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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 4, Iss. 9 — Sep. 1, 2013
  • pp: 1646–1653
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Enumerating virus-like particles in an optically concentrated suspension by fluorescence correlation spectroscopy

Yi Hu, Xuanhong Cheng, and H. Daniel Ou-Yang  »View Author Affiliations


Biomedical Optics Express, Vol. 4, Issue 9, pp. 1646-1653 (2013)
http://dx.doi.org/10.1364/BOE.4.001646


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Abstract

Fluorescence correlation spectroscopy (FCS) is one of the most sensitive methods for enumerating low concentration nanoparticles in a suspension. However, biological nanoparticles such as viruses often exist at a concentration much lower than the FCS detection limit. While optically generated trapping potentials are shown to effectively enhance the concentration of nanoparticles, feasibility of FCS for enumerating field-enriched nanoparticles requires understanding of the nanoparticle behavior in the external field. This paper reports an experimental study that combines optical trapping and FCS to examine existing theoretical predictions of particle concentration. Colloidal suspensions of polystyrene (PS) nanospheres and HIV-1 virus-like particles are used as model systems. Optical trapping energies and statistical analysis are used to discuss the applicability of FCS for enumerating nanoparticles in a potential well produced by a force field.

© 2013 OSA

1. Introduction

Sensitive detection of pathogenic nanoparticles, such as viruses, is key to prevention of infectious diseases. Compared to sensing their molecular fingerprints, direct detection of whole particle viruses offers the advantage of easy sample preparation and fast assay. Fluorescence correlation spectroscopy (FCS) is one of the most sensitive methods for detecting suspended nanoparticles [1

1. D. Magde, E. Elson, and W. W. Webb, “Thermodynamic fluctuations in a reacting system measurement by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972). [CrossRef]

, 2

2. E. L. Elson and D. Magde, “Fluorescence correlation spectroscopy. I. conceptual basis and theory,” Biopolymers 13, 1–27 (1974). [CrossRef]

]. However, the detection limit of FCS, on the order of sub nano-molar [3

3. S. T. Hess, S. Huang, A. A. Heikal, and W. W. Webb, “Biological and chemical applications of fluorescence correlation spectroscopy: A review,” Biochemistry 41, 697–705 (2002). [CrossRef] [PubMed]

], does not meet the needs for clinical analysis of viral samples. The use of force fields, such as di-electrophoresis [4

4. F. Grom, J. Kentsch, T. Muller, T. Schnelle, and M. Stelzle, “Accumulation and trapping of hepatitis a virus particles by electrohydrodynamic flow and dielectrophoresis,” Electrophoresis 27, 1386–1393 (2006). [CrossRef] [PubMed]

, 5

5. K. T. Liao and C. F. Chou, “Nanoscale molecular traps and dams for ultrafast protein enrichment in high-conductivity buffers,” J. Am. Chem. Soc. 134, 8742–8745 (2012). [CrossRef] [PubMed]

] and optical trapping, to concentrate nanoparticles [6

6. J. Junio, S. Park, M.-W. Kim, and H. D. Ou-Yang, “Optical bottles: A quantitative analysis of optically confined nanoparticle ensembles in suspension,” Solid State Commun. 150, 1003–1008 (2010). [CrossRef]

, 7

7. J. Junio, J. Ng, J. A. Cohen, Z. Lin, and H. D. Ou-Yang, “Ensemble method to measure the potential energy of nanoparticles in an optical trap,” Opt. Lett. 36, 1497–1499 (2011). [CrossRef] [PubMed]

], are an appealing approach to lower the FCS detection limit. Lacking an analytical expression for the FCS autocorrelation function, we need to examine experimentally the applicability of existing models for using FCS to measure the concentration of nanoparticles by enriching them in a potential well produced by a force field.

