Letter pubs.acs.org/NanoLett
Three-Dimensional Orientation Determination of Stationary Anisotropic Nanoparticles with Sub-Degree Precision under Total Internal Reflection Scattering Microscopy Kyle Marchuk and Ning Fang* Ames Laboratory-USDOE and Department of Chemistry, Iowa State University, Ames, Iowa 50011, United States S Supporting Information *
ABSTRACT: Single-particle and single-molecule orientation determination plays a vital role in deciphering nanoscale motion in complex environments. Previous attempts to determine the absolute three-dimensional orientation of anisotropic particles rely on subjective pattern matching and are inherently plagued by high degrees of uncertainty. Herein, we describe a method utilizing total internal reflection scattering microscopy to determine the 3D orientation of gold nanorods with subdegree uncertainty. The method is then applied to the biologically relevant system of microtubule cargo loading. Finally, we demonstrate the method holds potential for identifying single particles versus proximate neighbors within the diffraction limited area. KEYWORDS: Total internal reflection scattering (TIRS), single-particle, orientation determination, microtubule cargo, localized surface plasmon resonance
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plane orientation associated with orientation dependent signal or the necessity to match defocused image patterns. Defocused imaging techniques such as those used with darkfield microscopy use pattern matching with simulated images to determine the 3D orientation of anisotropic metallic nanoparticles. The resolution of which is dependent on the ability of a researcher to determine whether or not a particular pattern matches. This requires the correct simulation input of the defocus depth that may not be accurately estimated if particles are in different sample planes. For convenience, Supporting Information Figure 1 displays examples of how a focal plane change of even a few hundred nanometers can affect pattern matching, while Supporting Information Figure 2 demonstrates how difficult it can be to match simulated defocused images. A more recent technique called focused orientation and position imaging (FOPI) induces an image charge-coupled effect with the substrate to determine 3D orientation information but also suffers from image correlation and has the added necessity of needing a particular substrate-particle interaction.19 Previously, we have demonstrated the ability to use both short- and long-axis surface plasmon resonance (SPR) enhancement to simultaneously probe the in-plane and outof-plane (tilt) motion of dynamic surface-bound AuNRs using TIRS microscopy.20 By illuminating the sample with two wavelengths of light that are orthogonally polarized, the particle intensity fluctuates correspondingly to the 3D orientation of
ingle particle orientation and rotational tracking (SPORT) techniques have made a large impact in studying molecular motions.1 This is due partially to the rise in use of plasmonic nanoparticles as imaging probes compared to organic fluorescent dyes or semiconductor quantum dots. The advantages of these nanoparticles include large absorption and scattering cross sections,2 high-photostability,2,3 biocompatibility,4 and shape-induced anisotropic optical properties.5 While the other traits are crucial to their application, it is the anisotropic optical properties that allows for the determination of particle orientation and thus the elucidation of molecular motions. Particle orientation determination for gold nanorods (AuNRs) in the plane of the sample substrate has been demonstrated by a few optical techniques including dark-field (DF) polarization microscopy,5−7 photothermal heterodyne imaging,8 and differential interference contrast (DIC) microscopy.9−13 Light scattered from AuNRs has been shown to be strongly polarized along the long axis,14 and the aforementioned techniques take advantage of this scattering trait by monitoring the intensity of orthogonally polarized light to determine the in-plane orientation of the nanoparticles. While these techniques are simple to implement, they lack the ability to determine the out-of-plane (tilt) orientation of the AuNRs. Image recognition has been implemented with DIC microscopy,15 defocused imaging techniques,16−18 and total internal reflection scattering (TIRS) microscopy19 to determine the three-dimensional (3D) particle orientation without angular degeneracy. Unfortunately, these techniques are accompanied by a large degree of error (>10°) in determining the out-of© XXXX American Chemical Society
Received: August 8, 2013 Revised: October 11, 2013
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Figure 1. (A) Diagram of the TIRS microscope illustrating laser geometry. M, mirror; S, shutter; FL, focusing lens; FR, Fresnel rhombs attached to a rotating stage. (B) Absorption curve of the 25 × 63 nm AuNRs used in the experiment. (C) The coordinate system for both the incoming polarization (left) and the 3D orientation of the AuNR. X and Y is the sample plane with X being the direction of the incoming laser. Z is the axial direction. ψ, azimuthal angle, θ, polar angle.
