Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Brief Communication
  • Published:

Optimized localization analysis for single-molecule tracking and super-resolution microscopy

Abstract

We optimally localized isolated fluorescent beads and molecules imaged as diffraction-limited spots, determined the orientation of molecules and present reliable formulas for the precision of various localization methods. Both theory and experimental data showed that unweighted least-squares fitting of a Gaussian squanders one-third of the available information, a popular formula for its precision exaggerates beyond Fisher's information limit, and weighted least-squares may do worse, whereas maximum-likelihood fitting is practically optimal.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Point spread functions for four fixed fluorophores with different spatial orientations.
Figure 2: Demonstration of MLEwT on fixed fluorophores.
Figure 3: The point spread function of a 40-nm fluorescent bead.
Figure 4: Comparing four estimators applied to the same data set.

Similar content being viewed by others

References

  1. Born, M. & Wolf, E. Principles of Optics (Cambridge University Press, New York, 1999).

  2. Barak, L.S. & Webb, W.W. J. Cell Biol. 95, 846–852 (1982).

    Article  CAS  Google Scholar 

  3. Yildiz, A. et al. Science 300, 2061–2065 (2003).

    Article  CAS  Google Scholar 

  4. Okten, Z., Churchman, L.S., Rock, R.S. & Spudich, J.A. Nat. Struct. Mol. Biol. 11, 884–887 (2004).

    Article  Google Scholar 

  5. Betzig, E. et al. Science 313, 1642–1645 (2006).

    Article  CAS  Google Scholar 

  6. Moerner, W.E. Proc. Natl. Acad. Sci. USA 104, 12596–12602 (2007).

    Article  CAS  Google Scholar 

  7. Abraham, A.V., Ram, S., Chao, J., Ward, E.S. & Ober, R.J. Opt. Express 17, 23352–23373 (2010).

    Article  Google Scholar 

  8. Rao, C.R. Linear Statistical Inference and Its Applications (Wiley, New York, New York, 1973).

  9. Ober, R.J., Ram, S. & Ward, E.S. Biophys. J. 86, 1185–1200 (2004).

    Article  CAS  Google Scholar 

  10. Robbins, M.S. & Hadwen, B.J. IEEE Trans. Electron. Dev. 50, 1227–1232 (2003).

    Article  Google Scholar 

  11. Enderlein, J., Toprak, E. & Selvin, P. Opt. Express 14, 8111–8120 (2006).

    Article  CAS  Google Scholar 

  12. Forkey, J.N., Quinlan, M.E., Shaw, M.A., Corrie, J.E.T. & Goldman, Y.E. Nature 422, 399–404 (2003).

    Article  CAS  Google Scholar 

  13. Toprak, E. et al. Proc. Natl. Acad. Sci. USA 103, 6495–6499 (2006).

    Article  CAS  Google Scholar 

  14. Aguet, F., Geissbühler, S., Märki, I., Lasser, T. & Unser, M. Opt. Express 17, 6829–6848 (2009).

    Article  CAS  Google Scholar 

  15. Toprak, E. & Selvin, P.R. Annu. Rev. Biophys. Biomol. Struct. 36, 349–369 (2007).

    Article  CAS  Google Scholar 

  16. Thompson, R.E., Larson, D.R. & Webb, W.W. Biophys. J. 82, 2775–2783 (2002).

    Article  CAS  Google Scholar 

  17. Bobroff, N. Rev. Sci. Instrum. 57, 1152–1157 (1986).

    Article  Google Scholar 

  18. Carter, A.R. et al. Appl. Opt. 46, 421–427 (2007).

    Article  Google Scholar 

  19. Berg-Sørensen, K. & Flyvbjerg, H. Rev. Sci. Instrum. 75, 594–612 (2004).

    Article  Google Scholar 

  20. Axelrod, D., Burghardt, T.P. & Thompson, N.L. Annu. Rev. Biophys. Bioeng. 13, 247–268 (1984).

    Article  CAS  Google Scholar 

  21. Ulbrich, M.H. & Isacoff, E.Y. Nat. Methods 4, 319–321 (2007).

    Article  CAS  Google Scholar 

  22. Churchman, L.S., Flyvbjerg, H. & Spudich, J.A. Biophys. J. 90, 668–671 (2006).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank S.M. Block, W.E. Moerner and R.S. Rock for discussions; Z.D. Bryant for allowing us to use his microscope for some of the data collection and M.W. Elting and J.M. Sung for assisting us. This work was supported by the European Union (FP7-HEALTH-F4-2008-201418, Revolutionary Approaches and Devices for Nucleic Acid Analysis to H.F.), by the US National Institutes of Health (GM33289 to L.S.C. and J.A.S.), by the Human Frontier Science Program (GP0054/2009-C to J.A.S. and H.F.) and the Damon Runyon Cancer Research Foundation (DRG-1997-08 to L.S.C.).

Author information

Authors and Affiliations

Authors

Contributions

H.F., K.I.M. and L.S.C. designed research; K.I.M. and H.F. performed the theoretical calculations and analyzed data; J.A.S. supervised the experiments; L.S.C. conducted experiments; K.I.M. did numerical simulations; H.F., K.I.M., L.S.C. and J.A.S. wrote the paper.

Corresponding author

Correspondence to Henrik Flyvbjerg.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1-2 and Supplementary Note 1 (PDF 737 kb)

Supplementary Software 1

Python script using MLEwT to estimate location and orientation of a fixed dipole. (ZIP 481 kb)

Supplementary Software 2

Python script using MLEwT to localize isotropic dipole distributions excited by TIR. (ZIP 236 kb)

Supplementary Software 3

MatLab script using MLEwG to estimate location of an isotropic distribution of dipoles. (ZIP 22 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mortensen, K., Churchman, L., Spudich, J. et al. Optimized localization analysis for single-molecule tracking and super-resolution microscopy. Nat Methods 7, 377–381 (2010). https://doi.org/10.1038/nmeth.1447

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmeth.1447

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing