Abstract

Fluorescence correlation spectroscopy (FCS) has become a powerful and sensitive research tool for the study of molecular dynamics at the single-molecule level. Because photophysical dynamics often dramatically influence FCS measurements, the role of various photophysical processes in FCS measurements must be understood to accurately interpret FCS data. We describe the role of excitation saturation in two-photon fluorescence correlation measurements. We introduce a physical model that characterizes the effects of excitation saturation on the size and shape of the two-photon fluorescence observation volume and derive a new analytical expression for fluorescence correlation functions that includes the influence of saturation. With this model, we can accurately describe both the temporal decay and the amplitude of measured fluorescence correlation functions over a wide range of illumination powers.

© 2003 Optical Society of America

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  1. D. Magde, E. Elson, W. W. Webb, “Thermodynamic fluctuations in a reacting system. Measurement by fluorescence Correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
  2. E. L. Elson, D. Magde, “Fluorescence correlation spectroscopy. I. Conceptual basis and theory,” Biopolymers 13, 1–27 (1974).
  3. D. Magde, E. L. Elson, W. W. Webb, “Fluorescence correlation spectroscopy. II. Experimental realization,” Biopolymers 13, 29–61 (1974).
  4. S. Maiti, U. Haupts, W. W. Webb, “Fluorescence correlation spectroscopy: diagnostics for sparse molecules,” Proc. Natl. Acad. Sci. USA 94, 11753–11757 (1997).
    [PubMed]
  5. N. L. Thompson, “Fluorescence correlation spectroscopy,” in Topics in Fluorescence Spectroscopy, J. R. Lakowicz, ed. (Plenum, New York, 1991), pp. 337–378.
  6. R. Rigler, E. S. Elson, eds., Fluorescence Correlation Spectroscopy Theory and Applications (Springer, New York, 2001), Vol. 45, p. 486.
  7. M. Eigen, R. Rigler, “Sorting single molecules: application to diagnostics and evolutionary biotechnology,” Proc. Natl. Acad. Sci. USA 91, 5740–5747 (1994).
    [CrossRef] [PubMed]
  8. N. L. Thompson, A. M. Leito, N. W. Allo, “Recent advances in fluorescence correlation spectroscopy,” Curr. Opin. Struct. Biol. 12, 634–641 (2002).
    [CrossRef] [PubMed]
  9. S. T. Hess, S. Huang, A. A. Heikal, W. W. Webb, “Biological and chemical applications of fluorescence correlation spectroscopy: a review,” Biochemistry 41, 697–705 (2002).
    [CrossRef] [PubMed]
  10. J. Widengren, R. Rigler, U. Mets, “Triplet-state monitoring by fluorescence correlation spectroscopy,” J. Fluoresc. 4(3), 255–258 (1994).
    [CrossRef]
  11. J. Widengren, R. Rigler, “Mechanisms of photobleaching investigated by fluorescence correlation spectroscopy,” Bioimaging 4(3), 149–157 (1996).
    [CrossRef]
  12. J. Widengren, B. Terry, R. Rigler, “Protonation kinetics of GFP and FITC investigated by FCS—aspects of the use of fluorescent indicators for measuring pH,” Chem. Phys. 249, 259–271 (1999).
    [CrossRef]
  13. J. Widengren, U. Mets, R. Rigler, “Photodynamic properties of green fluorescent proteins investigated by fluorescence correlation spectroscopy,” Chem. Phys. 250, 171–186 (1999).
    [CrossRef]
  14. J. Widengren, U. Mets, R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem. 99, 13368–13379 (1995).
    [CrossRef]
  15. P. Schulk, S. Kummer, A. A. Heikel, W. E. Moeiner, W. W. Webb, “Fluorescence Correlation Spectroscopy reveals fast optical excitation-driven intramolecular dynamics of yellow fluorescent proteins,” Proc. Natl. Acad. USA 97, 151–156 (2000).
    [CrossRef]
  16. F. Malvezzi-Campeggi, M. Jahnz, K. G. Heinze, P. Dittrich, P. Schwille, “Light-induced flickering of DsRed provides evidence for distinct and interconvertible fluorescent states,” Biophys. J. 81, 1776–1785 (2001).
    [CrossRef] [PubMed]
  17. U. Haupts, S. Maiti, P. Schwille, W. W. Webb, “Dynamics of fluorescence fluctuations in green fluorescent protein observed by fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 95, 13573–13578 (1998).
    [CrossRef] [PubMed]
  18. J. Mertz, “Molecular photodynamics involved in multi-photon excitation microscopy,” Eur. Phys. J. D. 3(24), 53–66 (1998).
    [CrossRef]
  19. W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science, 248, 73–76 (1990).
    [CrossRef] [PubMed]
  20. C. Xu, W. W. Webb, “Multiphoton excitation of molecular fluorophores and nonlinear laser microscopy,” Top. Fluoresc. Spectrosc. 5, 471–540 (1997).
    [CrossRef]
  21. K. M. Berland, P. T. C. So, E. Gratton, “Two-photon fluorescence correlation spectroscopy: method and application to the intracellular environment,” Biophys. J. 68, 694–701 (1995).
    [CrossRef] [PubMed]
  22. P. Schwille, U. Haupts, S. Maiti, W. W. Webb, Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two-photon excitation, Biophys. J. 77, 2251–2265 (1999).
    [CrossRef] [PubMed]
  23. P. S. Dittrich, P. Schwille, “Photobleaching and stabilization of fluorophores used for single-molecule analysis with one- and two-photon excitation,” Appl. Phys. B 73, 829–873 (2001).
    [CrossRef]
  24. C. Eggeling, J. Widengren, R. Rigler, C. A. M. SeidelG. G. Max-Planck-Institut fuer Biophysikalische Chemie, “Photobleaching of fluorescent dyes under conditions used for single-molecule detection: evidence of two-step photolysis,” Anal. Chem. 70, 2651–2659 (1998).
    [CrossRef] [PubMed]
  25. T. Wohland, R. Rigler, H. Vogel, “The standard deviation in fluorescence correlation spectroscopy,” Biophys. J. 80, 2987–2999 (2001).
    [CrossRef] [PubMed]
  26. Our fitting routines are programmed with conditional statements in the fit function definitions such that the parameter alpha is assigned the value zero whenever the power is less than the saturation threshold parameter. This allows for simultaneous fitting of the entire curve, both above and below the saturation threshold, with asingle fitting function.

