High-Speed Angle-Resolved Imaging of a Single Gold Nanorod with

Feb 3, 2015 - We developed two types of high-speed angle-resolved imaging methods for single gold nanorods (SAuNRs) using objective-type vertical illu...
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High-Speed Angle-Resolved Imaging of a Single Gold Nanorod with Microsecond Temporal Resolution and One-Degree Angle Precision Sawako Enoki,†,‡ Ryota Iino,§,∥ Yamato Niitani,⊥ Yoshihiro Minagawa,†,‡ Michio Tomishige,⊥ and Hiroyuki Noji*,†,‡ †

Department of Applied Chemistry, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan CREST, Japan Science and Technology Agency, Tokyo 102-8666, Japan § Okazaki Institute for Integrative Bioscience, Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki, Aichi 444-8787, Japan ∥ Department of Functional Molecular Science, School of Physical Sciences, The Graduate University for Advanced Studies (SOKENDAI), Hayama, Kanagawa 240-0193, Japan ⊥ Department of Applied Physics, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan ‡

S Supporting Information *

ABSTRACT: We developed two types of high-speed angle-resolved imaging methods for single gold nanorods (SAuNRs) using objective-type vertical illumination dark-field microscopy and a high-speed CMOS camera to achieve microsecond temporal and onedegree angle resolution. These methods are based on: (i) an intensity analysis of focused images of SAuNR split into two orthogonally polarized components and (ii) the analysis of defocused SAuNR images. We determined the angle precision (statistical error) and accuracy (systematic error) of the resultant SAuNR (80 nm × 40 nm) images projected onto a substrate surface (azimuthal angle) in both methods. Although both methods showed a similar precision of ∼1° for the azimuthal angle at a 10 μs temporal resolution, the defocused image analysis showed a superior angle accuracy of ∼5°. In addition, the polar angle was also determined from the defocused SAuNR images with a precision of ∼1°, by fitting with simulated images. By taking advantage of the defocused image method’s full revolution measurement range in the azimuthal angle, the rotation of the rotary molecular motor, F1-ATPase, was measured with 3.3 μs temporal resolution. The time constants of the pauses waiting for the elementary steps of the ATP hydrolysis reaction and the torque generated in the mechanical steps have been successfully estimated. The high-speed angle-resolved SAuNR imaging methods will be applicable to the monitoring of the fast conformational changes of many biological molecular machines.

S

rotational motion is detectable with an adequate angle-resolved imaging method. Several angle-resolved imaging methods have been reported previously.2,3 Among them, single fluorescent dyes are often used as probes to detect orientation, for a transition dipole in polarized excitation and/or emission.4,5 Due to their small size relative to the target molecule, fluorescent dyes can be attached to target molecules without affecting their function. However, angle-resolved imaging with high temporal resolution is inherently difficult to conduct as a result of low signal intensity and signal-to-noise ratio and relatively short duration of fluorescence before photobleaching. Compared with single fluorophore imaging, single gold nanoparticle (SAuNP) scattering imaging exhibits a signal intensity that is several orders of magnitude higher at the plasmon resonance wavelength.6−10 SAuNP, therefore, allows

ingle-molecule imaging based on optical microscopy is playing a pivotal role in modern analytical chemistry, providing data on the conformational dynamics of individual molecules of proteins and nucleic acids. Although translational motion measurement is usually the preferred option in singlemolecule imaging experiments, because of the relative simplicity of both the optical system and the subsequent data analysis, angle-resolved imaging is more desirable for the observation of the conformational dynamics of biomolecules. This is because the magnitude of the conformational change for biomolecules is generally smaller than the size of the molecule and is usually below or comparable to the optical imaging localization precision,1 unless the molecule undergoes an exceptionally large conformational change or translational movement as in the case of linear molecular motors. On the other hand, a conformational change in a molecule often accompanies the rotational motion of part of the molecule, for example, in the case of a domain rotation in proteins. Because the angle resolution is not limited by the localization precision, such a © XXXX American Chemical Society

