Papers in Physics, vol. 2, art. 020010 (2010) Received: 22 April 2010, Accepted: 2 December 2010 Edited by: V. Lakshminarayanan Reviewed by: S. Roy, Dayalbagh Educational Institute, Agra, India. Licence: Creative Commons Attribution 3.0 DOI: 10.4279/PIP.020010 www.papersinphysics.org ISSN 1852-4249 Experimental determination of distance and orientation of metallic nanodimers by polarization dependent plasmon coupling H. E. Grecco,1, 2∗ O. E. Mart́ınez1† Live cell imaging using metallic nanoparticles as tags is an emerging technique to visualize long and highly dynamic processes due to the lack of photobleaching and high photon rate. However, the lack of excited states as compared to fluorescent dyes prevents the use of resonance energy transfer and recently developed super resolution methods to measure distances between objects closer than the diffraction limit. In this work, we experimentally demonstrate a technique to determine subdiffraction distances based on the near field coupling of metallic nanoparticles. Due to the symmetry breaking in the scattering cross section, not only distances but also relative orientations can be measured. Single gold nanoparticles were prepared on glass, statistically yielding a small fraction of dimers. The sample was sequentially illuminated with two wavelengths to separate background from nanoparticle scattering based on their spectral properties. A novel total internal reflection illumination scheme in which the polarization can be rotated was used to further minimize background contributions. In this way, radii, distance and orientation were measured for each individual dimer, and their statistical distributions were found to be in agreement with the expected ones. We envision that this technique will allow fast and long term tracking of relative distance and orientation in biological processes. I. Introduction Microscopy is an example of the ongoing symbiotic relationship between physics and biology: as early microscopes allowed fundamental discoveries like microorganisms or DNA; the need to see smaller, faster and deeper has pushed the development of a plethora of optical concepts and microscopy tech- niques. Today, fluorescence microscopy is an es- ∗E-mail: hgrecco@df.uba.ar †E-mail: oem@df.uba.ar 1 Laboratorio de Electrónica Cuántica, Universidad de Buenos Aires. Buenos Aires, Argentina. 2 Current address: Department of Systemic Cell Biology Max Planck Institute of Molecular Physiology. Dort- mund, Germany sential tool in biology as it can visualize the spatio- temporal dynamics of intracellular processes. How- ever, many important mechanisms, like protein in- teraction, clustering or conformational changes, oc- cur at length scales smaller than the resolution limit of conventional microscopy and therefore cannot be assessed by standard imaging. Unraveling the dy- namics of such inter- and intramolecular mecha- nisms that provides function richness to molecules and molecular complexes is essential to understand key biological processes such as cellular signal prop- agation. Subdiffraction distances have been determined by exploiting quantum and near field proper- ties of the interaction between light and matter in the nanometer scale. For example, Fluores- cence/Förster Resonance Energy Transfer (FRET) 020010-1 Papers in Physics, vol. 2, art. 020010 (2010) / H. E. Grecco et al. [5–7, 14] has proven to be a valuable technique as it provides an optical signal directly related to the proximity of the molecules. The desire to extend this technique to other biological systems with dif- ferent time and length scales has been hindered by the inherent limitations of fluorescent dyes (i.e. lack of photostability, low brightness and short range of interaction). Super resolution techniques such as STED [23] or PALM [2] have recently gained momentum to directly observe fluorescent molecules spaced closer than the diffraction limit. Although much work has been done to increase the total acquisition time and frame rate, these meth- ods are still limited by the lack of photostability and the need to image a single resolvable structure per diffraction limited spot at a time. In the past, it has been shown that scattering microscopy using metallic nanoparticles can com- plement its fluorescence sibling as it uses an ev- erlasting tag with no rate-limited amount of pho- tons [10]. Metallic nanoparticles are stable, bio- compatible and easy to synthesize and conjugate to biological targets and thereby ideal as contrast agents. A landmark example of the biological ap- plication of such techniques was the direct obser- vation of receptors hopping across previously un- known membrane domains. This provided valu- able insight into the spatial regulation of signaling complexes and closed a 30-year controversy about the diffusion coefficients of membrane proteins [21]. While previous experiments using fluorescent tags yielded a diffusion coefficient in biological mem- branes much slower than the one observed in syn- thetic membranes, the fast acquisition speed (40 103 frames per second) enabled by scattering mi- croscopy showed that this is the result of a fast diffusion and a slow hopping rate between domains [9]. In addition, the presence of a plasmon, i.e. a col- lective oscillation of the free electrons