2002

N. L. Thompson, A. M. Leito, N. W. Allo, “Recent advances in fluorescence correlation spectroscopy,” Curr. Opin. Struct. Biol. 12, 634–641 (2002).
[CrossRef] [PubMed]

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

2001

F. Malvezzi-Campeggi, M. Jahnz, K. G. Heinze, P. Dittrich, P. Schwille, “Light-induced flickering of DsRed provides evidence for distinct and interconvertible fluorescent states,” Biophys. J. 81, 1776–1785 (2001).
[CrossRef] [PubMed]

P. S. Dittrich, P. Schwille, “Photobleaching and stabilization of fluorophores used for single-molecule analysis with one- and two-photon excitation,” Appl. Phys. B 73, 829–873 (2001).
[CrossRef]

T. Wohland, R. Rigler, H. Vogel, “The standard deviation in fluorescence correlation spectroscopy,” Biophys. J. 80, 2987–2999 (2001).
[CrossRef] [PubMed]

2000

P. Schulk, S. Kummer, A. A. Heikel, W. E. Moeiner, W. W. Webb, “Fluorescence Correlation Spectroscopy reveals fast optical excitation-driven intramolecular dynamics of yellow fluorescent proteins,” Proc. Natl. Acad. USA 97, 151–156 (2000).
[CrossRef]

1999

P. Schwille, U. Haupts, S. Maiti, W. W. Webb, Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two-photon excitation, Biophys. J. 77, 2251–2265 (1999).
[CrossRef] [PubMed]

J. Widengren, B. Terry, R. Rigler, “Protonation kinetics of GFP and FITC investigated by FCS—aspects of the use of fluorescent indicators for measuring pH,” Chem. Phys. 249, 259–271 (1999).
[CrossRef]

