Global fitting for high-accuracy multi-channel single-molecule localization

Multi-channel detection in single-molecule localization microscopy greatly increases information content for various biological applications. Here, we present globLoc, a graphics processing unit based global fitting algorithm with flexible PSF modeling and parameter sharing, to extract maximum information from multi-channel single molecule data. As signals in multi-channel data are highly correlated, globLoc links parameters such as 3D coordinates or photon counts across channels, improving localization precision and robustness. We show, both in simulations and experiments, that global fitting can substantially improve the 3D localization precision for biplane and 4Pi single-molecule localization microscopy and color assignment for ratiometric multicolor imaging.

S ingle-molecule localization microscopy (SMLM) achieves nanometer superresolution and has become an important method for structural cell biology. Various extensions of SMLM using two or more detection channels are instrumental for this success, as they greatly increase the information content that can be extracted from samples: Multi-color SMLM imaging of proteins labeled with fluorophores of different color can probe their spatial relations and interactions. It is usually realized using two spectral channels [1][2][3] or one spatial channel combined with spectral detection in a second channel 4 . Three-dimensional (3D) SMLM techniques using two or more detection channels, such as biplane 5 or multi-plane 6 detection, self-bending point spread functions 7 (PSFs), supercritical-angle fluorescence detection 8,9 and multi-phase interference 10,11 , are powerful in investigating the intrinsic 3D organization of biological structures. Two or more fluorescence polarization channels are used to probe the orientation of fluorophores 12 , offering insight into the orientation of proteins in a molecular machinery. Recently, modulation enhanced localization microscopy that uses patterned excitation with rapid detection of different phases of the pattern on multiple parts of a camera, was used to increase the resolution of SMLM by a factor of two [13][14][15][16] .
Compared to the single-channel SMLM, data analysis for all these methods is complicated by the fact that measures from two or more channels have to be combined to result in the additional information (color, z-position, polarization state, interference phase, etc.). Typically, this is achieved by first fitting the fluorophores individually in each channel to extract corresponding parameters, and then combining the returned parameters from different channels to obtain the extra information [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] . Separate fitting of an individual fluorophore present in two channels is not optimal, as we neglect the information that the fitting parameters (e.g., 3D positions and photons) are highly correlated. If instead we were to use a global fitter that links the correlated parameters across different channels, this would decrease the number of fitting parameters, improve precision and robustness of the fit and avoid ambiguity when pairing corresponding parameters. Additionally, it would allow precise analysis of a fluorophore that is very dim in one of the channels and thus would escape molecule detection when fitted separately. Despite the many benefits of analyzing separate channels simultaneously, global fitting is not widely used for the multi-channel single molecule localization. First approaches for global fitting 17-20 lack flexibility with respect to the PSF models and fitting parameters. They are often designed for a specific imaging modality and difficult to be integrated into complete analysis workflows to be of general use. Deep-learning based SMLM data analysis software such as DECODE 21 or deepSTORM3D 22 , have outperformed conventional fitting-based software on singlechannel data, especially for dense activations beyond the singleemitter regime. However, extension to multi-channel analysis is challenging, as the complex transformations between the channels are not shift-invariant operators, and thus are difficult to be learned efficiently 23 for a fully convolutional neuronal network.
Here, we develop globLoc, a general data analysis workflow and easy to use software for global fitting of single molecule data detected in separate channels. Its optimized analysis pipeline includes: the generation of a precise transformation among the channels, calibration of a global multi-channel PSF, a GPU based global fitter that achieves maximum accuracy ( Supplementary  Fig. 1, 2 and 3) and ultra-fast fitting speed ( Supplementary Fig. 4), as well as post-processing routines to extract the additional information (z, color, interference phase, polarization, etc.). Both, in simulations and on experimental data, we show that global fitting indeed leads to a substantially improved localization precision for biplane and 4Pi-SMLM and color assignment in multicolor astigmatic SMLM.