To create a stationary environment with randomly oriented particles, AuNRs were diluted in a 0.5% (w/v) solution of agarose gel before being deposited on a quartz slide. The slide was then placed on the prism, focused under the microscope, and allowed to settle for 30 min to reduce sample drift. Using the HWP, the polarization of the incoming laser was carefully aligned to produce s-pol light (light with the electric field parallel to the substrate surface). Light that has the electric field aligned perpendicular to the substrate surface is considered ppolarized (p-pol). The EMCCD exposure time was 30 ms in frame transfer mode while the stage rotated the HWP at 15°/s. The illumination polarization rotates at double the speed of the HWP producing a speed of 30°/s and 0.9° of polarization rotation per frame. The sample was then defocused by ∼1.0 μm, and the procedure was repeated producing two data sets for each area of interest. The ∼1.0 μm defocus depth was chosen to produce defocused images dissimilar to images that would be produced at nearby focal depths (Supporting Information Figure 1) and maximize the effect the polar angle has on the image pattern. The coordinate system for the electric field, particle orientation, and polarization direction is similar to that used by Beausang et al. and has been defined in Figure 1C.21 In the microscope coordinate system, x and y comprise the sample plane, and x is the direction of illumination propagation. The optical axis is z. The AuNR orientation is defined by the polar angle (0° ≤ θ ≤ 90°) and the azimuthal angle (0° ≤ φ ≤ 360°), which originates on the x axis. The angle of the incoming polarization (ζ) is defined as 0° when the polarization is
rotating particles. While the previous technique is useful to the study of dynamic movement of nanorods, the present study has a new focus on the accuracy in determining the orientation of stationary probes. Using a combination of defocused imaging and the rotation of the polarization direction of light incident upon the sample, we resolve the 3D orientation of stationary AuNRs with unprecedented precision in TIRS microscopy. AuNRs with an aspect ratio of 2.4 (25 nm × 60 nm) and a long axis SPR absorption peak centered at 628 nm were used. The instrument is a TIRS microscope modified from its previous description (Figure 1A).19,20 Briefly, our prism-based TIRS microscope consists of a 660 nm continuous wave (CW) linearly polarized laser directed through periscope optics and focused under the objective. Placed after the periscope, a double Fresnel rhomb acting as a λ/2 wave plate (HWP) was inserted into the light path of the 660 nm laser. This HWP was attached to a computer-controlled rotating stage that allows light to pass through its center. We used this stage/HWP combination to accurately control the polarization componentsunder TIR. It should be noted that a double Fresnel rhomb is not considered a polarization rotator like that of a half-wave plate made from birefringent material. The double Fresnel rhomb HWP will actually produce elliptically or circularly polarized light depending upon its orientation when it is not modifying the light by a full 90°, but since we are using a TIR method where the incoming radiation generates an evanescent field, the effect at the sample interface is identical. A more detailed explanation can be found in Supporting Information Methods. B
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Figure 2. Simulated intensity profiles for various polar and azimuthal angles with respect to ζ.
Figure 3. Representation of the dependence of azimuthal angle determination upon signal intensity. (A) Plots of the intensity difference for the symmetry axis determination of the same AuNR at six different total intensities. The yellow line represents the trace with the highest intensity, which was set to 1.0 normalized intensity (NI). The rest of the plots represent the symmetry determination for the same particle at different angles ζ. The gray line represents the intensity level of uncertainty. (B) Surface plot of the lowest intensity symmetry determination (0.22NI) corresponding to the particle image (C). (D,E) Surface plot and particle image corresponding to the 0.38NI plot, respectively. (F,G) Surface plot and particle image corresponding to the 1.0NI plot, respectively. C
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Figure 4. Data and representations of a single AuNR with a polar angle of 23.4 ± 0.8°. (A) Raw intensity versus the first 180° of ζ fit with a higherorder polynomial. (B) Representation of the azimuthal angle determination using the defocused image with the highest contrast. The angle was determined to be 44.1 ± 0.9° with respect to the x-axis. (C) Plot portraying the alignment of the data with the simulated curves. (D) The 3D representation of the AuNR in space. (E) Actual defocused imaged taken at the angle ζ of highest intensity. (F) Simulated image of a AuNR with the angles calculated for the particle (φ = 135.9°, θ = 23.4°).
