One of the main issues of light microscopy has always been the limited resolution caused by diffraction effects which were described by Ernst Abbe in 1873 . This leads to the problem that microscopy images with a high magnification look blurry and hide information about structural details in the respective sample. In recent years a couple of techniques spread which breaking Abbe’s diffraction limit gaining microscopy images with much higher resolution. These so called super-resolution techniques use either physical (i.e. STED  or SIM ) or chemical approaches (i.e. GSDIM  or DNA-PAINT ) to increase the optical resolution. This breakthrough was awarded with the Nobel Prize for chemistry in 2014. However, for a long time these methods had the problem that there was no standardized way for a quantitative determination of the achieved resolution of a certain super-resolution microscope. Additionally, it is often not clear which of the super-resolution methods is the most appropriate to answer a specific biological question. So far the most common way to demonstrate the performance of a super-resolution technique has been imaging the cytoskeleton. Hereby structures from eukaryotic cytoskeleton like microtubules or actin filaments are imaged diffraction limited as well as in super-resolution configuration. Then both images are shown together (Figure 1a, b) highlighting qualitatively the resolution improvement in an eye-catching, however just qualitative way. For a quantitative determination of the spatial resolution usually two filaments which lie parallel close to each other and are narrow resolvable are picked out (Figure 1c) and underwent a distance measurement. The shortest distance found that way then is called the achieved spatial resolution (Figure 1d).
This of course seems to be very arbitrary since there is no control on the distribution of the imaged filaments and especially the distances between them. In addition due to the fact that every distance is unique there is no statistical analysis possible. The quest to develop better resolution standards in every respect yielded to the development of DNA origami based super-resolution standards .
The DNA origami technique
The basic technology for constructing these defined structures on the nanoscale, invented in the year 2006 by Paul Rothemund, is the so called "DNA origami" technique . A DNA origami structure is constructed out of a long (about 7,000 to 8,000 base pairs) single stranded DNA molecule the so called "scaffold strand" (Figure 2a). By adding ~200 short single stranded DNA molecules (so called "staple strands") which have complementary sequences to different parts of the scaffold strand, the respective parts of the scaffold can be connected to each other (Figure 2b-d). By these defined connections the scaffold can be folded into any structure at will whereby the programming of the shape is carried out by the right choice of the staple strand sequences. By heating up the scaffold strands together with the short staple strands, buffer and salts and slowly cooling down to room-temperature the folding process occurs and the DNA origami structure folds self-assembled into the designed structure.
Typical DNA origami structures have dimensions of around 50 to 300 nm and can have the shape of flat rectangles, rods, cubes but essentially every shape, as seen in Figure 3.
The fact that the position of every short staple strand in the DNA origami structure is known offers the possibility to position organic dye-molecules with nanometer precision on the DNA origami structures. Therefore the respective staple strand needs to be labeled with an organic dye-molecule which is then incorporated into the DNA origami structure during the folding process (Figure 2e). Since every of the ~200 staple strands can be labeled individually at will, the DNA origami structures can be regarded as molecular breadboard which allow to position organic dye-molecules and essentially every object which can be attached to single-stranded DNA with nanometer precision (Figure 2f). This allows generating fluorescent marks on the DNA origami structures with defined distances and also defined numbers of dye-molecules which is then the ideal structure to test the achievable spatial resolution of fluorescence and especially super-resolution microscopes.
Because of the high parallelism of the DNA origami technique every image contains not only one single nanoruler but millions of identical nanorulers which ensures the possibility of measuring the achievable spatial resolution of super-resolution microscopes and to calculate statistical errors of this measurement . Also the imaging buffer as well as the density of dye molecules can be adjusted to the conditions which can be found in real samples of interest.
The GATTAquant GmbH is a young start-up company which is focused on the design and fabrication of DNA origami based nanorulers for any type of super-resolution microscopy. As a spin-off from the group of Prof. Philip Tinnefeld at TU Braunschweig the company holds immense expertise in the field of DNA nanotechnology, the field of photophysics and super-resolution imaging and especially the combination of both.
