We present a fundamentally new approach to 3D superresolution microscopy based on the principle of surface-generated fluorescence. This near-field fluorescence is strongly dependent on the distance of fluorophores from the coverslip and can therefore be used to estimate their axial positions. We established a robust and simple implementation of supercritical angle fluorescence detection for single-molecule localization microscopy, calibrated it using fluorescent bead samples, validated the method with DNA origami tetrahedra, and present proof-of-principle data on biological samples.
© 2014 Optical Society of America
Single-molecule localization-based superresolution microscopy (localization microscopy: Photoactivated Localization Microscopy, PALM ; Stochastic Optical Reconstruction Microscopy, STORM ; Fluorescence Photoactivation Localization Microscopy, FPALM ) has been a major breakthrough for cell biology, since it improves the resolution of fluorescence microscopy by an order of magnitude, reaching a lateral resolution comparable to that of electron microscopy. However, obtaining structural information on multi-protein complexes in the cellular context often requires an axial resolution on a similar scale.
Currently, two general approaches allow for three-dimensional resolution in localization microscopy. On one hand, the z position of single emitters can be determined from the shape of the point spread function (PSF) either by imaging two focal planes (bi-plane ) or after PSF engineering (e.g. astigmatic PSF , double helix PSF , self-bending PSF ). Nevertheless, the axial resolution is usually worse than the lateral one, which itself is compromised by the modification of the PSF. On the other hand, the z position can be extracted from relative intensities of single-molecule images when employing an interferometric detection scheme (iPALM , 4Pi-SMS ), reaching unprecedented z resolution. Unfortunately, such interferometric microscopes are very difficult to built and cumbersome to use.
Here we present a fundamentally different way of achieving 3D resolution in localization microscopy without significant loss in lateral resolution, called supercritical angle localization microscopy (SALM), which is based on the principle of surface-generated fluorescence. Surface-generated fluorescence occurs when a fluorophore is in the vicinity of an interface with different refractive indices, such as the water – coverslip interface. This fluorescence is emitted into large angles above the critical angle and is therefore also called supercritical angle fluorescence  (Fig. 1(a)). Its intensity depends approximately exponentially on the distance of the fluorophore from the interface (Fig. 1(b)). Supercritical angle and far-field undercritical angle fluorescence are radially separated in the back focal plane (conjugate plane) of a high numerical aperture (NA) microscope objective and can thus be easily detected individually (Fig. 1(c)).
This principle has been exploited previously in conventional fluorescence microscopy. For example, blocking of undercritical angle fluorescence leads to optical sectioning in microscopy [11–13] and fluorescence correlation spectroscopy , with a confinement similar to total internal reflection fluorescence (TIRF) microscopy. By separately imaging supercritical angle emission and undercritical angle emission, objects such as beads or biological membranes can be axially localized with nanometer accuracy in sample-scanning microscopy  and wide-field microscopy .
Here we apply a detection scheme that separates super- from undercritical angle fluorescence to infer the axial position of single fluorophores, and thereby achieve three-dimensional superresolution microscopy with a simple to implement and robust to operate optical setup.
2. Supercritical angle localization microscopy
Localization microscopy relies on stochastic blinking of single fluorescent molecules. As their brightness fluctuates dramatically, measuring the number of photons in the supercritical angle region alone does not give sufficient information on the emitter’s axial position. However, simultaneous imaging of supercritical and undercritical angle emission in two channels in a ratiometric approach allows normalizing the supercritical to the undercritical angle emission and thus overcomes this problem.
