Abstract

To date, the suitability of a fluorophore for applications involving two-photon absorption has generally been characterized by its two-photon cross-section. Here we consider the robustness and significance of an alternative measure termed the molecular brightness—the fluorescence emission per molecule—which can be obtained readily by use of photon-counting techniques such as fluorescence correlation spectroscopy. The peak molecular brightness attained with increasing excitation intensity is shown to be a reliable benchmark for various fluorescent dye solutions. This figure of merit is considered both theoretically and experimentally and found to be related to the two-photon quantum efficiency and the photostability properties of a dye solution, while it is independent of the solution’s two-photon cross section. This benchmark carries considerable practical as well as scientific interest.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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  37. This was accomplished by variation of the intracavity group velocity dispersion. A Gaussian pulse shape was assumed, for which Delta τ Delta v=0.441, where v=c/lambda.
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    [CrossRef] [PubMed]
  39. K. Konig, T. W. Becker, P. Fischer, I. Riemann, and K. J. Halbhuber, "Pulse-length dependence of cellular response to intense near-infrared laser pulses in multiphoton microscopes," Opt. Lett. 24, 113-115 (1999).
    [CrossRef]
  40. R. M. Dickson, A. B. Cubitt, R. Y. Tsien, and W. E. Moerner, "On/off blinking and switching behaviour of single molecules of green fluorescent protein," Nature 388, 355-358 (1997).
    [CrossRef] [PubMed]
  41. G. H. Patterson and D. W. Piston, "Photobleaching in two-photon excitation microscopy," Biophys. J. 78, 2159-2162 (2000).
    [CrossRef] [PubMed]
  42. D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, "Water-soluble quantum dots for multiphoton fluorescence imaging in vivo," Science 300, 1434-1436 (2003).
    [CrossRef] [PubMed]
  43. H. Wang, T. B. Huff, D. A. Zweifel, W. He, P. S. Low, A. Wei, and J. X. Cheng, "In vitro and in vivo two-photon luminescence imaging of single gold nanorods," Proc. Natl. Acad. Sci. U.S.A. 102, 15,752-15,756 (2005).
    [CrossRef]

2005 (5)

H. Ow, D. R. Larson, M. Srivastava, B. A. Baird, W. W. Webb, and U. Wiesner, "Bright and stable core-shell fluorescent silica nanoparticles," Nano Lett. 5, 113-117 (2005).
[CrossRef] [PubMed]

J. Yao, D. R. Larson, H. D. Viswasrao, W. R. Zipfel, and W. W. Webb, "Blinking and nonradiant dark fraction of water-soluble quantum dots in aqueous solution," Proc. Natl. Acad. Sci. U.S.A. 102, 14,284-14,289 (2005).
[CrossRef]

A. Nagy, J. Wu, and K. M. Berland, "Observation volumes and gamma-factors in two-photon fluorescence fluctuation spectroscopy," Biophys. J. 89, 2077-2090 (2005).
[CrossRef] [PubMed]

M. Hammer, D. Schweitzer, S. Richter, and E. Königsdörffer, "Sodium fluorescein as a retinal pH indicator?" Physiol. Meas. 26(4), N9-N12 (2005).
[CrossRef] [PubMed]

H. Wang, T. B. Huff, D. A. Zweifel, W. He, P. S. Low, A. Wei, and J. X. Cheng, "In vitro and in vivo two-photon luminescence imaging of single gold nanorods," Proc. Natl. Acad. Sci. U.S.A. 102, 15,752-15,756 (2005).
[CrossRef]

2004 (3)

D. L. Wokosin, C. M. Loughrey, and G. L. Smith, "Characterization of a range of fura dyes with two-photon excitation," Biophys. J. 86, 1726-1738 (2004).
[CrossRef] [PubMed]

K. G. Heinze, M. Jahnz, and P. Schwille, "Triple-color coincidence analysis: one step further in following higher order molecular complex formation," Biophys. J. 86, 506-516 (2004).
[CrossRef]

F. Cannone, M. Caccia, S. Bologna, A. Diaspro, and G. Chirico, "Single molecule spectroscopic characterization of GFP-MUT2 mutant for two-photon microscopy applications," Microsc. Res. Tech. 65, 186-193 (2004).
[CrossRef]

2003 (4)

W. R. Zipfel, R. M. Williams, and W. W. Webb, "Nonlinear magic: multiphoton microscopy in the biosciences," Nat. Biotechnol. 21, 1369-1377 (2003).
[CrossRef] [PubMed]