This expertise led to the development of many high quality nanoruler products for different super-resolution methods STED, SIM, GSDIM (dSTORM) and DNA-PAINT but also for conventional diffraction limited confocal microscopy (Figure 3) .
Super-Resolution microscopy with DNA-PAINT
In the following the localization based approach especially the DNA-PAINT method shall be explained in more detail. Localization based microscopy uses the fact that the centroid of a single dye‑molecule, although its signal on the detector is a blurred spot, can be calculated with high precision and a standard deviation (which depends on the number of photons) much smaller than the size of the blurred spot. Currently the typical localization precision (standard deviation) of organic dye-molecules is in the range of 5–10 nm . However in order to calculate the centroids of organic dye-molecules one has to make sure that at any given point in time only one dye-molecule is emitting light within the area of a diffraction limited spot. To ensure this, the emission of overlapping molecules has to be separated temporally by inducing a "blinking" emission characteristic. Then the blinking molecules can be localized subsequently and finally from all these localizations a super-resolved image can be reconstructed. The main difference between all the localization based super-resolution methods is the way they use to make the molecules blink. Most techniques (like GSDIM, dSTORM or PALM) use a photo physical switching of the molecules between a fluorescent on- and a non-fluorescent off-state, which is photoinduced or induced by chemical reactions. A completely different approach is applied by the DNA-PAINT method. Here the structure to be imaged is not directly labeled with fluorescent molecules but with single-stranded DNA strands which work as binding sites for complementary dye-labeled single stranded DNA, so called imager strands. The length of the imager strands is short enough to bind only transiently leading to multiple binding and unbinding events on each binding site. Since the organic dye-molecules of the imager strands are only visible when binding to the DNA origami structures on the surface and invisible when they are freely diffusing in solution, such a binding site has a similar emitting characteristic as a single blinking dye molecule (Figure 4) .
However, there are a couple of advantages compared to a single blinking dye-molecule. The most important one is the fact that the DNA-PAINT samples are not prone to dye-bleaching since the organic dye-molecules are exchanged every time a new imager strand binds to the DNA origami structure. In addition, the techniques requires only a single excitation source and multiplexing is straightforward. Based on the DNA-PAINT technique, the GATTA-PAINT series provides nanorulers containing three marks with mark-to-mark distances of 20 nm, 40 nm or 80 nm. In order to test the achievable spatial resolution of localization based microscopes in 3D localization based superresolution, GATTAquant currently develops nanorulers which provide intermark distances also in axial direction. One promising DNA origami structure has the shape of a tetrahedron with an axial distance of 80 nm.
Drift correction in DNA-PAINT
A common issue especially in localization-based super-resolution microscopy - where an image recording time can easily exceed several minutes - is the problem of lateral and axial sample drift caused by mechanical and/or thermal instability leading to a smeared image which does not contain any resolvable structures.
Drift can be avoided during image acquisition by using a drift stable imaging platform (the Leica SR GSD 3D equipped with Suppressed Motion (SuMo) Stage) or by using an autofocus. A lateral drift correction can be carried out after image acquisition by postprocessing the gained data. Therefore so-called fiducial markers which serve as reference points are added to the sample. The fiducials are localized in every frame during image acquisition resulting in a time trace of x- and y-coordinates of every fiducial marker. The individual traces of all selected fiducial markers are then combined to one single time trace for the x- and the y-coordinate.
For both a compensating curve is calculated, which is usually done by a polynom fit or some sliding average algorithm. This compensating curve is then substracted from all coordinates within the super-resolution image. Common fiducial markers are fluorescent beads i.e. nanospheres filled with dye molecules. However, they show a couple of disadvantages: the fluorescence signal is usually too bright i.e. it saturates the detector whose dynamic range is optimized to single molecule detection. The bead signal is not constant over time and decreases by photobleaching effects and the beads are usually not perfectly sticked to the surface, i.e. their positions are not stable over time.
