title: Symmetries of a generic utricular projection: neural connectivity and the distribution of utricular information.
abstract: Sensory contribution to perception and action depends on both sensory receptors and the organization of pathways (or projections) reaching the central nervous system. Unlike the semicircular canals that are divided into three discrete sensitivity directions, the utricle has a relatively complicated anatomical structure, including sensitivity directions over essentially 360° of a curved, two-dimensional disk. The utricle is not flat, and we do not assume it to be. Directional sensitivity of individual utricular afferents decreases in a cosine-like fashion from peak excitation for movement in one direction to a null or near null response for a movement in an orthogonal direction. Directional sensitivity varies slowly between neighboring cells except within the striolar region that separates the medial from the lateral zone, where the directional selectivity abruptly reverses along the reversal line. Utricular primary afferent pathways reach the vestibular nuclei and cerebellum and, in many cases, converge on target cells with semicircular canal primary afferents and afference from other sources. Mathematically, some canal pathways are known to be characterized by symmetry groups related to physical space. These groups structure rotational information and movement. They divide the target neural center into distinct populations according to the innervation patterns they receive. Like canal pathways, utricular pathways combine symmetries from the utricle with those from target neural centers. This study presents a generic set of transformations drawn from the known structure of the utricle and therefore likely to be found in utricular pathways, but not exhaustive of utricular pathway symmetries. This generic set of transformations forms a 32-element group that is a semi-direct product of two simple abelian groups. Subgroups of the group include order-four elements corresponding to discrete rotations. Evaluation of subgroups allows us to functionally identify the spatial implications of otolith and canal symmetries regarding action and perception. Our results are discussed in relation to observed utricular pathways, including those convergent with canal pathways. Oculomotor and other sensorimotor systems are organized according to canal planes. However, the utricle is evolutionarily prior to the canals and may provide a more fundamental spatial framework for canal pathways as well as for movement. The fullest purely otolithic pathway is likely that which reaches the lumbar spine via Deiters' cells in the lateral vestibular nucleus. It will be of great interest to see whether symmetries predicted from the utricle are identified within this pathway.
authors.affiliation: Graduate Group in Applied Mathematics, University of California, Davis, CA, 95618, USA.
authors.forename: Thomas
authors.initials: T
authors.lastname: Chartrand
authors.affiliation: Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, PO Box 751, Portland, OR, 97207-751, USA. gin.mccollum@pdx.edu.
authors.forename: Gin
authors.initials: G
authors.lastname: McCollum
authors.affiliation: School of Research and Graduate Studies, National College of Natural Medicine, Portland, OR, 97201, USA. douglas.hanes@gmail.com.
authors.forename: Douglas A
authors.initials: DA
authors.lastname: Hanes
authors.affiliation: Vestibular Biophysics Laboratory, Ames Research Center, NASA, Moffett Field, CA, 94035-1000, USA.
authors.forename: Richard D
authors.initials: RD
authors.lastname: Boyle
mesh_terms: D000818:Animals; D001306:Auditory Pathways / Q000502:physiology; D019295:Computational Biology; D006801:Humans; D055641:Mathematical Concepts; D008959:Models, Neurological; D012444:Saccule and Utricle / Q000033:anatomy & histology / Q000294:innervation* / Q000502:physiology; D066191:Sensorimotor Cortex / Q000502:physiology; D011984:Sensory Receptor Cells / Q000502:physiology; D014722:Vestibule, Labyrinth / Q000033:anatomy & histology / Q000294:innervation / Q000502:physiology
keywords: Group; Projection; Symmetry; Utricle