Abstract

The dead time of the detector significantly distorts the fluorescence correlation function of fluorescent particles in solution. This distortion of the correlation function is similar to the saturation effect of the correlation function in a high-power excitation region. The correlation amplitude is significantly reduced by the dead time. The deviations in the number of molecules and the diffusion time are empirically given by the deviation of the fluorescence intensity linearity. The empirical curves of the deviations can be applied to the systematic error estimation of the parameters. The proportionality of the number of molecules to the concentration of fluorophores is no longer maintained with a large dead time, although almost all of the proportionality of the diffusion time to the inverse diffusion constant remains. This fact makes the dead-time effect different from the saturation effect, which is due to photokinetics. In practice, these distortions can be reduced by use of a smaller excitation power in which the proportionality of the fluorescence intensity is maintained.

© 2005 Optical Society of America

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  1. R. Rigler, E. S. Elson, eds., Fluorescence Correlation Spectroscopy: Theory and Applications (Springer-Verlag, Berlin, 2001).
    [CrossRef]
  2. G. Nishimura, M. Kinjo, “Systematic error in fluorescence correlation measurements identified by a simple saturation model of fluorescence,” Anal. Chem. 76, 1963–1970 (2004).
    [CrossRef] [PubMed]
  3. J. Enderlein, I. Gregor, D. Patra, J. Fitter, “Art and artifacts of fluorescence correlation spectroscopy,” Curr. Pharm. Biotechnol. 5, 155–161 (2004).
    [CrossRef] [PubMed]
  4. D. E. Koppel, “Statistical accuracy in fluorescence correlation spectroscopy,” Phys. Rev. A 10, 1938–1945 (1974).
    [CrossRef]
  5. A. G. Palmer, N. L. Thompson, “Intensity dependence of high-order autocorrelation functions in fluorescence correlation spectroscopy,” Rev. Sci. Instrum. 60, 624–633 (1989).
    [CrossRef]
  6. L. N. Hillesheim, J. D. Müller, “The photon counting histogram in fluorescence fluctuation spectroscopy with non-ideal photodetectors,” Biophys. J. 85, 1948–1958 (2003).
  7. M. Zhao, L. Jin, B. Chen, Y. Ding, H. Ma, D. Chen, “Afterpulsing and its correction in fluorescence correlation spectroscopy experiments,” Appl. Opt. 42, 4031–4036 (2003).
    [CrossRef] [PubMed]
  8. L. M. Davis, P. E. Williams, D. A. Ball, K. M. Swift, E. D. Matayoshi, “Data reduction methods for application of fluorescence correlation spectroscopy to pharmaceutical drug discovery,” Curr. Pharm. Biotechnol. 4, 451–462 (2003).
    [CrossRef] [PubMed]
  9. J. Widengren, Ü. Mets, R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem. 99, 13368–13379 (1995).
    [CrossRef]
  10. K. Schätzel, “Dead time correction of photon correlation functions,” Appl. Phys. B 41, 95–102 (1986).
    [CrossRef]
  11. C. Eggeling, J. Widengren, R. Rigler, C. A. M. Seidel, “Photobleaching of fluorescent dyes under conditions used for single-molecule detection: evidence of two-step photolysis,” Anal. Chem. 70, 2651–2659 (1998).
    [CrossRef] [PubMed]
  12. J. Widengren, R. Rigler, “Mechanisms of photobleaching investigated by fluorescence correlation spectroscopy,” Bioim-aging 4, 149–157 (1996).
    [CrossRef]
  13. 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).
  14. P. Schwille, S. Kummer, A. A. Heikal, W. E. Moerner, W. W. Webb, “Fluorescence correlation spectroscopy reveals fast optical excitation-driven intramolecular dynamics of yellow fluorescent proteins,” Proc. Natl. Acad. Sci. USA 97, 151–156 (2000).

