We propose a robust method to distinguish isolated single gold nanoparticles (AuNP monomers) and their dimers under Brownian motion, a key for ultrasensitive homogeneous bioassays, including AuNP sandwich assays. To detect dimers and distinguish them from a larger number of monomers in aqueous solution, single-particle polarization microscopy was performed. For the accurate detection of individual particles, the optical anisotropy and rotational diffusion time are measured because a dimer is much more anisotropic than the nearly spherical monomer and the rotational diffusion time of a dimer is four times that of a monomer. By employing an autocorrelation analysis, we defined a measure of distinguishing that simultaneously enables high detection probability and low error probability. The detection platform offers homogeneous DNA hybridization assays and immunoassays at the subpicomolar level.

1. Introduction

Immunoassays and DNA hybridization assays are widely used in biomedical research and clinical diagnostics to detect target analytes. In these application fields, there is a considerable demand for the development of more sensitive, quantitative, rapid, and low-cost methods for target detection. To meet these requirements, gold nanoparticles (AuNPs) are attracting increasing attention as labels for probe molecules that hybridize to the target molecules [1]. This is because AuNPs are especially bright (large scattering cross section) at the plasmon resonance and chemically stable. They also provide excellent biocompatibility by employing the appropriate ligands and good tunability by varying their size and shape [2, 3].

So far, Mirkin et al. have proposed colorimetric detection methods for DNA hybridization, in which aggregation of AuNPs induced by target oligonucleotides can be monitored by a visible change in the color of the solution [46]. These methods take advantage of homogeneous assays in contrast to heterogeneous formats, such as southern blotting and northern blotting, which require complicated oligonucleotide immobilization and long hybridization and washing steps [7, 8]. Although the time-consuming sample handling is avoided, the detection limit in the nM range is unsatisfactory for direct detection of analytes in clinical diagnostics.

To improve the sensitivity of colorimetric detection, Huo et al. successfully combined AuNP labeling with a dynamic scattering method. Change in the average particle diameter due to the formation of nanoparticle dimers, trimers, and oligomers is sensed by quantitative correlation analysis, and the detection limit of 1 pM is demonstrated [911].

In this study, we propose a more robust and highly sensitive approach based on digitally counting individual AuNPs and distinguishing between isolated single AuNPs (monomers) and their dimers. We employ polarization microscopy to distinguish dimers from monomers through anisotropy measurements on individual particles [12, 13]. The difference in rotational diffusion time, which is four times larger for dimers than for monomers, is also monitored for more reliable differentiation [14, 15]. In principle, the detection limit is determined only by the uniformity of the particle shape, and thus, a higher sensitivity compared to existing methods is expected.

2. Experimental

In order to assess the accuracy of AuNP differentiation, we performed polarization microscopy measurements on solutions of AuNP monomers and their dimers formed by DNA hybridization. We used a colloidal solution of AuNPs with a diameter of  nm, and the initial concentration was 170 pM (1 × 1011 particles/mL, Tanaka Kikinzoku Kogyo). The procedure for the synthesis of an AuNP dimer is as follows [1618]. The AuNP solution was divided into two equal parts to be functionalized with two single-stranded DNA probes complementary to each other (Figure 1(a)): Probe 1: [ThiSS] 5′-AAACACTCCATCAGCGATGTAACCATG-3′ and Probe 2: [ThiSS] 5′-AAACATGGTTACATCGCTGATGGAGTG-3′. Probe 1 and Probe 2 were added to the two AuNP solutions, respectively, at a molar ratio of 30 : 1 (DNA : AuNP). The solutions (hereinafter probe1 and probe2) were mixed well and incubated at room temperature to promote DNA hybridization (dimer formation, Figure 1(a)).

Agarose gel electrophoresis and transmission electron microscope (TEM) imaging confirmed that trimers and higher oligomers were also formed in the dimer solution as shown in Figure 1(b). The number ratio of monomer, dimer, trimer, and the higher oligomers was estimated to be 70 : 23 : 6 : 1.

The optical measurement setup is illustrated in Figure 2. A laser diode with a wavelength of 660 nm was used as the illumination source. The laser beam (5 mW) was focused inside the AuNP solution through an objective (NA0.85, 60X) 10 μm above the glass surface. The light scattering from a single AuNP monomer or dimer moving under Brownian motion in the observation volume was collected by the same objective. A pinhole with a diameter of 100 μm was used to reject the out-of-focus light, thus, increasing the signal-to-noise ratio (SNR). The scattered light was split into two orthogonal - and -polarization components by a polarization beam splitter, and the corresponding intensities, and , were detected by two photodiodes and current amplifiers (10 MV/A). The difference in intensity, , is a measure of the optical anisotropy of the AuNP monomers and dimers.

According to the calculation of plasmon coupling effect based on the quasistatic dipolar coupling approximation [19], the scattering cross section for the longitudinal plasmon mode in the dimer is expected to be approximately eight times larger than that for the monomer at the wavelength of 660 nm. Also, the polarization anisotropy defined as , where and are scattering cross sections along the long and short dimer axes, is estimated to be 0.4. Here, we assumed the surface-to-surface separation of dimer to be 10 nm and employed gold dielectric function reported in [20]. Although a higher contrast in the scattering cross section between monomers and dimers and larger polarization anisotropy can be obtained at the wavelength of green light, we chose a laser diode at 660 nm due to its low cost and ready availability, which makes our approach very attractive for practical applications.

3. Results and Discussion

Figures 3(a) and 3(b) are time traces of , , and for an AuNP monomer and dimer, respectively. Figure 3(a) for the monomer contains high frequency noise, and a noticeable difference signal was not observed owing to the isotropy of the spherical particle. In contrast, for the dimer in Figure 3(b), we obtained a significant difference signal, indicating a large optical anisotropy. The slow fluctuation of the difference signal reflects the rotational motion of the dimer under Brownian motion.

To obtain a quantitative measure for differentiating monomers and dimers, we performed a statistical analysis, in which for the time trace of we calculated an autocorrelation function, . Figure 4 shows curves calculated from the time traces in Figures 3(a) and 3(b). As can be seen in Figure 3, the noise frequency is higher than , where μs is the detection time interval in the measurement ( is much smaller than the rotational diffusion time). The value is a good measure for differentiation, rejecting the undesired high frequency noise component, because includes three important features of the dimer as compared to the monomer: (1) larger anisotropy, (2) larger scattering cross section, and (3) slower translational diffusion (longer signal duration time). To enhance the effectiveness of this measure, we also employ the decay time constant, , which reflects the difference in the rotational diffusion time between monomers and dimers. Since the diffusion time constant of the dimer is four times that of the monomer, at an appropriate time delay , will provide a more robust measure for differentiation. In this study, we adopted μs to avoid the artifact of the oscillation of due to the limited measurement time.

Figure 5 shows a histogram of (40 μs) for 1,000 particles obtained from a measurement of an AuNP dimer solution in 3 min. In the same measurement time, 120 particles were detected in a monomer solution conjugated with probe1 and the distribution of is also shown in Figure 5. For smaller , the distributions come from both a monomer passing through the center of the observation volume which may have a larger and a dimer that just grazes the observation volume boundary. By contrast, for larger , dimers are dominant. However, we still have a small number of particles with a large in the monomer solution. These probably originate from unexpected AuNP dimerization due to the entanglement of DNA strands. By TEM observation, we confirmed that 1% of monomers form such entangled pairs in the monomer solution. For , the number of particles obtained from the dimer solution is 910 and that from the monomer solution is only 12, which yields a ratio of 1.3%. The ratio is much smaller than the concentration ratio of dimer in the monomer solution (1%) to dimer, trimer, and higher oligomers in the dimer solution (23% + 6% + 1% = 30%). This means particles with are identified as dimers and higher oligomers with sufficient accuracy; we can distinguish hybridized dimers (oligomers) from monomers with extremely low error probability.

Finally, we discuss the sensitivity of the proposed method under the assumption that the probe1-AuNP conjugate is the probe solution and probe2-AuNP is the target solution. By using a dissociation constant, , for the hybridization of probe1 and probe2, we can estimate the dimer concentration to be , where and are the concentrations of the probe and target solutions, respectively. Here, we assume . The probe solution contains unexpectedly large nonspherical monomers or dimers due to DNA entanglement with a probability of . If , we can confirm the existence of the target. Thus, the detection limit of the target concentration is . If is sufficiently small, a reduction in will improve the detection limit because our strategy relies on the digital counting method. However, a reduction in also leads to a longer measurement time. Decreasing is a more realistic approach that can be attempted. The current conditions,  pM and , will yield  pM.

4. Conclusion

By employing single-particle polarization microscopy under Brownian motion in water, sensitive and robust differentiation of isolated single gold nanoparticles (monomer) and dimers was demonstrated. We measured the optical anisotropy and the rotational diffusion time of individual particles using autocorrelation analysis. A robust measure for differentiation was defined, involving data on both optical anisotropy and rotational diffusion time. We were able to place a threshold on this measure, simultaneously achieving sufficient detection probability and extremely low error probability.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.


The authors are grateful to Tanaka Kikinzoku Kogyo for providing high-quality gold nanoparticles for this study. This work was supported by JSPS KAKENHI Grant no. 24226006 and partially by Advanced Photon Science Alliance Project from MEXT.