1. Introduction

By using the unique capabilities of single-molecule imaging to monitor the motion of individual molecules in real time with sub-nanometer accuracy, the mechanistic intermediate steps of molecular reactions hidden within ensemble averages become accessible. As a result, single-molecule fluorescence imaging has been widely used to understand detailed operational mechanisms of many biomolecular systems [1–4]. Single-molecule observations performed for several hours, however, remain challenging due to the focal and lateral drifts of the single-molecule imaging system. Because the lateral drift does not deteriorate image quality, it can be corrected after data acquisition using the spatial cross-correlation method [5–7]. However, the focal drift, which blurs single-molecule images, should be corrected in real time.

To solve the defocusing problem of single-molecule fluorescence microscopes, two different methods have been developed. First, in an image-based approach, fluorescence beads were used as fiducial markers, and an objective lens was scanned to find the focal plane [8]. This approach exposed several disadvantages. Because axial scanning of the objective lens was required to find the focal plane, the temporal resolution of the single-molecule imaging experiments was hampered. The bead-injection step during sample preparation may cause additional difficulties. To minimize photobleaching of the single-molecule fluorophores, beads with separated emission spectra are used, limiting the spectral freedom of single-molecule experiments.

To solve some of these problems, a reflection-based method was developed. In this approach, the infrared laser beam reflected from a cover slip is monitored using a position detector to track the focal plane [9,10]. Because this method does not require the scanning process to find the focal plane, the time response of the autofocusing system was not hampered. Furthermore, the potentially problematic bead-injection step can be avoided. A disadvantage of this reflection-based scheme is that the additional laser used for position detection could limit the spectral freedom of single-molecule fluorescence imaging. In single-molecule multi-color imaging that uses near-infrared fluorophores [11–13], this limitation can be more serious.

Here, we developed an autofocusing system based on optical astigmatism analysis of single-molecule images [14,15]. Because single-molecule images are used to track the focal plane, neither an additional laser/detector system nor a fluorescent bead is required, making the implementation of this autofocusing system simple and economic. Because axial scanning is not required, the temporal resolution of single-molecule experiments is not hampered. Finally, any available spectral region can be freely used for single-molecule fluorescence imaging, and this autofocusing system is fully compatible with current single-molecule multi-color fluorescence imaging [11–13].

2. Scheme of the autofocusing system

2.1 Optical setup

The autofocusing system was built by introducing two additional components to a conventional single-molecule FRET (fluorescence resonance energy transfer) microscope (Fig. 1(a) ) [16]. First, to follow the focal plane in real time, the objective was mounted on a piezoelectric actuator (PZT, Fig. 1(a)). Second, to generate asymmetric single-molecule images for the positive and negative defocusing, we placed a cylindrical lens (CL, Fig. 1(a)) in front of the camera [14,15]. The single-molecule images were elongated in the horizontal direction of the camera (the x-axis) for the negative defocus (z < 0, the focal plane is positioned below the glass surface) and were elongated in the vertical direction of the camera (the y-axis) for the positive defocus (z > 0, the focal plane is positioned above the glass surface). Figure 1(b) shows Cy3 single-molecule fluorescence images of the surface-immobilized DNA1 (Materials and methods) at three different objective positions.

 

Fig. 1 A schematic of the autofocusing system. (a) The optical setup. To add the autofocusing capability to a conventional single-molecule FRET microscope [16], we installed a piezoelectric stage (PZT, Physick Instrument, P-721) and a cylindrical lens (CL, Thorlabs, LJ1516L1-A, f = 1000 mm), which was positioned 75 mm from the camera (EM-CCD). The other key elements are as follows. OBJ: an objective lens (Olympus, UPlanSApo 60X), F: a longpass filter (Chroma, LP03-532RU), L2: a plano-convex lens (Melles Griot, 01 LAO 538, f = 120 mm), D: a dichroic mirror (Chroma, 640dcxr), L3: a plano-convex lens (Melles Griot, 01 LAO 638, f = 260.1 mm), M: a dielectric mirror (Thorlabs, BB2-E02), and EM-CCD: an electron multiplying charge coupled device (Andor, iXon DV897). (b) Cy3 images of immobilized DNA1 at different axial positions. The single-molecule images, which are circular in focus (top), become elongated in the x-direction for negative defocus (z = −0.5 µm, bottom left) and in the y-direction for positive defocus (z = + 0.5 µm, bottom right). (c) FOM at varying axial positions. (d) The FOMs in the range −0.2–0.2 μm (solid squares) and their linear fit (red line). The error bars in (c) and (d) were generated from 30 independent measurements.

