Abstract

Measurements of the orientational freedom with which a single molecule may rotate or ‘wobble’ about a fixed axis have provided researchers invaluable clues about the underlying behavior of a variety of biological systems. In this paper, we propose a measurement and data analysis procedure based on a widefield fluorescence microscope image for quantitatively distinguishing individual molecules that exhibit varying degrees of rotational mobility. Our proposed technique is especially applicable to cases in which the molecule undergoes rotational motions on a timescale much faster than the framerate of the camera used to record fluorescence images. Unlike currently available methods, sophisticated hardware for modulating the polarization of light illuminating the sample is not required. Additional polarization optics may be inserted in the microscope’s imaging pathway to achieve superior measurement precision, but are not essential. We present a theoretical analysis, and benchmark our technique with numerical simulations using typical experimental parameters for single-molecule imaging.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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2014 (4)

A. S. Backer, M. P. Backlund, A. R. Diezmann, S. J. Sahl, and W. E. Moerner, “A bisected pupil for studying single-molecule orientational dynamics and its application to 3D super-resolution microscopy,” Appl. Phys. Lett. 104, 193701 (2014).
[Crossref] [PubMed]

A. S. Backer and W. E. Moerner, “Extending single-molecule microscopy using optical Fourier processing,” J. Phys. Chem. B 118(28), 8313–8329 (2014).
[Crossref] [PubMed]

J. A. Hutchison, H. Uji-i, A. Deres, T. Vosch, S. Rocha, S. Müller, A. A. Bastian, J. Enderlein, H. Nourouzi, C. Li, A. Herrmann, K. Müllen, F. De Schryver, and J. Hofkens, “A surface-bound molecule that undergoes optically biased Brownian rotation,” Nat. Nanotechnol. 9(2), 131–136 (2014).
[Crossref] [PubMed]

S. Ham, J. Yang, F. Schlosser, F. Wurthner, and D. Kim, “Reconstruction of the molecular structure of a multichromophoric system using single-molecule defocused wide-field imaging,” J. Phys. Chem. Lett. 5(16), 2830–2835 (2014).
[Crossref]

2013 (8)

Y. Zhang, L. Gu, H. Chang, W. Ji, Y. Chen, M. Zhang, L. Yang, B. Liu, L. Chen, and T. Xu, “Ultrafast, accurate, and robust localization of anisotropic dipoles,” Protein Cell 4(8), 598–606 (2013).
[Crossref] [PubMed]

M. D. Lew, M. P. Backlund, and W. E. Moerner, “Rotational mobility of single molecules affects localization accuracy in super-resolution fluorescence microscopy,” Nano Lett. 13(9), 3967–3972 (2013).
[Crossref] [PubMed]

A. S. Backer, M. P. Backlund, M. D. Lew, and W. E. Moerner, “Single-molecule orientation measurements with a quadrated pupil,” Opt. Lett. 38(9), 1521–1523 (2013).
[Crossref] [PubMed]

J. F. Beausang, D. Y. Shroder, P. C. Nelson, and Y. E. Goldman, “Tilting and wobble of Myosin V by high-speed single-molecule polarized fluorescence microscopy,” Biophys. J. 104(6), 1263–1273 (2013).
[Crossref] [PubMed]

C. Phelps, W. Lee, D. Jose, P. H. von Hippel, and A. H. Marcus, “Single-molecule FRET and linear dichroism studies of DNA breathing and helicase binding at replication fork junctions,” Proc. Natl. Acad. Sci. U.S.A. 110(43), 17320–17325 (2013).
[Crossref] [PubMed]

M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, and D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices--from theory to practice,” PLoS ONE 8(1), e53671 (2013).
[Crossref] [PubMed]

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
[Crossref] [PubMed]

S. Liu, E. B. Kromann, W. D. Krueger, J. Bewersdorf, and K. A. Lidke, “Three dimensional single molecule localization using a phase retrieved pupil function,” Opt. Express 21(24), 29462–29487 (2013).
[Crossref] [PubMed]

2012 (6)

I. Izeddin, M. El Beheiry, J. Andilla, D. Ciepielewski, X. Darzacq, and M. Dahan, “PSF shaping using adaptive optics for three-dimensional single-molecule super-resolution imaging and tracking,” Opt. Express 20(5), 4957–4967 (2012).
[PubMed]

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. U.S.A. 109(3), 675–679 (2012).
[Crossref] [PubMed]

D. Axelrod, “Fluorescence excitation and imaging of single molecules near dielectric-coated and bare surfaces: a theoretical study,” J. Microsc. 247(2), 147–160 (2012).
[Crossref] [PubMed]

A. Agrawal, S. Quirin, G. Grover, and R. Piestun, “Limits of 3D dipole localization and orientation estimation for single-molecule imaging: towards Green’s tensor engineering,” Opt. Express 20(24), 26667–26680 (2012).
[Crossref] [PubMed]

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. U.S.A. 109(47), 19087–19092 (2012).
[Crossref] [PubMed]

S. Stallinga and B. Rieger, “Position and orientation estimation of fixed dipole emitters using an effective Hermite point spread function model,” Opt. Express 20(6), 5896–5921 (2012).
[Crossref] [PubMed]

2011 (2)

A. Cyphersmith, A. Maksov, R. Hassey-Paradise, K. D. McCarthy, and M. D. Barnes, “Defocused emission patterns from chiral fluorophores: application to chiral axis orientation determination,” J. Phys. Chem. Lett. 2(6), 661–665 (2011).
[Crossref]

M. R. Foreman and P. Török, “Fundamental limits in single-molecule orientation measurements,” New J. Phys. 13(9), 093013 (2011).
[Crossref]

2010 (2)

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7(5), 373–375 (2010).
[Crossref] [PubMed]

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7(5), 377–381 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (2)

T. J. Gould, M. S. Gunewardene, M. V. Gudheti, V. V. Verkhusha, S. R. Yin, J. A. Gosse, and S. T. Hess, “Nanoscale imaging of molecular positions and anisotropies,” Nat. Methods 5(12), 1027–1030 (2008).
[Crossref] [PubMed]

I. Testa, A. Schönle, C. von Middendorff, C. Geisler, R. Medda, C. A. Wurm, A. C. Stiel, S. Jakobs, M. Bossi, C. Eggeling, S. W. Hell, and A. Egner, “Nanoscale separation of molecular species based on their rotational mobility,” Opt. Express 16(25), 21093–21104 (2008).
[Crossref] [PubMed]

2006 (1)

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A. 103(17), 6495–6499 (2006).
[Crossref] [PubMed]

2005 (3)

