Abstract

Volumetric imaging and 3D particle tracking are becoming increasingly common and have a variety of microscopy applications including in situ fluorescent imaging, in-vitro single-molecule characterization, and analysis of colloidal systems. While recent interest has generated discussion of optimal schemes for localizing diffraction-limited fluorescent puncta, there have been relatively few published routines for tracking particles imaged with bright-field illumination. To address this, we outline a simple, look-up-table based 3D tracking strategy, which can be adapted to most commercially available wide-field microscopes, and present two image processing algorithms that together yield high-precision localization and return estimates of statistical accuracy. Under bright-field illumination, a particle’s depth can be determined based on the size and shape of its diffractive pattern due to Mie scattering. Contrary to typical “super-resolution” fluorescence tracking routines, which typically fit a diffraction-limited spot to a model point-spread-function, the lateral (XY) tracking routine relies on symmetry to locate a particle without prior knowledge of the form of the particle. At low noise levels (signal:noise > 1000), the symmetry routine estimates particle positions with accuracy better than 0.01 pixel. Depth localization is accomplished by matching images of particles to those in a pre-recorded look-up-table. The routine presented here optimally interpolates between LUT entries with better than 0.05 step accuracy. Both routines are tolerant of high levels of image noise, yielding sub-pixel/step accuracy with signal-to-noise ratios as small as 1, and, by design, return confidence intervals indicating the expected accuracy of each calculated position. The included implementations operate extremely quickly and are amenable to real-time analysis at frame rates exceeding several hundred frames per second.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
3D localization of high particle density images using sparse recovery

Saiwen Zhang, Danni Chen, and Hanben Niu
Appl. Opt. 54(26) 7859-7864 (2015)

Experimental characterization of 3D localization techniques for particle-tracking and super-resolution microscopy

Michael J. Mlodzianoski, Manuel F. Juette, Glen L. Beane, and Joerg Bewersdorf
Opt. Express 17(10) 8264-8277 (2009)

Measurement-based estimation of global pupil functions in 3D localization microscopy

Petar N. Petrov, Yoav Shechtman, and W. E. Moerner
Opt. Express 25(7) 7945-7959 (2017)

References

  • View by:
  • |
  • |
  • |

  1. T. Plénat, C. Tardin, P. Rousseau, and L. Salomé, “High-throughput single-molecule analysis of DNA-protein interactions by tethered particle motion,” Nucleic Acids Res. 40(12), e89 (2012).
    [Crossref] [PubMed]
  2. P. Daldrop, H. Brutzer, A. Huhle, D. J. Kauert, and R. Seidel, “Extending the range for force calibration in magnetic tweezers,” Biophys. J. 108(10), 2550–2561 (2015).
    [Crossref] [PubMed]
  3. I. De Vlaminck and C. Dekker, “Recent Advances In Magnetic Tweezers,” Annu. Rev. Biophys. 41(1), 453–472 (2012).
    [Crossref] [PubMed]
  4. D. T. Kovari, Y. Yan, L. Finzi, and D. Dunlap, “Tethered Particle Motion: An Easy Technique for Probing DNA Topology and Interactions with Transcription Factors,” in Single Molecule Analysis. Methods in Molecular Biology (Springer, 2018) pp. 317–340.
  5. M. Bierbaum, B. D. Leahy, A. A. Alemi, I. Cohen, and J. P. Sethna, “Light microscopy at maximal precision,” Phys. Rev. X 7(4), 1–10 (2017).
    [Crossref]
  6. Y. Seol and K. C. Neuman, “Magnetic tweezers for single-molecule manipulation,” Methods Mol. Biol. 783, 265–293 (2011).
    [Crossref] [PubMed]
  7. G. Sitters, D. Kamsma, G. Thalhammer, M. Ritsch-Marte, E. J. G. Peterman, and G. J. L. Wuite, “Acoustic force spectroscopy,” Nat. Methods 12(1), 47–50 (2015).
    [Crossref] [PubMed]
  8. B. M. Lansdorp and O. A. Saleh, “Power spectrum and Allan variance methods for calibrating single-molecule video-tracking instruments,” Rev. Sci. Instrum. 83(2), 025115 (2012).
    [Crossref] [PubMed]
  9. B. M. Lansdorp, S. J. Tabrizi, A. Dittmore, and O. A. Saleh, “A high-speed magnetic tweezer beyond 10,000 frames per second,” Rev. Sci. Instrum. 84(4), 044301 (2013).
    [Crossref] [PubMed]
  10. R. Parthasarathy, “Rapid, accurate particle tracking by calculation of radial symmetry centers,” Nat. Methods 9(7), 724–726 (2012).
    [Crossref] [PubMed]
  11. C. Gosse and V. Croquette, “Magnetic tweezers: micromanipulation and force measurement at the molecular level,” Biophys. J. 82(6), 3314–3329 (2002).
    [Crossref] [PubMed]
  12. M. T. J. van Loenhout, J. W. J. Kerssemakers, I. De Vlaminck, and C. Dekker, “Non-bias-limited tracking of spherical particles, enabling nanometer resolution at low magnification,” Biophys. J. 102(10), 2362–2371 (2012).
    [Crossref] [PubMed]
  13. S.-H. Lee, Y. Roichman, G.-R. Yi, S.-H. Kim, S.-M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 15(26), 18275–18282 (2007).
    [Crossref] [PubMed]
  14. J. C. Crocker and D. G. Grier, “Methods of Digital Video Microscopy for Colloidal Studies,” J. Colloid Interface Sci. 179(1), 298–310 (1996).
    [Crossref]
  15. I. D. Vilfan, J. Lipfert, D. A. Koster, S. G. Lemay, and N. H. Dekker, “Magnetic Tweezers for Single-Molecule Experiments,” in Handbook of Single-Molecule Biophysics (Springer US, 2009), pp. 371–395.
  16. A. von Diezmann, Y. Shechtman, and W. E. Moerner, “Three-Dimensional Localization of Single Molecules for Super-Resolution Imaging and Single-Particle Tracking,” Chem. Rev. 117(11), 7244–7275 (2017).
    [Crossref] [PubMed]
  17. T. Lionnet, J. F. Allemand, A. Revyakin, T. R. Strick, O. A. Saleh, D. Bensimon, and V. Croquette, “Single-molecule studies using magnetic traps,” Cold Spring Harb. Protoc. 2012(1), 34–49 (2012).
    [Crossref] [PubMed]
  18. N. Ribeck and O. A. Saleh, “Multiplexed single-molecule measurements with magnetic tweezers,” Rev. Sci. Instrum. 79(9), 094301 (2008).
    [Crossref] [PubMed]
  19. S. F. Nørrelykke and H. Flyvbjerg, “Power spectrum analysis with least-squares fitting: Amplitude bias and its elimination, with application to optical tweezers and atomic force microscope cantilevers,” Rev. Sci. Instrum. 81(7), 075103 (2010).
    [Crossref] [PubMed]
  20. M. T. Heath, Scientific Computing: An Introductory Survey, 2nd ed. (McGraw-Hill, 2002).
  21. C. H. Reinsch, “Smoothing by spline functions, II,” Numer. Math. 16(5), 451–454 (1971).
    [Crossref]
  22. Z. Vörös, Y. Yan, D. T. Kovari, L. Finzi, and D. Dunlap, “Proteins mediating DNA loops effectively block transcription,” Protein Sci. 26(7), 1427–1438 (2017).
    [Crossref] [PubMed]
  23. V. T. Dung and T. Tjahjowidodo, “A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting,” PLoS One 12(3), e0173857 (2017).
    [Crossref] [PubMed]
  24. D. T. Kovari, “Radial Symmetry and Spline Look-up-table Inversion” figshare (2019) [retrieved 28 Jun. 2019], https://figshare.com/articles/Radial_Symmetry_LUT_Tracking_Code/8317136 .

