Abstract

Fluorescence correlation spectroscopy examines the chemical and the photophysical dynamics of dilute molecular solutions by measurement of the dynamic optical fluctuations of the fluorescence of a few molecules, even averaging less than one molecule at a time, in open focal volumes that are usually less than a femtoliter (<10-18 m3). It applies the same principles of statistical thermodynamics as does quasi-elastic light scattering. Molecular interactions, conformational changes, chemical reactions, and photophysical dynamics that are not ordinarily detectable by quasi-elastic light scattering can be analyzed by fluorescence correlation spectroscopy in cases in which molecular fluorescence changes in the dynamic range 10-7–102 s.

© 2001 Optical Society of America

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    [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [PubMed]
  69. J. Korlach, M. Levene, S. W. Turner, D. R. Larson, M. E. Foquet, H. G. Craighead, W. W. Webb, “A new method for sequencing individual molecules of DNA,” paper presented at the Sixth International Workshop on Single Molecule Detection and Ultra Sensitive Analysis in Life Sciences, Berlin, Germany (2000).
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  71. A. A. Heikal, J. Korlach, W. W. Webb, “Time-resolved fluorescence and anisotropy of free and DNA-bound fluorescently labeled nucleotides,” Biophys. J. 80, 8 (2001).
  72. M. Levene, J. Korlach, S. W. Turner, H. G. Craighead, W. W. Webb, “Near-field apertures for reduced-volume fluorescence correlation spectroscopy and single molecule studies,” Biophys. J. 80, 149 (2001).
  73. S. T. Hess, A. A. Heikal, W. W. Webb, “Reversible light-assisted proton transfer reaction in ecliptic green fluorescent protein,” Biophys. J. 78, 75 (2000).
  74. M. Levene, D. Larson, J. Korlach, M. Foquet, S. W. Turner, H. G. Craighead, W. W. Webb, “Nanometer constrained observation volumes for high concentration fluorescence correlation spectroscopy and single molecule dynamics,” Biophys. J. 78, 2368 (2000).
  75. D. R. Larson, M. Levene, S. W. Turner, H. G. Craighead, W. W. Webb, “Fluorescence correlation spectroscopy in zeptoliter volumes,” Biophys. J. 80, 149 (2001).
  76. 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]
  77. R. M. Dickson, A. B. Cubitt, R. Y. Tsien, W. E. Moerner, “On/off blinking and switching behaviour of single molecules of green fluorescent protein,” Nature 388(6840), 355–358 (1997).
  78. P. Schwille, S. Kummer, 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).
    [CrossRef] [PubMed]
  79. D. A. DeAngelis, G. Miesenböch, B. V. Zemelman, J. E. Rothman, “PRIM: proximity imaging of green fluorescent protein-tagged polypeptides,” Proc. Natl. Acad. Sci. USA 95, 12312–12316 (1998).
    [CrossRef]
  80. A. A. Heikal, S. T. Hess, G. S. Baird, R. Y. Tsien, W. W. Webb, “Molecular spectroscopy and dynamics of intrinsically fluorescent proteins: coral red (dsRed) and yellow (Citrine),” Proc. Natl. Acad. Sci. USA 97, 11996–12001 (2000).
    [CrossRef] [PubMed]
  81. P. F. Fahey, D. E. Koppel, L. S. Barak, D. E. Wolf, E. L. Elson, W. W. Webb, “Lateral diffusion in planar lipid bilayers,” Science 195(4275), 305–306 (1977).
  82. P. Schwille, J. Korlach, W. W. Webb, “Fluorescence correlation spectroscopy with single-molecule sensitivity on cell and model membranes,” Cytometry 36, 176–182 (1999).
    [CrossRef] [PubMed]
  83. J. Korlach, P. Schwille, W. W. Webb, G. W. Feigenson, “Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 96, 8461–8466 (1999).
    [CrossRef] [PubMed]
  84. C. Xu, W. W. Webb, “Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 nm to 1050 nm,” J. Opt. Soc. Am. B 13, 481–491 (1996).
    [CrossRef]
  85. M. Williams, D. W. Piston, W. W. Webb, “Two-photon molecular excitation provides intrinsic three-dimensional resolution for laser-based microscopy and microphotochemistry,” FASEB J. 8, 804–813 (1994).
    [PubMed]
  86. S. T. Hess, A. A. Heikal, G. S. Baird, R. Y. Tsien, W. W. Webb, “Advantageous molecular photophysical fluorescence properties of dsRed and Citrine,” Biophys. J. 80, 7 (2001).
  87. A. A. Heikal, S. T. Hess, P. Schwille, W. W. Webb, “Ultrafast molecular dynamics of selected green fluorescent protein mutants,” Biophys. J. 78, 752 (2000).
  88. P. Pyenta, P. Schwille, School of Applied and Engineering Physics, Cornell University, 233 Clark Hall, Ithaca, N.Y. 14853-0001 (personal communication, 1998).
  89. J. Thomas, W. W. Webb, “Fluorescence photobleaching recovery: a probe of membrane dynamics,” in Non-Invasive Techniques in Cell Biology, S. Grinstein, K. Foskett, eds. (Wiley, New York, 1990), pp. 129–152.
  90. M. Albota, D. Beljonne, J. Brédas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. Hess, T. Kogej, M. D. Levin, S. Marder, D. McCord-Maughon, J. W. Perry, H. Röckel, M. Rumi, G. Subramaniam, W. W. Webb, X.-L. Wu, C. Xu, “Design of organic molecules with large two-photon absorption cross sections,” Science 281, 1653–1656 (1998).
    [CrossRef] [PubMed]
  91. J. L. Thomas, D. Holowka, B. Baird, W. W. Webb, “Large-scale co-aggregation of fluorescent lipid probes with cell surface proteins,” J. Cell Biol. 125, 795–802 (1994).
    [CrossRef] [PubMed]

2001 (5)

J. Korlach, M. Levene, S. W. Turner, D. R. Larson, M. Foquet, H. G. Craighead, W. W. Webb, “A new strategy for sequencing individual molecules of DNA,” Biophys. J. 80, 147 (2001).

A. A. Heikal, J. Korlach, W. W. Webb, “Time-resolved fluorescence and anisotropy of free and DNA-bound fluorescently labeled nucleotides,” Biophys. J. 80, 8 (2001).

M. Levene, J. Korlach, S. W. Turner, H. G. Craighead, W. W. Webb, “Near-field apertures for reduced-volume fluorescence correlation spectroscopy and single molecule studies,” Biophys. J. 80, 149 (2001).

D. R. Larson, M. Levene, S. W. Turner, H. G. Craighead, W. W. Webb, “Fluorescence correlation spectroscopy in zeptoliter volumes,” Biophys. J. 80, 149 (2001).

S. T. Hess, A. A. Heikal, G. S. Baird, R. Y. Tsien, W. W. Webb, “Advantageous molecular photophysical fluorescence properties of dsRed and Citrine,” Biophys. J. 80, 7 (2001).

2000 (7)

A. A. Heikal, S. T. Hess, P. Schwille, W. W. Webb, “Ultrafast molecular dynamics of selected green fluorescent protein mutants,” Biophys. J. 78, 752 (2000).

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

R. H. Köhler, P. Schwille, W. W. Webb, M. Hanson, “Active protein transport through plastid tubules: velocity quantified by fluorescence correlation spectroscopy,” J. Cell Sci. 113, 3921–3930 (2000).
[PubMed]

P. Schwille, S. Kummer, 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).
[CrossRef] [PubMed]

S. T. Hess, A. A. Heikal, W. W. Webb, “Reversible light-assisted proton transfer reaction in ecliptic green fluorescent protein,” Biophys. J. 78, 75 (2000).

M. Levene, D. Larson, J. Korlach, M. Foquet, S. W. Turner, H. G. Craighead, W. W. Webb, “Nanometer constrained observation volumes for high concentration fluorescence correlation spectroscopy and single molecule dynamics,” Biophys. J. 78, 2368 (2000).

P. Kloppenburg, W. R. Zipfel, W. W. Webb, R. M. Harris-Warrick, “Highly localized Ca2+ accumulation revealed by multiphoton microscopy in an identified motoneuron, and its modulation by dopamine,” J. Neurosci. 20, 2523–2533 (2000).
[PubMed]

1999 (5)

E. Brown, E. Wu, W. Zipfel, W. W. Webb, “Measurement of molecular diffusion in solution by multiphoton fluorescence photobleaching recovery,” Biophys. J. 77, 2837–2849 (1999).
[CrossRef] [PubMed]

P. Kask, K. Palo, D. Ullmann, K. Gall, “Fluorescence-intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. USA 96, 13756–13761 (1999).
[CrossRef] [PubMed]

P. Schwille, J. Korlach, W. W. Webb, “Fluorescence correlation spectroscopy with single-molecule sensitivity on cell and model membranes,” Cytometry 36, 176–182 (1999).
[CrossRef] [PubMed]

J. Korlach, P. Schwille, W. W. Webb, G. W. Feigenson, “Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 96, 8461–8466 (1999).
[CrossRef] [PubMed]

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

1998 (3)

D. A. DeAngelis, G. Miesenböch, B. V. Zemelman, J. E. Rothman, “PRIM: proximity imaging of green fluorescent protein-tagged polypeptides,” Proc. Natl. Acad. Sci. USA 95, 12312–12316 (1998).
[CrossRef]

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]

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

1997 (4)

R. M. Dickson, A. B. Cubitt, R. Y. Tsien, W. E. Moerner, “On/off blinking and switching behaviour of single molecules of green fluorescent protein,” Nature 388(6840), 355–358 (1997).

D.-O. D. Mak, W. W. Webb, “Conductivity noise in transmembrane ion channels due to ion concentration fluctuations via diffusion,” Biophys. J. 72, 1153–1164 (1997).
[CrossRef] [PubMed]

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, W. W. Webb, “Measuring serotonin distribution in live cells with three-photon excitation,” Science 275, 530–532 (1997).
[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).
[CrossRef] [PubMed]

1996 (2)

T. J. Feder, I. Brust-Mascher, J. P. Slattery, B. Baird, W. W. Webb, “Constrained diffusion or immobile fraction on the cell surfaces: a new interpretation,” Biophys. J. 70, 2767–2773 (1996).
[CrossRef] [PubMed]

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

1995 (3)

1994 (5)

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

R. N. Ghosh, W. W. Webb, “Automated detection and tracking of individual and clustered cell surface low density lipoprotein receptor molecules,” Biophys. J. 66, 1301–1318 (1994).
[CrossRef] [PubMed]

L. R. Opsahl, W. W. Webb, “Transduction of membrane tension by the ion channel alamethicin,” Biophys. J. 66, 71–74 (1994).
[CrossRef] [PubMed]

M. Williams, D. W. Piston, W. W. Webb, “Two-photon molecular excitation provides intrinsic three-dimensional resolution for laser-based microscopy and microphotochemistry,” FASEB J. 8, 804–813 (1994).
[PubMed]

J. L. Thomas, D. Holowka, B. Baird, W. W. Webb, “Large-scale co-aggregation of fluorescent lipid probes with cell surface proteins,” J. Cell Biol. 125, 795–802 (1994).
[CrossRef] [PubMed]

1992 (1)

W. Denk, R. M. Keolian, W. W. Webb, “Mechanical response of frog saccular hair bundles to the aminoglycoside block of mechano-electrical transduction,” J. Neurophysiol. 68, 927–932 (1992).
[PubMed]

1991 (1)

1990 (6)

H. Qian, “On the statistics of fluorescence correlation spectroscopy,” Biophys. Chem. 38(1-2), 49–57 (1990).
[PubMed]

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

H. Qian, E. L. Elson, “Distribution of molecular aggregation by analysis of fluctuation moments,” Proc. Natl. Acad. Sci. USA 87, 5479–5483 (1990).
[CrossRef] [PubMed]

H. Qian, E. L. Elson, “On the analysis of high-order moments of fluorescence fluctuations,” Biophys. J. 57, 375–380 (1990).
[CrossRef] [PubMed]

W. Denk, W. W. Webb, “Optical measurement of picometer displacements of transparent, microscopic objects,” Appl. Opt. 29, 2382–2391 (1990).
[CrossRef] [PubMed]

N. M. Zimmerman, W. W. Webb, “1/f resistance noise complements anelasticity measurements of hydrogen motion in amorphous Pd80Si20,” Phys. Rev. Lett. 65, 1040–1043 (1990).
[CrossRef] [PubMed]

1989 (4)

D. C. Wack, W. W. Webb, “Measurement by x-ray diffraction methods of the layer compressional elastic constant B in the lyotropic smectic-A (La) phase of the lecithin–water system,” Phys. Rev. A 40, 1627–1636 (1989).
[CrossRef] [PubMed]

W. Denk, W. W. Webb, “Thermal-noise-limited transduction observed in mechanosensory receptors of the inner ear,” Phys. Rev. Lett. 63, 207–210 (1989).
[CrossRef] [PubMed]

W. Denk, W. W. Webb, A. J. Hudspeth, “Mechanical properties of sensory hair bundles are reflected in their Brownian motion measured with a laser differential interferometer,” Proc. Natl. Acad. Sci. USA 86, 5371–5375 (1989).
[CrossRef] [PubMed]

T. Ryan, J. Myers, W. W. Webb, “Molecular interactions on the cell surface revealed by electrophoresis,” Biol. Bull. 176(S), 164–169 (1989).