M. E. Quinlan, J. N. Forkey, and Y. E. Goldman, “Orientation of the Myosin Light Chain Region by Single Molecule Total Internal Reflection Fluorescence Polarization Microscopy,” Biophys. J. 89(2), 1132–1142 (2005).
[Crossref] [PubMed]

J. N. Forkey, M. E. Quinlan, and Y. E. Goldman, “Measurement of single macromolecule orientation by total internal reflection fluorescence polarization microscopy,” Biophys. J. 89(2), 1261–1271 (2005).
[Crossref] [PubMed]

S. A. Rosenberg, M. E. Quinlan, J. N. Forkey, and Y. E. Goldman, “Rotational motions of macro-molecules by single-molecule fluorescence microscopy,” Acc. Chem. Res. 38(7), 583–593 (2005).
[Crossref] [PubMed]

2004 (4)

D. Patra, I. Gregor, and J. Enderlein, “Image analysis of defocused single-molecule images for three-dimensional molecule orientation studies,” J. Phys. Chem. A 108(33), 6836–6841 (2004).
[Crossref]

M. A. Lieb, J. M. Zavislan, and L. Novotny, “Single-molecule orientations determined by direct emission pattern imaging,” J. Opt. Soc. Am. B 21(6), 1210–1215 (2004).
[Crossref]

B. Huang, T. D. Perroud, and R. N. Zare, “Photon counting histogram: one-photon excitation,” ChemPhysChem 5(10), 1523–1531 (2004).
[Crossref] [PubMed]

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[Crossref] [PubMed]

2003 (1)

2001 (2)

H. Sosa, E. J. G. Peterman, W. E. Moerner, and L. S. B. Goldstein, “ADP-induced rocking of the kinesin motor domain revealed by single-molecule fluorescence polarization microscopy,” Nat. Struct. Biol. 8(6), 540–544 (2001).
[Crossref] [PubMed]

E. J. G. Peterman, H. Sosa, L. S. B. Goldstein, and W. E. Moerner, “Polarized fluorescence microscopy of individual and many kinesin motors bound to axonemal microtubules,” Biophys. J. 81(5), 2851–2863 (2001).
[Crossref] [PubMed]

1999 (1)

A. P. Bartko and R. M. Dickson, “Imaging three-dimensional single molecule orientations,” J. Phys. Chem. B 103(51), 11237–11241 (1999).
[Crossref]

1998 (2)

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(24), 5322–5325 (1998).
[Crossref]

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(10), 2093–2096 (1998).
[Crossref]

1996 (1)

T. Ha, T. Enderle, S. Chemla, R. Selvin, and S. Weiss, “Single molecule dynamics studied by polarization modulation,” Phys. Rev. Lett. 77(19), 3979–3982 (1996).
[Crossref] [PubMed]

1989 (1)

D. Axelrod, “Fluorescence polarization microscopy,” Methods Cell Biol. 30, 333–352 (1989).
[Crossref] [PubMed]

1987 (1)

1977 (1)

K. Kinosita, S. Kawato, and A. Ikegami, “A theory of fluorescence polarization decay in membranes,” Biophys. J. 20(3), 289–305 (1977).
[Crossref] [PubMed]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Agrawal, A.

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. U.S.A. 109(47), 19087–19092 (2012).
[Crossref] [PubMed]

A. Agrawal, S. Quirin, G. Grover, and R. Piestun, “Limits of 3D dipole localization and orientation estimation for single-molecule imaging: towards Green’s tensor engineering,” Opt. Express 20(24), 26667–26680 (2012).
[Crossref] [PubMed]

Aguet, F.

Andilla, J.

Axelrod, D.

D. Axelrod, “Fluorescence excitation and imaging of single molecules near dielectric-coated and bare surfaces: a theoretical study,” J. Microsc. 247(2), 147–160 (2012).
[Crossref] [PubMed]

D. Axelrod, “Fluorescence polarization microscopy,” Methods Cell Biol. 30, 333–352 (1989).
[Crossref] [PubMed]

E. H. Hellen and D. Axelrod, “Fluorescence emission at dielectric and metal-film interfaces,” J. Opt. Soc. Am. B 4(3), 337–350 (1987).
[Crossref]

Backer, A. S.

A. S. Backer, M. P. Backlund, A. R. Diezmann, S. J. Sahl, and W. E. Moerner, “A bisected pupil for studying single-molecule orientational dynamics and its application to 3D super-resolution microscopy,” Appl. Phys. Lett. 104, 193701 (2014).
[Crossref] [PubMed]

A. S. Backer and W. E. Moerner, “Extending single-molecule microscopy using optical Fourier processing,” J. Phys. Chem. B 118(28), 8313–8329 (2014).
[Crossref] [PubMed]

A. S. Backer, M. P. Backlund, M. D. Lew, and W. E. Moerner, “Single-molecule orientation measurements with a quadrated pupil,” Opt. Lett. 38(9), 1521–1523 (2013).
[Crossref] [PubMed]

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. U.S.A. 109(47), 19087–19092 (2012).
[Crossref] [PubMed]

Backlund, M. P.

A. S. Backer, M. P. Backlund, A. R. Diezmann, S. J. Sahl, and W. E. Moerner, “A bisected pupil for studying single-molecule orientational dynamics and its application to 3D super-resolution microscopy,” Appl. Phys. Lett. 104, 193701 (2014).
[Crossref] [PubMed]

M. D. Lew, M. P. Backlund, and W. E. Moerner, “Rotational mobility of single molecules affects localization accuracy in super-resolution fluorescence microscopy,” Nano Lett. 13(9), 3967–3972 (2013).
[Crossref] [PubMed]

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J. F. Beausang, D. Y. Shroder, P. C. Nelson, and Y. E. Goldman, “Tilting and wobble of Myosin V by high-speed single-molecule polarized fluorescence microscopy,” Biophys. J. 104(6), 1263–1273 (2013).
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F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
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Bossi, M.

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Y. Zhang, L. Gu, H. Chang, W. Ji, Y. Chen, M. Zhang, L. Yang, B. Liu, L. Chen, and T. Xu, “Ultrafast, accurate, and robust localization of anisotropic dipoles,” Protein Cell 4(8), 598–606 (2013).
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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(10), 2093–2096 (1998).
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T. Ha, T. Enderle, S. Chemla, R. Selvin, and S. Weiss, “Single molecule dynamics studied by polarization modulation,” Phys. Rev. Lett. 77(19), 3979–3982 (1996).
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Geissbühler, S.

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(10), 2093–2096 (1998).
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Goldman, Y. E.