2017 (4)

M. Bierbaum, B. D. Leahy, A. A. Alemi, I. Cohen, and J. P. Sethna, “Light microscopy at maximal precision,” Phys. Rev. X 7(4), 1–10 (2017).
[Crossref]

A. von Diezmann, Y. Shechtman, and W. E. Moerner, “Three-Dimensional Localization of Single Molecules for Super-Resolution Imaging and Single-Particle Tracking,” Chem. Rev. 117(11), 7244–7275 (2017).
[Crossref] [PubMed]

Z. Vörös, Y. Yan, D. T. Kovari, L. Finzi, and D. Dunlap, “Proteins mediating DNA loops effectively block transcription,” Protein Sci. 26(7), 1427–1438 (2017).
[Crossref] [PubMed]

V. T. Dung and T. Tjahjowidodo, “A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting,” PLoS One 12(3), e0173857 (2017).
[Crossref] [PubMed]

2015 (2)

P. Daldrop, H. Brutzer, A. Huhle, D. J. Kauert, and R. Seidel, “Extending the range for force calibration in magnetic tweezers,” Biophys. J. 108(10), 2550–2561 (2015).
[Crossref] [PubMed]

G. Sitters, D. Kamsma, G. Thalhammer, M. Ritsch-Marte, E. J. G. Peterman, and G. J. L. Wuite, “Acoustic force spectroscopy,” Nat. Methods 12(1), 47–50 (2015).
[Crossref] [PubMed]

2013 (1)

B. M. Lansdorp, S. J. Tabrizi, A. Dittmore, and O. A. Saleh, “A high-speed magnetic tweezer beyond 10,000 frames per second,” Rev. Sci. Instrum. 84(4), 044301 (2013).
[Crossref] [PubMed]

2012 (6)

R. Parthasarathy, “Rapid, accurate particle tracking by calculation of radial symmetry centers,” Nat. Methods 9(7), 724–726 (2012).
[Crossref] [PubMed]

B. M. Lansdorp and O. A. Saleh, “Power spectrum and Allan variance methods for calibrating single-molecule video-tracking instruments,” Rev. Sci. Instrum. 83(2), 025115 (2012).
[Crossref] [PubMed]

I. De Vlaminck and C. Dekker, “Recent Advances In Magnetic Tweezers,” Annu. Rev. Biophys. 41(1), 453–472 (2012).
[Crossref] [PubMed]

T. Lionnet, J. F. Allemand, A. Revyakin, T. R. Strick, O. A. Saleh, D. Bensimon, and V. Croquette, “Single-molecule studies using magnetic traps,” Cold Spring Harb. Protoc. 2012(1), 34–49 (2012).
[Crossref] [PubMed]

M. T. J. van Loenhout, J. W. J. Kerssemakers, I. De Vlaminck, and C. Dekker, “Non-bias-limited tracking of spherical particles, enabling nanometer resolution at low magnification,” Biophys. J. 102(10), 2362–2371 (2012).
[Crossref] [PubMed]

T. Plénat, C. Tardin, P. Rousseau, and L. Salomé, “High-throughput single-molecule analysis of DNA-protein interactions by tethered particle motion,” Nucleic Acids Res. 40(12), e89 (2012).
[Crossref] [PubMed]

2011 (1)

Y. Seol and K. C. Neuman, “Magnetic tweezers for single-molecule manipulation,” Methods Mol. Biol. 783, 265–293 (2011).
[Crossref] [PubMed]

2010 (1)