J. Widengren and R. Rigler, "Mechanisms of photobleaching investigated by fluoresence correlation spectroscopy," Bioimaging 4, 149-157 (2003).
[CrossRef]

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, "Water-soluble quantum dots for multiphoton fluorescence imaging in vivo," Science 300, 1434-1436 (2003).
[CrossRef] [PubMed]

K. Berland and G. Shen, "Excitation saturation in two-photon fluorescence correlation spectroscopy," Appl. Opt. 42, 5566-5576 (2003).
[CrossRef] [PubMed]

2002 (1)

Y. Chen, J. D. Muller, Q. Ruan, and E. Gratton, "Molecular brightness characterization of EGFP in vivo by fluorescence fluctuation spectroscopy," Biophys. J. 82, 133-144 (2002).
[CrossRef]

2001 (2)

S. M. Kirkpatrick, R. R. Naik, and M. O. Stone, "Nonlinear saturation and determination of the two-photon absorption cross section of green fluorescent protein," J. Phys. Chem. B 105, 2867-2873 (2001).
[CrossRef]

P. Dittrich and P. Schwille, "Photobleaching and stabilization of fluorophores used for single-molecule analysis with one- and two-photon excitation," Appl. Phys. B 73, 829-837 (2001).
[CrossRef]

2000 (1)

G. H. Patterson and D. W. Piston, "Photobleaching in two-photon excitation microscopy," Biophys. J. 78, 2159-2162 (2000).
[CrossRef] [PubMed]

1999 (4)

Y. Chen, J. D. Muller, P. T. So, and E. Gratton, "The photon counting histogram in fluoresence fluctuation spectroscopy," Biophys. J. 77, 553-567 (1999).
[CrossRef] [PubMed]

P. Schwille, U. Haupts, S. Maiti, and 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]

H. J. Koester, D. Baur, R. Uhl, and S. W. Hell, "Ca2+ fluorescence Imaging with pico- and femtosecond two-photon excitation: signal and photodamage," Biophys. J. 77, 2226-2236 (1999).
[CrossRef] [PubMed]

K. Konig, T. W. Becker, P. Fischer, I. Riemann, and K. J. Halbhuber, "Pulse-length dependence of cellular response to intense near-infrared laser pulses in multiphoton microscopes," Opt. Lett. 24, 113-115 (1999).
[CrossRef]

1998 (2)

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J. Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, W. W. Webb, X. L. Wu, and C. Xu, "Design of organic molecules with large two-photon absorption cross sections," Science 281, 1653-1656 (1998).
[CrossRef] [PubMed]

J. Mertz, "Molecular photodynamics involved in multi-photon excitation fluorescence microscopy," Eur. Biophys. J. 3, 53-66 (1998).

1997 (2)

S. Maiti, U. Haupts, and W. W. Webb, "Fluorescence Correlation spectroscopy: diagnostics for sparse molecules," Proc. Natl. Acad. Sci. U.S.A. 94, 11,753-11,757 (1997).
[CrossRef]

R. M. Dickson, A. B. Cubitt, R. Y. Tsien, and W. E. Moerner, "On/off blinking and switching behaviour of single molecules of green fluorescent protein," Nature 388, 355-358 (1997).
[CrossRef] [PubMed]

1996 (2)

C. Xu, W. Zipfel, J. B. Shear, R. M. Williams, and W. W. Webb, "Multiphoton fluorescence excitation: new spectral windows for biological nonlinear microscopy," Proc. Natl. Acad. Sci. U.S.A. 93, 10,763-10,768 (1996).
[CrossRef]

C. Xu and W. W. Webb, "Measurement of two-photon excitation cross sections of molecular fluorophores with date from 690 to 1050nm," J. Opt. Soc. Am. B 13, 481-491 (1996).
[CrossRef]

1991 (1)

1990 (1)

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

1980 (1)

D. M. Friedrich and W. M. McClain, "Two-photon molecular electronic spectroscopy," Annu. Rev. Phys. Chem. 31, 559-577 (1980).
[CrossRef]

1978 (1)

S. S. Lehrer and P. C. Leavis, "Solute quenching of protein fluorescence," Methods Enzymol. 49, 222-236 (1978).
[CrossRef] [PubMed]

1974 (2)

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

E. L. Elson and D. Magde, "Fluorescence correlation spectroscopy. I. Conceptual basis and theory," Biopolymers 13, 29-61 (1974).
[CrossRef] [PubMed]

1973 (1)

R. M. Hochstrasser, H. N. Sung, and J. E. Wessel, "Two photon excitation spectra. New and versatile spectroscopic tool," J. Am. Chem. Soc. 95, 8179-8180 (1973).
[CrossRef]