J. Widengren, U. Mets, R. Rigler, “Photodynamic properties of green fluorescent proteins investigated by fluorescence correlation spectroscopy,” Chem. Phys. 250, 171–186 (1999).
[CrossRef]

1998

U. Haupts, S. Maiti, P. Schwille, W. W. Webb, “Dynamics of fluorescence fluctuations in green fluorescent protein observed by fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 95, 13573–13578 (1998).
[CrossRef] [PubMed]

J. Mertz, “Molecular photodynamics involved in multi-photon excitation microscopy,” Eur. Phys. J. D. 3(24), 53–66 (1998).
[CrossRef]

C. Eggeling, J. Widengren, R. Rigler, C. A. M. SeidelG. G. Max-Planck-Institut fuer Biophysikalische Chemie, “Photobleaching of fluorescent dyes under conditions used for single-molecule detection: evidence of two-step photolysis,” Anal. Chem. 70, 2651–2659 (1998).
[CrossRef] [PubMed]

1997

C. Xu, W. W. Webb, “Multiphoton excitation of molecular fluorophores and nonlinear laser microscopy,” Top. Fluoresc. Spectrosc. 5, 471–540 (1997).
[CrossRef]

S. Maiti, U. Haupts, W. W. Webb, “Fluorescence correlation spectroscopy: diagnostics for sparse molecules,” Proc. Natl. Acad. Sci. USA 94, 11753–11757 (1997).
[PubMed]

1996

J. Widengren, R. Rigler, “Mechanisms of photobleaching investigated by fluorescence correlation spectroscopy,” Bioimaging 4(3), 149–157 (1996).
[CrossRef]

1995

K. M. Berland, P. T. C. So, E. Gratton, “Two-photon fluorescence correlation spectroscopy: method and application to the intracellular environment,” Biophys. J. 68, 694–701 (1995).
[CrossRef] [PubMed]

J. Widengren, U. Mets, R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem. 99, 13368–13379 (1995).
[CrossRef]

1994

J. Widengren, R. Rigler, U. Mets, “Triplet-state monitoring by fluorescence correlation spectroscopy,” J. Fluoresc. 4(3), 255–258 (1994).
[CrossRef]

M. Eigen, R. Rigler, “Sorting single molecules: application to diagnostics and evolutionary biotechnology,” Proc. Natl. Acad. Sci. USA 91, 5740–5747 (1994).
[CrossRef] [PubMed]

1990

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

1974

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

D. Magde, E. L. Elson, W. W. Webb, “Fluorescence correlation spectroscopy. II. Experimental realization,” Biopolymers 13, 29–61 (1974).

1972

D. Magde, E. Elson, W. W. Webb, “Thermodynamic fluctuations in a reacting system. Measurement by fluorescence Correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).

Allo, N. W.

N. L. Thompson, A. M. Leito, N. W. Allo, “Recent advances in fluorescence correlation spectroscopy,” Curr. Opin. Struct. Biol. 12, 634–641 (2002).
[CrossRef] [PubMed]

Berland, K. M.

K. M. Berland, P. T. C. So, E. Gratton, “Two-photon fluorescence correlation spectroscopy: method and application to the intracellular environment,” Biophys. J. 68, 694–701 (1995).
[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]

Dittrich, P.

F. Malvezzi-Campeggi, M. Jahnz, K. G. Heinze, P. Dittrich, P. Schwille, “Light-induced flickering of DsRed provides evidence for distinct and interconvertible fluorescent states,” Biophys. J. 81, 1776–1785 (2001).
[CrossRef] [PubMed]

Dittrich, P. S.

P. S. Dittrich, P. Schwille, “Photobleaching and stabilization of fluorophores used for single-molecule analysis with one- and two-photon excitation,” Appl. Phys. B 73, 829–873 (2001).
[CrossRef]

Eggeling, C.