within the nanoparticle, converts metallic nanoparticles into very effective scatterers when illuminated at their resonance optical frequency. The resulting strong electromagnetic enhancement in the vicinity of the particle provides a near field effect that can be used to sense information about their surroundings such as the effective index of refraction or the presence of other scatterers [8, 16]. For example, it has been experimentally shown that the shift in the plasmon resonance can be used to determine the length of DNA molecules attached to a metallic nanoparticle [13]. Moreover, the coupling between two nanopar- ticles in close proximity produces an alteration of the plasmon spectra. This alteration has been used as a nanometric ruler to determine the distance between them [19, 20]. In a previous work, [4] we theoretically showed that the coupling between two nanoparticles is highly sensitive to the polar- ization of the external field. The scattering cross section (Csca) is maximum when the incident po- larization is parallel to the dimer orientation due to the reinforcement of the external field by the in- duced dipoles [Fig. 1(a)]. As the coupling decreases monotonically with the distance between nanopar- ticles, so does the average Csca over all polariza- tions (vm) [Fig. 1(b)] and the anisotropy [Fig. 1(c)] defined as: η = C ‖ sca − C⊥sca C ‖ sca + C⊥sca . (1) We have proposed, in our previous work, that by measuring the scattering cross section as a function of the incident polarization angle, the axis of the dimer and the distance between nanoparticles could be determined. In this work, we provide experimen- tal evidence supporting this concept by measuring gold nanodimers on a glass surface and we intro- duce a novel total internal reflection experimental setup that provides polarized illumination with a high NA objective. II. Materials and methods i. Sample preparation Coverslips were cleaned by sonication at 50◦ for 20 minutes in Milli-Q water, and then sequentially im- mersed for 5 seconds in HFL 5%, sodium bicarbon- ate and acetone (analytic level). After the cleaning process, coverslips were dried and stored in a cham- ber overpressurized with nitrogen until further use. Before sample preparation, a Parafilm chamber was assembled on top of the coverslip. To create a hy- drophilic surface, bovine serum albumina (BSA) in phosphate buffer solution (PBS) was incubated for 15 min and then rinsed with PBS. Fluorescein- streptavidin in PBS (50 mg/ml) was then incubated for 30 min and rinsed with PBS, to obtain an ad- 020010-2 Papers in Physics, vol. 2, art. 020010 (2010) / H. E. Grecco et al. Figure 1: Conceptual idea of the technique. (a) Two metallic nanoparticles of radii a located at a distance d are illuminated with a linearly polar- ized electromagnetic field. (b) Theoretical results as a function of the interparticle distance for the av- erage Csca over all polarizations (vm) and (c) the anisotropy. Parameters of the calculation: a = 20 nm, wavelength of the light: 532 nm. sorbed layer that was verified using confocal fluo- rescence microscopy. Finally, a solution of biotiny- lated gold nanoparticles, nominal radius (20 ± 5) nm (GB-01-40. EY Laboratories, USA), was in- cubated for 15 min and then rinsed by washing 5 times with PBS. The concentration and incubation time where empirically chosen to provide a con- centration about 1 nanoparticle/10 µm2. As the particles are randomly distributed, it is expected to find many monomers, some dimers, and very few trimers and higher n-mers. A negative control sam- ple was prepared in the same way but omitting the incubation of gold nanoparticles. ii. Dual color scheme Spurious reflections and scattering centers other than gold will produce unwanted bright spots in the images. Even thresholding the image taken at the resonance peak (532 nm) will result in many false positive regions. The presence of a plasmon reso- nance in the scattering spectrum of gold nanopar- ticles was used as a signature to distinguish them. The ratio between the scattering cross section at 532 nm and 473 nm was found to be larger than 1.4 for gold monomers [Fig. 2(a), solid thin line] using Mie theory [3] and even larger for dimers (dashed line) as calculated using GMMie, a mul- tiparticle extension of the Mie theory [11, 12]. In contrast, non metallic scattering centers lack of a plasmon resonance and therefore yield a smaller ra- tio between 532 nm and 473 nm Csca (solid thick line). Therefore, by imaging at these two wave- lengths and thresholding the ratio image above 1.4, the pixels containing gold nanoparticles were fur- ther segmented. iii. Polarization control in Total Internal Reflection We used Total Internal Reflection (TIR) mi- croscopy [1] to restrict the illumination to the sur- face of the coverslip using an evanescent wave. In objective-based TIR, the beam is focused off-axis in the back focal plane (BFP) of the objective to achieve critical illumination. The components of evanescent field are defined by the angle of inci- dence (θ) and the incident polarization with respect to the plane of incidence. Indeed, rotating the exci- tation polarization before entering the microscope does not produce a constant intensity in the sample plane as the transmission efficiency for the parallel polarization [Fig. 2(b), left] will be much smaller than for the perpendicular one [Fig. 2(b), center]. A circularly polarized beam before the objective re- sults in an “elliptically”1 polarized field which has the minor axis in the plane of incidence [Fig. 2(b), right]. The ratio between the major and minor axis of this evanescent “elliptical” beam depends on θ and if the plane of incidence is changed, the ellipse will rotate with it. We therefore modified 1The electromagnetic field in the sample cannot be said to be strictly elliptically polarized as an evanescent field (not a propagating beam) is generated after the interface. Never- theless, an elliptical rotation of the electric field is achieved. 