physiological and spatial transformations. The symmetry group shapes the information the projection conveys to the uvula-nodulus; this shaping may depend on a physiological choice of generators, in the same way that function depends on the physiological choice of coordinates. We discuss the implications of the symmetry group for uvula-nodulus function, evolution, and functions of the vestibular system in general.