This thesis explores advanced computational techniques in super-resolution microscopy (SRM), with the primary goal of pushing the limits of achievable resolution towards the 1 nm scale. It includes developments in particle fusion algorithms, data analysis of complex biological structures, and exploration of the impact of molecular dipole orientation on MINFLUX localization accuracy and precision. In the first part, we present a novel fast particle fusion method tailored to single molecule localization microscopy (SMLM). This method first registers particles based on Joint Registration of Multiple Point Clouds (JRMPC) and then classifies and reconnects misaligned locally optimally clustered sets of particles. This approach significantly reduces computational cost compared to earlier template free methods in particular for a large number of particles.. This advancement enables more detailed and accurate reconstructions of super-particles, enhancing the capabilities of SMLM. The second part of the dissertation deals with a data analysis of nuclear pore complexes (NPCs) reconstructed by the earlier developed particle fusion technique. By fusing thousands of NPCs labeled at nucleoporin Nup96 and analyzing the high-resolution reconstructions, we reveal intricate details of the NPC structure, in particular the unit structure of Nup96. This analysis showcases the potential of SRM in combination with advanced data analysis to contribute to structural biology on the length scale below 10 nm. The third part focuses on the influence of the dipole orientation on the localization accuracy and precision of MINFLUX. We simulate the imaging process with a physically realistic vector diffraction Point Spread Function (PSF) model and then localize the emitters based on the simplified Gaussian doughnut PSF model used in MINFLUX so far. Our study, including dipoles with free and fixed orientations and key simulation parameters, reveals the need for more refined modeling to overcome the bias, especially for fixed dipole orientations and background fluorescence. This investigation helps to understand the limitations of MINFLUX in its current form and paves the way for future improvements of the technique. Finally, we discuss potential future directions for improving SRM techniques. These include refining the fast particle fusion method by incorporating localization uncertainties and prior knowledge, optimizing experimental parameters in MINFLUX, and developing advanced localization strategies to improve accuracy and efficiency. By addressing these future challenges, SRM technologies can move closer to the goal of 1 nm resolution in super-resolution imaging.@en

Correction to: Scientific Reports, published online 16 August 2023 The original version of this Article contained an error in the upper inset of Figure 4, where the atomic model was missing. The original Figure 4 and accompanying legend appear below. (Figure presented.) Overlay of the fluorophore positions from the SMLM particle fusion data (pink) and the SNAP-tag derived from the cryo-EM data (purple). For our overall SMLM emitters (pink), the lateral distance between a unit are 9.1 nm for NR and 10.0 nm for CR. The axial distances between a unit are 2.4 nm for NR and 1.2 nm for CR. The SNAP tags (purple) have lateral distances between a unit of 11.6 nm for NR and 11.5 nm for CR as well as axial distances of 2.5 nm for NR and 2.9 nm for CR. The original Article has been corrected.@en

Single molecule localization microscopy offers resolution nearly down to the molecular level with specific molecular labelling, and is thereby a promising tool for structural biology. In practice, however, the actual value to this field is limited primarily by incomplete fluorescent labelling of the structure. This missing information can be completed by merging information from many structurally identical particles in a particle fusion approach similar to cryo-EM single-particle analysis. In this paper, we present a data analysis of particle fusion results of fluorescently labelled Nup96 nucleoporins in the Nuclear Pore Complex to show that Nup96 occurs in a spatial arrangement of two rings of 8 units with two Nup96 copies per unit giving a total of 32 Nup96 copies per pore. We use Artificial Intelligence assisted modeling in Alphafold to extend the existing cryo-EM model of Nup96 to accurately pinpoint the positions of the fluorescent labels and show the accuracy of the match between fluorescent and cryo-EM data to be better than 3 nm in-plane and 5 nm out-of-plane.@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