Abstract

Bio-mechanism investigations demand single particle tracking with high spatial and temporal resolutions which require single fluorophore 3D localization measurements with matching precision and speed. Although the precision for lateral-localization measurements is well described by an analytical expression, for the axial direction, it is often obtained by repeating location measurements or by estimating a lower bound. Here, we report a precision expression for an axial-localization method that analyzes the standard deviations of single fluorophores’ intensity profiles. Like the lateral-localization precision, this expression includes all relevant experimental effects measurable from a Gaussian intensity profile of the fluorophore. This expression completes the precision analysis for single-image 3D localization of individual fluorophores and lifts the temporal resolution to the typical exposure timescales of milliseconds.

© 2012 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  22. N. Adir, Department of Chemistry, Technion, Israel Institute of Technology, Israel, is preparing a manuscript.
  23. H. P. Kao and A. S. Verkman, “Tracking of single fluorescent particles in three dimensions: Use of cylindrical optics to encode particle position,” Biophys. J. 67, 1291–1300 (1994).
    [CrossRef] [PubMed]
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2010 (2)

2009 (4)

A. A. Arteni, G. Ajlani, and E. J. Boekema, “Structural organisation of phycobilisomes from Synechocystis sp. strain PCC6803 and their interaction with the membrane,” Biochim. Biophys. Acta 1787, 272–279 (2009).
[CrossRef] [PubMed]

Y. Deng and J. W. Shaevitz, “Effect of aberration on height calibration in three-dimensional localization-based microscopy and particle tracking,” Appl. Opt. 48, 1886–1890 (2009).
[CrossRef] [PubMed]

J. W. Shaevitz, “Bayesian estimation of the axial position in astigmatism-based three-dimensional particle tracking,” Int. J. Opt. 2009, 896208 (2009).

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[CrossRef] [PubMed]

2008 (5)

B. Huang, S. A. Jones, B. Brandenburg, and X. Zhuang, “Whole-cell 3D STORM reveals interactions between cellular structures with nanometer-scale resolution,” Nat. Methods 5, 1047–1052 (2008).
[CrossRef] [PubMed]

Z. Zhang and C.-H. Menq, “Three-dimensional particle tracking with subnanometer resolution using off-focus images,” Appl. Optics 47, 2361–2370 (2008).
[CrossRef]

C. Joo, H. Balci, Y. Ishitsuka, C. Buranachai, and T. Ha, “Advances in single-molecule fluorescence methods for molecular biology,” Annu. Rev. Biochem. 77, 51–76 (2008).
[CrossRef] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[CrossRef] [PubMed]

2007 (2)

L. Holtzer, T. Meckel, and T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90, 053902 (2007).
[CrossRef]

E. Toprak, H. Balci, B. H. Blehm, and P. R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7, 2043–2045 (2007).
[CrossRef] [PubMed]

2006 (1)

Y. M. Wang, R. H. Austin, and E. C. Cox, “Single molecule measurements of repressor protein 1D diffusion on DNA,” Phys. Rev. Lett. 97, 048302 (2006).
[CrossRef] [PubMed]

2005 (1)

2003 (2)

M. Speidel, A. Jonáš, and E.-L. Florin, “Three-dimensional tracking of fluorescent nanoparticles with sub-nanometer precision by use of off-focus imaging,” Opt. Lett. 28, 69–71 (2003).
[CrossRef] [PubMed]

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-overhand: Single fluorophore imaging with 1.5-nm localization,” Science 300, 2061–2065 (2003).
[CrossRef] [PubMed]

2002 (1)

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82, 2775–2783 (2002).
[CrossRef] [PubMed]

2000 (1)

G. J. Schütz, V. P. Pastushenko, H. J. Gruber, H.-G. Knaus, B. Pragl, and H. Schindler, “3D imaging of individual ion channels in live cells at 40nm resolution,” Single Mol. 1, 25–31 (2000).
[CrossRef]

1998 (1)

A. M. van Oijen, J. Köhler, J. Schmidt, M. Müller, and G. J. Brakenhoff, “3-Dimensional super-resolution by spectrally selective imaging,” Chem. Phys. Lett. 292, 183–187 (1998).
[CrossRef]

1995 (1)

G. Ajlani, C. Vernotte, L. DiMagno, and R. Haselkorn, “Phycobilisome core mutants of Synechocystis PCC 6803,” Biochim. Biophys. Acta 1231, 189–196 (1995).
[CrossRef]

1994 (1)

H. P. Kao and A. S. Verkman, “Tracking of single fluorescent particles in three dimensions: Use of cylindrical optics to encode particle position,” Biophys. J. 67, 1291–1300 (1994).
[CrossRef] [PubMed]

Adir, N.