1988 (1)

T. A. Ryan, J. Myers, D. Holowka, B. Baird, W. W. Webb, “Molecular crowding on the cell surface,” Science 239, 61–64 (1988).
[CrossRef] [PubMed]

1986 (3)

D. Gross, W. W. Webb, “Molecular counting of low-density lipoprotein particles as individuals and small clusters on cell surfaces,” Biophys. J. 49, 901–911 (1986).
[CrossRef] [PubMed]

N. O. Peterson, D. C. Johnson, M. J. Schlessinger, “Scanning fluorescence correlation spectroscopy. 2. Application to virus glycoprotein aggregation,” Biophys. J. 49, 817–820 (1986).
[CrossRef]

J. V. Mantese, W. A. Curtin, W. W. Webb, “Two-component model for the resistivity and noise of tunneling metal-insulator composites,” Phys. Rev. B 33, 7897–7901 (1986).
[CrossRef]

1985 (3)

J. H. Scofield, W. W. Webb, “Resistance fluctuations due to hydrogen diffusion in niobium thin films,” Phys. Rev. Lett. 54, 353–356 (1985).
[CrossRef] [PubMed]

J. V. Mantese, W. W. Webb, “1/f noise of granular metal-insulator composites,” Phys. Rev. Lett. 55, 2212–2215 (1985).
[CrossRef] [PubMed]

D. W. Tank, W. J. Fredericks, L. S. Barak, W. W. Webb, “Electric field-induced redistribution and postfield relaxation of low density lipoprotein receptors on cultured human fibroblasts,” J. Cell Biol. 101, 148–157 (1985).
[CrossRef] [PubMed]

1984 (2)

M. B. Schneider, J. T. Jenkins, W. W. Webb, “Thermal fluctuations of large cylindrical phospholipid vesicles,” Biophys. J. 45, 891–899 (1984).
[CrossRef] [PubMed]

M. B. Schneider, J. T. Jenkins, W. W. Webb, “Thermal fluctuations of large quasi-spherical bimolecular phospholipid vesicles,” J. Phys. (Paris) 45, 1457–1472 (1984).
[CrossRef]

1983 (3)

D. W. Tank, R. L. Huganir, P. Greengard, W. W. Webb, “Patch-recorded single-channel currents of the purified and reconstituted torpedo acetylcholine receptor,” Proc. Natl. Acad. Sci. USA 80, 5129–5133 (1983).
[CrossRef] [PubMed]

R. D. Icenogle, E. L. Elson, “Fluorescence correlation spectroscopy and photobleaching recovery of multiple binding reactions. I. Theory and FCS measurements,” Biopolymers 22, 1919–1948 (1983).
[CrossRef] [PubMed]

R. D. Icenogle, E. L. Elson, “Fluorescence correlation spectroscopy and photobleaching recovery of multiple binding reactions. II. FPR and FCS measurements at low and high DNA concentrations,” Biopolymers 22, 1949–1966 (1983).
[CrossRef] [PubMed]

1982 (1)

L. S. Barak, W. W. Webb, “Diffusion of low density lipoprotein–receptor complex on human fibroblasts,” J. Cell Biol. 95, 846–852 (1982).
[CrossRef] [PubMed]

1981 (1)

M. B. Frish, W. W. Webb, “Direct measurement of vorticity by optical probe,” J. Fluid Mech. 107, 173–200 (1981).
[CrossRef]

1977 (1)

P. F. Fahey, D. E. Koppel, L. S. Barak, D. E. Wolf, E. L. Elson, W. W. Webb, “Lateral diffusion in planar lipid bilayers,” Science 195(4275), 305–306 (1977).

1976 (2)

W. W. Webb, “Applications of fluorescence correlation spectroscopy,” Quart. Rev. Biophys. 9, 49–68 (1976).
[CrossRef]

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, A216 (1976).
[CrossRef]

1975 (2)

P. Leiderer, D. R. Nelson, D. R. Watts, W. W. Webb, “Tricritical slowing down of superfluid dynamics in 3He–4He mixtures,” Phys. Rev. Lett. 34, 1080–1083 (1975).
[CrossRef]

E. L. Elson, W. W. Webb, “Concentration correlation spectroscopy: a new biophysical probe based on occupation number fluctuations,” Ann. Rev. Biophys. Bioeng. 4, 311–334 (1975).
[CrossRef]

1974 (5)

P. Leiderer, D. R. Watts, W. W. Webb, “Light scattering by 3He–4He mixtures near the tricritical point,” Phys. Rev. Lett. 33, 483–485 (1974).
[CrossRef]

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

D. Magde, E. L. Elson, W. W. Webb, “Fluorescence correlation spectroscopy II. An experimental realization,” Biopolymers 13, 29–61 (1974).
[CrossRef] [PubMed]

A. Ehrenberg, R. Rigler, “Rotational Brownian-motion and fluorescence intensity fluctuations,” Chem. Phys. 4(3), 390–401 (1974).

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

1972 (1)

D. Magde, E. Elson, W. W. Webb, “Thermodynamic fluctuations in a reacting system—measurements by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[CrossRef]

1971 (1)

W. H. Henkels, W. W. Webb, “Intrinsic fluctuations in the driven Josephson oscillator,” Phys. Rev. Lett. 26, 1164–1167 (1971).
[CrossRef]

1970 (1)

J. E. Lukens, R. J. Warburton, W. W. Webb, “Onset of quantized thermal fluctuations in ‘one-dimensional’ superconductors,” Phys. Rev. Lett. 25, 1180–1184 (1970).
[CrossRef]

1969 (3)

R. Beasley, R. Labusch, W. W. Webb, “Flux creep in type-II superconductors,” Phys. Rev. 181, 682–700 (1969).
[CrossRef]

J. S. Huang, W. W. Webb, “Diffuse interface in a critical fluid mixture,” J. Chem. Phys. 50, 3677–3693 (1969).
[CrossRef]

J. S. Huang, W. W. Webb, “Viscous damping of thermal excitations on the interface of critical fluid mixtures,” Phys. Rev. Lett. 23, 160–163 (1969).
[CrossRef]

1968 (1)

W. W. Webb, R. J. Warburton, “Intrinsic quantum fluctuations in uniform filamentary superconductors,” Phys. Rev. Lett. 30, 461–465 (1968).
[CrossRef]

1965 (2)

R. Beasley, W. A. Fietz, R. W. Rollins, J. Silcox, W. W. Webb, “Annihilation instability in hard superconductors,” Phys. Rev. A 137, 1205–1208 (1965).
[CrossRef]

G. H. Gilmer, W. C. Gilmore, J. S. Huang, W. W. Webb, “Diffuse interface in a critical fluid mixture,” Phys. Rev. Lett. 14, 491–494 (1965).
[CrossRef]

Albota, M.

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

Ambegaokor, V.

B. Widom, M. Fisher, V. Ambegaokor, J. Langer, J. Wilkens, M. Nelkin, K. Wilson, and their students, Cornell University, Ithaca, N.Y. (personal communication, 1970).

Axelrod, D.

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, A216 (1976).
[CrossRef]

Baird, B.

T. J. Feder, I. Brust-Mascher, J. P. Slattery, B. Baird, W. W. Webb, “Constrained diffusion or immobile fraction on the cell surfaces: a new interpretation,” Biophys. J. 70, 2767–2773 (1996).
[CrossRef] [PubMed]

J. L. Thomas, D. Holowka, B. Baird, W. W. Webb, “Large-scale co-aggregation of fluorescent lipid probes with cell surface proteins,” J. Cell Biol. 125, 795–802 (1994).
[CrossRef] [PubMed]

T. A. Ryan, J. Myers, D. Holowka, B. Baird, W. W. Webb, “Molecular crowding on the cell surface,” Science 239, 61–64 (1988).
[CrossRef] [PubMed]

Baird, G. S.

S. T. Hess, A. A. Heikal, G. S. Baird, R. Y. Tsien, W. W. Webb, “Advantageous molecular photophysical fluorescence properties of dsRed and Citrine,” Biophys. J. 80, 7 (2001).

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

Barak, L. S.

D. W. Tank, W. J. Fredericks, L. S. Barak, W. W. Webb, “Electric field-induced redistribution and postfield relaxation of low density lipoprotein receptors on cultured human fibroblasts,” J. Cell Biol. 101, 148–157 (1985).
[CrossRef] [PubMed]

L. S. Barak, W. W. Webb, “Diffusion of low density lipoprotein–receptor complex on human fibroblasts,” J. Cell Biol. 95, 846–852 (1982).
[CrossRef] [PubMed]

P. F. Fahey, D. E. Koppel, L. S. Barak, D. E. Wolf, E. L. Elson, W. W. Webb, “Lateral diffusion in planar lipid bilayers,” Science 195(4275), 305–306 (1977).

Beasley, R.

R. Beasley, R. Labusch, W. W. Webb, “Flux creep in type-II superconductors,” Phys. Rev. 181, 682–700 (1969).
[CrossRef]

R. Beasley, W. A. Fietz, R. W. Rollins, J. Silcox, W. W. Webb, “Annihilation instability in hard superconductors,” Phys. Rev. A 137, 1205–1208 (1965).
[CrossRef]

Beljonne, D.

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

Berne, B. J.

B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

Brédas, J.

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

Brown, E.

E. Brown, E. Wu, W. Zipfel, W. W. Webb, “Measurement of molecular diffusion in solution by multiphoton fluorescence photobleaching recovery,” Biophys. J. 77, 2837–2849 (1999).
[CrossRef] [PubMed]

Brust-Mascher, I.

T. J. Feder, I. Brust-Mascher, J. P. Slattery, B. Baird, W. W. Webb, “Constrained diffusion or immobile fraction on the cell surfaces: a new interpretation,” Biophys. J. 70, 2767–2773 (1996).
[CrossRef] [PubMed]

Craighead, H. G.

D. R. Larson, M. Levene, S. W. Turner, H. G. Craighead, W. W. Webb, “Fluorescence correlation spectroscopy in zeptoliter volumes,” Biophys. J. 80, 149 (2001).

J. Korlach, M. Levene, S. W. Turner, D. R. Larson, M. Foquet, H. G. Craighead, W. W. Webb, “A new strategy for sequencing individual molecules of DNA,” Biophys. J. 80, 147 (2001).

M. Levene, J. Korlach, S. W. Turner, H. G. Craighead, W. W. Webb, “Near-field apertures for reduced-volume fluorescence correlation spectroscopy and single molecule studies,” Biophys. J. 80, 149 (2001).

M. Levene, D. Larson, J. Korlach, M. Foquet, S. W. Turner, H. G. Craighead, W. W. Webb, “Nanometer constrained observation volumes for high concentration fluorescence correlation spectroscopy and single molecule dynamics,” Biophys. J. 78, 2368 (2000).

J. Korlach, M. Levene, S. W. Turner, D. R. Larson, M. E. Foquet, H. G. Craighead, W. W. Webb, “A new method for sequencing individual molecules of DNA,” paper presented at the Sixth International Workshop on Single Molecule Detection and Ultra Sensitive Analysis in Life Sciences, Berlin, Germany (2000).

Cubitt, A. B.

R. M. Dickson, A. B. Cubitt, R. Y. Tsien, W. E. Moerner, “On/off blinking and switching behaviour of single molecules of green fluorescent protein,” Nature 388(6840), 355–358 (1997).

Curtin, W. A.

J. V. Mantese, W. A. Curtin, W. W. Webb, “Two-component model for the resistivity and noise of tunneling metal-insulator composites,” Phys. Rev. B 33, 7897–7901 (1986).
[CrossRef]

DeAngelis, D. A.