020010-3 Papers in Physics, vol. 2, art. 020010 (2010) / H. E. Grecco et al. Figure 2: Experimental Setup. (a) Comparison of spectra averaging over all polarizations. While the spectrum of dielectric particles (thick solid line) decreases monotonically, the spectra of metallic monomers and dimers (thin lines) show a plasmon resonance. (b) The polarization of the refracted wave is dependent on the direction of the incident polarization with respect to the displacement in the back focal plane (BFP) of the objective which de- fines the plane of incidence. (c) The sample is il- luminated in Total Internal Reflection and imaged using a cooled CCD. Laser light is tightly focused off-center in the back focal plane of the objective and the angle β is moved using a pair of galvanome- ter scanners moving in orthogonal directions. a wide-field inverted microscope (IX71. Olympus, Japan) using a TIRF objective (Olympus TIRFM 63X/1.45 PlanApo Oil) to allow rotating the plane of incidence [Fig. 2(c)] by changing the position in which the beam is focused in the BFP. Two lasers were used: one near the gold particle plasmon res- onance (532 nm, Compass C315M. Coherent Inc., USA) and another shifted towards shorter wave- lengths (473 nm, VA-I-N-473. Viasho Technology, China). The power of the lasers after the objec- tive was 13 µW. Circularly polarized light was achieved at the BFP by inserting a quarter and a half wave plate in the beam path adjusted to pre- compensate for the polarization dependent trans- mission of the beam splitter, filters and mirrors. The beam was expanded and filtered to achieve a diffraction limited spot in the BFP. In order to dis- place the beam in the BFP and therefore change the plane of incidence, a pair of computer controlled galvanometer scanners (SC2000 controller, Minisax amplifier and M2 galvanometer. GSI Group, USA) were used. The polarization distortion due to the change in the angle of incidence onto the mirrors of the scanners (while moving) was verified to be negligible. Images of the sample were acquired us- ing a cooled monochrome CCD camera (Alta U32. Apogee Instruments, USA. 2148 × 1472 pixels each 6.8 × 6.8 µm2) through a dichroic filter for the fluo- rescence sample (XF2009 550DCLP. Chroma Tech- nology, USA) or a 30/70 beam splitter for the gold nanoparticles (21009. Chroma Technology, USA). iv. Intrinsic anisotropy determination To assure a constant ratio between the two po- larizations of the beam and a uniform intensity, the beam needed to be moved on the BFP in a circle centered in the optical axis. Failure to do this would have reduced the dynamic range of the system by introducing an intrinsic anisotropy. To minimize this value, the path of the beam was it- eratively modified while measuring the anisotropy (see below) of a diluted solution of Rhodamine 101. The emission of such a sample is independent of the excitation polarization and thus the measured anisotropy can be assigned only to the system. Af- ter optimization, the obtained anisotropy for the 532 and 473 channels was 0.06 and 0.05 in a region of 50 × 50 µm2 (440 × 440 pixel2). It is worth not- ing than these values are five times smaller than 020010-4 Papers in Physics, vol. 2, art. 020010 (2010) / H. E. Grecco et al. the expected anisotropy for a 20 nm homodimer. v. Image acquisition and processing The acquisition process consisted in sequentially imaging at 473 nm and 532 nm while changing the angle β in 20 discrete steps over 2π to sample dif- ferent polarizations. An image with both lasers off was also acquired to account for ambient light and dark counts of the camera. Each image was back- ground corrected and normalized by the excitation power and detection efficiency at the corresponding wavelength. Mean images (m473 and m532) were obtained by averaging over all polarizations and, from these, the ratio image m = m532/m473 was calculated. The scattering image at the resonance peak (m532) was segmented by Otsu’s thresholding and masked with the ratio image thresholded above 1.4 to detect pixels containing gold. A connected re- gion analysis was performed to keep only those re- gions with area between 3 and 15 pixels. The up- per bound was chosen to be slightly bigger than the airy diffraction limited spot for the system, but still much smaller than the mean distance between gold nanoparticles. Regions containing single gold nanoparticles should have a constant intensity over the stack of frames acquired for different polariza- tion orientation, while dimers should provide an os- cillating signal with period π. Therefore, a