Received: June 30, 2014 Accepted: January 22, 2015

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Analytical Chemistry imaging at very high spatiotemporal resolution, revealing a very rapid conformational change of biomolecules. In addition, the SAuNP scattering image does not suffer from the photobleaching or blinking issues that are commonly observed in single fluorophore or single quantum dot imaging.10 This enables stable and long-term recordings. Furthermore, the small sizes and low viscous frictional coefficients of SAuNP allow us to observe intrinsic conformational dynamics that are not affected by viscous friction on the probe. Currently, a single gold nanorod (SAuNR) with anisotropic shape is commercially available. As a result of this anisotropic shape, the scattered light from a SAuNR is strongly polarized along the axis of the rod11,12 and has been used for angle-resolved imaging in similar methods to those applied to the angle-resolved imaging of single fluorescent dye.2−5,13 So far, an orientation imaging system for gold nanorods has been used to analyze molecular dynamics of various important biological and chemical systems14 such as intracellular internalization,15−17 intracellular transportation,18−20 motor protein,21 a detection system for the antibody−antigen reaction,22 and orientation dynamics of nanoparticles at liquid/solid interfaces.23 Several types of angle-resolved SAuNR imaging have been reported to date, such as dark-field imaging,24,25 photothermal imaging,26 and differential interference contrast imaging.19,27 Among them, dark-field imaging has demonstrated the highest signal intensity and signal-to-noise ratio. For the dark-field imaging of SAuNR, several kinds of analytical methods for the determination of the rod’s three-dimensional orientation have been reported. One is the intensity analysis of focused images of AuNR split into two orthogonally polarized components. This method can determine the azimuthal angle (φ) and polar angle (θ) (Figure 1C), from the relative intensity difference and the intensity sum of the two components.15,18,23 The second method is analysis of the defocused image of the SAuNR. The point spread function (PSF) in the imaging plane of the defocused image contains information on the three-dimensional orientation.17,25,28 Therefore, φ and θ can be determined simultaneously. The third approach is dual color imaging of SAuNR based on a total-internal reflection scattering technique.29 Although these methods are useful, the accuracy of the φ and θ has not been assessed in detail. In addition, angle-resolved SAuNR imaging has not been well-exploited for high-speed imaging, while a microsecond time resolution has been reported by photon-counting detection of the intensity fluctuation of a single polarized component.21,30 In this study, we have developed two kinds of high-speed angle-resolved imaging methods for SAuNR, using objectivetype vertical illumination dark-field microscopy equipped with a high-speed CMOS camera with microsecond temporal resolution. The first technique employs an intensity analysis of focused SAuNR images split into two orthogonally polarized components, while the second method analyzes defocused SAuNR images. We compared the angle precision (statistical error) and accuracy (systematic error) of the two methods for two-dimensional angle-resolved SAuNR imaging projected onto a substrate surface (azimuthal angle, φ). Although both systems showed a similar precision of ∼1° for φ, the defocused image analysis displayed superior angle accuracy. The defocused SAuNR image was also subject to analysis of the polar angle measurement, θ, by fitting with simulated images. The defocused SAuNR imaging method was also applied to monitor fast rotary dynamics of a rotary molecular motor F1ATPase with 3.3 μs temporal resolution.

Figure 1. Experimental setups for high-speed angle-resolved imaging of SAuNR. (A) Setup for two orthogonally polarized components analysis (TOPCA). (B) Setup for analysis of defocused image (ADI). Both systems are combined with objective-type vertical-illumination dark-field microscopy.10 Examples of images are also shown in the bottom. In (B), an arrow shown in the left of the image indicates the orientation of SAuNR. (BE) beam expander, (DP) diaphragm, (L) lens, (M) mirror, (WP) quarter-wave plate, and (DM) dot mirror. (C) The spatial orientation of SAuNR. The φ and θ correspond to the azimuthal and polar angles, respectively.

