The patterning of retinal horizontal cells: normalizing the regularity index enhances the detection of genomic linkage

Patrick W. Keeley, Benjamin E. Reese

Retinal neurons are often arranged as non-random distributions called "mosaics," as their somata minimize proximity to neighboring cells of the same type. The horizontal cells serve as an example of such a mosaic, but little is known about the developmental mechanisms that underlie their patterning. To identify genes involved in this process, we have used three different spatial statistics to assess the patterning of the horizontal cell mosaic across a panel of genetically distinct recombinant inbred strains. To avoid the confounding effect of cell density, which varies twofold across these different strains, we computed the "real/random regularity ratio," expressing the regularity of a mosaic relative to a randomly distributed simulation of similarly sized cells. To test whether this latter statistic better reflects the variation in biological processes that contribute to horizontal cell spacing, we subsequently compared the genomic linkage for each of these two traits, the regularity index, and the real/random regularity ratio, each computed from the distribution of nearest neighbor (NN) distances and from the Voronoi domain (VD) areas. Finally, we compared each of these analyses with another index of patterning, the packing factor. Variation in the regularity indexes, as well as their real/random regularity ratios, and the packing factor, mapped quantitative trait loci to the distal ends of Chromosomes 1 and 14. For the NN and VD analyses, we found that the degree of linkage was greater when using the real/random regularity ratio rather than the respective regularity index. Using informatic resources, we narrowed the list of prospective genes positioned at these two intervals to a small collection of six genes that warrant further investigation to determine their potential role in shaping the patterning of the horizontal cell mosaic.