DNA-PAINT MINFLUX nanoscopy

MINimal fluorescence photon FLUXes (MINFLUX) nanoscopy, providing photon-efficient fluorophore localizations, has brought about three-dimensional resolution at nanometer scales. However, by using an intrinsic on–off switching process for single fluorophore separation, initial MINFLUX implementations have been limited to two color channels. Here we show that MINFLUX can be effectively combined with sequentially multiplexed DNA-based labeling (DNA-PAINT), expanding MINFLUX nanoscopy to multiple molecular targets. Our method is exemplified with three-color recordings of mitochondria in human cells.

fluorophore does not need to be intrinsically switchable or activatable, bright and stable fluorophores can be employed.
As it typically uses widefield illumination and recording with a camera, establishing the 'on/off ' state contrast in DNA-PAINT is challenged by the 'background' fluorescence from diffusing ('off ' state) imager strands. This is particularly true when the desire to increase imaging speed calls for high concentrations of diffusing imager strands. As a result, most cellular DNA-PAINT recordings are performed in the total internal reflection fluorescence or highly inclined and laminated optical mode 15,16 .
We reasoned that by combining DNA-PAINT with MINFLUX recording, we could synergistically benefit from the advantages of both methods. As in the current MINFLUX nanoscopy implementations, the 'background' fluorescence stemming from diffusing imager strands is suppressed by the confocal pinhole, DNA-PAINT MINFLUX nanoscopy can be used in the far-field mode. DNA-PAINT MINFLUX nanoscopy is expected to provide the same single-digit nanometer resolution as conventional MINFLUX nanoscopy. As the state-switching kinetics are determined by the binding of an imager strand to a docking strand, no dedicated buffer systems are required and the kinetics can be adapted to the density of the targets by tuning the concentration of the imager strand. As in conventional MINFLUX nanoscopy using photoswitchable dyes, also in DNA-PAINT MINFLUX nanoscopy the individual localizations are recorded one by one. Thus, the imaging time scales with the number of targets, making single-beam scanning MINFLUX particularly suited for recording small regions of interest. An intrinsic benefit of using PAINT is the fact that when densely packed molecules are imaged, successive fluorophore docking avoids the interaction of fluorophores belonging to neighboring target molecules. Hence coactivation and mutual fluorophore quenching is largely avoided. Finally, as multiple orthogonal imager strands can be applied sequentially, each binding to a different docking strand (Exchange DNA-PAINT) 17 , addressing multiple targets should also be straightforward. For an overview of synergies, see Extended Data Fig. 1.
To establish DNA-PAINT MINFLUX nanoscopy, we first systematically explored the influence of the experimental key parameters laser power, confocal pinhole diameter and imager strand concentration on the image quality and the recording speed. Specifically, we determined the influence of these three parameters on (1) the time between valid events (t btw ), (2) the background emission frequency (f bg ), which is determined by the microscope, (3) the center-frequency ratio (CFR), a filter parameter for localizations during image acquisition 4 and (4) the localization precision (σ r ). These parameters together provide a measure of the image quality, the average success of the localization process and the time for

