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.

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.

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.

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 unfavourably 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 labelling and for 3D data. Availability The code is available for download from https://github.com/wexw/Joint-Registration-of-Multiple-Point-Clouds-for-Fast-Particle-Fusion-in-Localization-Microscopy. Supplementary information Supplementary data are available at Bioinformatics online.

We present an approach for 3D particle fusion in localization microscopy which dramatically increases signal-to-noise ratio and resolution in single particle analysis. Our method does not require a structural template, and properly handles anisotropic localization uncertainties. We demonstrate 3D particle reconstructions of the Nup107 subcomplex of the nuclear pore complex (NPC), cross-validated using multiple localization microscopy techniques, as well as two-color 3D reconstructions of the NPC, and reconstructions of DNA-origami tetrahedrons. Main textSingle molecule localization microscopy (SMLM) is capable of resolving biological structure at the nanometer scale. However, SMLM image resolution is ultimately limited by the density of the fluorescent labels on the structure of interest and the finite precision of each localization 1, 2 . Recently, methods for obtaining higher precision localizations have been reported, which work by either increasing the number of collected photons per molecule via e.g. cryogenic imaging 3, 4 , or by introducing patterned illumination 5, 6 . The first limitation remains, however, and one approach to boosting the apparent degree of labeling (DOL) and filling in missing labels can be applied when the sample consists of many identical copies of the structure of interest (e.g. a protein complex). In this case, by combining many structures into a single "super-particle", the effective labelling density is increased, and the resulting super-particle has a high number of localizations leading to a significantly improved signal-to-noise ratio and resolution.Previous approaches to this problem can be classified as either template-based or adaptations of existing single particle analysis (SPA) algorithms originally developed for cryo-electron microscopy (EM). Template-based methods 7, 8 are computationally efficient, however, they are susceptible to template bias artefacts. Methods derived from SPA for cryo-EM have previously been adapted 9, 10 and employed to generate 3D volumes from 2D projection data. These approaches are, however, intrinsically 2D to 3D, as they assume that the raw data are projections. Recently, Shi et. al 11 also described a structure-specific method for 3D fusion, although they implicitly assume cylindrical particles and projected the volume onto top views only.