N. Adir, Department of Chemistry, Technion, Israel Institute of Technology, Israel, is preparing a manuscript.

Aguet, F.

Ajlani, G.

A. A. Arteni, G. Ajlani, and E. J. Boekema, “Structural organisation of phycobilisomes from Synechocystis sp. strain PCC6803 and their interaction with the membrane,” Biochim. Biophys. Acta 1787, 272–279 (2009).
[CrossRef] [PubMed]

G. Ajlani, C. Vernotte, L. DiMagno, and R. Haselkorn, “Phycobilisome core mutants of Synechocystis PCC 6803,” Biochim. Biophys. Acta 1231, 189–196 (1995).
[CrossRef]

Arteni, A. A.

A. A. Arteni, G. Ajlani, and E. J. Boekema, “Structural organisation of phycobilisomes from Synechocystis sp. strain PCC6803 and their interaction with the membrane,” Biochim. Biophys. Acta 1787, 272–279 (2009).
[CrossRef] [PubMed]

Austin, R. H.

Y. M. Wang, R. H. Austin, and E. C. Cox, “Single molecule measurements of repressor protein 1D diffusion on DNA,” Phys. Rev. Lett. 97, 048302 (2006).
[CrossRef] [PubMed]

Balci, H.

C. Joo, H. Balci, Y. Ishitsuka, C. Buranachai, and T. Ha, “Advances in single-molecule fluorescence methods for molecular biology,” Annu. Rev. Biochem. 77, 51–76 (2008).
[CrossRef] [PubMed]

E. Toprak, H. Balci, B. H. Blehm, and P. R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7, 2043–2045 (2007).
[CrossRef] [PubMed]

Bates, M.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

Biteen, J. S.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[CrossRef] [PubMed]

Blehm, B. H.

E. Toprak, H. Balci, B. H. Blehm, and P. R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7, 2043–2045 (2007).
[CrossRef] [PubMed]

Boekema, E. J.

A. A. Arteni, G. Ajlani, and E. J. Boekema, “Structural organisation of phycobilisomes from Synechocystis sp. strain PCC6803 and their interaction with the membrane,” Biochim. Biophys. Acta 1787, 272–279 (2009).
[CrossRef] [PubMed]

Brakenhoff, G. J.

A. M. van Oijen, J. Köhler, J. Schmidt, M. Müller, and G. J. Brakenhoff, “3-Dimensional super-resolution by spectrally selective imaging,” Chem. Phys. Lett. 292, 183–187 (1998).
[CrossRef]

Brandenburg, B.

B. Huang, S. A. Jones, B. Brandenburg, and X. Zhuang, “Whole-cell 3D STORM reveals interactions between cellular structures with nanometer-scale resolution,” Nat. Methods 5, 1047–1052 (2008).
[CrossRef] [PubMed]

Buranachai, C.

C. Joo, H. Balci, Y. Ishitsuka, C. Buranachai, and T. Ha, “Advances in single-molecule fluorescence methods for molecular biology,” Annu. Rev. Biochem. 77, 51–76 (2008).
[CrossRef] [PubMed]

Chao, J.

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[CrossRef] [PubMed]

Cox, E. C.

Y. M. Wang, R. H. Austin, and E. C. Cox, “Single molecule measurements of repressor protein 1D diffusion on DNA,” Phys. Rev. Lett. 97, 048302 (2006).
[CrossRef] [PubMed]

DeCenzo, S. H.

Deng, Y.

DeSantis, M. C.

DiMagno, L.

G. Ajlani, C. Vernotte, L. DiMagno, and R. Haselkorn, “Phycobilisome core mutants of Synechocystis PCC 6803,” Biochim. Biophys. Acta 1231, 189–196 (1995).
[CrossRef]

Florin, E.-L.

Forkey, J. N.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-overhand: Single fluorophore imaging with 1.5-nm localization,” Science 300, 2061–2065 (2003).
[CrossRef] [PubMed]

Goldman, Y. E.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-overhand: Single fluorophore imaging with 1.5-nm localization,” Science 300, 2061–2065 (2003).
[CrossRef] [PubMed]

Gruber, H. J.

