Abstract

A theoretical study of the effect of a harmonic trapping force on the distribution of the fluorescence photon counts from Brownian particles is reported. The research of by Chen et al. [Biophys. J. 77, 553 (1999)] is extended. Simulations of the photon-counting histograms indicate that the trapping force parameters can be estimated from changes in the shapes of the histograms, at least for microspheres.

© 2002 Optical Society of America

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  1. U. Kettling, A. Koltermann, P. Schwille, M. Eigen, “Real-time enzyme kinetics monitored by dual-color fluorescence cross-correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 95, 1416–1420 (1998).
    [CrossRef] [PubMed]
  2. E. L. Elson, D. Magde, “Fluorescence correlation spectroscopy. I. Conceptual basis and theory,” Biopolymers 13, 1–27 (1974).
    [CrossRef]
  3. M. Eherneberg, R. Rigler, “Rotational Brownian motion and fluorescence intensity fluctuations,” Chem. Phys. 4, 390–410 (1974).
    [CrossRef]
  4. S. R. Aragon, R. Pecora, “Fluorescence correlation spectroscopy as a probe of molecular dynamics,” J. Chem. Phys. 64, 1791–1803 (1976).
    [CrossRef]
  5. H. Qian, E. L. Elson, “Analysis of confocal laser-microscope optics for 3-D fluorescence correlation spectroscopy,” Appl. Opt. 30, 1185–1195 (1991).
    [CrossRef] [PubMed]
  6. R. Rigler, U. Mets, J. Windengren, P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
    [CrossRef]
  7. D. E. Koppel, F. Morgan, A. E. Cowan, J. H. Carson, “Scanning concentration correlation spectroscopy using the confocal laser microscope,” Biophys. J. 66, 502–507 (1994).
    [CrossRef] [PubMed]
  8. W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
    [CrossRef] [PubMed]
  9. W. Denk, D. W. Piston, W. W. Webb, “Two-photon molecular excitation in laser scanning microscopy,” in Handbook of Biological Confocal Microscopy, J. Pawley, ed., (Plenum, New York, 1995), pp. 445–458.
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  12. H. Qian, E. L. Elson, “On the analysis of high order moments of fluorescence fluctuations,” Biophys. J. 57, 375–380 (1990).
    [CrossRef] [PubMed]
  13. H. Qian, E. L. Elson, “Distribution of molecular aggregation by analysis of fluctuation moments,” Proc. Natl. Acad. Sci. USA 85, 5473–5483 (1990).
  14. J. D. Müller, Y. Chen, E. Gratton, “Resolving heterogeneity on the single molecular level with the photon-counting histogram,” Biophys. J. 78, 474–486 (2000).
    [CrossRef] [PubMed]
  15. P. Kask, K. Palo, D. Ullmann, K. Gall, “Fluorescence-intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. USA 96, 13,756–13,761 (1999).
    [CrossRef]
  16. J. Bieschke, A. Giese, W. Schulz-Schaeffer, I. Zerr, S. Poser, M. Eigen, H. Kretzschmar, “Ultrasensitive detection of pathological prion protein aggregates by dual-color scanning for intensely fluorescent targets,” Proc. Natl. Acad. Sci. USA 97, 5468–5473 (2000).
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    [CrossRef] [PubMed]
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    [CrossRef]
  20. R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, S. A. Safran, “Localized dynamic light scattering: probing single particle dynamics at the nanoscale,” Phys. Rev. Lett. 78, 154–157 (1997).
    [CrossRef]
  21. P. Zemánek, A. Jonás, L. Šrámek, M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998).
    [CrossRef]
  22. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, 9th ed. (Dover, New York, 1965).
  23. K. Svoboda, S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
    [CrossRef] [PubMed]

2000 (2)

J. D. Müller, Y. Chen, E. Gratton, “Resolving heterogeneity on the single molecular level with the photon-counting histogram,” Biophys. J. 78, 474–486 (2000).
[CrossRef] [PubMed]

J. Bieschke, A. Giese, W. Schulz-Schaeffer, I. Zerr, S. Poser, M. Eigen, H. Kretzschmar, “Ultrasensitive detection of pathological prion protein aggregates by dual-color scanning for intensely fluorescent targets,” Proc. Natl. Acad. Sci. USA 97, 5468–5473 (2000).
[CrossRef] [PubMed]

1999 (2)

