Single-molecule localization microscopy (SMLM) has become an essential tool for examining a wide variety of biological structures and processes. However, the relatively long acquisition time makes SMLM prone to drift-induced artifacts. Here we report an optical design with an electrically tunable lens (ETL) that actively stabilizes a SMLM in three dimensions and nearly eliminates the mechanical drift (RMS ~0.7 nm lateral and ~2.7 nm axial). The bifocal design that employed fiducial markers on the coverslip was able to stabilize the sample regardless of the imaging depth. The effectiveness of the ETL was demonstrated by imaging endosomal transferrin receptors near the apical surface of B-lymphocytes at a depth of 8 µm. The drift-free images obtained with the stabilization system showed that the transferrin receptors were present in distinct but heterogeneous clusters with a bimodal size distribution. In contrast, the images obtained without the stabilization system showed a broader unimodal size distribution. Thus, this stabilization system enables a more accurate analysis of cluster topology. Additionally, this ETL-based stabilization system is cost-effective and can be integrated into existing microscopy systems.
© 2016 Optical Society of America
Designing new lenses with sophisticated geometry that yield higher magnification and lower aberration was thought to be the way to infinitely increase the resolution of optical microscopes until Abbe  and Rayleigh  formulated the theoretical resolution limit. On the basis of wave optics, it was shown that two objects were spatially irresolvable if the separation is less than , where was the wavelength of the illumination light, and was the numerical aperture of the objective lens. However, the diffraction limit can be overcome when localizing a single molecule. The prior knowledge that a molecule is spatially isolated allows one to determine its position with an uncertainty of less than 10 nm. This concept was described in the 1960s  and applied to single-particle tracking experiments [4, 5]. Recently, the emergence of new photo-switchable fluorophores and labelling methods has made it possible to accumulate millions of spatially isolated fluorophores from tens of thousands of images, which can then be used to reconstruct a super-resolution image. Single-molecule localization microscopy (SMLM), such as photo-activated localization microscopy (PALM) , stochastic optical reconstruction microscopy (STORM) , and universal point accumulation for imaging in nanoscale topography (uPAINT) , use this prior knowledge to resolve the structures of biological systems with nanometer-scale resolution. Although the accuracy of the single fluorophore localization can be better than 10 nm, sample drift due to thermal gradients or mechanical motion is often in the range of hundreds of nanometers. As 5-10 min is usually needed to acquire tens of thousands of frames for reconstructing an informative super-resolution image, the spatial stability of the sample often becomes the most important factor determining the performance of a super-resolution microscope. To achieve the highest resolution, the sample drift has to be significantly smaller than the precision of the single molecule localization.
Several methods have been proposed to correct sample drift, including stabilization methods using fiducial markers as reference points [9–11], image correlation analysis of bright field images [12, 13], and post-processing of single-molecule localization data (i.e. blink tracking) [14, 15]. Because of the superior photon budget of fiducial markers, sample stabilization using fiducial markers has produced the best stability. For instance, Lee et al.  achieved nanometer-scale 3D stability by tracking a fluorescent bead attached to the coverslip. However, practical issues arise when fiducial markers are used. In particular, fiducial markers such as fluorescent beads affixed to the coverslip, become out of focus when the imaging focal plane moves beyond 0.5 µm into a cell. Recently, it was shown that nanometer 3D stabilization with fiducial markers on the coverslip can be achieved for deep imaging by using a bifocal design with a movable lens . However, in this system the mechanical translation of the lens results in a change in the magnification as the magnification of an image depends on the relative distance between two lenses in the optical path.
In this paper, we present an optical design using an electrically tunable lens (ETL) to produce an electronically movable focal plane and actively stabilize the sample using the fiducial markers on the coverslip. Typically, moving the focal plane of a microscope involves physically moving either the sample or a lens. An alternative way to achieve focal shifting without any mechanical motion is to use electronically tunable liquid lenses or acoustic tunable lenses [17–21]. An electronically tunable liquid lens was chosen for the current study because of its lower cost. In the design presented herein, the focal planes of the sample and the fiducial markers can be shifted relative to each other without any moving components. This enables high accuracy drift-free super-resolution imaging, regardless of the imaging depth. Since the design has no moving parts, better stability and user-friendliness can be obtained, particularly when a z-scan is performed.