Multiple attempts have been made to interpret FCS data obtained from colloidal nanoparticles in a gradient force field. The experiment of Osborne et al. [8

8. M. A. Osborne, S. Balasubramanian, W. S. Furey, and D. Klenerman, “Optically biased diffusion of single molecules studied by confocal fluorescence microscopy,” J. Phys. Chem. B 102, 3160–3167 (1998). [CrossRef]

] showed that optical trapping can affect diffusion of molecules in the vicinity of the optical trap. Hosokawa et al. [9

9. C. Hosokawa, H. Yoshikawa, and H. Masuhara, “Cluster formation of nanoparticles in an optical trap studied by fluorescence correlation spectroscopy,” Phys. Rev. E 72, 021408 (2005). [CrossRef]

] used optically biased diffusion to study the cluster formation of nanoparticles in a highly focused laser beam. They demonstrated that it might be possible to quantify the relationships between the cluster size, trapping energy and the decay time of the FCS autocorrelation function (ACF). More recently, Wang et al. [10

10. J. Wang, Z. Li, C. P. Yao, F. Xue, Z. X. Zhang, and G. Huttmann, “Brownian diffusion of gold nanoparticles in an optical trap studied by fluorescence correlation spectroscopy,” Laser Phys. 21, 130–136 (2011). [CrossRef]

] studied the diffusion dynamics of gold nanoparticles in optical confinement and reported a laser-induced rise in temperature changed the diffusion behavior and the average number of gold nanoparticles in the focal area of the laser beam. Ito et al. [11

11. S. Ito, N. Toitani, H. Yamauchi, and H. Miyasaka, “Evaluation of radiation force acting on macromolecules by combination of brownian dynamics simulation with fluorescence correlation spectroscopy,” Phys. Rev. E 81, 061402 (2010). [CrossRef]

] used a Brownian dynamics simulation to investigate the FCS ACF of colloidal nanoparticles in an optical gradient force field. They found the standard FCS ACF for free diffusing particles is applicable for particles in an optical trap with potential energies lower than 1kBT. Meng et al. [12

12. F. Meng and H. Ma, “Fluorescence correlation spectroscopy analysis of diffusion in a laser gradient field: A numerical approach,” J. Phys. Chem. B 109, 5580–5585 (2005). [CrossRef]

] compared the ACF obtained by numerical calculation and Monte Carlo simulation for non-interacting particles in an isotropic Gaussian potential with trapping energies up to 1.8kBT and showed the ACF amplitude is equal to the inverse of the mean number of particles in the optical trap.

In this paper we report an experimental study that combines optical trapping and FCS to examine the influence of trapping potential energy on the ACF amplitude. We compare the experimental ACF amplitude with the experimentally determined 1/〈N〉 using colloidal suspensions of polystyrene nanoparticles and HIV-1 virus-like particles (VLPs) to verify the predictions by Meng et al. [12

12. F. Meng and H. Ma, “Fluorescence correlation spectroscopy analysis of diffusion in a laser gradient field: A numerical approach,” J. Phys. Chem. B 109, 5580–5585 (2005). [CrossRef]

]. Our experimental results are also compared with the Brownian dynamics simulation results by Ito et al. [11

11. S. Ito, N. Toitani, H. Yamauchi, and H. Miyasaka, “Evaluation of radiation force acting on macromolecules by combination of brownian dynamics simulation with fluorescence correlation spectroscopy,” Phys. Rev. E 81, 061402 (2010). [CrossRef]

]. We further explain that the equality of the ACF amplitude to 1/〈N〉 under optical trapping requires that the particle number density fluctuation follows the Poisson statistics.