C. Eggeling, J. Widengren, R. Rigler, C. A. M. SeidelG. G. Max-Planck-Institut fuer Biophysikalische Chemie, “Photobleaching of fluorescent dyes under conditions used for single-molecule detection: evidence of two-step photolysis,” Anal. Chem. 70, 2651–2659 (1998).
[CrossRef] [PubMed]

Eigen, M.

M. Eigen, R. Rigler, “Sorting single molecules: application to diagnostics and evolutionary biotechnology,” Proc. Natl. Acad. Sci. USA 91, 5740–5747 (1994).
[CrossRef] [PubMed]

Elson, E.

D. Magde, E. Elson, W. W. Webb, “Thermodynamic fluctuations in a reacting system. Measurement by fluorescence Correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).

Elson, E. L.

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

D. Magde, E. L. Elson, W. W. Webb, “Fluorescence correlation spectroscopy. II. Experimental realization,” Biopolymers 13, 29–61 (1974).

Gratton, E.

K. M. Berland, P. T. C. So, E. Gratton, “Two-photon fluorescence correlation spectroscopy: method and application to the intracellular environment,” Biophys. J. 68, 694–701 (1995).
[CrossRef] [PubMed]

Haupts, U.

P. Schwille, U. Haupts, S. Maiti, W. W. Webb, Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two-photon excitation, Biophys. J. 77, 2251–2265 (1999).
[CrossRef] [PubMed]

U. Haupts, S. Maiti, P. Schwille, W. W. Webb, “Dynamics of fluorescence fluctuations in green fluorescent protein observed by fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 95, 13573–13578 (1998).
[CrossRef] [PubMed]

S. Maiti, U. Haupts, W. W. Webb, “Fluorescence correlation spectroscopy: diagnostics for sparse molecules,” Proc. Natl. Acad. Sci. USA 94, 11753–11757 (1997).
[PubMed]

Heikal, A. A.

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

Heikel, A. A.

P. Schulk, S. Kummer, A. A. Heikel, W. E. Moeiner, W. W. Webb, “Fluorescence Correlation Spectroscopy reveals fast optical excitation-driven intramolecular dynamics of yellow fluorescent proteins,” Proc. Natl. Acad. USA 97, 151–156 (2000).
[CrossRef]

Heinze, K. G.

F. Malvezzi-Campeggi, M. Jahnz, K. G. Heinze, P. Dittrich, P. Schwille, “Light-induced flickering of DsRed provides evidence for distinct and interconvertible fluorescent states,” Biophys. J. 81, 1776–1785 (2001).
[CrossRef] [PubMed]

Hess, S. T.

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

Huang, S.

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

Jahnz, M.

F. Malvezzi-Campeggi, M. Jahnz, K. G. Heinze, P. Dittrich, P. Schwille, “Light-induced flickering of DsRed provides evidence for distinct and interconvertible fluorescent states,” Biophys. J. 81, 1776–1785 (2001).
[CrossRef] [PubMed]

Kummer, S.

P. Schulk, S. Kummer, A. A. Heikel, W. E. Moeiner, W. W. Webb, “Fluorescence Correlation Spectroscopy reveals fast optical excitation-driven intramolecular dynamics of yellow fluorescent proteins,” Proc. Natl. Acad. USA 97, 151–156 (2000).
[CrossRef]

Leito, A. M.

N. L. Thompson, A. M. Leito, N. W. Allo, “Recent advances in fluorescence correlation spectroscopy,” Curr. Opin. Struct. Biol. 12, 634–641 (2002).
[CrossRef] [PubMed]

Magde, D.

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

D. Magde, E. L. Elson, W. W. Webb, “Fluorescence correlation spectroscopy. II. Experimental realization,” Biopolymers 13, 29–61 (1974).

D. Magde, E. Elson, W. W. Webb, “Thermodynamic fluctuations in a reacting system. Measurement by fluorescence Correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).

Maiti, S.

