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.