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，在于观测到的分子空间分布究竟是随机无序的，还是以簇状形式有序组织的。事实上，此类分析可揭示分子间的相互作用，以及分子与周遭环境的物理互作关系。用于统计分析分子空间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，临界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类临界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；同时我们还通过里普利K函数的峰值，推导出了簇状结构的特征尺寸。随后，我们针对细胞膜表面的内吞斑点的空间组织模式展开分析，结果显示：网格蛋白（clathrin）斑点的分布呈随机状态，而非网格蛋白依赖的内吞斑点则以半径为（原文此处缺失具体数值）的簇状结构聚集。这一发现表明两类内吞通路拥有截然不同的物理机制与细胞功能。