P. Kask, K. Palo, D. Ullmann, K. Gall, “Fluorescence-intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. USA 96, 13,756–13,761 (1999).
[CrossRef]

Y. Chen, J. D. Muller, P. T. C. So, E. Gratton, “The photon counting histogram in fluorescence fluctuation spectroscopy,” Biophys. J. 77, 553–567 (1999).
[CrossRef] [PubMed]

1998 (3)

U. Kettling, A. Koltermann, P. Schwille, M. Eigen, “Real-time enzyme kinetics monitored by dual-color fluorescence cross-correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 95, 1416–1420 (1998).
[CrossRef] [PubMed]

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

P. Zemánek, A. Jonás, L. Šrámek, M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998).
[CrossRef]

1997 (2)

R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, S. A. Safran, “Localized dynamic light scattering: probing single particle dynamics at the nanoscale,” Phys. Rev. Lett. 78, 154–157 (1997).
[CrossRef]

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. USA 94, 4853–4860 (1997).
[CrossRef] [PubMed]

1994 (2)

K. Svoboda, S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef] [PubMed]

D. E. Koppel, F. Morgan, A. E. Cowan, J. H. Carson, “Scanning concentration correlation spectroscopy using the confocal laser microscope,” Biophys. J. 66, 502–507 (1994).
[CrossRef] [PubMed]

1993 (1)

R. Rigler, U. Mets, J. Windengren, P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
[CrossRef]

1991 (1)

1990 (3)

W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

H. Qian, E. L. Elson, “On the analysis of high order moments of fluorescence fluctuations,” Biophys. J. 57, 375–380 (1990).
[CrossRef] [PubMed]

H. Qian, E. L. Elson, “Distribution of molecular aggregation by analysis of fluctuation moments,” Proc. Natl. Acad. Sci. USA 85, 5473–5483 (1990).

1986 (1)

1976 (1)

S. R. Aragon, R. Pecora, “Fluorescence correlation spectroscopy as a probe of molecular dynamics,” J. Chem. Phys. 64, 1791–1803 (1976).
[CrossRef]

1974 (2)

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

M. Eherneberg, R. Rigler, “Rotational Brownian motion and fluorescence intensity fluctuations,” Chem. Phys. 4, 390–410 (1974).
[CrossRef]

Abramowitz, M.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, 9th ed. (Dover, New York, 1965).

Aragon, S. R.

S. R. Aragon, R. Pecora, “Fluorescence correlation spectroscopy as a probe of molecular dynamics,” J. Chem. Phys. 64, 1791–1803 (1976).
[CrossRef]

Ashkin, A.

Balasubramanian, S.

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

Bar-Ziv, R.

R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, S. A. Safran, “Localized dynamic light scattering: probing single particle dynamics at the nanoscale,” Phys. Rev. Lett. 78, 154–157 (1997).
[CrossRef]

Bieschke, J.

J. Bieschke, A. Giese, W. Schulz-Schaeffer, I. Zerr, S. Poser, M. Eigen, H. Kretzschmar, “Ultrasensitive detection of pathological prion protein aggregates by dual-color scanning for intensely fluorescent targets,” Proc. Natl. Acad. Sci. USA 97, 5468–5473 (2000).
[CrossRef] [PubMed]

Bjorkholm, J. E.

Block, S. M.

K. Svoboda, S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef] [PubMed]

Carson, J. H.

D. E. Koppel, F. Morgan, A. E. Cowan, J. H. Carson, “Scanning concentration correlation spectroscopy using the confocal laser microscope,” Biophys. J. 66, 502–507 (1994).
[CrossRef] [PubMed]

Chen, Y.

J. D. Müller, Y. Chen, E. Gratton, “Resolving heterogeneity on the single molecular level with the photon-counting histogram,” Biophys. J. 78, 474–486 (2000).
[CrossRef] [PubMed]

Y. Chen, J. D. Muller, P. T. C. So, E. Gratton, “The photon counting histogram in fluorescence fluctuation spectroscopy,” Biophys. J. 77, 553–567 (1999).
[CrossRef] [PubMed]

Chu, S.

Cowan, A. E.

D. E. Koppel, F. Morgan, A. E. Cowan, J. H. Carson, “Scanning concentration correlation spectroscopy using the confocal laser microscope,” Biophys. J. 66, 502–507 (1994).
[CrossRef] [PubMed]

Denk, W.