P. Schwille, U. Haupts, S. Maiti, W. W. Webb, Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two-photon excitation, Biophys. J. 77, 2251–2265 (1999).
[CrossRef] [PubMed]

U. Haupts, S. Maiti, P. Schwille, W. W. Webb, “Dynamics of fluorescence fluctuations in green fluorescent protein observed by fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 95, 13573–13578 (1998).
[CrossRef] [PubMed]

S. Maiti, U. Haupts, W. W. Webb, “Fluorescence correlation spectroscopy: diagnostics for sparse molecules,” Proc. Natl. Acad. Sci. USA 94, 11753–11757 (1997).
[PubMed]

Malvezzi-Campeggi, F.

F. Malvezzi-Campeggi, M. Jahnz, K. G. Heinze, P. Dittrich, P. Schwille, “Light-induced flickering of DsRed provides evidence for distinct and interconvertible fluorescent states,” Biophys. J. 81, 1776–1785 (2001).
[CrossRef] [PubMed]

Mertz, J.

J. Mertz, “Molecular photodynamics involved in multi-photon excitation microscopy,” Eur. Phys. J. D. 3(24), 53–66 (1998).
[CrossRef]

Mets, U.

J. Widengren, U. Mets, R. Rigler, “Photodynamic properties of green fluorescent proteins investigated by fluorescence correlation spectroscopy,” Chem. Phys. 250, 171–186 (1999).
[CrossRef]

J. Widengren, U. Mets, R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem. 99, 13368–13379 (1995).
[CrossRef]

J. Widengren, R. Rigler, U. Mets, “Triplet-state monitoring by fluorescence correlation spectroscopy,” J. Fluoresc. 4(3), 255–258 (1994).
[CrossRef]

Moeiner, W. E.

P. Schulk, S. Kummer, A. A. Heikel, W. E. Moeiner, W. W. Webb, “Fluorescence Correlation Spectroscopy reveals fast optical excitation-driven intramolecular dynamics of yellow fluorescent proteins,” Proc. Natl. Acad. USA 97, 151–156 (2000).
[CrossRef]

Rigler, R.

T. Wohland, R. Rigler, H. Vogel, “The standard deviation in fluorescence correlation spectroscopy,” Biophys. J. 80, 2987–2999 (2001).
[CrossRef] [PubMed]

J. Widengren, U. Mets, R. Rigler, “Photodynamic properties of green fluorescent proteins investigated by fluorescence correlation spectroscopy,” Chem. Phys. 250, 171–186 (1999).
[CrossRef]

J. Widengren, B. Terry, R. Rigler, “Protonation kinetics of GFP and FITC investigated by FCS—aspects of the use of fluorescent indicators for measuring pH,” Chem. Phys. 249, 259–271 (1999).
[CrossRef]

C. Eggeling, J. Widengren, R. Rigler, C. A. M. SeidelG. G. Max-Planck-Institut fuer Biophysikalische Chemie, “Photobleaching of fluorescent dyes under conditions used for single-molecule detection: evidence of two-step photolysis,” Anal. Chem. 70, 2651–2659 (1998).
[CrossRef] [PubMed]

J. Widengren, R. Rigler, “Mechanisms of photobleaching investigated by fluorescence correlation spectroscopy,” Bioimaging 4(3), 149–157 (1996).
[CrossRef]

J. Widengren, U. Mets, R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem. 99, 13368–13379 (1995).
[CrossRef]

J. Widengren, R. Rigler, U. Mets, “Triplet-state monitoring by fluorescence correlation spectroscopy,” J. Fluoresc. 4(3), 255–258 (1994).
[CrossRef]

M. Eigen, R. Rigler, “Sorting single molecules: application to diagnostics and evolutionary biotechnology,” Proc. Natl. Acad. Sci. USA 91, 5740–5747 (1994).
[CrossRef] [PubMed]

Schulk, P.

P. Schulk, S. Kummer, A. A. Heikel, W. E. Moeiner, W. W. Webb, “Fluorescence Correlation Spectroscopy reveals fast optical excitation-driven intramolecular dynamics of yellow fluorescent proteins,” Proc. Natl. Acad. USA 97, 151–156 (2000).
[CrossRef]

Schwille, P.

