Statistical Analysis of Diffusion Coefficient Determination by Fluorescence Correlation Spectroscopy

Abstract

Fluorescence correlation spectroscopy (FCS) has become an important and widely used technique for many applications in physics, chemistry, and biology. The parameter most frequently addressed by FCS is the diffusion of molecules in solution. Due to the highly non-linear connection between the diffusion coefficient and a measured autocorrelation function, it is extremely difficult to analyse the accuracy of the diffusion-coefficient determination in a FCS experiment. Here, we present a simplified analysis based on some general maximum-likelihood considerations, and numerical result are given for the dependence of the accuracy of the diffusion-coefficient determination on sample concentration, brightness, and measurement time. Optimal concentration values for performing FCS are found.

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References

  1. 1.

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

    Google Scholar 

  2. 2.

    E. L. Elson and D. Magde (1974). Fluorescence Correlation Spectroscopy. I. Conceptual basis and theory. Bioploymers 13, 1–27.

    Google Scholar 

  3. 3.

    D. Magde, E. Elson, and W. W. Webb (1974). Fluorescence Correlation Spectroscopy. II. An experimental realization. Biopolymers 13, 29–61.

    Google Scholar 

  4. 4.

    N. L. Thompson (1991). Fluorescence correlation spectroscopy. in J. R. Lakowicz (Ed.), Topics in Fluorescence Spectroscopy 1, Plenum Press, New York, pp. 337–378.

    Google Scholar 

  5. 5.

    J. Widengren and ¨. Mets (2002). Conceptual basis of Fluorescence Correlation Spectroscopy and related techniques as tools in bioscience. in C. Zander, J. Enderlein, and R. A. Keller (Eds.), Single-Molecule Detection in Solution—Methods and Applications, Wiley-VCH, Berlin, pp. 69–95.

  6. 6.

    J. Korlach, P. Schwille, W. W. Webb, and G. W. Feigenson (1999). Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy. Proc. Nat. Acad. Sci. USA 69, 8461–8466.

    Google Scholar 

  7. 7.

    C. Gell, D. J. Brockwell, G. S. Beddard, S. E. Radford, A. P. Kalverda, and D. A. Smith (2001). Accurate use of single molecule fluorescence correlation spectroscopy to determine molecular diffusion times. Single Mol. 2, 177–181.

    Google Scholar 

  8. 8.

    N. Yoshida, M. Tamura, and M. Kinjo (2000). Fluorescence Correlation Spectroscopy: A new tool for probing the microenvironment of the internal space of organelles. Single Mol. 1, 279–283.

    Google Scholar 

  9. 9.

    J. Widengren and R. Rigler (1998). Fluorescence correlation spectroscopy as a tool to investigate chemical reactions in solution and on cell surfaces. Cell. Mol. Biol. 44, 857–879.

    Google Scholar 

  10. 10.

    S. Bj¨rling, M. Kinjo, Z. F¨ldes-Papp, E. Hagman, P. Thyberg, and R. Rigler (1998). Fluorescence Correlation Spectroscopy of enzymatic DNA polymerization. Biochemisrty 37, 12971–12978.

    Google Scholar 

  11. 11.

    K. H¨sler, O. P¨nke, and W. Junge (1999). On the stator of rotary ATP synthase: The binding strength of subunit δ to αβ3 as determined by Fluorescence Correlation Spectroscopy. Biochemistry 38, 13759–13765.

    Google Scholar 

  12. 12.

    P. Schwille, J. Bieschke, and F. Oehlenschlager (1997). Kinetic investigations by Fluorescence Correlation Spectroscopy: The analytical and diagnostic potential of diffusion studies. Biophys. Chem. 66, 211–228.

    Google Scholar 

  13. 13.

    T. Wohland, K. Friedrich, R. Hovius, and H. Vogel (1999). Study of ligand-receptor interactions by Fluorescence Correlation Spectroscopy with different fluorophores: Evidence that the homopentameric 5-hydroxytryptamine type 3 as receptor binds only one ligand. Biochemistry 38, 8671–8681.

    Google Scholar 

  14. 14.

    K. G. Heinze, M. Rarbach, M. Jahnz, and P. Schwille (2002). Two-photon fluorescence coincidence analysis: Rapid measurements of enzyme kinetics. Biophys. J. 83, 1671–1681.

    Google Scholar 

  15. 15.