2. Experimental

2.1. FCS data analysis

A typical FCS experiment measures ACF of the fluorescence intensity from a detection volume defined by the focus of a laser beam. The FCS ACF G(τ) is defined as:
G(τ)=δF(t)δF(t+τ)F(t)2,
(1)
where τ is the correlation delay time, F(t) is the instantaneous fluorescence intensity at time t, and δF(t) = F(t) − 〈F(t)〉 is the fluctuation of the fluorescence intensity around its mean value. For a dilute solution of non-interacting, point-like particles, G(τ) can be expressed as [2

2. E. L. Elson and D. Magde, “Fluorescence correlation spectroscopy. I. conceptual basis and theory,” Biopolymers 13, 1–27 (1974). [CrossRef]

]:
G(τ)=ΔN2N2(1+4Dτw02)1(1+4Dτz02)1/2
(2)
where 〈ΔN2〉 and 〈N〉 are the variance and the mean number of particles in the volume, respectively; D is the diffusion coefficient of the particles; w0 and z0 are the radial and axial dimensions of the detection volume, respectively. G(τ), the amplitude of the ACF at zero delay time, is the normalized variance of the particle number fluctuations 〈ΔN2〉/〈N2. As moving particles pass the observation volume, the fluorescence intensity fluctuates and thus affects the amplitude of ACF. When the probability of finding a particular particle in the laser focus is much less than 1, the number fluctuation of particles in this region follows a Poisson distribution in which the variance of the distribution 〈ΔN2〉 equals the mean number density 〈N〉, and
G(0)=N1
(3)

2.2. Optical instrument

A schematic of the optical apparatus is illustrated in Fig. 1. An IR laser (1064nm, TREMC1, Spectra-Physics) is used for trapping fluorescent nanoparticles. A blue laser (488nm) of a confocal laser scanning microscopy (FV-1000, Olympus, Japan) is used for fluorescence excitation. A half-wave plate and a polarization beam splitter are used for adjusting the power of the trapping laser. The power of the 488 nm excitation laser at the focal point is maintained at a low power of 5 μW to minimize photo bleaching of the fluorescent particles in the observation volume. The trapping and excitation beams are combined by a dichromatic mirror and confocally aligned at the detection point. A microscope objective lens (UPlanFluor 100X, NA1.3, Olympus, Japan) is used to focus the laser beams and to collect fluorescence emission. The fluorescence emission passing through a band-pass filter and a beam splitter is detected by two photon-counting avalanche photo diodes (APD: SPCM-AQRH-13-FC, Perkin Elmer). Since the fluorescence emission from the two channels are correlated, while the dark counts produced by thermal noise in the two APD are not, we can minimize the adverse effects due to the APD dark counts by taking the cross-correlation of the two APD outputs to obtain G(τ). The cross-correlation calculation is made by the use of a digital correlator (Flex02-01D, correlator.com, USA). The geometrical parameters of the FCS detection volume w0, z0 are determined by using a 10nM solution of Alexa 488 dye. Using the known diffusivity of Alexa 488 molecules in water (430 μm2/s) in fitting Eq. (2) to ACF, w0 and z0 are determined to be 0.22 μm and 2 μm, respectively.

Fig. 1 Illustration of the experiment apparatus.

2.3. Sample preparation

2.3.1. Colloidal polystyrene (PS) nanoparticles

An aqueous suspension of 100nm diameter PS particles with a volume fraction of 1% is purchased from Thermo Scientific (Fremont, USA). The PS particles are fluorescently labelled with Firefli red (excitation maximum 543nm, emission maximum 612nm). The ionic (salt) concentration of the stock suspension is estimated to be 2 mM. The stock suspension is diluted 100 times in deionized water for all the FCS measurements. The ionic strength of the diluted sample solution was estimated to be 20 μM. A 20 L sample is held between a microscope cover-glass and a slide and sealed with wax. The chamber thickness of the gap between the two glass substrates is 60 ± 10 μm. FCS measurements are positioned at ∼ 10 μm above the cover glass.