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EXPERIMENTAL SECTION Microscopy. Figure 1 is a schematic drawing of the optical systems used to observe scattered light from SAuNR in the form of split images of two orthogonally polarized components (Figure 1A) and as a defocused image (Figure 1B), respectively. Both systems were based on objective-type vertical illumination dark-field microscopy, as previously described.10 An inverted microscope (IX71; Olympus, Tokyo, Japan) was used, and illumination was provided by a 640 nm laser (Cube640; Coherent Inc., United States). The collimated incident laser beam was converted to circularly polarized light by a quarterwave plate (WP) and reflected by a dot mirror (DM), while a lens (L1, f = 450 mm) was used to focus the beam onto the back focal plane of the objective lens (APON60X0TIRF, numerical aperture = 1.45, Olympus, Tokyo, Japan). The light scattered by the SAuNR was collected using the same objective lens. The DM has an elliptical reflecting surface (minor axis = 3.0 mm, major axis = 4.2 mm) in its central region, and it transmits scattered light through other areas. The scattering image was recorded as an eight-bit AVI file with a high-speed CMOS camera (FASTCAM-SA5; Photron, Tokyo, Japan). The pixel size was either 211 or 338 nm. For the two orthogonally polarized component analyses, the incident laser power was set to 8.5 μW/μm2 before it entered the objective lens, and the scattered light was then separated into two orthogonally B

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and polar angle, η′, in the imaging space (Figure S1, Supporting Information), with ψ varying from 0 to 2π and η′ varying from 0 to ηmax ′ . The value of ηmax ′ is given by

polarized light beams by the introduction of a birefringent calcite crystal (beam displacer, BD, Thorlab) in the optical path between the relay optics constructed by two lenses (L3 and L4, f = 60 mm for both). Two separated light beams were imaged as two spots on the COMS camera, which were separated from each other slightly. For the defocused image analysis, the incident laser power was set to 29.6 μW/μm2 before entering the objective lens and the scattered light was imaged as a slightly defocused spot. The defocus distances of the objective lens were set to 1.0−1.5 μm. For the analysis of the SAuNR attached to a glass surface, the time resolution was set to 10 μs. Two Orthogonally Polarized Component Analysis (TOPCA). The value for φ was calculated from the intensities of two separated orthogonally polarized scattering light beams using the following equation, where I1 and I2 are scattering intensities through channel 1 (Ch1) and channel 2 (Ch2), respectively (Figure 1A). φ = arccos I1/(I1 + I2)

⎛ NA ⎞ ⎟ ′ = arcsin⎜ ηmax ⎝ Mn′ ⎠

(2)

where NA is the numerical aperture of the objective, M is the magnification, and η′ is the refractive index of the imaging medium. Because the scattering light close to the optical axis is cut off by the dot mirror in our imaging system, we performed an integration of η′ in the region between the nonzero value, ηmin ′ to ηmax ′ . ηmin ′ is described as ⎞ ⎛ r r ′ = arcsin⎜ ′ ⎟≈ sin ηmax ηmin η′ NA f NA · ·f max′ ⎠ ⎝

(3)

