Nanoscale pattern extraction from relative positions of sparse 3D localisations

We present a method for extracting high-resolution ordered features from localisation microscopy data by analysis of relative molecular positions in 2D or 3D. This approach allows pattern recognition at sub-1% protein detection efficiencies, in large and heterogeneous samples, and in 2D and 3D datasets. We used this method to infer ultrastructure of the nuclear pore, the cardiomyocyte Z-disk, DNA origami structures and the centriole.