Abstract

Optical techniques in single molecule imaging rely heavily on photon counting for data acquisition. Extraction of information from the recorded readings is often done by means of statistical signal processing, however this requires a full knowledge of the photoelectron statistics. In addition to counting statistics we include a specific form of random signal variations namely reorientational dynamics, or wobble to derive the general probability density function of the number of detected photons. The relative importance of the two factors is dependent upon the total number of photons in the system and results are given in all regimes.

© 2007 Optical Society of America

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    [CrossRef]
  2. D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, "Myosin conformational states determined by single fluorophore polarization," Proc. Natl. Acad. Sci. U.S.A. 95, 8034-8039 (1998).
    [CrossRef] [PubMed]
  3. H. P. Lu, L. Y. Xun, and X. S. Xie, "Single molecule enzymatic dynamics," Science 282, 1877-1882 (1998).
    [CrossRef] [PubMed]
  4. R. E. Dale and S. C. Hopkins "Model-Independent analysis of the orientation of fluorescent probes with restricted mobility in muscle fibers," Biophys. J. 76, 1606-1618 (1999).
    [CrossRef] [PubMed]
  5. T. M. Jovin, M. Bartholdi, W. L. C. Vaz, and R. H. Austin, "Rotational diffusion of biological macromolecules by time-resolved delayed luminescence (phosphorescence, fluorescence) anisotropy," Ann. N. Y. Acad. Sci. 366, 176-196 (1981).
    [CrossRef] [PubMed]
  6. T. Ha, T. Enderle, D. F. Ogletree, D. S. Chemla, P. R. Selvin and S. Weiss, "Probing the interaction between two single molecules: Fluorescence resonance energy transfer between a single donor and a single acceptor," Proc. Natl. Acad. Sci. U.S.A. 93, 6264-6268 (1996).
    [CrossRef] [PubMed]
  7. T. Ha, J. Glass, T. Enderle, D. S. Chemla, and S. Weiss, "Hindered rotational diffusion and rotational jumps of single molecules," Phys. Rev. Lett. 80, 2093-2096 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  10. D. J. Pikas, S. M. Kirkpatrick, E. Tewksbury, L. L. Brott, R. R. Naik, M. O. Stone, and W.M. Dennis, "Nonlinear saturation and lasing characteristics of green fluorescent protein," J. Phys. Chem. B 106, 4831-4837 (2002).
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    [CrossRef] [PubMed]
  13. B. Sick, B. Hecht, and L. Novotny "Orientational imaging of single molecules by annular illumination," Phys. Rev. Lett. 85, 4482-4485 (2000).
    [CrossRef] [PubMed]
  14. R. M. Dickson, D. J. Norris, and W. E. Moerner, "Simultaneous imaging of individual molecules aligned both parallel and perpendicular to the optic axis," Phys. Rev. Lett. 81, 5322-5325 (1998).
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    [CrossRef] [PubMed]
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  22. I. Munro, I. Pecht, and L. Stryer "Subnanosecond motions of Tryptophan residues in proteins," Proc. Natl. Acad. Sci. USA 76, 56-60 (1979).
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2003 (1)

W. E. Moerner and D. P. Fromm, "Methods of single molecule fluorescence spectroscopy and microscopy," Rev. Sci. Instrum. 74, 3597-3619 (2003).
[CrossRef]

2002 (1)

D. J. Pikas, S. M. Kirkpatrick, E. Tewksbury, L. L. Brott, R. R. Naik, M. O. Stone, and W.M. Dennis, "Nonlinear saturation and lasing characteristics of green fluorescent protein," J. Phys. Chem. B 106, 4831-4837 (2002).
[CrossRef]

2001 (1)

K. D. Weston and L. S. Goldner "Orientation imaging and reorientation dynamics of single dye molecules," J. Phys. Chem. B 105, 3453-3462 (2001).
[CrossRef]

2000 (1)

B. Sick, B. Hecht, and L. Novotny "Orientational imaging of single molecules by annular illumination," Phys. Rev. Lett. 85, 4482-4485 (2000).
[CrossRef] [PubMed]

1999 (1)

R. E. Dale and S. C. Hopkins "Model-Independent analysis of the orientation of fluorescent probes with restricted mobility in muscle fibers," Biophys. J. 76, 1606-1618 (1999).
[CrossRef] [PubMed]