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recording a DNA-PAINT MINFLUX image. For a description of the detailed analysis, see Supplementary Notes. In brief, we found that in DNA-PAINT MINFLUX imaging a sufficiently low imager strand concentration is a key determinant of the localization precision; a too low imager strand concentration, however, increases t btw , and thereby the overall recording time. Reducing background by decreasing the pinhole diameter improves the localization precision. Conversely, a smaller pinhole increases t btw , ultimately requiring the identification of an optimal pinhole size. The localization precision scales with increasing laser intensity. At the available laser intensities, we did not observe a relevant effect on t btw . The CFR proved to be an easily accessible and reliable indicator for the expectable localization precision within an experimental series. For measurements with Atto 655 bound to the imager strand, the analysis suggested as a good starting point an excitation laser power (at 640 nm) of roughly 62 µW in the sample for the first MINFLUX iteration, a pinhole diameter of 0.4 Airy units (AU) and, for proteins with an overall density similar to nuclear pore proteins, an imager strand concentration of 2 nM. Using these parameters, we first recorded two-dimensional (2D) DNA-PAINT MINFLUX images of various cellular structures exhibiting different densities of the target proteins (Fig. 1). To this end, chemically fixed genome-edited U2OS and HeLa cell lines, endogenously expressing fusions of a host protein and a fluorescent protein, were used. The fluorescent proteins were decorated with a nanobody featuring a docking strand. Confocal overview images recording the fluorescent protein fluorescence were used to identify smaller regions that were subsequently imaged by MINFLUX nanoscopy. As the cell lines expressing TOM70-Dreiklang (mitochondrial outer membrane), Nup96-GFP (subunit of the nuclear pore complex) and Vimentin-rsEGFP2 (vimentin cytoskeleton) exhibited a moderate target protein density, we chose an imager strand concentration of 2 nM. For the Zyxin-rsEGFP2 expressing cells that exhibited a slightly less dense distribution of target proteins, we chose 2.5 nM imager strand. For all images, the localization precision (σ r ) of an individual localization event was in the range of 2.4 to 2.7 nm (Supplementary Table 1 and Extended Data Fig. 2); note that the images display all recorded valid localization events (Fig. 1). As previously demonstrated, the individual localizations of single binding events can also be combined 7 , resulting in higher nominal localization precisions of 0.8 to 1.1 nm (σ rc ) (Supplementary Table 1). The localization precisions achieved with DNA-PAINT MINFLUX were comparable to the localization precision achieved when using the photo-switching of Alexa Fluor 647 for MINFLUX nanoscopy (σ r =3.0 nm; σ rc =1.4 nm) ( Fig. 1e and Supplementary Table 1).
To investigate whether DNA-PAINT MINFLUX nanoscopy is indeed suitable for addressing densely packed protein distributions, we imaged U2OS cells in which the abundant nonhistone chromatin protein HMG-I/Y was endogenously tagged with the fluorescent protein rsEGFP2. An imager strand concentration of 0.5 nM enabled recordings of the distribution of HMG-I/Y (Fig. 1c) with a localization precision (σ r ) of 2.3 nm (Supplementary Table 1 and Extended Data Fig. 2).
Cryo-electron tomography of in vitro reconstituted vimentin filaments suggested the assembly of four-stranded protofibrils with a right-handed supertwist 18 . In parts of the DNA-PAINT MINFLUX recorded filaments we indeed identified patterns that were highly suggestive of a twist, whereas in other parts this was not obvious (Fig. 1f). To determine whether insufficient sampling of localization events was causing these differences in the visibility of twists, we analyzed the accumulated localizations at different time points during a prolonged DNA-PAINT MINFLUX recording. Visual inspection suggested that in the first 4-5 hours of the DNA-PAINT MINFLUX recording new localizations continuously enhanced the vimentin imaging, while after 6-7 hours, new localizations did not add to the vimentin structure (Extended Data Fig. 3). This impression

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was fully in line with a Fourier ring correlation (FRC) analysis 19 of the images recorded at the different time points. After 6-7 hours, the FRC resolution value reached a plateau (Extended Data Fig. 3). We conclude that most of the accessible binding sites had been captured, and that a prolongation of the recoding time would not have improved the recording further. We also note that the progression of the FRC resolution values could be used as an abort criterion to determine the endpoint of DNA-PAINT MINFLUX recordings.
So far, all MINFLUX recordings were restricted to at most two-color channels. To demonstrate three-channel DNA-PAINT MINFLUX nanoscopy, we decorated TOM70-Dreiklang expressing cells with an anti-GFP nanobody conjugated to a docking strand, whereas the inner membrane proteins Mic60 and the subunit beta of the F 1 F O -ATP synthase (ATP5B) were labeled using specific antibodies. The three-dimensional (3D) MINFLUX imaging of the three channels was performed sequentially by adding and washing out the respective imager strands. The obtained localizations were rendered in three dimensions and overlayed (Fig. 2). The resulting 3D localization precision for all three target proteins was roughly 5.4 nm (σ r ) and 3.1 nm (σ z ) (Supplementary Table 1). When the individual localizations of single binding events were combined 7 , we achieved localization precisions of roughly 2.0 nm (σ rc ) and 0.8 nm (σ zc ) (Supplementary Table 1).
Altogether, this study quantified the influence of the laser power, pinhole size and imager strand concentration on the image quality, thereby narrowing down the parameter space for future DNA-PAINT MINFLUX applications (Supplementary Notes). Since fluorescence microscopes render nothing but the fluorophores in the sample, the concept of optical resolution can only be applied to the fluorophores. To be able to draw meaningful conclusions about the target molecules at the <5 nm scale, the size and mobility of the linker between the molecule and the fluorophore have to be taken into account. To fully harness the nanometer optical resolution potential of MINFLUX nanoscopy, these sample parameters deserve further attention and improvement. In addition to the size of the label, the completeness of the labeling and the fraction of fluorophores that can be successfully localized must also be taken into account. DNA-PAINT MINFLUX makes it possible to localize each binding site several times. Therefore, missing localizations due to premature bleaching of the fluorophore are avoided with this technique.
Compared to initial MINFLUX implementations that relied on the popular STORM dyes Alexa Fluor 647, CF660C and CF680 as switchable fluorophores, (multicolor) DNA-PAINT MINFLUX nanoscopy is simpler to apply, as it avoids the use of complex buffer systems and the need to adjust to different blinking kinetics of the fluorophores in use (for a detailed comparison of the concepts, see Extended Data Fig. 1). The MINFLUX localization process remains unchanged compared to previous implementations. Therefore, DNA-PAINT MINFLUX nanoscopy provides the same unbiased, high-precision localization demonstrated in previous studies 2, 3 . Finally, we note that by multiplexing DNA-PAINT labeling through the application of multiple orthogonal strands, our study paves the way for 3D MINFLUX imaging with nanometer resolution within cells with n > 3 channels.

