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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 7, Iss. 3 — Feb. 29, 2012
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Single-image axial localization precision analysis for individual fluorophores

Michael C. DeSantis, Shannon Kian Zareh, Xianglu Li, Robert E. Blankenship, and Y. M. Wang  »View Author Affiliations


Optics Express, Vol. 20, Issue 3, pp. 3057-3065 (2012)
http://dx.doi.org/10.1364/OE.20.003057


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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

1. Introduction

Single particle tracking (SPT), whose building blocks are consecutive 3D localization measurements of the investigated particle, is important for many biological investigations [1

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]

3

3. 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]

]. To achieve SPT studies with high spatial and temporal resolutions, it is essential to determine the precisions to the 3D localization measurements of the investigated particle in an accurate and timely manner [2

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]

].

In current single molecule localization measurements using standard imaging setups, such as in epifluorescence and total internal reflection fluorescence (TIRF) imaging measurements, the intensity profile of a stationary or a slowly moving molecule (relative to the imaging timescale) is called a point spread function (PSF) and can be approximated by a Gaussian function. The centroid of the Gaussian fit to the PSF yields the lateral location of the molecule, and the standard deviation (SD) can be used to determine the molecule’s axial position or defocusing distance (relative to the focal plane) [4

4. 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]

] as well as the precision to the lateral location measurements [5

5. 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]

, 6

6. 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]

]. Although the lateral-localization precision can be expressed by fitting parameters of an individual fluorophore’s single image (PSF and background intensities) [5

5. 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]

, 6

6. 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]

], thus enabling lateral localization with lateral precision in the typical single-image exposure timescales of milliseconds, the axial-localization precision awaits an analogous expression to complete 3D localization with 3D precision in milliseconds.

Current single fluorophore axial-localization methods – which include methods that analyze PSFs obtained using standard imaging setups, such as inferring the axial location from the measured PSF SD [4

4. 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]

, 7

7. 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]

10

10. 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]

] and using novel algorithms [11

11. 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]

14

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

], and methods that require instrumentation modifications [4

4. 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]

, 14

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

17

17. 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]

] – use two approaches in quantifying precision: (i) experimentally repeating the axial-location measurement and using the SD of the axial-location distribution for precision [4

4. 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]

, 11

11. 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]

, 12

12. F. Aguet, D. van de Ville, and M. Unser, “A maximum-likelihood formalism for sub-resolution axial localization of fluorescent nanoparticles,” Opt. Express 13, 10503–10522 (2005). [CrossRef] [PubMed]

, 15

15. 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]

17

17. 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]

], and (ii) using an estimation, either the SD of the calculated axial locations according to novel algorithms [12

12. F. Aguet, D. van de Ville, and M. Unser, “A maximum-likelihood formalism for sub-resolution axial localization of fluorescent nanoparticles,” Opt. Express 13, 10503–10522 (2005). [CrossRef] [PubMed]

, 14

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

] or a Cramér-Rao lower bound that predicts the lowest possible error to the axial location measurements [9

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

,12

12. F. Aguet, D. van de Ville, and M. Unser, “A maximum-likelihood formalism for sub-resolution axial localization of fluorescent nanoparticles,” Opt. Express 13, 10503–10522 (2005). [CrossRef] [PubMed]

,13

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

]. For the first approach, although the results include the instrumentation and fluorophore effects (camera’s readout noise and pixelation effect; PSF’s photon noise, respectively), it decreases the temporal resolution of SPT by at least 20-fold due to repeated imaging; for the second approach, (i) the Cramér-Rao calculation is an estimation of the lower bound, rather than a precise description of the axial-localization precision, and (ii) it does not consider the instrumentation and fluorophore effects, which can affect the precision determination considerably [5

5. 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]

, 6

6. 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]

]. Furthermore, due to the lack of an expression that includes all experimental noise parameters, neither method can be used to assess axial-localization precisions in alternative experimental settings.