2. Materials and methods
2.1. Optical setup
Figure 1 shows the home-built SMLM system with a stabilization system using an ETL. The system is an inverted microscope equipped with an apochromatic TIRF oil-immersion objective lens (60X; NA 1.49; Nikon). A 639 nm laser (Genesis MX639, Coherent) was used for exciting Alexa 647 fluorophores (Life Technologies) and near infrared beads (100 nm; FluoSpheres, F8799, Life Technologies). Re-activation of the Alexa 647 fluorophores (i.e. increasing the transition rate of fluorophores between dark and bright states) was achieved using a 405 nm laser (LRD 0405, Laserglow Technologies). The laser beams were collimated, combined, circularly polarized and focused onto the back aperture of the objective lens (L1 and L3; AC127-030-A, L2 and L4; AC127-075-A, DM1; FF560-FDi01, QWP; AQWP05M-600, L5; AC254-150-A, Thorlabs). Mirrors M3 and M4 were mounted on a translation stage (PT1, Thorlabs) to control the incident beam angle and to switch between epi-illumination and oblique incident illumination modes. A quad-band polychroic mirror (DM2; Di01-R405/488/532/636, Semrock) was used to reflect the excitation beams and transmit the fluorescence signal. A 3D piezo stage (Max311D, Thorlabs), a 16-bit digital-to-analog converter (PCI6323, National Instruments), and a piezo-stage controller (MDT693B, Thorlabs) were used to stabilize the microscope during data acquisition. A quad-notch filter (NF; 405/488/532/636, Semrock) was placed in the detection path to further block the excitation/activation lasers. A short-pass dichroic mirror (DM3; FF720-FDi01, Semrock) was used to separate the fluorescence emission of Alexa 647 from that of the fiducial markers.
The imaging path for the Alexa 647 fluorescence contains a cylindrical lens assembly (CL1; effective focal length (EFL) = 10 m) consisting of a plano-convex cylindrical lens (focal length = 400 mm) and a plano-concave cylindrical lens (focal length = −400 mm). CL1 introduces astigmatism into the imaging path, creating slightly different focal lengths in the x and y directions. This produces an elliptical point spread function (PSF) (i.e. the aspect ratio and orientation of the PSF varies along the optical axis), which allows determining the axial position of a fluorophore within ~250 nm above and below the focal plane of the objective lens . After the cylindrical lens assembly, the emission light passes through a band-pass filter (BPF1; FF01-676/37, Semrock) and a 200 mm tube lens (TL1; ACA254-200-B, Thorlabs) before being imaged by a electron multiplying charge-coupled device (EMCCD; iXon Ultra DU-897U, Andor). A 2.5 × zoom lens (ZL) was placed between DM3 and CL1 to increase the overall magnification to 150 times.
In the imaging path of the fiducial markers, the emission light passed through a 250 mm achromatic doublet lens (TL2; AC254-250-A, Thorlabs) and a relay imaging lens (RL1; AC254-100-A, Thorlabs). An ETL (EL-10-30-Ci-VIS-LD, Optotune, Switzerland) was placed after the relay system such that it was conjugate to the back focal plane of the objective lens. The emitted light then passed through a cylindrical lens assembly (CL2; EFL = 2 m), which had a design similar to that of CL1. The focal lengths of the concave and convex cylindrical lenses in CL2 were ± 200 mm (LJ1653RM-B, LK1069RM-A, Thorlabs). The emission light then passed through a band-pass filter (BPF2; FF01-747/33, Semrock) and a 200 mm achromatic doublet lens (RL2; ACA254-200-B, Thorlabs) before being imaged by the CCD (Newton 970 UBV, Andor).