1998 (4)

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, "Myosin conformational states determined by single fluorophore polarization," Proc. Natl. Acad. Sci. U.S.A. 95, 8034-8039 (1998).
[CrossRef] [PubMed]

H. P. Lu, L. Y. Xun, and X. S. Xie, "Single molecule enzymatic dynamics," Science 282, 1877-1882 (1998).
[CrossRef] [PubMed]

T. Ha, J. Glass, T. Enderle, D. S. Chemla, and S. Weiss, "Hindered rotational diffusion and rotational jumps of single molecules," Phys. Rev. Lett. 80, 2093-2096 (1998).
[CrossRef]

R. M. Dickson, D. J. Norris, and W. E. Moerner, "Simultaneous imaging of individual molecules aligned both parallel and perpendicular to the optic axis," Phys. Rev. Lett. 81, 5322-5325 (1998).
[CrossRef]

1997 (1)

G. H. Patterson, S. N. Knobel, W. D. Sharif, S. R. Kain, and D. W. Piston, "Use of the green flurorescent protein and its mutants in quantitative fluorescence microscopy," Biophys. J. 73, 2782-2790 (1997).
[CrossRef] [PubMed]

1996 (2)

T. Ha, T. Enderle, D. F. Ogletree, D. S. Chemla, P. R. Selvin and S. Weiss, "Probing the interaction between two single molecules: Fluorescence resonance energy transfer between a single donor and a single acceptor," Proc. Natl. Acad. Sci. U.S.A. 93, 6264-6268 (1996).
[CrossRef] [PubMed]

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, "Single molecule dynamics studied by polarization modulation," Phys. Rev. Lett. 77, 3979-3982 (1996).
[CrossRef] [PubMed]

1992 (1)

Th. Basché, W. P. Ambrose, and W. E. Moerner, "Optical spectra and kinetics of single impurity molecules in a polymer: spectral diffusion and persistent spectral hole burning," J. Opt. Soc. Am. B. 9, 829-836 (1992).
[CrossRef]

1981 (1)

T. M. Jovin, M. Bartholdi, W. L. C. Vaz, and R. H. Austin, "Rotational diffusion of biological macromolecules by time-resolved delayed luminescence (phosphorescence, fluorescence) anisotropy," Ann. N. Y. Acad. Sci. 366, 176-196 (1981).
[CrossRef] [PubMed]

1979 (1)

I. Munro, I. Pecht, and L. Stryer "Subnanosecond motions of Tryptophan residues in proteins," Proc. Natl. Acad. Sci. USA 76, 56-60 (1979).
[CrossRef] [PubMed]

1978 (1)

P. Wahl, K. Tawada, and J. C. Auchet, "Study of tropomyosin labelled with a fluorescent probe by pulse fluorimetry in polarized light. Interaction of that protein with troponin and actin," Eur. J. Biochem. 88, 421-424 (1978).
[CrossRef] [PubMed]

1970 (1)

J. Yguerabide, H. F. Epstein, and L. Stryer, "Segmental flexibility in an antibody molecule," J. Mol. Biol. 51, 573-590 (1970).
[CrossRef] [PubMed]

Ambrose, W. P.

Th. Basché, W. P. Ambrose, and W. E. Moerner, "Optical spectra and kinetics of single impurity molecules in a polymer: spectral diffusion and persistent spectral hole burning," J. Opt. Soc. Am. B. 9, 829-836 (1992).
[CrossRef]

Auchet, J. C.

P. Wahl, K. Tawada, and J. C. Auchet, "Study of tropomyosin labelled with a fluorescent probe by pulse fluorimetry in polarized light. Interaction of that protein with troponin and actin," Eur. J. Biochem. 88, 421-424 (1978).
[CrossRef] [PubMed]

Austin, R. H.

T. M. Jovin, M. Bartholdi, W. L. C. Vaz, and R. H. Austin, "Rotational diffusion of biological macromolecules by time-resolved delayed luminescence (phosphorescence, fluorescence) anisotropy," Ann. N. Y. Acad. Sci. 366, 176-196 (1981).
[CrossRef] [PubMed]

Bartholdi, M.

