A statistical analysis of spatial clustering along cell filaments using Ripley´s K function

The analysis of the spatial distribution of molecules along one dimensional structures, such as filaments of the cell´s cytoskeleton, gives essential information on intracellular transport mechanisms. The standard tool for analyzing molecules´ organizationis the Ripley´s K function, which permits to statistically test the hypothesis of molecules´ random distribution against clustering or dispersion. However, the computation of the critical quantiles of Ripley´s K function is currently based on Monte-Carlo simulations, which induces a high computational load and hinders its use. Here, we present an analytical expression of these quantiles for 1D filaments, leading to a fast and robust statistical test. Thereafter, we used our statistical test to analyze the spatial distribution of proteins involved in intraflagellar transport along the flagellum of the parasite Typanosoma brucei.