P. S. Dittrich, P. Schwille, “Photobleaching and stabilization of fluorophores used for single-molecule analysis with one- and two-photon excitation,” Appl. Phys. B 73, 829–873 (2001).
[CrossRef]

F. Malvezzi-Campeggi, M. Jahnz, K. G. Heinze, P. Dittrich, P. Schwille, “Light-induced flickering of DsRed provides evidence for distinct and interconvertible fluorescent states,” Biophys. J. 81, 1776–1785 (2001).
[CrossRef] [PubMed]

P. Schwille, U. Haupts, S. Maiti, W. W. Webb, Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two-photon excitation, Biophys. J. 77, 2251–2265 (1999).
[CrossRef] [PubMed]

U. Haupts, S. Maiti, P. Schwille, W. W. Webb, “Dynamics of fluorescence fluctuations in green fluorescent protein observed by fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 95, 13573–13578 (1998).
[CrossRef] [PubMed]

Seidel, C. A. M.

C. Eggeling, J. Widengren, R. Rigler, C. A. M. SeidelG. G. Max-Planck-Institut fuer Biophysikalische Chemie, “Photobleaching of fluorescent dyes under conditions used for single-molecule detection: evidence of two-step photolysis,” Anal. Chem. 70, 2651–2659 (1998).
[CrossRef] [PubMed]

So, P. T. C.

K. M. Berland, P. T. C. So, E. Gratton, “Two-photon fluorescence correlation spectroscopy: method and application to the intracellular environment,” Biophys. J. 68, 694–701 (1995).
[CrossRef] [PubMed]

Strickler, J. H.

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

Terry, B.

J. Widengren, B. Terry, R. Rigler, “Protonation kinetics of GFP and FITC investigated by FCS—aspects of the use of fluorescent indicators for measuring pH,” Chem. Phys. 249, 259–271 (1999).
[CrossRef]

Thompson, N. L.

N. L. Thompson, A. M. Leito, N. W. Allo, “Recent advances in fluorescence correlation spectroscopy,” Curr. Opin. Struct. Biol. 12, 634–641 (2002).
[CrossRef] [PubMed]

N. L. Thompson, “Fluorescence correlation spectroscopy,” in Topics in Fluorescence Spectroscopy, J. R. Lakowicz, ed. (Plenum, New York, 1991), pp. 337–378.

Vogel, H.

T. Wohland, R. Rigler, H. Vogel, “The standard deviation in fluorescence correlation spectroscopy,” Biophys. J. 80, 2987–2999 (2001).
[CrossRef] [PubMed]

Webb, W. W.

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

P. Schulk, S. Kummer, A. A. Heikel, W. E. Moeiner, W. W. Webb, “Fluorescence Correlation Spectroscopy reveals fast optical excitation-driven intramolecular dynamics of yellow fluorescent proteins,” Proc. Natl. Acad. USA 97, 151–156 (2000).
[CrossRef]

P. Schwille, U. Haupts, S. Maiti, W. W. Webb, Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two-photon excitation, Biophys. J. 77, 2251–2265 (1999).
[CrossRef] [PubMed]

U. Haupts, S. Maiti, P. Schwille, W. W. Webb, “Dynamics of fluorescence fluctuations in green fluorescent protein observed by fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 95, 13573–13578 (1998).
[CrossRef] [PubMed]

C. Xu, W. W. Webb, “Multiphoton excitation of molecular fluorophores and nonlinear laser microscopy,” Top. Fluoresc. Spectrosc. 5, 471–540 (1997).
[CrossRef]

S. Maiti, U. Haupts, W. W. Webb, “Fluorescence correlation spectroscopy: diagnostics for sparse molecules,” Proc. Natl. Acad. Sci. USA 94, 11753–11757 (1997).
[PubMed]

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

D. Magde, E. L. Elson, W. W. Webb, “Fluorescence correlation spectroscopy. II. Experimental realization,” Biopolymers 13, 29–61 (1974).

D. Magde, E. Elson, W. W. Webb, “Thermodynamic fluctuations in a reacting system. Measurement by fluorescence Correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).

Widengren, J.