T. M. Jovin, M. Bartholdi, W. L. C. Vaz, and R. H. Austin, "Rotational diffusion of biological macromolecules by time-resolved delayed luminescence (phosphorescence, fluorescence) anisotropy," Ann. N. Y. Acad. Sci. 366, 176-196 (1981).
[CrossRef] [PubMed]

Basché, Th.

Th. Basché, W. P. Ambrose, and W. E. Moerner, "Optical spectra and kinetics of single impurity molecules in a polymer: spectral diffusion and persistent spectral hole burning," J. Opt. Soc. Am. B. 9, 829-836 (1992).
[CrossRef]

Berger, C.

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, "Myosin conformational states determined by single fluorophore polarization," Proc. Natl. Acad. Sci. U.S.A. 95, 8034-8039 (1998).
[CrossRef] [PubMed]

Brott, L. L.

D. J. Pikas, S. M. Kirkpatrick, E. Tewksbury, L. L. Brott, R. R. Naik, M. O. Stone, and W.M. Dennis, "Nonlinear saturation and lasing characteristics of green fluorescent protein," J. Phys. Chem. B 106, 4831-4837 (2002).
[CrossRef]

Chemla, D. S.

T. Ha, J. Glass, T. Enderle, D. S. Chemla, and S. Weiss, "Hindered rotational diffusion and rotational jumps of single molecules," Phys. Rev. Lett. 80, 2093-2096 (1998).
[CrossRef]

T. Ha, T. Enderle, D. F. Ogletree, D. S. Chemla, P. R. Selvin and S. Weiss, "Probing the interaction between two single molecules: Fluorescence resonance energy transfer between a single donor and a single acceptor," Proc. Natl. Acad. Sci. U.S.A. 93, 6264-6268 (1996).
[CrossRef] [PubMed]

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, "Single molecule dynamics studied by polarization modulation," Phys. Rev. Lett. 77, 3979-3982 (1996).
[CrossRef] [PubMed]

Dale, R. E.

R. E. Dale and S. C. Hopkins "Model-Independent analysis of the orientation of fluorescent probes with restricted mobility in muscle fibers," Biophys. J. 76, 1606-1618 (1999).
[CrossRef] [PubMed]

Dennis, W.M.

D. J. Pikas, S. M. Kirkpatrick, E. Tewksbury, L. L. Brott, R. R. Naik, M. O. Stone, and W.M. Dennis, "Nonlinear saturation and lasing characteristics of green fluorescent protein," J. Phys. Chem. B 106, 4831-4837 (2002).
[CrossRef]

Dickson, R. M.

R. M. Dickson, D. J. Norris, and W. E. Moerner, "Simultaneous imaging of individual molecules aligned both parallel and perpendicular to the optic axis," Phys. Rev. Lett. 81, 5322-5325 (1998).
[CrossRef]

Enderle, T.

T. Ha, J. Glass, T. Enderle, D. S. Chemla, and S. Weiss, "Hindered rotational diffusion and rotational jumps of single molecules," Phys. Rev. Lett. 80, 2093-2096 (1998).
[CrossRef]

T. Ha, T. Enderle, D. F. Ogletree, D. S. Chemla, P. R. Selvin and S. Weiss, "Probing the interaction between two single molecules: Fluorescence resonance energy transfer between a single donor and a single acceptor," Proc. Natl. Acad. Sci. U.S.A. 93, 6264-6268 (1996).
[CrossRef] [PubMed]

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, "Single molecule dynamics studied by polarization modulation," Phys. Rev. Lett. 77, 3979-3982 (1996).
[CrossRef] [PubMed]

Epstein, H. F.

J. Yguerabide, H. F. Epstein, and L. Stryer, "Segmental flexibility in an antibody molecule," J. Mol. Biol. 51, 573-590 (1970).
[CrossRef] [PubMed]

Fromm, D. P.

W. E. Moerner and D. P. Fromm, "Methods of single molecule fluorescence spectroscopy and microscopy," Rev. Sci. Instrum. 74, 3597-3619 (2003).
[CrossRef]

Gaffney, D.

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, "Myosin conformational states determined by single fluorophore polarization," Proc. Natl. Acad. Sci. U.S.A. 95, 8034-8039 (1998).
[CrossRef] [PubMed]

Glass, J.

T. Ha, J. Glass, T. Enderle, D. S. Chemla, and S. Weiss, "Hindered rotational diffusion and rotational jumps of single molecules," Phys. Rev. Lett. 80, 2093-2096 (1998).
[CrossRef]

Goldner, L. S.