where r is the dot mirror radius and f is the objective focal length. Observed images were fit to simulated PSF based on the Levenberg−Marquardt method. The fit parameters used were the defocus distance of the objective lens, the intensity ratio between the longitudinal and transverse dipole modes, the azimuthal and polar angles of the longitudinal dipole mode, the centroid position, signal intensity, and background. We fixed the intensity ratio between two short axial transverse dipole modes, assuming that the contributions of these two dipole modes to the total emission intensity are identical. When sequential images of identical SAuNR were fitted, the defocus distance of the objective lens and intensity ratio between the longitudinal and transverse dipole modes were set to the value determined by averaging the fitting results of the initial 5−8 frames, so as to reduce the computation time. The program was written in C++ with a library named Eigen (Guennebaud and Beno, Eigen v3, http://eigen.tuxfamily.org, 2010) which was used for matrix and vector calculation and Levenberg− Marquardt optimization. For the analysis of F1-ATPase rotation, the angle φ was sometimes assigned to two values separated by 180°, as two dark portions which were separated by 180° occasionally occurred. In such cases, the value of φ closer to that of the last frame was selected. F1-ATPase and Gold Nanorod Preparation. The α(His6 at N terminus/C193S)3β(His10 at N terminus)3γ(S108C/ I211C) subcomplex of F1-ATPase from thermophilic Bacillus PS3, which was modified for the rotation assay, was expressed in E. coli, purified, and biotinylated as described previously.32 The gold nanorod (80 nm × 40 nm) was purchased from NanoPartz Inc. and coated with streptavidin, as described previously.10 Rotation Assay. The rotary motion of F1 was visualized by attaching SAuNR (80 nm × 40 nm) onto the rotor γ subunit of F1 and immobilizing the α3β3 stator ring on a nickelnitrilotriacetic acid glass surface. The experimental procedures of the rotational assay were the same as those described previously except for the buffer content.10 The buffer for the rotation assay contained 10 mM MOPS-KOH at pH 7.0, 50 mM KCl, 2−5 mM MgCl2, 1 mM phospho(enol)pyrubate, 0.1 mg/mL pyruvate kinase, and the indicated concentration of ATP (0.3−3 mM). Temperature for the rotation assay was 26− 31 °C. Estimation of Torque. For the estimation of the torque, N, generated by F1-ATPase from the viscous drag on the SAuNR, the following equation was used:

(1)

Geometric Analysis of Defocused Image (gADI). In this method, the angle of the vector from the center of a doughnutshaped image to a dark peripheral portion, which represents the φ value of the SAuNR, was determined. (The example is indicated by an arrow in Figure 1B.) In order to determine the angle, the following image processing was performed, using ImageJ software. Each pixel was divided into 5 × 5 subpixels to determine the angle with higher accuracy. Inner and outer circles were set to surround the bright doughnut shaped area of the scattering image. Then, the intensity of each pixel within the area enclosed between the outer and inner circles was normalized by setting the maximum pixel to 255 and the minimum pixel to 0. This procedure reduces variations in intensities among different frames. The intensity of each pixel outside the area was set to 0 (Image 1). Then, the new reference images (Image 2), which had a bright, similar doughnut-shaped area, were generated as follows. The intensity of each pixel in the area between the inner and outer circles was set to 255 and that of the outside area was set to 0, and 3 × 3 pixel averaging was then performed. Next, Image 1 was subtracted from Image 2 to obtain Image 3. This procedure resulted in the conversion of the dark portion into a high peak. Then, the centroid of Image 3 was calculated, and the angle of the vector from the center of the doughnut-shaped image to the dark peripheral portion was determined. For the analysis of the F1-ATPase rotation, two dark portions separated by 180°, which corresponds to the SAuNR being almost parallel to the substrate surface (θ ∼90° in Figure 1C), sometimes appeared due to intensity fluctuations. This resulted in two possible values for φ. In such cases, the φ value closer to that of the last frame was selected. Fitting Analysis of Defocused Image with the Simulated Images (fADI). In this method, the PSF of SAuNR in the imaging plane was fit with simulated images, and φ and θ were determined simultaneously. A dark-field SAuNR image was simulated using the 3-dipole mode.25,31 The dipole PSF was calculated as previously described using a MATLAB program “QDControl” (http://www.joerg-enderlein.de/ imagingOfSingleMolecules.html [accessed April 4, 2014]),13 except that the effect of the dot mirror on the PSF was taken into account. In the previous study,13 the light intensity on the imaging plane was calculated by integrating the amplitudes of plane waves emitted from a dipole over the azimuthal angle, ψ,

