Skip to main content
PMC home page
Biophysical Journal logoLink to Biophysical Journal
. 1999 Jul;77(1):553–567. doi: 10.1016/S0006-3495(99)76912-2

The photon counting histogram in fluorescence fluctuation spectroscopy.

Y Chen 1, J D Müller 1, P T So 1, E Gratton 1
PMCID: PMC1300352  PMID: 10388780

Abstract

Fluorescence correlation spectroscopy (FCS) is generally used to obtain information about the number of fluorescent particles in a small volume and the diffusion coefficient from the autocorrelation function of the fluorescence signal. Here we demonstrate that photon counting histogram (PCH) analysis constitutes a novel tool for extracting quantities from fluorescence fluctuation data, i.e., the measured photon counts per molecule and the average number of molecules within the observation volume. The photon counting histogram of fluorescence fluctuation experiments, in which few molecules are present in the excitation volume, exhibits a super-Poissonian behavior. The additional broadening of the PCH compared to a Poisson distribution is due to fluorescence intensity fluctuations. For diffusing particles these intensity fluctuations are caused by an inhomogeneous excitation profile and the fluctuations in the number of particles in the observation volume. The quantitative relationship between the detected photon counts and the fluorescence intensity reaching the detector is given by Mandel's formula. Based on this equation and considering the fluorescence intensity distribution in the two-photon excitation volume, a theoretical expression for the PCH as a function of the number of molecules in the excitation volume is derived. For a single molecular species two parameters are sufficient to characterize the histogram completely, namely the average number of molecules within the observation volume and the detected photon counts per molecule per sampling time epsilon. The PCH for multiple molecular species, on the other hand, is generated by successively convoluting the photon counting distribution of each species with the others. The influence of the excitation profile upon the photon counting statistics for two relevant point spread functions (PSFs), the three-dimensional Gaussian PSF conventionally employed in confocal detection and the square of the Gaussian-Lorentzian PSF for two photon excitation, is explicitly treated. Measured photon counting distributions obtained with a two-photon excitation source agree, within experimental error with the theoretical PCHs calculated for the square of a Gaussian-Lorentzian beam profile. We demonstrate and discuss the influence of the average number of particles within the observation volume and the detected photon counts per molecule per sampling interval upon the super-Poissonian character of the photon counting distribution.

Full Text

The Full Text of this article is available as a PDF (168.7 KB).

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Berland K. M., So P. T., Chen Y., Mantulin W. W., Gratton E. Scanning two-photon fluctuation correlation spectroscopy: particle counting measurements for detection of molecular aggregation. Biophys J. 1996 Jul;71(1):410–420. doi: 10.1016/S0006-3495(96)79242-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Berland K. M., So P. T., Gratton E. Two-photon fluorescence correlation spectroscopy: method and application to the intracellular environment. Biophys J. 1995 Feb;68(2):694–701. doi: 10.1016/S0006-3495(95)80230-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Borejdo J. Motion of myosin fragments during actin-activated ATPase: fluorescence correlation spectroscopy study. Biopolymers. 1979 Nov;18(11):2807–2820. doi: 10.1002/bip.1979.360181111. [DOI] [PubMed] [Google Scholar]
  4. Braun H. A., Wissing H., Schäfer K., Hirsch M. C. Oscillation and noise determine signal transduction in shark multimodal sensory cells. Nature. 1994 Jan 20;367(6460):270–273. doi: 10.1038/367270a0. [DOI] [PubMed] [Google Scholar]
  5. Eigen M., Rigler R. Sorting single molecules: application to diagnostics and evolutionary biotechnology. Proc Natl Acad Sci U S A. 1994 Jun 21;91(13):5740–5747. doi: 10.1073/pnas.91.13.5740. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Kask P., Piksarv P., Pooga M., Mets U., Lippmaa E. Separation of the rotational contribution in fluorescence correlation experiments. Biophys J. 1989 Feb;55(2):213–220. doi: 10.1016/S0006-3495(89)82796-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Kinjo M., Rigler R. Ultrasensitive hybridization analysis using fluorescence correlation spectroscopy. Nucleic Acids Res. 1995 May 25;23(10):1795–1799. doi: 10.1093/nar/23.10.1795. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Koppel D. E., Axelrod D., Schlessinger J., Elson E. L., Webb W. W. Dynamics of fluorescence marker concentration as a probe of mobility. Biophys J. 1976 Nov;16(11):1315–1329. doi: 10.1016/S0006-3495(76)85776-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Koppel D. E., Morgan F., Cowan A. E., Carson J. H. Scanning concentration correlation spectroscopy using the confocal laser microscope. Biophys J. 1994 Feb;66(2 Pt 1):502–507. doi: 10.1016/s0006-3495(94)80801-x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Magde D., Elson E. L., Webb W. W. Fluorescence correlation spectroscopy. II. An experimental realization. Biopolymers. 1974 Jan;13(1):29–61. doi: 10.1002/bip.1974.360130103. [DOI] [PubMed] [Google Scholar]
  11. Palmer A. G., 3rd, Thompson N. L. Fluorescence correlation spectroscopy for detecting submicroscopic clusters of fluorescent molecules in membranes. Chem Phys Lipids. 1989 Jun;50(3-4):253–270. doi: 10.1016/0009-3084(89)90053-4. [DOI] [PubMed] [Google Scholar]
  12. Palmer A. G., 3rd, Thompson N. L. High-order fluorescence fluctuation analysis of model protein clusters. Proc Natl Acad Sci U S A. 1989 Aug;86(16):6148–6152. doi: 10.1073/pnas.86.16.6148. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Palmer A. G., 3rd, Thompson N. L. Molecular aggregation characterized by high order autocorrelation in fluorescence correlation spectroscopy. Biophys J. 1987 Aug;52(2):257–270. doi: 10.1016/S0006-3495(87)83213-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Qian H., Elson E. L. Distribution of molecular aggregation by analysis of fluctuation moments. Proc Natl Acad Sci U S A. 1990 Jul;87(14):5479–5483. doi: 10.1073/pnas.87.14.5479. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Rauer B., Neumann E., Widengren J., Rigler R. Fluorescence correlation spectrometry of the interaction kinetics of tetramethylrhodamin alpha-bungarotoxin with Torpedo californica acetylcholine receptor. Biophys Chem. 1996 Jan 16;58(1-2):3–12. doi: 10.1016/0301-4622(95)00080-1. [DOI] [PubMed] [Google Scholar]
  16. Schwille P., Meyer-Almes F. J., Rigler R. Dual-color fluorescence cross-correlation spectroscopy for multicomponent diffusional analysis in solution. Biophys J. 1997 Apr;72(4):1878–1886. doi: 10.1016/S0006-3495(97)78833-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Schwille P., Oehlenschläger F., Walter N. G. Quantitative hybridization kinetics of DNA probes to RNA in solution followed by diffusional fluorescence correlation analysis. Biochemistry. 1996 Aug 6;35(31):10182–10193. doi: 10.1021/bi960517g. [DOI] [PubMed] [Google Scholar]
  18. Thompson N. L., Axelrod D. Immunoglobulin surface-binding kinetics studied by total internal reflection with fluorescence correlation spectroscopy. Biophys J. 1983 Jul;43(1):103–114. doi: 10.1016/S0006-3495(83)84328-8. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES