Tiling mechanisms of the Drosophila compound eye through geometrical tessellation.

Tiling patterns are observed in many biological structures. The compound eye is an interesting example of tiling and is often constructed by hexagonal arrays of ommatidia, the optical unit of the compound eye. Hexagonal tiling may be common due to mechanical restrictions such as structural robustness, minimal boundary length, and space-filling efficiency. However, some insects exhibit tetragonal facets.1-4 Some aquatic crustaceans, such as shrimp and lobsters, have evolved with tetragonal facets.5-8 Mantis shrimp is an insightful example as its compound eye has a tetragonal midband region sandwiched between hexagonal hemispheres.9,10 This casts doubt on the naive explanation that hexagonal tiles recur in nature because of their mechanical stability. Similarly, tetragonal tiling patterns are also observed in some Drosophila small-eye mutants, whereas the wild-type eyes are hexagonal, suggesting that the ommatidial tiling is not simply explained by such mechanical restrictions. If so, how are the hexagonal and tetragonal patterns controlled during development? Here, we demonstrate that geometrical tessellation determines the ommatidial tiling patterns. In small-eye mutants, the hexagonal pattern is transformed into a tetragonal pattern as the relative positions of neighboring ommatidia are stretched along the dorsal-ventral axis. We propose that the regular distribution of ommatidia and their uniform growth collectively play an essential role in the establishment of tetragonal and hexagonal tiling patterns in compound eyes.

DWnt4 and DWnt10 Regulate Morphogenesis and Arrangement of Columnar Units via Fz2/PCP Signaling in the Drosophila Brain.

Columns are structural and functional units of the brain. However, the mechanism of column formation remains unclear. The medulla of the fly visual center shares features with the mammalian cerebral cortex, such as columnar and layered structures, and provides a good opportunity to study the mechanisms of column formation. Column formation is initiated by three core neurons in the medulla, namely, Mi1, R8, and R7. The proper orientation of neurons is required for the orientation and arrangement of multiple columns. Their orientations may be under the control of planar cell polarity (PCP) signaling, because it is known to regulate the orientation of cells in two-dimensional tissue structures. In this study, we demonstrate that the ligands DWnt4 and DWnt10 expressed specifically in the ventral medulla and dorsal medulla, respectively, globally regulate the columnar arrangement and orientation of Mi1 and R8 terminals through Fz2/PCP signaling in a three-dimensional space.