horizontal and therefore producing s-pol illumination and 90° when the polarization is vertical and producing p-pol illumination. For 0° < ζ < 90° and 90° < ζ < 180°, the polarization components under total internal reflection (TIR) are a ratio of s-pol and p-pol illumination corresponding to the illumination produced by the HWP (see Supporting Information Methods). By changing the ratio of s-pol and p-pol light at the surface of TIR, the electric field polarization (ε̂) is affected. Since the particles are anisotropic dipoles, the scattering intensity from the AuNR is dependent on both the 3D particle orientation and ε̂. It is therefore possible to simulate the scattering intensity based on the incident polarization (see Methods in Supporting Information for details). As can be seen in Figure 2, the intensity profile is dependent on both the polar and azimuthal angle. By first determining the azimuthal angle, it then becomes possible to fit the scattering intensity profile to the simulated curve to calculate the polar angle. There is a particular trend that is depicted in the simulated data. As φ changes from 90° to 0°, the range of the peak position of the curve is found to be narrower. This is due to the s-pol component of the evanescent field no longer influencing the overall SPR enhancement and is associated with increasing uncertainty in the polar angle fitting. The uncertainty increases to the point that when the AuNR is perfectly aligned with the x-
axis, the polar angle can no longer be determined. This limitation can be overcome by either adding a second illumination line perpendicular to the original line or by rotating the sample 90° and collecting a second set of data. Though we previously mentioned that defocused imaging techniques are difficult to interpret for polar angle determination, high azimuthal angle precision can be achieved under the proper conditions. The defocusing of a AuNR produces an image pattern with an axis of symmetry corresponding to the long axis of the particle (Figure 3G). The simplest method of determining symmetry involves slicing the particle image into two halves through the center point and comparing the integrated intensity. A MATLAB code was written that rotates the axis in which the image is sliced and calculates the differences in integrated intensities (see Supporting Information Methods for details). The angle at which the integrated intensity difference is least is considered the angle of symmetry. The precision of the azimuthal angle determination is highly dependent on overall image intensity as can be seen in Figure 3, which displays the plots of the same particle at different angles ζ and therefore different intensities. The gray line represents the uncertainty caused by noise within the signal collection. The uncertainty of the azimuthal angle is determined by multiplying the noise by the total image area and adding it to the integrated intensity difference at the angle of symmetry. D
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Figure 5. The recorded and simulated defocused images for AuNRs colocalized with stationary microtubules. The defocused image in (A) and the simulated image in (B) correspond to the particle (Nr1) in (C). (D,E) Images correspond to the particle (Nr2) in (C). The 3D orientation of Nr1 is φ = 77.9° ± 0.8°, θ = 37.5° ± 0.7°, and Nr2 is φ = 29.9° ± 3.9° and θ = 84.5° ± 0.6°. Scale bar is 5 μm. White line represents the approximate center of the microtubule fluorescence.
angle determination arises from a combination of the intensity and the orientation of the particle. This technique was then applied to the loading of cargo onto surface-bound microtubules. AuNRs were attached to microtubules through the biotin−neutravidin interaction before the microtubules were attached to a poly-L-lysine modified glass coverslide (Corning). Figure 5 shows two examples of particles (Nr1 & Nr2) attached to a microtubule. The defocused image (Figure 5A) and simulated image (Figure 5B) correspond to particle Nr1 in Figure 5C with angles φ = 77.9° ± 0.8° and θ = 37.5° ± 0.7°. Even with particles attached to biological structures on a nonquartz substrate, the technique can achieve high precision for both in-plane and out-of-plane orientation. More particles attached to stationary microtubules were analyzed. Particle Nr2, Nr3, and Nr4 (Nr3 and Nr4 can be seen in Supporting Information Figure 5) have 3D orientations of φ = 29.9° ± 3.9° and θ = 84.5° ± 0.6°, φ = 22.1° ± 1.7° and θ = 59.3° ± 2.7°, φ = 138.6° ± 1.3° and θ = 55.9° ± 1.5°, respectively. Overall, the particles with enough lateral distance between neighboring particles had 3D orientation with precision typically better than 5° and routinely neared single degree uncertainty. We found that a majority of the particles typically had relatively large polar angles (>45°) when attached to the stationary microtubules. Microtubules have a diameter of ∼25 nm, which is similar to the width of the AuNRs. These sizes suggest the majority of AuNRs will have a rather flat profile relative to the sample substrate. Proximate neighbors, meaning multiple uncoupled particles within a diffraction limited spot, are commonly found in singleparticle imaging experiments.22 Our technique supplies an opportunity to distinguish proximate neighbors with a large difference in polar angles from single particles through either focused or defocused imaging. The detailed explanation can be found in the Supporting Information. In summary, a method for determining the 3D orientation of stationary metallic anisotropic nanoparticles with subdegree uncertainty has been demonstrated in TIRS microscopy. Rotating the incoming polarization produces intensity curves that are unique to the 3D orientation of the particle. Determining the azimuthal angle by precisely calculating the symmetry axis of a defocused image allows for the fitting of the polarization data to simulations to determine the polar angle. The 3D orientation of AuNRs attached to stationary microtubules in engineered environments with near single-degree precision can be realized despite the complex environment. We foresee this technique being applied to various studies such as nanoparticle loading before cargo transport in engineered