These disadvantages can be overcome by using DNA-origami-based DNA-PAINT fiducial markers (in the following referred as PAINT-FMs). PAINT-FMs are DNA-origami structures which carry a plurality of DNA-PAINT binding sites ensuring that under DNA-PAINT conditions in any given moment a couple of dye molecules is located on the PAINT-FM. This yields in a not-bleaching fluorescence signal originated from the PAINT-FM which is bright enough to ensure a sufficiently precise localization of the PAINT-FM but not too bright for the detector. Furthermore the PAINT-FMs can be stably connected to the surface via biotin-neutravidin-biotin binding, i.e. they hold a stable position over time. These advantages over conventional beads make the PAINT-FMs in combination with GATTA-PAINT nanorulers the ideal test sample for localization-based super-resolution microscopy.
Illumination options of the Leica SR GSD 3D
The measurements of GATTA-PAINT nanorulers within this article were exclusively carried out on a Leica SR GSD 3D microscope which is based on a Leica DMi8 fully automated TIRF system allowing the combination of 2D and 3D super-resolution with TIRF and oblique illumination microscopy. High power lasers in various laser lines allow efficient switching of a wide range of fluorophores and the collection of many photons for highest localization precision. 3D localization measurements are facilitated by an astigmatism-based optical feature using a cylindrical lens.
TIRF microscopy uses an evanescent wave to selectively illuminate and excite fluorophores in a restricted region of the specimen immediately adjacent to the glass-water interface. This evanescent wave is generated when the incident light meets the glass-water-interface at a greater angle than the critical angle and is totally reflected. Its propagation in z-direction gradually degrades so that the penetration depth is limited to some hundred nanometers dependent on wave length, refractive indices, the numerical aperture of the objective and the angle of incident light.
TIRF microscopy is commonly used for imaging of dynamic events in and close to the plasma membrane, like vesicle transport, membrane trafficking and endocytosis.
However, to make precise statements about the localization of the observed molecules, reliable control of the penetration depth of the evanescent wave is mandatory. Leica microsystems offers a special hardware for a fully automated TIRF alignment controlled by a TIRF scanner, collimator and sensor and the penetration depth can be precisely set via automated software control.
The knowledge of where total internal reflection occurs exactly can be used for a special illumination of the sample, the so called HILO-like mode providing oblique illumination.
Fig. 5: Schematic illustration of a Leica SR GSD 3D microscope with TIRF illumination. Automated TIRF alignment and reproducible penetration depths controled by a TIRF scanner, collimator and sensor. The scanner-sensor technology automatically matches the TIRF angle to the desired penetration depth at all wavelengths and positions the laser in such a way that the TIRF penetration depth automatically remains constant even when the wavelength is changed.
The Leica LAS X imaging and analysis software offers several options for setting the TIRF and oblique illumination (Figure 6). The automatic mode gives the researcher the possibility to define the penetration depths of the evanescent wave into the specimen by selecting one of the predefined penetration depths. The Expert mode enables the possibility to define the penetrations depth of the evanescent wave in nm precision (by moving the slider in the green area). When the slider is moved out of the green area the angle of oblique illumination can be defined. This angle is lower than the critical angle and the laser will pass the specimen inclined. The freely definable TIRF Scanner also offers the possibility to choose the direction of the evanescent field (azimuth) in both modes.
By using these techniques in combination with GSD, real time imaging and tracking in high resolution of single fluorophores while they label their targets like in DNA-PAINT is possible.
Fig. 6: Leica software environment: The automatic mode presents predefined penetration depths and free selection of one azimuth. The expert mode offers the option for TIRF (green area) and oblique illumination. Simple movement of a slider enables the definition of the penetration depth in nm precision.
Measuring the resolution of the Leica SR GSD 3D
To perform a GSD super-resolution measurement the slide containing the ready to use GATTA-PAINT nanorulers (Figure 7a) has to be fixed in the insert of the SuMo sample stage. Further sample preparation is not necessary. After adjustment of the camera and imaging settings and defining the penetration depth via software the super-resolution image is directly reconstructed during image acquisition. The single emitter signals are fitted by a Gaussian or center of mass algorithm.