The intuitive way of separately imaging supercritical and undercritical angle emission is to use a circular mask in a conjugate plane. This approach, known as supercritical angle fluorescence microscopy , suffers from diffraction at the edge of the mask. The result is a largely inflated point spread function, which makes it difficult to estimate the number of emitted photons. Therefore, we use virtual supercritical angle fluorescence microscopy (vSAF ) for localization microscopy (Fig. 1(d)). The fluorescence collected by the objective is laterally constricted in an image plane by a slit and subsequently split by a 50:50 beam splitter. In one channel, total fluorescence is detected, which strongly depends on the axial position of the fluorophore due to the contribution of supercritical angle fluorescence. In the second channel, a ring aperture in the conjugate plane (image of the back focal plane) blocks supercritical angle fluorescence. Thus, only undercritical angle emission is detected, which is only marginally dependent on the fluorophore’s axial position. The two channels are then simultaneously imaged onto two parts of an emCCD camera.
After calibration, we calculate the axial position of the emitter from the relative intensities in the two channels. By additionally localizing the single molecules in the image plane, we achieve three-dimensional superresolution. As the emission light is split in two channels, the lateral localization precision is reduced by a factor of in each channel. However, averaging the position of the fluorophores in both channels restores the lateral localization precision to that of a 2D one-channel setup.
3. Theoretical resolution
We determine the maximum theoretical resolution that can be achieved with SALM, by relating the error in with the error in determining accurate intensities. The latter can be estimated using the Cramer-Rao Lower Bound (CRLB ).
In localization microscopy, the and position of a single emitter is determined directly by fitting single-molecule images. Its z coordinate however has to be inferred indirectly by measuring a property that depends on .
The precision with which can be determined depends on the error associated with the measurement of as well as on how strongly changes with , i.e. the partial derivative of with respect to , :14,19]:20]:
For fluorophores with a low quantum yield, supercritical angle emission does not compete with undercritical angle emission. ThenEqs. (1), (5) and (6) we can calculate (Fig. 2(a)).
In an analogous way we can calculate the axial resolution, if a circular aperture is used instead of a ring aperture to block all undercritical light in one channel (Fig. 2(b)). Here, the theoretical resolution is better, since a direct quantification of the supercritical angle emission is much more accurate than measuring it on top of the undercritical angle emission. However, diffraction caused by the circular aperture is not taken into account here, which impedes an accurate measurement of the supercritical angle fluorescence .
Optical aberrations as well as imperfect shape and alignment of the apertures complicate the use of a theoretical description (section 3) to directly calculate absolute z positions from the intensities in both channels. Therefore, we chose to experimentally calibrate the relative intensities in both channels using fluorescent objects with known axial positions.
To this end, we embedded 40 nm fluorescent beads in an agarose gel at different heights above the coverslip. For each field of view, we first acquired a z-stack with an astigmatic lens in the beam path to precisely determine the axial positions of the beads (see methods). Afterwards we measured total and undercritical angle emission for the same beads. The calibration curve is obtained by plotting vs. for all beads and approximating the data with an exponential (Fig. 3). This curve is then used to determine z positions of single fluorophores from their relative intensities in both channels.
4.2. Validation using DNA origami tetrahedra
To validate the calibration and to characterize the single-molecule localization precision, we made use of DNA origami technology that allows placing a defined number of dyes in a specific three-dimensional arrangement . Here we imaged recently developed DNA origami tetrahedra . These commercially available tetrahedra (GATTAquant GmbH) have a well-defined three-dimensional geometry with a side length of 100 nm (Fig. 4(a)) and feature 12 single-stranded DNA docking strands on each of their four vertices that can be imaged using the DNA-PAINT method [23,24]. To this end, short fluorescently labeled DNA imager strands complementary to the single-stranded DNA docking strands were added into the buffer solution. Binding of imager strands results in their immobilization and a bright single-molecule localization event (Fig. 4(b)). Figure 4(c) shows typical three-dimensional images of the tetrahedra obtained with SALM. For further analysis, only complete and isolated tetrahedra were selected (Fig. 4(d)), and the four corners were automatically identified by k-means clustering of the single molecule localizations. From the centers of these clusters we calculated the height of the tetrahedra (Fig. 4(e)) by averaging the z positions of the three bottom clusters and subtracting it from the z position of the top cluster. The average height of (80.5 ± 14.5) nm (mean ± SD, N = 113) is in good agreement with the expected height of the tetrahedra of 82 nm. The spread in heights could be due to a fraction of slightly tilted tetrahedra (visible in Fig. 4(d), where some tetrahedra show deviations from the predicted geometry depicted in Fig. 4(a)) and due to slight deformation of the tetrahedra resulting from limited rigidity (compare Fig. 3 in Iinuma et al. ). The localization precision (standard deviation of the localizations at each corner) was σx = (11.2 ± 4.7) nm in the lateral and σz = (26.4 ± 8.4) nm in the axial direction. This is only an upper bound for the localization precision due to imperfect immobilization of the tetrahedra.