G. J. Schütz, V. P. Pastushenko, H. J. Gruber, H.-G. Knaus, B. Pragl, and H. Schindler, “3D imaging of individual ion channels in live cells at 40nm resolution,” Single Mol. 1, 25–31 (2000).
[CrossRef]

Ha, T.

C. Joo, H. Balci, Y. Ishitsuka, C. Buranachai, and T. Ha, “Advances in single-molecule fluorescence methods for molecular biology,” Annu. Rev. Biochem. 77, 51–76 (2008).
[CrossRef] [PubMed]

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-overhand: Single fluorophore imaging with 1.5-nm localization,” Science 300, 2061–2065 (2003).
[CrossRef] [PubMed]

Haselkorn, R.

G. Ajlani, C. Vernotte, L. DiMagno, and R. Haselkorn, “Phycobilisome core mutants of Synechocystis PCC 6803,” Biochim. Biophys. Acta 1231, 189–196 (1995).
[CrossRef]

Holtzer, L.

L. Holtzer, T. Meckel, and T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90, 053902 (2007).
[CrossRef]

Huang, B.

B. Huang, S. A. Jones, B. Brandenburg, and X. Zhuang, “Whole-cell 3D STORM reveals interactions between cellular structures with nanometer-scale resolution,” Nat. Methods 5, 1047–1052 (2008).
[CrossRef] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

Ishitsuka, Y.

C. Joo, H. Balci, Y. Ishitsuka, C. Buranachai, and T. Ha, “Advances in single-molecule fluorescence methods for molecular biology,” Annu. Rev. Biochem. 77, 51–76 (2008).
[CrossRef] [PubMed]

Jonáš, A.

Jones, S. A.

B. Huang, S. A. Jones, B. Brandenburg, and X. Zhuang, “Whole-cell 3D STORM reveals interactions between cellular structures with nanometer-scale resolution,” Nat. Methods 5, 1047–1052 (2008).
[CrossRef] [PubMed]

Joo, C.

C. Joo, H. Balci, Y. Ishitsuka, C. Buranachai, and T. Ha, “Advances in single-molecule fluorescence methods for molecular biology,” Annu. Rev. Biochem. 77, 51–76 (2008).
[CrossRef] [PubMed]

Kao, H. P.

H. P. Kao and A. S. Verkman, “Tracking of single fluorescent particles in three dimensions: Use of cylindrical optics to encode particle position,” Biophys. J. 67, 1291–1300 (1994).
[CrossRef] [PubMed]

Kessler, J.

S. K. Zareh, M. C. DeSantis, J. Kessler, J.-L. Li, and Y. M. Wang, “Single-image diffusion coefficient measurements of proteins in free solution,” Biophys. J. (in review).

Knaus, H.-G.

G. J. Schütz, V. P. Pastushenko, H. J. Gruber, H.-G. Knaus, B. Pragl, and H. Schindler, “3D imaging of individual ion channels in live cells at 40nm resolution,” Single Mol. 1, 25–31 (2000).
[CrossRef]

Köhler, J.

A. M. van Oijen, J. Köhler, J. Schmidt, M. Müller, and G. J. Brakenhoff, “3-Dimensional super-resolution by spectrally selective imaging,” Chem. Phys. Lett. 292, 183–187 (1998).
[CrossRef]

Larson, D. R.

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82, 2775–2783 (2002).
[CrossRef] [PubMed]

Li, J.-L.

M. C. DeSantis, S. H. DeCenzo, J.-L. Li, and Y. M. Wang, “Precision analysis for standard deviation measurements of single fluorescent molecule images,” Opt. Express 18, 6563–6576 (2010).
[CrossRef] [PubMed]

S. K. Zareh, M. C. DeSantis, J. Kessler, J.-L. Li, and Y. M. Wang, “Single-image diffusion coefficient measurements of proteins in free solution,” Biophys. J. (in review).

Liu, N.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[CrossRef] [PubMed]

Lord, S. J.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[CrossRef] [PubMed]

McKinney, S. A.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-overhand: Single fluorophore imaging with 1.5-nm localization,” Science 300, 2061–2065 (2003).
[CrossRef] [PubMed]

Meckel, T.

L. Holtzer, T. Meckel, and T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90, 053902 (2007).
[CrossRef]

Menq, C.-H.

