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Considerable efforts have been deployed towards measuring molecular range distances in fluorescence microscopy. In the 1–10 nm range, Förster energy transfer microscopy is difficult to beat. Above 300 nm, conventional diffraction limited microscopy is suitable. We introduce a simple experimental technique that allows bridging the gap between those two resolution scales in both 2D and 3D with a resolution of about 20 nm. The method relies on a computational approach to accurately correct optical aberrations over the whole field of view. The method is differential because the probes of interest are affected in exactly the same manner by aberrations as are the reference probes used to construct the aberration deformation field. We expect that this technique will have significant implications for investigating structural and functional questions in bio-molecular sciences.
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The Abbe diffraction limit of approximately 0.2 μm reminds us of the smallest distance at which two point sources can still be resolved under far-field optical microscopy (Hell, 2007). A number of investigators have succeeded in mitigating the impact of this limit by using either hardware or software based approaches. For example, scanning near-field optical microscopy exploits the near-field scattered by a sharp tip to obtain high-resolution imaging conditions (Muramatsu et al., 1996). In 4PI microscopy, the volume of the point spread function is reduced by using two high numerical aperture objectives facing each other (Schrader et al., 1998). In total internal reflection fluorescence microscopy, shallow excitation of the sample is realized by the evanescent field at the interface between two media (Axelrod et al., 1983). A standing wave embodiment of this technology has been reported that allows improving the lateral resolution down to 100 nm (Gliko et al., 2006). Gordon et al. measure nanometre range distances between two single identical fluorophores by relying on the analysis of the Airy-like intensity patterns, before and subsequent to the photo-bleaching of one of the fluorophores (Gordon et al., 2004). This powerful approach demands acquisition of relatively long time-lapse sequence to record photo-bleaching events, and it is limited to 2D. A related technique achieved similar performance by using a nanometre piezo stage that scans the sample in the centre of the field of view, where very limited optical aberrations are present (Michalet et al., 2001; Lacoste et al., 2000). Recently, the exciting technique of stochastic optical reconstruction microscopy has been described, which relies on iterative, stochastic activation of photo-switchable probes to achieve high resolution (Huang et al., 2008) in 2D and 3D. In the 1–10 nm range, the favoured technique is fluorescence resonance energy transfer (FRET) microscopy whereby excitation is transferred non-radiatively from a donor fluorophore to an acceptor dye with an efficiency that depends sensitively on the distance between the two probes (Jares-Erijman & Jovin, 2006). The careful interpretation of FRET data requires that the relative orientation of the two probes be known – a condition rarely met (Lakowicz, 2006).
Computational approaches for resolution improvement include a variety of deconvolution techniques. For example, Scalettar et al. report a deconvolution scheme constrained by the measured optical aberrations (Scalettar et al., 1996). The vertical dependence of the point spread function was also taken into account to obtain more accurate deconvolution results (Shaevitz & Fletcher, 2007).
We describe a novel and practical approach, called differential aberration correction (DAC) microscopy that combines super-resolution with multi-colour fluorescence microscopy to measure distances with nanometre accuracy over the whole field of view in both 2D and 3D. Classically, if two identical probes are placed closer than approximately 0.2 μm from each other, their images overlap to such an extent that it is deemed impossible to separate them (Abbe limit). In our method, two single fluorescent interrogation probes emitting at two different wavelengths are imaged (see Fig. 1). Under a first configuration of the microscope, the first probe is observed. Under a second configuration of the instrument, the second probe is observed. The two corresponding images do not overlap exactly because of chromatic aberrations. The precise positions of the single probes in the two images are measured with nanometre precision by fitting with a Gaussian intensity profile. These positions are affected by a multitude of aberrations including chromatic aberrations. We use a reference probe consisting of exactly the same two dyes as the interrogation probe pairs, but such that the two dyes are physically co-localized. Based on the positional shifts obtained for these reference probes, we estimate a deformation field across the whole field of view by interpolation. The positions of the interrogation probes are then corrected by using the deformation field to deliver the distance that separates them. In the present proof-of-concept manuscript, both our interrogation probes and the reference probes consisted of 100 nm multi-colour fluorescent microspheres. In an application setting, emission at a third wavelength could allow distinguishing reference probes from interrogation probes. In contrast to a technique such as stochastic optical reconstruction microscopy, DAC is limited to samples consisting of isolated pairs of dyes. It is not meant therefore to replace such techniques. However, DAC promises to become a useful technology for structural studies on purified proteins in homogeneous media.
Material and methods
We used an upright BX61 epifluorescence microscope from Olympus equipped with a Plan Apo 60x 0.9 air objective and a HBO 100 W lamp (Olympus, Tokyo, Japan). The first configuration of the instrument used the filter set U-MWIG2 (Olympus), appropriate for dyes such as CY3, and the second configuration used filter set U-MWU2, appropriate for dyes such as diamidino phenylindole (DAPI). Our cooled charge-coupled device (CCD) camera was an Evolution QEi (sensor pixel size 6.45 μm; Media Cybernetics, Bethesda, MD, USA), producing images of size 1394 × 1040 pixels. The microscope and the camera were controlled by Image Pro 5 (Media Cybernetics). Our motorized stepper Z-stage was from Prior Scientific, model H101 and the Z-spacing was set to 100 nm to obtain a cubic aspect ratio in 3D.