Results
Workflow of globLoc. We now give an overview of the globLoc analysis workflow (Fig. 1). Details can be found in the Methods. We describe it on the example of dual-channel single molecule data. The extension to multi-channel data is straightforward. We first generate a global multi-channel experimental PSF model from image stacks of beads immobilized on a coverslip. To this end, we first calculate spline PSF models for each channel independently 24 and fit each channel individually with the corresponding PSF model to obtain the precise bead positions. From corresponding bead positions in the two channels, we calculate the transformation between the channels. We then use cubic interpolation to register and average many bead stacks 24 , while keeping the fixed spatial relationship between the channels described by the transformation. Optionally, we re-calculate the transformation based on the actual SMLM experiment to account for channel drift. For this, we fit a sub-set of single molecule data in each channel separately using the corresponding PSF model and calculate the transformation based on the fitted coordinates. Besides using an experimental PSF model, our software also supports global fitting with a Gaussian PSF model (Supplementary Software).
After calibration of the multi-channel PSF model and the transformation between different channels, the next step of the workflow is to perform global fitting to jointly analyze the multichannel data using maximum likelihood estimation (MLE). On a standard GPU (NVIDIA RTX3090), our implementation reached 35,000 fits/s for regions of interest (ROI) with a size of 13×13 pixels, while the speed was~1,000 fits/s on a CPU (Intel Core i7-8700, Supplementary Fig. 4). On simulated data for biplane SMLM, global fitting reached the Cramer-Rao-Lower-Bound (CRLB) in 3D over a large axial range (±600 nm, Supplementary  Fig. 1a, b).
Performance of globLoc on Biplane data. As globLoc is very flexible to link or unlink parameters between different channels, we compared the localization precision in the conditions of individual fit, global fit with only linking xyz positions and linking xyz positions plus photons per localization. Compared to individual fitting of the channels followed by CRLB-weighted averaging of positions 9 (Supplementary Note 1 and 2), globLoc achieved about 1.5 times better z localization precision ( Fig. 2a and Supplementary Fig. 1c) and more robust parameter estimation ( Supplementary Fig. 1d). This resolution improvement was further confirmed by participating in the continuously running 2016 SMLM Software Challenge 25 , in which globLoc improved the 3D localization precision by almost a factor of two on biplane data, compared to the second-best performing algorithm LEAP (Fig. 2b). Our own comparison on the training data set (simulated microtubules) showed a clear improvement compared to the popular SMLM analysis software ThunderSTORM 26 (Fig. 2c). The improvement of globLoc compared to ThunderSTORM was even more apparent when we analyzed experimental SMLM data of nuclear pore complex (NPC) protein Nup96, which we used as a reference standard 27 . In contrast to ThunderSTORM, globLoc was able to clearly resolve the two-ring structure of the NPC (Fig. 2d). This is likely not only due to a better localization precision, but also an improved robustness of the fit.
Performance of globLoc on 4Pi-SMLM data. GlobLoc is not limited to 2 channels. We implemented four-channel fitting for 4Pi-SMLM with multi-phase interference, using an advanced experimental 4Pi-PSF model that we developed recently 28 (Supplementary Note 3). By fitting all four phase images globally with such a spline-interpolated experimental PSF model, globLoc achieved the CRLB in all dimensions, and greatly improved precision as well as accuracy compared to the state-of-the-art analysis ( Fig. 3a and Supplementary Fig. 3). As for biplane data, we found that additionally linking the photon number between different channels improved the localization precision in z by up to 1.5 times compared to only linking xyz ( Supplementary Fig. 3). We also demonstrated the resolution improvement with experimental 4Pi-SMLM data of Nup96. The clusters, which represent the eight corners of the Nup96 within the nuclear pore complex, reconstructed by globLoc with all parameters linked are smaller than those from photometry and globLoc without linking photons (Fig. 3b).