S. F. Nørrelykke and H. Flyvbjerg, “Power spectrum analysis with least-squares fitting: Amplitude bias and its elimination, with application to optical tweezers and atomic force microscope cantilevers,” Rev. Sci. Instrum. 81(7), 075103 (2010).
[Crossref] [PubMed]

2008 (1)

N. Ribeck and O. A. Saleh, “Multiplexed single-molecule measurements with magnetic tweezers,” Rev. Sci. Instrum. 79(9), 094301 (2008).
[Crossref] [PubMed]

2007 (1)

2002 (1)

C. Gosse and V. Croquette, “Magnetic tweezers: micromanipulation and force measurement at the molecular level,” Biophys. J. 82(6), 3314–3329 (2002).
[Crossref] [PubMed]

1996 (1)

J. C. Crocker and D. G. Grier, “Methods of Digital Video Microscopy for Colloidal Studies,” J. Colloid Interface Sci. 179(1), 298–310 (1996).
[Crossref]

1971 (1)

C. H. Reinsch, “Smoothing by spline functions, II,” Numer. Math. 16(5), 451–454 (1971).
[Crossref]

Alemi, A. A.

M. Bierbaum, B. D. Leahy, A. A. Alemi, I. Cohen, and J. P. Sethna, “Light microscopy at maximal precision,” Phys. Rev. X 7(4), 1–10 (2017).
[Crossref]

Allemand, J. F.

T. Lionnet, J. F. Allemand, A. Revyakin, T. R. Strick, O. A. Saleh, D. Bensimon, and V. Croquette, “Single-molecule studies using magnetic traps,” Cold Spring Harb. Protoc. 2012(1), 34–49 (2012).
[Crossref] [PubMed]

Bensimon, D.

T. Lionnet, J. F. Allemand, A. Revyakin, T. R. Strick, O. A. Saleh, D. Bensimon, and V. Croquette, “Single-molecule studies using magnetic traps,” Cold Spring Harb. Protoc. 2012(1), 34–49 (2012).
[Crossref] [PubMed]

Bierbaum, M.

M. Bierbaum, B. D. Leahy, A. A. Alemi, I. Cohen, and J. P. Sethna, “Light microscopy at maximal precision,” Phys. Rev. X 7(4), 1–10 (2017).
[Crossref]

Brutzer, H.

P. Daldrop, H. Brutzer, A. Huhle, D. J. Kauert, and R. Seidel, “Extending the range for force calibration in magnetic tweezers,” Biophys. J. 108(10), 2550–2561 (2015).
[Crossref] [PubMed]

Cohen, I.

M. Bierbaum, B. D. Leahy, A. A. Alemi, I. Cohen, and J. P. Sethna, “Light microscopy at maximal precision,” Phys. Rev. X 7(4), 1–10 (2017).
[Crossref]

Crocker, J. C.

J. C. Crocker and D. G. Grier, “Methods of Digital Video Microscopy for Colloidal Studies,” J. Colloid Interface Sci. 179(1), 298–310 (1996).
[Crossref]

Croquette, V.

T. Lionnet, J. F. Allemand, A. Revyakin, T. R. Strick, O. A. Saleh, D. Bensimon, and V. Croquette, “Single-molecule studies using magnetic traps,” Cold Spring Harb. Protoc. 2012(1), 34–49 (2012).
[Crossref] [PubMed]

C. Gosse and V. Croquette, “Magnetic tweezers: micromanipulation and force measurement at the molecular level,” Biophys. J. 82(6), 3314–3329 (2002).
[Crossref] [PubMed]

Daldrop, P.

P. Daldrop, H. Brutzer, A. Huhle, D. J. Kauert, and R. Seidel, “Extending the range for force calibration in magnetic tweezers,” Biophys. J. 108(10), 2550–2561 (2015).
[Crossref] [PubMed]

De Vlaminck, I.

I. De Vlaminck and C. Dekker, “Recent Advances In Magnetic Tweezers,” Annu. Rev. Biophys. 41(1), 453–472 (2012).
[Crossref] [PubMed]

M. T. J. van Loenhout, J. W. J. Kerssemakers, I. De Vlaminck, and C. Dekker, “Non-bias-limited tracking of spherical particles, enabling nanometer resolution at low magnification,” Biophys. J. 102(10), 2362–2371 (2012).
[Crossref] [PubMed]

Dekker, C.

M. T. J. van Loenhout, J. W. J. Kerssemakers, I. De Vlaminck, and C. Dekker, “Non-bias-limited tracking of spherical particles, enabling nanometer resolution at low magnification,” Biophys. J. 102(10), 2362–2371 (2012).
[Crossref] [PubMed]

I. De Vlaminck and C. Dekker, “Recent Advances In Magnetic Tweezers,” Annu. Rev. Biophys. 41(1), 453–472 (2012).
[Crossref] [PubMed]

Dittmore, A.

B. M. Lansdorp, S. J. Tabrizi, A. Dittmore, and O. A. Saleh, “A high-speed magnetic tweezer beyond 10,000 frames per second,” Rev. Sci. Instrum. 84(4), 044301 (2013).
[Crossref] [PubMed]

Dung, V. T.

V. T. Dung and T. Tjahjowidodo, “A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting,” PLoS One 12(3), e0173857 (2017).
[Crossref] [PubMed]

Dunlap, D.

Z. Vörös, Y. Yan, D. T. Kovari, L. Finzi, and D. Dunlap, “Proteins mediating DNA loops effectively block transcription,” Protein Sci. 26(7), 1427–1438 (2017).
[Crossref] [PubMed]

Finzi, L.