N = ωξ C

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had an average size of 80 nm × 40 nm (aspect ratio of 2.0), and the maximum absorption wavelengths for the long and short axes were 660 and 529 nm, respectively. For precision and accuracy analysis of the two methods, the sample stage was manually rotated between 0° and 360°, incremented by 10°, in the counterclockwise direction (corresponding to φ), and the same SAuNRs were observed using both methods at each angle. The standard deviation of the sample angle difference between each 10 degrees rotated manually was determined to be 0.3°. For the TOPCA (Figure 1A), two orthogonally polarized components from the SAuNR were observed as two bright spots adjacent to each other (Figure 2A, top). The intensities of the two spots changed as the sample stage was rotated and showed clear anticorrelation. While φ determined with this analytical method is principally projected in the first quadrant, 0−90° (Figure 2B, left), we converted the obtained values of φ into equivalent values for a 0−360° projection, taking the counterclockwise rotation of the sample stage into account. The resultant values of φ are plotted against the angle of the sample stage in Figure 3A (blue squares). The φ essentially showed a good linear correlation with the angle of the sample stage. However, the data points deviated around the polarization axis of the birefringent calcite crystal (0° and 90° in Figure 2B, left; or 0°, 90°, 180°, and 270° in Figure 3A). As a result, the residual of the linear fit to φ as a function of the sample stage angle showed slight deviations around 0°, 90°, 180°, and 270° (Figure 3B). There are two causes of these deviations. One is an error in calculation when the intensity of one spot is close to 0. Another is a change of polarization direction inside the objective lens, especially for a high NA objective lens.18,35 This systematic error of the φ caused by change of polarization direction inside the objective lens could be corrected by theoretical calculation in principle. However, in order to correct the angles, the maximum intensity value corresponding to θ = 90° is necessary. In our experiments, it was difficult to correct the φ of SAuNR fixed on the glass surface because it is not assured that the θ of the SAuNR is 90°. The average residual value for all sample stage angles collected from three SAuNRs was 7.9 ± 5.8°. This value corresponds to the accuracy of the φ value determined by this method (Table 1). Next, we evaluated the precision (reproducibility) of the φ determination. A total of 10 000 image sequences were recorded at each sample stage angle. The value of φ was then determined for each image frame, and the standard deviation (SD) was calculated (Figure 3C). The computation time was 0.3 ms per image frame. The SD was distributed around 1° at all sample stage angles. Thus, the result for φ showed good precision. The average value of the SD was 1.0 ± 0.4°. Evaluation of Angle Accuracy and Precision Determined by Analysis of Defocused Image (ADI). In defocused images, the SAuNRs displayed a doughnut-shaped pattern with two dark portions, separated by 180° (Figure 2 middle). When the long axis of the SAuNR was parallel to the coverslip (θ, angle from z-axis is 90° in Figure 1C), intensities of two dark portions are comparable. When the θ is less than 90°, the intensity of one dark portion is lower than the other dark portion. Here, we selectively analyzed defocused images with one darker portion. It was found that the dark portion rotated as the sample stage was turned. Then, φ was determined using two analytical methods. In the geometric analysis of the defocused image (gADI), the orientation of the SAuNR was determined from the vector that starts from the

where ω is the angular velocity and ξ is the frictional drag coefficient. The ω was calculated by fitting the averaged trajectory of 18 superimposed successive steps. The ξ is dependent on how SAuNR attaches to F1-ATPase, according to the following equation:33 ξ=

3 3 4π η(L1 + L 2 ) 3 ⎡ln L + ν ⎤ ⎣ 2r ⎦

( )

ν = −0.662 +

0.917 L 2r

(5)

−

0.050 2

( 2Lr )

(6)

where r is the radius of the short axis of SAuNR, L is the length of the SAuNR long axis, L1 and L2 are the lengths of the long axis of the SAuNR from each end to the attachment point, and η is the viscosity of the medium. To estimate N using the fluctuation theorem,34 the following equation was used: N=

kBT ⎡ P(Δφ) ⎤ ln⎢ ⎥ Δφ ⎣ P( −Δφ) ⎦

(7)

where P(Δφ) is the probability distribution for Δφ = φ(t + Δt) − φ(t), kB is the Boltzmann constant, and T is the absolute temperature. For the torque estimation, 70 successive steps were analyzed.