Performance of globLoc on ratiometric multicolor SMLM data. Ratiometric multicolor SMLM images two or more dyes with overlapping emission spectra in two spectral channels and assigns the color of single molecules based on the relative number of photons detected in each channel ( Fig. 4a and Supplementary  Fig. 5a). It has many advantages over conventional multicolor superresolution imaging using dyes with well separated emission spectra 1,3,29 : (1) it has a negligible channel shift and chromatic aberration; (2) many of the best "blinking" dyes have similar emission spectra in the dark red range and are compatible with similar imaging conditions; (3) multi-color imaging can be performed simultaneously with one excitation laser. A key challenge for ratiometric color assignment is to precisely determine the photon number of the single molecules to distinguish their color. By using salvaged fluorescence reflected by the main excitation dichroic mirror, Zhang et al. have shown 3 color superresolution imaging of biological structures in 3D at 5-10 nm localization precision using 4Pi-SMS microscopy 3 . However, the salvaged fluorescence was only used for color assignment and did not contribute to the molecule localization.
Global fitting with globLoc improves the accuracy of determining the photons per localization ( Supplementary Fig. 2c) and thus the color assignment in both simulation and experiment (Fig. 4b, Supplementary Figs. 5, 6 and 7), while utilizing all detected photons for localization. To exploit our finding that linking photon numbers across channels increases the accuracy, we implemented a fitting approach in which globLoc fixes the relative photon numbers across the channels to different precalculated values and chooses the solution with the maximum likelihood ( Supplementary Fig. 6). This approach reduced crosstalk during color assignment and minimized rejection of single molecules with close intensity ratios. It also makes a postprocessing step for color assignment obsolete ( Supplementary  Fig. 7).
These innovations of globLoc enabled us to image and faithfully distinguish a record of 4 colors simultaneously in ratiometric 3D SMLM (Fig. 4c, Supplementary Fig. 8 and Supplementary Video 1) and image Nup96, Nup62, Elys and WGA within single NPCs labeled with the dyes AF647, DY634, CF660C and CF680 with no apparent cross-talk. We averaged 200 NPC images by registering the Nup96 structures that we used as a reference 30 . This protein density map shows the average positions of the four NPC proteins, with Nup96 forming two rings with an 8-fold symmetry, Elys forming a large ring and Nup62 and WGA localizing at the central channel of the pore. It is worth noting that these are the average distributions of the fluorophores, which can be different from the distribution of the epitopes due to linkage errors introduced by the size of the antibodies and their non-random orientations.
To demonstrate the performance of globLoc on an especially challenging sample, we performed ratiometric three color 3D imaging of the synaptonemal complex in C. elegans (Fig. 5a). Individual synaptonemal complexes could be clearly resolved in 3D (Fig. 5b)  complex, HTP-3, HIM-3 and the N-terminus of SYP-5, were well separated without visible cross-talk. The spatial arrangement of these 3 components were in well agreement with previous research [31][32][33] (Fig. 5c-f).
Taken together, we demonstrated the potential of globLoc on the challenging experiments such as 3 color and 4 color 3D super resolution imaging of various biological samples.

Discussion
To summarize, we demonstrated that linking shared parameters during multi-channel single molecule localization substantially improves localization accuracy and reduces color assignment crosstalk. globLoc not only improves the localization accuracy, but also increases the robustness of the fit compared to fitting multiple channels individually (Supplementary Fig. 1d and Supplementary Fig. 2d). This is important, as the information is split into different channels and the signal to noise ratio (SNR) is poorer in each individual channel, which results in a large error in the parameter estimation. As a result, globLoc could precisely reconstruct biplane and 4Pi-SMLM data over a large axial range and faithfully distinguished a record of ratiometric 4 color data imaged simultaneously.
Deep learning based SMLM analysis has been shown to greatly improve precision, especially for imaging data with a high density of single molecules 21,22 . However, these methods rely on welltrained networks, which need to be retrained for different imaging conditions, such as different SNR. For multi-channel data analysis, the situation is much more complex as different parameter linking schemes need be exploited for different imaging modalities (e.g., biplane, ratiometric multicolor). Furthermore, incorporating a shift-variant channel transformation operator to the convolutional neuron network (CNN) is still challenging as conventional CNN cannot learn the spatial information efficiently. In contrast, globloc is very convenient in terms of parameters sharing and flexible PSF modeling. It is capable to analyze different multi-channel data by easily incorporating the transformation function in the fitter. Therefore, deep learning-based algorithms are well suited for single-channel high-density data, whereas globLoc will be the method of choice for multi-channel data analysis of standard emitter densities.