Z. Vörös, Y. Yan, D. T. Kovari, L. Finzi, and D. Dunlap, “Proteins mediating DNA loops effectively block transcription,” Protein Sci. 26(7), 1427–1438 (2017).
[Crossref] [PubMed]

Flyvbjerg, H.

S. F. Nørrelykke and H. Flyvbjerg, “Power spectrum analysis with least-squares fitting: Amplitude bias and its elimination, with application to optical tweezers and atomic force microscope cantilevers,” Rev. Sci. Instrum. 81(7), 075103 (2010).
[Crossref] [PubMed]

Gosse, C.

C. Gosse and V. Croquette, “Magnetic tweezers: micromanipulation and force measurement at the molecular level,” Biophys. J. 82(6), 3314–3329 (2002).
[Crossref] [PubMed]

Grier, D. G.

Huhle, A.

P. Daldrop, H. Brutzer, A. Huhle, D. J. Kauert, and R. Seidel, “Extending the range for force calibration in magnetic tweezers,” Biophys. J. 108(10), 2550–2561 (2015).
[Crossref] [PubMed]

Kamsma, D.

G. Sitters, D. Kamsma, G. Thalhammer, M. Ritsch-Marte, E. J. G. Peterman, and G. J. L. Wuite, “Acoustic force spectroscopy,” Nat. Methods 12(1), 47–50 (2015).
[Crossref] [PubMed]

Kauert, D. J.

P. Daldrop, H. Brutzer, A. Huhle, D. J. Kauert, and R. Seidel, “Extending the range for force calibration in magnetic tweezers,” Biophys. J. 108(10), 2550–2561 (2015).
[Crossref] [PubMed]

Kerssemakers, J. W. J.

M. T. J. van Loenhout, J. W. J. Kerssemakers, I. De Vlaminck, and C. Dekker, “Non-bias-limited tracking of spherical particles, enabling nanometer resolution at low magnification,” Biophys. J. 102(10), 2362–2371 (2012).
[Crossref] [PubMed]

Kim, S.-H.

Kovari, D. T.

Z. Vörös, Y. Yan, D. T. Kovari, L. Finzi, and D. Dunlap, “Proteins mediating DNA loops effectively block transcription,” Protein Sci. 26(7), 1427–1438 (2017).
[Crossref] [PubMed]

Lansdorp, B. M.

B. M. Lansdorp, S. J. Tabrizi, A. Dittmore, and O. A. Saleh, “A high-speed magnetic tweezer beyond 10,000 frames per second,” Rev. Sci. Instrum. 84(4), 044301 (2013).
[Crossref] [PubMed]

B. M. Lansdorp and O. A. Saleh, “Power spectrum and Allan variance methods for calibrating single-molecule video-tracking instruments,” Rev. Sci. Instrum. 83(2), 025115 (2012).
[Crossref] [PubMed]

Leahy, B. D.

M. Bierbaum, B. D. Leahy, A. A. Alemi, I. Cohen, and J. P. Sethna, “Light microscopy at maximal precision,” Phys. Rev. X 7(4), 1–10 (2017).
[Crossref]

Lee, S.-H.

Lionnet, T.

T. Lionnet, J. F. Allemand, A. Revyakin, T. R. Strick, O. A. Saleh, D. Bensimon, and V. Croquette, “Single-molecule studies using magnetic traps,” Cold Spring Harb. Protoc. 2012(1), 34–49 (2012).
[Crossref] [PubMed]

Moerner, W. E.

A. von Diezmann, Y. Shechtman, and W. E. Moerner, “Three-Dimensional Localization of Single Molecules for Super-Resolution Imaging and Single-Particle Tracking,” Chem. Rev. 117(11), 7244–7275 (2017).
[Crossref] [PubMed]

Neuman, K. C.

Y. Seol and K. C. Neuman, “Magnetic tweezers for single-molecule manipulation,” Methods Mol. Biol. 783, 265–293 (2011).
[Crossref] [PubMed]

Nørrelykke, S. F.

S. F. Nørrelykke and H. Flyvbjerg, “Power spectrum analysis with least-squares fitting: Amplitude bias and its elimination, with application to optical tweezers and atomic force microscope cantilevers,” Rev. Sci. Instrum. 81(7), 075103 (2010).
[Crossref] [PubMed]

Parthasarathy, R.

R. Parthasarathy, “Rapid, accurate particle tracking by calculation of radial symmetry centers,” Nat. Methods 9(7), 724–726 (2012).
[Crossref] [PubMed]

Peterman, E. J. G.

G. Sitters, D. Kamsma, G. Thalhammer, M. Ritsch-Marte, E. J. G. Peterman, and G. J. L. Wuite, “Acoustic force spectroscopy,” Nat. Methods 12(1), 47–50 (2015).
[Crossref] [PubMed]

Plénat, T.

T. Plénat, C. Tardin, P. Rousseau, and L. Salomé, “High-throughput single-molecule analysis of DNA-protein interactions by tethered particle motion,” Nucleic Acids Res. 40(12), e89 (2012).
[Crossref] [PubMed]

Reinsch, C. H.

C. H. Reinsch, “Smoothing by spline functions, II,” Numer. Math. 16(5), 451–454 (1971).
[Crossref]

Revyakin, A.

T. Lionnet, J. F. Allemand, A. Revyakin, T. R. Strick, O. A. Saleh, D. Bensimon, and V. Croquette, “Single-molecule studies using magnetic traps,” Cold Spring Harb. Protoc. 2012(1), 34–49 (2012).
[Crossref] [PubMed]

Ribeck, N.

N. Ribeck and O. A. Saleh, “Multiplexed single-molecule measurements with magnetic tweezers,” Rev. Sci. Instrum. 79(9), 094301 (2008).
[Crossref] [PubMed]

Ritsch-Marte, M.