Samples consisted of 100 nm in diameter Tetraspeck multicolour fluorescent beads from Invitrogen (Carlsbad, CA, USA). The beads contain four undisclosed dyes with absorption/emission maxima at 365/430, 505/515, 560/580 and 660/680 nm. The Tetraspeck stock solution was diluted 1/100 in UV grade EtOH and 1 μL of this solution was diluted 1/100 in ProLong Gold media (Invitrogen). Two microlitres of this solution were placed under a glass cover slip and let to settle for 2 days before imaging.
Each field was acquired five times and averaged in order to increase the signal-to-noise ratio. A first Z-stack (a single image in case of 2D data) was captured under the DAPI configuration, followed by the second Z-stack immediately afterwards in the CY3 configuration.
The precise location of the geometric centre of the microspheres was obtained using iterative fitting of Gaussian profiles using an object tracking software (Diatrack, Semasopht). A half-width at half maximum equal to 1.4 pixels was given as parameter for the 2D and 3D Gaussians (Charannes, Switzerland). The beads are shown with their fitted centres indicated by black dots in Fig. 2(A), where the background image is a maximum projection across the 16 slices of the 3D stack. The 2D projections of the displacement vectors reflecting the aberration shifts in position between the two stacks were obtained by particle tracking. They are shown, scaled for visibility in Fig. 2(B).
The purpose of the reference probe is to generate a value for the aberration field at every position of interest. In order to generate this field, the software uses kernel-based interpolation:
where the ri's denote the position of the reference probe, r0 is the position at which the field is to be estimated (i.e. probe B in Fig. 1), and the vi's are the measured displacement vectors for each reference probe. The expression σ is a parameter that controls the bias–variance trade-off. The value of σ was set equal to 100 pixels as this value appeared to capture well the smooth variations of the aberration field, while ensuring that a sufficient number of data points contributed in forming estimates at each point. A portion of the resulting interpolation field is shown on a grid in Fig. 2(C).
To precisely measure the distance between a pair of interrogation probes, the displacement vector for this pair is corrected by subtraction of the deformation field at the position of the probe.
To validate the methodology, we arbitrarily picked one of the reference probes and assumed for a moment that it corresponded to a pair of interrogation probes. Then we attempted to measure the corresponding displacement for this pair using the methodology outlined above. The resulting distance indicates the precision of the technique, as it should ideally be equal to zero. To be consistent, the probe selected for measurement should not be used for the purpose of constructing the aberration field. Therefore, the whole procedure was repeated in turn for each of the reference probe picked as the interrogation probe. The procedure was repeated 20 times, producing the distribution of measured distances shown in Fig. 3(A) in the case of 2D experiments and Fig. 3(B) in the case of 3D experiments. The mean amplitude of the displacements (i.e. the errors) were equal to 20 ± 10 nm and 19 ± 7 nm in 2D and 3D, respectively, which indicate the current resolution of the method.
Discussion and conclusion
Using a single type of fluorescent microspheres serving both as interrogation and reference probe in the same sample, we have demonstrated the principle of a new method, called DAC microscopy. DAC is capable of measuring nanometre scale distances in 2D and 3D on a conventional fluorescence microscope. Our relatively modest instrument and methodology for estimating the deformation field gives hope that it will be possible to increase yet the resolution in the future beyond the demonstrated 20 nm. Notably, we are optimistic that the image signal-to-noise ratio can be improved by selecting an objective with higher numerical aperture, as well as an electron multiplying CCD camera. More careful sample preparation and cleaning of the optical components is also expected to help. This will be particularly important in applying the technique to much fainter samples comprising single fluorescent molecules attached to proteins (Fig. 1).
Note that our method only corrects for chromatic aberrations and not for spherical or other types of aberrations. However for the vanishingly small distances that we intend to measure in practice, these other aberrations may safely be neglected. More precisely, the defining quantity is the difference in spherical-like aberrations between two locations, say 100 nm away from each other. Assuming that the maximum spherical-like aberration over the field of view is 2 pixels, that the whole field is 1000 pixels, and that 1 pixel measures 100 nm, we expect at most (2/1000) × 100 = 0.2 nm of error. Other factors, such as the orientation of the dye dipole moment may have an influence on the ultimate resolution of DAC. In the present study, this effect was completely randomized by the large number of fluophores contributing to the signal.
In Fig. 2, it is apparent that the intensity distributions corresponding to beads are not exactly Gaussian, but Airy-like, as can be seen from the faint intensity rings surrounding the beads. In the future, we plan to use Airy functions for fitting the positions as it potentially could improve the localization precision.
The methodology assumes that a pair of different fluorescent probes is sitting in close proximity, isolated from all the other probes. The same limitation holds for FRET, which is an established technique. Used in static mode, DAC microscopy promises to reveal useful structural information on proteins and complexes that are difficult to crystallize. Used in time-lapse mode, the method promises to refresh understanding of protein function and dynamics.
We are grateful to Luke Domanski, David Lovell and the two reviewers for their helpful suggestions.