In the continuously running SMLM Challenge 25 , globLoc improved the localization precision by almost a factor of 2 compared to the second-best software, showcasing the limited performance of current analysis software for multi-channel data. To allow anyone to directly and easily use the full functionality of globLoc (complete multi-channel calibration pipeline, versatile PSF model, flexible parameter sharing and fast fitting speed accelerated by GPU), we fully integrated it in SMAP 34 . In addition, we provide open-source example code in MATLAB and Python to allow simple and direct integration in custom software. We believe that globLoc will enable many groups to substantially improve their analysis workflows for multi-channel SMLM.

Methods
Calculation of multi-channel transformation. Global fitting of multi-channel data relies on knowing the precise transformation among the channels. We developed a routine to calculate transformations from coordinates (bead positions or positions of single fluorophores) that we used during the generation of the multi-channel PSF model and for global fitting of multi-channel single molecule data. We describe our algorithm for a two-channel transformation (referencex r and target channel x t ). A multi-channel transformation is represented as several two-channel transformations from all target channels to the same reference channel. Our algorithm is as follows (Fig. 1): 1. Obtain approximate transformation T 0 . This can be the transformation calculated in a previous experiment. Alternatively, we calculate it by first binning the coordinates in super pixels with a size of 50 nm. Then, we calculate the image cross-correlation and determine the position of the cross-correlation peak with sub-pixel accuracy from the position of the brightest pixel in a 4-fold upscaled image calculated by Gaussian filtering followed by cubic interpolation. The position of the cross-correlation peak corresponds to the shift between the channels, which we then use as T 0 . 2. We transform all target coordinates to the reference channel using T 0 : 3. We link coordinates in the reference and target channel if they are closer than a maximum distance ρ:x 0 t Àx r < ρ. For fluorophores from SMLM experiments we only link coordinates from the same frame. 4. We calculate the precise transformation T based on the linkedx r andx t as anchor points. Usually, we use a projective transformation where T is represented by a 3 3 matrix, but we can use all transformations supported by Matlab, e.g., polynomial transformations. 5. If necessary, we repeat steps 3 and 4 with reduced ρ.
Generation of multi-channel PSF models. Our algorithm to generate multichannel PSF models from bead stacks is an extension of our work on generating single-channel experimental PSF models 24 . Again, we illustrate the steps of our algorithm on the dual-channel example, an extension to N channels is straight forward (Fig. 1): 1. We find candidate bead positions in each channel by calculating the mean image over all z-positions, Gaussian filtering and finding of local maxima above a user-defined threshold. These candidate positions are integers in the unit of camera pixels. 2. If no transformation among the channels exists, we first generate singlechannel PSF models for each channel separately. We then fit the bead images using these new PSF models and finally use the fitted localizations to calculate T as described above. 3. We transform the coordinates of the candidate bead positions from the reference to the target channel:x 0 r ¼ Tx r . These target coordinates are continuous coordinates; thus we calculate the nearest integer pixel position by rounding the transformed coordinatesx 0 r Ä Å and calculating the shift between the rounded and original transformed coordinatess ¼x 0 r Àx 0 r Ä Å . 4. We cut out ROIs aroundx r andx 0 r Ä Å out of the bead stacks and shift the ROIs of the target channel bys using cubic interpolation. If the target channel is mirrored with respect to the reference channel, we mirror the target ROI. This ensures that beads in both channels are shifted in the same direction during registration. Finally, we concatenate image stacks in both channels to form a single 3D array. 5. We create an initial template by averaging the 3D arrays over all beads and use 3D cross-correlation to register all beads to this template. 6. We reject those beads that have an insufficient overlap with the template (quality control) and calculate the next template as the average of the remaining shifted beads. We then register the central part of each bead to the new template. 7. We normalize the beads by the sum of the central slice of the reference stack.