1972 (2)

T. W. Hänsch, "Repetitively pulsed tunable dye laser for high resolution spectroscopy," Appl. Opt. 11, 895-898 (1972).
[CrossRef] [PubMed]

D. Magde, E. L. Elson, and W. W. Webb, "Thermodynamic fluctuations in a reacting system—measurement by fluorescene correlation spectroscopy," Phys. Rev. Lett. 29, 705-708 (1972).
[CrossRef]

1971 (1)

G. A. Crosby and J. N. Demans, "Measurement of photoluminescence quantum yields. Review," J. Phys. Chem. 75, 991-1024 (1971).
[CrossRef]

1961 (1)

W. Kaiser and C. G. B. Garrett, "Two photon excitation in CaF2:Eu2+," Phys. Rev. Lett. 7, 229-231 (1961).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, "Electromagnetic diffraction in the optical systems II. Structure of the image field in aplanatic system," Proc. R. Soc. London, Ser. A 253, 358-379 (1959).
[CrossRef]

1931 (1)

M. Göppert-Mayer, "Ueber Elementarakte mit zwei Quanenspruengen," Ann. Phys. 9, 273-294 (1931).
[CrossRef]

Albota, M.

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J. Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, W. W. Webb, X. L. Wu, and C. Xu, "Design of organic molecules with large two-photon absorption cross sections," Science 281, 1653-1656 (1998).
[CrossRef] [PubMed]

Baird, B. A.

H. Ow, D. R. Larson, M. Srivastava, B. A. Baird, W. W. Webb, and U. Wiesner, "Bright and stable core-shell fluorescent silica nanoparticles," Nano Lett. 5, 113-117 (2005).
[CrossRef] [PubMed]

Baur, D.

H. J. Koester, D. Baur, R. Uhl, and S. W. Hell, "Ca2+ fluorescence Imaging with pico- and femtosecond two-photon excitation: signal and photodamage," Biophys. J. 77, 2226-2236 (1999).
[CrossRef] [PubMed]

Becker, T. W.

Beljonne, D.

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J. Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, W. W. Webb, X. L. Wu, and C. Xu, "Design of organic molecules with large two-photon absorption cross sections," Science 281, 1653-1656 (1998).
[CrossRef] [PubMed]

Berland, K.

Berland, K. M.

A. Nagy, J. Wu, and K. M. Berland, "Observation volumes and gamma-factors in two-photon fluorescence fluctuation spectroscopy," Biophys. J. 89, 2077-2090 (2005).
[CrossRef] [PubMed]

Bevington, P.

P. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, 2003).

Bologna, S.

F. Cannone, M. Caccia, S. Bologna, A. Diaspro, and G. Chirico, "Single molecule spectroscopic characterization of GFP-MUT2 mutant for two-photon microscopy applications," Microsc. Res. Tech. 65, 186-193 (2004).
[CrossRef]

Bredas, J. L.

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J. Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, W. W. Webb, X. L. Wu, and C. Xu, "Design of organic molecules with large two-photon absorption cross sections," Science 281, 1653-1656 (1998).
[CrossRef] [PubMed]

Bruchez, M. P.

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, "Water-soluble quantum dots for multiphoton fluorescence imaging in vivo," Science 300, 1434-1436 (2003).
[CrossRef] [PubMed]

Caccia, M.

F. Cannone, M. Caccia, S. Bologna, A. Diaspro, and G. Chirico, "Single molecule spectroscopic characterization of GFP-MUT2 mutant for two-photon microscopy applications," Microsc. Res. Tech. 65, 186-193 (2004).
[CrossRef]

Cannone, F.

F. Cannone, M. Caccia, S. Bologna, A. Diaspro, and G. Chirico, "Single molecule spectroscopic characterization of GFP-MUT2 mutant for two-photon microscopy applications," Microsc. Res. Tech. 65, 186-193 (2004).
[CrossRef]

Chen, Y.

Y. Chen, J. D. Muller, Q. Ruan, and E. Gratton, "Molecular brightness characterization of EGFP in vivo by fluorescence fluctuation spectroscopy," Biophys. J. 82, 133-144 (2002).
[CrossRef]

Y. Chen, J. D. Muller, P. T. So, and E. Gratton, "The photon counting histogram in fluoresence fluctuation spectroscopy," Biophys. J. 77, 553-567 (1999).
[CrossRef] [PubMed]

Cheng, J. X.