K. D. Weston and L. S. Goldner "Orientation imaging and reorientation dynamics of single dye molecules," J. Phys. Chem. B 105, 3453-3462 (2001).
[CrossRef]

Ha, T.

T. Ha, J. Glass, T. Enderle, D. S. Chemla, and S. Weiss, "Hindered rotational diffusion and rotational jumps of single molecules," Phys. Rev. Lett. 80, 2093-2096 (1998).
[CrossRef]

T. Ha, T. Enderle, D. F. Ogletree, D. S. Chemla, P. R. Selvin and S. Weiss, "Probing the interaction between two single molecules: Fluorescence resonance energy transfer between a single donor and a single acceptor," Proc. Natl. Acad. Sci. U.S.A. 93, 6264-6268 (1996).
[CrossRef] [PubMed]

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, "Single molecule dynamics studied by polarization modulation," Phys. Rev. Lett. 77, 3979-3982 (1996).
[CrossRef] [PubMed]

Hayes, E.

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, "Myosin conformational states determined by single fluorophore polarization," Proc. Natl. Acad. Sci. U.S.A. 95, 8034-8039 (1998).
[CrossRef] [PubMed]

Hecht, B.

B. Sick, B. Hecht, and L. Novotny "Orientational imaging of single molecules by annular illumination," Phys. Rev. Lett. 85, 4482-4485 (2000).
[CrossRef] [PubMed]

Hopkins, S. C.

R. E. Dale and S. C. Hopkins "Model-Independent analysis of the orientation of fluorescent probes with restricted mobility in muscle fibers," Biophys. J. 76, 1606-1618 (1999).
[CrossRef] [PubMed]

Jovin, T. M.

T. M. Jovin, M. Bartholdi, W. L. C. Vaz, and R. H. Austin, "Rotational diffusion of biological macromolecules by time-resolved delayed luminescence (phosphorescence, fluorescence) anisotropy," Ann. N. Y. Acad. Sci. 366, 176-196 (1981).
[CrossRef] [PubMed]

Kain, S. R.

G. H. Patterson, S. N. Knobel, W. D. Sharif, S. R. Kain, and D. W. Piston, "Use of the green flurorescent protein and its mutants in quantitative fluorescence microscopy," Biophys. J. 73, 2782-2790 (1997).
[CrossRef] [PubMed]

Kennedy, G.

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, "Myosin conformational states determined by single fluorophore polarization," Proc. Natl. Acad. Sci. U.S.A. 95, 8034-8039 (1998).
[CrossRef] [PubMed]

Kirkpatrick, S. M.

D. J. Pikas, S. M. Kirkpatrick, E. Tewksbury, L. L. Brott, R. R. Naik, M. O. Stone, and W.M. Dennis, "Nonlinear saturation and lasing characteristics of green fluorescent protein," J. Phys. Chem. B 106, 4831-4837 (2002).
[CrossRef]

Knobel, S. N.

G. H. Patterson, S. N. Knobel, W. D. Sharif, S. R. Kain, and D. W. Piston, "Use of the green flurorescent protein and its mutants in quantitative fluorescence microscopy," Biophys. J. 73, 2782-2790 (1997).
[CrossRef] [PubMed]

Lauzon, A. M.

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, "Myosin conformational states determined by single fluorophore polarization," Proc. Natl. Acad. Sci. U.S.A. 95, 8034-8039 (1998).
[CrossRef] [PubMed]

Lowey, S.

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, "Myosin conformational states determined by single fluorophore polarization," Proc. Natl. Acad. Sci. U.S.A. 95, 8034-8039 (1998).
[CrossRef] [PubMed]

Lu, H. P.

H. P. Lu, L. Y. Xun, and X. S. Xie, "Single molecule enzymatic dynamics," Science 282, 1877-1882 (1998).
[CrossRef] [PubMed]

Moerner, W. E.