ELYS-CF660C
Nup62-DY634 WGA-CF680 x-y 8. We slightly filter the PSF models in z with a smoothing bspline and calculate a cspline representation for each channel. 9. To validate the PSF calibration, we fit each bead in the bead stack and compare the fitted z position with the true z position as denoted by the frame in the image stack.
Extraction of multi-channel single molecule data. We implemented the workflow for global fitting of single molecule blinking events in the following way (again illustrated for two channels): 1. We calculate the global PSF model as described above from bead stacks. 2. Optionally, especially if we did not acquire bead stacks on the same day as the SMLM measurements, we calculate an improved transformation by fitting single molecule localizations in each channel independently and then using these localizations as anchor points to calculate T as described above. Otherwise, we use the transformation from the bead calibration. 3. We find candidate peaks in all channels using a difference of Gaussian filter and maximum finding. We then transform all candidates back to the first channel and average close-by candidate positions to obtain the coordinates of the candidates in the reference channel. Finally, we round to the nearest integer pixels to obtainx r . 4. As described for the beads, we transform the candidate positions to the target channelsx 0 r ¼ Tx r and calculate the shift between the rounded and original transformed coordinatess ¼x 0 r Àx 0 r Ä Å . 5. Then we cut out ROIs aroundx r andx 0 r Ä Å . If the two channels are mirrored, we additionally mirror the ROIs ands.
Maximum likelihood estimation of multi-channel single molecule data. We use a maximum likelihood estimator that jointly optimizes the combined likelihood across different channels. The objective function for MLE across different channels is given by: Here, M ki is the measured photon number in the kth pixel of the ith channel. μ ki is the expected photon number in the kth pixel of the ith channel. Similar to previous implementations 24  optimization process, the parameters can be classified as either shared (global) or non-shared (local) parameters, (θ 2 ðθ p ; θ qi ). Here, θ p is the set of global parameters and θ qi is the set of local parameters of ith channel. The global parameters appear in all channels while the local parameters appear only in the individual channel. Depending on the imaging modality, any fitting parameter θ (x, y, z/σ PSF , photons, background) can be either linked as a global parameter among the channels or treated as a local parameter with different values in each channel. For global parameters, we define a transformation function to link parameters of different channels (translation and scale). The shared parameter in the ith channel can be written as: θ pi ¼ S pi θ p þ 4θ pi : Here, S pi and 4θ pi are the scaling and translation factor, respectively. In this work, 4θ xi and 4θ yi are defined as the shifts s between the transformed ROI position and the actual ROI position which is rounded to integer pixels, as defined in item 4 of the section: Extraction of multichannel single molecule data. The ratio of the photons between different channels S Ni , used for fixed photon ratio fitting, is determined from experimental single molecule data as the mean of the detected photons per localization for each dye. Therefore, the first derivative for a global parameter θ pi in the ith channel is given by: The first derivative for a local parameter θ qj in the ith channel is 0 when i is not equal to j: Therefore, the Jacobian matrix can be defined as: The Hessian matrix is defined as: In the L-M algorithm, we updated the parameters by solving the linear equations: ðH þ λIÞ4θ ¼ J, with λ the damping factor and I a diagonal matrix equal to the diagonal elements of the Hessian matrix. The detailed algorithm can be found in Supplementary Note 4. Depending on different fitting modalities, we then calculate parameters of interest (e.g., color, polarization or z-position) from the fitted parameters (e.g., number of photons in each channel). Finally, we perform the usual post processing steps such as merging of localizations persisting over consecutive frames, drift correction and filtering based on log-likelihood and localization precision.