2004

G. Nishimura, M. Kinjo, “Systematic error in fluorescence correlation measurements identified by a simple saturation model of fluorescence,” Anal. Chem. 76, 1963–1970 (2004).
[CrossRef] [PubMed]

J. Enderlein, I. Gregor, D. Patra, J. Fitter, “Art and artifacts of fluorescence correlation spectroscopy,” Curr. Pharm. Biotechnol. 5, 155–161 (2004).
[CrossRef] [PubMed]

2003

L. N. Hillesheim, J. D. Müller, “The photon counting histogram in fluorescence fluctuation spectroscopy with non-ideal photodetectors,” Biophys. J. 85, 1948–1958 (2003).

L. M. Davis, P. E. Williams, D. A. Ball, K. M. Swift, E. D. Matayoshi, “Data reduction methods for application of fluorescence correlation spectroscopy to pharmaceutical drug discovery,” Curr. Pharm. Biotechnol. 4, 451–462 (2003).
[CrossRef] [PubMed]

M. Zhao, L. Jin, B. Chen, Y. Ding, H. Ma, D. Chen, “Afterpulsing and its correction in fluorescence correlation spectroscopy experiments,” Appl. Opt. 42, 4031–4036 (2003).
[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).

2000

P. Schwille, S. Kummer, A. A. Heikal, W. E. Moerner, W. W. Webb, “Fluorescence correlation spectroscopy reveals fast optical excitation-driven intramolecular dynamics of yellow fluorescent proteins,” Proc. Natl. Acad. Sci. USA 97, 151–156 (2000).

1998

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

1996

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

1995

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

1989

A. G. Palmer, N. L. Thompson, “Intensity dependence of high-order autocorrelation functions in fluorescence correlation spectroscopy,” Rev. Sci. Instrum. 60, 624–633 (1989).
[CrossRef]

1986

K. Schätzel, “Dead time correction of photon correlation functions,” Appl. Phys. B 41, 95–102 (1986).
[CrossRef]

1974

D. E. Koppel, “Statistical accuracy in fluorescence correlation spectroscopy,” Phys. Rev. A 10, 1938–1945 (1974).
[CrossRef]

Ball, D. A.

L. M. Davis, P. E. Williams, D. A. Ball, K. M. Swift, E. D. Matayoshi, “Data reduction methods for application of fluorescence correlation spectroscopy to pharmaceutical drug discovery,” Curr. Pharm. Biotechnol. 4, 451–462 (2003).
[CrossRef] [PubMed]

Chen, B.

Chen, D.

Davis, L. M.

L. M. Davis, P. E. Williams, D. A. Ball, K. M. Swift, E. D. Matayoshi, “Data reduction methods for application of fluorescence correlation spectroscopy to pharmaceutical drug discovery,” Curr. Pharm. Biotechnol. 4, 451–462 (2003).
[CrossRef] [PubMed]

Ding, Y.

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).

Eggeling, C.

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

Enderlein, J.

J. Enderlein, I. Gregor, D. Patra, J. Fitter, “Art and artifacts of fluorescence correlation spectroscopy,” Curr. Pharm. Biotechnol. 5, 155–161 (2004).
[CrossRef] [PubMed]

Fitter, J.

J. Enderlein, I. Gregor, D. Patra, J. Fitter, “Art and artifacts of fluorescence correlation spectroscopy,” Curr. Pharm. Biotechnol. 5, 155–161 (2004).
[CrossRef] [PubMed]

Gregor, I.

J. Enderlein, I. Gregor, D. Patra, J. Fitter, “Art and artifacts of fluorescence correlation spectroscopy,” Curr. Pharm. Biotechnol. 5, 155–161 (2004).
[CrossRef] [PubMed]

Heikal, A. A.

P. Schwille, S. Kummer, A. A. Heikal, W. E. Moerner, W. W. Webb, “Fluorescence correlation spectroscopy reveals fast optical excitation-driven intramolecular dynamics of yellow fluorescent proteins,” Proc. Natl. Acad. Sci. USA 97, 151–156 (2000).

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).