W. E. Moerner and D. P. Fromm, "Methods of single molecule fluorescence spectroscopy and microscopy," Rev. Sci. Instrum. 74, 3597-3619 (2003).
[CrossRef]

R. M. Dickson, D. J. Norris, and W. E. Moerner, "Simultaneous imaging of individual molecules aligned both parallel and perpendicular to the optic axis," Phys. Rev. Lett. 81, 5322-5325 (1998).
[CrossRef]

Th. Basché, W. P. Ambrose, and W. E. Moerner, "Optical spectra and kinetics of single impurity molecules in a polymer: spectral diffusion and persistent spectral hole burning," J. Opt. Soc. Am. B. 9, 829-836 (1992).
[CrossRef]

Munro, I.

I. Munro, I. Pecht, and L. Stryer "Subnanosecond motions of Tryptophan residues in proteins," Proc. Natl. Acad. Sci. USA 76, 56-60 (1979).
[CrossRef] [PubMed]

Naik, R. R.

D. J. Pikas, S. M. Kirkpatrick, E. Tewksbury, L. L. Brott, R. R. Naik, M. O. Stone, and W.M. Dennis, "Nonlinear saturation and lasing characteristics of green fluorescent protein," J. Phys. Chem. B 106, 4831-4837 (2002).
[CrossRef]

Norris, D. J.

R. M. Dickson, D. J. Norris, and W. E. Moerner, "Simultaneous imaging of individual molecules aligned both parallel and perpendicular to the optic axis," Phys. Rev. Lett. 81, 5322-5325 (1998).
[CrossRef]

Novotny, L.

B. Sick, B. Hecht, and L. Novotny "Orientational imaging of single molecules by annular illumination," Phys. Rev. Lett. 85, 4482-4485 (2000).
[CrossRef] [PubMed]

Ogletree, D. F.

T. Ha, T. Enderle, D. F. Ogletree, D. S. Chemla, P. R. Selvin and S. Weiss, "Probing the interaction between two single molecules: Fluorescence resonance energy transfer between a single donor and a single acceptor," Proc. Natl. Acad. Sci. U.S.A. 93, 6264-6268 (1996).
[CrossRef] [PubMed]

Patterson, G. H.

G. H. Patterson, S. N. Knobel, W. D. Sharif, S. R. Kain, and D. W. Piston, "Use of the green flurorescent protein and its mutants in quantitative fluorescence microscopy," Biophys. J. 73, 2782-2790 (1997).
[CrossRef] [PubMed]

Pecht, I.

I. Munro, I. Pecht, and L. Stryer "Subnanosecond motions of Tryptophan residues in proteins," Proc. Natl. Acad. Sci. USA 76, 56-60 (1979).
[CrossRef] [PubMed]

Pikas, D. J.

D. J. Pikas, S. M. Kirkpatrick, E. Tewksbury, L. L. Brott, R. R. Naik, M. O. Stone, and W.M. Dennis, "Nonlinear saturation and lasing characteristics of green fluorescent protein," J. Phys. Chem. B 106, 4831-4837 (2002).
[CrossRef]

Piston, D.W.

G. H. Patterson, S. N. Knobel, W. D. Sharif, S. R. Kain, and D. W. Piston, "Use of the green flurorescent protein and its mutants in quantitative fluorescence microscopy," Biophys. J. 73, 2782-2790 (1997).
[CrossRef] [PubMed]

Selvin, P. R.

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, "Single molecule dynamics studied by polarization modulation," Phys. Rev. Lett. 77, 3979-3982 (1996).
[CrossRef] [PubMed]

T. Ha, T. Enderle, D. F. Ogletree, D. S. Chemla, P. R. Selvin and S. Weiss, "Probing the interaction between two single molecules: Fluorescence resonance energy transfer between a single donor and a single acceptor," Proc. Natl. Acad. Sci. U.S.A. 93, 6264-6268 (1996).
[CrossRef] [PubMed]

Sharif, W. D.

G. H. Patterson, S. N. Knobel, W. D. Sharif, S. R. Kain, and D. W. Piston, "Use of the green flurorescent protein and its mutants in quantitative fluorescence microscopy," Biophys. J. 73, 2782-2790 (1997).
[CrossRef] [PubMed]

Sick, B.

B. Sick, B. Hecht, and L. Novotny "Orientational imaging of single molecules by annular illumination," Phys. Rev. Lett. 85, 4482-4485 (2000).
[CrossRef] [PubMed]

Stone, M. O.

D. J. Pikas, S. M. Kirkpatrick, E. Tewksbury, L. L. Brott, R. R. Naik, M. O. Stone, and W.M. Dennis, "Nonlinear saturation and lasing characteristics of green fluorescent protein," J. Phys. Chem. B 106, 4831-4837 (2002).
[CrossRef]

Stryer, L.

I. Munro, I. Pecht, and L. Stryer "Subnanosecond motions of Tryptophan residues in proteins," Proc. Natl. Acad. Sci. USA 76, 56-60 (1979).
[CrossRef] [PubMed]

J. Yguerabide, H. F. Epstein, and L. Stryer, "Segmental flexibility in an antibody molecule," J. Mol. Biol. 51, 573-590 (1970).
[CrossRef] [PubMed]

Tawada, K.

P. Wahl, K. Tawada, and J. C. Auchet, "Study of tropomyosin labelled with a fluorescent probe by pulse fluorimetry in polarized light. Interaction of that protein with troponin and actin," Eur. J. Biochem. 88, 421-424 (1978).
[CrossRef] [PubMed]

Tewksbury, E.

D. J. Pikas, S. M. Kirkpatrick, E. Tewksbury, L. L. Brott, R. R. Naik, M. O. Stone, and W.M. Dennis, "Nonlinear saturation and lasing characteristics of green fluorescent protein," J. Phys. Chem. B 106, 4831-4837 (2002).
[CrossRef]

Trybus, K.

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, "Myosin conformational states determined by single fluorophore polarization," Proc. Natl. Acad. Sci. U.S.A. 95, 8034-8039 (1998).
[CrossRef] [PubMed]

Vaz, W. L. C.

T. M. Jovin, M. Bartholdi, W. L. C. Vaz, and R. H. Austin, "Rotational diffusion of biological macromolecules by time-resolved delayed luminescence (phosphorescence, fluorescence) anisotropy," Ann. N. Y. Acad. Sci. 366, 176-196 (1981).
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P. Wahl, K. Tawada, and J. C. Auchet, "Study of tropomyosin labelled with a fluorescent probe by pulse fluorimetry in polarized light. Interaction of that protein with troponin and actin," Eur. J. Biochem. 88, 421-424 (1978).
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D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, "Myosin conformational states determined by single fluorophore polarization," Proc. Natl. Acad. Sci. U.S.A. 95, 8034-8039 (1998).
[CrossRef] [PubMed]

Weiss, S.

T. Ha, J. Glass, T. Enderle, D. S. Chemla, and S. Weiss, "Hindered rotational diffusion and rotational jumps of single molecules," Phys. Rev. Lett. 80, 2093-2096 (1998).
[CrossRef]

T. Ha, T. Enderle, D. F. Ogletree, D. S. Chemla, P. R. Selvin and S. Weiss, "Probing the interaction between two single molecules: Fluorescence resonance energy transfer between a single donor and a single acceptor," Proc. Natl. Acad. Sci. U.S.A. 93, 6264-6268 (1996).
[CrossRef] [PubMed]

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, "Single molecule dynamics studied by polarization modulation," Phys. Rev. Lett. 77, 3979-3982 (1996).
[CrossRef] [PubMed]

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K. D. Weston and L. S. Goldner "Orientation imaging and reorientation dynamics of single dye molecules," J. Phys. Chem. B 105, 3453-3462 (2001).
[CrossRef]

Wu, J. R.

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, "Myosin conformational states determined by single fluorophore polarization," Proc. Natl. Acad. Sci. U.S.A. 95, 8034-8039 (1998).
[CrossRef] [PubMed]

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H. P. Lu, L. Y. Xun, and X. S. Xie, "Single molecule enzymatic dynamics," Science 282, 1877-1882 (1998).
[CrossRef] [PubMed]

Xun, L. Y.

H. P. Lu, L. Y. Xun, and X. S. Xie, "Single molecule enzymatic dynamics," Science 282, 1877-1882 (1998).
[CrossRef] [PubMed]

Yguerabide, J.

