Abstract

Simultaneous measurements of single-molecule positions and orientations provide critical insight into a variety of biological and chemical processes. Various engineered point spread functions (PSFs) have been introduced for measuring the orientation and rotational diffusion of dipole-like emitters, but the widely used Cramér-Rao bound (CRB) only evaluates performance for one specific orientation at a time. Here, we report a performance metric, termed variance upper bound (VUB), that yields a global maximum CRB for all possible molecular orientations, thereby enabling the measurement performance of any PSF to be computed efficiently (${\sim}1000 \times$ faster than calculating average CRB). Our VUB reveals that the simple polarized standard PSF provides robust and precise orientation measurements if emitters are near a refractive index interface. Using this PSF, we measure the orientations and positions of Nile red (NR) molecules transiently bound to amyloid aggregates. Our super-resolved images reveal the main binding mode of NR on amyloid fiber surfaces, as well as structural heterogeneities along amyloid fibrillar networks, that cannot be resolved by single-molecule localization alone.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (6)

A. S. Backer, A. S. Biebricher, G. A. King, G. J. L. Wuite, I. Heller, and E. J. G. Peterman, “Single-molecule polarization microscopy of DNA intercalators sheds light on the structure of S-DNA,” Sci. Adv. 5, eaav1083 (2019).
[Crossref]

B. Dong, Y. Pei, N. Mansour, X. Lu, K. Yang, W. Huang, and N. Fang, “Deciphering nanoconfinement effects on molecular orientation and reaction intermediate by single molecule imaging,” Nat. Commun. 10, 4815 (2019).
[Crossref]

T. Chandler, H. Shroff, R. Oldenbourg, and P. La Rivière, “Spatio-angular fluorescence microscopy i. basic theory,” J. Opt. Soc. Am. A 36, 1334–1345 (2019).
[Crossref]

T. Chandler, H. Shroff, R. Oldenbourg, and P. La Rivière, “Spatio-angular fluorescence microscopy ii. paraxial 4f imaging,” J. Opt. Soc. Am. A 36, 1346–1360 (2019).
[Crossref]

T. Ding, K. Spehar, J. Bieschke, and M. D. Lew, “Long-term, super-resolution imaging of amyloid structures using transient amyloid binding microscopy,” Proc. SPIE 10884, 108840J (2019).
[Crossref]

A. K. Buell, “The growth of amyloid fibrils: rates and mechanisms,” Biochem. J. 476, 2677–2703 (2019).
[Crossref]

2018 (5)

J. A. Varela, M. Rodrigues, S. De, P. Flagmeier, S. Gandhi, C. M. Dobson, D. Klenerman, and S. F. Lee, “Optical structural analysis of individual$\alpha$α-synuclein oligomers,” Angew. Chem. Int. Ed. 57, 4886–4890 (2018).
[Crossref]

J.-E. Lee, J. C. Sang, M. Rodrigues, A. R. Carr, M. H. Horrocks, S. De, M. N. Bongiovanni, P. Flagmeier, C. M. Dobson, D. J. Wales, S. F. Lee, and D. Klenerman, “Mapping surface hydrophobicity of $\alpha$α-synuclein oligomers at the nanoscale,” Nano Lett. 18, 7494–7501 (2018).
[Crossref]

M. G. Iadanza, M. P. Jackson, E. W. Hewitt, N. A. Ranson, and S. E. Radford, “A new era for understanding amyloid structures and disease,” Nat. Rev. Mol. Cell Biol. 19, 755–773 (2018).
[Crossref]

O. Zhang, J. Lu, T. Ding, and M. D. Lew, “Imaging the three-dimensional orientation and rotational mobility of fluorescent emitters using the Tri-spot point spread function,” Appl. Phys. Lett. 113, 031103 (2018).
[Crossref]

K. Spehar, T. Ding, Y. Sun, N. Kedia, J. Lu, G. R. Nahass, M. D. Lew, and J. Bieschke, “Super-resolution imaging of amyloid structures over extended times by using transient binding of single Thioflavin T molecules,” ChemBioChem 19, 1944–1948 (2018).
[Crossref]

2017 (5)