H. Wang, T. B. Huff, D. A. Zweifel, W. He, P. S. Low, A. Wei, and J. X. Cheng, "In vitro and in vivo two-photon luminescence imaging of single gold nanorods," Proc. Natl. Acad. Sci. U.S.A. 102, 15,752-15,756 (2005).
[CrossRef]

Chirico, G.

F. Cannone, M. Caccia, S. Bologna, A. Diaspro, and G. Chirico, "Single molecule spectroscopic characterization of GFP-MUT2 mutant for two-photon microscopy applications," Microsc. Res. Tech. 65, 186-193 (2004).
[CrossRef]

Clark, S. W.

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, "Water-soluble quantum dots for multiphoton fluorescence imaging in vivo," Science 300, 1434-1436 (2003).
[CrossRef] [PubMed]

Crosby, G. A.

G. A. Crosby and J. N. Demans, "Measurement of photoluminescence quantum yields. Review," J. Phys. Chem. 75, 991-1024 (1971).
[CrossRef]

Cubitt, A. B.

R. M. Dickson, A. B. Cubitt, R. Y. Tsien, and W. E. Moerner, "On/off blinking and switching behaviour of single molecules of green fluorescent protein," Nature 388, 355-358 (1997).
[CrossRef] [PubMed]

Demans, J. N.

G. A. Crosby and J. N. Demans, "Measurement of photoluminescence quantum yields. Review," J. Phys. Chem. 75, 991-1024 (1971).
[CrossRef]

Denk, W.

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

Diaspro, A.

F. Cannone, M. Caccia, S. Bologna, A. Diaspro, and G. Chirico, "Single molecule spectroscopic characterization of GFP-MUT2 mutant for two-photon microscopy applications," Microsc. Res. Tech. 65, 186-193 (2004).
[CrossRef]

Dickson, R. M.

R. M. Dickson, A. B. Cubitt, R. Y. Tsien, and W. E. Moerner, "On/off blinking and switching behaviour of single molecules of green fluorescent protein," Nature 388, 355-358 (1997).
[CrossRef] [PubMed]

Dittrich, P.

P. Dittrich and P. Schwille, "Photobleaching and stabilization of fluorophores used for single-molecule analysis with one- and two-photon excitation," Appl. Phys. B 73, 829-837 (2001).
[CrossRef]

Ehrlich, J. E.

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J. Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, W. W. Webb, X. L. Wu, and C. Xu, "Design of organic molecules with large two-photon absorption cross sections," Science 281, 1653-1656 (1998).
[CrossRef] [PubMed]

Elson, E. L.

E. L. Elson and D. Magde, "Fluorescence correlation spectroscopy. I. Conceptual basis and theory," Biopolymers 13, 29-61 (1974).
[CrossRef] [PubMed]

D. Magde, E. L. Elson, and W. W. Webb, "Thermodynamic fluctuations in a reacting system—measurement by fluorescene correlation spectroscopy," Phys. Rev. Lett. 29, 705-708 (1972).
[CrossRef]

Fischer, P.

Friedrich, D. M.

D. M. Friedrich and W. M. McClain, "Two-photon molecular electronic spectroscopy," Annu. Rev. Phys. Chem. 31, 559-577 (1980).
[CrossRef]

Fu, J. Y.

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J. Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, W. W. Webb, X. L. Wu, and C. Xu, "Design of organic molecules with large two-photon absorption cross sections," Science 281, 1653-1656 (1998).
[CrossRef] [PubMed]

Garrett, C. G. B.

W. Kaiser and C. G. B. Garrett, "Two photon excitation in CaF2:Eu2+," Phys. Rev. Lett. 7, 229-231 (1961).
[CrossRef]

Göppert-Mayer, M.

M. Göppert-Mayer, "Ueber Elementarakte mit zwei Quanenspruengen," Ann. Phys. 9, 273-294 (1931).
[CrossRef]

Gratton, E.

Y. Chen, J. D. Muller, Q. Ruan, and E. Gratton, "Molecular brightness characterization of EGFP in vivo by fluorescence fluctuation spectroscopy," Biophys. J. 82, 133-144 (2002).
[CrossRef]