The precision can be increased by collecting more signal until, ultimately, it is limited by the amount of photons the camera can collect. While stacking images is a common method to increase the signal-to-noise ratio, it would necessitate the starting and stopping of the rotational stage inducing error in polarization orientation. The azimuthal angle for example particle 1 (P1) in Figure 4B was determined to be 44.1 ± 0.9° with respect to the x-axis. By fitting the simulated curve to the data using nonlinear least squared fitting, the polar angle for P1 was calculated to be 23.4° ± 0.8° at the 68% confidence interval using χ2 fitting. It should be noted that the curve fitting and uncertainty is only dependent upon the azimuthal angle with respect to the xaxis. This four quadrant degeneracy is overcome through defocused image interpretation leading to φ = 135.9 ± 0.9°. These angles match well with the simulated defocused image (Figure 4F). It is important to reiterate how the simulated curves relate to both θ and φ (Figure 2). When the azimuthal angle is at 90° it means the longitudinal axis is aligned for maximum scattering with the incoming laser. Under this condition, the peak maxima are closely related to the polar angle. This relates to low uncertainty when fitting the data. When the azimuthal angle is 0°, the peak positions are at 90° no matter the polar angle, resulting in a higher uncertainty of the polar angle when the particle is closely aligned with the x-axis. The high degree of precision in determining the azimuthal angle from the defocused images is therefore paramount to the determination of the polar angle. It also becomes obvious that in the instances where the long axis of the AuNR is exactly aligned with the xaxis of the system, the technique cannot extrapolate the polar angle. This can be overcome by changing the orientation of the sample by some known amount before again rotating the HWP. To demonstrate these influencing factors in the uncertainty, more particles were analyzed to compare the precision of the 3D orientation to a particle (P2) that had a less obvious axis of symmetry (Supporting Information Figure 3) and a particle (P3) that has an azimuthal angle closer to 0° and thus larger uncertainty in fitting (Supporting Information Figure 4). P2 (φ = 254.8° ± 2.7°, θ = 81.5° ± 0.3°) has an azimuthal angle uncertainty larger than P1, but due to the near 90° in-plane orientation, the fit generates a small uncertainty in the polar angle. Just the opposite is true in P3 (φ = 351.4° ± 0.4°, θ = 48.3° ± 2.4°) in which the azimuthal has subdegree uncertainty but due to the in-plane orientation being near the x-axis the resulting polar angle has a larger uncertainty than P1. Through these examples, it is apparent that the uncertainty in the polar E
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(20) Marchuk, K.; Ha, J. W.; Fang, N. Nano Lett. 2013, 13, 1245− 1250. (21) Beausang, J. F.; Schroeder, H. W., III; Nelson, P. C.; Goldman, Y. E. Biophys. J. 2008, 95, 5820−5831. (22) Stender, A. S.; Wang, G. F.; Sun, W.; Fang, N. ACS Nano 2010, 4, 7667−7675.
environments, surface mapping, and other applications involving particle interaction.
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ASSOCIATED CONTENT
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AUTHOR INFORMATION
S Supporting Information *
Additional information, methods, and figures. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author
*E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors of this paper would like to thank Keith Fritzsching from Iowa State University for his help regarding the home written MATLAB codes. Keith provided valuable discussions concerning the design of the programs along with help in the coding itself. This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences through the Ames Laboratory. The Ames Laboratory is operated for the U.S. Department of Energy by Iowa State University under contract no. DE-AC02- 07CH11358.
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REFERENCES
(1) Stender, A. S.; Marchuk, K.; Liu, C.; Sander, S.; Meyer, M. W.; Smith, E. A.; Neupane, B.; Wang, G.; Li, J.; Cheng, J.-X.; Huang, B.; Fang, N. Chem. Rev. 2013, 113, 2469−2527. (2) Sperling, R. A.; Rivera gil, P.; Zhang, F.; Zanella, M.; Parak, W. J. Chem. Soc. Rev. 2008, 37, 1896−1908. (3) Wu, X. Y.; Yeow, E. K. L. Nanotechnology 2008, 19, 035706. (4) Murphy, C. J.; Gole, A. M.; Stone, J. W.; Sisco, P. N.; Alkilany, A. M.; Goldsmith, E. C.; Baxter, S. C. Acc. Chem. Res. 2008, 41, 1721− 1730. (5) Sonnichsen, C.; Alivisatos, A. P. Nano Lett. 2005, 5, 301−304. (6) Xiao, L. H.; Qiao, Y. X.; He, Y.; Yeung, E. S. J. Am. Chem. Soc. 2011, 133, 10638−10645. (7) Pierrat, S.; Hartinger, E.; Faiss, S.; Janshoff, A.; Soennichsen, C. J. Phys. Chem. C 2009, 113, 11179−11183. (8) Chang, W. S.; Ha, J. W.; Slaughter, L. S.; Link, S. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 2781−2786. (9) Ha, J. W.; Sun, W.; Wang, G. F.; Fang, N. Chem. Commun. 2011, 47, 7743−7745. (10) Ha, J. W.; Sun, W.; Stender, A. S.; Fang, N. J. Phys. Chem. C 2012, 116, 2766−2771. (11) Wang, G. F.; Sun, W.; Luo, Y.; Fang, N. J. Am. Chem. Soc. 2010, 132, 16417−16422. (12) Gu, Y.; Sun, W.; Wang, G.; Fang, N. J. Am. Chem. Soc. 2011, 133, 5720−5723. (13) Gu, Y.; Sun, W.; Wang, G.; Jeftinija, K.; Jeftinija, S.; Fang, N. Nat. Commun 2012, 3, 1030. (14) Sonnichsen, C.; Franzl, T.; Wilk, T.; von Plessen, G.; Feldmann, J.; Wilson, O.; Mulvaney, P. Phys. Rev. Lett. 2002, 88, 077402. (15) Xiao, L.; Ha, J. W.; Wei, L.; Wang, G.; Fang, N. Angew. Chem., Int. Ed. 2012, 51, 7734−7738. (16) Toprak, E.; Enderlein, J.; Syed, S.; McKinney, S. A.; Petschek, R. G.; Ha, T.; Goldman, Y. E.; Selvin, P. R. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 6495−6499. (17) Li, T.; Li, Q.; Xu, Y.; Chen, X.-J.; Dai, Q.-F.; Liu, H.; Lan, S.; Tie, S.; Wu, L.-J. ACS Nano 2012, 6, 1268−1277. (18) Xiao, L. H.; Qiao, Y. X.; He, Y.; Yeung, E. S. Anal. Chem. 2010, 82, 5268−5274. (19) Ha, J. W.; Marchuk, K.; Fang, N. Nano Lett. 2012, 12, 4282− 4288. F
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Three-Dimensional Orientation Determination of Stationary Anisotropic Nanoparticles with Sub-Degree Precision under Total Internal Reflection Scattering Microscopy Kyle Marchuk and Ning Fang* Ames Laboratory-USDOE and Department of Chemistry, Iowa State University, Ames, Iowa 50011, United States S Supporting Information *
ABSTRACT: Single-particle and single-molecule orientation determination plays a vital role in deciphering nanoscale motion in complex environments. Previous attempts to determine the absolute three-dimensional orientation of anisotropic particles rely on subjective pattern matching and are inherently plagued by high degrees of uncertainty. Herein, we describe a method utilizing total internal reflection scattering microscopy to determine the 3D orientation of gold nanorods with subdegree uncertainty. The method is then applied to the biologically relevant system of microtubule cargo loading. Finally, we demonstrate the method holds potential for identifying single particles versus proximate neighbors within the diffraction limited area. KEYWORDS: Total internal reflection scattering (TIRS), single-particle, orientation determination, microtubule cargo, localized surface plasmon resonance
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plane orientation associated with orientation dependent signal or the necessity to match defocused image patterns. Defocused imaging techniques such as those used with darkfield microscopy use pattern matching with simulated images to determine the 3D orientation of anisotropic metallic nanoparticles. The resolution of which is dependent on the ability of a researcher to determine whether or not a particular pattern matches. This requires the correct simulation input of the defocus depth that may not be accurately estimated if particles are in different sample planes. For convenience, Supporting Information Figure 1 displays examples of how a focal plane change of even a few hundred nanometers can affect pattern matching, while Supporting Information Figure 2 demonstrates how difficult it can be to match simulated defocused images. A more recent technique called focused orientation and position imaging (FOPI) induces an image charge-coupled effect with the substrate to determine 3D orientation information but also suffers from image correlation and has the added necessity of needing a particular substrate-particle interaction.19 Previously, we have demonstrated the ability to use both short- and long-axis surface plasmon resonance (SPR) enhancement to simultaneously probe the in-plane and outof-plane (tilt) motion of dynamic surface-bound AuNRs using TIRS microscopy.20 By illuminating the sample with two wavelengths of light that are orthogonally polarized, the particle intensity fluctuates correspondingly to the 3D orientation of
ingle particle orientation and rotational tracking (SPORT) techniques have made a large impact in studying molecular motions.1 This is due partially to the rise in use of plasmonic nanoparticles as imaging probes compared to organic fluorescent dyes or semiconductor quantum dots. The advantages of these nanoparticles include large absorption and scattering cross sections,2 high-photostability,2,3 biocompatibility,4 and shape-induced anisotropic optical properties.5 While the other traits are crucial to their application, it is the anisotropic optical properties that allows for the determination of particle orientation and thus the elucidation of molecular motions. Particle orientation determination for gold nanorods (AuNRs) in the plane of the sample substrate has been demonstrated by a few optical techniques including dark-field (DF) polarization microscopy,5−7 photothermal heterodyne imaging,8 and differential interference contrast (DIC) microscopy.9−13 Light scattered from AuNRs has been shown to be strongly polarized along the long axis,14 and the aforementioned techniques take advantage of this scattering trait by monitoring the intensity of orthogonally polarized light to determine the in-plane orientation of the nanoparticles. While these techniques are simple to implement, they lack the ability to determine the out-of-plane (tilt) orientation of the AuNRs. Image recognition has been implemented with DIC microscopy,15 defocused imaging techniques,16−18 and total internal reflection scattering (TIRS) microscopy19 to determine the three-dimensional (3D) particle orientation without angular degeneracy. Unfortunately, these techniques are accompanied by a large degree of error (>10°) in determining the out-of© XXXX American Chemical Society
Received: August 8, 2013 Revised: October 11, 2013
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Figure 1. (A) Diagram of the TIRS microscope illustrating laser geometry. M, mirror; S, shutter; FL, focusing lens; FR, Fresnel rhombs attached to a rotating stage. (B) Absorption curve of the 25 × 63 nm AuNRs used in the experiment. (C) The coordinate system for both the incoming polarization (left) and the 3D orientation of the AuNR. X and Y is the sample plane with X being the direction of the incoming laser. Z is the axial direction. ψ, azimuthal angle, θ, polar angle.