L. G. Lippert, T. Dadosh, J. A. Hadden, V. Karnawat, B. T. Diroll, C. B. Murray, E. L. F. Holzbaur, K. Schulten, S. L. Reck-Peterson, and Y. E. Goldman, “Angular measurements of the dynein ring reveal a stepping mechanism dependent on a flexible stalk,” Proc. Natl. Acad. Sci. USA 114, E4564–E4573 (2017).
[Crossref]

L. M. Young, L.-H. Tu, D. P. Raleigh, A. E. Ashcroft, and S. E. Radford, “Understanding co-polymerization in amyloid formation by direct observation of mixed oligomers,” Chem. Sci. 8, 5030–5040 (2017).
[Crossref]

G. Fusco, S. W. Chen, P. T. F. Williamson, R. Cascella, M. Perni, J. A. Jarvis, C. Cecchi, M. Vendruscolo, F. Chiti, N. Cremades, L. Ying, C. M. Dobson, and A. De Simone, “Structural basis of membrane disruption and cellular toxicity by $\alpha$α-synuclein oligomers,” Science 358, 1440–1443 (2017).
[Crossref]

H. A. Shaban, C. A. Valades-Cruz, J. Savatier, and S. Brasselet, “Polarized super-resolution structural imaging inside amyloid fibrils using Thioflavine T,” Sci. Rep. 7, 12482 (2017).
[Crossref]

L. J. Young, G. S. Kaminski Schierle, and C. Kaminski, “Imaging (1–42) fibril elongation reveals strongly polarised growth and growth incompetent states,” Phys. Chem. Chem. Phys. 19, 27987–27996 (2017).
[Crossref]

2016 (3)

T. Watanabe-Nakayama, K. Ono, M. Itami, R. Takahashi, D. B. Teplow, and M. Yamada, “High-speed atomic force microscopy reveals structural dynamics of amyloid $\beta_{1-42}$β1−42 aggregates,” Proc. Natl. Acad. Sci. USA 113, 5835–5840 (2016).
[Crossref]

M. N. Bongiovanni, J. Godet, M. H. Horrocks, L. Tosatto, A. R. Carr, D. C. Wirthensohn, R. T. Ranasinghe, J. E. Lee, A. Ponjavic, J. V. Fritz, C. M. Dobson, D. Klenerman, and S. F. Lee, “Multi-dimensional super-resolution imaging enables surface hydrophobicity mapping,” Nat. Commun. 7, 13544 (2016).
[Crossref]

M. Serra-Batiste, M. Ninot-Pedrosa, M. Bayoumi, M. Gairí, G. Maglia, and N. Carulla, “$\beta$β assembles into specific $\beta$β-barrel pore-forming oligomers in membrane-mimicking environments,” Proc. Natl. Acad. Sci. USA 113, 10866–10871 (2016) .
[Crossref]

2015 (2)

2014 (4)

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

Y. Shechtman, S. J. Sahl, A. S. Backer, and W. E. Moerner, “Optimal point spread function design for 3D imaging,” Phys. Rev. Lett. 113, 1–5 (2014).
[Crossref]

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, and W. Moerner, “The role of molecular dipole orientation in single-molecule fluorescence microscopy and implications for super-resolution imaging,” ChemPhysChem. 15, 587–599 (2014).
[Crossref]

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

2013 (1)

2012 (3)

2011 (1)

T. Eichner and S. E. Radford, “A diversity of assembly mechanisms of a generic amyloid fold,” Mol. Cell 43, 8–18 (2011).
[Crossref]

2010 (1)

M. Biancalana and S. Koide, “Molecular mechanism of Thioflavin-T binding to amyloid fibrils,” Biochimica et Biophys. Acta—Proteins Proteomics 1804, 1405–1412 (2010).
[Crossref]

2009 (1)

C. B. Andersen, H. Yagi, M. Manno, V. Martorana, T. Ban, G. Christiansen, D. E. Otzen, Y. Goto, and C. Rischel, “Branching in amyloid fibril growth,” Biophys. J. 96, 1529–1536 (2009).
[Crossref]

2006 (2)

A. Sharonov and R. M. Hochstrasser, “Wide-field subdiffraction imaging by accumulated binding of diffusing probes,” Proc. Natl. Acad. Sci. USA 103, 18911–18916 (2006).
[Crossref]

E. Cohen, J. Bieschke, R. M. Perciavalle, J. W. Kelly, and A. Dillin, “Opposing activities protect against age-onset proteotoxicity,” Science 313, 1604–1610 (2006).
[Crossref]

2004 (3)

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

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86, 200–1185 (2004).
[Crossref]

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

2003 (1)

2001 (2)

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

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

1998 (1)

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]

1987 (1)

D. L. Sackett and J. Wolff, “Nile red as a polarity-sensitive fluorescent probe of hydrophobic protein surfaces,” Anal. Biochem. 167, 228–234 (1987).
[Crossref]

Agrawal, A.

