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Single molecule localization microscopy offers in principle resolution down to the molecular level, but in practice this is limited primarily by incomplete fluorescent labeling of the structure. This missing information can be completed by merging information from many structurally identical particles. In this work, we present an approach for 3D single particle analysis in localization microscopy which hugely increases signal-to-noise ratio and resolution and enables determining the symmetry groups of macromolecular complexes. Our method does not require a structural template, and handles anisotropic localization uncertainties. We demonstrate 3D reconstructions of DNA-origami tetrahedrons, Nup96 and Nup107 subcomplexes of the nuclear pore complex acquired using multiple single molecule localization microscopy techniques, with their structural symmetry deducted from the data.@en

Particle fusion for single molecule localization microscopy improves signal-to-noise ratio and overcomes underlabeling, but ignores structural heterogeneity or conformational variability. We present a-priori knowledge-free unsupervised classification of structurally different particles employing the Bhattacharya cost function as dissimilarity metric. We achieve 96% classification accuracy on mixtures of up to four different DNA-origami structures, detect rare classes of origami occuring at 2% rate, and capture variation in ellipticity of nuclear pore complexes.@en

Single molecule localization microscopy (SMLM) shows promise for quantitative structural analysis of subcellular complexes and organelles with a resolution well below the diffraction limit. This superresolution microscopy technique relies on the blinking events of fluorescent molecules that labeled the structure of interest and are spatiotemporally spread over the entire field of view and time. Once hundred thousands frames of these sparse events are recorded, single molecule positions are localized with nanometer precision to form a 2D/3D point set of coordinates. Therefore, SMLM images are not conventional pixelated images but rather spatial point patterns. Photon scarcity and incomplete labeling of the imaged structure, however, limit the resolution that can possibly be achieved by means of SMLM. Moreover, due to experimental limitations the axial resolution is typically ~2-3 times worse than the lateral resolution in conventional setups. Inspired by single particle analysis (SPA) in cryo-electron microscopy (cryo-EM), proper alignment of repeated structures ("particle fusion") in a 2D/3D SMLM measurement can overcome these limiting factors and so push for isotropic resolution. The existing approaches for particle fusion in SMLM can be classified into customized routines that are borrowed from SPA in EM or methods that use strong prior knowledge about the structure to be reconstructed. While the first approaches are completely ignoring the differences in image formation model between EM and SMLM, the second ones are highly prone to the template-bias problem. In this thesis, a dedicated particle fusion pipeline for 2D/3D SMLM data is proposed. The approach properly considers the pointillistic nature of the SMLM modality and takes into account the localization uncertainties. Furthermore, while it does not require any prior knowledge about the underlying structure of the particles, it can incorporate certain features such as symmetry into the fusion process. Owing to the novel all-to-all registration scheme, the application of the devised pipeline on experimental data with very poor labeling density has been successfully demonstrated. The requirements for successful particle fusion for different SMLM modalities, namely PAINT and STORM, have been characterized through extensive study on 2D and 3D experimental and simulation data. In 2D, an FRC resolution of 3.3 nm on DNA-origami nanostructures has been achieved, and, in 3D, it was demonstrated how the combination of SMLM as a light microscopy technique and a computational approach enables structural analysis of the Nuclear Pore Complex. Future advances of SMLM rely highly on computational routines after data acquisition. Advanced data analysis techniques such as particle fusion can help pushing the boundaries of structural biology using light microscopy.@en

Summary: We present a fast particle fusion method for particles imaged with single-molecule localization microscopy. The state-of-the-art approach based on all-to-all registration has proven to work well but its computational cost scales unfavorably with the number of particles N, namely as N2. Our method overcomes this problem and achieves a linear scaling of computational cost with N by making use of the Joint Registration of Multiple Point Clouds (JRMPC) method. Straightforward application of JRMPC fails as mostly locally optimal solutions are found. These usually contain several overlapping clusters that each consist of well-aligned particles, but that have different poses. We solve this issue by repeated runs of JRMPC for different initial conditions, followed by a classification step to identify the clusters, and a connection step to link the different clusters obtained for different initializations. In this way a single well-aligned structure is obtained containing the majority of the particles. Results: We achieve reconstructions of experimental DNA-origami datasets consisting of close to 400 particles within only 10 min on a CPU, with an image resolution of 3.2 nm. In addition, we show artifact-free reconstructions of symmetric structures without making any use of the symmetry. We also demonstrate that the method works well for poor data with a low density of labeling and for 3D data. @en

Methods that fuse multiple localization microscopy images of a single structure can improve signal-to-noise ratio and resolution, but they generally suffer from template bias or sensitivity to registration errors. We present a template-free particle-fusion approach based on an all-to-all registration that provides robustness against individual misregistrations and underlabeling. We achieved 3.3-nm Fourier ring correlation (FRC) image resolution by fusing 383 DNA origami nanostructures with 80% labeling density, and 5.0-nm resolution for structures with 30% labeling density.@en