smoppix: unified nonparametric analysis of single-molecule spatial omics data using probabilistic indices

Spatial omics technologies localize individual molecules at subcellular resolution, yet growing numbers of molecules, features and replicates set analysis challenges. We present smoppix, a nonparametric analysis method based on the probabilistic index, to test for several uni- and bivariate localization patterns. It exploits the high-dimensionality of the data for variance weighting and for providing a background null distribution, unique for every molecule. Moreover, smoppix sidesteps segmentation, edge correction, warping and density estimation, and is scalable thanks to an exact permutation null distribution. We unearth spatial patterns in datasets from four kingdoms, and validate some findings experimentally on spikemoss roots.