J. Widengren, U. Mets, R. Rigler, “Photodynamic properties of green fluorescent proteins investigated by fluorescence correlation spectroscopy,” Chem. Phys. 250, 171–186 (1999).
[CrossRef]

J. Widengren, B. Terry, R. Rigler, “Protonation kinetics of GFP and FITC investigated by FCS—aspects of the use of fluorescent indicators for measuring pH,” Chem. Phys. 249, 259–271 (1999).
[CrossRef]

C. Eggeling, J. Widengren, R. Rigler, C. A. M. SeidelG. G. Max-Planck-Institut fuer Biophysikalische Chemie, “Photobleaching of fluorescent dyes under conditions used for single-molecule detection: evidence of two-step photolysis,” Anal. Chem. 70, 2651–2659 (1998).
[CrossRef] [PubMed]

J. Widengren, R. Rigler, “Mechanisms of photobleaching investigated by fluorescence correlation spectroscopy,” Bioimaging 4(3), 149–157 (1996).
[CrossRef]

J. Widengren, U. Mets, R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem. 99, 13368–13379 (1995).
[CrossRef]

J. Widengren, R. Rigler, U. Mets, “Triplet-state monitoring by fluorescence correlation spectroscopy,” J. Fluoresc. 4(3), 255–258 (1994).
[CrossRef]

Wohland, T.

T. Wohland, R. Rigler, H. Vogel, “The standard deviation in fluorescence correlation spectroscopy,” Biophys. J. 80, 2987–2999 (2001).
[CrossRef] [PubMed]

Xu, C.

C. Xu, W. W. Webb, “Multiphoton excitation of molecular fluorophores and nonlinear laser microscopy,” Top. Fluoresc. Spectrosc. 5, 471–540 (1997).
[CrossRef]

Anal. Chem.

C. Eggeling, J. Widengren, R. Rigler, C. A. M. SeidelG. G. Max-Planck-Institut fuer Biophysikalische Chemie, “Photobleaching of fluorescent dyes under conditions used for single-molecule detection: evidence of two-step photolysis,” Anal. Chem. 70, 2651–2659 (1998).
[CrossRef] [PubMed]

Appl. Phys. B

P. S. Dittrich, P. Schwille, “Photobleaching and stabilization of fluorophores used for single-molecule analysis with one- and two-photon excitation,” Appl. Phys. B 73, 829–873 (2001).
[CrossRef]

Biochemistry

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

Bioimaging

J. Widengren, R. Rigler, “Mechanisms of photobleaching investigated by fluorescence correlation spectroscopy,” Bioimaging 4(3), 149–157 (1996).
[CrossRef]

Biophys. J.

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Our fitting routines are programmed with conditional statements in the fit function definitions such that the parameter alpha is assigned the value zero whenever the power is less than the saturation threshold parameter. This allows for simultaneous fitting of the entire curve, both above and below the saturation threshold, with asingle fitting function.

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Figures (10)

Fig. 1
Fig. 1

FCS correlation curves for a single R6G sample in Tris buffer (pH 8). We observe substantial variations in both the amplitude and the temporal relaxation of these FCS curves as the average excitation power is varied between 2.2 and 53 mW. For visual clarity, some of the FCS measurements used in the analysis are not shown on this graph.

Fig. 2
Fig. 2

Schematic diagram for excitation saturation. As the molecular excitation probability exceeds a threshold level, it cannot be further increased. Saturation will be reached in the central regions of the focused laser before the tails. The net effect of saturation is thus a flatter top-hat profile for the excitation probability.

Fig. 3
Fig. 3

Quantitative model for the saturation-corrected excitation profiles. Shown are the squared profiles for the incident laser, the subtracted profile to correct for saturation, and the resulting effective excitation profile. The threshold excitation rate is also shown.

Fig. 4
Fig. 4

Excitation saturation will increase the size of the observation volume and flatten its shape. These surface plots show the profiles of the excitation source S 0 2 (k, z) and the saturation-corrected effective excitation profile S E 2 (r, z).