Simulation and analysis of multi-channel data with experimental PSF models. For biplane data simulation ( Fig. 2a and Supplementary Fig. 1 For the ratiometric astigmatic simulation ( Supplementary Fig. 2, Supplementary  Fig. 5 and Supplementary Fig. 6), a dual channel astigmatic experimental PSF acquired from multicolor beads was used. The photon distribution of these 4 different dyes were used for simulation: DY634, AF647, CF660C and CF680. The ratio of photons between two channels for the different dyes was determined from experimental data corresponding to Fig. 4c as the mean of the detected photons per localization for each dye. We found photon ratios of I 2 =I 1 ¼ 0.39, 0.21, 0.07 and 0.02 for DY634, AF647, CF660C and CF680, respectively. Here, I 1 and I 2 are the photons from the bright and dark channels, respectively. For comparison of localization accuracy and CRLB ( Supplementary Fig. 2), the photon ratio of 0.25 was used. 1,000 molecules with a ROI size of 15 × 15 pixels at each z position were used to calculate the RMSE. For ratiometric color separation ( Supplementary Fig. 5 and Supplementary Fig. 6), 50,000 single molecules were randomly placed at axial positions between −600 and 600 nm. The photon distribution of each dye follows the distribution of the experimentally acquired single molecules ( Supplementary   Fig. 6a). Three different methods were used to determine the color information: (1) The dual channel data was fitted separately; (2) The dual channel data was fitted globally with x, y and z as global parameters, photons and background as local parameters; (3) The dual channel data was fitted globally with x, y, z and photons as global parameters, background photons as shared parameter. The ratio of the photons between different channels was fixed during fit. For the first two methods, the color discrimination was realized by thresholding the normalized photon ratio: ðI 1 À I 2 Þ=ðI 1 þ I 2 Þ. For the third method, the dual channel data was fitted with different fixed and pre-determined photon ratios of all 4 dyes between the two channels and we then chose the solution with the maximum likelihood.
For 4Pi single molecule data simulation ( Supplementary Fig. 3), 2000 photons/ localization and 20 background photons/pixel were used for each objective. A full vectorial PSF model 37 was used for simulations with the following parameters: NA 1.35, refractive index 1.40 (immersion medium and sample) and 1.518 (cover glass), emission wavelength 668 nm, astigmatism 100 mλ. 1000 4Pi single molecule images with a ROI size of 15 × 15 pixels were simulated at each z position with four phase channels (0, π/2, π, 3π/2). The x and y positions are randomly distributed within −1 to 1 pixels around the center of each ROI. The simulated 4Pi single molecule data was then fitted with three different approaches: (1) global fit using IAB-based 4Pi-PSF model with x, y, z, phase, photons and background photons shared; (2) global fit using IAB-based 4Pi-PSF model with x, y, z and phase, parameters shared; (3) photometry based methods 11 .
GPU implementation of globLoc and speed evaluation. We implemented the globLoc fitter with both spline and pixelated Gaussian PSF model 38 using CUDA C/C++ in NVIDIA CUDA®-enabled graphic cards. The framework of the L-M iterative fitting method follows the previous work 24 . Each thread is pointed to a multi-channel single-molecule data and performs the entire fitting process for each single molecule. We put the single-molecule data in the global memory of the GPU and employed 64 threads for each block for the computation. Both the CPU and GPU based C++ code were compiled in Microsoft Visual Studio 2019 and called via Matlab 2019a (Mathworks) MEX files. For speed evaluation ( Supplementary  Fig. 4), we ran the CPU code on a personal computer using an Intel Core i7-8700 processor clocked at 3.2 GHz with 16GB memory. For the GPU-based evaluation, an NIVDA GeForce GTX 3090 graphics card with 24.0 GB memory was used.
State-of-the-art workflows used for comparison. For biplane data analysis, we compared globLoc with the widely used ThunderSTORM software 26 . In the ThunderSTORM biplane analysis pipeline, a homography transformation is constructed from paired coordinates of the two channels. The biplane data is then fitted simultaneously using an astigmatic Gaussian PSF model. The detailed parameters used are shown in Supplementary Fig. 9 and Supplementary Table 1. For ratiometric multi-color assignment, we also compared to a workflow similar to that presented by Lehann et al ( Supplementary Fig. 8) 29 . In short, localizations are fitted separately in the two channels. We then construct the transformation as described above and associate corresponding localizations in the two channels. Color assignment is then based on the relative fitted photon numbers.
Cell culture. Before seeding of cells, high-precision 24 mm round glass coverslips (No. 1.5H, catalog no. 117640, Marienfeld) were cleaned by placing them overnight in a methanol:hydrochloric acid (50:50) mixture while stirring. After that, the coverslips were repeatedly rinsed with water until they reached a neutral pH. They were then placed overnight into a laminar flow cell culture hood to dry them before finally irradiating the coverslips by ultraviolet light for 30 min.