D. A. DeAngelis, G. Miesenböch, B. V. Zemelman, J. E. Rothman, “PRIM: proximity imaging of green fluorescent protein-tagged polypeptides,” Proc. Natl. Acad. Sci. USA 95, 12312–12316 (1998).
[CrossRef]

DeGroot, S. R.

S. R. DeGroot, Thermodynamics of Irreversible Processes (North-Holland, Amsterdam, 1952).

Denk, W.

W. Denk, R. M. Keolian, W. W. Webb, “Mechanical response of frog saccular hair bundles to the aminoglycoside block of mechano-electrical transduction,” J. Neurophysiol. 68, 927–932 (1992).
[PubMed]

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

W. Denk, W. W. Webb, “Optical measurement of picometer displacements of transparent, microscopic objects,” Appl. Opt. 29, 2382–2391 (1990).
[CrossRef] [PubMed]

W. Denk, W. W. Webb, “Thermal-noise-limited transduction observed in mechanosensory receptors of the inner ear,” Phys. Rev. Lett. 63, 207–210 (1989).
[CrossRef] [PubMed]

W. Denk, W. W. Webb, A. J. Hudspeth, “Mechanical properties of sensory hair bundles are reflected in their Brownian motion measured with a laser differential interferometer,” Proc. Natl. Acad. Sci. USA 86, 5371–5375 (1989).
[CrossRef] [PubMed]

Dickson, R. M.

R. M. Dickson, A. B. Cubitt, R. Y. Tsien, W. E. Moerner, “On/off blinking and switching behaviour of single molecules of green fluorescent protein,” Nature 388(6840), 355–358 (1997).

Ehrenberg, A.

A. Ehrenberg, R. Rigler, “Rotational Brownian-motion and fluorescence intensity fluctuations,” Chem. Phys. 4(3), 390–401 (1974).

Ehrlich, J. E.

M. Albota, D. Beljonne, J. Brédas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. Hess, T. Kogej, M. D. Levin, S. Marder, D. McCord-Maughon, J. W. Perry, H. Röckel, M. Rumi, G. Subramaniam, W. W. Webb, X.-L. Wu, C. Xu, “Design of organic molecules with large two-photon absorption cross sections,” Science 281, 1653–1656 (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]

Elson, E.

D. Magde, E. Elson, W. W. Webb, “Thermodynamic fluctuations in a reacting system—measurements by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[CrossRef]

Elson, E. L.

H. Qian, E. L. Elson, “Analysis of confocal laser–microscope optics for 3-D fluorescence correlation spectroscopy,” Appl. Opt. 30, 1185–1195 (1991).
[CrossRef] [PubMed]

H. Qian, E. L. Elson, “On the analysis of high-order moments of fluorescence fluctuations,” Biophys. J. 57, 375–380 (1990).
[CrossRef] [PubMed]

H. Qian, E. L. Elson, “Distribution of molecular aggregation by analysis of fluctuation moments,” Proc. Natl. Acad. Sci. USA 87, 5479–5483 (1990).
[CrossRef] [PubMed]

R. D. Icenogle, E. L. Elson, “Fluorescence correlation spectroscopy and photobleaching recovery of multiple binding reactions. I. Theory and FCS measurements,” Biopolymers 22, 1919–1948 (1983).
[CrossRef] [PubMed]

R. D. Icenogle, E. L. Elson, “Fluorescence correlation spectroscopy and photobleaching recovery of multiple binding reactions. II. FPR and FCS measurements at low and high DNA concentrations,” Biopolymers 22, 1949–1966 (1983).
[CrossRef] [PubMed]

P. F. Fahey, D. E. Koppel, L. S. Barak, D. E. Wolf, E. L. Elson, W. W. Webb, “Lateral diffusion in planar lipid bilayers,” Science 195(4275), 305–306 (1977).

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, A216 (1976).
[CrossRef]

E. L. Elson, W. W. Webb, “Concentration correlation spectroscopy: a new biophysical probe based on occupation number fluctuations,” Ann. Rev. Biophys. Bioeng. 4, 311–334 (1975).
[CrossRef]

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

D. Magde, E. L. Elson, W. W. Webb, “Fluorescence correlation spectroscopy II. An experimental realization,” Biopolymers 13, 29–61 (1974).
[CrossRef] [PubMed]

Fahey, P. F.

P. F. Fahey, D. E. Koppel, L. S. Barak, D. E. Wolf, E. L. Elson, W. W. Webb, “Lateral diffusion in planar lipid bilayers,” Science 195(4275), 305–306 (1977).

Feder, T. J.

T. J. Feder, I. Brust-Mascher, J. P. Slattery, B. Baird, W. W. Webb, “Constrained diffusion or immobile fraction on the cell surfaces: a new interpretation,” Biophys. J. 70, 2767–2773 (1996).
[CrossRef] [PubMed]

Feigenson, G. W.

J. Korlach, P. Schwille, W. W. Webb, G. W. Feigenson, “Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 96, 8461–8466 (1999).
[CrossRef] [PubMed]

Ferguson, D.

D. Ferguson, W. W. Webb, “The vorticity optical probe: a fast multicomponent model,” in Proceedings of the Eighth Biennial Symposium on Turbulence, 26–28 September 1983, University of Missouri, Rolla, Missouri, pp. 272–281.

Fietz, W. A.

R. Beasley, W. A. Fietz, R. W. Rollins, J. Silcox, W. W. Webb, “Annihilation instability in hard superconductors,” Phys. Rev. A 137, 1205–1208 (1965).
[CrossRef]

Fisher, M.

B. Widom, M. Fisher, V. Ambegaokor, J. Langer, J. Wilkens, M. Nelkin, K. Wilson, and their students, Cornell University, Ithaca, N.Y. (personal communication, 1970).

Foquet, M.

J. Korlach, M. Levene, S. W. Turner, D. R. Larson, M. Foquet, H. G. Craighead, W. W. Webb, “A new strategy for sequencing individual molecules of DNA,” Biophys. J. 80, 147 (2001).

M. Levene, D. Larson, J. Korlach, M. Foquet, S. W. Turner, H. G. Craighead, W. W. Webb, “Nanometer constrained observation volumes for high concentration fluorescence correlation spectroscopy and single molecule dynamics,” Biophys. J. 78, 2368 (2000).

Foquet, M. E.

J. Korlach, M. Levene, S. W. Turner, D. R. Larson, M. E. Foquet, H. G. Craighead, W. W. Webb, “A new method for sequencing individual molecules of DNA,” paper presented at the Sixth International Workshop on Single Molecule Detection and Ultra Sensitive Analysis in Life Sciences, Berlin, Germany (2000).

Fredericks, W. J.

D. W. Tank, W. J. Fredericks, L. S. Barak, W. W. Webb, “Electric field-induced redistribution and postfield relaxation of low density lipoprotein receptors on cultured human fibroblasts,” J. Cell Biol. 101, 148–157 (1985).
[CrossRef] [PubMed]

Frish, M. B.

M. B. Frish, W. W. Webb, “Direct measurement of vorticity by optical probe,” J. Fluid Mech. 107, 173–200 (1981).
[CrossRef]

Fu, J.-Y.

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

Gall, K.

P. Kask, K. Palo, D. Ullmann, K. Gall, “Fluorescence-intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. USA 96, 13756–13761 (1999).
[CrossRef] [PubMed]

Ghosh, R. N.

R. N. Ghosh, W. W. Webb, “Automated detection and tracking of individual and clustered cell surface low density lipoprotein receptor molecules,” Biophys. J. 66, 1301–1318 (1994).
[CrossRef] [PubMed]

Gilmer, G. H.

G. H. Gilmer, W. C. Gilmore, J. S. Huang, W. W. Webb, “Diffuse interface in a critical fluid mixture,” Phys. Rev. Lett. 14, 491–494 (1965).
[CrossRef]

Gilmore, W. C.

G. H. Gilmer, W. C. Gilmore, J. S. Huang, W. W. Webb, “Diffuse interface in a critical fluid mixture,” Phys. Rev. Lett. 14, 491–494 (1965).
[CrossRef]

Greengard, P.

D. W. Tank, R. L. Huganir, P. Greengard, W. W. Webb, “Patch-recorded single-channel currents of the purified and reconstituted torpedo acetylcholine receptor,” Proc. Natl. Acad. Sci. USA 80, 5129–5133 (1983).
[CrossRef] [PubMed]

Gross, D.

D. Gross, W. W. Webb, “Molecular counting of low-density lipoprotein particles as individuals and small clusters on cell surfaces,” Biophys. J. 49, 901–911 (1986).
[CrossRef] [PubMed]

D. Gross, W. W. Webb, “Cell surface clustering and mobility of the liganded LDL receptor measured by digital video fluorescence microscopy,” in Spectroscopic Membrane Probes, L. M. Loew, ed. (CRC Press, Boca Raton, Fla., 1988), Vol. II, pp. 19–43.

Hanson, M.

R. H. Köhler, P. Schwille, W. W. Webb, M. Hanson, “Active protein transport through plastid tubules: velocity quantified by fluorescence correlation spectroscopy,” J. Cell Sci. 113, 3921–3930 (2000).
[PubMed]

Harris-Warrick, R. M.

P. Kloppenburg, W. R. Zipfel, W. W. Webb, R. M. Harris-Warrick, “Highly localized Ca2+ accumulation revealed by multiphoton microscopy in an identified motoneuron, and its modulation by dopamine,” J. Neurosci. 20, 2523–2533 (2000).
[PubMed]

Haupts, U.

P. Schwille, U. Haupts, S. Maiti, W. W. Webb, “Molecular dynamics of 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).
[CrossRef] [PubMed]

Heikal, A.

P. Schwille, S. Kummer, 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).
[CrossRef] [PubMed]

Heikal, A. A.

A. A. Heikal, J. Korlach, W. W. Webb, “Time-resolved fluorescence and anisotropy of free and DNA-bound fluorescently labeled nucleotides,” Biophys. J. 80, 8 (2001).

S. T. Hess, A. A. Heikal, G. S. Baird, R. Y. Tsien, W. W. Webb, “Advantageous molecular photophysical fluorescence properties of dsRed and Citrine,” Biophys. J. 80, 7 (2001).

A. A. Heikal, S. T. Hess, P. Schwille, W. W. Webb, “Ultrafast molecular dynamics of selected green fluorescent protein mutants,” Biophys. J. 78, 752 (2000).

S. T. Hess, A. A. Heikal, W. W. Webb, “Reversible light-assisted proton transfer reaction in ecliptic green fluorescent protein,” Biophys. J. 78, 75 (2000).

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

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

Henkels, W. H.

W. H. Henkels, W. W. Webb, “Intrinsic fluctuations in the driven Josephson oscillator,” Phys. Rev. Lett. 26, 1164–1167 (1971).
[CrossRef]

Hess, S.

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

Hess, S. T.

S. T. Hess, A. A. Heikal, G. S. Baird, R. Y. Tsien, W. W. Webb, “Advantageous molecular photophysical fluorescence properties of dsRed and Citrine,” Biophys. J. 80, 7 (2001).

A. A. Heikal, S. T. Hess, P. Schwille, W. W. Webb, “Ultrafast molecular dynamics of selected green fluorescent protein mutants,” Biophys. J. 78, 752 (2000).

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

S. T. Hess, A. A. Heikal, W. W. Webb, “Reversible light-assisted proton transfer reaction in ecliptic green fluorescent protein,” Biophys. J. 78, 75 (2000).

Holowka, D.

J. L. Thomas, D. Holowka, B. Baird, W. W. Webb, “Large-scale co-aggregation of fluorescent lipid probes with cell surface proteins,” J. Cell Biol. 125, 795–802 (1994).
[CrossRef] [PubMed]

T. A. Ryan, J. Myers, D. Holowka, B. Baird, W. W. Webb, “Molecular crowding on the cell surface,” Science 239, 61–64 (1988).
[CrossRef] [PubMed]

Huang, J. S.

J. S. Huang, W. W. Webb, “Diffuse interface in a critical fluid mixture,” J. Chem. Phys. 50, 3677–3693 (1969).
[CrossRef]

J. S. Huang, W. W. Webb, “Viscous damping of thermal excitations on the interface of critical fluid mixtures,” Phys. Rev. Lett. 23, 160–163 (1969).
[CrossRef]

G. H. Gilmer, W. C. Gilmore, J. S. Huang, W. W. Webb, “Diffuse interface in a critical fluid mixture,” Phys. Rev. Lett. 14, 491–494 (1965).
[CrossRef]

Hudspeth, A. J.