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

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, 26667–26680 (2012).
[Crossref]

Andersen, C. B.

C. B. Andersen, H. Yagi, M. Manno, V. Martorana, T. Ban, G. Christiansen, D. E. Otzen, Y. Goto, and C. Rischel, “Branching in amyloid fibril growth,” Biophys. J. 96, 1529–1536 (2009).
[Crossref]

Ashcroft, A. E.

L. M. Young, L.-H. Tu, D. P. Raleigh, A. E. Ashcroft, and S. E. Radford, “Understanding co-polymerization in amyloid formation by direct observation of mixed oligomers,” Chem. Sci. 8, 5030–5040 (2017).
[Crossref]

Backer, A. S.

A. S. Backer, A. S. Biebricher, G. A. King, G. J. L. Wuite, I. Heller, and E. J. G. Peterman, “Single-molecule polarization microscopy of DNA intercalators sheds light on the structure of S-DNA,” Sci. Adv. 5, eaav1083 (2019).
[Crossref]

A. S. Backer and W. Moerner, “Determining the rotational mobility of a single molecule from a single image: a numerical study,” Opt. Express 23, 4255–4276 (2015).
[Crossref]

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

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, and W. Moerner, “The role of molecular dipole orientation in single-molecule fluorescence microscopy and implications for super-resolution imaging,” ChemPhysChem. 15, 587–599 (2014).
[Crossref]

Y. Shechtman, S. J. Sahl, A. S. Backer, and W. E. Moerner, “Optimal point spread function design for 3D imaging,” Phys. Rev. Lett. 113, 1–5 (2014).
[Crossref]

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

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

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

Backlund, M. P.

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

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, and W. Moerner, “The role of molecular dipole orientation in single-molecule fluorescence microscopy and implications for super-resolution imaging,” ChemPhysChem. 15, 587–599 (2014).
[Crossref]

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

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

Ban, T.

C. B. Andersen, H. Yagi, M. Manno, V. Martorana, T. Ban, G. Christiansen, D. E. Otzen, Y. Goto, and C. Rischel, “Branching in amyloid fibril growth,” Biophys. J. 96, 1529–1536 (2009).
[Crossref]

Bayoumi, M.

M. Serra-Batiste, M. Ninot-Pedrosa, M. Bayoumi, M. Gairí, G. Maglia, and N. Carulla, “$\beta$β assembles into specific $\beta$β-barrel pore-forming oligomers in membrane-mimicking environments,” Proc. Natl. Acad. Sci. USA 113, 10866–10871 (2016) .
[Crossref]

Biancalana, M.

M. Biancalana and S. Koide, “Molecular mechanism of Thioflavin-T binding to amyloid fibrils,” Biochimica et Biophys. Acta—Proteins Proteomics 1804, 1405–1412 (2010).
[Crossref]

Biebricher, A. S.

A. S. Backer, A. S. Biebricher, G. A. King, G. J. L. Wuite, I. Heller, and E. J. G. Peterman, “Single-molecule polarization microscopy of DNA intercalators sheds light on the structure of S-DNA,” Sci. Adv. 5, eaav1083 (2019).
[Crossref]

Bieschke, J.