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

    Google Scholar 

  16. 16.

    J. Widengren, ¨. Mets, and R. Rigler (1999). Photodynamic properties of green fluorescent proteins investigated by fluorescence correlation spectroscopy. Chem. Phys. 250, 171–186.

    Google Scholar 

  17. 17.

    U. Haupts, S. Maiti, P. Schwille, and W. W. Webb (1998). Dynamics of fluorescence fluctuations in green fluorescent protein observed by fluorescence correlation spectroscopy. Proc. Nat. Acad. Sci. USA 95, 13573–13578.

    Google Scholar 

  18. 18.

    A. A. Heikal, S. T. Hess, G. S. Baird, R. Y. Tsien, and W. W. Webb (2000). Molecular spectroscopy and dynamics of intrinsically fluorescent proteins: Coral red (dsRed) and yellow (Citrine). Proc. Natl. Acad. Sci. USA 97, 11996–12001.

    Google Scholar 

  19. 19.

    R. Brock, G. Vàmosi, G. Vereb, and T. M. Jovin (1999). Rapid characterization of green fluorescent protein fusion proteins on the molecular and cellular level by fluorescence correlation microscopy. Proc. Natl. Acad. Sci. USA 96, 10123–10128.

    Google Scholar 

  20. 20.

    A. A. Heikal, S. T. Hess, and W. W. Webb (2001). Multiphoton molecular spectroscopy and excited-state dynamics of enhanced green fluorescent protein (EGFP): Acid–base specificity. Chem. Phys. 274, 37–55.

    Google Scholar 

  21. 21.

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

    Google Scholar 

  22. 22.

    J. Widengren and C. A. M Seidel (2000). Manipulation and characterization of photo-induced transient states of Merocyanine 540 by fluorescence correlation spectroscopy. Phys. Chem. Chem. Phys. 2, 3435–3441.

    Google Scholar 

  23. 23.

    S. Huang, A. A. Heikal, and W. W. Webb (2002). Two-Photon Fluorescence Spectroscopy and Microscopy of NAD(P)H and Flavoprotein. Biophys. J. 82, 2811–2825.

    Google Scholar 

  24. 24.

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

    Google Scholar 

  25. 25.

    J. Widengren and P. Schwille (2000). Characterization of photoinduced isomerization and back-isomerization of the cyanine dye Cy5 by fluorescence correlation spectroscopy. J. Phys. Chem. A 104, 6416–6428.

    Google Scholar 

  26. 26.

    P. Schwille (2001). Fluorescence correlation spectroscopy and its potential for intracellular applications. Cell. Biochem. Biophys. 34, 383–408.

    Google Scholar 

  27. 27.

    S. T. Hess, S. Huang, A. A. Heikal, and W. W. Webb (2002). Biological and chemical applications of Fluorescence Correlation Spectroscopy: A review. Biochem. 41, 697–705.

    Google Scholar 

  28. 28.

    R. Rigler and E. Elson (Eds.) (2001). Fluorescence Correlation Spectroscopy, Springer, Berlin.

    Google Scholar 

  29. 29.

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

    Google Scholar 

  30. 30.

    H. Qian (1990). On the statistics of fluorescence correlation spectroscopy. Biophys. Chem. 38, 49–57.

    Google Scholar 

  31. 31.

    P. Kask, R. G¨nther, and P. Axhausen (1997). Statistical accuracy in fluorescence fluctuation experiments Eur. Biophys. J. 25, 163–169.

    Google Scholar 

  32. 32.

    U. Meseth, T. Wohland, R. Rigler, and H. Vogel (1999). Resolution of fluorescence correlation measurements. Biophys. J. 76, 1619– 1631.

    Google Scholar 

  33. 33.

    T. Wohland, R. Rigler, and H. Vogel (2001). The standard deviation in fluorescence correlation spectroscopy. Biophys. J. 80, 2987–2999.

    Google Scholar 

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Correspondence to Jörg Enderlein.

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Enderlein, J., Gregor, I., Patra, D. et al. Statistical Analysis of Diffusion Coefficient Determination by Fluorescence Correlation Spectroscopy. J Fluoresc 15, 415–422 (2005). https://doi.org/10.1007/s10895-005-2633-0

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Key Words

  • Fluorescence correlation spectroscopy
  • diffusion coefficient
  • statistical accuracy