Fourier analysis [Eq. (2)] was performed. For each pixel, the following coefficients were calculated: c̃2 = 2∑ β I(β) ∑ β I(β)cos(2β) (2a) s̃2 = 2∑ β I(β) ∑ β I(β)sin(2β) (2b) η = √ c̃2n + s̃ 2 n (2c) tan(δ) = s̃2 c̃2 (2d) This was done for each wavelength obtaining val- ues for the anisotropy (η473 and η532) and orienta- tion (δ473 and δ532) in each pixel. The acquisition and analysis process were repeated for 30 and 10 fields of view of the sample and negative control sample respectively. Retrieval uncertainty was es- timated by performing the same numerical analysis Figure 3: Experimental results (a) Representative images of a field of view for single wavelength (left) and a ratio (right) imaging. Some points (cir- cles) are bright in both images (gold) while oth- ers squares faint in the ratio image (not gold). Gold containing regions were segmented by finding bright pixels in both images. Images size: 50x50 µm2. 440x440 pixels. (b) Anisotropy vs. mean value. A strong correlation is observed between anisotropy and mean value for both wavelengths as expected. The 473 nm data shows a plateau due to the intrinsic anisotropy of the system. on simulated data calculated by adding two terms to the theoretical response for different dimers. The first, an oscillating term with 2π periodicity, emu- lated a small misalignment that produced a non- constant illumination while rotating the beam in the BFP. The amplitude of this term was obtained from the Rhodamine calibration. The second term simulated coherent background and its values for each pixel were drawn from a Gaussian distribu- tion obtained from the control images. 020010-5 Papers in Physics, vol. 2, art. 020010 (2010) / H. E. Grecco et al. III. Results and discussion The need for a two color approach is evident when comparing single wavelength with ratio images: while regions with and without nanoparticles [Fig. 3(a), circles and squares respectively] were bright due to the high background in the single chan- nel image, only gold nanoparticles were above the threshold in the ratio image. Importantly, in the negative control stack, no pixel was found above the a priori defined threshold. For the 35 regions iden- tified as gold monomers/dimer, a strong correlation between anisotropy and mean value was found as expected [Fig. 3(b)]. The variance over each re- gion for all values was below the corresponding re- trieval uncertainty. A plateau was observed for the 473 nm channel due to the intrinsic anisotropy of the system. In this set of candidates for dimers, eight points presented an unexpected high individ- ual anisotropy and hence were rejected. Although the exact origin of this eight scattering centers could not be established, it is worthwhile noting that it is extremely relevant in a tracking exper- iment to avoid false positives that would severely distort the retrieved information, and this ability to reject scattering centers based on their response is an additional advantage of the technique. The recovered scattering parameters were com- pared with the expected results for a homodimer configuration (Fig. 4) obtaining a good correspon- dence with the nominal size of the nanoparticles used (20 nm). Indeed, the mesh shown in Fig. 4 was calculated using only the photophysical and geometrical properties of the dimer (no fitted pa- rameters). The ability of the technique to blindly recover the correct size of the particles was a cross- check for its reliability. The actual configuration of each dimer was ob- tained by fitting the theoretical model to the ex- perimental values. The in-plane orientation was directly obtained as a weighted average of these values. To fit the radii of each particle and the dis- tance between them, the values of η473, η532 and m were used. The values were first fitted using the analytical solution of a homodimer configuration in the dipole-dipole approach, in which the induced dipole moment ~p of each particle in an incident field Figure 4: Comparison between experimental data and homodimer model. The mean value ratio is plotted against the anisotropy ratio for the regions segmented from the images (blue dots). Theoret- ical calculations for different homodimers are also plotted. The vertical lines show the results keep- ing constant the surface to surface distance (dss) while changing the radii (a). The opposite is shown in the horizontal lines. Remarkably, experimental data distributed close to the curve for 20 nm ho- modimers (solid line) as expected as this is in fact the mean radii of the particles used. Notice that this is not a fit (no free parameters), but the pre- dictions from the homodimer model superimposed to the experimental data. ~Einc can be expressed as: ~p‖ = 1 1 − α 2d3π �mα~Einc (3a) ~p⊥ = 1 2 + α 2d3π �mα~Einc (3b) �m being the dielectric constant of the medium and α the polarizability of the sphere which is propor- tional to the cube of its radius [3, 4]. This ho- modimer configuration was used as an initial value in the time consuming iterative process of find- ing a heterodimer configuration compatible with the experimental data using GMMie calculation. The traveling wave approximation of the evanes- cent field was used as the particles are small com- pared to the decay length of the field [18,22] and the collection efficiency is much smaller for the dipole 020010-6 Papers in Physics, vol. 2, art. 020010 (2010) / H. E. Grecco et al. induced in the optical axis orientation than for the one perpendicular to it. In this way, the two radii, orientation and dis- tance for each dimer were obtained (Fig. 5). The distribution of radii was found to be centered in 20 nm, compatible with the nominal size of the par- ticles. For the interparticle distances, the distribu- tion showed an increase as expected but then a de- crease for distances at which the anisotropy is close to the intrinsic anisotropy of the system. This mis- match at larger distances is due to the conservative criterion to separate dimers from monomers that fails to identify correctly nanoparticles that cou- ple weakly. The dimer orientation was uniformly distributed between −π and π, as expected. To further test this, we compared the experimental and simulated distributions using a Kolmogorov- Smirnov [15] statistical test. The level of signifi- cance set at the usual value of 5%. The expected distributions (Fig. 5, right column) were obtained from the nominal radius of the nanoparticles and Monte Carlo simulation of the adsorption process. The experimental and simulated distributions for radii and orientation were found in close agree- ment. For the interparticle distance, the distribu- tions were found compatible when compared up to 70 nm. IV. Conclusions We have experimentally shown that distance be- tween two nanoparticles, as well as their individ- ual radii, can be obtained by measuring the inten- sity of spot as a function of the incident polariza- tion. Additionally, the in-plane orientation of the dimer was obtained with less than 10◦ uncertainty. The presented method strongly exploits the partic- ular spectroscopic properties of metallic nanoparti- cles to sense their environment. It is worth noting that the distance in which the technique is sensi- tive scales with the radii of the used particles. By using nanoparticles with radius between 4 and 20 nm, the gap between FRET and standard super- resolution techniques (10 nm to 50 nm) could be bridged. This fact, together with the ability to re- cover orientation, makes this approach unique. A non-uniform anisotropic illumination is the major source of uncertainty as it will mask the anisotropy of the dimers, specially for those in Figure 5: Fit to a heterodimer configuration us- ing GMMie. For each dimer (left column, x axis), the radii (top), the distance (middle) and the angle (bottom) were obtained. Experimental and sim- ulated histograms are shown for each magnitude (middle and right columns). which the distance is much larger than the radius of the particles. This should be properly controlled by measuring an isotropic sample as it was done in this work. Additionally, it is important to mention that various factors such as a non-monodisperse or non-spherical population of particles will have an incidence in the recovery of dimer distance, size and orientation from model based fittings. However, having a multiparametric readout (i.e. m532, m473, η473 and η532) with a non-trivial dependence of the physical parameters (i.e. distance, size, shape) pro- vides a way to control for this and exclude points that do no match the expected relations between photophysical properties. Such conservative crite- rion would be recommended for tracking experi- ments where false negatives have minor impact as they only reduce the amount of information gath- ered per frame. If the yield of dimers can be raised and several dozens of dimers can be imaged in the same field of view, we expect that the presented technique will be useful to add information about the relative movement of the two particles to al- ready existing tracking assays. Numerical simula- tions showed that if coherent background can be diminished, an order of magnitude (i.e. by the use of broader band excitation source), distance and 020010-7 Papers in Physics, vol. 2, art. 020010 (2010) / H. E. Grecco et al. orientation could be tracked at 100 Hz. If just the rotation and the movement of the center of mass is desired, the retrieval can be performed much faster as only one wavelength (532 nm) would be neces- sary after an initial identification of the dimers is made by the two color method. As other scattering based techniques, the lack of photobleaching constitutes a major advantage of this approach. Moreover, the absence of satura- tion in the light scattering of metallic nanoparti- cles, as compared to the absorption of fluorescent molecules, provides an acquisition rate only lim- ited by the detector speed. The combination of these two aspects means that scattering based mi- croscopy does not need to make compromises be- tween experiment length and temporal resolution. We have also demonstrated that the use of two color imaging can provide an efficient way to detect scattering centers that have plasmon resonances. Recent work by Olk et al. [17] has shown that upon illumination with a wideband light source, a mod- ulation of the spectra due to far-field effects can be observed as a function of the incident polarization. The combination of the two techniques could lead to a more robust detection of both, orientation and distance. 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