Hillesheim, L. N.

L. N. Hillesheim, J. D. Müller, “The photon counting histogram in fluorescence fluctuation spectroscopy with non-ideal photodetectors,” Biophys. J. 85, 1948–1958 (2003).

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).

Jin, L.

Kinjo, M.

G. Nishimura, M. Kinjo, “Systematic error in fluorescence correlation measurements identified by a simple saturation model of fluorescence,” Anal. Chem. 76, 1963–1970 (2004).
[CrossRef] [PubMed]

Koppel, D. E.

D. E. Koppel, “Statistical accuracy in fluorescence correlation spectroscopy,” Phys. Rev. A 10, 1938–1945 (1974).
[CrossRef]

Kummer, S.

P. Schwille, S. Kummer, A. A. Heikal, W. E. Moerner, W. W. Webb, “Fluorescence correlation spectroscopy reveals fast optical excitation-driven intramolecular dynamics of yellow fluorescent proteins,” Proc. Natl. Acad. Sci. USA 97, 151–156 (2000).

Ma, H.

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).

Matayoshi, E. D.

L. M. Davis, P. E. Williams, D. A. Ball, K. M. Swift, E. D. Matayoshi, “Data reduction methods for application of fluorescence correlation spectroscopy to pharmaceutical drug discovery,” Curr. Pharm. Biotechnol. 4, 451–462 (2003).
[CrossRef] [PubMed]

Mets, Ü.

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

Moerner, W. E.

P. Schwille, S. Kummer, A. A. Heikal, W. E. Moerner, W. W. Webb, “Fluorescence correlation spectroscopy reveals fast optical excitation-driven intramolecular dynamics of yellow fluorescent proteins,” Proc. Natl. Acad. Sci. USA 97, 151–156 (2000).

Müller, J. D.

L. N. Hillesheim, J. D. Müller, “The photon counting histogram in fluorescence fluctuation spectroscopy with non-ideal photodetectors,” Biophys. J. 85, 1948–1958 (2003).

Nishimura, G.

G. Nishimura, M. Kinjo, “Systematic error in fluorescence correlation measurements identified by a simple saturation model of fluorescence,” Anal. Chem. 76, 1963–1970 (2004).
[CrossRef] [PubMed]

Palmer, A. G.

A. G. Palmer, N. L. Thompson, “Intensity dependence of high-order autocorrelation functions in fluorescence correlation spectroscopy,” Rev. Sci. Instrum. 60, 624–633 (1989).
[CrossRef]

Patra, D.

J. Enderlein, I. Gregor, D. Patra, J. Fitter, “Art and artifacts of fluorescence correlation spectroscopy,” Curr. Pharm. Biotechnol. 5, 155–161 (2004).
[CrossRef] [PubMed]

Rigler, R.

C. Eggeling, J. Widengren, R. Rigler, C. A. M. Seidel, “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,” Bioim-aging 4, 149–157 (1996).
[CrossRef]

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

Schätzel, K.

K. Schätzel, “Dead time correction of photon correlation functions,” Appl. Phys. B 41, 95–102 (1986).
[CrossRef]

Schwille, 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).

P. Schwille, S. Kummer, A. A. Heikal, W. E. Moerner, W. W. Webb, “Fluorescence correlation spectroscopy reveals fast optical excitation-driven intramolecular dynamics of yellow fluorescent proteins,” Proc. Natl. Acad. Sci. USA 97, 151–156 (2000).

Seidel, C. A. M.

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

Swift, K. M.

L. M. Davis, P. E. Williams, D. A. Ball, K. M. Swift, E. D. Matayoshi, “Data reduction methods for application of fluorescence correlation spectroscopy to pharmaceutical drug discovery,” Curr. Pharm. Biotechnol. 4, 451–462 (2003).
[CrossRef] [PubMed]

Thompson, N. L.