J. F. Beausang, D. Y. Shroder, P. C. Nelson, and Y. E. Goldman, “Tilting and wobble of Myosin V by high-speed single-molecule polarized fluorescence microscopy,” Biophys. J. 104(6), 1263–1273 (2013).
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E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A. 103(17), 6495–6499 (2006).
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M. E. Quinlan, J. N. Forkey, and Y. E. Goldman, “Orientation of the Myosin Light Chain Region by Single Molecule Total Internal Reflection Fluorescence Polarization Microscopy,” Biophys. J. 89(2), 1132–1142 (2005).
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J. N. Forkey, M. E. Quinlan, and Y. E. Goldman, “Measurement of single macromolecule orientation by total internal reflection fluorescence polarization microscopy,” Biophys. J. 89(2), 1261–1271 (2005).
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D. Patra, I. Gregor, and J. Enderlein, “Image analysis of defocused single-molecule images for three-dimensional molecule orientation studies,” J. Phys. Chem. A 108(33), 6836–6841 (2004).
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M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. U.S.A. 109(47), 19087–19092 (2012).
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T. J. Gould, M. S. Gunewardene, M. V. Gudheti, V. V. Verkhusha, S. R. Yin, J. A. Gosse, and S. T. Hess, “Nanoscale imaging of molecular positions and anisotropies,” Nat. Methods 5(12), 1027–1030 (2008).
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T. J. Gould, M. S. Gunewardene, M. V. Gudheti, V. V. Verkhusha, S. R. Yin, J. A. Gosse, and S. T. Hess, “Nanoscale imaging of molecular positions and anisotropies,” Nat. Methods 5(12), 1027–1030 (2008).
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E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A. 103(17), 6495–6499 (2006).
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T. Ha, T. Enderle, S. Chemla, R. Selvin, and S. Weiss, “Single molecule dynamics studied by polarization modulation,” Phys. Rev. Lett. 77(19), 3979–3982 (1996).
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S. Ham, J. Yang, F. Schlosser, F. Wurthner, and D. Kim, “Reconstruction of the molecular structure of a multichromophoric system using single-molecule defocused wide-field imaging,” J. Phys. Chem. Lett. 5(16), 2830–2835 (2014).
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F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
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A. Cyphersmith, A. Maksov, R. Hassey-Paradise, K. D. McCarthy, and M. D. Barnes, “Defocused emission patterns from chiral fluorophores: application to chiral axis orientation determination,” J. Phys. Chem. Lett. 2(6), 661–665 (2011).
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Hellen, E. H.

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J. A. Hutchison, H. Uji-i, A. Deres, T. Vosch, S. Rocha, S. Müller, A. A. Bastian, J. Enderlein, H. Nourouzi, C. Li, A. Herrmann, K. Müllen, F. De Schryver, and J. Hofkens, “A surface-bound molecule that undergoes optically biased Brownian rotation,” Nat. Nanotechnol. 9(2), 131–136 (2014).
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T. J. Gould, M. S. Gunewardene, M. V. Gudheti, V. V. Verkhusha, S. R. Yin, J. A. Gosse, and S. T. Hess, “Nanoscale imaging of molecular positions and anisotropies,” Nat. Methods 5(12), 1027–1030 (2008).
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M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, and D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices--from theory to practice,” PLoS ONE 8(1), e53671 (2013).
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M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, and D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices--from theory to practice,” PLoS ONE 8(1), e53671 (2013).
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J. A. Hutchison, H. Uji-i, A. Deres, T. Vosch, S. Rocha, S. Müller, A. A. Bastian, J. Enderlein, H. Nourouzi, C. Li, A. Herrmann, K. Müllen, F. De Schryver, and J. Hofkens, “A surface-bound molecule that undergoes optically biased Brownian rotation,” Nat. Nanotechnol. 9(2), 131–136 (2014).
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J. A. Hutchison, H. Uji-i, A. Deres, T. Vosch, S. Rocha, S. Müller, A. A. Bastian, J. Enderlein, H. Nourouzi, C. Li, A. Herrmann, K. Müllen, F. De Schryver, and J. Hofkens, “A surface-bound molecule that undergoes optically biased Brownian rotation,” Nat. Nanotechnol. 9(2), 131–136 (2014).
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Y. Zhang, L. Gu, H. Chang, W. Ji, Y. Chen, M. Zhang, L. Yang, B. Liu, L. Chen, and T. Xu, “Ultrafast, accurate, and robust localization of anisotropic dipoles,” Protein Cell 4(8), 598–606 (2013).
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C. Phelps, W. Lee, D. Jose, P. H. von Hippel, and A. H. Marcus, “Single-molecule FRET and linear dichroism studies of DNA breathing and helicase binding at replication fork junctions,” Proc. Natl. Acad. Sci. U.S.A. 110(43), 17320–17325 (2013).
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C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7(5), 373–375 (2010).
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S. Ham, J. Yang, F. Schlosser, F. Wurthner, and D. Kim, “Reconstruction of the molecular structure of a multichromophoric system using single-molecule defocused wide-field imaging,” J. Phys. Chem. Lett. 5(16), 2830–2835 (2014).
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Krueger, W. D.

Lasser, T.

Lee, W.

C. Phelps, W. Lee, D. Jose, P. H. von Hippel, and A. H. Marcus, “Single-molecule FRET and linear dichroism studies of DNA breathing and helicase binding at replication fork junctions,” Proc. Natl. Acad. Sci. U.S.A. 110(43), 17320–17325 (2013).
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M. D. Lew, M. P. Backlund, and W. E. Moerner, “Rotational mobility of single molecules affects localization accuracy in super-resolution fluorescence microscopy,” Nano Lett. 13(9), 3967–3972 (2013).
[Crossref] [PubMed]

A. S. Backer, M. P. Backlund, M. D. Lew, and W. E. Moerner, “Single-molecule orientation measurements with a quadrated pupil,” Opt. Lett. 38(9), 1521–1523 (2013).
[Crossref] [PubMed]

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. U.S.A. 109(47), 19087–19092 (2012).
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J. A. Hutchison, H. Uji-i, A. Deres, T. Vosch, S. Rocha, S. Müller, A. A. Bastian, J. Enderlein, H. Nourouzi, C. Li, A. Herrmann, K. Müllen, F. De Schryver, and J. Hofkens, “A surface-bound molecule that undergoes optically biased Brownian rotation,” Nat. Nanotechnol. 9(2), 131–136 (2014).
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S. Liu, E. B. Kromann, W. D. Krueger, J. Bewersdorf, and K. A. Lidke, “Three dimensional single molecule localization using a phase retrieved pupil function,” Opt. Express 21(24), 29462–29487 (2013).
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C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7(5), 373–375 (2010).
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Lin, Y.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
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Liu, B.