Here we report a precision expression for a fluorophore’s single-image axial location measurement that includes the instrumentation and fluorophore’s noise effects, based on the axial-localization method that measures PSF’s SDs. This axial-localization method involves minimal modifications to standard single-molecule imaging setups, and all the parameters in the axial precision expression can be obtained from a single Gaussian fit to the PSF of the fluorophore: SD, photon count, pixel size, and background noise values. This axial-precision expression is a new addition to our single-image molecular analysis (SIMA) studies [19

19. 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]

]; it completes individual fluorophores’ single-image 3D localization measurements by providing the axial-direction precision, and lifts the temporal resolution of SPT to the typical single-image exposure timescales of milliseconds.

2. Materials and methods

2.1. Sample preparation and imaging

In this study, we used phycobilisome (PBS; Synechosystis PCC 6803) protein complexes for our z and Δz investigations. PBSs are large hemidiscoidal-shaped light harvesting antenna protein complexes in cyanobacteria; the molecular weight is ≈ 10 MDa and it measures 60 × 30 × 20 nm in width, height, and length [20

20. 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]

]. A PBS molecule contains 144 fluorophores distributed throughout the complex; consequently, it serves as an ideal emitter to meet the demands of our study due to its brightness and long fluorescence lifetime. PBSs were purified following the method described in Ref. [21

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

]; the purified PBSs were then crosslinked according to a protocol from the Noam Adir group [22

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

]. The PBSs were diluted in 20 mM Tris-HCl buffer (pH 8.0) to approximately 0.1 nM. Manufacturer pre-cleaned fused-silica chips (6W675-575 20C, Hoya Corporation USA, San Jose, CA) were used, where isolated PBS molecules were adsorbed to surfaces at low concentration. A PBS solution of 5 μL was sandwiched between the fused-silica surface and an oxygen-plasma-cleaned coverslip (2.2 × 2.2 cm2), resulting in a 10.5 μm thick water layer. Because of the prism TIRF imaging setup, our sample on the fused-silica surface is 10.5 μm away from the coverslip surface; therefore, refractive index mismatch will affect the PBS SD versus z relation [17

17. 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]

, 18

18. 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]

].

Single-molecule imaging was performed using a Nikon Eclipse TE2000-S inverted microscope (Nikon, Melville, NY) in combination with a Nikon 100X objective (Nikon, 1.49 N.A., oil immersion). Samples were excited by prism-type TIRF microscopy with a linearly polarized 568 nm laser line (I70C-SPECTRUM Argon/Krypton laser, Coherent Inc., Santa Clara, CA) focused on a 40 × 20 μm2 region. The incident angle at the fused-silica water interface was 70° with respect to the normal. The 568 nm line was filtered from the multiline laser emission using a polychromatic acousto-optic filter (48062 PCAOM model, NEOS Technologies, Melbourne, FL). The laser excitation was pulsed with illumination intervals of 10 ms; the excitation intensity was 5.2 kW/cm2. Images were captured by an iXon back-illuminated electron multiplying charge coupled device (EMCCD) camera (DV897ECS-BV, Andor Technology, Belfast, Northern Ireland). An additional 2X expansion lens was placed before the EMCCD, producing a pixel size of 79 nm. The excitation filter was 568/20 nm, and the emission filter was a 580 nm long pass filter.

2.2. Data acquisition and selection

3. Results

In the PSF SD-based axial-localization method, the measured fluorophore’s PSF SD in the x-or y-direction, sx,y, is frequently described by a symmetric [7

7. 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]

9

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

] or an asymmetric function of the defocusing distance z [4

4. 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]

, 10

10. 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]

]. Since z is a function of sx,y, by using a single image of the fluorophore, we should be able to represent the precision in z, Δz, by the precision in sx,y, Δsx,y, via error propagation calculation. Since we have recently obtained an expression for a PSF’s root mean square (rms) Δsx,y as a function of sx,y=s0x,0y2+a2/12 where s0x,0y is the PSF SD without the pixelation effect, pixel size a, number of detected photons N, and the mean 〈b〉 and variance σb2, of the background’s photon noise [5

5. 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]

]
Δsx,rms=s0x2+a2/12N+16π(s0x2+a2/12)3/2(s0y2+a2/12)1/2(σb2b)3a2N2,
(2)
we can obtain Δz by studying a single image of a fluorophore. (Note that for the remainder of this article, we use i to denote x or y and Δsi to denote Δsx,y,rms.)