A. G. Palmer, N. L. Thompson, “Intensity dependence of high-order autocorrelation functions in fluorescence correlation spectroscopy,” Rev. Sci. Instrum. 60, 624–633 (1989).
[CrossRef]

Webb, W. W.

P. Schwille, S. Kummer, A. A. Heikal, W. E. Moerner, W. W. Webb, “Fluorescence correlation spectroscopy reveals fast optical excitation-driven intramolecular dynamics of yellow fluorescent proteins,” Proc. Natl. Acad. Sci. USA 97, 151–156 (2000).

Widengren, J.

C. Eggeling, J. Widengren, R. Rigler, C. A. M. Seidel, “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,” Bioim-aging 4, 149–157 (1996).
[CrossRef]

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

Williams, P. E.

L. M. Davis, P. E. Williams, D. A. Ball, K. M. Swift, E. D. Matayoshi, “Data reduction methods for application of fluorescence correlation spectroscopy to pharmaceutical drug discovery,” Curr. Pharm. Biotechnol. 4, 451–462 (2003).
[CrossRef] [PubMed]

Zhao, M.

Anal. Chem.

G. Nishimura, M. Kinjo, “Systematic error in fluorescence correlation measurements identified by a simple saturation model of fluorescence,” Anal. Chem. 76, 1963–1970 (2004).
[CrossRef] [PubMed]

C. Eggeling, J. Widengren, R. Rigler, C. A. M. Seidel, “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. Opt.

Appl. Phys. B

K. Schätzel, “Dead time correction of photon correlation functions,” Appl. Phys. B 41, 95–102 (1986).
[CrossRef]

Bioim-aging

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

Biophys. J.

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).

L. N. Hillesheim, J. D. Müller, “The photon counting histogram in fluorescence fluctuation spectroscopy with non-ideal photodetectors,” Biophys. J. 85, 1948–1958 (2003).

Curr. Pharm. Biotechnol.

L. M. Davis, P. E. Williams, D. A. Ball, K. M. Swift, E. D. Matayoshi, “Data reduction methods for application of fluorescence correlation spectroscopy to pharmaceutical drug discovery,” Curr. Pharm. Biotechnol. 4, 451–462 (2003).
[CrossRef] [PubMed]

J. Enderlein, I. Gregor, D. Patra, J. Fitter, “Art and artifacts of fluorescence correlation spectroscopy,” Curr. Pharm. Biotechnol. 5, 155–161 (2004).
[CrossRef] [PubMed]

J. Phys. Chem.

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

Phys. Rev. A

D. E. Koppel, “Statistical accuracy in fluorescence correlation spectroscopy,” Phys. Rev. A 10, 1938–1945 (1974).
[CrossRef]

Proc. Natl. Acad. Sci. USA

P. Schwille, S. Kummer, A. A. Heikal, W. E. Moerner, W. W. Webb, “Fluorescence correlation spectroscopy reveals fast optical excitation-driven intramolecular dynamics of yellow fluorescent proteins,” Proc. Natl. Acad. Sci. USA 97, 151–156 (2000).

Rev. Sci. Instrum.

A. G. Palmer, N. L. Thompson, “Intensity dependence of high-order autocorrelation functions in fluorescence correlation spectroscopy,” Rev. Sci. Instrum. 60, 624–633 (1989).
[CrossRef]

Other

R. Rigler, E. S. Elson, eds., Fluorescence Correlation Spectroscopy: Theory and Applications (Springer-Verlag, Berlin, 2001).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

FCFs of a 4.1-nM R123 aqueous solution obtained with a ConfoCor system with excitation powers at 13, 55, 142, 357, and 698 µW, from larger to smaller amplitudes (the arrow indicates the direction). The inset shows the normalized FCFs with the amplitude of the diffusion part of the correlation function to 1. The amplitude of the diffusion part was obtained by fitting to the one-component model.