W. Denk, W. W. Webb, A. J. Hudspeth, “Mechanical properties of sensory hair bundles are reflected in their Brownian motion measured with a laser differential interferometer,” Proc. Natl. Acad. Sci. USA 86, 5371–5375 (1989).
[CrossRef] [PubMed]

Huganir, R. L.

D. W. Tank, R. L. Huganir, P. Greengard, W. W. Webb, “Patch-recorded single-channel currents of the purified and reconstituted torpedo acetylcholine receptor,” Proc. Natl. Acad. Sci. USA 80, 5129–5133 (1983).
[CrossRef] [PubMed]

Icenogle, R. D.

R. D. Icenogle, E. L. Elson, “Fluorescence correlation spectroscopy and photobleaching recovery of multiple binding reactions. II. FPR and FCS measurements at low and high DNA concentrations,” Biopolymers 22, 1949–1966 (1983).
[CrossRef] [PubMed]

R. D. Icenogle, E. L. Elson, “Fluorescence correlation spectroscopy and photobleaching recovery of multiple binding reactions. I. Theory and FCS measurements,” Biopolymers 22, 1919–1948 (1983).
[CrossRef] [PubMed]

Jenkins, J. T.

M. B. Schneider, J. T. Jenkins, W. W. Webb, “Thermal fluctuations of large cylindrical phospholipid vesicles,” Biophys. J. 45, 891–899 (1984).
[CrossRef] [PubMed]

M. B. Schneider, J. T. Jenkins, W. W. Webb, “Thermal fluctuations of large quasi-spherical bimolecular phospholipid vesicles,” J. Phys. (Paris) 45, 1457–1472 (1984).
[CrossRef]

Johnson, D. C.

N. O. Peterson, D. C. Johnson, M. J. Schlessinger, “Scanning fluorescence correlation spectroscopy. 2. Application to virus glycoprotein aggregation,” Biophys. J. 49, 817–820 (1986).
[CrossRef]

Kask, P.

P. Kask, K. Palo, D. Ullmann, K. Gall, “Fluorescence-intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. USA 96, 13756–13761 (1999).
[CrossRef] [PubMed]

Keolian, R. M.

W. Denk, R. M. Keolian, W. W. Webb, “Mechanical response of frog saccular hair bundles to the aminoglycoside block of mechano-electrical transduction,” J. Neurophysiol. 68, 927–932 (1992).
[PubMed]

Kloppenburg, P.

P. Kloppenburg, W. R. Zipfel, W. W. Webb, R. M. Harris-Warrick, “Highly localized Ca2+ accumulation revealed by multiphoton microscopy in an identified motoneuron, and its modulation by dopamine,” J. Neurosci. 20, 2523–2533 (2000).
[PubMed]

Kogej, T.

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

Köhler, R. H.

R. H. Köhler, P. Schwille, W. W. Webb, M. Hanson, “Active protein transport through plastid tubules: velocity quantified by fluorescence correlation spectroscopy,” J. Cell Sci. 113, 3921–3930 (2000).
[PubMed]

Koppel, D. E.

P. F. Fahey, D. E. Koppel, L. S. Barak, D. E. Wolf, E. L. Elson, W. W. Webb, “Lateral diffusion in planar lipid bilayers,” Science 195(4275), 305–306 (1977).

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, A216 (1976).
[CrossRef]

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

Korlach, J.

M. Levene, J. Korlach, S. W. Turner, H. G. Craighead, W. W. Webb, “Near-field apertures for reduced-volume fluorescence correlation spectroscopy and single molecule studies,” Biophys. J. 80, 149 (2001).

A. A. Heikal, J. Korlach, W. W. Webb, “Time-resolved fluorescence and anisotropy of free and DNA-bound fluorescently labeled nucleotides,” Biophys. J. 80, 8 (2001).

J. Korlach, M. Levene, S. W. Turner, D. R. Larson, M. Foquet, H. G. Craighead, W. W. Webb, “A new strategy for sequencing individual molecules of DNA,” Biophys. J. 80, 147 (2001).

M. Levene, D. Larson, J. Korlach, M. Foquet, S. W. Turner, H. G. Craighead, W. W. Webb, “Nanometer constrained observation volumes for high concentration fluorescence correlation spectroscopy and single molecule dynamics,” Biophys. J. 78, 2368 (2000).

J. Korlach, P. Schwille, W. W. Webb, G. W. Feigenson, “Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 96, 8461–8466 (1999).
[CrossRef] [PubMed]

P. Schwille, J. Korlach, W. W. Webb, “Fluorescence correlation spectroscopy with single-molecule sensitivity on cell and model membranes,” Cytometry 36, 176–182 (1999).
[CrossRef] [PubMed]

J. Korlach, M. Levene, S. W. Turner, D. R. Larson, M. E. Foquet, H. G. Craighead, W. W. Webb, “A new method for sequencing individual molecules of DNA,” paper presented at the Sixth International Workshop on Single Molecule Detection and Ultra Sensitive Analysis in Life Sciences, Berlin, Germany (2000).

Kummer, S.

P. Schwille, S. Kummer, 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).
[CrossRef] [PubMed]

Labusch, R.

R. Beasley, R. Labusch, W. W. Webb, “Flux creep in type-II superconductors,” Phys. Rev. 181, 682–700 (1969).
[CrossRef]

Langer, J.

B. Widom, M. Fisher, V. Ambegaokor, J. Langer, J. Wilkens, M. Nelkin, K. Wilson, and their students, Cornell University, Ithaca, N.Y. (personal communication, 1970).

Larson, D.

M. Levene, D. Larson, J. Korlach, M. Foquet, S. W. Turner, H. G. Craighead, W. W. Webb, “Nanometer constrained observation volumes for high concentration fluorescence correlation spectroscopy and single molecule dynamics,” Biophys. J. 78, 2368 (2000).

Larson, D. R.

D. R. Larson, M. Levene, S. W. Turner, H. G. Craighead, W. W. Webb, “Fluorescence correlation spectroscopy in zeptoliter volumes,” Biophys. J. 80, 149 (2001).

J. Korlach, M. Levene, S. W. Turner, D. R. Larson, M. Foquet, H. G. Craighead, W. W. Webb, “A new strategy for sequencing individual molecules of DNA,” Biophys. J. 80, 147 (2001).

J. Korlach, M. Levene, S. W. Turner, D. R. Larson, M. E. Foquet, H. G. Craighead, W. W. Webb, “A new method for sequencing individual molecules of DNA,” paper presented at the Sixth International Workshop on Single Molecule Detection and Ultra Sensitive Analysis in Life Sciences, Berlin, Germany (2000).

Leiderer, P.

P. Leiderer, D. R. Nelson, D. R. Watts, W. W. Webb, “Tricritical slowing down of superfluid dynamics in 3He–4He mixtures,” Phys. Rev. Lett. 34, 1080–1083 (1975).
[CrossRef]

P. Leiderer, D. R. Watts, W. W. Webb, “Light scattering by 3He–4He mixtures near the tricritical point,” Phys. Rev. Lett. 33, 483–485 (1974).
[CrossRef]

Levene, M.

J. Korlach, M. Levene, S. W. Turner, D. R. Larson, M. Foquet, H. G. Craighead, W. W. Webb, “A new strategy for sequencing individual molecules of DNA,” Biophys. J. 80, 147 (2001).

M. Levene, J. Korlach, S. W. Turner, H. G. Craighead, W. W. Webb, “Near-field apertures for reduced-volume fluorescence correlation spectroscopy and single molecule studies,” Biophys. J. 80, 149 (2001).

D. R. Larson, M. Levene, S. W. Turner, H. G. Craighead, W. W. Webb, “Fluorescence correlation spectroscopy in zeptoliter volumes,” Biophys. J. 80, 149 (2001).

M. Levene, D. Larson, J. Korlach, M. Foquet, S. W. Turner, H. G. Craighead, W. W. Webb, “Nanometer constrained observation volumes for high concentration fluorescence correlation spectroscopy and single molecule dynamics,” Biophys. J. 78, 2368 (2000).

J. Korlach, M. Levene, S. W. Turner, D. R. Larson, M. E. Foquet, H. G. Craighead, W. W. Webb, “A new method for sequencing individual molecules of DNA,” paper presented at the Sixth International Workshop on Single Molecule Detection and Ultra Sensitive Analysis in Life Sciences, Berlin, Germany (2000).

Levin, M. D.

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

Lukens, J. E.

J. E. Lukens, R. J. Warburton, W. W. Webb, “Onset of quantized thermal fluctuations in ‘one-dimensional’ superconductors,” Phys. Rev. Lett. 25, 1180–1184 (1970).
[CrossRef]

Magde, D.

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

D. Magde, E. L. Elson, W. W. Webb, “Fluorescence correlation spectroscopy II. An experimental realization,” Biopolymers 13, 29–61 (1974).
[CrossRef] [PubMed]

D. Magde, E. Elson, W. W. Webb, “Thermodynamic fluctuations in a reacting system—measurements by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[CrossRef]

Maiti, S.

P. Schwille, U. Haupts, S. Maiti, W. W. Webb, “Molecular dynamics of 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).
[CrossRef] [PubMed]

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, W. W. Webb, “Measuring serotonin distribution in live cells with three-photon excitation,” Science 275, 530–532 (1997).
[CrossRef] [PubMed]

Mak, D.-O. D.

D.-O. D. Mak, W. W. Webb, “Conductivity noise in transmembrane ion channels due to ion concentration fluctuations via diffusion,” Biophys. J. 72, 1153–1164 (1997).
[CrossRef] [PubMed]

D.-O. D. Mak, W. W. Webb, “Molecular dynamics of alamethicin transmembrane channels from open-channel current noise analysis,” Biophys. J. 69, 2337–2349 (1995).
[CrossRef] [PubMed]

Mantese, J. V.

J. V. Mantese, W. A. Curtin, W. W. Webb, “Two-component model for the resistivity and noise of tunneling metal-insulator composites,” Phys. Rev. B 33, 7897–7901 (1986).
[CrossRef]

J. V. Mantese, W. W. Webb, “1/f noise of granular metal-insulator composites,” Phys. Rev. Lett. 55, 2212–2215 (1985).
[CrossRef] [PubMed]

Marder, S.

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

McCord-Maughon, D.

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

Mertz, J.

Miesenböch, G.

D. A. DeAngelis, G. Miesenböch, B. V. Zemelman, J. E. Rothman, “PRIM: proximity imaging of green fluorescent protein-tagged polypeptides,” Proc. Natl. Acad. Sci. USA 95, 12312–12316 (1998).
[CrossRef]

Moerner, W. E.

P. Schwille, S. Kummer, 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).
[CrossRef] [PubMed]

R. M. Dickson, A. B. Cubitt, R. Y. Tsien, W. E. Moerner, “On/off blinking and switching behaviour of single molecules of green fluorescent protein,” Nature 388(6840), 355–358 (1997).

Myers, J.

T. Ryan, J. Myers, W. W. Webb, “Molecular interactions on the cell surface revealed by electrophoresis,” Biol. Bull. 176(S), 164–169 (1989).

T. A. Ryan, J. Myers, D. Holowka, B. Baird, W. W. Webb, “Molecular crowding on the cell surface,” Science 239, 61–64 (1988).
[CrossRef] [PubMed]

Nelkin, M.

B. Widom, M. Fisher, V. Ambegaokor, J. Langer, J. Wilkens, M. Nelkin, K. Wilson, and their students, Cornell University, Ithaca, N.Y. (personal communication, 1970).

Nelson, D. R.

P. Leiderer, D. R. Nelson, D. R. Watts, W. W. Webb, “Tricritical slowing down of superfluid dynamics in 3He–4He mixtures,” Phys. Rev. Lett. 34, 1080–1083 (1975).
[CrossRef]

Opsahl, L. R.

L. R. Opsahl, W. W. Webb, “Transduction of membrane tension by the ion channel alamethicin,” Biophys. J. 66, 71–74 (1994).
[CrossRef] [PubMed]

Palo, K.

P. Kask, K. Palo, D. Ullmann, K. Gall, “Fluorescence-intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. USA 96, 13756–13761 (1999).
[CrossRef] [PubMed]

Pecora, R.

B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

Perry, J. W.

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

Peterson, N. O.

N. O. Peterson, D. C. Johnson, M. J. Schlessinger, “Scanning fluorescence correlation spectroscopy. 2. Application to virus glycoprotein aggregation,” Biophys. J. 49, 817–820 (1986).
[CrossRef]

Piston, D. W.