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RESULTS AND DISCUSSION Evaluation of Angle Accuracy and Precision of Two Orthogonally Polarized Components Analysis (TOPCA). In order to evaluate the two methods, the two orthogonally polarized components analysis (TOPCA) of the focused SAuNR image, and the analysis of the defocused image (ADI), we imaged SAuNR fixed onto a glass surface with 10 μs temporal resolution (Figure 2). The AuNRs used in this study

Figure 2. (A) Dark-field images of SAuNR fixed onto a glass surface obtained at 10 μs temporal resolution. The sample stage was rotated from 0° to 360° in the counterclockwise direction. (Top) Split images of two orthogonally polarized components. Upper and lower correspond to the Ch1 and Ch2 in Figure 1A, respectively. (Middle) Observed defocused images. (Bottom) Simulated defocused images. (B) Correspondence of angles analyzed by the two orthogonally polarized component analysis (TOPCA) (left) and the analysis of the defocused image (ADI) (right). D

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Table 1. Comparison of Three Methods of Angle-Resolved Analysis two orthogonally polarized components (TOPCA) φ, angle range (deg) φ, angle accuracy (deg)a φ, angle precision (deg)b computation time (ms)c 3D angleresolved analysis θ, angle precision (deg)b

defocused, geometric analysis (gADI)

defocused, fit with simulation (fADI)

0−90

0−360

0−360

7.9 ± 5.8

4.2 ± 3.3

5.2 ± 3.7

1.0 ± 0.4

0.8 ± 0.3

0.8 ± 0.4

0.3

1.8

130

no

no

yes

NDd

ND

1.1 ± 1.3

Angle accuracy is the average of absolute residual of linear fit for all sample angles from three SAuNRs observed at 10 μs temporal resolution. bAverage of SD for 10 000 frames. cComputation time required to analyze a single image frame. dNot determined. a

gADI and fADI showed good precision for the φ value, compared to that obtained by the TOPCA. Another advantage of fADI is the capability to determine the value of θ. The values of θ can be directly obtained by the fitting of the observed images with simulated images (Figure 3D). It was found that the average value of θ for all sample stage angles was 75.5 ± 9.0°. However, we could not evaluate the accuracy of the θ because it was difficult to determine the correct values of θ in our experiments. On the other hand, the precision of the θ was calculated to be 1.1 ± 1.3° and comparable to that of the φ value (Table 1). This angular precision of the gold nanorod was much better than that of fluorescent dye previously reported while the temporal resolution increased significantly in our study.36,37 One drawback of fADI is longer computation time. It takes 1.8 and 130 ms per image frame for gADI and fADI, respectively. It is 6-times or 133-times longer than that (0.3 ms) for TOPCA, respectively. Therefore, if we focus on only the φ, gADI would be the best choice for the high throughput analysis. Analysis of the Pauses in the Rotation of a Molecular Motor F1-ATPase. As a demonstration of our method applied to the single-molecule study of molecular motors, we observed the rotation of F1-ATPase at a 3.3 μs temporal resolution using SAuNR as a probe. F1-ATPase is an ATP-driven rotary molecular motor in which the γ subunit rotates against the α3β3 cylinder. Three catalytic β subunits hydrolyze the ATP cooperatively.38 The unitary step of γ-rotation is 120° composed of 80° and 40° substeps. The 80° substeps are initiated after a pause for ATP binding and ADP release (binding pause), and the 40° substeps are initiated after a pause for ATP cleavage and phosphate release (catalytic pause).6,39,40 At saturated ATP concentration, previous high-speed imaging of the rotation using SAuNP as a probe has shown that F1ATPase rotates with ∼1 ms catalytic pauses separated by 120°.10 In the present study, we attached streptavidin-coated SAuNR to the biotinylated γ subunit and observed the rotation at a saturated 3 mM ATP concentration. Note that it has been