Fig. 2
Fig. 2

Fitting results for the FCFs of the R123 solution. The measurements by ConfoCor and ConfoCor2 are denoted by open circles and filled squares, respectively. (a) Average fluorescence intensity and the average fluorescence intensity per molecule (inset), which is the ratio of the intensity to the number of molecules. (b) Number of molecules in the volume element and the concentration estimated by the volume at each excitation (inset). The volume was determined by the diffusion time and the structure parameter. (c) Diffusion time and structure parameter (inset). (d) Fraction of the triplet term and the triplet time constant (inset).

Fig. 3
Fig. 3

FCFs with different dead times of the detector, τdead0 = 0 (ideal detector), 0.002, 0.004, 0.008, 0.01 from the solid curve to the dashed–dotted curve (the arrows indicate the direction of the dead-time increase), with excitation powers (a) σIex(0)Δt = 0.08 and (b) σIex(0)Δt = 0.4. The curves with the number of molecules normalized to 1 are also shown in the insets.

Fig. 4
Fig. 4

Fitting results for FCFs obtained by the MC simulation with different excitations and different dead times. (a) Average intensity and the intensity per molecule (inset). (b) Number of molecules and the concentrations estimated from the volume at each excitation (inset). The arrows indicate the expected values. (c) Diffusion time τc scaled by τ0 and the structure parameter (inset). (d) Fraction of the triplet term and the triplet time constant τT scaled by τ0 (inset). The dead times are τdead0 = 0 (ideal detector, open circles), 0.001 (filled circles), 0.002 (open squares), 0.004 (filled squares), 0.01 (open triangles).

Fig. 5
Fig. 5

Deviations from the ideal results of (a) the intensity and (b) the correlation amplitude. The results are scaled by ν = Iidealτdead. The dead times of the detector are denoted by different symbols (open circles, τdead0 = 0.002; filled circles, 0.004; open squares, 0.004; filled squares, 0.01). The curves are the theoretical predictions (solid curve, Schätzel; dashed curve, Koppel).

Fig. 6
Fig. 6

Deviations of (a) the intensity and (b) the number of molecules from the linear relation to the dye concentration. The different dead times are denoted by the different symbols (circles, τdead0 = 0; squares, τ0 = 0.002; triangles, τdead0 = 0.01). The excitation intensities are σIex(0)Δt = 0.4 (open symbols) and 2 (filled symbols).

Fig. 7
Fig. 7

Deviation of the diffusion time from the linear relation to the inverse of the diffusion coefficient. The different dead times are denoted by the different symbols (circles, τdead0 = 0; squares, τdead0 = 0.01). The excitation intensities are σIex(0)Δt = 0.4 (open symbols) and 2 (filled symbols).

Fig. 8
Fig. 8

Deviations of (a) the number of molecules and (b) the diffusion time with respect to the deviation of the observed emission intensity. The figure plots the simulation results of the different concentrations of molecules (open circles, excitation 0.04, τdead0 = 0.002; open squares, excitation 0.04, τdead0 = 0.01; open up triangles, excitation 2, τdead0 = 0.002; open down triangles, excitation 2, τdead0 = 0.01) and the different excitation powers (filled circles, τdead0 = 0; filled squares, τdead0 = 0.001; filled up triangles, τdead0 = 0.002; filled down triangles, τdead0 = 0.004; filled diamonds, τdead0 = 0.01). The experimental results are superimposed (pluses, ConfoCor; crosses, ConfoCor2). The solid lines show the profiles of the change.

Equations (3)

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g ( τ ) = I ( t ) I ( t + τ ) / I ( t ) 2 1 = n 1 [ ( 1 + τ / τ c ) 1 ( 1 + τ / τ c / q 2 ) 1 / 2 + f T × exp ( τ / τ T ) ] ,
I = I ideal ( 1 + ν β ) 1 1 / β ,
g ( 0 ) 1 = 1 + β ( 1 2 ν 2 β ν 2 ) ( 1 + β ν ) 2 + β 2 ν 2 ( 1 + β ν ) 2 [ 1 β 2 ν 2 ( 1 + β ν ) 2 ] 2 + 1 / β ,

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