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Y. Chen, J. D. Muller, Q. Ruan, and E. Gratton, "Molecular brightness characterization of EGFP in vivo by fluorescence fluctuation spectroscopy," Biophys. J. 82, 133-144 (2002).
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M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J. Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, W. W. Webb, X. L. Wu, and C. Xu, "Design of organic molecules with large two-photon absorption cross sections," Science 281, 1653-1656 (1998).
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M. Hammer, D. Schweitzer, S. Richter, and E. Königsdörffer, "Sodium fluorescein as a retinal pH indicator?" Physiol. Meas. 26(4), N9-N12 (2005).
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C. Xu, W. Zipfel, J. B. Shear, R. M. Williams, and W. W. Webb, "Multiphoton fluorescence excitation: new spectral windows for biological nonlinear microscopy," Proc. Natl. Acad. Sci. U.S.A. 93, 10,763-10,768 (1996).
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D. L. Wokosin, C. M. Loughrey, and G. L. Smith, "Characterization of a range of fura dyes with two-photon excitation," Biophys. J. 86, 1726-1738 (2004).
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Y. Chen, J. D. Muller, P. T. So, and E. Gratton, "The photon counting histogram in fluoresence fluctuation spectroscopy," Biophys. J. 77, 553-567 (1999).
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H. Ow, D. R. Larson, M. Srivastava, B. A. Baird, W. W. Webb, and U. Wiesner, "Bright and stable core-shell fluorescent silica nanoparticles," Nano Lett. 5, 113-117 (2005).
[CrossRef] [PubMed]

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S. M. Kirkpatrick, R. R. Naik, and M. O. Stone, "Nonlinear saturation and determination of the two-photon absorption cross section of green fluorescent protein," J. Phys. Chem. B 105, 2867-2873 (2001).
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W. Denk, J. H. Strickler, and W. W. Webb, "Two-photon laser scanning fluorescence microscopy," Science 248, 73-76 (1990).
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M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J. Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, W. W. Webb, X. L. Wu, and C. Xu, "Design of organic molecules with large two-photon absorption cross sections," Science 281, 1653-1656 (1998).
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R. M. Hochstrasser, H. N. Sung, and J. E. Wessel, "Two photon excitation spectra. New and versatile spectroscopic tool," J. Am. Chem. Soc. 95, 8179-8180 (1973).
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R. M. Dickson, A. B. Cubitt, R. Y. Tsien, and W. E. Moerner, "On/off blinking and switching behaviour of single molecules of green fluorescent protein," Nature 388, 355-358 (1997).
[CrossRef] [PubMed]

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H. J. Koester, D. Baur, R. Uhl, and S. W. Hell, "Ca2+ fluorescence Imaging with pico- and femtosecond two-photon excitation: signal and photodamage," Biophys. J. 77, 2226-2236 (1999).
[CrossRef] [PubMed]

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J. Yao, D. R. Larson, H. D. Viswasrao, W. R. Zipfel, and W. W. Webb, "Blinking and nonradiant dark fraction of water-soluble quantum dots in aqueous solution," Proc. Natl. Acad. Sci. U.S.A. 102, 14,284-14,289 (2005).
[CrossRef]

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H. Wang, T. B. Huff, D. A. Zweifel, W. He, P. S. Low, A. Wei, and J. X. Cheng, "In vitro and in vivo two-photon luminescence imaging of single gold nanorods," Proc. Natl. Acad. Sci. U.S.A. 102, 15,752-15,756 (2005).
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H. Ow, D. R. Larson, M. Srivastava, B. A. Baird, W. W. Webb, and U. Wiesner, "Bright and stable core-shell fluorescent silica nanoparticles," Nano Lett. 5, 113-117 (2005).
[CrossRef] [PubMed]

J. Yao, D. R. Larson, H. D. Viswasrao, W. R. Zipfel, and W. W. Webb, "Blinking and nonradiant dark fraction of water-soluble quantum dots in aqueous solution," Proc. Natl. Acad. Sci. U.S.A. 102, 14,284-14,289 (2005).
[CrossRef]

W. R. Zipfel, R. M. Williams, and W. W. Webb, "Nonlinear magic: multiphoton microscopy in the biosciences," Nat. Biotechnol. 21, 1369-1377 (2003).
[CrossRef] [PubMed]

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, "Water-soluble quantum dots for multiphoton fluorescence imaging in vivo," Science 300, 1434-1436 (2003).
[CrossRef] [PubMed]

P. Schwille, U. Haupts, S. Maiti, and 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]

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J. Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, W. W. Webb, X. L. Wu, and C. Xu, "Design of organic molecules with large two-photon absorption cross sections," Science 281, 1653-1656 (1998).
[CrossRef] [PubMed]

S. Maiti, U. Haupts, and W. W. Webb, "Fluorescence Correlation spectroscopy: diagnostics for sparse molecules," Proc. Natl. Acad. Sci. U.S.A. 94, 11,753-11,757 (1997).
[CrossRef]

C. Xu, W. Zipfel, J. B. Shear, R. M. Williams, and W. W. Webb, "Multiphoton fluorescence excitation: new spectral windows for biological nonlinear microscopy," Proc. Natl. Acad. Sci. U.S.A. 93, 10,763-10,768 (1996).
[CrossRef]

C. Xu and W. W. Webb, "Measurement of two-photon excitation cross sections of molecular fluorophores with date from 690 to 1050nm," J. Opt. Soc. Am. B 13, 481-491 (1996).
[CrossRef]

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

D. Magde, E. L. Elson, and W. W. Webb, "Thermodynamic fluctuations in a reacting system—measurement by fluorescene correlation spectroscopy," Phys. Rev. Lett. 29, 705-708 (1972).
[CrossRef]

Wei, A.