G. Sitters, D. Kamsma, G. Thalhammer, M. Ritsch-Marte, E. J. G. Peterman, and G. J. L. Wuite, “Acoustic force spectroscopy,” Nat. Methods 12(1), 47–50 (2015).
[Crossref] [PubMed]

Roichman, Y.

Rousseau, P.

T. Plénat, C. Tardin, P. Rousseau, and L. Salomé, “High-throughput single-molecule analysis of DNA-protein interactions by tethered particle motion,” Nucleic Acids Res. 40(12), e89 (2012).
[Crossref] [PubMed]

Saleh, O. A.

B. M. Lansdorp, S. J. Tabrizi, A. Dittmore, and O. A. Saleh, “A high-speed magnetic tweezer beyond 10,000 frames per second,” Rev. Sci. Instrum. 84(4), 044301 (2013).
[Crossref] [PubMed]

B. M. Lansdorp and O. A. Saleh, “Power spectrum and Allan variance methods for calibrating single-molecule video-tracking instruments,” Rev. Sci. Instrum. 83(2), 025115 (2012).
[Crossref] [PubMed]

T. Lionnet, J. F. Allemand, A. Revyakin, T. R. Strick, O. A. Saleh, D. Bensimon, and V. Croquette, “Single-molecule studies using magnetic traps,” Cold Spring Harb. Protoc. 2012(1), 34–49 (2012).
[Crossref] [PubMed]

N. Ribeck and O. A. Saleh, “Multiplexed single-molecule measurements with magnetic tweezers,” Rev. Sci. Instrum. 79(9), 094301 (2008).
[Crossref] [PubMed]

Salomé, L.

T. Plénat, C. Tardin, P. Rousseau, and L. Salomé, “High-throughput single-molecule analysis of DNA-protein interactions by tethered particle motion,” Nucleic Acids Res. 40(12), e89 (2012).
[Crossref] [PubMed]

Seidel, R.

P. Daldrop, H. Brutzer, A. Huhle, D. J. Kauert, and R. Seidel, “Extending the range for force calibration in magnetic tweezers,” Biophys. J. 108(10), 2550–2561 (2015).
[Crossref] [PubMed]

Seol, Y.

Y. Seol and K. C. Neuman, “Magnetic tweezers for single-molecule manipulation,” Methods Mol. Biol. 783, 265–293 (2011).
[Crossref] [PubMed]

Sethna, J. P.

M. Bierbaum, B. D. Leahy, A. A. Alemi, I. Cohen, and J. P. Sethna, “Light microscopy at maximal precision,” Phys. Rev. X 7(4), 1–10 (2017).
[Crossref]

Shechtman, Y.

A. von Diezmann, Y. Shechtman, and W. E. Moerner, “Three-Dimensional Localization of Single Molecules for Super-Resolution Imaging and Single-Particle Tracking,” Chem. Rev. 117(11), 7244–7275 (2017).
[Crossref] [PubMed]

Sitters, G.

G. Sitters, D. Kamsma, G. Thalhammer, M. Ritsch-Marte, E. J. G. Peterman, and G. J. L. Wuite, “Acoustic force spectroscopy,” Nat. Methods 12(1), 47–50 (2015).
[Crossref] [PubMed]

Strick, T. R.

T. Lionnet, J. F. Allemand, A. Revyakin, T. R. Strick, O. A. Saleh, D. Bensimon, and V. Croquette, “Single-molecule studies using magnetic traps,” Cold Spring Harb. Protoc. 2012(1), 34–49 (2012).
[Crossref] [PubMed]

Tabrizi, S. J.

B. M. Lansdorp, S. J. Tabrizi, A. Dittmore, and O. A. Saleh, “A high-speed magnetic tweezer beyond 10,000 frames per second,” Rev. Sci. Instrum. 84(4), 044301 (2013).
[Crossref] [PubMed]

Tardin, C.

T. Plénat, C. Tardin, P. Rousseau, and L. Salomé, “High-throughput single-molecule analysis of DNA-protein interactions by tethered particle motion,” Nucleic Acids Res. 40(12), e89 (2012).
[Crossref] [PubMed]

Thalhammer, G.

G. Sitters, D. Kamsma, G. Thalhammer, M. Ritsch-Marte, E. J. G. Peterman, and G. J. L. Wuite, “Acoustic force spectroscopy,” Nat. Methods 12(1), 47–50 (2015).
[Crossref] [PubMed]

Tjahjowidodo, T.

V. T. Dung and T. Tjahjowidodo, “A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting,” PLoS One 12(3), e0173857 (2017).
[Crossref] [PubMed]

van Blaaderen, A.

van Loenhout, M. T. J.

M. T. J. van Loenhout, J. W. J. Kerssemakers, I. De Vlaminck, and C. Dekker, “Non-bias-limited tracking of spherical particles, enabling nanometer resolution at low magnification,” Biophys. J. 102(10), 2362–2371 (2012).
[Crossref] [PubMed]

van Oostrum, P.

von Diezmann, A.

A. von Diezmann, Y. Shechtman, and W. E. Moerner, “Three-Dimensional Localization of Single Molecules for Super-Resolution Imaging and Single-Particle Tracking,” Chem. Rev. 117(11), 7244–7275 (2017).
[Crossref] [PubMed]

Vörös, Z.

Z. Vörös, Y. Yan, D. T. Kovari, L. Finzi, and D. Dunlap, “Proteins mediating DNA loops effectively block transcription,” Protein Sci. 26(7), 1427–1438 (2017).
[Crossref] [PubMed]

Wuite, G. J. L.