W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

W. Denk, D. W. Piston, W. W. Webb, “Two-photon molecular excitation in laser scanning microscopy,” in Handbook of Biological Confocal Microscopy, J. Pawley, ed., (Plenum, New York, 1995), pp. 445–458.
[CrossRef]

Dziedzic, J. M.

Eherneberg, M.

M. Eherneberg, R. Rigler, “Rotational Brownian motion and fluorescence intensity fluctuations,” Chem. Phys. 4, 390–410 (1974).
[CrossRef]

Eigen, M.

J. Bieschke, A. Giese, W. Schulz-Schaeffer, I. Zerr, S. Poser, M. Eigen, H. Kretzschmar, “Ultrasensitive detection of pathological prion protein aggregates by dual-color scanning for intensely fluorescent targets,” Proc. Natl. Acad. Sci. USA 97, 5468–5473 (2000).
[CrossRef] [PubMed]

U. Kettling, A. Koltermann, P. Schwille, M. Eigen, “Real-time enzyme kinetics monitored by dual-color fluorescence cross-correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 95, 1416–1420 (1998).
[CrossRef] [PubMed]

Elson, E. L.

H. Qian, E. L. Elson, “Analysis of confocal laser-microscope optics for 3-D fluorescence correlation spectroscopy,” Appl. Opt. 30, 1185–1195 (1991).
[CrossRef] [PubMed]

H. Qian, E. L. Elson, “On the analysis of high order moments of fluorescence fluctuations,” Biophys. J. 57, 375–380 (1990).
[CrossRef] [PubMed]

H. Qian, E. L. Elson, “Distribution of molecular aggregation by analysis of fluctuation moments,” Proc. Natl. Acad. Sci. USA 85, 5473–5483 (1990).

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

Furey, W. S.

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

Gall, K.

P. Kask, K. Palo, D. Ullmann, K. Gall, “Fluorescence-intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. USA 96, 13,756–13,761 (1999).
[CrossRef]

Giese, A.

J. Bieschke, A. Giese, W. Schulz-Schaeffer, I. Zerr, S. Poser, M. Eigen, H. Kretzschmar, “Ultrasensitive detection of pathological prion protein aggregates by dual-color scanning for intensely fluorescent targets,” Proc. Natl. Acad. Sci. USA 97, 5468–5473 (2000).
[CrossRef] [PubMed]

Gratton, E.

J. D. Müller, Y. Chen, E. Gratton, “Resolving heterogeneity on the single molecular level with the photon-counting histogram,” Biophys. J. 78, 474–486 (2000).
[CrossRef] [PubMed]

Y. Chen, J. D. Muller, P. T. C. So, E. Gratton, “The photon counting histogram in fluorescence fluctuation spectroscopy,” Biophys. J. 77, 553–567 (1999).
[CrossRef] [PubMed]

Jonás, A.

P. Zemánek, A. Jonás, L. Šrámek, M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998).
[CrossRef]

Kask, P.

P. Kask, K. Palo, D. Ullmann, K. Gall, “Fluorescence-intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. USA 96, 13,756–13,761 (1999).
[CrossRef]

R. Rigler, U. Mets, J. Windengren, P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
[CrossRef]

Kettling, U.

U. Kettling, A. Koltermann, P. Schwille, M. Eigen, “Real-time enzyme kinetics monitored by dual-color fluorescence cross-correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 95, 1416–1420 (1998).
[CrossRef] [PubMed]

Klenerman, D.

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

Koltermann, A.

U. Kettling, A. Koltermann, P. Schwille, M. Eigen, “Real-time enzyme kinetics monitored by dual-color fluorescence cross-correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 95, 1416–1420 (1998).
[CrossRef] [PubMed]

Koppel, D. E.

D. E. Koppel, F. Morgan, A. E. Cowan, J. H. Carson, “Scanning concentration correlation spectroscopy using the confocal laser microscope,” Biophys. J. 66, 502–507 (1994).
[CrossRef] [PubMed]

Kretzschmar, H.

J. Bieschke, A. Giese, W. Schulz-Schaeffer, I. Zerr, S. Poser, M. Eigen, H. Kretzschmar, “Ultrasensitive detection of pathological prion protein aggregates by dual-color scanning for intensely fluorescent targets,” Proc. Natl. Acad. Sci. USA 97, 5468–5473 (2000).
[CrossRef] [PubMed]

Liška, M.

