Neuroscience Research Institute, University of California at Santa Barbara, Santa Barbara, California.
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK.
J Comp Neurol. 2020 Sep 1;528(13):2135-2160. doi: 10.1002/cne.24880. Epub 2020 Mar 3.
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.
视网膜神经元的各种类型分别位于视网膜的各自深度处，据信它们在那里被组装成有序的镶嵌图案，其中相似类型的神经元彼此之间的接近度最小。评估视网膜镶嵌图案空间特性的两种常见统计分析包括最近邻分析，通常从中计算其“规则性”的指数，以及源自自相关分析的密度恢复轮廓，揭示存在排斥区指示抗聚类。虽然从这些分析中得出的每个空间统计数据，即规则性指数和有效半径，都可以用于表征有序视网膜镶嵌图案的这些特性，但它们很少足以传达不同类型的视网膜神经元的自间隔行为的自然变化以及该行为在镶嵌图案中产生均匀细胞间间隔的程度。我们考虑了这些和其他空间统计分析评估视网膜镶嵌图案中的模式的优缺点，强调了一些误解及其常见的误用。它们不应被视为确定群体是否“规则”的诊断标准，而应被视为描述性统计数据，传达影响神经元定位的因素的变化。随后，我们将多种空间统计数据应用于分析小鼠视网膜中的八个不同镶嵌图案，展示了存在的模式化程度的明显可变性，从本质上的随机到明显的规则。这种模式化的可变性具有发育和功能意义，反映了在组装视网膜结构时不同类型的神经元定位的规则以及它们调节树突生长以产生其特征覆盖和连接的不同机制。