2.3.2. Preparation of virus-like particles (VLP)

HEK 293T cells (ATCC No. CRL-11268) are cultured in DMEM supplemented with 10% fetal calf serum at 37°C and 5% CO2. The cells at 60% confluency are transfected with the GAG-EGFP plasmid (AIDS reagent program Cat. No. 11468) and incubated for 48 hours. The super-natant containing virus-like particles is then collected, filtered using 0.2 μm filter and centrifuged for 3 hours at 20,000 rpm to concentrate the virus-like particle at the bottom of the test tube by sucrose density centrifugation. The pellet containing the virus-like particles is then resuspended in the cell culture medium. These particles have a similar capsid structure to the wild-type HIV virion, but lack some of the viral genome, which minimizes their pathogenicity. Moreover, these particles are genetically engineered to carry green fluorescent protein (excitation maximum at 488nm and emission maximum at 509nm) tagged to Gag, the primary structural protein of HIV.

SEM and confocal microscope images are acquired to examine the size and fluorescence of the VLPs [13

13. B. Wu, Y. Chen, and J. D. Muller, “Fluorescence correlation spectroscopy of finite-sized particles,” Biophys. J. 94, 2800–2808 (2008). [CrossRef]

]. To prepare SEM samples, glutaraldehyde is added to the VLPs suspension to a final concentration of 2.5% followed by incubation at room temperature for 1 hour. A 20 μL suspension is then pipetted onto an autoclaved cover glass, dehydrated in ethanol, dried at room temperature and sputter-coated with gold palladium for 60 seconds before imaging.

3. Results and discussion

3.1. Fluorescence correlation spectroscopy in an optical trap

The ACF G(τ) from 110nm PS nanoparticle suspensions in the presence of optical trapping with laser powers between 0 and 18mW are shown in Fig. 2. Each ACF curve represents an average of 10 independent measurements. Fitting Eq. (2) to the trap-free (0mW) curve yields a particle number density 〈N0〉= 0.165 in the observation volume and diffusivity D = 4.5 μm2/s. The measured diffusivity agrees with that obtained by the Stokes-Einstein equation D = kBT /(6πηa) = 4.35 μm2/s, where η is the viscosity of water at the ambient temperature and a is the particle radius.

Fig. 2 FCS autocorrelation functions of 0.01% (v/v) 110nm PS particle suspensions at selected trapping laser powers. Each curve represents an average of 10 measurements.

To examine the range of trapping powers at which Eq. (2) can be used to describe the experimental ACFs, we plot in Fig. 3 the same data shown in Fig. 2 and fit curves using Eq. (2) for various trapping energies, 0mW, 6mW, 12mW and 18mW, respectively. The excellent match between Eq. (2) and the experimental ACF data suggests that the conventional ACF can be used to describe the motion of the nanoparticles in a potential well with a depth up to 1.8kBT. This range of trapping powers exceeds that examined by Ito et al. through Brownian dynamic simulation [11

11. S. Ito, N. Toitani, H. Yamauchi, and H. Miyasaka, “Evaluation of radiation force acting on macromolecules by combination of brownian dynamics simulation with fluorescence correlation spectroscopy,” Phys. Rev. E 81, 061402 (2010). [CrossRef]

], where Eq. (2) is shown to be applicable for trapping energies only up to 1kBT. The trapping energy will be discussed later.

Fig. 3 The experimental ACFs (black) are fitted using Eq. (2) (red) for trapping laser powers of (a) 0mW ; (b) 6mW ; (c) 12mW ; (d) 18mW.

In the presence of the optical trap, the average number of particles in the trap can be determined independently by total photon counts: 〈Ntrap〉= 〈Ftrap〉/ε. Here, ε is the average fluorescence luminosity per particle at fixed excitation light intensity, which can be determined by the ratio F0/G(0)01, where 〈F0〉 is the average fluorescence photon counts at zero trapping laser power, and G(0)−1 at zero trapping laser power is equal to the mean number of particle in the FCS observation volume.

Figure 4(a) shows a plot of G(0)trap1 vs. 〈Ntrap〉. The linearity in Fig. 4(a) with a slope of 1 suggests G(0)trap1 equals the average number of particles in the presence of optical trapping for all trapping powers tested between 0mW to 18mW.

A semi-log plot of G(0)trap1/G(0)01 vs. the power of trapping laser is shown in Fig. 4(b). Since G(0)trap1/G(0)01=Ntrap/N0, Fig. 4(b) implies the number of particles in the optical trap follows a Boltzmann distribution with the trapping potential energy:
Ntrap=N0exp(Utrap/kBT)
(4)
where Utrap [14

14. Assuming the trapping potential has an isotropic Gaussian distribution U(r) = U(0)exp(−2r2/R2), where R is the beam waist of the 1064nm trapping laser, estimated to be 0.97 μm. The experimentally determined trapping potential Utrap is the integration of U(r) in the illumination volume with beam waist 0.23 μm. Therefore, Utrap= 0.978U(0).

], the average single-particle trapping potential energy is the slope of the semilog plot in Fig. 4(b). The Boltzmann distribution is expected when particle interactions are negligible. The trapping energies at which the particle distribution are no longer Boltzmann depends on the bulk concentration and the ionic strength of the buffer [6

6. J. Junio, S. Park, M.-W. Kim, and H. D. Ou-Yang, “Optical bottles: A quantitative analysis of optically confined nanoparticle ensembles in suspension,” Solid State Commun. 150, 1003–1008 (2010). [CrossRef]

, 7

7. J. Junio, J. Ng, J. A. Cohen, Z. Lin, and H. D. Ou-Yang, “Ensemble method to measure the potential energy of nanoparticles in an optical trap,” Opt. Lett. 36, 1497–1499 (2011). [CrossRef] [PubMed]

]. The trapping energy of the 110nm PS spheres is found to be 0.1 ± 0.04kBT per mW of laser. This result is in good agreement with trapping energies reported previously by other methods [7

7. J. Junio, J. Ng, J. A. Cohen, Z. Lin, and H. D. Ou-Yang, “Ensemble method to measure the potential energy of nanoparticles in an optical trap,” Opt. Lett. 36, 1497–1499 (2011). [CrossRef] [PubMed]

, 15

15. C. Hosokawa, H. Yoshikawa, and H. Masuhara, “Optical assembling dynamics of individual polymer nanospheres investigated by single-particle fluorescence detection,” Phys. Rev. E 70, 061410 (2004). [CrossRef]

].

Fig. 4 (a) G(0)trap1 from 3(a) is found to increase linearly with 〈Ntrap〉 measured by 〈Ftrap〉/ε; the dashed line is a fit with slope = 1 and intercept = 0. (b) Semi-natural log plot of G(0)trap1/G(0)01 vs. the trapping power suggests the average number of particles in the optical trap follows a Boltzmann distribution. (c) G(0)trap1/Ntrap=1 for trapping energies up to 1.8kBT. (d) The decay time τ=w02/4D decreases with increasing trapping laser power.

Figure 4(c) shows a constant ratio of G(0)trap1/Ntrap=1 for trapping potential energies up to 1.8kBT, suggesting our experimental result agrees with the theoretical prediction by Meng et al. [12

12. F. Meng and H. Ma, “Fluorescence correlation spectroscopy analysis of diffusion in a laser gradient field: A numerical approach,” J. Phys. Chem. B 109, 5580–5585 (2005). [CrossRef]

].

The decay time τ=w02/4D of our experimental ACF decreases with increasing trapping laser power as shown in Fig. 4(d). This trend agrees with the result reported by Hosokawa et al. [9

9. C. Hosokawa, H. Yoshikawa, and H. Masuhara, “Cluster formation of nanoparticles in an optical trap studied by fluorescence correlation spectroscopy,” Phys. Rev. E 72, 021408 (2005). [CrossRef]

]. However, a theoretical model will be needed to describe the influence of the particle motion in an optical trap to the FCS ACF.

3.2. Optical trapping of VLPs

Fig. 5 (a) A SEM image of one VLP. Diameter of the particles is 110 ± 11nm. (b) A fluorescent image of VLPs under 100X objective. (c) Autocorrelation curve of VLPs in culture medium, from which a hydrodynamic size of 115 ± 14nm is obtained. All standard deviation represents 10 independent measurements.