P. Zemánek, A. Jonás, L. Šrámek, M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998).
[CrossRef]

Magde, D.

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

Meller, A.

R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, S. A. Safran, “Localized dynamic light scattering: probing single particle dynamics at the nanoscale,” Phys. Rev. Lett. 78, 154–157 (1997).
[CrossRef]

Mets, U.

R. Rigler, U. Mets, J. Windengren, P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
[CrossRef]

Morgan, F.

D. E. Koppel, F. Morgan, A. E. Cowan, J. H. Carson, “Scanning concentration correlation spectroscopy using the confocal laser microscope,” Biophys. J. 66, 502–507 (1994).
[CrossRef] [PubMed]

Moses, E.

R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, S. A. Safran, “Localized dynamic light scattering: probing single particle dynamics at the nanoscale,” Phys. Rev. Lett. 78, 154–157 (1997).
[CrossRef]

Muller, J. D.

Y. Chen, J. D. Muller, P. T. C. So, E. Gratton, “The photon counting histogram in fluorescence fluctuation spectroscopy,” Biophys. J. 77, 553–567 (1999).
[CrossRef] [PubMed]

Müller, J. D.

J. D. Müller, Y. Chen, E. Gratton, “Resolving heterogeneity on the single molecular level with the photon-counting histogram,” Biophys. J. 78, 474–486 (2000).
[CrossRef] [PubMed]

Osborne, M. A.

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

Palo, K.

P. Kask, K. Palo, D. Ullmann, K. Gall, “Fluorescence-intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. USA 96, 13,756–13,761 (1999).
[CrossRef]

Pecora, R.

S. R. Aragon, R. Pecora, “Fluorescence correlation spectroscopy as a probe of molecular dynamics,” J. Chem. Phys. 64, 1791–1803 (1976).
[CrossRef]

Piston, D. W.

W. Denk, D. W. Piston, W. W. Webb, “Two-photon molecular excitation in laser scanning microscopy,” in Handbook of Biological Confocal Microscopy, J. Pawley, ed., (Plenum, New York, 1995), pp. 445–458.
[CrossRef]

Poser, S.

J. Bieschke, A. Giese, W. Schulz-Schaeffer, I. Zerr, S. Poser, M. Eigen, H. Kretzschmar, “Ultrasensitive detection of pathological prion protein aggregates by dual-color scanning for intensely fluorescent targets,” Proc. Natl. Acad. Sci. USA 97, 5468–5473 (2000).
[CrossRef] [PubMed]

Qian, H.

H. Qian, E. L. Elson, “Analysis of confocal laser-microscope optics for 3-D fluorescence correlation spectroscopy,” Appl. Opt. 30, 1185–1195 (1991).
[CrossRef] [PubMed]

H. Qian, E. L. Elson, “On the analysis of high order moments of fluorescence fluctuations,” Biophys. J. 57, 375–380 (1990).
[CrossRef] [PubMed]

H. Qian, E. L. Elson, “Distribution of molecular aggregation by analysis of fluctuation moments,” Proc. Natl. Acad. Sci. USA 85, 5473–5483 (1990).

Rigler, R.

R. Rigler, U. Mets, J. Windengren, P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
[CrossRef]

M. Eherneberg, R. Rigler, “Rotational Brownian motion and fluorescence intensity fluctuations,” Chem. Phys. 4, 390–410 (1974).
[CrossRef]

Safran, S. A.

R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, S. A. Safran, “Localized dynamic light scattering: probing single particle dynamics at the nanoscale,” Phys. Rev. Lett. 78, 154–157 (1997).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978).
[CrossRef]

Schulz-Schaeffer, W.

J. Bieschke, A. Giese, W. Schulz-Schaeffer, I. Zerr, S. Poser, M. Eigen, H. Kretzschmar, “Ultrasensitive detection of pathological prion protein aggregates by dual-color scanning for intensely fluorescent targets,” Proc. Natl. Acad. Sci. USA 97, 5468–5473 (2000).
[CrossRef] [PubMed]

Schwille, P.

U. Kettling, A. Koltermann, P. Schwille, M. Eigen, “Real-time enzyme kinetics monitored by dual-color fluorescence cross-correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 95, 1416–1420 (1998).
[CrossRef] [PubMed]

So, P. T. C.