Y. Zhang, L. Gu, H. Chang, W. Ji, Y. Chen, M. Zhang, L. Yang, B. Liu, L. Chen, and T. Xu, “Ultrafast, accurate, and robust localization of anisotropic dipoles,” Protein Cell 4(8), 598–606 (2013).
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Liu, S.

Long, J. J.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
[Crossref] [PubMed]

Maksov, A.

A. Cyphersmith, A. Maksov, R. Hassey-Paradise, K. D. McCarthy, and M. D. Barnes, “Defocused emission patterns from chiral fluorophores: application to chiral axis orientation determination,” J. Phys. Chem. Lett. 2(6), 661–665 (2011).
[Crossref]

Marcus, A. H.

C. Phelps, W. Lee, D. Jose, P. H. von Hippel, and A. H. Marcus, “Single-molecule FRET and linear dichroism studies of DNA breathing and helicase binding at replication fork junctions,” Proc. Natl. Acad. Sci. U.S.A. 110(43), 17320–17325 (2013).
[Crossref] [PubMed]

Märki, I.

Martin-Fernandez, M. L.

M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, and D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices--from theory to practice,” PLoS ONE 8(1), e53671 (2013).
[Crossref] [PubMed]

McCarthy, K. D.

A. Cyphersmith, A. Maksov, R. Hassey-Paradise, K. D. McCarthy, and M. D. Barnes, “Defocused emission patterns from chiral fluorophores: application to chiral axis orientation determination,” J. Phys. Chem. Lett. 2(6), 661–665 (2011).
[Crossref]

McKinney, S. A.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A. 103(17), 6495–6499 (2006).
[Crossref] [PubMed]

Medda, R.

Moerner, W. E.

A. S. Backer, M. P. Backlund, A. R. Diezmann, S. J. Sahl, and W. E. Moerner, “A bisected pupil for studying single-molecule orientational dynamics and its application to 3D super-resolution microscopy,” Appl. Phys. Lett. 104, 193701 (2014).
[Crossref] [PubMed]

A. S. Backer and W. E. Moerner, “Extending single-molecule microscopy using optical Fourier processing,” J. Phys. Chem. B 118(28), 8313–8329 (2014).
[Crossref] [PubMed]

M. D. Lew, M. P. Backlund, and W. E. Moerner, “Rotational mobility of single molecules affects localization accuracy in super-resolution fluorescence microscopy,” Nano Lett. 13(9), 3967–3972 (2013).
[Crossref] [PubMed]

A. S. Backer, M. P. Backlund, M. D. Lew, and W. E. Moerner, “Single-molecule orientation measurements with a quadrated pupil,” Opt. Lett. 38(9), 1521–1523 (2013).
[Crossref] [PubMed]

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. U.S.A. 109(47), 19087–19092 (2012).
[Crossref] [PubMed]

E. J. G. Peterman, H. Sosa, L. S. B. Goldstein, and W. E. Moerner, “Polarized fluorescence microscopy of individual and many kinesin motors bound to axonemal microtubules,” Biophys. J. 81(5), 2851–2863 (2001).
[Crossref] [PubMed]

H. Sosa, E. J. G. Peterman, W. E. Moerner, and L. S. B. Goldstein, “ADP-induced rocking of the kinesin motor domain revealed by single-molecule fluorescence polarization microscopy,” Nat. Struct. Biol. 8(6), 540–544 (2001).
[Crossref] [PubMed]

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(24), 5322–5325 (1998).
[Crossref]

Mortensen, K. I.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7(5), 377–381 (2010).
[Crossref] [PubMed]

Mothes, W.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
[Crossref] [PubMed]

Müllen, K.

J. A. Hutchison, H. Uji-i, A. Deres, T. Vosch, S. Rocha, S. Müller, A. A. Bastian, J. Enderlein, H. Nourouzi, C. Li, A. Herrmann, K. Müllen, F. De Schryver, and J. Hofkens, “A surface-bound molecule that undergoes optically biased Brownian rotation,” Nat. Nanotechnol. 9(2), 131–136 (2014).
[Crossref] [PubMed]

Müller, S.

J. A. Hutchison, H. Uji-i, A. Deres, T. Vosch, S. Rocha, S. Müller, A. A. Bastian, J. Enderlein, H. Nourouzi, C. Li, A. Herrmann, K. Müllen, F. De Schryver, and J. Hofkens, “A surface-bound molecule that undergoes optically biased Brownian rotation,” Nat. Nanotechnol. 9(2), 131–136 (2014).
[Crossref] [PubMed]

Myers, J. R.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
[Crossref] [PubMed]

Nelson, P. C.

J. F. Beausang, D. Y. Shroder, P. C. Nelson, and Y. E. Goldman, “Tilting and wobble of Myosin V by high-speed single-molecule polarized fluorescence microscopy,” Biophys. J. 104(6), 1263–1273 (2013).
[Crossref] [PubMed]

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(24), 5322–5325 (1998).
[Crossref]

Nourouzi, H.

J. A. Hutchison, H. Uji-i, A. Deres, T. Vosch, S. Rocha, S. Müller, A. A. Bastian, J. Enderlein, H. Nourouzi, C. Li, A. Herrmann, K. Müllen, F. De Schryver, and J. Hofkens, “A surface-bound molecule that undergoes optically biased Brownian rotation,” Nat. Nanotechnol. 9(2), 131–136 (2014).
[Crossref] [PubMed]

Novotny, L.

Ober, R. J.

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[Crossref] [PubMed]

Patra, D.

D. Patra, I. Gregor, and J. Enderlein, “Image analysis of defocused single-molecule images for three-dimensional molecule orientation studies,” J. Phys. Chem. A 108(33), 6836–6841 (2004).
[Crossref]

Pavani, S. R. P.

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. U.S.A. 109(3), 675–679 (2012).
[Crossref] [PubMed]

Perroud, T. D.

B. Huang, T. D. Perroud, and R. N. Zare, “Photon counting histogram: one-photon excitation,” ChemPhysChem 5(10), 1523–1531 (2004).
[Crossref] [PubMed]

Peterman, E. J. G.

H. Sosa, E. J. G. Peterman, W. E. Moerner, and L. S. B. Goldstein, “ADP-induced rocking of the kinesin motor domain revealed by single-molecule fluorescence polarization microscopy,” Nat. Struct. Biol. 8(6), 540–544 (2001).
[Crossref] [PubMed]

E. J. G. Peterman, H. Sosa, L. S. B. Goldstein, and W. E. Moerner, “Polarized fluorescence microscopy of individual and many kinesin motors bound to axonemal microtubules,” Biophys. J. 81(5), 2851–2863 (2001).
[Crossref] [PubMed]

Petschek, R. G.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A. 103(17), 6495–6499 (2006).
[Crossref] [PubMed]

Phelps, C.