D. R. Sandison, D. W. Piston, R. M. Williams, W. W. Webb, “Quantitative comparison of background rejection, signal-to-noise ratio, and resolution in confocal and full-field laser scanning microscopes,” Appl. Opt. 34, 3576–3588 (1995).
[CrossRef] [PubMed]

M. Williams, D. W. Piston, W. W. Webb, “Two-photon molecular excitation provides intrinsic three-dimensional resolution for laser-based microscopy and microphotochemistry,” FASEB J. 8, 804–813 (1994).
[PubMed]

Pyenta, P.

P. Pyenta, P. Schwille, School of Applied and Engineering Physics, Cornell University, 233 Clark Hall, Ithaca, N.Y. 14853-0001 (personal communication, 1998).

Qian, H.

H. Qian, E. L. Elson, “Analysis of confocal laser–microscope optics for 3-D fluorescence correlation spectroscopy,” Appl. Opt. 30, 1185–1195 (1991).
[CrossRef] [PubMed]

H. Qian, “On the statistics of fluorescence correlation spectroscopy,” Biophys. Chem. 38(1-2), 49–57 (1990).
[PubMed]

H. Qian, E. L. Elson, “Distribution of molecular aggregation by analysis of fluctuation moments,” Proc. Natl. Acad. Sci. USA 87, 5479–5483 (1990).
[CrossRef] [PubMed]

H. Qian, E. L. Elson, “On the analysis of high-order moments of fluorescence fluctuations,” Biophys. J. 57, 375–380 (1990).
[CrossRef] [PubMed]

Rigler, R.

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

A. Ehrenberg, R. Rigler, “Rotational Brownian-motion and fluorescence intensity fluctuations,” Chem. Phys. 4(3), 390–401 (1974).

Röckel, H.

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

Rollins, R. W.

R. Beasley, W. A. Fietz, R. W. Rollins, J. Silcox, W. W. Webb, “Annihilation instability in hard superconductors,” Phys. Rev. A 137, 1205–1208 (1965).
[CrossRef]

Rothman, J. E.

D. A. DeAngelis, G. Miesenböch, B. V. Zemelman, J. E. Rothman, “PRIM: proximity imaging of green fluorescent protein-tagged polypeptides,” Proc. Natl. Acad. Sci. USA 95, 12312–12316 (1998).
[CrossRef]

Rumi, M.

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

Ryan, T.

T. Ryan, J. Myers, W. W. Webb, “Molecular interactions on the cell surface revealed by electrophoresis,” Biol. Bull. 176(S), 164–169 (1989).

Ryan, T. A.

T. A. Ryan, J. Myers, D. Holowka, B. Baird, W. W. Webb, “Molecular crowding on the cell surface,” Science 239, 61–64 (1988).
[CrossRef] [PubMed]

Sandison, D. R.

Schlessinger, J.

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, A216 (1976).
[CrossRef]

Schlessinger, M. J.

N. O. Peterson, D. C. Johnson, M. J. Schlessinger, “Scanning fluorescence correlation spectroscopy. 2. Application to virus glycoprotein aggregation,” Biophys. J. 49, 817–820 (1986).
[CrossRef]

Schneider, M. B.

M. B. Schneider, J. T. Jenkins, W. W. Webb, “Thermal fluctuations of large cylindrical phospholipid vesicles,” Biophys. J. 45, 891–899 (1984).
[CrossRef] [PubMed]

M. B. Schneider, J. T. Jenkins, W. W. Webb, “Thermal fluctuations of large quasi-spherical bimolecular phospholipid vesicles,” J. Phys. (Paris) 45, 1457–1472 (1984).
[CrossRef]

Schwille, P.

R. H. Köhler, P. Schwille, W. W. Webb, M. Hanson, “Active protein transport through plastid tubules: velocity quantified by fluorescence correlation spectroscopy,” J. Cell Sci. 113, 3921–3930 (2000).
[PubMed]

P. Schwille, S. Kummer, 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).
[CrossRef] [PubMed]

A. A. Heikal, S. T. Hess, P. Schwille, W. W. Webb, “Ultrafast molecular dynamics of selected green fluorescent protein mutants,” Biophys. J. 78, 752 (2000).

P. Schwille, J. Korlach, W. W. Webb, “Fluorescence correlation spectroscopy with single-molecule sensitivity on cell and model membranes,” Cytometry 36, 176–182 (1999).
[CrossRef] [PubMed]

J. Korlach, P. Schwille, W. W. Webb, G. W. Feigenson, “Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 96, 8461–8466 (1999).
[CrossRef] [PubMed]

P. Schwille, U. Haupts, S. Maiti, W. W. Webb, “Molecular dynamics of 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]

P. Pyenta, P. Schwille, School of Applied and Engineering Physics, Cornell University, 233 Clark Hall, Ithaca, N.Y. 14853-0001 (personal communication, 1998).

Scofield, J. H.

J. H. Scofield, W. W. Webb, “Resistance fluctuations due to hydrogen diffusion in niobium thin films,” Phys. Rev. Lett. 54, 353–356 (1985).
[CrossRef] [PubMed]

Shear, J. B.

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, W. W. Webb, “Measuring serotonin distribution in live cells with three-photon excitation,” Science 275, 530–532 (1997).
[CrossRef] [PubMed]

Silcox, J.

R. Beasley, W. A. Fietz, R. W. Rollins, J. Silcox, W. W. Webb, “Annihilation instability in hard superconductors,” Phys. Rev. A 137, 1205–1208 (1965).
[CrossRef]

Slattery, J. P.

T. J. Feder, I. Brust-Mascher, J. P. Slattery, B. Baird, W. W. Webb, “Constrained diffusion or immobile fraction on the cell surfaces: a new interpretation,” Biophys. J. 70, 2767–2773 (1996).
[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]

Subramaniam, G.

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

Tank, D. W.

D. W. Tank, W. J. Fredericks, L. S. Barak, W. W. Webb, “Electric field-induced redistribution and postfield relaxation of low density lipoprotein receptors on cultured human fibroblasts,” J. Cell Biol. 101, 148–157 (1985).
[CrossRef] [PubMed]

D. W. Tank, R. L. Huganir, P. Greengard, W. W. Webb, “Patch-recorded single-channel currents of the purified and reconstituted torpedo acetylcholine receptor,” Proc. Natl. Acad. Sci. USA 80, 5129–5133 (1983).
[CrossRef] [PubMed]

Thomas, J.

J. Thomas, W. W. Webb, “Fluorescence photobleaching recovery: a probe of membrane dynamics,” in Non-Invasive Techniques in Cell Biology, S. Grinstein, K. Foskett, eds. (Wiley, New York, 1990), pp. 129–152.

Thomas, J. L.

J. L. Thomas, D. Holowka, B. Baird, W. W. Webb, “Large-scale co-aggregation of fluorescent lipid probes with cell surface proteins,” J. Cell Biol. 125, 795–802 (1994).
[CrossRef] [PubMed]

Thompson, N. L.

N. L. Thompson, “Fluorescence correlation spectroscopy,” in Topics in Fluorescence Spectroscopy VI, J. R. Lakowicz, ed. (Plenum, New York, 1991), pp. 337–338.

Tsien, R. Y.

S. T. Hess, A. A. Heikal, G. S. Baird, R. Y. Tsien, W. W. Webb, “Advantageous molecular photophysical fluorescence properties of dsRed and Citrine,” Biophys. J. 80, 7 (2001).

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

R. M. Dickson, A. B. Cubitt, R. Y. Tsien, W. E. Moerner, “On/off blinking and switching behaviour of single molecules of green fluorescent protein,” Nature 388(6840), 355–358 (1997).

Turner, S. W.

D. R. Larson, M. Levene, S. W. Turner, H. G. Craighead, W. W. Webb, “Fluorescence correlation spectroscopy in zeptoliter volumes,” Biophys. J. 80, 149 (2001).

M. Levene, J. Korlach, S. W. Turner, H. G. Craighead, W. W. Webb, “Near-field apertures for reduced-volume fluorescence correlation spectroscopy and single molecule studies,” Biophys. J. 80, 149 (2001).

J. Korlach, M. Levene, S. W. Turner, D. R. Larson, M. Foquet, H. G. Craighead, W. W. Webb, “A new strategy for sequencing individual molecules of DNA,” Biophys. J. 80, 147 (2001).

M. Levene, D. Larson, J. Korlach, M. Foquet, S. W. Turner, H. G. Craighead, W. W. Webb, “Nanometer constrained observation volumes for high concentration fluorescence correlation spectroscopy and single molecule dynamics,” Biophys. J. 78, 2368 (2000).

J. Korlach, M. Levene, S. W. Turner, D. R. Larson, M. E. Foquet, H. G. Craighead, W. W. Webb, “A new method for sequencing individual molecules of DNA,” paper presented at the Sixth International Workshop on Single Molecule Detection and Ultra Sensitive Analysis in Life Sciences, Berlin, Germany (2000).

Tyndall, J.

J. Tyndall, “Scientific materialism,” in Fragments of Science, A Series of Detached Essays, Addresses and Reviews (Longmans, Green, London, 1892), Vol. 2, p. 77.

Ullmann, D.

P. Kask, K. Palo, D. Ullmann, K. Gall, “Fluorescence-intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. USA 96, 13756–13761 (1999).
[CrossRef] [PubMed]

Wack, D. C.

D. C. Wack, W. W. Webb, “Measurement by x-ray diffraction methods of the layer compressional elastic constant B in the lyotropic smectic-A (La) phase of the lecithin–water system,” Phys. Rev. A 40, 1627–1636 (1989).
[CrossRef] [PubMed]

Warburton, R. J.

J. E. Lukens, R. J. Warburton, W. W. Webb, “Onset of quantized thermal fluctuations in ‘one-dimensional’ superconductors,” Phys. Rev. Lett. 25, 1180–1184 (1970).
[CrossRef]

W. W. Webb, R. J. Warburton, “Intrinsic quantum fluctuations in uniform filamentary superconductors,” Phys. Rev. Lett. 30, 461–465 (1968).
[CrossRef]

Watts, D. R.

P. Leiderer, D. R. Nelson, D. R. Watts, W. W. Webb, “Tricritical slowing down of superfluid dynamics in 3He–4He mixtures,” Phys. Rev. Lett. 34, 1080–1083 (1975).
[CrossRef]

P. Leiderer, D. R. Watts, W. W. Webb, “Light scattering by 3He–4He mixtures near the tricritical point,” Phys. Rev. Lett. 33, 483–485 (1974).
[CrossRef]

Webb, W. W.

A. A. Heikal, J. Korlach, W. W. Webb, “Time-resolved fluorescence and anisotropy of free and DNA-bound fluorescently labeled nucleotides,” Biophys. J. 80, 8 (2001).

J. Korlach, M. Levene, S. W. Turner, D. R. Larson, M. Foquet, H. G. Craighead, W. W. Webb, “A new strategy for sequencing individual molecules of DNA,” Biophys. J. 80, 147 (2001).

M. Levene, J. Korlach, S. W. Turner, H. G. Craighead, W. W. Webb, “Near-field apertures for reduced-volume fluorescence correlation spectroscopy and single molecule studies,” Biophys. J. 80, 149 (2001).

D. R. Larson, M. Levene, S. W. Turner, H. G. Craighead, W. W. Webb, “Fluorescence correlation spectroscopy in zeptoliter volumes,” Biophys. J. 80, 149 (2001).

S. T. Hess, A. A. Heikal, G. S. Baird, R. Y. Tsien, W. W. Webb, “Advantageous molecular photophysical fluorescence properties of dsRed and Citrine,” Biophys. J. 80, 7 (2001).

A. A. Heikal, S. T. Hess, P. Schwille, W. W. Webb, “Ultrafast molecular dynamics of selected green fluorescent protein mutants,” Biophys. J. 78, 752 (2000).

M. Levene, D. Larson, J. Korlach, M. Foquet, S. W. Turner, H. G. Craighead, W. W. Webb, “Nanometer constrained observation volumes for high concentration fluorescence correlation spectroscopy and single molecule dynamics,” Biophys. J. 78, 2368 (2000).

P. Schwille, S. Kummer, 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).
[CrossRef] [PubMed]

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

S. T. Hess, A. A. Heikal, W. W. Webb, “Reversible light-assisted proton transfer reaction in ecliptic green fluorescent protein,” Biophys. J. 78, 75 (2000).