Z. Zhang and C.-H. Menq, “Three-dimensional particle tracking with subnanometer resolution using off-focus images,” Appl. Optics 47, 2361–2370 (2008).
[CrossRef]

Moerner, W. E.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[CrossRef] [PubMed]

Müller, M.

A. M. van Oijen, J. Köhler, J. Schmidt, M. Müller, and G. J. Brakenhoff, “3-Dimensional super-resolution by spectrally selective imaging,” Chem. Phys. Lett. 292, 183–187 (1998).
[CrossRef]

Ober, R. J.

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[CrossRef] [PubMed]

Pastushenko, V. P.

G. J. Schütz, V. P. Pastushenko, H. J. Gruber, H.-G. Knaus, B. Pragl, and H. Schindler, “3D imaging of individual ion channels in live cells at 40nm resolution,” Single Mol. 1, 25–31 (2000).
[CrossRef]

Pavani, S. R. P.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[CrossRef] [PubMed]

Piestun, R.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[CrossRef] [PubMed]

Prabhat, P.

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[CrossRef] [PubMed]

Pragl, B.

G. J. Schütz, V. P. Pastushenko, H. J. Gruber, H.-G. Knaus, B. Pragl, and H. Schindler, “3D imaging of individual ion channels in live cells at 40nm resolution,” Single Mol. 1, 25–31 (2000).
[CrossRef]

Ram, S.

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[CrossRef] [PubMed]

Schindler, H.

G. J. Schütz, V. P. Pastushenko, H. J. Gruber, H.-G. Knaus, B. Pragl, and H. Schindler, “3D imaging of individual ion channels in live cells at 40nm resolution,” Single Mol. 1, 25–31 (2000).
[CrossRef]

Schmidt, J.

A. M. van Oijen, J. Köhler, J. Schmidt, M. Müller, and G. J. Brakenhoff, “3-Dimensional super-resolution by spectrally selective imaging,” Chem. Phys. Lett. 292, 183–187 (1998).
[CrossRef]

Schmidt, T.

L. Holtzer, T. Meckel, and T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90, 053902 (2007).
[CrossRef]

Schütz, G. J.

G. J. Schütz, V. P. Pastushenko, H. J. Gruber, H.-G. Knaus, B. Pragl, and H. Schindler, “3D imaging of individual ion channels in live cells at 40nm resolution,” Single Mol. 1, 25–31 (2000).
[CrossRef]

Selvin, P. R.

E. Toprak, H. Balci, B. H. Blehm, and P. R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7, 2043–2045 (2007).
[CrossRef] [PubMed]

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-overhand: Single fluorophore imaging with 1.5-nm localization,” Science 300, 2061–2065 (2003).
[CrossRef] [PubMed]

Shaevitz, J. W.

J. W. Shaevitz, “Bayesian estimation of the axial position in astigmatism-based three-dimensional particle tracking,” Int. J. Opt. 2009, 896208 (2009).

Y. Deng and J. W. Shaevitz, “Effect of aberration on height calibration in three-dimensional localization-based microscopy and particle tracking,” Appl. Opt. 48, 1886–1890 (2009).
[CrossRef] [PubMed]

Speidel, M.

Thompson, M. A.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[CrossRef] [PubMed]

Thompson, R. E.

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82, 2775–2783 (2002).
[CrossRef] [PubMed]

Toprak, E.

E. Toprak, H. Balci, B. H. Blehm, and P. R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7, 2043–2045 (2007).
[CrossRef] [PubMed]

Twieg, R. J.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[CrossRef] [PubMed]

Unser, M.

van de Ville, D.

van Oijen, A. M.

A. M. van Oijen, J. Köhler, J. Schmidt, M. Müller, and G. J. Brakenhoff, “3-Dimensional super-resolution by spectrally selective imaging,” Chem. Phys. Lett. 292, 183–187 (1998).
[CrossRef]

Verkman, A. S.

H. P. Kao and A. S. Verkman, “Tracking of single fluorescent particles in three dimensions: Use of cylindrical optics to encode particle position,” Biophys. J. 67, 1291–1300 (1994).
[CrossRef] [PubMed]

Vernotte, C.

G. Ajlani, C. Vernotte, L. DiMagno, and R. Haselkorn, “Phycobilisome core mutants of Synechocystis PCC 6803,” Biochim. Biophys. Acta 1231, 189–196 (1995).
[CrossRef]

Wang, W.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

Wang, Y. M.