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Sample preparation. The cells were cultured for 1 day on cover slips (Marienfeld) or in eight-well chambered cover slips (ibidi) and fixed in prewarmed 8% formaldehyde in PBS for 10 min. Cells were identified and placed in the focus using the 488 nm confocal scan of the microscope. If necessary, the persistent binding-unbinding activity of imager strands was verified in the 642-nm confocal scan. Before starting a MINFLUX measurement, the stabilization system of the microscope was activated. Measurements were conducted with a stabilization precision of typically below 1 nm. A region of interest was selected in the confocal scan image and laser power and pinhole size were adjusted in the software (indicated pinhole sizes in AU refer to the emission maximum of Atto 655 at 680 nm). For MINFLUX measurements of Alexa Fluor 647 (Fig. 1e) a laser power of 12 µW in the first iteration and a pinhole diameter of 0.6 AU were used. Finally, the MINFLUX measurement was started in the region of interest.
Quantification measurement series. In a measurement series (Supplementary Notes) one of the experimental parameters, namely laser power, pinhole size or imager concentration, was varied, while the other parameters were kept constant. Within one measurement series, we recorded 2D MINFLUX images of labeled nuclear pores close to the cover slip and kept the image size and the recording time (1 h) constant. All images were taken with the same MINFLUX iteration sequence. Multiple regions (1 × 1 µm) of the lower envelope of one nucleus were measured. Each region was imaged with a different experimental parameter. Each measurement series was repeated three times on different days with fresh samples.
Daily alignment of the MINFLUX nanoscope. The shape of the intensity pattern ('donut') for fluorescence excitation was evaluated using immobilized fluorescent beads (GATTA-BEAD R, Gattaquant GmbH) and if necessary optimized by changing the spatial light modulator parameters. Additionally, the position of the pinhole was adjusted so that the confocal detection matched the excitation volume. If during measurement series more than one pinhole size was used, all pinhole positions were determined before starting the measurement series. The pinhole position was then adjusted before each measurement.
MINFLUX data analysis. Data export. Each MINFLUX measurement was exported using Imspector Software (Abberior Instruments). The exported files contained a collection of recorded parameters for all valid localizations and also included discarded nonvalid localization attempts. Additional information of the measurement (laser power and so on) was stored manually. Both were imported in a custom analysis script written in MATLAB (R2018b) to calculate the following quantification parameters in an automated manner.
Quantification. For all calculations, only data of the last MINFLUX iterations (in two dimensions fourth, in three dimensions nineth, after one prelocalization iteration), which were also identified as valid (exported parameter VLD = 1), were used.
The first quantification parameter to be calculated was the time that passed between the localization of two valid events, in short, the time between events or t btw . An emitting molecule is usually localized by the microscope several times in direct succession by repeating the last two MINFLUX iterations. These successive localizations are assigned to the same event via the same trace ID (exported parameter TID). Moreover, for each individual localization the time at which its localization process started was saved (exported parameter TIM). This allowed the determination of the start and end time of each molecule binding event. Each event (TID) was terminated after a predefined number of nonvalid localization attempts. The time of the first final nonvalid localization attempt was defined as the end time of the molecule binding event. Finally, t btw was calculated as the time difference between two consecutive valid events by subtracting the end time of the first molecule from the start time of the second molecule. For each measurement, the median of the first 100 events was determined as t btw .