R. H. Köhler, P. Schwille, W. W. Webb, M. Hanson, “Active protein transport through plastid tubules: velocity quantified by fluorescence correlation spectroscopy,” J. Cell Sci. 113, 3921–3930 (2000).
[PubMed]

P. Kloppenburg, W. R. Zipfel, W. W. Webb, R. M. Harris-Warrick, “Highly localized Ca2+ accumulation revealed by multiphoton microscopy in an identified motoneuron, and its modulation by dopamine,” J. Neurosci. 20, 2523–2533 (2000).
[PubMed]

E. Brown, E. Wu, W. Zipfel, W. W. Webb, “Measurement of molecular diffusion in solution by multiphoton fluorescence photobleaching recovery,” Biophys. J. 77, 2837–2849 (1999).
[CrossRef] [PubMed]

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

J. Korlach, P. Schwille, W. W. Webb, G. W. Feigenson, “Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 96, 8461–8466 (1999).
[CrossRef] [PubMed]

P. Schwille, J. Korlach, W. W. Webb, “Fluorescence correlation spectroscopy with single-molecule sensitivity on cell and model membranes,” Cytometry 36, 176–182 (1999).
[CrossRef] [PubMed]

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

D.-O. D. Mak, W. W. Webb, “Conductivity noise in transmembrane ion channels due to ion concentration fluctuations via diffusion,” Biophys. J. 72, 1153–1164 (1997).
[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).
[CrossRef] [PubMed]

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, W. W. Webb, “Measuring serotonin distribution in live cells with three-photon excitation,” Science 275, 530–532 (1997).
[CrossRef] [PubMed]

T. J. Feder, I. Brust-Mascher, J. P. Slattery, B. Baird, W. W. Webb, “Constrained diffusion or immobile fraction on the cell surfaces: a new interpretation,” Biophys. J. 70, 2767–2773 (1996).
[CrossRef] [PubMed]

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

D.-O. D. Mak, W. W. Webb, “Molecular dynamics of alamethicin transmembrane channels from open-channel current noise analysis,” Biophys. J. 69, 2337–2349 (1995).
[CrossRef] [PubMed]

D. R. Sandison, D. W. Piston, R. M. Williams, W. W. Webb, “Quantitative comparison of background rejection, signal-to-noise ratio, and resolution in confocal and full-field laser scanning microscopes,” Appl. Opt. 34, 3576–3588 (1995).
[CrossRef] [PubMed]

J. Mertz, C. Xu, W. W. Webb, “Single-molecule detection by two-photon excited fluorescence,” Opt. Lett. 20, 2532–2534 (1995).
[CrossRef]

R. N. Ghosh, W. W. Webb, “Automated detection and tracking of individual and clustered cell surface low density lipoprotein receptor molecules,” Biophys. J. 66, 1301–1318 (1994).
[CrossRef] [PubMed]

L. R. Opsahl, W. W. Webb, “Transduction of membrane tension by the ion channel alamethicin,” Biophys. J. 66, 71–74 (1994).
[CrossRef] [PubMed]

M. Williams, D. W. Piston, W. W. Webb, “Two-photon molecular excitation provides intrinsic three-dimensional resolution for laser-based microscopy and microphotochemistry,” FASEB J. 8, 804–813 (1994).
[PubMed]

J. L. Thomas, D. Holowka, B. Baird, W. W. Webb, “Large-scale co-aggregation of fluorescent lipid probes with cell surface proteins,” J. Cell Biol. 125, 795–802 (1994).
[CrossRef] [PubMed]

W. Denk, R. M. Keolian, W. W. Webb, “Mechanical response of frog saccular hair bundles to the aminoglycoside block of mechano-electrical transduction,” J. Neurophysiol. 68, 927–932 (1992).
[PubMed]

N. M. Zimmerman, W. W. Webb, “1/f resistance noise complements anelasticity measurements of hydrogen motion in amorphous Pd80Si20,” Phys. Rev. Lett. 65, 1040–1043 (1990).
[CrossRef] [PubMed]

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

W. Denk, W. W. Webb, “Optical measurement of picometer displacements of transparent, microscopic objects,” Appl. Opt. 29, 2382–2391 (1990).
[CrossRef] [PubMed]

W. Denk, W. W. Webb, A. J. Hudspeth, “Mechanical properties of sensory hair bundles are reflected in their Brownian motion measured with a laser differential interferometer,” Proc. Natl. Acad. Sci. USA 86, 5371–5375 (1989).
[CrossRef] [PubMed]

W. Denk, W. W. Webb, “Thermal-noise-limited transduction observed in mechanosensory receptors of the inner ear,” Phys. Rev. Lett. 63, 207–210 (1989).
[CrossRef] [PubMed]

T. Ryan, J. Myers, W. W. Webb, “Molecular interactions on the cell surface revealed by electrophoresis,” Biol. Bull. 176(S), 164–169 (1989).

D. C. Wack, W. W. Webb, “Measurement by x-ray diffraction methods of the layer compressional elastic constant B in the lyotropic smectic-A (La) phase of the lecithin–water system,” Phys. Rev. A 40, 1627–1636 (1989).
[CrossRef] [PubMed]

T. A. Ryan, J. Myers, D. Holowka, B. Baird, W. W. Webb, “Molecular crowding on the cell surface,” Science 239, 61–64 (1988).
[CrossRef] [PubMed]

D. Gross, W. W. Webb, “Molecular counting of low-density lipoprotein particles as individuals and small clusters on cell surfaces,” Biophys. J. 49, 901–911 (1986).
[CrossRef] [PubMed]

J. V. Mantese, W. A. Curtin, W. W. Webb, “Two-component model for the resistivity and noise of tunneling metal-insulator composites,” Phys. Rev. B 33, 7897–7901 (1986).
[CrossRef]

J. H. Scofield, W. W. Webb, “Resistance fluctuations due to hydrogen diffusion in niobium thin films,” Phys. Rev. Lett. 54, 353–356 (1985).
[CrossRef] [PubMed]

J. V. Mantese, W. W. Webb, “1/f noise of granular metal-insulator composites,” Phys. Rev. Lett. 55, 2212–2215 (1985).
[CrossRef] [PubMed]

D. W. Tank, W. J. Fredericks, L. S. Barak, W. W. Webb, “Electric field-induced redistribution and postfield relaxation of low density lipoprotein receptors on cultured human fibroblasts,” J. Cell Biol. 101, 148–157 (1985).
[CrossRef] [PubMed]

M. B. Schneider, J. T. Jenkins, W. W. Webb, “Thermal fluctuations of large quasi-spherical bimolecular phospholipid vesicles,” J. Phys. (Paris) 45, 1457–1472 (1984).
[CrossRef]

M. B. Schneider, J. T. Jenkins, W. W. Webb, “Thermal fluctuations of large cylindrical phospholipid vesicles,” Biophys. J. 45, 891–899 (1984).
[CrossRef] [PubMed]

D. W. Tank, R. L. Huganir, P. Greengard, W. W. Webb, “Patch-recorded single-channel currents of the purified and reconstituted torpedo acetylcholine receptor,” Proc. Natl. Acad. Sci. USA 80, 5129–5133 (1983).
[CrossRef] [PubMed]

L. S. Barak, W. W. Webb, “Diffusion of low density lipoprotein–receptor complex on human fibroblasts,” J. Cell Biol. 95, 846–852 (1982).
[CrossRef] [PubMed]

M. B. Frish, W. W. Webb, “Direct measurement of vorticity by optical probe,” J. Fluid Mech. 107, 173–200 (1981).
[CrossRef]

P. F. Fahey, D. E. Koppel, L. S. Barak, D. E. Wolf, E. L. Elson, W. W. Webb, “Lateral diffusion in planar lipid bilayers,” Science 195(4275), 305–306 (1977).

W. W. Webb, “Applications of fluorescence correlation spectroscopy,” Quart. Rev. Biophys. 9, 49–68 (1976).
[CrossRef]

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, A216 (1976).
[CrossRef]

E. L. Elson, W. W. Webb, “Concentration correlation spectroscopy: a new biophysical probe based on occupation number fluctuations,” Ann. Rev. Biophys. Bioeng. 4, 311–334 (1975).
[CrossRef]

P. Leiderer, D. R. Nelson, D. R. Watts, W. W. Webb, “Tricritical slowing down of superfluid dynamics in 3He–4He mixtures,” Phys. Rev. Lett. 34, 1080–1083 (1975).
[CrossRef]

D. Magde, E. L. Elson, W. W. Webb, “Fluorescence correlation spectroscopy II. An experimental realization,” Biopolymers 13, 29–61 (1974).
[CrossRef] [PubMed]

P. Leiderer, D. R. Watts, W. W. Webb, “Light scattering by 3He–4He mixtures near the tricritical point,” Phys. Rev. Lett. 33, 483–485 (1974).
[CrossRef]

D. Magde, E. Elson, W. W. Webb, “Thermodynamic fluctuations in a reacting system—measurements by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[CrossRef]

W. H. Henkels, W. W. Webb, “Intrinsic fluctuations in the driven Josephson oscillator,” Phys. Rev. Lett. 26, 1164–1167 (1971).
[CrossRef]

J. E. Lukens, R. J. Warburton, W. W. Webb, “Onset of quantized thermal fluctuations in ‘one-dimensional’ superconductors,” Phys. Rev. Lett. 25, 1180–1184 (1970).
[CrossRef]

R. Beasley, R. Labusch, W. W. Webb, “Flux creep in type-II superconductors,” Phys. Rev. 181, 682–700 (1969).
[CrossRef]

J. S. Huang, W. W. Webb, “Viscous damping of thermal excitations on the interface of critical fluid mixtures,” Phys. Rev. Lett. 23, 160–163 (1969).
[CrossRef]

J. S. Huang, W. W. Webb, “Diffuse interface in a critical fluid mixture,” J. Chem. Phys. 50, 3677–3693 (1969).
[CrossRef]

W. W. Webb, R. J. Warburton, “Intrinsic quantum fluctuations in uniform filamentary superconductors,” Phys. Rev. Lett. 30, 461–465 (1968).
[CrossRef]

R. Beasley, W. A. Fietz, R. W. Rollins, J. Silcox, W. W. Webb, “Annihilation instability in hard superconductors,” Phys. Rev. A 137, 1205–1208 (1965).
[CrossRef]

G. H. Gilmer, W. C. Gilmore, J. S. Huang, W. W. Webb, “Diffuse interface in a critical fluid mixture,” Phys. Rev. Lett. 14, 491–494 (1965).
[CrossRef]

W. W. Webb, “Fluorescence correlation spectroscopy: genesis, evolution, maturation and prognosis,” in Fluorescence Correlation Spectroscopy, R. Rigler, E. Elson, eds. (Springer-Verlag, Berlin, 2001), Chap. 14, pp. 305–330.
[CrossRef]

C. Xu, W. W. Webb, “Multiphoton excitation of molecular fluorophores and nonlinear laser microscopy,” in Topics in Fluorescence Spectroscopy: Nonlinear and Two-Photon-Induced Fluorescence, J. Lakowicz, ed. (Plenum, N.Y., 1997), Vol. 5, pp. 471–540.
[CrossRef]

D. Gross, W. W. Webb, “Cell surface clustering and mobility of the liganded LDL receptor measured by digital video fluorescence microscopy,” in Spectroscopic Membrane Probes, L. M. Loew, ed. (CRC Press, Boca Raton, Fla., 1988), Vol. II, pp. 19–43.

D. Ferguson, W. W. Webb, “The vorticity optical probe: a fast multicomponent model,” in Proceedings of the Eighth Biennial Symposium on Turbulence, 26–28 September 1983, University of Missouri, Rolla, Missouri, pp. 272–281.

J. Korlach, M. Levene, S. W. Turner, D. R. Larson, M. E. Foquet, H. G. Craighead, W. W. Webb, “A new method for sequencing individual molecules of DNA,” paper presented at the Sixth International Workshop on Single Molecule Detection and Ultra Sensitive Analysis in Life Sciences, Berlin, Germany (2000).

J. Thomas, W. W. Webb, “Fluorescence photobleaching recovery: a probe of membrane dynamics,” in Non-Invasive Techniques in Cell Biology, S. Grinstein, K. Foskett, eds. (Wiley, New York, 1990), pp. 129–152.

Widom, B.

B. Widom, M. Fisher, V. Ambegaokor, J. Langer, J. Wilkens, M. Nelkin, K. Wilson, and their students, Cornell University, Ithaca, N.Y. (personal communication, 1970).

Wilkens, J.

B. Widom, M. Fisher, V. Ambegaokor, J. Langer, J. Wilkens, M. Nelkin, K. Wilson, and their students, Cornell University, Ithaca, N.Y. (personal communication, 1970).

Williams, M.