2.2. Sample preparation for 3D stabilization tests
To measure the performance of the active stabilization system, 100 nm multi-color TetraSpeck beads (T7279; Life Technologies; 1:200 dilution) were mixed with 100 nm near infrared FluoSpheres (excitation 715 nm; emission 755 nm; diameter 100 nm; F8800, Life Technologies, 1:200,000 dilution) and affixed to a poly-L-lysine-coated coverslip. The coverslip was then rinsed to remove beads that had not firmly attached and mounted in phosphate buffered saline (PBS). The FluoSpheres were tracked on the CCD to provide drift correction feedback. The TetraSpeck beads were imaged simultaneously using the EMCCD to measure the stability of the sample.
2.3. Cell labeling and preparation for SMLM
Splenic B cells from 8-week old C57BL/6 mice were used. Splenic B cells were isolated, as previously described , using a B cell isolation kit (#19854, Stemcell Technologies) to deplete non-B cells. B cells were cultured in RPMI-1640 supplemented with 10% fetal calf serum, 2 mM glutamine, 1 mM pyruvate, 50 μM 2-mercaptoethanol, 50 U/ml penicillin and 50 μg/ml streptomycin (complete medium).To increase transferrin receptor (TfR) expression levels, the B cells were stimulated with 5 μg/ml E. coli 0111:B4 LPS (#L2630, Sigma-Aldrich) for 12 hr, as described in [24, 25].
Glass coverslips (#1.5H, Marienfeld) were coated with the non-stimulatory M5/114 anti-MHCII monoclonal antibody (#12-5321, eBioscience) as described in reference . B cells were then allowed to adhere to these coverslips for 10 min at 4 °C, before being fixed for 90 min with ice cold PBS containing 4% paraformaldehyde and 0.2% glutaraldehyde. The fixed cells were then washed three times with PBS, permeabilized with 0.1% Triton X-100 for 5 min, and then again washed three times with PBS. After incubating the cells with blocking buffer (10% normal goat serum in PBS) for 1 hr at 4 °C, the cells were stained overnight at 4°C with an anti-TfR antibody (#13-6800, Invitrogen, 1:100 dilution). The cells were then washed three times with PBS, incubated at room temperature for 30 min with Alexa 647-conjugated goat anti-mouse IgG (A21244, Life Technologies), and washed five times with PBS. This was followed by a second fixation step (4% paraformaldehyde for 10 min) and a final series of five PBS washes. Fluorescent fiducial markers (100 nm, F8800, Life Technologies) were allowed to settle on the coverslip overnight at 4°C. Imaging was performed in a GLOX-thiol solution consisting of 50 mM Tris-HCl, pH 8.0, 10 mM NaCl, 0.5 mg/ml glucose oxidase, 40 μg/ml catalase, 10% (w/v) glucose and 140 mM 2-mercaptoethanol). The coverslip was mounted onto depression slides and sealed with Twinsil two-component silicone-glue (#13001000, Picodent).
Initially the 639 nm laser was used at a relatively low intensity (< 2 W/cm2 at the sample) for illumination. A region of interest within the cell was chosen and the actual imaging depth was measured using the piezo stage controller. Before turning on the feedback loop, an appropriate current was applied to the ETL through the lens controller to obtain a clear image of the fiducial markers on the CCD. The current was adjusted such that the aspect ratio (Rxy ≡ PSF’s width in x / width in y) of the beads was in the range of 0.75 - 1.5. Up to five fiducial markers were typically tracked during image acquisition at a rate of 3 Hz. The intensity of the 639 nm laser was then increased to ~5 kW/cm2, and the sample was photobleached for ~30 s before acquiring 40,000 frames on the EMCCD at a rate of ~50 Hz. To re-activate Alexa 647 fluorophores and compensate for a decreasing number of blinks due to photobleaching, the intensity of the 405 nm laser was increased during the image acquisition in a stepwise fashion from 0 to ~1 W/cm2. The post-acquisition processing of images to determine the positions of single-molecules was performed using a previously described MATLAB program .