Y. Chen, J. D. Muller, P. T. C. So, E. Gratton, “The photon counting histogram in fluorescence fluctuation spectroscopy,” Biophys. J. 77, 553–567 (1999).
[CrossRef] [PubMed]

Šrámek, L.

P. Zemánek, A. Jonás, L. Šrámek, M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998).
[CrossRef]

Stavans, J.

R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, S. A. Safran, “Localized dynamic light scattering: probing single particle dynamics at the nanoscale,” Phys. Rev. Lett. 78, 154–157 (1997).
[CrossRef]

Stegun, I. A.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, 9th ed. (Dover, New York, 1965).

Strickler, J. H.

W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Svoboda, K.

K. Svoboda, S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef] [PubMed]

Tlusty, T.

R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, S. A. Safran, “Localized dynamic light scattering: probing single particle dynamics at the nanoscale,” Phys. Rev. Lett. 78, 154–157 (1997).
[CrossRef]

Ullmann, D.

P. Kask, K. Palo, D. Ullmann, K. Gall, “Fluorescence-intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. USA 96, 13,756–13,761 (1999).
[CrossRef]

Webb, W. W.

W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

W. Denk, D. W. Piston, W. W. Webb, “Two-photon molecular excitation in laser scanning microscopy,” in Handbook of Biological Confocal Microscopy, J. Pawley, ed., (Plenum, New York, 1995), pp. 445–458.
[CrossRef]

Windengren, J.

R. Rigler, U. Mets, J. Windengren, P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
[CrossRef]

Zemánek, P.

P. Zemánek, A. Jonás, L. Šrámek, M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998).
[CrossRef]

Zerr, I.

J. Bieschke, A. Giese, W. Schulz-Schaeffer, I. Zerr, S. Poser, M. Eigen, H. Kretzschmar, “Ultrasensitive detection of pathological prion protein aggregates by dual-color scanning for intensely fluorescent targets,” Proc. Natl. Acad. Sci. USA 97, 5468–5473 (2000).
[CrossRef] [PubMed]

Annu. Rev. Biophys. Biomol. Struct. (1)

K. Svoboda, S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef] [PubMed]

Appl. Opt. (1)

Biophys. J. (4)

D. E. Koppel, F. Morgan, A. E. Cowan, J. H. Carson, “Scanning concentration correlation spectroscopy using the confocal laser microscope,” Biophys. J. 66, 502–507 (1994).
[CrossRef] [PubMed]

J. D. Müller, Y. Chen, E. Gratton, “Resolving heterogeneity on the single molecular level with the photon-counting histogram,” Biophys. J. 78, 474–486 (2000).
[CrossRef] [PubMed]

Y. Chen, J. D. Muller, P. T. C. So, E. Gratton, “The photon counting histogram in fluorescence fluctuation spectroscopy,” Biophys. J. 77, 553–567 (1999).
[CrossRef] [PubMed]

H. Qian, E. L. Elson, “On the analysis of high order moments of fluorescence fluctuations,” Biophys. J. 57, 375–380 (1990).
[CrossRef] [PubMed]

Biopolymers (1)

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

Chem. Phys. (1)

M. Eherneberg, R. Rigler, “Rotational Brownian motion and fluorescence intensity fluctuations,” Chem. Phys. 4, 390–410 (1974).
[CrossRef]

Eur. Biophys. J. (1)

R. Rigler, U. Mets, J. Windengren, P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
[CrossRef]

J. Chem. Phys. (1)

S. R. Aragon, R. Pecora, “Fluorescence correlation spectroscopy as a probe of molecular dynamics,” J. Chem. Phys. 64, 1791–1803 (1976).
[CrossRef]

J. Phys. Chem. B (1)

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

Opt. Commun. (1)

P. Zemánek, A. Jonás, L. Šrámek, M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, S. A. Safran, “Localized dynamic light scattering: probing single particle dynamics at the nanoscale,” Phys. Rev. Lett. 78, 154–157 (1997).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Single-molecule PCH (bottom) and the super-Poissonian Π(0) (k) (top) computed according to Eq. (9) for several values of trapping parameter kρ. Solid curves, from bottom to top, kρ = 0, 1, 10, 15, 20, 25, 35, 45, 70 µm-2 and kz = 0. The computations are for single-photon excitation, C = 560 pM, V0/Vpsf = 10, and ∊T = 20. Insets, values of the single-molecule PCH and of the super-Poissonian for k = 20 when kρ changes (kz = 0; filled squares) and when kz changes in the range (kρ = 0; open circles).