M. Williams, D. W. Piston, W. W. Webb, “Two-photon molecular excitation provides intrinsic three-dimensional resolution for laser-based microscopy and microphotochemistry,” FASEB J. 8, 804–813 (1994).
[PubMed]

Williams, R. M.

Wilson, K.

B. Widom, M. Fisher, V. Ambegaokor, J. Langer, J. Wilkens, M. Nelkin, K. Wilson, and their students, Cornell University, Ithaca, N.Y. (personal communication, 1970).

Wolf, D. E.

P. F. Fahey, D. E. Koppel, L. S. Barak, D. E. Wolf, E. L. Elson, W. W. Webb, “Lateral diffusion in planar lipid bilayers,” Science 195(4275), 305–306 (1977).

Wu, E.

E. Brown, E. Wu, W. Zipfel, W. W. Webb, “Measurement of molecular diffusion in solution by multiphoton fluorescence photobleaching recovery,” Biophys. J. 77, 2837–2849 (1999).
[CrossRef] [PubMed]

Wu, X.-L.

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

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

J. Mertz, C. Xu, W. W. Webb, “Single-molecule detection by two-photon excited fluorescence,” Opt. Lett. 20, 2532–2534 (1995).
[CrossRef]

C. Xu, W. W. Webb, “Multiphoton excitation of molecular fluorophores and nonlinear laser microscopy,” in Topics in Fluorescence Spectroscopy: Nonlinear and Two-Photon-Induced Fluorescence, J. Lakowicz, ed. (Plenum, N.Y., 1997), Vol. 5, pp. 471–540.
[CrossRef]

Zemelman, B. V.

D. A. DeAngelis, G. Miesenböch, B. V. Zemelman, J. E. Rothman, “PRIM: proximity imaging of green fluorescent protein-tagged polypeptides,” Proc. Natl. Acad. Sci. USA 95, 12312–12316 (1998).
[CrossRef]

Zimmerman, N. M.

N. M. Zimmerman, W. W. Webb, “1/f resistance noise complements anelasticity measurements of hydrogen motion in amorphous Pd80Si20,” Phys. Rev. Lett. 65, 1040–1043 (1990).
[CrossRef] [PubMed]

Zipfel, W.

E. Brown, E. Wu, W. Zipfel, W. W. Webb, “Measurement of molecular diffusion in solution by multiphoton fluorescence photobleaching recovery,” Biophys. J. 77, 2837–2849 (1999).
[CrossRef] [PubMed]

Zipfel, W. R.

P. Kloppenburg, W. R. Zipfel, W. W. Webb, R. M. Harris-Warrick, “Highly localized Ca2+ accumulation revealed by multiphoton microscopy in an identified motoneuron, and its modulation by dopamine,” J. Neurosci. 20, 2523–2533 (2000).
[PubMed]

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, W. W. Webb, “Measuring serotonin distribution in live cells with three-photon excitation,” Science 275, 530–532 (1997).
[CrossRef] [PubMed]

Ann. Rev. Biophys. Bioeng. (1)

E. L. Elson, W. W. Webb, “Concentration correlation spectroscopy: a new biophysical probe based on occupation number fluctuations,” Ann. Rev. Biophys. Bioeng. 4, 311–334 (1975).
[CrossRef]

Appl. Opt. (3)

Biol. Bull. (1)

T. Ryan, J. Myers, W. W. Webb, “Molecular interactions on the cell surface revealed by electrophoresis,” Biol. Bull. 176(S), 164–169 (1989).

Biophys. Chem. (1)

H. Qian, “On the statistics of fluorescence correlation spectroscopy,” Biophys. Chem. 38(1-2), 49–57 (1990).
[PubMed]

Biophys. J. (20)

N. O. Peterson, D. C. Johnson, M. J. Schlessinger, “Scanning fluorescence correlation spectroscopy. 2. Application to virus glycoprotein aggregation,” Biophys. J. 49, 817–820 (1986).
[CrossRef]

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, A216 (1976).
[CrossRef]

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

D. Gross, W. W. Webb, “Molecular counting of low-density lipoprotein particles as individuals and small clusters on cell surfaces,” Biophys. J. 49, 901–911 (1986).
[CrossRef] [PubMed]

R. N. Ghosh, W. W. Webb, “Automated detection and tracking of individual and clustered cell surface low density lipoprotein receptor molecules,” Biophys. J. 66, 1301–1318 (1994).
[CrossRef] [PubMed]

T. J. Feder, I. Brust-Mascher, J. P. Slattery, B. Baird, W. W. Webb, “Constrained diffusion or immobile fraction on the cell surfaces: a new interpretation,” Biophys. J. 70, 2767–2773 (1996).
[CrossRef] [PubMed]

E. Brown, E. Wu, W. Zipfel, W. W. Webb, “Measurement of molecular diffusion in solution by multiphoton fluorescence photobleaching recovery,” Biophys. J. 77, 2837–2849 (1999).
[CrossRef] [PubMed]

D.-O. D. Mak, W. W. Webb, “Conductivity noise in transmembrane ion channels due to ion concentration fluctuations via diffusion,” Biophys. J. 72, 1153–1164 (1997).
[CrossRef] [PubMed]

D.-O. D. Mak, W. W. Webb, “Molecular dynamics of alamethicin transmembrane channels from open-channel current noise analysis,” Biophys. J. 69, 2337–2349 (1995).
[CrossRef] [PubMed]

L. R. Opsahl, W. W. Webb, “Transduction of membrane tension by the ion channel alamethicin,” Biophys. J. 66, 71–74 (1994).
[CrossRef] [PubMed]

H. Qian, E. L. Elson, “On the analysis of high-order moments of fluorescence fluctuations,” Biophys. J. 57, 375–380 (1990).
[CrossRef] [PubMed]

M. B. Schneider, J. T. Jenkins, W. W. Webb, “Thermal fluctuations of large cylindrical phospholipid vesicles,” Biophys. J. 45, 891–899 (1984).
[CrossRef] [PubMed]

J. Korlach, M. Levene, S. W. Turner, D. R. Larson, M. Foquet, H. G. Craighead, W. W. Webb, “A new strategy for sequencing individual molecules of DNA,” Biophys. J. 80, 147 (2001).

A. A. Heikal, J. Korlach, W. W. Webb, “Time-resolved fluorescence and anisotropy of free and DNA-bound fluorescently labeled nucleotides,” Biophys. J. 80, 8 (2001).

M. Levene, J. Korlach, S. W. Turner, H. G. Craighead, W. W. Webb, “Near-field apertures for reduced-volume fluorescence correlation spectroscopy and single molecule studies,” Biophys. J. 80, 149 (2001).

S. T. Hess, A. A. Heikal, W. W. Webb, “Reversible light-assisted proton transfer reaction in ecliptic green fluorescent protein,” Biophys. J. 78, 75 (2000).

M. Levene, D. Larson, J. Korlach, M. Foquet, S. W. Turner, H. G. Craighead, W. W. Webb, “Nanometer constrained observation volumes for high concentration fluorescence correlation spectroscopy and single molecule dynamics,” Biophys. J. 78, 2368 (2000).

D. R. Larson, M. Levene, S. W. Turner, H. G. Craighead, W. W. Webb, “Fluorescence correlation spectroscopy in zeptoliter volumes,” Biophys. J. 80, 149 (2001).

S. T. Hess, A. A. Heikal, G. S. Baird, R. Y. Tsien, W. W. Webb, “Advantageous molecular photophysical fluorescence properties of dsRed and Citrine,” Biophys. J. 80, 7 (2001).

A. A. Heikal, S. T. Hess, P. Schwille, W. W. Webb, “Ultrafast molecular dynamics of selected green fluorescent protein mutants,” Biophys. J. 78, 752 (2000).

Biopolymers (4)

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

D. Magde, E. L. Elson, W. W. Webb, “Fluorescence correlation spectroscopy II. An experimental realization,” Biopolymers 13, 29–61 (1974).
[CrossRef] [PubMed]

R. D. Icenogle, E. L. Elson, “Fluorescence correlation spectroscopy and photobleaching recovery of multiple binding reactions. I. Theory and FCS measurements,” Biopolymers 22, 1919–1948 (1983).
[CrossRef] [PubMed]

R. D. Icenogle, E. L. Elson, “Fluorescence correlation spectroscopy and photobleaching recovery of multiple binding reactions. II. FPR and FCS measurements at low and high DNA concentrations,” Biopolymers 22, 1949–1966 (1983).
[CrossRef] [PubMed]

Chem. Phys. (1)

A. Ehrenberg, R. Rigler, “Rotational Brownian-motion and fluorescence intensity fluctuations,” Chem. Phys. 4(3), 390–401 (1974).

Cytometry (1)

P. Schwille, J. Korlach, W. W. Webb, “Fluorescence correlation spectroscopy with single-molecule sensitivity on cell and model membranes,” Cytometry 36, 176–182 (1999).
[CrossRef] [PubMed]

FASEB J. (1)

M. Williams, D. W. Piston, W. W. Webb, “Two-photon molecular excitation provides intrinsic three-dimensional resolution for laser-based microscopy and microphotochemistry,” FASEB J. 8, 804–813 (1994).
[PubMed]

J. Cell Biol. (3)

J. L. Thomas, D. Holowka, B. Baird, W. W. Webb, “Large-scale co-aggregation of fluorescent lipid probes with cell surface proteins,” J. Cell Biol. 125, 795–802 (1994).
[CrossRef] [PubMed]

L. S. Barak, W. W. Webb, “Diffusion of low density lipoprotein–receptor complex on human fibroblasts,” J. Cell Biol. 95, 846–852 (1982).
[CrossRef] [PubMed]

D. W. Tank, W. J. Fredericks, L. S. Barak, W. W. Webb, “Electric field-induced redistribution and postfield relaxation of low density lipoprotein receptors on cultured human fibroblasts,” J. Cell Biol. 101, 148–157 (1985).
[CrossRef] [PubMed]

J. Cell Sci. (1)

R. H. Köhler, P. Schwille, W. W. Webb, M. Hanson, “Active protein transport through plastid tubules: velocity quantified by fluorescence correlation spectroscopy,” J. Cell Sci. 113, 3921–3930 (2000).
[PubMed]

J. Chem. Phys. (1)

J. S. Huang, W. W. Webb, “Diffuse interface in a critical fluid mixture,” J. Chem. Phys. 50, 3677–3693 (1969).
[CrossRef]

J. Fluid Mech. (1)

M. B. Frish, W. W. Webb, “Direct measurement of vorticity by optical probe,” J. Fluid Mech. 107, 173–200 (1981).
[CrossRef]

J. Neurophysiol. (1)

W. Denk, R. M. Keolian, W. W. Webb, “Mechanical response of frog saccular hair bundles to the aminoglycoside block of mechano-electrical transduction,” J. Neurophysiol. 68, 927–932 (1992).
[PubMed]

J. Neurosci. (1)

P. Kloppenburg, W. R. Zipfel, W. W. Webb, R. M. Harris-Warrick, “Highly localized Ca2+ accumulation revealed by multiphoton microscopy in an identified motoneuron, and its modulation by dopamine,” J. Neurosci. 20, 2523–2533 (2000).
[PubMed]

J. Opt. Soc. Am. B (1)

J. Phys. (Paris) (1)

M. B. Schneider, J. T. Jenkins, W. W. Webb, “Thermal fluctuations of large quasi-spherical bimolecular phospholipid vesicles,” J. Phys. (Paris) 45, 1457–1472 (1984).
[CrossRef]

Nature (1)

R. M. Dickson, A. B. Cubitt, R. Y. Tsien, W. E. Moerner, “On/off blinking and switching behaviour of single molecules of green fluorescent protein,” Nature 388(6840), 355–358 (1997).