J. Yguerabide, H. F. Epstein, and L. Stryer, "Segmental flexibility in an antibody molecule," J. Mol. Biol. 51, 573-590 (1970).
[CrossRef] [PubMed]

Ann. N. Y. Acad. Sci. (1)

T. M. Jovin, M. Bartholdi, W. L. C. Vaz, and R. H. Austin, "Rotational diffusion of biological macromolecules by time-resolved delayed luminescence (phosphorescence, fluorescence) anisotropy," Ann. N. Y. Acad. Sci. 366, 176-196 (1981).
[CrossRef] [PubMed]

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R. E. Dale and S. C. Hopkins "Model-Independent analysis of the orientation of fluorescent probes with restricted mobility in muscle fibers," Biophys. J. 76, 1606-1618 (1999).
[CrossRef] [PubMed]

G. H. Patterson, S. N. Knobel, W. D. Sharif, S. R. Kain, and D. W. Piston, "Use of the green flurorescent protein and its mutants in quantitative fluorescence microscopy," Biophys. J. 73, 2782-2790 (1997).
[CrossRef] [PubMed]

Eur. J. Biochem. (1)

P. Wahl, K. Tawada, and J. C. Auchet, "Study of tropomyosin labelled with a fluorescent probe by pulse fluorimetry in polarized light. Interaction of that protein with troponin and actin," Eur. J. Biochem. 88, 421-424 (1978).
[CrossRef] [PubMed]

J. Mol. Biol. (1)

J. Yguerabide, H. F. Epstein, and L. Stryer, "Segmental flexibility in an antibody molecule," J. Mol. Biol. 51, 573-590 (1970).
[CrossRef] [PubMed]

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

Th. Basché, W. P. Ambrose, and W. E. Moerner, "Optical spectra and kinetics of single impurity molecules in a polymer: spectral diffusion and persistent spectral hole burning," J. Opt. Soc. Am. B. 9, 829-836 (1992).
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D. J. Pikas, S. M. Kirkpatrick, E. Tewksbury, L. L. Brott, R. R. Naik, M. O. Stone, and W.M. Dennis, "Nonlinear saturation and lasing characteristics of green fluorescent protein," J. Phys. Chem. B 106, 4831-4837 (2002).
[CrossRef]

K. D. Weston and L. S. Goldner "Orientation imaging and reorientation dynamics of single dye molecules," J. Phys. Chem. B 105, 3453-3462 (2001).
[CrossRef]

Phys. Rev. Lett. (4)

T. Ha, J. Glass, T. Enderle, D. S. Chemla, and S. Weiss, "Hindered rotational diffusion and rotational jumps of single molecules," Phys. Rev. Lett. 80, 2093-2096 (1998).
[CrossRef]

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, "Single molecule dynamics studied by polarization modulation," Phys. Rev. Lett. 77, 3979-3982 (1996).
[CrossRef] [PubMed]

B. Sick, B. Hecht, and L. Novotny "Orientational imaging of single molecules by annular illumination," Phys. Rev. Lett. 85, 4482-4485 (2000).
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R. M. Dickson, D. J. Norris, and W. E. Moerner, "Simultaneous imaging of individual molecules aligned both parallel and perpendicular to the optic axis," Phys. Rev. Lett. 81, 5322-5325 (1998).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (2)

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, "Myosin conformational states determined by single fluorophore polarization," Proc. Natl. Acad. Sci. U.S.A. 95, 8034-8039 (1998).
[CrossRef] [PubMed]

T. Ha, T. Enderle, D. F. Ogletree, D. S. Chemla, P. R. Selvin and S. Weiss, "Probing the interaction between two single molecules: Fluorescence resonance energy transfer between a single donor and a single acceptor," Proc. Natl. Acad. Sci. U.S.A. 93, 6264-6268 (1996).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

I. Munro, I. Pecht, and L. Stryer "Subnanosecond motions of Tryptophan residues in proteins," Proc. Natl. Acad. Sci. USA 76, 56-60 (1979).
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W. E. Moerner and D. P. Fromm, "Methods of single molecule fluorescence spectroscopy and microscopy," Rev. Sci. Instrum. 74, 3597-3619 (2003).
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Science (1)

H. P. Lu, L. Y. Xun, and X. S. Xie, "Single molecule enzymatic dynamics," Science 282, 1877-1882 (1998).
[CrossRef] [PubMed]

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K. Itô, Introduction to Probability Theory (Cambridge University Press, 1984).

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W. Feller, Probability Theory and its Applications (John Wiley and Sons Inc., New York, 1950).

P. Debye, Polar Molecules (Dover Publications, New York, 1945).

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Figures (3)

Fig. 1.
Fig. 1.