H. Wang, T. B. Huff, D. A. Zweifel, W. He, P. S. Low, A. Wei, and J. X. Cheng, "In vitro and in vivo two-photon luminescence imaging of single gold nanorods," Proc. Natl. Acad. Sci. U.S.A. 102, 15,752-15,756 (2005).
[CrossRef]

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R. M. Hochstrasser, H. N. Sung, and J. E. Wessel, "Two photon excitation spectra. New and versatile spectroscopic tool," J. Am. Chem. Soc. 95, 8179-8180 (1973).
[CrossRef]

Widengren, J.

J. Widengren and R. Rigler, "Mechanisms of photobleaching investigated by fluoresence correlation spectroscopy," Bioimaging 4, 149-157 (2003).
[CrossRef]

Wiesner, U.

H. Ow, D. R. Larson, M. Srivastava, B. A. Baird, W. W. Webb, and U. Wiesner, "Bright and stable core-shell fluorescent silica nanoparticles," Nano Lett. 5, 113-117 (2005).
[CrossRef] [PubMed]

Williams, R. M.

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, "Water-soluble quantum dots for multiphoton fluorescence imaging in vivo," Science 300, 1434-1436 (2003).
[CrossRef] [PubMed]

W. R. Zipfel, R. M. Williams, and W. W. Webb, "Nonlinear magic: multiphoton microscopy in the biosciences," Nat. Biotechnol. 21, 1369-1377 (2003).
[CrossRef] [PubMed]

C. Xu, W. Zipfel, J. B. Shear, R. M. Williams, and W. W. Webb, "Multiphoton fluorescence excitation: new spectral windows for biological nonlinear microscopy," Proc. Natl. Acad. Sci. U.S.A. 93, 10,763-10,768 (1996).
[CrossRef]

Wise, F. W.

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, "Water-soluble quantum dots for multiphoton fluorescence imaging in vivo," Science 300, 1434-1436 (2003).
[CrossRef] [PubMed]

Wokosin, D. L.

D. L. Wokosin, C. M. Loughrey, and G. L. Smith, "Characterization of a range of fura dyes with two-photon excitation," Biophys. J. 86, 1726-1738 (2004).
[CrossRef] [PubMed]

Wolf, E.

B. Richards and E. Wolf, "Electromagnetic diffraction in the optical systems II. Structure of the image field in aplanatic system," Proc. R. Soc. London, Ser. A 253, 358-379 (1959).
[CrossRef]

Wu, J.

A. Nagy, J. Wu, and K. M. Berland, "Observation volumes and gamma-factors in two-photon fluorescence fluctuation spectroscopy," Biophys. J. 89, 2077-2090 (2005).
[CrossRef] [PubMed]

Wu, X. L.

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J. Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, W. W. Webb, X. L. Wu, and C. Xu, "Design of organic molecules with large two-photon absorption cross sections," Science 281, 1653-1656 (1998).
[CrossRef] [PubMed]

Xu, C.

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J. Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, W. W. Webb, X. L. Wu, and C. Xu, "Design of organic molecules with large two-photon absorption cross sections," Science 281, 1653-1656 (1998).
[CrossRef] [PubMed]

C. Xu, W. Zipfel, J. B. Shear, R. M. Williams, and W. W. Webb, "Multiphoton fluorescence excitation: new spectral windows for biological nonlinear microscopy," Proc. Natl. Acad. Sci. U.S.A. 93, 10,763-10,768 (1996).
[CrossRef]

C. Xu and W. W. Webb, "Measurement of two-photon excitation cross sections of molecular fluorophores with date from 690 to 1050nm," J. Opt. Soc. Am. B 13, 481-491 (1996).
[CrossRef]

Yao, J.

J. Yao, D. R. Larson, H. D. Viswasrao, W. R. Zipfel, and W. W. Webb, "Blinking and nonradiant dark fraction of water-soluble quantum dots in aqueous solution," Proc. Natl. Acad. Sci. U.S.A. 102, 14,284-14,289 (2005).
[CrossRef]

Zipfel, W.

