Abstract

We present an algorithm to estimate the location of single fluorescent molecule with both high speed and high precision. This algorithm is based on finding the subpixel position with maximum radial symmetry in a pixelated single molecule fluorescence image. Compared with conventional algorithms, this algorithm does not rely on point-spread-function or noise model. Through numerical simulation and experimental analysis, we found that this algorithm exhibits localization precision very close to the maximum likelihood estimator (MLE), while executes 1000 times faster than the MLE and 6 times faster than the fluoroBancroft algorithm.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. Huang, H. Babcock, and X. W. Zhuang, Cell 143, 1047 (2010).
    [CrossRef]
  2. R. J. Ober, S. Ram, and E. S. Ward, Biophys. J. 86, 1185 (2004).
    [CrossRef]
  3. Z. L. Shen and S. B. Andersson, IEEE Trans. Signal Process. 59, 4041 (2011).
    [CrossRef]
  4. B. Yu, D. N. Chen, J. L. Qu, and H. B. Niu, Opt. Lett. 36, 4317 (2011).
    [CrossRef]
  5. R. Starr, S. Stahlheber, and A. Small, Opt. Lett. 37, 413 (2012).
    [CrossRef]
  6. T. W. Quan, P. C. Li, F. Long, S. Q. Zeng, Q. M. Luo, P. N. Hedde, G. U. Nienhaus, and Z. L. Huang, Opt. Express 18, 11867 (2010).
    [CrossRef]
  7. C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, Nat. Meth. 7, 373 (2010).
    [CrossRef]
  8. Z. L. Huang, H. Y. Zhu, F. Long, H. Q. Ma, L. S. Qin, Y. F. Liu, J. P. Ding, Z. H. Zhang, Q. M. Luo, and S. Q. Zeng, Opt. Express 19, 19156 (2011).
    [CrossRef]
  9. P. Friedl and D. Gilmour, Nat. Rev. Mol. Cell Biol. 10, 445 (2009).
    [CrossRef]
  10. J. B. Pawley, Handbook of Biological Confocal Microscopy, 3rd ed. (Springer, 2006).
  11. P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, Nat. Meth. 6, 689 (2009).
    [CrossRef]
  12. K. Nienhaus, G. U. Nienhaus, J. Wiedenmann, and H. Nar, Proc. Natl. Acad. Sci. USA 102, 9156 (2005).
    [CrossRef]

2012 (1)

2011 (3)

2010 (3)

B. Huang, H. Babcock, and X. W. Zhuang, Cell 143, 1047 (2010).
[CrossRef]

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, Nat. Meth. 7, 373 (2010).
[CrossRef]

T. W. Quan, P. C. Li, F. Long, S. Q. Zeng, Q. M. Luo, P. N. Hedde, G. U. Nienhaus, and Z. L. Huang, Opt. Express 18, 11867 (2010).
[CrossRef]

2009 (2)

P. Friedl and D. Gilmour, Nat. Rev. Mol. Cell Biol. 10, 445 (2009).
[CrossRef]

P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, Nat. Meth. 6, 689 (2009).
[CrossRef]

2005 (1)

K. Nienhaus, G. U. Nienhaus, J. Wiedenmann, and H. Nar, Proc. Natl. Acad. Sci. USA 102, 9156 (2005).
[CrossRef]

2004 (1)

R. J. Ober, S. Ram, and E. S. Ward, Biophys. J. 86, 1185 (2004).
[CrossRef]

Andersson, S. B.

Z. L. Shen and S. B. Andersson, IEEE Trans. Signal Process. 59, 4041 (2011).
[CrossRef]

Babcock, H.

B. Huang, H. Babcock, and X. W. Zhuang, Cell 143, 1047 (2010).
[CrossRef]

Chen, D. N.

Ding, J. P.

Friedl, P.

P. Friedl and D. Gilmour, Nat. Rev. Mol. Cell Biol. 10, 445 (2009).
[CrossRef]

Fuchs, J.

P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, Nat. Meth. 6, 689 (2009).
[CrossRef]

Gilmour, D.

P. Friedl and D. Gilmour, Nat. Rev. Mol. Cell Biol. 10, 445 (2009).
[CrossRef]

Hedde, P. N.

Huang, B.

B. Huang, H. Babcock, and X. W. Zhuang, Cell 143, 1047 (2010).
[CrossRef]

Huang, Z. L.

Joseph, N.

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, Nat. Meth. 7, 373 (2010).
[CrossRef]

Li, P. C.

Lidke, K. A.

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, Nat. Meth. 7, 373 (2010).
[CrossRef]

Liu, Y. F.

Long, F.

Luo, Q. M.

Ma, H. Q.

Nar, H.

K. Nienhaus, G. U. Nienhaus, J. Wiedenmann, and H. Nar, Proc. Natl. Acad. Sci. USA 102, 9156 (2005).
[CrossRef]

Nienhaus, G. U.

