Detecting continuous structural heterogeneity in single molecule localization microscopy data with a point cloud variational auto-encoder

The low degree of labeling and limited photon count of fluorescent emitters in single molecule localization microscopy results in poor quality images of macro-molecular complexes. Particle fusion provides a single reconstruction with high signal-to-noise ratio by combining many single molecule localization microscopy images of the same structure. The underlying assumption of homogeneity is not always valid, heterogeneity can arise due to geometrical shape variations or distinct conformational states. We introduce a Point Cloud Variational Auto-Encoder that works directly on 2D and 3D localization data, to detect multiple modes of variation in such datasets. The computing time is on the order of a few minutes, enabled by the linear scaling with dataset size, and fast network training in just four epochs. The use of lists of localization data instead of pixelated images leads to just minor differences in computational burden between 2D and 3D cases. With the proposed method, we detected radius variation in 2D Nuclear Pore Complex data, height variations in 3D DNA origami tetrahedron data, and both radius and height variations in 3D Nuclear Pore Complex data. In all cases, the detected variations were on the few nanometer scale.