M. C. DeSantis, S. H. DeCenzo, J.-L. Li, and Y. M. Wang, “Precision analysis for standard deviation measurements of single fluorescent molecule images,” Opt. Express 18, 6563–6576 (2010).
[CrossRef] [PubMed]

S. H. DeCenzo, M. C. DeSantis, and Y. M. Wang, “Single-image separation measurements of two unresolved fluorophores,” Opt. Express 18, 16628–16639 (2010).
[CrossRef] [PubMed]

Y. M. Wang, R. H. Austin, and E. C. Cox, “Single molecule measurements of repressor protein 1D diffusion on DNA,” Phys. Rev. Lett. 97, 048302 (2006).
[CrossRef] [PubMed]

S. K. Zareh, M. C. DeSantis, J. Kessler, J.-L. Li, and Y. M. Wang, “Single-image diffusion coefficient measurements of proteins in free solution,” Biophys. J. (in review).

Ward, E. S.

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[CrossRef] [PubMed]

Webb, W. W.

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82, 2775–2783 (2002).
[CrossRef] [PubMed]

Yildiz, A.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-overhand: Single fluorophore imaging with 1.5-nm localization,” Science 300, 2061–2065 (2003).
[CrossRef] [PubMed]

Zareh, S. K.

S. K. Zareh, M. C. DeSantis, J. Kessler, J.-L. Li, and Y. M. Wang, “Single-image diffusion coefficient measurements of proteins in free solution,” Biophys. J. (in review).

Zhang, Z.

Z. Zhang and C.-H. Menq, “Three-dimensional particle tracking with subnanometer resolution using off-focus images,” Appl. Optics 47, 2361–2370 (2008).
[CrossRef]

Zhuang, X.

B. Huang, S. A. Jones, B. Brandenburg, and X. Zhuang, “Whole-cell 3D STORM reveals interactions between cellular structures with nanometer-scale resolution,” Nat. Methods 5, 1047–1052 (2008).
[CrossRef] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

Annu. Rev. Biochem. (1)

C. Joo, H. Balci, Y. Ishitsuka, C. Buranachai, and T. Ha, “Advances in single-molecule fluorescence methods for molecular biology,” Annu. Rev. Biochem. 77, 51–76 (2008).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Optics (1)

Z. Zhang and C.-H. Menq, “Three-dimensional particle tracking with subnanometer resolution using off-focus images,” Appl. Optics 47, 2361–2370 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

L. Holtzer, T. Meckel, and T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90, 053902 (2007).
[CrossRef]

Biochim. Biophys. Acta (2)

A. A. Arteni, G. Ajlani, and E. J. Boekema, “Structural organisation of phycobilisomes from Synechocystis sp. strain PCC6803 and their interaction with the membrane,” Biochim. Biophys. Acta 1787, 272–279 (2009).
[CrossRef] [PubMed]

G. Ajlani, C. Vernotte, L. DiMagno, and R. Haselkorn, “Phycobilisome core mutants of Synechocystis PCC 6803,” Biochim. Biophys. Acta 1231, 189–196 (1995).
[CrossRef]

Biophys. J. (4)

H. P. Kao and A. S. Verkman, “Tracking of single fluorescent particles in three dimensions: Use of cylindrical optics to encode particle position,” Biophys. J. 67, 1291–1300 (1994).
[CrossRef] [PubMed]

S. K. Zareh, M. C. DeSantis, J. Kessler, J.-L. Li, and Y. M. Wang, “Single-image diffusion coefficient measurements of proteins in free solution,” Biophys. J. (in review).

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82, 2775–2783 (2002).
[CrossRef] [PubMed]

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[CrossRef] [PubMed]

Chem. Phys. Lett. (1)

A. M. van Oijen, J. Köhler, J. Schmidt, M. Müller, and G. J. Brakenhoff, “3-Dimensional super-resolution by spectrally selective imaging,” Chem. Phys. Lett. 292, 183–187 (1998).
[CrossRef]

Int. J. Opt. (1)

J. W. Shaevitz, “Bayesian estimation of the axial position in astigmatism-based three-dimensional particle tracking,” Int. J. Opt. 2009, 896208 (2009).