Figure 3. (A) The φ as a function of the sample stage angle determined by TOPCA (blue squares), gADI (red circles), and fADI (green circles). The φ determined by TOPCA was converted to 0− 360° based on the correspondence shown in Figure 2B. Each solid line is the linear fit of φ against the angle of the sample stage, in which the slope was set at 1. (B) Residuals of the linear fit. (C) Standard deviation (SD) of the φ for 10 000 image sequences recorded and analyzed at each angle. (D) The θ determined by fADI.

center and ends at the low intensity portion of the doughnut. We also determined φ from a fitting analysis of the defocused image with the simulated images (fADI) (for details, see the Experimental Section). The resultant values of φ determined by gADI and fADI are plotted in Figure 3A (red and green circles). Both of the φ values showed good agreement with the angle of the sample stage. The residuals of the linear fit to the φ values, as a function of the sample stage angle, were within ±15° for all sample angles, and the average values of the residuals for all sample stage angles collected from three SAuNRs were 4.2 ± 3.3° and 5.2 ± 3.7° for gADI and fADI, respectively (Figure 3B). Therefore, the defocused image analysis produced a more accurate φ result than the TOPCA (Table 1). The precision was also estimated as described above, by calculating the SD of φ for 10 000 image sequences at each sample stage angle (Figure 3C). The averaged values of 0.8 ± 0.3° and 0.8 ± 0.4° were obtained for gADI and fADI, respectively. Thus, both E

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0.16 ms and that for binding pause was 0.24 ± 0.03 ms. The time constants for catalytic pause were therefore comparable to those reported previously.10 On the other hand, the time constant for the binding pause is much longer than the predicted value for the ATP binding pause (∼0.01 ms).6 This may correspond to the time constant for a temperature sensitive reaction, which occurs at the angle for the binding pause and is highly dependent on temperature.42−44 The time constant was almost the same with the estimated time constant for a temperature sensitive reaction (0.3 ms).42 The standard deviations of φ in the catalytic pause were 15.0° and 15.2° for gADI and fADI, respectively, and therefore almost identical. The distribution of φ during the catalytic pause would reflect the rotary potential of F1-ATPase. Furthermore, from the fit with simulation, not only the time course of the φ but also that of the θ value was obtained (Figure 4B, bottom). The average value of θ during the rotation was measured at 56.3 ± 7.7°. Estimation of the Torque Generated during the Mechanical Step of F1-ATPase. Next, the torque generated by F1-ATPase was estimated from the time course of the φ value obtained through gADI. Figure 5 shows the 18 successive

reported in the previous studies that the gold surface does not inhibit the activity of F1-ATPase.6 The rotation was analyzed using gADI and fADI because of the high accuracy of the φ and its wide angle range of 0−360°. In the absence of ATP, there were no rotating SAuNRs (0.0%) among 1343 SAuNRs (Figure S2, Supporting Information). On the other hand, at saturated ATP concentration, 32 SAuNRs (2.3%) among 1343 SAuNRs rotated. The probability of finding rotating particles at saturated ATP concentration was comparable to a previous one.41 As shown in Figure 4A, the stepwise counterclockwise rotation of

Figure 5. Mechanical steps for three different F1-ATPase molecules. Thin lines and red thick lines show the superimposed 18 successive steps and averaged steps, respectively. Gray horizontal dashed lines show the average angle of the pause (top and bottom: catalytic pause; middle: binding pause). The angular velocity was obtained by the slope of linear fit between binding and catalytic pauses (blue dashed lines). The values of the torque estimated by angular velocity and the frictional drag coefficient are shown in black, and those estimated by the fluctuation theorem are shown in blue.