Opt. Lett. (1)

Phys. Rev. (1)

R. Beasley, R. Labusch, W. W. Webb, “Flux creep in type-II superconductors,” Phys. Rev. 181, 682–700 (1969).
[CrossRef]

Phys. Rev. A (3)

R. Beasley, W. A. Fietz, R. W. Rollins, J. Silcox, W. W. Webb, “Annihilation instability in hard superconductors,” Phys. Rev. A 137, 1205–1208 (1965).
[CrossRef]

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

D. C. Wack, W. W. Webb, “Measurement by x-ray diffraction methods of the layer compressional elastic constant B in the lyotropic smectic-A (La) phase of the lecithin–water system,” Phys. Rev. A 40, 1627–1636 (1989).
[CrossRef] [PubMed]

Phys. Rev. B (1)

J. V. Mantese, W. A. Curtin, W. W. Webb, “Two-component model for the resistivity and noise of tunneling metal-insulator composites,” Phys. Rev. B 33, 7897–7901 (1986).
[CrossRef]

Phys. Rev. Lett. (12)

N. M. Zimmerman, W. W. Webb, “1/f resistance noise complements anelasticity measurements of hydrogen motion in amorphous Pd80Si20,” Phys. Rev. Lett. 65, 1040–1043 (1990).
[CrossRef] [PubMed]

W. Denk, W. W. Webb, “Thermal-noise-limited transduction observed in mechanosensory receptors of the inner ear,” Phys. Rev. Lett. 63, 207–210 (1989).
[CrossRef] [PubMed]

J. H. Scofield, W. W. Webb, “Resistance fluctuations due to hydrogen diffusion in niobium thin films,” Phys. Rev. Lett. 54, 353–356 (1985).
[CrossRef] [PubMed]

J. V. Mantese, W. W. Webb, “1/f noise of granular metal-insulator composites,” Phys. Rev. Lett. 55, 2212–2215 (1985).
[CrossRef] [PubMed]

G. H. Gilmer, W. C. Gilmore, J. S. Huang, W. W. Webb, “Diffuse interface in a critical fluid mixture,” Phys. Rev. Lett. 14, 491–494 (1965).
[CrossRef]

W. W. Webb, R. J. Warburton, “Intrinsic quantum fluctuations in uniform filamentary superconductors,” Phys. Rev. Lett. 30, 461–465 (1968).
[CrossRef]

J. E. Lukens, R. J. Warburton, W. W. Webb, “Onset of quantized thermal fluctuations in ‘one-dimensional’ superconductors,” Phys. Rev. Lett. 25, 1180–1184 (1970).
[CrossRef]

J. S. Huang, W. W. Webb, “Viscous damping of thermal excitations on the interface of critical fluid mixtures,” Phys. Rev. Lett. 23, 160–163 (1969).
[CrossRef]

D. Magde, E. Elson, W. W. Webb, “Thermodynamic fluctuations in a reacting system—measurements by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[CrossRef]

W. H. Henkels, W. W. Webb, “Intrinsic fluctuations in the driven Josephson oscillator,” Phys. Rev. Lett. 26, 1164–1167 (1971).
[CrossRef]

P. Leiderer, D. R. Watts, W. W. Webb, “Light scattering by 3He–4He mixtures near the tricritical point,” Phys. Rev. Lett. 33, 483–485 (1974).
[CrossRef]

P. Leiderer, D. R. Nelson, D. R. Watts, W. W. Webb, “Tricritical slowing down of superfluid dynamics in 3He–4He mixtures,” Phys. Rev. Lett. 34, 1080–1083 (1975).
[CrossRef]

Proc. Natl. Acad. Sci. USA (11)

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

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

P. Kask, K. Palo, D. Ullmann, K. Gall, “Fluorescence-intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. USA 96, 13756–13761 (1999).
[CrossRef] [PubMed]

H. Qian, E. L. Elson, “Distribution of molecular aggregation by analysis of fluctuation moments,” Proc. Natl. Acad. Sci. USA 87, 5479–5483 (1990).
[CrossRef] [PubMed]

W. Denk, W. W. Webb, A. J. Hudspeth, “Mechanical properties of sensory hair bundles are reflected in their Brownian motion measured with a laser differential interferometer,” Proc. Natl. Acad. Sci. USA 86, 5371–5375 (1989).
[CrossRef] [PubMed]

D. W. Tank, R. L. Huganir, P. Greengard, W. W. Webb, “Patch-recorded single-channel currents of the purified and reconstituted torpedo acetylcholine receptor,” Proc. Natl. Acad. Sci. USA 80, 5129–5133 (1983).
[CrossRef] [PubMed]

P. Schwille, S. Kummer, 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).
[CrossRef] [PubMed]

D. A. DeAngelis, G. Miesenböch, B. V. Zemelman, J. E. Rothman, “PRIM: proximity imaging of green fluorescent protein-tagged polypeptides,” Proc. Natl. Acad. Sci. USA 95, 12312–12316 (1998).
[CrossRef]

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

J. Korlach, P. Schwille, W. W. Webb, G. W. Feigenson, “Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 96, 8461–8466 (1999).
[CrossRef] [PubMed]

Quart. Rev. Biophys. (1)

W. W. Webb, “Applications of fluorescence correlation spectroscopy,” Quart. Rev. Biophys. 9, 49–68 (1976).
[CrossRef]

Science (5)

T. A. Ryan, J. Myers, D. Holowka, B. Baird, W. W. Webb, “Molecular crowding on the cell surface,” Science 239, 61–64 (1988).
[CrossRef] [PubMed]

P. F. Fahey, D. E. Koppel, L. S. Barak, D. E. Wolf, E. L. Elson, W. W. Webb, “Lateral diffusion in planar lipid bilayers,” Science 195(4275), 305–306 (1977).

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

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, W. W. Webb, “Measuring serotonin distribution in live cells with three-photon excitation,” Science 275, 530–532 (1997).
[CrossRef] [PubMed]

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

Other (12)

P. Pyenta, P. Schwille, School of Applied and Engineering Physics, Cornell University, 233 Clark Hall, Ithaca, N.Y. 14853-0001 (personal communication, 1998).

J. Thomas, W. W. Webb, “Fluorescence photobleaching recovery: a probe of membrane dynamics,” in Non-Invasive Techniques in Cell Biology, S. Grinstein, K. Foskett, eds. (Wiley, New York, 1990), pp. 129–152.

D. Ferguson, W. W. Webb, “The vorticity optical probe: a fast multicomponent model,” in Proceedings of the Eighth Biennial Symposium on Turbulence, 26–28 September 1983, University of Missouri, Rolla, Missouri, pp. 272–281.

J. Korlach, M. Levene, S. W. Turner, D. R. Larson, M. E. Foquet, H. G. Craighead, W. W. Webb, “A new method for sequencing individual molecules of DNA,” paper presented at the Sixth International Workshop on Single Molecule Detection and Ultra Sensitive Analysis in Life Sciences, Berlin, Germany (2000).

D. Gross, W. W. Webb, “Cell surface clustering and mobility of the liganded LDL receptor measured by digital video fluorescence microscopy,” in Spectroscopic Membrane Probes, L. M. Loew, ed. (CRC Press, Boca Raton, Fla., 1988), Vol. II, pp. 19–43.

N. L. Thompson, “Fluorescence correlation spectroscopy,” in Topics in Fluorescence Spectroscopy VI, J. R. Lakowicz, ed. (Plenum, New York, 1991), pp. 337–338.

C. Xu, W. W. Webb, “Multiphoton excitation of molecular fluorophores and nonlinear laser microscopy,” in Topics in Fluorescence Spectroscopy: Nonlinear and Two-Photon-Induced Fluorescence, J. Lakowicz, ed. (Plenum, N.Y., 1997), Vol. 5, pp. 471–540.
[CrossRef]

B. Widom, M. Fisher, V. Ambegaokor, J. Langer, J. Wilkens, M. Nelkin, K. Wilson, and their students, Cornell University, Ithaca, N.Y. (personal communication, 1970).

B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

S. R. DeGroot, Thermodynamics of Irreversible Processes (North-Holland, Amsterdam, 1952).

J. Tyndall, “Scientific materialism,” in Fragments of Science, A Series of Detached Essays, Addresses and Reviews (Longmans, Green, London, 1892), Vol. 2, p. 77.

W. W. Webb, “Fluorescence correlation spectroscopy: genesis, evolution, maturation and prognosis,” in Fluorescence Correlation Spectroscopy, R. Rigler, E. Elson, eds. (Springer-Verlag, Berlin, 2001), Chap. 14, pp. 305–330.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Fluorescence-excitation spectra of EGFP in 100mM potassium phosphate, 10nM citrate buffer at various pH levels (top-most curve through bottom-most curve): 9.0, 8.0, 11.0, 7.0, 6.5, 6.0, 5.5, 5.0. The inset shows the fluorescence-emission intensity at 510 nm (squares), the fluorescence-excitation intensity at 490 nm (circles), and the absorption at 488 nm (diamonds) plotted versus the pH. The solid curve in the inset shows the fit to the emission intensity from pH = 4.0 to pH = 9.0, yielding pK a = 5.8 ± 0.1. Norm., normalized.

Fig. 2
Fig. 2

Autocorrelation G(t) curves (normalized to 1 at 10 ms) for EGFP at different pH levels (back curve to front curve): 1, 10, 9.0, 8.0, 7.0, 6.5, 6.0, 5.5, 5.0. The appropriate theoretical fits are shown as dotted curves. The decay of G(t) at high pH is dominated by diffusional relaxation, whereas on decreasing the pH the chemical relaxation at shorter times is growing in amplitude and speed. The autocorrelations of GFP mutant Y66W, which lacks a protonatable hydroxyl on the chromophore, at pH = 9.0 (solid curve) and pH = 5.5 (dashed curve) show an absence of pH-dependent fast fluorescence flicker.

Fig. 3
Fig. 3

Excitation intensity I ex dependence of normalized fluorescence correlation curves for T203Y at pH = 8 with 514-nm excitation. From right to left, I ex increases from 5 to 50 kW/cm2 in 0.1-OD (optical density) steps. The average dark fraction F (∼60%) is determined by the fitted amplitude of the fast flicker process and remains constant although the time constants have decreased by an order of magnitude as the intensity decreases.

Fig. 4
Fig. 4

Confocal fluorescence imaging and FCS applied to the characterization of lipid-bilayer models for biomembranes. GUVs composed of dilauroyl phosphatidylcholine (DLPC) and dipalmitoyl phosphatidylcholine (DPPC) were imaged by confocal fluorescence by use of two fluorescent probes: (a) DiI-C20 and (b) Bodipy-PC. Shown are three-dimensional image reconstructions of confocal z scans through GUVs, revealing the morphology of coexisting phase domains on the surfaces of these vesicles. Phase separation is visualized by differential probe partitioning into coexisting phases with DiI-C20 partitioning into the spatially ordered phase (slow diffusion) and Bodipy-PC partitioning into fluid phases (fast diffusion). (c) FCS autocorrelation curves for samples with DLPC/DPPC compositions of 1/10 (squares) for the top row of images, 0.60/0.40 (circles) for the middle row, and 0.20/0.80 (triangles) for the bottom row. At DLPC/DPPC 1/10 a single fluid phase is present, whereas ordered-fluid two-phase coexistence is present in the other two cases. These phase states are reflected by the shape of the corresponding correlation curves, which represent sampling of both phases. FCS could thus accurately determine the phase state of the lipid mixture as well as distinguish two different diffusion coefficients in a region of two-phase coexistence on a single vesicle. The solid curves are data-fitting curves for diffusion theory from which the diffusion-coefficient values were determined. The correlation amplitudes were normalized to 1 by the multiplication of G(t) by the average number of fluorescent molecules in the focal area 〈N〉 to compare the shapes of the curves for different compositions. Fluorescent probes were added to the lipid mixture at a concentration of 10-1 mol % for confocal imaging and 10-4 mol % for FCS.

Fig. 5
Fig. 5

Coexisting cytoplasmic and membrane diffusion spatially resolved by FCS with quasi-confocal optics: z stepping with 1-µm steps (a 100-µm pinhole at low resolution) through a RBL cell that expresses GFP-labeled palmitoylated Lyn analogs distributed in the cytoplasm and on membranes. Close to the cell surface both intracellular (fast) and membrane (slow) mobilities are represented; in deeper z positions the membrane contribution can be avoided. The fast intracellular part is always present.

Fig. 6
Fig. 6

Measurements of the pH in cellular cytoplasm by use of FCS correlations of proton-binding dynamics by EGFP to determine the dark fraction that corresponds to the mean fraction of EGFP anionic molecules neutralized by the binding of external protons. External calibrations of the pH are quite uncertain in these illustrative experiments, so the results are not precise. pH values for the curves from top to bottom: 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8, 9, 10.

Equations (9)

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t δCjr¯, t=Dj2δCjr¯, t+ΣkTjkδCkr¯, t,
δFr¯, t=ϕr¯δCr¯, t.
δFt= ϕr¯δCr¯, td3r,
Ft= ϕr¯Cr, td3r.
V= ϕr¯d3r2 ϕr¯2d3r.
C=N/V.
GτδFtδFt+τ/Ft2
G0δFt2Ft2=1N=1CV.
Gfτ= ϕr¯δCr¯, tϕr¯δCr¯, t+τd3rd3r.

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