To create a stationary environment with randomly oriented particles, AuNRs were diluted in a 0.5% (w/v) solution of agarose gel before being deposited on a quartz slide. The slide was then placed on the prism, focused under the microscope, and allowed to settle for 30 min to reduce sample drift. Using the HWP, the polarization of the incoming laser was carefully aligned to produce s-pol light (light with the electric field parallel to the substrate surface). Light that has the electric field aligned perpendicular to the substrate surface is considered ppolarized (p-pol). The EMCCD exposure time was 30 ms in frame transfer mode while the stage rotated the HWP at 15°/s. The illumination polarization rotates at double the speed of the HWP producing a speed of 30°/s and 0.9° of polarization rotation per frame. The sample was then defocused by ∼1.0 μm, and the procedure was repeated producing two data sets for each area of interest. The ∼1.0 μm defocus depth was chosen to produce defocused images dissimilar to images that would be produced at nearby focal depths (Supporting Information Figure 1) and maximize the effect the polar angle has on the image pattern. The coordinate system for the electric field, particle orientation, and polarization direction is similar to that used by Beausang et al. and has been defined in Figure 1C.21 In the microscope coordinate system, x and y comprise the sample plane, and x is the direction of illumination propagation. The optical axis is z. The AuNR orientation is defined by the polar angle (0° ≤ θ ≤ 90°) and the azimuthal angle (0° ≤ φ ≤ 360°), which originates on the x axis. The angle of the incoming polarization (ζ) is defined as 0° when the polarization is
rotating particles. While the previous technique is useful to the study of dynamic movement of nanorods, the present study has a new focus on the accuracy in determining the orientation of stationary probes. Using a combination of defocused imaging and the rotation of the polarization direction of light incident upon the sample, we resolve the 3D orientation of stationary AuNRs with unprecedented precision in TIRS microscopy. AuNRs with an aspect ratio of 2.4 (25 nm × 60 nm) and a long axis SPR absorption peak centered at 628 nm were used. The instrument is a TIRS microscope modified from its previous description (Figure 1A).19,20 Briefly, our prism-based TIRS microscope consists of a 660 nm continuous wave (CW) linearly polarized laser directed through periscope optics and focused under the objective. Placed after the periscope, a double Fresnel rhomb acting as a λ/2 wave plate (HWP) was inserted into the light path of the 660 nm laser. This HWP was attached to a computer-controlled rotating stage that allows light to pass through its center. We used this stage/HWP combination to accurately control the polarization componentsunder TIR. It should be noted that a double Fresnel rhomb is not considered a polarization rotator like that of a half-wave plate made from birefringent material. The double Fresnel rhomb HWP will actually produce elliptically or circularly polarized light depending upon its orientation when it is not modifying the light by a full 90°, but since we are using a TIR method where the incoming radiation generates an evanescent field, the effect at the sample interface is identical. A more detailed explanation can be found in Supporting Information Methods. B
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Figure 2. Simulated intensity profiles for various polar and azimuthal angles with respect to ζ.
