Topological data analysis quantifies biological nano-structure from single molecule localization microscopy

The study of complex molecular organisation and nano-structure by localization based microscopy is limited by the available analysis tools. We present a segmentation protocol which, through the application of persistence based clustering, is capable of probing densely packed structures which vary in scale. An increase in segmentation performance over state-of-the-art methods is demonstrated. Moreover we employ persistence homology to move beyond clustering, and quantify the topological structure within data. This provides new information about the preserved shapes formed by molecular architecture. Our methods are flexible and we demonstrate this by applying them to receptor clustering in platelets, nuclear pore components and endocytic proteins. Both 2D and 3D implementations are provided within RSMLM, an R package for pointillist based analysis and batch processing of localization microscopy data.