Analysis of the Spatial Organization of Molecules with Robust Statistics

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.

分子生物学领域的核心问题之一，在于观测到的分子的空间分布究竟是随机的，还是以簇状形式有序排布的。事实上，这类分析能够揭示分子间的相互作用，以及分子与所处环境的物理互作关系。用于统计分析分子分布的标准工具为里普利K函数（Ripley’s K function），该函数通过计算其临界分位数来检验空间随机性。然而，分位数的计算过程极为繁琐，极大限制了该工具的实际应用。本研究推导得到了这些分位数的解析表达式，由此构建出一种快速且稳健的统计检验方法，并通过里普利K函数的峰值计算得到了簇状结构的特征尺寸。随后，我们对细胞膜上的内吞位点的空间排布进行了分析，结果发现网格蛋白（clathrin）位点呈随机分布，而非依赖网格蛋白的位点则以半径为 的簇状结构排布，这表明两种内吞通路拥有截然不同的物理机制与细胞功能。