C. Phelps, W. Lee, D. Jose, P. H. von Hippel, and A. H. Marcus, “Single-molecule FRET and linear dichroism studies of DNA breathing and helicase binding at replication fork junctions,” Proc. Natl. Acad. Sci. U.S.A. 110(43), 17320–17325 (2013).
[Crossref] [PubMed]

Piestun, R.

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. U.S.A. 109(47), 19087–19092 (2012).
[Crossref] [PubMed]

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. U.S.A. 109(3), 675–679 (2012).
[Crossref] [PubMed]

A. Agrawal, S. Quirin, G. Grover, and R. Piestun, “Limits of 3D dipole localization and orientation estimation for single-molecule imaging: towards Green’s tensor engineering,” Opt. Express 20(24), 26667–26680 (2012).
[Crossref] [PubMed]

Quinlan, M. E.

S. A. Rosenberg, M. E. Quinlan, J. N. Forkey, and Y. E. Goldman, “Rotational motions of macro-molecules by single-molecule fluorescence microscopy,” Acc. Chem. Res. 38(7), 583–593 (2005).
[Crossref] [PubMed]

M. E. Quinlan, J. N. Forkey, and Y. E. Goldman, “Orientation of the Myosin Light Chain Region by Single Molecule Total Internal Reflection Fluorescence Polarization Microscopy,” Biophys. J. 89(2), 1132–1142 (2005).
[Crossref] [PubMed]

J. N. Forkey, M. E. Quinlan, and Y. E. Goldman, “Measurement of single macromolecule orientation by total internal reflection fluorescence polarization microscopy,” Biophys. J. 89(2), 1261–1271 (2005).
[Crossref] [PubMed]

Quirin, S.

A. Agrawal, S. Quirin, G. Grover, and R. Piestun, “Limits of 3D dipole localization and orientation estimation for single-molecule imaging: towards Green’s tensor engineering,” Opt. Express 20(24), 26667–26680 (2012).
[Crossref] [PubMed]

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. U.S.A. 109(3), 675–679 (2012).
[Crossref] [PubMed]

Ram, S.

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[Crossref] [PubMed]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Rieger, B.

S. Stallinga and B. Rieger, “Position and orientation estimation of fixed dipole emitters using an effective Hermite point spread function model,” Opt. Express 20(6), 5896–5921 (2012).
[Crossref] [PubMed]

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7(5), 373–375 (2010).
[Crossref] [PubMed]

Rivera-Molina, F. E.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
[Crossref] [PubMed]

Rocha, S.

J. A. Hutchison, H. Uji-i, A. Deres, T. Vosch, S. Rocha, S. Müller, A. A. Bastian, J. Enderlein, H. Nourouzi, C. Li, A. Herrmann, K. Müllen, F. De Schryver, and J. Hofkens, “A surface-bound molecule that undergoes optically biased Brownian rotation,” Nat. Nanotechnol. 9(2), 131–136 (2014).
[Crossref] [PubMed]

Rolfe, D. J.

M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, and D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices--from theory to practice,” PLoS ONE 8(1), e53671 (2013).
[Crossref] [PubMed]

Rosenberg, S. A.

S. A. Rosenberg, M. E. Quinlan, J. N. Forkey, and Y. E. Goldman, “Rotational motions of macro-molecules by single-molecule fluorescence microscopy,” Acc. Chem. Res. 38(7), 583–593 (2005).
[Crossref] [PubMed]

Sahl, S. J.

A. S. Backer, M. P. Backlund, A. R. Diezmann, S. J. Sahl, and W. E. Moerner, “A bisected pupil for studying single-molecule orientational dynamics and its application to 3D super-resolution microscopy,” Appl. Phys. Lett. 104, 193701 (2014).
[Crossref] [PubMed]

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. U.S.A. 109(47), 19087–19092 (2012).
[Crossref] [PubMed]

Schlosser, F.

S. Ham, J. Yang, F. Schlosser, F. Wurthner, and D. Kim, “Reconstruction of the molecular structure of a multichromophoric system using single-molecule defocused wide-field imaging,” J. Phys. Chem. Lett. 5(16), 2830–2835 (2014).
[Crossref]

Schönle, A.

Selvin, P. R.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A. 103(17), 6495–6499 (2006).
[Crossref] [PubMed]

Selvin, R.

T. Ha, T. Enderle, S. Chemla, R. Selvin, and S. Weiss, “Single molecule dynamics studied by polarization modulation,” Phys. Rev. Lett. 77(19), 3979–3982 (1996).
[Crossref] [PubMed]

Shroder, D. Y.

J. F. Beausang, D. Y. Shroder, P. C. Nelson, and Y. E. Goldman, “Tilting and wobble of Myosin V by high-speed single-molecule polarized fluorescence microscopy,” Biophys. J. 104(6), 1263–1273 (2013).
[Crossref] [PubMed]

Smith, C. S.

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7(5), 373–375 (2010).
[Crossref] [PubMed]

Sosa, H.

E. J. G. Peterman, H. Sosa, L. S. B. Goldstein, and W. E. Moerner, “Polarized fluorescence microscopy of individual and many kinesin motors bound to axonemal microtubules,” Biophys. J. 81(5), 2851–2863 (2001).
[Crossref] [PubMed]

H. Sosa, E. J. G. Peterman, W. E. Moerner, and L. S. B. Goldstein, “ADP-induced rocking of the kinesin motor domain revealed by single-molecule fluorescence polarization microscopy,” Nat. Struct. Biol. 8(6), 540–544 (2001).
[Crossref] [PubMed]

Spudich, J. A.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7(5), 377–381 (2010).
[Crossref] [PubMed]

Stallinga, S.

Stiel, A. C.

Syed, S.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A. 103(17), 6495–6499 (2006).
[Crossref] [PubMed]

Testa, I.

Toomre, D.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
[Crossref] [PubMed]

Toprak, E.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A. 103(17), 6495–6499 (2006).
[Crossref] [PubMed]

Török, P.

M. R. Foreman and P. Török, “Fundamental limits in single-molecule orientation measurements,” New J. Phys. 13(9), 093013 (2011).
[Crossref]

Uchil, P. D.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
[Crossref] [PubMed]

Uji-i, H.