C. Xu, W. Zipfel, J. B. Shear, R. M. Williams, and W. W. Webb, "Multiphoton fluorescence excitation: new spectral windows for biological nonlinear microscopy," Proc. Natl. Acad. Sci. U.S.A. 93, 10,763-10,768 (1996).
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This was accomplished by variation of the intracavity group velocity dispersion. A Gaussian pulse shape was assumed, for which Delta τ Delta v=0.441, where v=c/lambda.

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This can be considered akin to the relationship of the laser pulse width measured by an interferometric autocorrelator to the true laser pulse width.

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Figures (8)

Fig. 1
Fig. 1

Schematic drawing of the two-photon FCS apparatus.

Fig. 2
Fig. 2

Robust power dependence of FCS measurements. (a) Series of FCS curves obtained for Alexa 546 dye collected at various intensity levels. As intensity increases, amplitudes are seen to first rise and then to decline, while the curve width decreases (see the amplitude-normalized curves in the inset). (b) The intensity trends quantified by their effects on FCS curve fit parameters N AC and τ D are robust. Two distinct intensity thresholds associated with the onset of photobleaching and pulse saturation effects can be identified. Error bars represent standard deviations. To pool data from n = 7 recordings obtained from different samples, we normalized intensity values the level yielding the minimum N AC in each series. N AC values were normalized to this minimum, while τ D values were not normalized.

Fig. 3
Fig. 3

Saturation model for a 3DG ellipsoid excitation volume. Intensity trends for the γ parameter (solid curve) and the autocorrelated excitation volume size V AC (dashed curve) of a focal spot described by a 3DG ellipsoid were calculated by numerical integration according to the pulse saturation model described in the text. Both parameters increase beyond a threshold intensity I sat 2 related to the dye’s cross section σ 2 . The γ parameter saturates asymptotically to 0.9 , while volume size V AC increases without bound. Note this model does not account for photobleaching.

Fig. 4
Fig. 4

Predicted molecular brightness intensity trends for various two-photon cross sections. Calculated power trends of normalized molecular brightness ( ϵ ) plotted for a range of two-photon cross-section ( σ 2 ) values, after the effects of pulse saturation on the excitation volume size and total emission rate have been accounted for. A focal spot size produced by focusing a collimated beam of λ = 850 nm with a 1.2 NA water immersion objective was assumed in order to convert powers into intensities. The value of σ 2 is seen to determine the initial slope of ϵ ( I 2 ) , but the same asymptotic limit is reached in all cases (inset).

Fig. 5
Fig. 5

Measured molecular brightness intensity curves are highly robust. (a) ϵ ( I 2 ) profiles were obtained from n = 7 series of FCS recordings taken from separate samples (same data as in Fig. 2). The curve shape is highly repeatable (mean ± standard deviation shown). The peak value ( ϵ peak ) obtained was similarly repeatable, 35.0 ± 1.4 kcpsm . Intensity values were normalized relative to the level yielding minimum N AC , for each series, to permit comparison. (b) Molecular brightness curves obtained from dilute solutions containing Alexa 546, Rhodamine 6G, and EGFP, each excited at λ = 850 nm . Dyes show clearly the distinct intensity curves and peak brightness values ϵ peak (mean ± standard deviation; Alexa 546, n = 7 ; Rhodamine 6G, n = 3 ; EGFP, n = 3 ). Additionally, a single measurement for Alexa 546 obtained with a GaAsP PMT instead of an APD is presented, showing a reduced ϵ peak value that is due to the lower quantum efficiency of the GaAsP detector. Intensities were normalized to a level giving rise to ϵ peak for each curve.

Fig. 6
Fig. 6

Effects of pure variations of η 2 or η B on ϵ peak can be discriminated. (a) Addition of 5 mM L-ascorbic acid, a photostabilizing agent that should reduce η B , to a solution of tetramethylrhodamine dye significantly increases ϵ peak , as expected. As this has no effect on η 2 or σ 2 , the initial slope of ϵ ( I 2 ) is unaffected (inset). (b) Furthermore, threshold I bl 2 at which bleaching effect becomes manifest increases in the presence of L-ascorbic acid, as expected for reduced η B . (c) The addition of 40 mM KI , a dynamic quenching molecule that should reduce η 2 , to the solution of Alexa 546 dye significantly decreases ϵ peak , as expected. Decreasing η 2 reduces initial slope of ϵ ( I 2 ) (inset). (d) However, the bleaching effect threshold I bl 2 is unaffected, suggesting that KI had no effect on either η B or σ 2 . The legends for (b) and (d) are identical those for (a) and (c), respectively.

