Retinal distribution of Disabled-1 in a diurnal murine rodent, the Nile grass rat Arvicanthis niloticus

From random to regular: Variation in the patterning of retinal mosaics

The various types of retinal neurons are each positioned at their respective depths within the retina where they are believed to be assembled as orderly mosaics, in which like-type neurons minimize proximity to one another. Two common statistical analyses for assessing the spatial properties of retinal mosaics include the nearest neighbor analysis, from which an index of their "regularity" is commonly calculated, and the density recovery profile derived from autocorrelation analysis, revealing the presence of an exclusion zone indicative of anti-clustering. While each of the spatial statistics derived from these analyses, the regularity index and the effective radius, can be useful in characterizing such properties of orderly retinal mosaics, they are rarely sufficient for conveying the natural variation in the self-spacing behavior of different types of retinal neurons and the extent to which that behavior generates uniform intercellular spacing across the mosaic. We consider the strengths and limitations of these and other spatial statistical analyses for assessing the patterning in retinal mosaics, highlighting a number of misconceptions and their frequent misuse. Rather than being diagnostic criteria for determining simply whether a population is "regular," they should be treated as descriptive statistics that convey variation in the factors that influence neuronal positioning. We subsequently apply multiple spatial statistics to the analysis of eight different mosaics in the mouse retina, demonstrating conspicuous variability in the degree of patterning present, from essentially random to notably regular. This variability in patterning has both a developmental as well as a functional significance, reflecting the rules governing the positioning of different types of neurons as the architecture of the retina is assembled, and the distinct mechanisms by which they regulate dendritic growth to generate their characteristic coverage and connectivity.

The somal patterning of the AII amacrine cell mosaic in the mouse retina is indistinguishable from random simulations matched for density and constrained by soma size

The orderly spacing of retinal neurons is commonly regarded as a characteristic feature of retinal nerve cell populations. Exemplars of this property include the horizontal cells and the cholinergic amacrine cells, where individual cells minimize the proximity to like-type neighbors, yielding regularity in the patterning of their somata. Recently, two types of retinal bipolar cells in the mouse retina were shown to exhibit an order in their somal patterning no different from density-matched simulations constrained by soma size but being otherwise randomly distributed. The present study has now extended this finding to a type of retinal amacrine cell, the AII amacrine cell. Voronoi domain analysis revealed the patterning in the population of AII amacrine somata to be no different from density-matched and soma-size-constrained random simulations, while analysis of the density recovery profile showed AII amacrine cells to exhibit a minimal intercellular spacing identical to that for those random simulations: AII amacrine somata were positioned side-by-side as often as chance would predict. Regularity indexes and packing factors (PF) were far lower than those achieved by either the horizontal cells or cholinergic amacrine cells, with PFs also being comparable to those derived from the constrained random simulations. These results extend recent findings that call into question the widespread assumption that all types of retinal neurons are assembled as regular somal arrays, and have implications for the way in which AII amacrine cells must distribute their processes to ensure a uniform coverage of the retinal surface.