4.3. Application to biological samples
To demonstrate the applicability of SALM to biological samples we imaged immunostained clathrin-coated pits (Fig. 5(a)) and microtubules (Fig. 5(b)) using the dSTORM approach . The expected three-dimensional geometry is clearly visible in the x-y and x-z projections. The quality is comparable to what we observed with PSF-engineering based 3D localization microscopy. Note that the fluorophores in dSTORM emit fewer photons than in DNA-PAINT, which leads to a lower localization precision here compared to Fig. 4.
5. Discussion and outlook
We have demonstrated that supercritical angle emission can be used to obtain three-dimensional position information in localization microscopy in a straightforward and robust manner. However, the axial resolution currently does not surpass that of established methods based on PSF engineering and is far away from the theoretical limit. This is due to several factors, discussed in the following together with possible solutions that we intend to implement in the future.
Supercritical angle emission could be quantified much more precisely if measured directly, and not on top of the undercritical angle emission (see Fig. 2). Unfortunately, a direct measurement of only the supercritical angle emission by blocking all undercritical angle emission with a circular aperture is not feasible with our current setup because of diffraction at the circular aperture. However, new high-NA objectives (up to NA = 1.70) will have a much larger supercritical area in the back focal plane and considerably reduced diffraction. Residual spherical aberrations, currently present in such objectives, can be reduced with adaptive optics . We furthermore intend to implement new fitting routines using refined PSF models to extract more precise brightness information even in case of a PSF deformed by diffraction or aberrations.
Inherently, using an aperture to block parts of the emission light leads to photon loss. This can be circumvented by splitting under- and supercritical angle fluorescence with an elliptical mirror at an intermediate image of the back focal plane that exclusively reflects out undercritical angle fluorescence.
With these measures, we hope to approach the theoretical resolution and to realize 3D localization microscopy with isotropic resolution, comparable to that of interferometric localization microscopy, albeit with a robust and much simpler setup.
One major limitation of this technique is its limited axial range. It is perfectly suited for studying samples that can typically be imaged by TIRF microscopy, such as membranes or membrane associated proteins. Isotropic resolution throughout thick samples can be realized using physical sections.
A general prerequisite for localization microscopy is the free rotation of detected fluorophores, but in biological samples images of fixed fluorophores show complex asymmetric patterns which can cause localization errors  and complicate the evaluation of z positions. Similarly for SALM the amount of supercritical angle emission depends on the orientation of single fluorophores. However, our dual-channel setup will easily allow to test fluorophore rotation by employing a polarizing beam splitter.
In summary, we presented a new approach for robust and simple three-dimensional superresolution microscopy. Our proof-of-principle experiments demonstrated the high potential of the method for DNA origami model structures as well as biological samples. We discussed how additional technical improvements will allow SALM to approach isotropic three-dimensional resolution in localization microscopy without compromising the lateral resolution. Due to the simple optical design of SALM, incorporation into existing setups will allow many laboratories to profit from this approach and to reach molecular resolution in the cellular context.