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.

Having obtained si as a function of z, we proceed to express z as a function of si
z(si)=±CA2B,
(4)
where C=A24B[1(si/s0i)2], and then to calculate Δz by using the error propagation calculation of Δz = (∂z/∂sisi:
Δz=siΔsis0i2C2BCA.
(5)
Now we have a Δz expression as a function of experimental parameters of a single PSF.

Using Eqs. (2), (3), and (5), we calculated and plotted the average Δsx and Δz values for PBS molecules in Fig. 1 (including modification to the Δsx values, and consequently the Δz values by the appropriate scaling factors; see Sec. 3.1) as the y- and x-axis error bars in Fig. 1(B), respectively. Since Δz diverges at low |z|, only Δz at |z| ≥ Δz(z) are shown.

In order to validate our method in obtaining Δz by error propagation calculation of z(si), we have performed repeated measurements of a single PBS molecule at three axial locations near z = −400 nm separated by 50 nm. Figures 1(C) and 1(D) show the sx and the corresponding z values [calculated from sx using Eq. (4)], respectively, at the three axial locations. The two error bars at each axial location compare the calculated with the experimentally determined Δsi and Δz [insets to Figs. 1(C) and 1(D)], showing agreement.

3.1. Theoretical Δsi scaling factor calculations

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.

4. Discussion

Unlike the lateral-localization precision, which is independent of the lateral position (Δx, Refs. [5

5. 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]

,6

6. 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]

]), the axial-localization precision varies with z. In Fig. 3, we plot Δz versus |z| for PBS PSFs for a range of photon counts, providing a direct guideline for the axial-localization precisions that can be achieved by using single fluorophore images at specific axial locations and photon counts.

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.

We discuss two features of Fig. 3 that will aid in generalizing our method to all SD-based axial-location precision studies using different fluorophores and experimental settings. (i) At high N and large |z|, the single-image determined Δz is in the nanometer range, allowing 3D localization measurements with simultaneous high spatial and temporal resolutions. (ii) As seen in Fig. 2, Δz diverges as |z| approaches 0 (this has been previously reported in Refs. [9

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

, 12

12. F. Aguet, D. van de Ville, and M. Unser, “A maximum-likelihood formalism for sub-resolution axial localization of fluorescent nanoparticles,” Opt. Express 13, 10503–10522 (2005). [CrossRef] [PubMed]

]). In order to obtain Δz at low |z|, one solution is to use astigmatism by introducing a cylindrical lens [23

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]

] that shifts the foci of sx(z) and sy(z) to be on opposite sides of z = 0 [4

4. 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]

]. In Fig. 4(A) we shift the PBS sx(z) and sy(z) foci by 300 nm, assuming that sx(z) and sy(z) remain the same shape and measurable range after the cylindrical lens modification. Figure 4(B) plots the corresponding Δz(z) curves to the shifted sx(z) and sy(z) for a range of photon counts. At all measurable z for PBS, appropriate si(z) values can be used to obtain the minimum Δz, marked as bold lines, and nanometer precision for single-image axial localization measurements can be achieved at high photon counts.

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.

The studies in this article are based on PBS molecules with a specific z(si) relation [Eq. (4)]. Because PBS differs from a single fluorophore in that it is an aggregate of 144 fluorophores, and our TIRF imaging setup further introduces the additional refractive index mismatch effect, our PBS si(z) relation, and thus our z(si) relation may differ slightly from those of single fluorophores at different depths in water (relative to the refractive index mismatch interface). Our group and two additional groups have observed that for single fluorophores in water, the si(z) curve is asymmetric and the degree of asymmetry varies with their depths [4

4. 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]

, 10

10. 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]

, 18

18. 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]

, 24

24. 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).