Fig. 2
Fig. 2

Distribution of the number of molecules P(N, β, NT). (a) kρ, kz = 0 and V0/Vpsf with the following values: 2.4 (filled circles), 3.6 (open triangles), 4.8 (open diamonds), 5.4 (filled downward-pointing triangles), 6.6 (crosses), and Poisson limit (solid curve). (b) kρ = 5 µm-2 and kz = 0. The symbols are the same as in (a). (c) kp = 0 and kz = 1 µm-2. The symbols are the same as in (a). The computations correspond to C = 560 pM and ∊T = 20.

Fig. 3
Fig. 3

Effect of molecular brightness on the PCH. Bottom, C = 112.5 pM and ∊T with the following values: 0.5 (solid curves), 1 (squares), 2 (circles), 4 (upward-pointing triangles), and 8 (downward pointing triangles). Top, C = 2.25 nM. Symbols have the same values of ∊T as at the bottom. The background is σbg = 0.02.

Fig. 4
Fig. 4

PCH for a number of photon counts (top) k = 1 and (bottom) k = 10 versus molecular brightness ∊T. Squares, the 3-D Gaussian profile; circles, Gaussian-Lorentzian laser profile. The curves through the symbols are guides for the eye.

Equations (24)

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Iexc1PEr=I0iexc1PEr=I0 exp-2x2+y2wxy2exp-2z2wz2.
Iexc2PEr=IL2r=I02iexc2PEr=I02w04π2w4zexp-4x2+y2w2z,
p1k, V0=V0dE Poik, aEPEEV0dEPEE,
p1k, V0=V0dr Poik, iexcrTPrrV0drPrr.
p1k, V0=1V0V0dr Poik, iexcrT.
Prrexp-UrKBT.
U(r)=KBTkρρ2+kzz2,
Ur=-nmαI02vDmD0 iexcrU0+nmI0αvDmD0wxy2 ρ2+nmI0αvDmD0wz2 z2,
Πk=N=0PoiN, N¯pNk, V0,
Vn=V0dr exp-kρρ2-kzz2=V0kρR02kz0.5Z01-exp-kρR02erfkz0.5Z0,
p1PE1k, V0=πVn0dρ20dz×Poik, TIexc1PEρ, zTexp-kρρ2-kzz2,
p1PE1k, V0=2π0.5Vpsf1PETμk!Vn0ds×exp-s2Ω4γk+μ, T exp-s22,
p2PE1k, V0=π2Vpsf2PEk!Vn0ds 1+s2exp-Ωs2αs0.5µ1+s2×γk+2µ1+s2, αs,
p2PE1,0k, V0=π2Vpsf2PEk!V00ds1+s2γk, αs.
β=VpsfdrPrrV0drPrr=β01+Γ Vpsfdriexcr/Vpsf1+Γ V0driexcr/V0,
PN, β, NT=βN1-βNT-NNT!N!NT-N! PN, β, NTPoiβNT, N =βNTNN!exp-βNT, β0,
β=β01+Γ Vpsfdriexcr/Vpsf.
p1PE1k, V0=πk!VnTk0dρ2-dz exp-2ρ2kwxy2-2z2kwz2exp-T exp-2ρ2wxy2-2z2wz2exp-kρρ2-kzz2.
p1PE1k, V0=Tkπwxy22k!Vn-dzαzk+μ+0.5Ω×01dyyk+μ-1 exp-Tαzy =πwxy2Tμk!Vn0dzγ[k+μ, Tαz]αz0.5Ω,
γk, s=0sdyyk-1 exp-y.
p1PE1k, V0=2π0.5Vpsf1PEk!TμVn0ds×exp-s2Ω/4γ[k+μ, T exp-s2/2],
p2PE1k, V0=πk!Vn0dρ -dzβzk×exp-4ρ kw2zexp-βz×exp-4ρ kw2z-kρρ-kzz2,
p2PE1k, V0=πk!4Vn-dzβzkw2z×exp-kzz201dξ×exp-βzξξk-1-kρw2z/4.
p2PE1k, V0=πk!4Vn-dz βz-kρw2z/4w2z×exp-kzz2γk+kρw2z/4, βz.

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