Cells were seeded on clean glass coverslips 2 days before fixation to reach a confluency of about 50 -70% on the day of fixation. They were grown in growth medium (DMEM (catalog no. 11880-02, Gibco)) containing 1× MEM NEAA (catalog no. 11140-035, Gibco), 1× GlutaMAX (catalog no. 35050-038, Gibco) and 10% (v/v) fetal bovine serum (catalog no. 10270-106, Gibco) for approximately 2 days at 37°C and 5% CO 2 . Before further processing, the growth medium was aspirated, and samples were rinsed with PBS (RT) to remove dead cells and debris. Unless otherwise stated, all experimental replicates were performed on cells of a different passage with separated sample preparation.
Preparation of four-color NPC samples. Cells (Nup96-SNAP-tag, catalog no. 300444, CLS Cell Line Service, Eppelheim, Germany) on glass coverslips were prefixed in 2.4% (w/v) Formaldehyde (FA, 28906, ThermoFischer Scientific) in PBS for 20 s before incubating them 10 min in 0.5% (v/v) Triton X-100 in PBS. Fixation was completed in 2.4% (w/v) FA in PBS for 20 min. FA was quenched for 5 min in 100 mM NH 4 Cl in PBS and then washed 3 × 5 min in PBS. Fixed cells were blocked with Image-IT signal enhancer for 30 min and then incubated with 1 µM BG-AF647(#S9136S, New England Biolabs), 0.5% BSA and 1 mM DTT(Dithiothreitol) in PBS for 1 h to stain Nup96-SNAP-tag. Cells were washed 3x for 5 min with PBS and subsequently blocked with 5% (v/v) NGS (normal goat serum, catalog no. PCN5000, lifeTech) in PBS for 1 h. Primary antibody labeling against ELYS was achieved by incubation with rabbit anti-AHCTF1 primary antibody(HPA031658, Sigma-Aldrich) diluted 1:40 in 5% (v/v) NGS in PBS for 1 h. Coverslips were washed 3 times for 5 min with PBS to remove unbound antibody and subsequently stained with CF660C labeled goat anti-rabbit antibody (20183, Biotium, Fremont, CA) diluted 1:150 in PBS containing 5% (v/v) NGS for 1 h. After 3 washes with PBS for 5 min, the sample was postfixed for 30 min using 2.4% (w/v) FA in PBS, rinsed with PBS, quenched in 50 mM NH 4 Cl for 5 min and rinsed 3 × 5 min with PBS. Labeling against Nup62 was performed by incubation with mouse anti-Nup-62 primary antibody (610498, BD Bioscience) diluted 1:50 in 5% NGS/PBS for 2 h, 3x 5 min washes of the coverslips with PBS and incubation over night at 4degC with 1:150 diluted secondary donkey anti-mouse-DY634 antibody in 5%NGS/PBS. Unbound antibody was removed from the sample by washing 5 times with PBS. All incubations except otherwise stated were carried out at RT. Buffers used were also pre-equilibrated to RT.
Shortly before imaging, the sample was incubated for 10 min with 1:5000 diluted WGA-CF680 (29029-1, Biotium, Fremont, CA) in 100 mM Tris, pH 8.0, 40 mM NaCl, rinsed 3x with PBS and mounted onto a custom manufactured sample holder in imaging buffer. The holder was sealed with parafilm.
Preparation of DY634-labeled secondary anti-mouse antibody. 50ul of donkey anti-mouse IgG (H+L) (1,3 mg/ml) (715-005-151, Dianova) was incubated with a 10-fold molar excess of DY634-NHS (634-01, Dyomics) in a final volume of 100ul PBS pH 7,4 overnight at RT. The labeled antibody was purified from free dye by running over an PBS equilibrated Zeba Spin desalting column (89889, Thermo Scientific) by gravity flow. Fractions containing the peak of the labeled antibody were identified by SDS-PAGE and pooled.