After finishing the measurement the data were displayed in a multicolor image (Figure 7b) and analyzed with the GATTAnalysis software tool. Therefore the localization data saved as spreadsheet file were imported to GATTAnalysis ensuring that the different columns of the data file were correctly connected to the respective data sets. After importing, the data were displayed as image on the main user interface. In the second step nanoruler structures were detected in the image. This either can be done fully automated by a spotfinder or manually by clicking on the respective structures. The selected structures then were analyzed concerning mark-to-mark distance and the FWHM (full width half maximum) of each mark. By a statistical analysis of these values the result were compared to the designed distance value (Figure 7c, d). This comparison done for the measurements of GATTA-PAINT 40RG nanorulers showed that the Leica GSD microscope is easily capable of resolving samples laterally with a designed distance of 40 nm in the red and in the green channel.
If distances are much smaller than these 40nm, commonly lateral drift becomes a significant issue. Therefore, we added PAINT-FMs to a sample with GATTA-PAINT 20R nanorulers. This combined sample was then also measured on the Leica SR GSD microscope and after measuring post-processed to correct for lateral drift (Figure 7e-g). This measurement proved that the resolution of the 20nm distance was as good as one of the larger distance. However, the uncorrected data indicate that in this case a sufficient drift correction is essential.
Fig. 7: (a): Scheme of the GATTA-PAINT 40RG nanoruler (red-green dual color triple mark with 40 nm distance). (b): GSD image of GATTA-PAINT 40RG nanorulers. (c): Evaluation of the red channel using the software tool GATTAnalysis. (d): Evaluation of the green channel using GATTAnalysis. (e): Schematic illustration of a DNA-PAINT nanoruler imaged together with a PAINT-FM. (f-g): Uncorrected (f) and drift-corrected (g) SR image of a sample containing GATTA‑PAINT 20 nm nanorulers and PAINT-FMs.
Additionally also a three-dimensional DNA origami based structure was measured on the Leica GSD setup. The structure was a tetrahedron with an edge length of 100 nm and a fluorescent mark (DNA-PAINT binding site) on each vertex . The axial distance was 80 nm. This structure also was easily resolvable by the Leica SR GSD 3D (Figure 8b).
To capture a super-resolution image in 3D a cylindrical lens is inserted into the emission beam path introducing an astigmatism. For every different z-position the shape of the signal spot is measured which finally leads to a correlation between spot shape and the z-position. This correlation then can be used for axial localization of dye molecules (Figure 8a).
For quantitative distance measurements the gained z-values had to be corrected due to a refractive index caused effect. This is due the following: Before absolute values for the z-coordinate of an emitter are measurable the system has to be calibrated. This is done by acquiring a fluorescent bead in 3D. The obtained values of the PSF shape as a function of the axial position is then used for the calculation of the coordinates of the sample molecules. However, since the bead used for calibration is directly attached to the surface, there is no light pathway through the solution like it is in the final super-resolution measurement. This leads to a diffractive index mismatch between calibration and measurement. To overcome this effect all z-values have to be corrected by a certain factor which can be determined according to Schmied, Forthmann et al. . For this measurement the correction factor was determined to a value of 0.42. After correction the measured mark-to-mark distance fitted the theoretical value of the tetrahedron.
Fig. 8: (a) 3D GSD principle: To enable the localization of molecules in z direction a cylindrical lens is implemented into the emission beam path of the Leica SR GSD 3D system introducing a characteristic astigmatism into the PSF. The amount of distortion allows determination of the exact position in z dimension. (b) 3D GSD image of GATTA-PAINT 3D sample. Tetrahedron with four spots 80 nm in distance and labeled with Atto655. Depth color coding shows the position in z dimension.
After breaking Abbe’s diffraction barrier by advanced microscopy techniques like STED, GSDIM/dSTORM or DNA-PAINT one of the main issues of super-resolution imaging was the lack of a standardized way to quantify the achievable spatial resolution. This was addressed by researchers of the TU Braunschweig by developing the DNA origami based nanorulers which are now commercialized by the GATTAquant company. We demonstrated these nanorulers on the Leica SR GSD 3D system showing these structures are ideal resolution standards which verify that the Leica setup is a very well performing imaging system with a lateral resolution better than 40 nm and an axial resolution better than 80 nm.
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