On-time (TIM 5 -TIM 2)
Time elapsed between valid events  t Time between molecule binding events t btw calculated from the exported measurement parameters. Saved localization attempts are depicted as colored rectangles, arranged in order of their appearance. Valid localization attempts were saved with the exported parameter VLD = 1 and are shown as green, while the nonvalid localization attempts were saved with VLD = 0 and are shown in yellow. The beginning of a localization attempt is saved as a time stamp (exported parameter TIM), here shown simplified as dimensionless values from 1 to 10. Localization events belonging to the same molecule have the same trace ID (exported parameter TID). Here, the time between the two consecutive valid molecules is calculated as the time difference between the start of molecule 4 (TIM = 7) and the end of molecule 2 (TIM = 5).
The second quantification parameter was the background emission frequency (f bg ). The f bg is continuously estimated by the MINFLUX microscope between valid events and is used by the system to identify emission events and to correct emission frequencies of localization events.
The third quantification parameter was the CFR. The CFR is the ratio of the effective emission frequency at the central position of the MINFLUX excitation pattern over the mean effective emission frequency over all outer positions and defined as CFR = f eff (central position)/f eff (outer positions). The effective

Brief CommuniCation
NATUrE METHODs frequencies f eff are the measured emission frequencies above a background automatically determined by the system. The value of the CFR is regarded as a quality measure for the localization process. For each measurement, the median CFR of all valid localizations in the last iteration was determined. The CFR is calculated directly by the microscope software and is also used for filtering in early iterations (exported parameter CFR). It therefore directly influences the measurement 4 .
To estimate the localization precision of a measurement as the third quantification parameter, the standard deviation σ r was calculated for each molecule (at least five localizations with the same exported parameter TID) as /2 with the standard deviations of the x and y coordinates as determined by the microscope (exported parameter POS). The median σ r represents the stated localization precision. The combined localization precision was estimated as σrc = ⟨⟨σr⟩ / √ n⟩ n , that is the weighted average of the average single localization precision σ r divided by √n and weighted by the occurrence of n being the number of single localizations with the same TID. The precision in the z direction is often different from x and y, therefore we separately computed the combined localization precision in z: σzc = ⟨⟨σz⟩ / √ n⟩ n .
CFR simulation. The CFR is a parameter that is directly calculated during image acquisition by the MINFLUX software. To understand and judge the CFR values from the experimental results we simulated the CFR dependency on pinhole size and imager strand concentration for a molecule that is located at the center of the MINFLUX targeted coordinate pattern (TCP) with background contributions included (Supplementary Notes and Supplementary Fig. 3). The excitation PSF hexc(x, y, z) in shape of a 2D donut was determined via fast focus field calculations 24 for high numerical apertures and using realistic values for the objective lens properties as well as an excitation wavelength λ exc = 642 nm. The confocal detection PSF h det (x,y,z) was calculated 25 for a detection wavelength of λ exc = 680 nm. We then calculated the resulting effective PSF h eff,i = hexc,ih det for each exposure i by shifting h exc to the according exposure position in the MINFLUX TCP while keeping the confocal detection h det centered. The background contribution due to diffusing imager strand was calculated in two steps. The resulting background intensity B i in the effective excitation volume was calculated as Bi ≈ ∫ x,y,z h eff,i (x, y, z) × cimagerdxdydz for each exposure. For the CFR calculation, we assumed that the central donut exposure of the MINFLUX TCP is placed directly on the molecule, chosen here as the origin. In the case of a perfect donut zero, this leads to a detected emitter intensity of I center = 0 for this exposure. The signal intensity detected at different exposures is calculated as Ii ≈ h eff,i (0, 0, 0). Correcting for the different total time spent in the inner and outer exposures, the mean background intensity B outer and mean signal intensity Ī outer was calculated for the outer exposures (i ̸ = 1). Therefore, we were able to calculate the CFR as CFR = Bcenter+Icenter ⟨Bouter+Īouter⟩ for different scenarios. We repeated the calculations for different concentrations c, adapted the pinhole size when determining h det and used different values for the TCP diameter L.
Sample drift correction. Sample drift was corrected from the extracted molecule event position and time pairs by dividing the events into overlapping time windows of approximately 2,000 events per window, and generating a 2D or 3D rendered MINFLUX image (placing a Gaussian peak with standard deviation sigma of 2 nm at each estimated molecule position) and calculating 2D or 3D cross-correlations between images from different time windows. The center of the cross-correlation peak was fitted with a Gaussian function and its offset relative to the center of the cross-correlation presented the spatial sample shift between the corresponding time points. The drift curve that fulfilled all possible sample drift estimations for all possible time window pairs was estimated in a least squares sense. A smooth (cubic spline) interpolation of the estimated drift curve for all time points of all events was then subtracted from the molecule coordinates. Table 1 and Extended Data Fig. 3 we implemented the algorithm described in ref. 19 . In brief, a dataset of combined localizations (only x and y positions) was divided into two statistically independent subsets resulting in two subimages, each containing 50% of the combined localizations of the original dataset. Then, the average correlation of the Fourier transform of these subimages was calculated on rings of constant spatial frequency. The inverse of the spatial frequency at which the FRC drops below one-seventh was taken as a measure of the FRC resolution. We used combined localizations instead of single localizations for the estimation of the FRC resolution, because for single localizations the FRC is dominated by the large number of repeated localizations during one binding event and the calculated FRC resolution is then strictly proportional to the single localization precision. To obtain a more robust result, the random division into subsets was repeated several times and the obtained FRC resolutions for each division were averaged.