7.1 Microscope setup
Single-molecule microscopy was performed with a custom-built microscope (Fig. 1). 405 nm, 488 nm, 561 nm and 640 nm lasers originating from a single-mode fiber of a laser combiner (Toptica) were focused onto the back focal plane of a Nikon objective (60x, NA = 1.49) for total internal reflection (TIRF) or epi illumination. Emission light was filtered by a 700/100 or 613/73 filter (Chroma), laterally confined in an intermediate image plane, split with a non-polarizing beam splitter and imaged onto two halves of an emCCD camera (Andor). In one channel, a custom-made ring aperture was placed in a back focal plane image (conjugate plane) and adjusted by imaging this plane with an additional lens. Images were acquired with Micromanager . For astigmatic imaging, a cylindrical lens (f = 500 mm, Thorlabs) was placed in front of the camera.
A focus stabilization was implemented by an electronic feedback loop based on the total internal reflection of a red laser at the coverslip and its detection by a quadrant photodiode; the z stability was better than ± 10 nm over several hours. The lateral drift was typically smaller than 50 nm/h; a drift-correction was implemented based on image-correlation .
7.2 Calibration sample
40 nm fluorescent beads (F-8770, Life technologies) were diluted 1:20000 in 50 µL of a warm, liquid 1% (w/w) solution of low melting point agarose (Sigma) in water. The solution was pipetted onto a clean glass coverslip. The gel was thinned to ~1 µm by centrifugation of the coverslip at 2500 g and imaged in water.
7.3 DNA-PAINT measurements on DNA origami tetrahedra
We used commercial DNA origami tetrahedra (GATTAquant GmbH, Braunschweig, Germany), which were prepared and measured as reported earlier [22,24]. In short, biotinylated DNA origami tetrahedra were immobilized on BSA-biotin-neutravidin coated coverslips. Docking strand sequences were used as previously  and consist of 10 nucleotides binding sequence and 1 nucleotide as spacer (TTAAATGCCCG). 3 nM of imaging DNA strands coupled to Atto655 (CGGGCATTTA-Atto655) were added to the imaging buffer comprised of 5 mM Tris pH 8, 10 mM MgCl2, 1 mM EDTA, 0.05% Tween-20. Single-molecule imaging was performed under total internal reflection excitation with a frame rate of 2.5 Hz.
7.4 Biological samples
To visualize clathrin-coated pits, cells were fixed with 3% Formaldehyde/PBS at room temperature for 10 minutes, quickly washed and reduced by 0.1% NaBH4/PBS for 7 minutes. Blocking and permeabilization was performed with 3% BSA/PBS containing 0.5% Triton X-100 for 30 minutes. Cells were immunostained with 1:300 mouse anti-clathrin heavy chain (cloneX22) (ab2731, abcam), 1:300 rabbit anti-clathrin light chain (sc-28276, Santa Cruz Biotechnology) and 1:300 mouse anti-clathrin heavy chain (msCHC5.9) (BM295, Acris) in 2% BSA/PBS for 2 hours to overnight. After washing, they were incubated with 1:200 anti-mouse (A21236, Molecular Probes) and anti-rabbit secondary antibodies conjugated to Alexa Fluor 647 (A31573, Molecular Probes) in 2% BSA/PBS for 2-3 hours.
To visualize microtubules, U2OS cells were prefixed and permeabilized with 0.3% glutaraldehyde in cytoskeleton buffer (10 mM MES pH 6.1, 150 mM NaCl, 5 mM EGTA, 5 mM glucose, 5 mM MgCl2) with 0.25% TX-100 for 1-2 minutes, and subsequently fixed with 2% glutaraldehyde in cytoskeleton buffer for 10 minutes. After a brief wash with PBS, samples were reduced with 0.1% NaBH4/PBS for 7 minutes to remove autofluorescence, washed 3 times with PBS, incubated with 1:500 mouse anti-alpha tubulin primary antibody (Neomarker, #MS581) in 3% BSA/PBS for 30 min, washed with PBS and stained with 1:500 of a secondary goat anti-mouse antibody conjugated to Alexa Fluor 647 (A21236 Molecular Probes) in 3% BSA/PBS for 2-3 hours.