T. W. Quan, P. C. Li, F. Long, S. Q. Zeng, Q. M. Luo, P. N. Hedde, G. U. Nienhaus, and Z. L. Huang, Opt. Express 18, 11867 (2010).
[CrossRef]

P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, Nat. Meth. 6, 689 (2009).
[CrossRef]

K. Nienhaus, G. U. Nienhaus, J. Wiedenmann, and H. Nar, Proc. Natl. Acad. Sci. USA 102, 9156 (2005).
[CrossRef]

Nienhaus, K.

K. Nienhaus, G. U. Nienhaus, J. Wiedenmann, and H. Nar, Proc. Natl. Acad. Sci. USA 102, 9156 (2005).
[CrossRef]

Niu, H. B.

Ober, R. J.

R. J. Ober, S. Ram, and E. S. Ward, Biophys. J. 86, 1185 (2004).
[CrossRef]

Oswald, F.

P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, Nat. Meth. 6, 689 (2009).
[CrossRef]

Pawley, J. B.

J. B. Pawley, Handbook of Biological Confocal Microscopy, 3rd ed. (Springer, 2006).

Qin, L. S.

Qu, J. L.

Quan, T. W.

Ram, S.

R. J. Ober, S. Ram, and E. S. Ward, Biophys. J. 86, 1185 (2004).
[CrossRef]

Rieger, B.

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, Nat. Meth. 7, 373 (2010).
[CrossRef]

Shen, Z. L.

Z. L. Shen and S. B. Andersson, IEEE Trans. Signal Process. 59, 4041 (2011).
[CrossRef]

Small, A.

Smith, C. S.

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, Nat. Meth. 7, 373 (2010).
[CrossRef]

Stahlheber, S.

Starr, R.

Ward, E. S.

R. J. Ober, S. Ram, and E. S. Ward, Biophys. J. 86, 1185 (2004).
[CrossRef]

Wiedenmann, J.

P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, Nat. Meth. 6, 689 (2009).
[CrossRef]

K. Nienhaus, G. U. Nienhaus, J. Wiedenmann, and H. Nar, Proc. Natl. Acad. Sci. USA 102, 9156 (2005).
[CrossRef]

Yu, B.

Zeng, S. Q.

Zhang, Z. H.

Zhu, H. Y.

Zhuang, X. W.

B. Huang, H. Babcock, and X. W. Zhuang, Cell 143, 1047 (2010).
[CrossRef]

Biophys. J. (1)

R. J. Ober, S. Ram, and E. S. Ward, Biophys. J. 86, 1185 (2004).
[CrossRef]

Cell (1)

B. Huang, H. Babcock, and X. W. Zhuang, Cell 143, 1047 (2010).
[CrossRef]

IEEE Trans. Signal Process. (1)

Z. L. Shen and S. B. Andersson, IEEE Trans. Signal Process. 59, 4041 (2011).
[CrossRef]

Nat. Meth. (2)

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, Nat. Meth. 7, 373 (2010).
[CrossRef]

P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, Nat. Meth. 6, 689 (2009).
[CrossRef]

Nat. Rev. Mol. Cell Biol. (1)

P. Friedl and D. Gilmour, Nat. Rev. Mol. Cell Biol. 10, 445 (2009).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Proc. Natl. Acad. Sci. USA (1)

K. Nienhaus, G. U. Nienhaus, J. Wiedenmann, and H. Nar, Proc. Natl. Acad. Sci. USA 102, 9156 (2005).
[CrossRef]

Other (1)

J. B. Pawley, Handbook of Biological Confocal Microscopy, 3rd ed. (Springer, 2006).

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 (3)

Fig. 1.
Fig. 1.

Principle of MrSE. (a) Single molecule fluorescence image, where the dot indicates the exact molecule position, the arrows show the gradient directions of the pixels beneath them, and the lines indicate the corresponding radial lines; (b) distribution of Dsum from an arbitrary subpixel point to the radial lines of all pixels inside the square in (a). Note that the point with minimum value (the darkest point) demonstrates the estimated position of the molecule.

Fig. 2.
Fig. 2.

Localization precision comparison with (a) simulated images with no background and (b) a background fluorescence (Ib) of 10 photons per pixel [6,7]. Note that the comparison is quantified as the standard deviation of localization error and is specified in x direction (σx) only.

Fig. 3.
Fig. 3.

Localization performance of the algorithms for experimental [(a)–(d)] and simulated (e) images: (a) overlay of the first 1000 original TIRF images, (b) super-resolution image reconstructed from MrSE, (c) normalized distributions of fluorescent molecules [in the box of (b)] deviating from their mean contour line, (d) SNR distribution from the experimental images, and (e) estimated localization precision in x direction using simulated images whose parameters were set to be the same as the real experiment.

Tables (1)

Tables Icon

Table 1. Average Time Consumption per Molecule Localizationa

Equations (5)

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

Gx=[110111101111011]*A,Gy=[111111000111111]*A.
θ(m,n)=arctan(Gy(m,n)/Gx(m,n)),
y=K(m,n)x+C(m,n),
Dsum(x,y)=mn(|K(m,n)xy+C(m,n)|1+K2(m,n))2.
{Dsum(x,y)x=0Dsum(x,y)y=0.

Metrics