FRC xy calculations. For the determination of the FRC shown in Supplementary
Image rendering in two dimensions. All valid localization events were rendered using Imspector Software and displayed as 2D histograms with the bin size 4 nm (Fig. 1a-f) and 1 nm (Fig. 1f, close-up).
Image rendering in three dimensions. Each MINFLUX measurement was exported with Imspector Software. The data were drift corrected (Sample drift correction) and the z position was scaled with the scaling factor 0.7 (ref. 3 ). A rendering of the resulting localizations where each localization was replaced by a Gaussian peak with sigma 5 nm was imported into the Imaris Software (Imaris x64, v.9.7.2, Bitplane AG). The data were displayed as a blend volume rendition.

MINFLUX sequences.
The MINFLUX microscope's data acquisition is controlled by a set of parameters that are specified within a text file (see seqIIF.json and seqDefaultIIF3d.json in the Supplementary Data). The set of parameters defines a sequence that controls the iterative zooming in on single molecule events and was provided and optimized by the manufacturer for samples with the dye Alexa Fluor 647. The MINFLUX iteration process is described in ref. 4 . In two dimensions, four iterations plus one prelocalization iteration were performed. In three dimensions, nine iterations plus one prelocalization iteration were performed. In the last iteration an L of 40 nm was used. Key parameters of the 2D iteration sequence include:

Statistics
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n/a Confirmed The exact sample size (n) for each experimental group/condition, given as a discrete number and unit of measurement A statement on whether measurements were taken from distinct samples or whether the same sample was measured repeatedly The statistical test(s) used AND whether they are one-or two-sided Only common tests should be described solely by name; describe more complex techniques in the Methods section.
A description of all covariates tested A description of any assumptions or corrections, such as tests of normality and adjustment for multiple comparisons A full description of the statistical parameters including central tendency (e.g. means) or other basic estimates (e.g. regression coefficient) AND variation (e.g. standard deviation) or associated estimates of uncertainty (e.g. confidence intervals) For null hypothesis testing, the test statistic (e.g. F, t, r) with confidence intervals, effect sizes, degrees of freedom and P value noted For manuscripts utilizing custom algorithms or software that are central to the research but not yet described in published literature, software must be made available to editors and reviewers. We strongly encourage code deposition in a community repository (e.g. GitHub). See the Nature Portfolio guidelines for submitting code & software for further information.

Data
Policy information about availability of data All manuscripts must include a data availability statement. This statement should provide the following information, where applicable: -Accession codes, unique identifiers, or web links for publicly available datasets -A description of any restrictions on data availability -For clinical datasets or third party data, please ensure that the statement adheres to our policy All DNA-PAINT MINFLUX localization data have been deposited at https://doi.org/10.5281/zenodo.6563100. The raw data as provided by the microscope software are available at https://doi.org/10.5281/zenodo.6562764