Fig. 7
Fig. 7

Effect of pH on ϵ peak of fluorescein. (a) Solutions of buffered fluorescein show reduced ϵ peak with decreasing pH. Initial slopes ϵ initial of ϵ ( I 0 2 ) curves also decline with pH, suggesting that σ 2 , η 2 , or both are decreasing. Intensities are plotted relative to global maximum value for all series. (b) Intensity curves of τ D show increasing bleaching effect thresholds I bl 2 with decreasing pH, implying that σ 2 must also decrease because a pure increase in η B would contradict the results in (a). Intensities were normalized to a median value. (c) Intensity values for each curve were reweighted by the inverse of their corresponding ϵ intial values to compensate for σ 2 variation. This procedure reverses the ordering of relative I 2 2 values. The resultant ordering is consistent with increasing η B , decreasing η 2 , or both, at reduced pH, either of which explains the observed ϵ peak trend. Reweighted intensities were normalized about the median value. (d) Intensity values for each curve were reweighted by the inverse of the corresponding I ϵ - peak 2 values, i.e., the intensity at which ϵ peak appears for each curve. As with I bl 2 , I ϵ - peak 2 depends inversely on η B and σ 2 . Thus reweighting causes the apparent I bl 2 values to coincide.

Fig. 8
Fig. 8

Spectral variation of ϵ peak for Alexa 546 dye. (a) Molecular brightness intensity curves were collected from an Alexa 546 solution at various excitation wavelengths, showing that ϵ peak varies significantly across λ = 770 to λ = 880 nm , reaching a maximal value at λ = 820 nm . (b) Intensity curves of τ D show increasing thresholds I bl 2 at off-peak wavelengths, particularly on the blue edge, implying a decreased σ 2 at these wavelengths that is consistent with a decreasing ϵ initial trend observed (not shown). Intensities were normalized to the median global value after weighting by wavelength-dependent factors (focal spot area and photon energy). (c) Intensities were reweighted by inverse ϵ initial values for each wavelength to compensate for the σ 2 effect, and the renormalization to the global median. The resultant reordering of the apparent I bl 2 values is consistent with increased η B , decreased η 2 , or both at off-peak wavelengths, with stronger shifts seen for the red edge. These trends are consistent with the ϵ peak spectrum observed in (a). (d) Intensities from (b) were reweighted by inverse I ϵ - peak 2 , and renormalized to the median value, which caused the I bl 2 values to coincide for all wavelengths.

Tables (1)

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Table 1 Measurand Correlations with Dye-Solution Parameters

Equations (14)

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G ( τ ) δ F ( t ) δ F ( t + τ ) F ( t ) 2 ,
g ( τ ) 1 ( 4 π D τ ) 3 2 I norm 2 ( r ) exp ( r r 2 4 D τ ) I norm 2 ( r ) d 3 r d 3 r .
k ab ( r ) = 1 2 σ 2 g p ( 2 ) ( f las τ las ) I 2 ( r ) ( h c λ ) 2 ,
K em = η 2 k ab , 0 C I norm 2 ( r ) d 3 r ,
G ( 0 ) = γ C V TRUE = γ N TRUE ,
γ I norm 4 ( r ) d 3 r I norm 2 ( r ) d 3 r .
V AC [ I norm 2 ( r ) d 3 r ] 2 I norm 4 ( r ) d 3 r .
G ( τ ) = 1 N AC ( 1 1 + τ τ D ) ( 1 1 + τ K 2 τ D ) 1 2 .
τ D , bl = τ D 1 1 + ( η B γ A ) k ab , 0 τ D = τ D 1 1 + A η B σ 2 I 0 2 τ D ,
I sat 2 2 f las 2 τ las σ 2 g p ( 2 ) ,
K em , sat = η 2 k ab , sat ( 0 ) C V TRUE , sat ,
I norm , sat 2 ( r ) = 1 exp [ ( I 0 2 I sat 2 ) I norm 2 ( r ) ] 1 exp [ ( I 0 2 I sat 2 ) ] .
ϵ = ϕ η 2 k ab , sat ( 0 ) V TRUE , sat V AC , sat = ϕ η 2 f las γ sat [ 1 exp ( I 0 2 I sat 2 ) ] ,
ϵ initial = ϕ η 2 γ ( I 0 2 I sat 2 ) = ϕ η 2 f las γ ( σ 2 g p (2) 2 f las τ las ) I 0 2

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