G. Sitters, D. Kamsma, G. Thalhammer, M. Ritsch-Marte, E. J. G. Peterman, and G. J. L. Wuite, “Acoustic force spectroscopy,” Nat. Methods 12(1), 47–50 (2015).
[Crossref] [PubMed]

Yan, Y.

Z. Vörös, Y. Yan, D. T. Kovari, L. Finzi, and D. Dunlap, “Proteins mediating DNA loops effectively block transcription,” Protein Sci. 26(7), 1427–1438 (2017).
[Crossref] [PubMed]

Yang, S.-M.

Yi, G.-R.

Annu. Rev. Biophys. (1)

I. De Vlaminck and C. Dekker, “Recent Advances In Magnetic Tweezers,” Annu. Rev. Biophys. 41(1), 453–472 (2012).
[Crossref] [PubMed]

Biophys. J. (3)

P. Daldrop, H. Brutzer, A. Huhle, D. J. Kauert, and R. Seidel, “Extending the range for force calibration in magnetic tweezers,” Biophys. J. 108(10), 2550–2561 (2015).
[Crossref] [PubMed]

C. Gosse and V. Croquette, “Magnetic tweezers: micromanipulation and force measurement at the molecular level,” Biophys. J. 82(6), 3314–3329 (2002).
[Crossref] [PubMed]

M. T. J. van Loenhout, J. W. J. Kerssemakers, I. De Vlaminck, and C. Dekker, “Non-bias-limited tracking of spherical particles, enabling nanometer resolution at low magnification,” Biophys. J. 102(10), 2362–2371 (2012).
[Crossref] [PubMed]

Chem. Rev. (1)

A. von Diezmann, Y. Shechtman, and W. E. Moerner, “Three-Dimensional Localization of Single Molecules for Super-Resolution Imaging and Single-Particle Tracking,” Chem. Rev. 117(11), 7244–7275 (2017).
[Crossref] [PubMed]

Cold Spring Harb. Protoc. (1)

T. Lionnet, J. F. Allemand, A. Revyakin, T. R. Strick, O. A. Saleh, D. Bensimon, and V. Croquette, “Single-molecule studies using magnetic traps,” Cold Spring Harb. Protoc. 2012(1), 34–49 (2012).
[Crossref] [PubMed]

J. Colloid Interface Sci. (1)

J. C. Crocker and D. G. Grier, “Methods of Digital Video Microscopy for Colloidal Studies,” J. Colloid Interface Sci. 179(1), 298–310 (1996).
[Crossref]

Methods Mol. Biol. (1)

Y. Seol and K. C. Neuman, “Magnetic tweezers for single-molecule manipulation,” Methods Mol. Biol. 783, 265–293 (2011).
[Crossref] [PubMed]

Nat. Methods (2)

G. Sitters, D. Kamsma, G. Thalhammer, M. Ritsch-Marte, E. J. G. Peterman, and G. J. L. Wuite, “Acoustic force spectroscopy,” Nat. Methods 12(1), 47–50 (2015).
[Crossref] [PubMed]

R. Parthasarathy, “Rapid, accurate particle tracking by calculation of radial symmetry centers,” Nat. Methods 9(7), 724–726 (2012).
[Crossref] [PubMed]

Nucleic Acids Res. (1)

T. Plénat, C. Tardin, P. Rousseau, and L. Salomé, “High-throughput single-molecule analysis of DNA-protein interactions by tethered particle motion,” Nucleic Acids Res. 40(12), e89 (2012).
[Crossref] [PubMed]

Numer. Math. (1)

C. H. Reinsch, “Smoothing by spline functions, II,” Numer. Math. 16(5), 451–454 (1971).
[Crossref]

Opt. Express (1)

Phys. Rev. X (1)

M. Bierbaum, B. D. Leahy, A. A. Alemi, I. Cohen, and J. P. Sethna, “Light microscopy at maximal precision,” Phys. Rev. X 7(4), 1–10 (2017).
[Crossref]

PLoS One (1)

V. T. Dung and T. Tjahjowidodo, “A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting,” PLoS One 12(3), e0173857 (2017).
[Crossref] [PubMed]

Protein Sci. (1)

Z. Vörös, Y. Yan, D. T. Kovari, L. Finzi, and D. Dunlap, “Proteins mediating DNA loops effectively block transcription,” Protein Sci. 26(7), 1427–1438 (2017).
[Crossref] [PubMed]

Rev. Sci. Instrum. (4)

B. M. Lansdorp and O. A. Saleh, “Power spectrum and Allan variance methods for calibrating single-molecule video-tracking instruments,” Rev. Sci. Instrum. 83(2), 025115 (2012).
[Crossref] [PubMed]

B. M. Lansdorp, S. J. Tabrizi, A. Dittmore, and O. A. Saleh, “A high-speed magnetic tweezer beyond 10,000 frames per second,” Rev. Sci. Instrum. 84(4), 044301 (2013).
[Crossref] [PubMed]

N. Ribeck and O. A. Saleh, “Multiplexed single-molecule measurements with magnetic tweezers,” Rev. Sci. Instrum. 79(9), 094301 (2008).
[Crossref] [PubMed]

S. F. Nørrelykke and H. Flyvbjerg, “Power spectrum analysis with least-squares fitting: Amplitude bias and its elimination, with application to optical tweezers and atomic force microscope cantilevers,” Rev. Sci. Instrum. 81(7), 075103 (2010).
[Crossref] [PubMed]

Other (4)

M. T. Heath, Scientific Computing: An Introductory Survey, 2nd ed. (McGraw-Hill, 2002).

I. D. Vilfan, J. Lipfert, D. A. Koster, S. G. Lemay, and N. H. Dekker, “Magnetic Tweezers for Single-Molecule Experiments,” in Handbook of Single-Molecule Biophysics (Springer US, 2009), pp. 371–395.

D. T. Kovari, Y. Yan, L. Finzi, and D. Dunlap, “Tethered Particle Motion: An Easy Technique for Probing DNA Topology and Interactions with Transcription Factors,” in Single Molecule Analysis. Methods in Molecular Biology (Springer, 2018) pp. 317–340.

D. T. Kovari, “Radial Symmetry and Spline Look-up-table Inversion” figshare (2019) [retrieved 28 Jun. 2019], https://figshare.com/articles/Radial_Symmetry_LUT_Tracking_Code/8317136 .

Supplementary Material (1)

NameDescription
» Code 1       Source code for Radial Symmetry and LUT routines

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1 Schematic of LUT-based 3D microscope. (A) A piezo objective scanner is used to capture focus-dependent images of particles for look-up tables (LUTs). (B) Particles imaged with brightfield are surrounded by diffraction fringes that vary depending on the distance of the particle from the focal plane. (C) Smoothed intensity-versus-Z plots of bright-field fringe pattern in (B). (C-Inset) Finite step size, image noise, and instrument drift cause scatter in the LUT. A smoothing spline suppresses noise while capturing the underlying trend.
Fig. 2
Fig. 2 Finding the origin of radial symmetry. (A) Gradient vectors (orange) in a noise-free, radially symmetric image follow lines intersecting the origin of symmetry. (B) Symmetry localization for a noisy image. Near the edges of the fringe pattern, where the gradient vectors are small, noise disperses vectors in random directions, biasing the least-squares fit to the center of the image (cyan x) and produces a large residual <d2> (cyan circle). Weighting the fit by the gradient magnitudes improves accuracy and decreases the residual (magenta x and circle). (C) Weighted standard error versus gradient exponent for SNR = 1,2.5,5,10 with distance exponent m = 0, defined in Eq. (11). (D) Fit error versus gradient exponent for SNR = 1,2,5,10 with distance exponent m = 0. (E) Effective pixel weight using Wii = |∇Ii|5.
Fig. 3
Fig. 3 Radial symmetry performance versus weight-factor distance exponent m with gradient exponent n = 5, for noise levels SNR = 1,2.5,5,10. (A) Weighted standard error of fit versus distance exponent. (B) Fit error versus distance exponent.
Fig. 4
Fig. 4 The noise sensitivity of X-Y localization. Images of particles were simulated on a 100 × 100 pixel grid, with center locations ranging from horizontal locations Xc = 49.5 to 51.5, in 0.05 pixel increments. Images were distorted with added noise. Error bars include 90% of data. The vertical axis indicates the absolute value of error, calculated as |E| = |X-Xc|. Signal:noise is defined in Eq. (19). Particle centers were determined using 1D convolution (XC1D, Blue), 2D convolution (XC2D, Red), Radial Symmetry (RS, Yellow) and Quadrant Interpolation (QI, Violet). Pixel-step artifacts (see Figs. 5 and 6), prevent XC and QI routines from correctly identifying the particle center, even without noise (SNR = ∞).
Fig. 5
Fig. 5 Comparison of the XY localization accuracy of bright-field diffraction patterns using image cross-correlation and radial symmetry algorithms. Particle images were simulated with the center (Xc,Yc) fixed at Yc = 40 pixels and the Xc position corresponding to the horizontal axis of the plots. 50 images were simulated at each position for signal-to-noise ratios corresponding to the legend. In all plots, the error bars include 90% of the data. Plots labeled “XC1D” correspond to results from 1D cross-correlation algorithm. Plots labeled “XC2D” correspond to 2D cross-correlation. Plots labeled “RS” correspond to the Radial Symmetry algorithm. All units are in Pixels. (A) Tracking error as a function of particle position varied across the entire window. The Fourier-space periodicity of the cross-correlation limits XC methods to accurately determining particle positions only within the inner quartile of the image (25-75 pixels in the plots). The gap in XC plots at 75 corresponds to a resulting circular convolution for which the peak would lie exactly between the upper (100 px) and lower (1 px) edge of the image, see Eq. (22) in Appendix for details. XC routines perform very poorly at the edges of the image (crosshatched boxes). At low noise levels, a radial symmetry routine is accurate across the entire range. Below SNR = 2, the performance of radial symmetry routines deteriorates due to noise-related center biasing. (B) Central (dashed) region of A corresponding to Xc ranging from 49.5 to 51.5. Finely spaced simulations reveal ½-pixel scale stepping artifacts in XC routines.
Fig. 6
Fig. 6 Noise sensitivity of Quadrant Interpolation algorithm for bright-field diffraction patterns. The QI algorithm presented by van Loenhout et al. was tested using the procedure from Fig. 4. (A) Localization error plotted as a function of position within the field of view. As noise increases, localization accuracy is very poor for particles that are not roughly centered in the image. (B) Tracking errors near the center of the image. ½-pixel scale artifacts are not as pronounced as for the convolution routines.
Fig. 7
Fig. 7 Sensitivity of XY localization to shading. Images generated according to Eq. (20). For each shading amplitude, A, and wavelength λ, 100 particles in simulated images were located. Error bars are centered on the average absolute error and range from the lowest quartile to upper quartile.
Fig. 8
Fig. 8 Sensitivity of XY localization to particle size and axial position. (A) Simulated images were rescaled and tracked using the radial symmetry routine. The particle pictured on the left corresponds to unscaled data, representative of 2.8 µm particles captured at 63 × magnification. The particle on far right corresponds to a three-fold reduction in size. (B) Images were generated over a range of Z-positions using the LUT shown in Fig. 1(b). Solid lines indicate mean error, colored bands span the lower and upper quartiles for each noise level.
Fig. 9
Fig. 9 LUT performance for bright-field fringes. Simulated intensity profiles spanning the inner 3 µm of the LUT were fit using the Gauss-Newton, discrete match, and Quadratic fitting routines. Each data point corresponds to the average of 100 simulations at 100 uniformly spaced positions within the range of the LUT. Inset: an enlarged view of the higher signal to noise data within the box (dashed line).
Fig. 10
Fig. 10 Gauss-Newton LUT performance for bright-field fringes. Radial profiles were generated using a spline look-up-table, corresponding to data in Fig. 1(b), and distorted by additive Gaussian noise. 100 profiles were generated for each position and noise level. (A) Average absolute error |Zc-Z|. (B) Standard Error calculated using a Gauss-Newton routine. Error bars indicate the medial 50% of data. (C) Sum of the square of the Jacobian (SSJ) at each position in the LUT, indicates how quickly the LUT changes with respect to Z. Near the optimal focal plane (Zc~49.25), the fringe pattern is changing fastest; consequently, localization is most accurate in that region. Although the LUT in Fig. 1(b) appears roughly symmetric the SSJ indicates the fringes change faster for Zc > 49.5 than for Zc < 49; as a result, localization is more accurate above Zc = 49.5 than below Zc = 49.
Fig. 11
Fig. 11 Bright-field LUT performance for discrete and quadratic fit routines. (A) Average absolute error |Zc-Z| for discrete fit. Performance is limited to ½ the LUT step size. (B) Average absolute error for quadratic fit. At high noise levels, quadratic fitting performs poorly, because the residual curve is not parabolic. Similar to the Gauss-Newton routine, Z-dependence in the performance of the quadratic and discrete routines manifest as a result of differences in the rate-of-change of the fringe pattern at different axial positions.
Fig. 12
Fig. 12 LUT fit error due to particle polydispersity. (A) Fit error for 1.04 ± 0.05 µm particles (B) Fit error for 2.8 ± 0.08 µm particles. For both data sets, histograms summarize average error for all fits. Blue curve corresponds to the distribution errors when fitting particles with their own spline LUT; orange curves correspond to the distribution of errors when fitting a particle’s image to a spline LUT for a different particle. Heat maps display the average error for each set of Particle-Spline comparisons. The diagonal for each map corresponds to a particle compared to its own spline LUT.

Equations (34)

Equations on this page are rendered with MathJax. Learn more.

d k 2 ( Δ y I k x k Δ x I k y k ( Δ u I k x 0 Δ x I k y 0 ) ) 2 Δ y I k 2 + Δ x I k 2
x= ( A T A ) -1 A T b,
A=[ Δ y I k Δ y I k 2 + Δ x I k 2 Δ x I k Δ y I k 2 + Δ x I k 2 ] b=[ Δ y I k x k Δ x I k y k Δ y I k 2 + Δ x I k 2 ].
W=[ 0 0 0 W ii 0 0 0 ], W ii =f( r i ) | I i | n ,
x=( A T WA ) -1 A T Wb,
σ 2 = b-Ax 2 N2
SE= σ 2 ( A T A) -1
d 2 = σ 2 = (b-Ax) T W(b-Ax) Tr(W)Tr( A T W 2 A( A T WA ) -1 ) R T WR Tr(W)2 Tr( W 2 ) Tr(W)
SE=σ ( A T WA) -1 Tr( W 2 ) Tr(W)
d k η( 0, ( 2σ r k | I k | ) 2 ),
W ii = r i m | I i | n ,
I n [i,j]=I[i,j]+ σ I SNR η[i,j]
|Error|= ( x fit x ˜ ) 2 + ( y fit y ˜ ) 2
R 2 [ z i ]= i (I[ z j ,r]I[ r i ]) 2 , z j * =argmin( R 2 [ z j ]).
I[ z j , r j ]I[ z i + δ i , r i ]+ η ij
{ f r i (z)I[ z j , r i ], z= z j I[ z j1 , r i ]< f r i (z)<I[ z j , r i ], z j1 <z< z j
ϕ(z)= i ( I r i f r i (z) ) 2 =R(z ) T R(z) ,
σ z σ 2 ( J( z ^ ) T J( z ^ ) ) 1 ,
σ ^ 2 = 1 N1 R ( z ^ ) T R( z ^ ),
I BG (x,y)= I part (x,y)A( cos( x 2π λ )cos( y 2π λ )+1 ),
x ^ x,y I[x,y]x x,y I[x,y] , y ^ x,y I[x,y]y x,y I[x,y]
x sym =argmax( I(x')I(xx')dx' ),
C[x,y]= F 1 ( F(I[x,y])F(I[x,y]) ),
[ x * , y * ]=arg max {x,y} ( C[x,y] ) x c = x * 2 + N 4 + 1 2 y c = y * 2 + M 4 + 1 2 .
x c = x * 4 + N 4 + 3 4 y c = y * 4 + M 4 + 3 4 .
u I[x,y]= i=1 i=1 j=1 j1 I[ (xi+1),(yj+1) ] I[ (xi),(yj) ]
ν I[x,y]= i=1 i=1 j=1 j1 I[ (xi+1),(yj) ] I[ (xi),(yj+1) ],
Δ y k = 1 2 ( u I k + ν I k )
Δ x k = 1 2 ( u I k ν I k ).
s k = ( Η ϕ (z) ) 1 ϕ(z),
z k+1 = z k + s k .
ϕ(z)=J (z) T R(z).
s k = J (z) T R(z) J (z) T J(z) .
E=p j ( y i f( x j ) ) 2 +(1p) |f''(t) | 2 dt .

Metrics