## Enumerating virus-like particles in an optically concentrated suspension by fluorescence correlation spectroscopy |

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

*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]

*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]

*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]

*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]

*k*. Meng

_{B}T*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]

*k*and showed the ACF amplitude is equal to the inverse of the mean number of particles in the optical trap.

_{B}T*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]

*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]

*N*〉 under optical trapping requires that the particle number density fluctuation follows the Poisson statistics.

## 2. Experimental

### 2.1. FCS data analysis

*G*(

*τ*) is defined as: 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]

*N*

^{2}〉 and 〈

*N*〉 are the variance and the mean number of particles in the volume, respectively;

*D*is the diffusion coefficient of the particles;

*w*

_{0}and

*z*

_{0}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 〈Δ

*N*

^{2}〉/〈

*N*〉

^{2}. 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 〈Δ

*N*

^{2}〉 equals the mean number density 〈

*N*〉, and

### 2.3. Sample preparation

#### 2.3.1. Colloidal polystyrene (PS) nanoparticles

*nm*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 543

*nm*, emission maximum 612

*nm*). 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)

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

*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

*G*(

*τ*) from 110

*nm*PS nanoparticle suspensions in the presence of optical trapping with laser powers between 0 and 18

*mW*are shown in Fig. 2. Each ACF curve represents an average of 10 independent measurements. Fitting Eq. (2) to the trap-free (0

*mW*) curve yields a particle number density 〈

*N*

_{0}〉= 0.165 in the observation volume and diffusivity

*D*= 4.5

*μm*

^{2}/

*s*. The measured diffusivity agrees with that obtained by the Stokes-Einstein equation

*D*=

*k*/(6

_{B}T*πηa*) = 4.35

*μm*

^{2}/

*s*, where

*η*is the viscosity of water at the ambient temperature and

*a*is the particle radius.

*mW*, 6

*mW*, 12

*mW*and 18

*mW*, 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 1.8

*k*. This range of trapping powers exceeds that examined by Ito

_{B}T*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]

*k*. The trapping energy will be discussed later.

_{B}T*N*〉= 〈

_{trap}*F*〉/

_{trap}*ε*. Here,

*ε*is the average fluorescence luminosity per particle at fixed excitation light intensity, which can be determined by the ratio

*F*

_{0}〉 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.

*N*〉. The linearity in Fig. 4(a) with a slope of 1 suggests

_{trap}*mW*to 18

*mW*.

*U*[14

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

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]

*nm*PS spheres is found to be 0.1 ± 0.04

*k*per

_{B}T*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. 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]

*k*, suggesting our experimental result agrees with the theoretical prediction by Meng

_{B}T*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]

*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]

### 3.2. Optical trapping of VLPs

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

*nm*(standard deviation from 10 VLPs), which agrees with previous studies [16

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]

*μm*

^{2}/

*s*. Using the Stokes-Einstein equation

*D*=

*k*/(6

_{B}T*πηa*) and medium viscosity

*η*= 0.98

*cP*, we determine the diameter of the VLPs to be 115 ± 14

*nm*(standard deviation from 10 independent measurements), which is consistent with results obtained by SEM.

*G*(0)

^{−1}vs. trapping laser power is shown in Fig. 5(b). For PBS buffer solutions containing 135

*mM*NaCl, the Debye screening length is on the order of 1

*nm*. 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 ± 0.003

*k*.

_{B}T/mW18. 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]

*μm*. For the 110

*nm*diameter PS spheres (refractive index 1.59) in water (refractive index 1.33), the calculated trapping energy is 0.13

*k*. Modeling VLPs as 100

_{B}T /mW*nm*inner diameter vesicles with a 10

*nm*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]

*k*, in reasonable agreement with the experimentally determined value for VLP.

_{B}T /mW## 4. Conclusions

*k*. We also found

_{B}T*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

**109**, 5580–5585 (2005). [CrossRef]

*k*per

_{B}T*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

## Acknowledgments

## 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. |

2. | E. L. Elson and D. Magde, “Fluorescence correlation spectroscopy. I. conceptual basis and theory,” Biopolymers |

3. | S. T. Hess, S. Huang, A. A. Heikal, and W. W. Webb, “Biological and chemical applications of fluorescence correlation spectroscopy: A review,” Biochemistry |

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 |

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. |

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. |

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. |

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 |

9. | C. Hosokawa, H. Yoshikawa, and H. Masuhara, “Cluster formation of nanoparticles in an optical trap studied by fluorescence correlation spectroscopy,” Phys. Rev. E |

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. |

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 |

12. | F. Meng and H. Ma, “Fluorescence correlation spectroscopy analysis of diffusion in a laser gradient field: A numerical approach,” J. Phys. Chem. B |

13. | B. Wu, Y. Chen, and J. D. Muller, “Fluorescence correlation spectroscopy of finite-sized particles,” Biophys. J. |

14. | Assuming the trapping potential has an isotropic Gaussian distribution U(r) = U(0)exp(−2r |

15. | C. Hosokawa, H. Yoshikawa, and H. Masuhara, “Optical assembling dynamics of individual polymer nanospheres investigated by single-particle fluorescence detection,” Phys. Rev. E |

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. |

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. |

18. | L. Ling, F. Zhou, L. Huang, and Z.-Y. Li, “Optical forces on arbitrary shaped particles in optical tweezers,” J. Appl. Phys. |

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. |

**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

- 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]
- E. L. Elson and D. Magde, “Fluorescence correlation spectroscopy. I. conceptual basis and theory,” Biopolymers13, 1–27 (1974). [CrossRef]
- S. T. Hess, S. Huang, A. A. Heikal, and W. W. Webb, “Biological and chemical applications of fluorescence correlation spectroscopy: A review,” Biochemistry41, 697–705 (2002). [CrossRef] [PubMed]
- F. Grom, J. Kentsch, T. Muller, T. Schnelle, and M. Stelzle, “Accumulation and trapping of hepatitis a virus particles by electrohydrodynamic flow and dielectrophoresis,” Electrophoresis27, 1386–1393 (2006). [CrossRef] [PubMed]
- 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]
- 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]
- 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]
- 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. B102, 3160–3167 (1998). [CrossRef]
- C. Hosokawa, H. Yoshikawa, and H. Masuhara, “Cluster formation of nanoparticles in an optical trap studied by fluorescence correlation spectroscopy,” Phys. Rev. E72, 021408 (2005). [CrossRef]
- 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]
- 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. E81, 061402 (2010). [CrossRef]
- F. Meng and H. Ma, “Fluorescence correlation spectroscopy analysis of diffusion in a laser gradient field: A numerical approach,” J. Phys. Chem. B109, 5580–5585 (2005). [CrossRef]
- B. Wu, Y. Chen, and J. D. Muller, “Fluorescence correlation spectroscopy of finite-sized particles,” Biophys. J.94, 2800–2808 (2008). [CrossRef]
- 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).
- C. Hosokawa, H. Yoshikawa, and H. Masuhara, “Optical assembling dynamics of individual polymer nanospheres investigated by single-particle fluorescence detection,” Phys. Rev. E70, 061410 (2004). [CrossRef]
- 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]
- 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]
- 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]
- 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]

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