Figure 3. Representation of the dependence of azimuthal angle determination upon signal intensity. (A) Plots of the intensity difference for the symmetry axis determination of the same AuNR at six different total intensities. The yellow line represents the trace with the highest intensity, which was set to 1.0 normalized intensity (NI). The rest of the plots represent the symmetry determination for the same particle at different angles ζ. The gray line represents the intensity level of uncertainty. (B) Surface plot of the lowest intensity symmetry determination (0.22NI) corresponding to the particle image (C). (D,E) Surface plot and particle image corresponding to the 0.38NI plot, respectively. (F,G) Surface plot and particle image corresponding to the 1.0NI plot, respectively. C
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Figure 4. Data and representations of a single AuNR with a polar angle of 23.4 ± 0.8°. (A) Raw intensity versus the first 180° of ζ fit with a higherorder polynomial. (B) Representation of the azimuthal angle determination using the defocused image with the highest contrast. The angle was determined to be 44.1 ± 0.9° with respect to the x-axis. (C) Plot portraying the alignment of the data with the simulated curves. (D) The 3D representation of the AuNR in space. (E) Actual defocused imaged taken at the angle ζ of highest intensity. (F) Simulated image of a AuNR with the angles calculated for the particle (φ = 135.9°, θ = 23.4°).
horizontal and therefore producing s-pol illumination and 90° when the polarization is vertical and producing p-pol illumination. For 0° < ζ < 90° and 90° < ζ < 180°, the polarization components under total internal reflection (TIR) are a ratio of s-pol and p-pol illumination corresponding to the illumination produced by the HWP (see Supporting Information Methods). By changing the ratio of s-pol and p-pol light at the surface of TIR, the electric field polarization (ε̂) is affected. Since the particles are anisotropic dipoles, the scattering intensity from the AuNR is dependent on both the 3D particle orientation and ε̂. It is therefore possible to simulate the scattering intensity based on the incident polarization (see Methods in Supporting Information for details). As can be seen in Figure 2, the intensity profile is dependent on both the polar and azimuthal angle. By first determining the azimuthal angle, it then becomes possible to fit the scattering intensity profile to the simulated curve to calculate the polar angle. There is a particular trend that is depicted in the simulated data. As φ changes from 90° to 0°, the range of the peak position of the curve is found to be narrower. This is due to the s-pol component of the evanescent field no longer influencing the overall SPR enhancement and is associated with increasing uncertainty in the polar angle fitting. The uncertainty increases to the point that when the AuNR is perfectly aligned with the x-
axis, the polar angle can no longer be determined. This limitation can be overcome by either adding a second illumination line perpendicular to the original line or by rotating the sample 90° and collecting a second set of data. Though we previously mentioned that defocused imaging techniques are difficult to interpret for polar angle determination, high azimuthal angle precision can be achieved under the proper conditions. The defocusing of a AuNR produces an image pattern with an axis of symmetry corresponding to the long axis of the particle (Figure 3G). The simplest method of determining symmetry involves slicing the particle image into two halves through the center point and comparing the integrated intensity. A MATLAB code was written that rotates the axis in which the image is sliced and calculates the differences in integrated intensities (see Supporting Information Methods for details). The angle at which the integrated intensity difference is least is considered the angle of symmetry. The precision of the azimuthal angle determination is highly dependent on overall image intensity as can be seen in Figure 3, which displays the plots of the same particle at different angles ζ and therefore different intensities. The gray line represents the uncertainty caused by noise within the signal collection. The uncertainty of the azimuthal angle is determined by multiplying the noise by the total image area and adding it to the integrated intensity difference at the angle of symmetry. D
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Figure 5. The recorded and simulated defocused images for AuNRs colocalized with stationary microtubules. The defocused image in (A) and the simulated image in (B) correspond to the particle (Nr1) in (C). (D,E) Images correspond to the particle (Nr2) in (C). The 3D orientation of Nr1 is φ = 77.9° ± 0.8°, θ = 37.5° ± 0.7°, and Nr2 is φ = 29.9° ± 3.9° and θ = 84.5° ± 0.6°. Scale bar is 5 μm. White line represents the approximate center of the microtubule fluorescence.
