Abstract
One major question in molecular biology is whether the spatial distribution of observed molecules is random or organized in clusters. Indeed, this analysis gives information about molecules’ interactions and physical interplay with their environment. The standard tool for analyzing molecules’ distribution statistically is the Ripley’s K function, which tests spatial randomness through the computation of its critical quantiles. However, quantiles’ computation is very cumbersome, hindering its use. Here, we present an analytical expression of these quantiles, leading to a fast and robust statistical test, and we derive the characteristic clusters’ size from the maxima of the Ripley’s K function. Subsequently, we analyze the spatial organization of endocytic spots at the cell membrane and we report that clathrin spots are randomly distributed while clathrin-independent spots are organized in clusters with a radius of , which suggests distinct physical mechanisms and cellular functions for each pathway.
Highlights
Spatial organization of objects is essential in many scientific areas because it provides information about objects’ interactions and their interplay with their environment
The analysis of spatial patterns across ten years in an aspen-white-pine forest [4] showed that tree distribution tended toward greater clumping than that expected from random mortality, which is due to the clonal nature of aspen
Construction of the Test Statistic We aim at constructing a statistic K~ to test whether a points’
Summary
Spatial organization of objects is essential in many scientific areas because it provides information about objects’ interactions and their interplay with their environment. In all spatial organization studies, objects (disease cases, trees, molecules ...) are represented as points in a delimited field of view (country, forest, cell ...) and quantitative methods are used to extract features about spatial point distributions.
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