superimposed steps in rotation for three different molecules. One method of estimating the torque utilizes the angular velocity during the mechanical step and the frictional drag coefficient of the probe.6,45,46 The average angular velocity of the three molecules was 1.76 × 104 rad/s. Because the frictional drag coefficient depends on how the SAuNR attaches to F1ATPase, the estimated torque has a relatively large range (Figure 5 values given in black), and the average torque for the three molecules was 16.1−64.5 pNnm. The lower and upper limits were the values assuming that the SAuNR was parallel to the sample plane and F1-ATPase was attached to the center and the end of the SAuNR, respectively. Because of difficulties in the accurate estimation of the frictional drag coefficient, the torque was also estimated by analysis of the mechanical steps using the fluctuation theorem (Figure S3, Supporting Information), which does not require the frictional drag coefficient (Figure 5, values given in blue).34 The average torque for the three molecules was found to be 44.2 ± 5.1 pNnm. This value was almost the same as those previously reported,34,45 indicating that torque can be quantitatively estimated by SAuNR.

Figure 4. Stepwise rotation of a single F1-ATPase observed by a defocused SAuNR image at 3.3 μs temporal resolution. (A) Example of defocused images of AuNR attached to the rotor γ subunit. Images were shown in every 30 frames (100 μs interval). These images correspond to the time courses indicated by a gray dashed square in B (0.0147−0.0177 s). (B) Time course of the φ determined by gADI (top, red) and fADI (middle, blue), and the θ determined by fADI (bottom, blue). Short binding pauses are shown in purple and cyan for gADI and fADI, respectively. Right figures show the angle distributions. (C) Distribution of the pause duration. (left) Pause at catalytic angle. Distribution was fit with an equation assuming the consecutive reaction with two time constants; A × [exp(−k1t) − exp(−k2t)]. (right) Pause at binding angle. Distribution was fit with single-exponential decay. Observations were recorded at 26 °C.

F1-ATPase was clearly observed. In contrast to the previous study, 6 pausing positions, which correspond to catalytic and binding pauses, were observed (Figure 4B). The distribution of the dwell time for catalytic pauses were reproduced by a fit with two consecutive reactions, and the dwell time for the binding pauses showed single-exponential decay (Figure 4C). The time constants for the catalytic pauses were 0.56 ± 0.23 and 0.34 ± F

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CONCLUSIONS In this study, we have shown that a combination of objectivetype vertical illumination dark-field microscopy and defocused image analysis enables the high-speed angle-resolved imaging of SAuNR with microsecond temporal resolution and one-degree angle precision. Our optical system can also be applied to the orientation determination of SAuNR through focused image analysis.31 This will further improve the temporal resolution with the help of the improved signal-to-noise ratio of the focused image. Furthermore, we have conducted a high-speed single-molecule analysis of the rotary molecular motor, F1ATPase. Because of improvement of the temporal resolution, we successfully estimated the rotary torque generated by F1ATPase accurately using the fluctuation theorem. Along with F1-ATPase or other molecular motors, the high-speed angleresolved imaging of SAuNR will be applicable to the monitoring of the fast conformational dynamics of enzymes which do not accompany rotary or translational movement. Our method will pave the way for the high-speed singlemolecule analysis of many biological molecular machines.

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ASSOCIATED CONTENT

S Supporting Information *

Figures S1−S3. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel: +81 3 5841 7252. Fax: +81 3 5841 1872. E-mail: hnoji@ appchem.t.u-tokyo.ac.jp. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by CREST (Core Research for Evolutional Science and Technology) of Japan Science and Technology Agency and Grant-in-Aids for Scientific Research (Nos. 25251016, 22247025 to H.N.; Nos. 26104507, 24370062 to R.I.) from the Ministry of Education, Science, Sports, and Culture of Japan.We thank Dr. R. Watanabe for the analysis program and discussion and members of the Noji laboratory for help and advice.

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DOI: 10.1021/ac502408c Anal. Chem. XXXX, XXX, XXX−XXX

Article

Analytical Chemistry (46) Sakaki, N.; Shimo-Kon, R.; Adachi, K.; Itoh, H.; Furuike, S.; Muneyuki, E.; Yoshida, M.; Kinosita, K., Jr. Biophys. J. 2005, 88, 2047− 2056.

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DOI: 10.1021/ac502408c Anal. Chem. XXXX, XXX, XXX−XXX