A FCS autocorrelation curve of the VLPs suspended in culture medium is shown in Fig. 5(c). By fitting the curve by Eq. (2), the ACF yields a diffusion coefficient 3.79 μm2/s. Using the Stokes-Einstein equation D = kBT /(6πηa) and medium viscosity η = 0.98cP, we determine the diameter of the VLPs to be 115 ± 14nm (standard deviation from 10 independent measurements), which is consistent with results obtained by SEM.

We use the procedures described in Section 3.1 to determine the trapping energy of VLP. Selected ACF curves for different laser powers are shown in Fig. 5(a). A semi-natural log plot of G(0)−1 vs. trapping laser power is shown in Fig. 5(b). For PBS buffer solutions containing 135mM NaCl, the Debye screening length is on the order of 1nm. Since the estimated average distance between two VLPs in our experiments is more than 1 μm, particle interactions can be neglected, and the number of particles in the optical trap follows Eq. (4). A semi-natural log plot of the average number of particles vs. the trapping power is shown in Fig. 5(b). The trapping energy for the VLPs is calculated to be 0.02 ± 0.003kBT/mW.

Because VLPs are hollow particles surrounded by capsid proteins and a thin shell of phospholipid bilayer their trapping energy is significantly smaller than that of comparably sized solid PS particles. We use a discrete dipole approximation method [18

18. L. Ling, F. Zhou, L. Huang, and Z.-Y. Li, “Optical forces on arbitrary shaped particles in optical tweezers,” J. Appl. Phys. 108, 073110–8 (2010). [CrossRef]

] to numerically calculate the optical trapping energies of these particles. The trapping beam used in the calculation is a fifth-order-corrected monochromatic Gaussian beam with beam waist 0.5 μm. For the 110nm diameter PS spheres (refractive index 1.59) in water (refractive index 1.33), the calculated trapping energy is 0.13kBT /mW. Modeling VLPs as 100nm inner diameter vesicles with a 10nm lipid bilayer wall (refractive index 1.46) [19

19. S. D. Fuller, T. Wilk, B. E. Gowen, H.-G. Krausslich, and V. M. Vogt, “Cryo-electron microscopy reveals ordered domains in the immature HIV-1 particle,” Curr. Biol. 7, 729–738 (1997). [CrossRef] [PubMed]

], we calculate their trapping energy to be 0.017kBT /mW, in reasonable agreement with the experimentally determined value for VLP.

Since the relationship G(0) = 〈N−1 is derived from the Poisson statistics, the fact that the relation holds for particles in an optical trap implies that the conditions required for Poisson distribution are satisfied. These conditions are i) the probability a particular particle in the trap is much less than one, and ii) the particle movements near the trap are uncorrelated. Thus, for extremely low particle concentrations, one can estimate the trapping energies under which G(0) = 〈N−1 is valid. As an example, for a sample of concentration C = 109particle/cm3 in a volume of V = 106μm3, the probability for a particular particle to be in the laser illuminated volume of v = 1 μm3 is p = 10−6, and the average number of particles in the illuminated volume is 〈N〉= v × C = 10−3. Limited by the intrinsic dark-count of a typically APD detector, 〈N〉 ≥ 0.1 is needed to ensure a statistical meaningful FCS measurement, which requires an enhancement of p by a factor of 100. As a result, p is enhanced from 10−6 to 10−4, at which the required condition (i) for Poisson distribution is still satisfied. Since the particle interactions are negligible at such low concentration the concentration enhancement by trapping follows a Boltzmann distribution of the trapping potential energy. The trapping energy needed for the concentration enhancement of 100 can be estimated by ln100kBT = 4.6kBT.

