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Many animals rely on vision to navigate through their environment. The pattern of changes in the visual scene induced by self-motion is the optic flow1, which is first estimated in local patches by directionally selective (DS) neurons2–4. But how should the arrays of DS neurons, each responsive to motion in a preferred direction at a specific retinal position, be organized to support robust decoding of optic flow by downstream circuits? Understanding this global organization is challenging because it requires mapping fine, local features of neurons across the animal’s field of view3. In Drosophila, the asymmetric dendrites of the T4 and T5 DS neurons establish their preferred direction, making it possible to predict DS responses from anatomy4,5. Here we report that the preferred directions of fly DS neurons vary at different retinal positions and show that this spatial variation is established by the anatomy of the compound eye. To estimate the preferred directions across the visual field, we reconstructed hundreds of T4 neurons in a full brain EM volume6 and discovered unexpectedly stereotypical dendritic arborizations that are independent of location. We then used whole-head μCT scans to map the viewing directions of all compound eye facets and found a non-uniform sampling of visual space that explains the spatial variation in preferred directions. Our findings show that the organization of preferred directions in the fly is largely determined by the compound eye, exposing an intimate and unexpected connection between the peripheral structure of the eye, functional properties of neurons deep in the brain, and the control of body movements.