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Supplementary Material (4)

NameDescription
» Dataset 1       Dataset 1
» Supplement 1       Supplemental document
» Visualization 1       Raw images of single NR molecules transiently binding to Aß42 fibrils
» Visualization 2       Individual azimuthal orientation measurements localized along fibril backbones

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Figures (3)

Fig. 1.
Fig. 1. Orientation measurement precision using various point spread functions (PSFs) for 380 signal photons and two background photons per pixel. (a) Average (over orientation space) trace ${R_\Sigma}$ of the CRB versus the trace ${\Gamma _\Sigma}$ of our variance upper bound (VUB) for various PSFs. Blue, unpolarized standard (std); red, polarized standard (polar); yellow, bifocal microscope (bif); purple, bisected (bi); green, double helix (DH); aqua, tri-spot (tri); maroon, quadrated (qua) PSF. Dark line: ${\Gamma _\Sigma} = {\rm mean}$ of ${R_\Sigma}$. Inset: error of ${\Gamma _\Sigma}$ relative to average ${R_\Sigma}$. Bars indicate minimum/maximum error relative to the mean (circle) over all of orientation space. (b) Fisher information (FI) lower bound ${[{{{\boldsymbol \Gamma}^{- 1}}}]_\textit{jj}}$ of each orientational second moment ${m_j}$. (c) Trace ${\Gamma _\Sigma}$ of VUB for various refractive indices. Dotted line: refractive index of water. Simulated orthogonally polarized images of (d) a fixed molecule with orientation $(\theta \;=\; 90^ {\circ}$, $\phi \;=\; 45^{\circ})$ and an isotropic emitter using (e) the polarized PSF and (f) the tri-spot PSF. Insets: normalized noiseless PSF images. Scale bars: 400 nm.
Fig. 2.
Fig. 2. Transient amyloid binding (TAB) SMLM and SMOLM images acquired using Nile red (NR). (a) SMLM image of a network of ${\rm A}\beta 42$ fibrils. Color bar: localizations per bin ($20 \times 20\,{{\rm nm}^2}$). Inset: diffraction-limited image. (b) TAB SMOLM image, color-coded according to the mean azimuthal ($\phi$) orientation of NR molecules measured within each bin. Inset: main binding mode of NR to $\beta$-sheets, i.e., dipole moments aligned mostly parallel to the long axis of a fibril (its backbone). (c-g) All individual orientation measurements localized along fibril backbones within the white boxes in (b). The lines are oriented and color-coded according to the direction of the estimated $\phi$ angle. Red dashed lines depict fibril backbones estimated from the SMLM image. Scale bars: (a,b) 1 µm, (f,g) 100 nm. Orientation-localization data are available in Dataset 1, Ref. [30].
Fig. 3.
Fig. 3. Structural heterogeneity of ${\rm A}\beta 42$ fibrils revealed by TAB SMOLM imaging. (a) SMLM image of fibril bundles. Color bar: localizations per bin ($20 \times 20\,{{\rm nm}^2}$). Inset: fibril cross-sections at the locations denoted by green and purple lines with measured full-width at half-maximum (FWHM) thicknesses. (b) TAB SMOLM image corresponding to (a), color-coded according to the mean ($\phi$) and standard deviation (${\sigma _\phi}$) of the azimuthal orientation measured within each bin. Inset: zoomed (i) thin and (ii) thick fibril regions isolated from background structures. (c) Histograms of measured azimuthal orientations relative to the fibril backbone within the regions denoted in (b), showing standard deviations (${\sigma _\phi}$) of (i) 18° and (ii) 37°. (d) Measured wobbling areas ($\Omega$) corresponding to the localizations in (c), yielding median wobbling areas (${\Omega _{{\rm med}}}$, cyan) of (i) 0.07 sr and (ii) 1.89 sr. (e-h) TAB SMLM and SMOLM images of another fibril field of view, as in (a-d). Although fibril regions (i) and (ii) in the inset of (f) show little difference in apparent width, the measured orientation distributions contain significant differences. The standard deviations of azimuthal angles ${\sigma _\phi}$ are (i) 20° vs (ii) 30°, and the median wobbling areas (${\Omega _{{\rm med}}}$, cyan) are (i) 0.07 sr vs (ii) 1.12 sr. Scale bars: 1 µm. Orientation-localization data are available in Dataset 1, Ref. [30].

Equations (5)

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I = s B m + b R n × 1 ,
= s [ B xx B yy B zz B xy B xz B yz ] m + b ,
J = i = 1 n s 2 I i B i T B i = A T A ,
| A ij | = | s B ij s B i m + b i | | s B ij s B i + b i | = | A ^ ij | .
Γ jj = [ ( A ^ T A ^ ) 1 ] jj [ J 1 ] jj = R jj ,

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