]. As a consequence, single fluorophore studies with different refractive index mismatch effects may have different z(si) and thus Δz relations. What our study has shown is that regardless of the sample or imaging setup, when a z(si) expression can be obtained for the molecule of interest, error propagation can be used to determine the axial-location precision from a single image of the fluorophore. In some complicated situations, such as when si(z) is asymmetric [4

4. 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]

, 10

10. 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]

, 18

18. 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]

], multiple si(z) functions can be used to describe different regions of the si(z) curve in order to obtain simple z(si) expressions for Δz calculation.

In summary, we have developed a precision expression for a fluorophore’s single-image axial localization measurement that includes all relevant experimental parameters. The improvement in temporal resolution will enable investigations of previously inaccessible SPT studies in the regime of milliseconds.

Acknowledgments

M. C. D. is supported by a National Institutes of Health predoctoral fellowship awarded under 5T90 DA022871. X. L. is supported by the Photosynthetic Antenna Research Center (PARC), an Energy Frontier Research Center funded by the US Department of Energy under Award Number DE-SC 0001035.

References and links

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]

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]

3.

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]

4.

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]

5.

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]

6.

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]

7.

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]

8.

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]

9.

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

10.

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]

11.

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]

12.

F. Aguet, D. van de Ville, and M. Unser, “A maximum-likelihood formalism for sub-resolution axial localization of fluorescent nanoparticles,” Opt. Express 13, 10503–10522 (2005). [CrossRef] [PubMed]

13.

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

14.

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

15.

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]

16.

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]

17.

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]

18.

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]

19.

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]

20.

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]

21.

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

24.

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).

OCIS Codes
(100.6640) Image processing : Superresolution
(100.6890) Image processing : Three-dimensional image processing
(110.2960) Imaging systems : Image analysis
(180.2520) Microscopy : Fluorescence microscopy
(180.6900) Microscopy : Three-dimensional microscopy

ToC Category:
Microscopy

History
Original Manuscript: September 6, 2011
Revised Manuscript: January 13, 2012
Manuscript Accepted: January 19, 2012
Published: January 25, 2012

Virtual Issues
Vol. 7, Iss. 3 Virtual Journal for Biomedical Optics

Citation
Michael C. DeSantis, Shannon Kian Zareh, Xianglu Li, Robert E. Blankenship, and Y. M. Wang, "Single-image axial localization precision analysis for individual fluorophores," Opt. Express 20, 3057-3065 (2012)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-3-3057


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References

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  5. 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. Express18, 6563–6576 (2010). [CrossRef] [PubMed]
  6. 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]
  7. 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]
  8. 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]
  9. L. Holtzer, T. Meckel, and T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett.90, 053902 (2007). [CrossRef]
  10. 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]
  11. 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]
  12. F. Aguet, D. van de Ville, and M. Unser, “A maximum-likelihood formalism for sub-resolution axial localization of fluorescent nanoparticles,” Opt. Express13, 10503–10522 (2005). [CrossRef] [PubMed]
  13. Z. Zhang and C.-H. Menq, “Three-dimensional particle tracking with subnanometer resolution using off-focus images,” Appl. Optics47, 2361–2370 (2008). [CrossRef]
  14. J. W. Shaevitz, “Bayesian estimation of the axial position in astigmatism-based three-dimensional particle tracking,” Int. J. Opt.2009, 896208 (2009).
  15. 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]
  16. 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]
  17. 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. USA106, 2995–2999 (2009). [CrossRef] [PubMed]
  18. B. Huang, S. A. Jones, B. Brandenburg, and X. Zhuang, “Whole-cell 3D STORM reveals interactions between cellular structures with nanometer-scale resolution,” Nat. Methods5, 1047–1052 (2008). [CrossRef] [PubMed]
  19. S. H. DeCenzo, M. C. DeSantis, and Y. M. Wang, “Single-image separation measurements of two unresolved fluorophores,” Opt. Express18, 16628–16639 (2010). [CrossRef] [PubMed]
  20. 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. Acta1787, 272–279 (2009). [CrossRef] [PubMed]
  21. G. Ajlani, C. Vernotte, L. DiMagno, and R. Haselkorn, “Phycobilisome core mutants of Synechocystis PCC 6803,” Biochim. Biophys. Acta1231, 189–196 (1995). [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]
  24. 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).

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