angle determination arises from a combination of the intensity and the orientation of the particle. This technique was then applied to the loading of cargo onto surface-bound microtubules. AuNRs were attached to microtubules through the biotin−neutravidin interaction before the microtubules were attached to a poly-L-lysine modified glass coverslide (Corning). Figure 5 shows two examples of particles (Nr1 & Nr2) attached to a microtubule. The defocused image (Figure 5A) and simulated image (Figure 5B) correspond to particle Nr1 in Figure 5C with angles φ = 77.9° ± 0.8° and θ = 37.5° ± 0.7°. Even with particles attached to biological structures on a nonquartz substrate, the technique can achieve high precision for both in-plane and out-of-plane orientation. More particles attached to stationary microtubules were analyzed. Particle Nr2, Nr3, and Nr4 (Nr3 and Nr4 can be seen in Supporting Information Figure 5) have 3D orientations of φ = 29.9° ± 3.9° and θ = 84.5° ± 0.6°, φ = 22.1° ± 1.7° and θ = 59.3° ± 2.7°, φ = 138.6° ± 1.3° and θ = 55.9° ± 1.5°, respectively. Overall, the particles with enough lateral distance between neighboring particles had 3D orientation with precision typically better than 5° and routinely neared single degree uncertainty. We found that a majority of the particles typically had relatively large polar angles (>45°) when attached to the stationary microtubules. Microtubules have a diameter of ∼25 nm, which is similar to the width of the AuNRs. These sizes suggest the majority of AuNRs will have a rather flat profile relative to the sample substrate. Proximate neighbors, meaning multiple uncoupled particles within a diffraction limited spot, are commonly found in singleparticle imaging experiments.22 Our technique supplies an opportunity to distinguish proximate neighbors with a large difference in polar angles from single particles through either focused or defocused imaging. The detailed explanation can be found in the Supporting Information. In summary, a method for determining the 3D orientation of stationary metallic anisotropic nanoparticles with subdegree uncertainty has been demonstrated in TIRS microscopy. Rotating the incoming polarization produces intensity curves that are unique to the 3D orientation of the particle. Determining the azimuthal angle by precisely calculating the symmetry axis of a defocused image allows for the fitting of the polarization data to simulations to determine the polar angle. The 3D orientation of AuNRs attached to stationary microtubules in engineered environments with near single-degree precision can be realized despite the complex environment. We foresee this technique being applied to various studies such as nanoparticle loading before cargo transport in engineered
The precision can be increased by collecting more signal until, ultimately, it is limited by the amount of photons the camera can collect. While stacking images is a common method to increase the signal-to-noise ratio, it would necessitate the starting and stopping of the rotational stage inducing error in polarization orientation. The azimuthal angle for example particle 1 (P1) in Figure 4B was determined to be 44.1 ± 0.9° with respect to the x-axis. By fitting the simulated curve to the data using nonlinear least squared fitting, the polar angle for P1 was calculated to be 23.4° ± 0.8° at the 68% confidence interval using χ2 fitting. It should be noted that the curve fitting and uncertainty is only dependent upon the azimuthal angle with respect to the xaxis. This four quadrant degeneracy is overcome through defocused image interpretation leading to φ = 135.9 ± 0.9°. These angles match well with the simulated defocused image (Figure 4F). It is important to reiterate how the simulated curves relate to both θ and φ (Figure 2). When the azimuthal angle is at 90° it means the longitudinal axis is aligned for maximum scattering with the incoming laser. Under this condition, the peak maxima are closely related to the polar angle. This relates to low uncertainty when fitting the data. When the azimuthal angle is 0°, the peak positions are at 90° no matter the polar angle, resulting in a higher uncertainty of the polar angle when the particle is closely aligned with the x-axis. The high degree of precision in determining the azimuthal angle from the defocused images is therefore paramount to the determination of the polar angle. It also becomes obvious that in the instances where the long axis of the AuNR is exactly aligned with the xaxis of the system, the technique cannot extrapolate the polar angle. This can be overcome by changing the orientation of the sample by some known amount before again rotating the HWP. To demonstrate these influencing factors in the uncertainty, more particles were analyzed to compare the precision of the 3D orientation to a particle (P2) that had a less obvious axis of symmetry (Supporting Information Figure 3) and a particle (P3) that has an azimuthal angle closer to 0° and thus larger uncertainty in fitting (Supporting Information Figure 4). P2 (φ = 254.8° ± 2.7°, θ = 81.5° ± 0.3°) has an azimuthal angle uncertainty larger than P1, but due to the near 90° in-plane orientation, the fit generates a small uncertainty in the polar angle. Just the opposite is true in P3 (φ = 351.4° ± 0.4°, θ = 48.3° ± 2.4°) in which the azimuthal has subdegree uncertainty but due to the in-plane orientation being near the x-axis the resulting polar angle has a larger uncertainty than P1. Through these examples, it is apparent that the uncertainty in the polar E
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(20) Marchuk, K.; Ha, J. W.; Fang, N. Nano Lett. 2013, 13, 1245− 1250. (21) Beausang, J. F.; Schroeder, H. W., III; Nelson, P. C.; Goldman, Y. E. Biophys. J. 2008, 95, 5820−5831. (22) Stender, A. S.; Wang, G. F.; Sun, W.; Fang, N. ACS Nano 2010, 4, 7667−7675.
environments, surface mapping, and other applications involving particle interaction.
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ASSOCIATED CONTENT
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AUTHOR INFORMATION
S Supporting Information *
Additional information, methods, and figures. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author
*E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors of this paper would like to thank Keith Fritzsching from Iowa State University for his help regarding the home written MATLAB codes. Keith provided valuable discussions concerning the design of the programs along with help in the coding itself. This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences through the Ames Laboratory. The Ames Laboratory is operated for the U.S. Department of Energy by Iowa State University under contract no. DE-AC02- 07CH11358.
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REFERENCES
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