Single-molecule fluorescence localization with minimum photon flux imaging (MINFLUX) can achieve localization precisions in the small nanometer range or better under suitable conditions. Potentially adverse conditions, such as a fixed fluorescence dipole or optical aberrations, that could cause systematic localization errors, have received little attention up to now. Here, we study these effects in simulation. We find that biases occur for fluorophores with a fixed absorption dipole tilted out of the imaging plane. These become larger (up to about 25% of the diameter of the circle spanned by the doughnut center positions), the larger the tilt angle gets. As a rule of thumb, the spread in bias is smaller than 5 nm in case the dipole orientation is less than 30° out of plane for the typical case of a doughnut probing circle of diameter 100 nm. For freely rotating dipoles, only the primary aberrations, astigmatism and coma, contribute to bias. This bias depends on the position of the fluorophore inside the circular probing area of MINFLUX and can be significantly larger than the localization precision. We show that increasing the number of measurements over the circle from a triangular to a hexagonal pattern is beneficial for reducing bias in all cases. Iterative shrinking of the probing area can eliminate the position-dependent bias completely, but a strong dependence on dipole orientation of the bias at the center of the probing area remains.

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.

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.

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.