The samples were imaged in 50 mM Tris pH 8, 10 mM NaCl, 10% glucose, 35 mM cysteamine, 0.5 mg/mL glucose oxidase and 40 µg/mL catalase. We used an exposure time of 30 ms and an EM gain of 200. Imaging laser intensity at 640 nm was 2-5 kW/cm2, the 405 nm activation laser intensity was automatically adjusted to ensure a constant number of localizations per frame. Typically 100000 frames were recorded.
7.5 Data analysis
All data analysis was performed with custom written Matlab software.
7.5.1 Localization analysis
Localization analysis was performed as described previously [29,31]. Briefly, pixel counts were converted to photons by subtracting the constant offset and multiplying by the inverse gain of the camera. Approximate locations of bright spots in each image were determined by smoothing, non-maximum suppression and thresholding. Selected regions of interest were fitted by a pixelized Gaussian function of free width and a homogeneous photon background with a maximum likelihood estimator (MLE) for Poisson distributed data using a freely available, fast GPU fitting routine  on a GeForce GTX760 (Nvidia). Lateral drift was corrected based on the imaged features: blocks of typically 10% of the total number of frames were used to reconstruct one superresolution image. Displacements among all reconstructed images were determined by image correlation and fitting of the maximum with an elliptical Gaussian. Displacements corresponding to each time point were averaged using a robust estimator, interpolated by a spline and used to correct the position of each localization. From the variation of the spline, we estimate that the residual error for the corrected positions was about 2 nm.
To evaluate relative intensities in both SALM channels, localizations in the two channels originating from one molecule had to be linked. This was achieved by calculating an approximate shift between the two channels by cross-correlating the images and linking the brightest molecules in each frame, which were then used to calculate an affine transformation between the two channels. This transformation was used to map the positions of channel 2 onto channel 1. Regions of interest around localizations in both channels were cut out and fitted again with a Gaussian function assuming a constant width of the PSF to determine the total number of photons per localization and to calculate .
Single bead images of the astigmatic z-stack were fitted with an elliptical Gaussian, resulting in the widths of the PSF in x and y, namely and . Localizations in different frames belonging to the same bead were associated by proximity. For each bead, and were fitted with a quadratic function in a range between their minima. The z position of the bead was chosen as the crossing point of the parabolas (position of symmetric PSF), after correcting for the refractive index mismatch .
Localizations from the same field of view, measured with SALM, were associated to the beads of the corresponding astigmatic z-stack and vs. was fitted with an exponential function. Since the offset for the scale is not absolute, each data set was shifted along the axis until the exponential fits overlapped at a defined value. The total data was finally fitted again to an exponential with a robust non-linear least squares fit to obtain the final calibration curve.
Locations of complete tetrahedra were manually selected in a reconstructed image. Localizations corresponding to the four corners were associated automatically by k-means clustering of the 3D coordinates into 4 clusters. For each cluster, the centroid, as well as the standard deviations of the positions in the lateral direction () and the axial direction () were calculated. The height of the tetrahedra was calculated as the distance in z between the top corner and the average z position of the three bottom corners.
We thank Philip Tinnefeld (Technische Universität Braunschweig) and Jürgen Schmied (GATTAquant GmbH) for providing the DNA origami tetrahedra and for help with DNA paint, Ulf Matti for preparing the biological samples and technical support and Jan Ellenberg, Ingmar Schön, Philip Tinnefeld and Jürgen Schmied for critical reading of the manuscript. This work was supported by the European Molecular Biology Laboratory (J. D., M. M., J. R.), the EMBL International PhD Programme (M. M.) and the Deutsche Forschungs Gemeinschaft (DFG RI 2380/2).
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