J. A. Hutchison, H. Uji-i, A. Deres, T. Vosch, S. Rocha, S. Müller, A. A. Bastian, J. Enderlein, H. Nourouzi, C. Li, A. Herrmann, K. Müllen, F. De Schryver, and J. Hofkens, “A surface-bound molecule that undergoes optically biased Brownian rotation,” Nat. Nanotechnol. 9(2), 131–136 (2014).
[Crossref] [PubMed]

Unser, M.

Verkhusha, V. V.

T. J. Gould, M. S. Gunewardene, M. V. Gudheti, V. V. Verkhusha, S. R. Yin, J. A. Gosse, and S. T. Hess, “Nanoscale imaging of molecular positions and anisotropies,” Nat. Methods 5(12), 1027–1030 (2008).
[Crossref] [PubMed]

von Hippel, P. H.

C. Phelps, W. Lee, D. Jose, P. H. von Hippel, and A. H. Marcus, “Single-molecule FRET and linear dichroism studies of DNA breathing and helicase binding at replication fork junctions,” Proc. Natl. Acad. Sci. U.S.A. 110(43), 17320–17325 (2013).
[Crossref] [PubMed]

von Middendorff, C.

Vosch, T.

J. A. Hutchison, H. Uji-i, A. Deres, T. Vosch, S. Rocha, S. Müller, A. A. Bastian, J. Enderlein, H. Nourouzi, C. Li, A. Herrmann, K. Müllen, F. De Schryver, and J. Hofkens, “A surface-bound molecule that undergoes optically biased Brownian rotation,” Nat. Nanotechnol. 9(2), 131–136 (2014).
[Crossref] [PubMed]

Ward, E. S.

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[Crossref] [PubMed]

Wareham, R. J.

M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, and D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices--from theory to practice,” PLoS ONE 8(1), e53671 (2013).
[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(10), 2093–2096 (1998).
[Crossref]

T. Ha, T. Enderle, S. Chemla, R. Selvin, and S. Weiss, “Single molecule dynamics studied by polarization modulation,” Phys. Rev. Lett. 77(19), 3979–3982 (1996).
[Crossref] [PubMed]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Wurm, C. A.

Wurthner, F.

S. Ham, J. Yang, F. Schlosser, F. Wurthner, and D. Kim, “Reconstruction of the molecular structure of a multichromophoric system using single-molecule defocused wide-field imaging,” J. Phys. Chem. Lett. 5(16), 2830–2835 (2014).
[Crossref]

Xu, T.

Y. Zhang, L. Gu, H. Chang, W. Ji, Y. Chen, M. Zhang, L. Yang, B. Liu, L. Chen, and T. Xu, “Ultrafast, accurate, and robust localization of anisotropic dipoles,” Protein Cell 4(8), 598–606 (2013).
[Crossref] [PubMed]

Yang, J.

S. Ham, J. Yang, F. Schlosser, F. Wurthner, and D. Kim, “Reconstruction of the molecular structure of a multichromophoric system using single-molecule defocused wide-field imaging,” J. Phys. Chem. Lett. 5(16), 2830–2835 (2014).
[Crossref]

Yang, L.

Y. Zhang, L. Gu, H. Chang, W. Ji, Y. Chen, M. Zhang, L. Yang, B. Liu, L. Chen, and T. Xu, “Ultrafast, accurate, and robust localization of anisotropic dipoles,” Protein Cell 4(8), 598–606 (2013).
[Crossref] [PubMed]

Yin, S. R.

T. J. Gould, M. S. Gunewardene, M. V. Gudheti, V. V. Verkhusha, S. R. Yin, J. A. Gosse, and S. T. Hess, “Nanoscale imaging of molecular positions and anisotropies,” Nat. Methods 5(12), 1027–1030 (2008).
[Crossref] [PubMed]

Zare, R. N.

B. Huang, T. D. Perroud, and R. N. Zare, “Photon counting histogram: one-photon excitation,” ChemPhysChem 5(10), 1523–1531 (2004).
[Crossref] [PubMed]

Zavislan, J. M.

Zhang, M.

Y. Zhang, L. Gu, H. Chang, W. Ji, Y. Chen, M. Zhang, L. Yang, B. Liu, L. Chen, and T. Xu, “Ultrafast, accurate, and robust localization of anisotropic dipoles,” Protein Cell 4(8), 598–606 (2013).
[Crossref] [PubMed]

Zhang, Y.

Y. Zhang, L. Gu, H. Chang, W. Ji, Y. Chen, M. Zhang, L. Yang, B. Liu, L. Chen, and T. Xu, “Ultrafast, accurate, and robust localization of anisotropic dipoles,” Protein Cell 4(8), 598–606 (2013).
[Crossref] [PubMed]

Acc. Chem. Res. (1)

S. A. Rosenberg, M. E. Quinlan, J. N. Forkey, and Y. E. Goldman, “Rotational motions of macro-molecules by single-molecule fluorescence microscopy,” Acc. Chem. Res. 38(7), 583–593 (2005).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

A. S. Backer, M. P. Backlund, A. R. Diezmann, S. J. Sahl, and W. E. Moerner, “A bisected pupil for studying single-molecule orientational dynamics and its application to 3D super-resolution microscopy,” Appl. Phys. Lett. 104, 193701 (2014).
[Crossref] [PubMed]

Biophys. J. (6)

E. J. G. Peterman, H. Sosa, L. S. B. Goldstein, and W. E. Moerner, “Polarized fluorescence microscopy of individual and many kinesin motors bound to axonemal microtubules,” Biophys. J. 81(5), 2851–2863 (2001).
[Crossref] [PubMed]

J. N. Forkey, M. E. Quinlan, and Y. E. Goldman, “Measurement of single macromolecule orientation by total internal reflection fluorescence polarization microscopy,” Biophys. J. 89(2), 1261–1271 (2005).
[Crossref] [PubMed]

M. E. Quinlan, J. N. Forkey, and Y. E. Goldman, “Orientation of the Myosin Light Chain Region by Single Molecule Total Internal Reflection Fluorescence Polarization Microscopy,” Biophys. J. 89(2), 1132–1142 (2005).
[Crossref] [PubMed]

J. F. Beausang, D. Y. Shroder, P. C. Nelson, and Y. E. Goldman, “Tilting and wobble of Myosin V by high-speed single-molecule polarized fluorescence microscopy,” Biophys. J. 104(6), 1263–1273 (2013).
[Crossref] [PubMed]

K. Kinosita, S. Kawato, and A. Ikegami, “A theory of fluorescence polarization decay in membranes,” Biophys. J. 20(3), 289–305 (1977).
[Crossref] [PubMed]

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[Crossref] [PubMed]

ChemPhysChem (1)