3. Results and discussion
3.1. The dynamic behavior of the electrically tunable lens
As shown in Fig. 2(a), the ETL consists of a polymer membrane enclosing a low dispersion fluid. The ETL changes its focal length via the current-controlled deformation of the membrane. The curvature of the membrane increases (i.e. the focal length decreases) as the applied current is increased. The focal length, , is specified to span from 200 mm to 80 mm. The ETL should be mounted horizontally to avoid the effect of gravity. The wavefront error (~0.25λ) and the aberration of an ETL are larger than a typical optical lens. However, these do not significantly affect the stabilization of the sample because the stabilization mechanism relies on the change of the PSF, instead of the absolute profile of the PSF. The response time of the ETL was measured to be less than 50 ms. A programmable lens driver with temperature compensation was used to control the ETL. When the imaging depth was changed, the applied current was adjusted to keep the fiducial markers in focus on the CCD.
Figure 2(b) shows the relationship between the applied current to and the imaging focal shift. The data was obtained by imaging TetraSpeck beads on coverslips. When the applied current was changed, the piezo stage was scanned in the axial direction to find the focal shift of the beads. When the applied current was increased from 0 to 250 mA, the axial focal shift () was ~11 µm, which is sufficient for most cell imaging.
To determine the positions of the fiducial markers for 3D drift correction, a compound cylindrical lens (CL2; focal length: ) was used to introduce an adjustable astigmatism into the imaging path of the fiducial markers. CL2 is composed of a convex and a concave cylindrical lenses with focal lengths () of ± 200 mm, separated by a distance . The effective focal length of CL2 can be varied by adjusting d. This setup is simpler and more cost-effective than previously reported methods based on a deformable mirror array [26, 27]. In contrast to the single-cylindrical-lens design used by Huang et al. , our design allows improved optimization of the depth-dependent astigmatic effect, which is particularly useful for deep imaging. Figures 2(d)-2(e) shows an optimized astigmatism effect that was used to track fluorescent beads when imaging at a depth of 8 µm ( = 10 mm). The distance was adjusted such that moving a bead in the z direction from + 200 nm to −200 nm changed its PSF aspect ratio, Rxy, from 1.4 to 0.8, which provides good sensitivity for tracking in the axial direction.
In this design, the imaging focal shift in the z-axis is inversely proportional to the effective focal length of the ETL, , and is given by 29, 30] with a ray matrix in the x direction () given byFig. 2(b). This is sufficient for imaging TfRs within B cells as the largest B cell had a diameter of ~10 µm.
3.2. Performance of the active 3D stabilization system
To determine the stability of the ETL, the positional stability of TetraSpeck beads on the EMCCD was measured over a period of 10 min while the near infrared FluoSpheres were tracked on the CCD. The positional feedback was carried out at a frequency of ~3 Hz. Both cameras were synchronized and had the same exposure time of 300 ms. Five FluoSpheres beads were tracked to provide the drift correction feedback. To determine the lateral positions of the FluoSpheres beads, each image of the FluoSpheres was fitted using an error functionFig. 2(e). The displacements of the beads were subsequently determined by comparing their shifts with respect to their initial positions. The mean of the displacements was then calculated, and an appropriate voltage was applied to the piezo stage to correct the drift in all axes.
Figure 3(a) shows the positional stability of the TetraSpeck beads on the EMCCD over a period of 10 min. Without the feedback loop, the system typically drifted ~100 nm in all directions over 10 min. With the feedback loop, the displacements in all three dimensions were reduced to a few nanometers. As shown in Fig. 3(b), the standard deviations of the beads’ positions was ~0.7 nm in the x and y directions and ~2.7 nm in the z direction. Compared with some commercially available auto-focusing systems, which monitor the reflection off the coverslip , the axial accuracy of the current system is more than 10 times higher.
3.3. Super-resolution imaging of transferrin receptors in B cells
To demonstrate the impact of the drift correction, endosomal TfRs in B cells were imaged at a depth of 8 µm. The TfR is a membrane glycoprotein that mediates cellular uptake of iron from a plasma glycoprotein, transferrin. Iron uptake from transferrin involves the binding of transferrin to the TfR, internalization of transferrin into endocytic vesicles via receptor-mediated endocytosis, and the subsequent release of iron from the transferrin, which is induced by a decrease in endosomal pH . TfR is a prototypical marker for endosomal recycling pathways and has been used as a marker of both cell surface and endosomal structures in mammalian cells [33–35].