Nano Lett. (1)

E. Toprak, H. Balci, B. H. Blehm, and P. R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7, 2043–2045 (2007).
[CrossRef] [PubMed]

Nat. Methods (1)

B. Huang, S. A. Jones, B. Brandenburg, and X. Zhuang, “Whole-cell 3D STORM reveals interactions between cellular structures with nanometer-scale resolution,” Nat. Methods 5, 1047–1052 (2008).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

Y. M. Wang, R. H. Austin, and E. C. Cox, “Single molecule measurements of repressor protein 1D diffusion on DNA,” Phys. Rev. Lett. 97, 048302 (2006).
[CrossRef] [PubMed]

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

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[CrossRef] [PubMed]

Science (2)

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-overhand: Single fluorophore imaging with 1.5-nm localization,” Science 300, 2061–2065 (2003).
[CrossRef] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

Single Mol. (1)

G. J. Schütz, V. P. Pastushenko, H. J. Gruber, H.-G. Knaus, B. Pragl, and H. Schindler, “3D imaging of individual ion channels in live cells at 40nm resolution,” Single Mol. 1, 25–31 (2000).
[CrossRef]

Other (1)

N. Adir, Department of Chemistry, Technion, Israel Institute of Technology, Israel, is preparing a manuscript.

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Figures (4)

Fig. 1
Fig. 1

PBS axial-localization precision studies. (A) Snapshots of a PBS molecule separated by 350 nm along z (the middle image is at z ≈ −50 nm). Scale bar, 500 nm. (B) Mean sx versus z for 6 simultaneously imaged PBS molecules. The solid line is a fit to the data according to Eq. (3), yielding s0x = 144.1 nm, A = 2.91 × 10−7 nm−2, and B = 1.87×10−11 nm−4. The y- and x-axis error bars are the average Δsi and Δz values of the 6 PBS molecules. Note that the errors increase as z decreases because the PBS molecules gradually bleached with imaging time from 4800 to 1400 mean photons per PSF. (C) 50 consecutive sx measurements for the PBS molecule in (A) at each of the three z locations in the blue circle in (B) (gray lines). The mean photon counts per image is ≈ 3000. (D) The corresponding z values to sx values in (C) (gray lines). At each axial location in (C) and (D), the black horizontal lines outline the average sx and z values, and the left (black) and right (red) error bars represent the respective experimental and theoretical Δsi and Δz values. Insets to (C) and (D) show Gaussian fits to the distributions of the experimental sx and z data for the middle axial location; the SDs of the fits (experimental error bars) are Δsx = 6.3 nm and Δz = 21.5 nm, in good agreement with the theoretical values of Δsx = 6.0 nm and Δz = 20.0 nm. Note that Δz is clearly less than the z increment size of 50 nm.

Fig. 2
Fig. 2

Simulation (circles) and theoretical (solid black line) Δsx versus a/s0x. The dashed (red) line is the theoretical Δsx results multiplied by 1.51 + 0.17a/s0x as a best fit to the simulated Δsx, showing agreement.

Fig. 3
Fig. 3

PBS Δz versus |z| calculations according to Eqs. (2), (3), and (5) at photon counts N, of 100, 500, 1000, 5000, and 2×104 (top to bottom). No background noise is included. Only Δz at |z| ≥ Δz(z) are shown.

Fig. 4
Fig. 4

(A) PBS sx(z) and sy(z) curves with shifted foci at z = ±300 nm. (B) Δz versus z for the shifted sx(z) and sy(z) for N = 100, 500, 1000, 5000, and 2×104 photons (top to bottom). Only Δz at |z ± 300 nm| = Δz(z) at N = 500 and 2×104 photons are shown, and since both sx and sy are required for the Δsi calculation, only Δz where both PBS sx and sy are valid in (A) are shown. The bold lines mark the minimal Δz values at all measurable z.

Equations (5)

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f ( x , y ) = f 0 exp [ ( x x 0 ) 2 2 s x 2 ( y y 0 ) 2 2 s y 2 ] + b ,
Δ s x , r m s = s 0 x 2 + a 2 / 12 N + 16 π ( s 0 x 2 + a 2 / 12 ) 3 / 2 ( s 0 y 2 + a 2 / 12 ) 1 / 2 ( σ b 2 b ) 3 a 2 N 2 ,
s i ( z ) = s 0 i 1 + A z 2 + B z 4 ,
z ( s i ) = ± C A 2 B ,
Δ z = s i Δ s i s 0 i 2 C 2 B C A .

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