4. Conclusions

This paper describes an experimental investigation of the use of FCS for analyzing the behavior of colloidal nanoparticles in an optical trap. Our experiments show the standard FCS autocorrelation function for free diffusing particles describes the behavior of particles in an optical trap with trapping energies up to 1.8kBT. We also found G(0) = 〈N−1 to be valid under such trapping energies, which is in good agreement with the results obtained by Meng et al. by Monte Carlo simulation [12

12. F. Meng and H. Ma, “Fluorescence correlation spectroscopy analysis of diffusion in a laser gradient field: A numerical approach,” J. Phys. Chem. B 109, 5580–5585 (2005). [CrossRef]

].

Our experiments demonstrate that the average number of nanoparticles in the trap increases exponentially with the power of the trapping laser for non-interacting particles in suspension. In this case, the concentration of the particles in the trap follows a Boltzmann distribution. We determine the trapping energy of HIV-1 virus-like particles (VLPs) to be 0.02kBT per mW of laser power, a value in good agreement with a discrete dipole approximation by modeling VLP as a hollow sphere with a thin shell of phosphor-lipid bilayer. Using probability theory and the requirements for Poisson statistics, we give an example to illustrate how to estimate the range of force-induced concentration enhancement within which the relationship G(0)trap1=Ntrap can be used to determine particle concentration.

Acknowledgments

The authors wish to thank Ming-Tzo Wei, Drs. Denis Pristinski, Ya Liu and Professor Dimitrios Vavylonis for their helpful suggestions during the course of this study, and Professor Olga Latinovic for her training on virus production. This project is supported in part by funds from NIAID-IR21AI081638, PA Department of Health CURE Formula Funds, NSF DMR 0923299, Lehigh University Center for Optical Technologies and Emulsion Polymers Institute.

References and links

1.

D. Magde, E. Elson, and W. W. Webb, “Thermodynamic fluctuations in a reacting system measurement by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972). [CrossRef]

2.

E. L. Elson and D. Magde, “Fluorescence correlation spectroscopy. I. conceptual basis and theory,” Biopolymers 13, 1–27 (1974). [CrossRef]

3.

S. T. Hess, S. Huang, A. A. Heikal, and W. W. Webb, “Biological and chemical applications of fluorescence correlation spectroscopy: A review,” Biochemistry 41, 697–705 (2002). [CrossRef] [PubMed]

4.

F. Grom, J. Kentsch, T. Muller, T. Schnelle, and M. Stelzle, “Accumulation and trapping of hepatitis a virus particles by electrohydrodynamic flow and dielectrophoresis,” Electrophoresis 27, 1386–1393 (2006). [CrossRef] [PubMed]

5.

K. T. Liao and C. F. Chou, “Nanoscale molecular traps and dams for ultrafast protein enrichment in high-conductivity buffers,” J. Am. Chem. Soc. 134, 8742–8745 (2012). [CrossRef] [PubMed]

6.

J. Junio, S. Park, M.-W. Kim, and H. D. Ou-Yang, “Optical bottles: A quantitative analysis of optically confined nanoparticle ensembles in suspension,” Solid State Commun. 150, 1003–1008 (2010). [CrossRef]

7.

J. Junio, J. Ng, J. A. Cohen, Z. Lin, and H. D. Ou-Yang, “Ensemble method to measure the potential energy of nanoparticles in an optical trap,” Opt. Lett. 36, 1497–1499 (2011). [CrossRef] [PubMed]

8.

M. A. Osborne, S. Balasubramanian, W. S. Furey, and D. Klenerman, “Optically biased diffusion of single molecules studied by confocal fluorescence microscopy,” J. Phys. Chem. B 102, 3160–3167 (1998). [CrossRef]

9.

C. Hosokawa, H. Yoshikawa, and H. Masuhara, “Cluster formation of nanoparticles in an optical trap studied by fluorescence correlation spectroscopy,” Phys. Rev. E 72, 021408 (2005). [CrossRef]

10.

J. Wang, Z. Li, C. P. Yao, F. Xue, Z. X. Zhang, and G. Huttmann, “Brownian diffusion of gold nanoparticles in an optical trap studied by fluorescence correlation spectroscopy,” Laser Phys. 21, 130–136 (2011). [CrossRef]

11.