Contour plot of SNR (dB) vs laser power and focused spot size (as parameterised by the NA of a focusing lens) assuming a wavelength of 395nm and the following parameter values based on use of GFP: D = 7%, q = 0.79 [9], t 0 = 0.01s, Cb = 2×108 photons/Ws, Nd = 50. For numerical apertures greater than unity we have assumed an oil immersion lens of refractive index 1.5. Saturation effects are included such that σ = σ0/(1 +I/Is ), where σ0 was taken to be 4×10-16 cm2, I = P/A and the saturation intensity Is was assumed to be 103 W/cm2 [10]. The inset shows the variation of the SNR versus integration time for a 5mW laser focused through a 0.95 NA lens.

Fig. 2.
Fig. 2.

An electric dipole p has a transverse orientation described by the angle θ. Here z describes the optical axis.

Fig. 3.
Fig. 3.

a) Histogram of the time averaged intensity for a dipole undergoing continuous angular diffusion with α = 5, β = π/4, t 0 = 10-3s and A = 105 photons/s shown with theoretical fits for differing diffusion coefficients. b) Variance of the number of detected photons as a function of the peak signal strength A and the cumulative probability functions for wobbly and stationary dipoles (inset) for the same parameter values as a).

Equations (31)

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SNR = DqσP t 0 AE p ( DqσP t 0 AE p ) + C b P t 0 + N d t 0
p N ( n ) = ( I ( t 0 ) ) n n ! exp ( I ( t 0 ) )
I ( t 0 ) = 0 t 0 ( t ) dt
( t ) = A cos 2 ( θ ( t ) β )
p N ( n | i ) = i n n ! e i
f N , I n i = p N ( n | i ) f I ( i )
p N ( n ) = 0 f I ( i ) ( ηi ) n n ! e ηi di .
i = A ( cos 2 ( θ 1 β ) τ 1 + cos 2 ( θ 2 β ) τ 2 + + cos 2 ( θ M β ) τ M )
f τ ( τ ) = v exp ( )
X * ( s ) = [ f X ( x ) ] = 0 f X ( x ) e sx dx = E [ e sX ]
I M * ( s ) = Z 1 * ( s ) Z 2 * ( s ) Z M * ( s )
f I ( i ) = m = 0 p M ( m ) f I ( i | m )
Z j * ( s ) = π π 0 f Θ , τ θ τ exp ( sA cos 2 ( θ β ) τ ) dτdθ
Z j * ( s ) = π π 0 f Θ ( θ ) v exp ( sA cos 2 ( θ β ) τ ) dτdθ
= π π v f Θ ( θ ) v + sA cos 2 ( θ β )
f Θ uni ( θ ) = { 1 / 2 Δ for Δ θ < Δ 0 otherwise
Z uni * ( s ) = 1 2 Δ sAv + v 2 ×
[ arctan ( v sA + v tan ( Δ β ) ) + arctan ( v sA + v tan ( Δ + β ) ) ]
f I ( i ) = f ( )
f I ( i ) = 1 2 π σ I 2 exp ( i 2 2 σ I 2 ) .
f Θ j ( θ j ) = f Θ ( θ θ j 1 )
f t = α 2 f θ 2
f Θ θ t = 1 4 παt exp ( ( θ θ 0 ) 2 4 αt ) .
f I ( i ) = 1 t 0 k 0 t 0 f Θ θ k t i ( A i ) dt .
f I ( i ) = 1 πα t 0 i ( A i ) k [ exp ( θ k 2 4 α t 0 ) θ k 2 α t 0 erfc ( θ k 2 4 α t 0 ) ]
= θ ϕ
f Θ , Φ θ ϕ = f Θ ( θ ) f Φ ( ϕ )
Z j * ( s ) = π π 0 π 0 f Θ ( θ ) f Φ ( ϕ ) f τ ( τ ) exp ( s ( θ , ϕ ) τ ) dτdϕdθ
f t = α ( 2 f θ 2 + 2 f ϕ 2 )
f Θ , Φ θ ϕ = 1 4 παt exp ( ( θ θ 0 ) 3 4 αt ) exp ( ( ϕ ϕ 0 ) 2 4 αt )
f I ( i ) = 1 8 πα t 0 i ( A i ) k [ Γ ( 0 , ( θ k θ 0 ) 2 + ( ϕ k ϕ 0 ) 2 4 t 0 α ) ]

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