B. Huang, T. D. Perroud, and R. N. Zare, “Photon counting histogram: one-photon excitation,” ChemPhysChem 5(10), 1523–1531 (2004).
[Crossref] [PubMed]

J. Microsc. (1)

D. Axelrod, “Fluorescence excitation and imaging of single molecules near dielectric-coated and bare surfaces: a theoretical study,” J. Microsc. 247(2), 147–160 (2012).
[Crossref] [PubMed]

J. Opt. Soc. Am. B (3)

J. Phys. Chem. A (1)

D. Patra, I. Gregor, and J. Enderlein, “Image analysis of defocused single-molecule images for three-dimensional molecule orientation studies,” J. Phys. Chem. A 108(33), 6836–6841 (2004).
[Crossref]

J. Phys. Chem. B (2)

A. P. Bartko and R. M. Dickson, “Imaging three-dimensional single molecule orientations,” J. Phys. Chem. B 103(51), 11237–11241 (1999).
[Crossref]

A. S. Backer and W. E. Moerner, “Extending single-molecule microscopy using optical Fourier processing,” J. Phys. Chem. B 118(28), 8313–8329 (2014).
[Crossref] [PubMed]

J. Phys. Chem. Lett. (2)

A. Cyphersmith, A. Maksov, R. Hassey-Paradise, K. D. McCarthy, and M. D. Barnes, “Defocused emission patterns from chiral fluorophores: application to chiral axis orientation determination,” J. Phys. Chem. Lett. 2(6), 661–665 (2011).
[Crossref]

S. Ham, J. Yang, F. Schlosser, F. Wurthner, and D. Kim, “Reconstruction of the molecular structure of a multichromophoric system using single-molecule defocused wide-field imaging,” J. Phys. Chem. Lett. 5(16), 2830–2835 (2014).
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Figures (9)

Fig. 1
Fig. 1 Examples of rotational behavior which yield identical linear dichroism measurements. (a) Immobile molecule aligned along the optical axis. Orientation of polarization analyzers indicated with respect to microscope focal plane. (b) Immobile molecule aligned in plane of coverslip, at 45° angle to each of the polarization analyzers. (c) Molecule rotating about the optical axis.
Fig. 2
Fig. 2 Parameterizations of single-molecule orientation and rotational mobility. (a) A rotationally fixed single molecule may be modeled as a fixed dipole with polar orientation Θ and azimuthal orientation Φ. Alternatively, orientation may be described as a unit vector μ, with x, y and z components μ x , μ y and μ z respectively. (b) Experimental schematic: A single molecule is placed a distance d from the focal plane of the objective, and a single widefield image is acquired. (c) Rotation within a cone model: A single molecule undergoes constrained rotation about some mean orientation { Φ 0 , Θ 0 } . The molecule may deviate by an angle α from the mean. (d) A molecule rotating in a cone may be alternatively parameterized by three orthogonal dipoles. One dipole will have amplitude equal to the square root of the largest eigenvalue of the M matrix, as defined in the main text. The other two dipoles will have amplitudes equal to the square root of the second largest eigenvalue. (e) In a more general case, a single molecule’s rotation may be confined to an elliptical region of the unit hemisphere, parameterized by two angles α and β. (f) For rotation within an elliptic region, the equivalent eigenvectors provide three different dipoles, each with a distinct amplitude determined from the square roots of the eigenvalues of the M matrix.
Fig. 3
Fig. 3 Images of single molecules simulated with mean orientation { Φ 0 = 45 , Θ 0 = 45 } , and varying α. For these images, the defocus was set to d = 1.25 μm. All other simulation parameters are specified in section 3.
Fig. 4
Fig. 4 Analytical calculation of the eigenvalues of the M matrix for different cone angles α and β. Note that these parameters do not change as a function of mean orientation, { Φ 0 , Θ 0 } . Furthermore, they are not affected by experimental variables such as defocus, emission wavelength, or microscope NA. (a)-(c) Eigenvalue calculations, β = α, β = α/2, and β = α/8 respectively.
Fig. 5
Fig. 5 The image of any single molecule, fixed or rotationally mobile, may be decomposed into a linear combination of six basis functions. These six basis functions have been calculated at three representative defocus depths, given the simulation parameters presented in the main text. The x/y polarized components of these basis functions are also shown with x/y superscripts. Units of intensity are scaled such that the brightest pixel for a dipole parallel to the focal plane at 0.55 μm defocus has a magnitude of 1.
Fig. 6
Fig. 6 Experimental schematic assumed for all numerical experiments.
Fig. 7
Fig. 7 Results of numerical experiment 1. (a) Mean angular error as a function of defocus, d, for unpolarized and (b) polarized image data, with varying numbers of background photons per pixel.
Fig. 8
Fig. 8 Results of numerical experiment 2. (a) and (b) Eigenvalue measurements from single-molecule images for unpolarized data (a) and polarized data (b). Overall standard deviations in eigenvalue measurements for each trial are noted on their respective plots. Error bars are ±σ . (c) Sample raw images of molecules with different α.
Fig. 9
Fig. 9 Results of numerical experiment 3. (a) Linear dichroism histogram. From this data alone, the presence of two distinct populations of molecules is not clearly evident. (b) Histogram of largest eigenvalues measured for each single-molecule image using unpolarized data. (c) Histogram of largest eigenvalues measured for each single-molecule image using polarized data.

Equations (35)

