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

Motivation: Localization microscopy data is represented by a set of spatial coordinates, each corresponding to a single detection, that form a point cloud. This can be analyzed either by rendering an image from these coordinates, or by analyzing the point cloud directly. Analysis of this type has focused on clustering detections into distinct groups which produces measurements such as cluster area, but has limited capacity to quantify complex molecular organization and nano-structure.

Results: 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 persistent 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, endocytic proteins and microtubule networks. Both 2D and 3D implementations are provided within RSMLM, an R package for pointillist-based analysis and batch processing of localization microscopy data.

Availability: RSMLM has been released under the GNU General Public License v3.0 and is available at https://github.com/JeremyPike/RSMLM. Tutorials for this library implemented as Binder ready Jupyter notebooks are available at https://github.com/JeremyPike/RSMLM-tutorials.