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

Nature Methods volume 7, pages 377–381 (2010)Cite this article

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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.

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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.

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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.).

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Author notes

  1. Kim I Mortensen and L Stirling Churchman: These authors contributed equally to this work.

Authors and Affiliations

  1. Department of Micro- and Nanotechnology, Technical University of Denmark, Kongens Lyngby, Denmark

    Kim I Mortensen & Henrik Flyvbjerg

  2. Department of Biochemistry, Stanford University School of Medicine, Stanford, California, USA

    L Stirling Churchman & James A Spudich

  3. Department of Physics, Stanford University School of Medicine, Stanford, California, USA

    L Stirling Churchman

Authors
  1. Kim I Mortensen
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  2. L Stirling Churchman
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  3. James A Spudich
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  4. Henrik Flyvbjerg
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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.

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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)

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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

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