S. Ito, N. Toitani, H. Yamauchi, and H. Miyasaka, “Evaluation of radiation force acting on macromolecules by combination of brownian dynamics simulation with fluorescence correlation spectroscopy,” Phys. Rev. E 81, 061402 (2010). [CrossRef]

12.

F. Meng and H. Ma, “Fluorescence correlation spectroscopy analysis of diffusion in a laser gradient field: A numerical approach,” J. Phys. Chem. B 109, 5580–5585 (2005). [CrossRef]

13.

B. Wu, Y. Chen, and J. D. Muller, “Fluorescence correlation spectroscopy of finite-sized particles,” Biophys. J. 94, 2800–2808 (2008). [CrossRef]

14.

Assuming the trapping potential has an isotropic Gaussian distribution U(r) = U(0)exp(−2r2/R2), where R is the beam waist of the 1064nm trapping laser, estimated to be 0.97 μm. The experimentally determined trapping potential Utrap is the integration of U(r) in the illumination volume with beam waist 0.23 μm. Therefore, Utrap= 0.978U(0).

15.

C. Hosokawa, H. Yoshikawa, and H. Masuhara, “Optical assembling dynamics of individual polymer nanospheres investigated by single-particle fluorescence detection,” Phys. Rev. E 70, 061410 (2004). [CrossRef]

16.

A. I. Shevchuk, P. Hobson, M. J. Lab, D. Klenerman, N. Krauzewicz, and Y. E. Korchev, “Imaging single virus particles on the surface of cell membranes by high-resolution scanning surface confocal microscopy,” Biophys. J. 94, 4089–4094 (2008). [CrossRef] [PubMed]

17.

Y. Chen, B. Wu, K. Musier-Forsyth, L. M. Mansky, and J. D. Mueller, “Fluorescence fluctuation spectroscopy on viral-like particles reveals variable gag stoichiometry,” Biophys. J. 96, 1961–1969 (2009). [CrossRef] [PubMed]

18.

L. Ling, F. Zhou, L. Huang, and Z.-Y. Li, “Optical forces on arbitrary shaped particles in optical tweezers,” J. Appl. Phys. 108, 073110–8 (2010). [CrossRef]

19.

S. D. Fuller, T. Wilk, B. E. Gowen, H.-G. Krausslich, and V. M. Vogt, “Cryo-electron microscopy reveals ordered domains in the immature HIV-1 particle,” Curr. Biol. 7, 729–738 (1997). [CrossRef] [PubMed]

OCIS Codes
(140.7010) Lasers and laser optics : Laser trapping
(170.1790) Medical optics and biotechnology : Confocal microscopy
(180.2520) Microscopy : Fluorescence microscopy
(290.1990) Scattering : Diffusion
(350.4855) Other areas of optics : Optical tweezers or optical manipulation

ToC Category:
Optical Traps, Manipulation, and Tracking

History
Original Manuscript: May 24, 2013
Revised Manuscript: July 14, 2013
Manuscript Accepted: July 23, 2013
Published: August 14, 2013

Virtual Issues
Optical Trapping and Applications (2013) Biomedical Optics Express

Citation
Yi Hu, Xuanhong Cheng, and H. Daniel Ou-Yang, "Enumerating virus-like particles in an optically concentrated suspension by fluorescence correlation spectroscopy," Biomed. Opt. Express 4, 1646-1653 (2013)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-4-9-1646


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References

  1. D. Magde, E. Elson, and W. W. Webb, “Thermodynamic fluctuations in a reacting system measurement by fluorescence correlation spectroscopy,” Phys. Rev. Lett.29, 705–708 (1972). [CrossRef]
  2. E. L. Elson and D. Magde, “Fluorescence correlation spectroscopy. I. conceptual basis and theory,” Biopolymers13, 1–27 (1974). [CrossRef]
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