Fig. 5
Fig. 5

Power dependence of the average fluorescence intensity for R6G excited at 780 nm. The inset shows the same data plotted on a log-log scale. Vertical axes show both the total fluorescence and the average fluorescence counts per molecule per second. At low power, the data follow the expected quadratic dependence on excitation intensity (dotted curve). It is clear that this quadratic relationship does not hold for the higher excitation levels. The data were fit to the saturation model of Eq. (9) with the amplitude and saturation threshold as parameters. We determine from FCS fitting that, for this sample and beam waist, saturation is reached with an average input power of 9 mW, corresponding to a peak photon flux of 8 × 1029 photons/cm2/s. The saturation model fits the data nicely up to around three times the threshold value. Beyond this level, the saturation model breaks down because the model volume stops increasing even though the actual measurement volume continues to increase, as discussed in the text.

Fig. 6
Fig. 6

Autocorrelation curve for R6G excitation with 16-mW average power, which is above the saturation threshold. Shown here are best fits from the saturation theory and the pure diffusion model. Both models appear to fit the data well, yet comparison of the recovered parameters from the full data set highlights the superiority of the saturation model.

Fig. 7
Fig. 7

Beam waist ω0, as a function of excitation power, recovered from FCS curves for R6G. If the pure diffusion model is used to fit the data, the recovered beam waist varies greatly. Such fits also require that the concentration C be released as a free parameter. For the saturation model, all data sets through 22-mW excitation are fit well with a single value for the beam waist and constant values of all other fitting parameters except the photobleaching rates. These findings indicate that saturation is the preferred model. We note that the three highest input powers shown in Fig. 1 (26, 40, and 53 mW—not shown here) can also be fit with this constant value for the beam waist; but at these higher powers, β must also be treated as a power-dependent fitting parameter as discussed in the text.

Fig. 8
Fig. 8

Concentration of R6G molecules obtained from fits to FCS measurements shown in Fig. 1. When applying the saturation theory introduced above, we can fit all the data sets with a single value for the molecular concentration, as one would expect should be possible. In contrast, fitting to the pure diffusion model produces a large increase in the recovered concentration as power is increased. The capability to recover a single, and thus meaningful, value for the concentration is an important result for FCS applications.

Fig. 9
Fig. 9

Photobleaching rates k B and the average bleached fraction B are shown for R6G as a function of excitation flux. These values were recovered from global fits to the saturation model.

Fig. 10
Fig. 10

Both saturation and photobleaching influence the amplitude of the measured correlation traces. To better illustrate the role of each process, we separated out their influence on the amplitude. Shown are the measured FCS amplitude, the expected correlation amplitude with saturation only in the absence of photobleaching, and the expected correlation amplitude given the recovered photobleaching parameters with no saturation. These values are calculated as described in the text.

Equations (12)

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δFtFt-F=ψ δCr, tI02S2rd3r.
Gτ=δFr, t δFr, t+τF2.
S3DGr, z=exp-2r2/ω02exp-2z2/z02.
GDτ=22π3/2ω02z0C11+τ/τD×11+ω0/z02τ/τD1/2,
α=IS2I02=ωS2ω02=zS2z02=I02-Ith2I02.
Ssr, z=exp-2r2/ωs2exp-2z2/zs2.
SE2r, z=I02S02r, z-Is2Ss2r, zIth2, for I02Ith2.
Vsat= SE2r, zd3r=π3/2ω02z081-α5/21-α=V3DG1-α5/21-α.
F=ψCIth2Vsat=ψCI02V3DG1-α5/2.
Gτ=22Cπ3/2ω02z01-α5/2211+τ/τD1+βτ/τD1/2+α7/21+τ/ατD1+βτ/ατD1/2-42α1+1/α+2τ/ατD1+1/α+2βτ/ατD1/2,
Gτ=221-B+B exp-kBτ/1-BCπ3/2 ω02z01-α5/2211+τ/τD1+βτ/τD1/2+α7/21+τ/ατD1+βτ/ατD1/2-42α1+1/α+2τ/ατD1+1/α+2βτ/ατD1/2.
B=kBkB+r/τD.

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