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2.2 Parameterization of the defocused state

The Brenner gradient (_B), a macro used to determine image focal quality, decreases as the defocus increases [17–19]. It is defined as$B= {\displaystyle {\sum }_{i,j}{{\displaystyle [I(i,j)-I(i+m,j)]}}^2}$, where $I\left(i,j\right)$ is the signal intensity at the $\left(i,j\right)$ pixel, and m is a certain small integer. We used the difference of the normalized Brenner gradients in the x and y directions as a quantity to parameterize the defocused state (FOM: a figure of merit) as follows.

2.3 Realization of the autofocusing system

Before starting the single-molecule experiments, we characterized the core properties of the FOM profile: the slope of FOM in the range −0.2–0.2 μm ($s=\frac{\Delta Position}{\Delta FOM}$) and the standard deviation of the FOM (σ, obtained from 100 image frames at z = 0). Once an experiment started, FOM was calculated for each frame, and the position of the objective lens was controlled to follow the movement of the focal plane. The displacement of the objective lens (D) was empirically determined as follows. When the FOM was small ($\left|FOM\right|<4\sigma$), the objective lens was moved by a small amount ($D=sign(FOM)\times 0.002\text{μm}$). The criteria $4\sigma$ and a displacement $0.002\text{μm}$were selected to avoid unnecessary focal plane fluctuations. When the FOM was large ($\left|FOM\right|>4\sigma$), the objective was displaced according to $D=\frac{s}{2}\times FOM.$ A factor of 2 was included in the denominator to avoid oscillatory behavior during the focal plane search. and are affected by the signal-to-noise ratio (SNR, a ratio of the mean to the standard deviation of the fluorescence intensity of individual fluorophoes) of the single-molecule images and the number of single-molecules in the imaging area. However, and do not need to be accurately determined for the operation of the autofocusing system. Although they affect the autofocusing time, the autofocusing system faithfully operates over a wide range of and .

3. Results

3.1 Autofocusing from large defocuses

To test how large defocuses could be corrected by the autofocusing system, we intentionally defocused single-molecule images of DNA1 and monitored the process in which the microscope located the focal plane (Fig. 2(a) ). The fluorescence intensities decreased with increasing defocus in both directions, but once the autofocusing system was activated, the original intensities were readily recovered, even from ± 0.8 μm defocusing (Fig. 2(a)). When the SNR of the Cy3 signal was greater than 4, the time required to locate the focal plane (the refocusing time) did not depend on either the SNR or the defocusing distance in the range −0.5–0.5 μm (Fig. 2(b)). By contrast, when the SNR was smaller than 3, the refocusing time increased with decreasing SNR or with increasing defocusing distance (Fig. 2(b)). In small SNR conditions, the FOM has a greater chance to remain smaller than $4\sigma$, resulting in a slow approach to the focal plane. Once the microscope was refocused, we found that the focal plane was stably maintained. The fluctuation of the objective lens was less than 10 nm, independent of the SNR (Fig. 2(c)).

 

Fig. 2 Autofocusing from large defocuses. (a) Representative time traces of the fluorescence intensities (top; Cy3: green line, Cy5: red line), the position of the objective lens (middle), and the displacement of the objective lens for each step of autofocusing (bottom). The orange and black bars on top of the graphs indicate the on and off states of the autofocusing system, respectively. While the autofocusing system was off, the microscope was intentionally defocused downward or upward. (b) The autofocusing time for varying defocusing distances. Four different SNR conditions of Cy3 signal (2.0, 2.9, 4.3 and 6.1) were tested. The error bars were generated from five measurements. (c) The position stability of the objective lens while the image focus was maintained. Four different SNR conditions of Cy3 signal (2.0, 2.9, 4.3 and 6.1) were tested. The error bars indicate the standard error of the mean generated from 4 independent movies. The experiments were performed with a 0.1-s exposure time.

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3.2 Focus maintenance

To test the long-time stability of the microscope, we performed single-molecule FRET experiments on DNA1 (Fig. 1(a)) for 15 hours. To reduce the photobleaching of the fluorophores, the experiments were performed with a 3-s exposure time. The lateral drift in the single-molecule images were corrected using the spatial cross-correlation method [5–7]. With the autofocusing system turned off, meaningful data could not be obtained after two hours because the SNR of the Cy3 signal gradually deteriorated as the fluorescence intensities decreased with time (Fig. 3(a) ). In contrast, with the activated autofocusing system, the single-molecule data could stably be obtained for more than 15 hours (Fig. 3(b)). Remarkably, during the measurement, 66% of the Cy3 molecules were photobleached, but no deterioration of the SNR was detected (Fig. 3(b)). This persistence of the SNR demonstrates the robustness of the autofocusing system.

 

Fig. 3 Focus maintenance. (a) Representative time traces of single molecule fluorescence intensities (top) and the SNR of the Cy3 signal (bottom). The experiment was performed with the autofocusing system turned off. (b) Representative time traces of the single-molecule fluorescence intensities (top panel), the SNR of the Cy3 signal (2nd panel), the FOM (3rd panel), the number of remaining Cy3 molecules (4th panel), and the position of the objective lens (bottom). The experiment was performed with the autofocusing system activated. The SNR was obtained by analyzing the nearest 50 frames of the Cy3 images (n = 10). The experiments were performed with a 3-s exposure time.