A drift-free super-resolution image of TfRs in a B cell is shown in Fig. 4(a). This image was obtained by plotting the density of single-molecule localizations. The corresponding image with drift shown in Fig. 4(b) was obtained by computationally adding the measured drift that occurred during the image acquisition, as shown in Fig. 4(c), to the drift-free image in Fig. 4(a). Insets of the regions marked by white boxes in Figs. 4(a) and 4(b) are shown in Figs. 4(d) and 4(e), respectively. Although Fig. 4(c) shows that the actual drift in this particular case is only ~100 nm over 10 min, the drift substantially impacts the conclusions that one would draw from these images about TfR clustering. The drift-free image in Fig. 4(d) reveals that TfRs were organized into well-defined, punctate clusters. In contrast, TfR clusters in the drifted image were elongated and blurred, with a lower apparent density those in the drift-free image in Fig. 4(j). The 3D representations of the regions within the green boxes in Figs. 4(d) and 4(e) are shown in Figs. 4(f) and 4(g), respectively. The clusters in the drift-free super-resolution image in Fig. 4(f) were isotropic and clearly separated from each other. However, the corresponding clusters in Fig. 4(g) were non-isotropic and difficult to discern as they were fused together.
To quantitatively analyze the effects of drift on topology and density of TfR clusters, a cluster analysis method based on Voronoï tessellation was used [36, 37]. Voronoï tessellation is based on the principle of subdividing an image into polygonal regions centered on seeds. Any point within a polygon is closer to its associated seed than it is to any other seeds. Figure 4(h) and 4(i) show the tessellation maps of the regions marked by red boxes in Figs. 4(d) and 4(e); segmented clusters are shown in blue. Segmentation of the localization points into clusters was performed using a single parameter, the density threshold, which was set to twice the average localization density, as described by Levet et al. . A comparison between the regions marked by the white dashed lines in Figs. 4(h) and 4(i) shows that the drift affects the separation of closely spaced TfR clusters (region A and B) and the topology of the clusters (region C).
Analysis of TfR clusters in Figs. 4(j) and 4(k) revealed that the drift had significant influences on the distribution of the cluster densities (i.e. number of localizations per cluster per unit area) and cluster sizes that were calculated using the Voronoï tessellation algorithm. Overall, the TfR clusters observed in the drift-free image were smaller than those in the drifted image and showed higher cluster density. This was attributed to sample drift, which extended the area of clusters, resulting in a lower cluster density. The drift-free image reveals that TfRs exist as heterogeneous nanoclusters in B cells and have a bimodal size distribution, as shown in red color in Fi. 4(k), which is consistent with electron microscopy studies showing that the size of TfR-containing vesicles varies from 30 nm to 160 nm [34, 38–40]. In contrast, the drifted image reveals a broader unimodal size distribution as shown in black color in Fig. 4(k). Moreover, Fig. 4(l) shows that the TfR clusters in the drift-free super-resolution image are more circular than those in the drifted image. These results highlight how this ETL-based drift correction system enables improved resolution as well as a more accurate description of receptor clustering.
We present an optical design using an ETL for real-time 3D drift correction of a super-resolution microscope. The positional fluctuation of the sample was shown to be ~0.7 nm in the lateral direction and ~2.7 nm in the axial direction. By decoupling the focal planes of the sample and the fiducial markers, this system enables drift-free super-resolution imaging regardless of the imaging depth. The impact of stability on super-resolution images was demonstrated by imaging the TfRs in B cells at a depth of 8 µm. The drift-free super-resolution image depicts the TfRs as distinct and heterogeneous clusters with a bimodal size distribution, whereas the image obtained without the stabilization system shows a broader unimodal size distribution. Additionally, the average density of fluorophores per unit area in these clusters was two times higher than that in the drifted image, presumably due to a sharper definition of the edges of the cluster.
Natural Sciences and Engineering Research Council of Canada (to K.C.C., Discovery Grant); the Canadian Institutes of Health Research (to M.R.G., grant #MOP-68865); the Canada Foundation for Innovation (to K.C.C., Leading Edge Fund).
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