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LD=( I 0° I 90° )/( I 0° + I 90° )
[ E x img ( r ) E y img ( r ) ]=[ E x μ x ( r ) E x μ y ( r ) E x μ z ( r ) E y μ x ( r ) E y μ y ( r ) E y μ z ( r ) ][ μ x μ y μ z ]=G( r )μ
A=|  μ |= μ x + μ y + μ z
μ | μ | =[ sin( Θ )cos( Φ ) sin( Θ )sin( Φ ) cos( Θ ) ]
U( r ) = ( E x img ( r ) ) * E x img ( r )+ ( E y img ( r ) ) * E y img ( r ) = j=x,y [ ( E j μ x ( r ) ) * ( E j μ y ( r ) ) * ( E j μ z ( r ) ) * ]( μ μ T )[ E j μ x ( r ) E j μ y ( r ) E j μ z ( r ) ]
M=[ M xx M xy M xz M xy M yy M yz M xz M yz M zz ]= 1 N n=1 N μ n μ n T
U( r )= j=x,y [ ( E j μ x ( r ) ) * ( E j μ y ( r ) ) * ( E j μ z ( r ) ) * ]M[ E j μ x ( r ) E j μ y ( r ) E j μ z ( r ) ]
M= j=1 3 λ j v j v j T
M= A 2 S ϕ =0 2π θ =0 α V V T sin( θ' )dθ'dϕ'
V=R[ sin( θ )cos( ϕ' ) sin( θ )sin( ϕ' ) cos( θ ) ]
μ | μ | =[ sin( Θ )cos( Φ ) sin( Θ )sin( Φ ) cos( Θ ) ]=R[ sin( θ )cos( ϕ' ) sin( θ )sin( ϕ' ) cos( θ ) ]
R=[ xxC+c xyC+zs xzC+ys xyC+zs yyC+c yzC+xs xzCys yzC+xs zzC+c ]
x= sin( Φ 0 ) y=cos( Φ 0 ) z=0 c=cos( Θ 0 ) s=sin( Θ 0 ) C=1c
M= A 2 R[ ( 1cos( α ) )( cos( α )+2 ) 6 0 0 0 ( 1cos( α ) )( cos( α )+2 ) 6 0 0 0 ( cos 3 ( α )1 ) ( 3cos( α )3 ) ] R T
λ 1 = A 2 ( cos 3 ( α )1 ) ( 3cos( α )3 )                        λ 2 = A 2 ( 1cos( α ) )( cos( α )+2 ) 6 λ 3 = A 2 ( 1cos( α ) )( cos( α )+2 ) 6
τ r τ f T
M= A 2 S' ϕ =0 2π θ =0 α 2 cos 2 ( ϕ' )+ β 2 sin 2 ( ϕ' ) V V T sin( θ' )dθ'dϕ'
M= A 2 S' R[ a 0 0 0 b 0 0 0 c ] R T
a = 1 3 ϕ =0 2π cos 2 ( ϕ ) ( cos( α 2 cos 2 ( ϕ )+ β 2 sin 2 ( ϕ ) )1 ) 2 ×( cos( α 2 cos 2 ( ϕ )+ β 2 sin 2 ( ϕ ) )+2 )d ϕ b = 1 3 ϕ =0 2π cos 2 ( ϕ ) ( cos( α 2 cos 2 ( ϕ )+ β 2 sin 2 ( ϕ ) )1 ) 2 ×( cos( α 2 cos 2 ( ϕ )+ β 2 sin 2 ( ϕ ) )+2 )d ϕ c = 1 3 ϕ =0 2π 1  cos 3 ( α 2 cos 2 ( ϕ )+ β 2 sin 2 ( ϕ ) )d ϕ
S' = ϕ =0 2π 1 cos( α 2 cos 2 ( ϕ )+ β 2 sin 2 ( ϕ ) )d ϕ
λ 1 = c A 2 S' λ 2 = a A 2 S' λ 3 = b A 2 S'
U( r ) = j=x,y | E j μ x ( r ) | 2 M xx + 2{ ( E j μ x ( r ) ) * E j μ y ( r ) } M xy + | E j μ y ( r ) | 2 M yy + 2{ ( E j μ x ( r ) ) * E j μ z ( r ) } M xz + | E j μ z ( r ) | 2 M zz + 2{ ( E j μ y ( r ) ) * E j μ z ( r ) } M yz
XX( r )= j=x,y | E j μ x ( r ) | 2 XY( r )=2 j=x,y { ( E j μ x ( r ) ) * E j μ y ( r ) } YY( r )= j=x,y | E j μ y ( r ) | 2 XZ( r )=2 j=x,y { ( E j μ x ( r ) ) * E j μ z ( r ) } ZZ( r )= j=x,y | E j μ z ( r ) | 2 YZ( r )=2 j=x,y { ( E j μ y ( r ) ) * E j μ z ( r ) }
U( r ) = [ XX( r ) YY( r ) ZZ( r ) XY( r ) XZ( r ) YZ( r ) ][ M xx M yy M zz M xy M xz M yz ] = [ XX( r ) YY( r ) ZZ( r ) XY( r ) XZ( r ) YZ( r ) ] M'
U = [ X X 1 X X 2 X X N Y Y 1 Y Y 2 Y Y N Z Z 1 Z Z 2 Z Z N X Y 1 X Y 2 X Y N X Z 1 X Z 2 X Z N Y Z 1 Y Z 2 Y Z N ]M' = [ | | | XX YY ZZ | | | | | | XY XZ YZ | | | ]M' = BM'
B + = ( B T B ) 1 B T
M' = B + U
[ | U x | | U y | ] = [ | X X x | | Y Y x | | Z Z x | | X Y x | | X Z x | | Y Z x | | X X y | | Y Y y | | Z Z y | | X Y y | | X Z y | | Y Z y | ]M' = B pol M'
U ˜ j = ois{ U j +b }
XX ^ =P XX j=1 N X X j YY ^ =P YY j=1 N X X j ZZ ^ =P ZZ j=1 N X X j XZ ^ =P XZ j=1 N X X j YZ ^ =P YZ j=1 N X X j XY ^ =P XY j=1 N X X j
U=[ | | | XX ^ YY ^ ZZ ^ | | | | | | XZ ^ YZ ^ XY ^ | | | ]M'= B ^ M'
Φ = 2πU{ 0,1 } Θ = cos 1 ( U{ 0,1 } )
error=| cos 1 ( μ true T μ estimated ) |
ξ x μ x ( ρ ) = e i n 1 kd 1  ρ 2 n 1 n 0 ( 1 ρ 2 ) 1/2 ( sin 2 ( ϕ )+ cos 2 ( ϕ ) 1  ρ 2 ) ξ x μ y ( ρ ) = e i n 1 kd 1  ρ 2 n 1 n 0 ( 1 ρ 2 ) 1/2 ( sin( 2ϕ )( 1  ρ 2 1 )/2 ) ξ x μ z ( ρ ) = e i n 1 kd 1  ρ 2 n 1 n 0 ( 1 ρ 2 ) 1/2 ( ρcos( ϕ ) ) ξ y μ x ( ρ ) = e i n 1 kd 1  ρ 2 n 1 n 0 ( 1 ρ 2 ) 1/2 ( sin( 2ϕ )( 1  ρ 2 1 )/2 ) ξ y μ y ( ρ ) = e i n 1 kd 1  ρ 2 n 1 n 0 ( 1 ρ 2 ) 1/2 ( cos 2 ( ϕ )+ sin 2 ( ϕ ) 1  ρ 2 ) ξ y μ z ( ρ ) = e i n 1 kd 1  ρ 2 n 1 n 0 ( 1 ρ 2 ) 1/2 ( ρsin( ϕ ) )
E x,y μ x,y,z ( r )={ ξ x,y μ x,y,z ( ρ ) }

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