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3.3 Real-time observation of B-Z transition dynamics at high salt conditions

Z-DNA is a left-handed isoform of double-stranded DNA [20,21] and is favorably formed in purine-pyrimidine repeats at high-salt conditions. By labeling the thymine bases flanking Z-DNA embedded in B-DNA (Fig. 4(a) ), we recently showed that the B-Z transition of CG repeats can be monitored via single-molecule FRET (Fig. 4(b)) [22]. In those studies, however, B-Z transition dynamics could not directly monitored in real time at the single-molecule level due to the slow dynamics of the B-Z transition.

 

Fig. 4 The real-time observation of B-Z transition kinetics at high-salt conditions. (a) The sequences of the DNA construct (B(CG)₆B). (b) The experimental scheme. The interdye distance increases in the Z-form, resulting in decreased FRET. (c) Representative time traces of the fluorescence intensities (top) and the corresponding FRET (gray, bottom). The most probable FRET time trace generated via hidden Markov modeling (HMM) [23] is overlaid (blue, bottom). (d) FRET histograms showing Z-DNA formation at 4.0 M NaClO₄. The histogram is fitted to two Gaussian functions. The low-FRET state (red) corresponds to Z-DNA, and the high-FRET state (green) corresponds to B-DNA. (e) The transition density plot at 4.0 M NaClO₄ obtained from hidden Markov modeling [24]. (f) The salt dependence of the B-Z transition rates. The experiments were performed with a 3-s exposure time.

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As an application of the autofocusing system to an interesting biophysical system, we studied salt-induced conformational dynamics of B(CG)₆B (Fig. 4(a), Materials and methods). We immobilized B(CG)₆B (Fig. 4(b)) in a buffer containing 4.0 M NaClO₄, and performed single-molecule FRET experiments using the autofocusing system. The FRET dynamics between the B-form (high FRET) and Z-form (low FRET) were clearly observed (Fig. 4(c)). The existence of two FRET states was also clear in the FRET histogram (Fig. 4(d)) and in the FRET transition density plot (Fig. 4(e)). Similar FRET dynamics were observed over a wide range of NaClO₄ concentrations. We found that the Z-to-B transition rate decreased with increasing NaClO₄ concentration, whereas the B-to-Z transition rate was affected only mildly (Fig. 4(f)).

4. Conclusion

Single-molecule fluorescence imaging has been applied to a variety of bio-molecular systems. Autofocusing systems, which can maintain single-molecule images in focus for several hours, will further extend the applicability of single-molecule fluorescence imaging techniques. Compared to the previously reported autofocusing systems, the autofocusing system introduced here has several advantages. First, this system is simple and economic in that neither a fiducial marker nor an extra position detection system is required. Second, it is fast in that the time resolution of single-molecule experiments is not hampered. Lastly, this system is fully compatible with single-molecule multi-color imaging [11,12,25,26] in that near-infrared fluorophores can be freely used. However, we should note that our autofocusing system cannot be used when fluorophores are distributed in three dimensions. Therefore, the new autofocusing system is expected to be widely used for surface-immobilized single-molecule fluorescence studies requiring long observation times.

5. Materials and methods

5.1 DNA preparation

The following DNA oligomers (written from 5′-3′) were purchased from Integrated DNA Technologies (Coralville, IA).

The DNA duplexes were prepared by annealing complementary strands (a and b for DNA1, and c and d for B(CG)₆B) as previously described.

5.2 Single-molecule experiments

DNA molecules were immobilized on a polyethylene glycol-coated surface via biotin-streptavidin interaction and imaged in 10 mM Tris-HCl buffer (pH 8.0) with oxygen scavenging system (saturated Trolox (Sigma-Aldrich), 0.4% w/v glucose (Sigma-Aldrich), 0.04 mg/ml catalase (Roche), and 1 mg/mL glucose oxidase (Sigma-Aldrich)), and salts (50 mM NaCl for Figs. 1-3 or varying concentration of NaClO₄ for Fig. 4). To reduce the air contact of the imaging buffer, the sample chambers were sealed with epoxy after the delivery of the imaging buffer. The raw image data (512 × 512 array of 32 bit signed integers) were background-subtracted and rescaled to an 8-bit unsigned integer array. The rescaled image array was used to extract the single-molecule intensity time traces. The 460 × 460 central area was used to calculate the Brenner gradients. Data acquisition and experimental control were performed using a custom LabVIEW (National Instrument) program run on a personal computer with 3.16 GHz processor (Intel Core2 Duo Processor E8500).