Abstract

Super-resolution techniques like PALM and STORM require accurate localization of single fluorophores detected using a CCD. Popular localization algorithms inefficiently assume each photon registered by a pixel can only come from an area in the specimen corresponding to that pixel (not from neighboring areas), before iteratively (slowly) fitting a Gaussian to pixel intensity; they fail with noisy images. We present an alternative; a probability distribution extending over many pixels is assigned to each photon, and independent distributions are joined to describe emitter location. We compare algorithms, and recommend which serves best under different conditions. At low signal-to-noise ratios, ours is 2-fold more precise than others, and 2 orders of magnitude faster; at high ratios, it closely approximates the maximum likelihood estimate.

© 2012 OSA

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2012

A. Löschberger, S. van de Linde, M.-C. Dabauvalle, B. Rieger, M. Heilemann, G. Krohne, and M. Sauer, “Super-resolution imaging visualizes the eightfold symmetry of gp210 proteins around the nuclear pore complex and resolves the central channel with nanometer resolution,” J. Cell Sci.125(3), 570–575 (2012).
[CrossRef] [PubMed]

2011

S. J. Holden, S. Uphoff, and A. N. Kapanidis, “DAOSTORM: an algorithm for high- density super-resolution microscopy,” Nat. Methods8(4), 279–280 (2011).
[CrossRef] [PubMed]

J. D. Larkin, N. G. Publicover, and J. L. Sutko, “Photon event distribution sampling: an image formation technique for scanning microscopes that permits tracking of sub-diffraction particles with high spatial and temporal resolutions,” J. Microsc.241(1), 54–68 (2011).
[CrossRef] [PubMed]

2010

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods7(5), 377–381 (2010).
[CrossRef] [PubMed]

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods7(5), 373–375 (2010).
[CrossRef] [PubMed]

S. Wolter, M. SchãœTtpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc.237(1), 12–22 (2010).
[CrossRef] [PubMed]

D. R. Larson, “The economy of photons,” Nat. Methods7(5), 357–359 (2010).
[CrossRef] [PubMed]

A. Papantonis, J. D. Larkin, Y. Wada, Y. Ohta, S. Ihara, T. Kodama, and P. R. Cook, “Active RNA polymerases: mobile or immobile molecular machines?” PLoS Biol.8(7), e1000419 (2010).
[CrossRef] [PubMed]

T. A. Laurence and B. A. Chromy, “Efficient maximum likelihood estimator fitting of histograms,” Nat. Methods7(5), 338–339 (2010).
[CrossRef] [PubMed]

2009

A. V. Abraham, S. Ram, J. Chao, E. S. Ward, and R. J. Ober, “Quantitative study of single molecule location estimation techniques,” Opt. Express17(26), 23352–23373 (2009).
[CrossRef] [PubMed]

P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, “Online image analysis software for photoactivation localization microscopy,” Nat. Methods6(10), 689–690 (2009).
[CrossRef] [PubMed]

2008

M. Xu and P. R. Cook, “Similar active genes cluster in specialized transcription factories,” J. Cell Biol.181(4), 615–623 (2008).
[CrossRef] [PubMed]

M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl.47(33), 6172–6176 (2008).
[CrossRef] [PubMed]

A. J. Berglund, M. D. McMahon, J. J. McClelland, and J. A. Liddle, “Fast, bias-free algorithm for tracking single particles with variable size and shape,” Opt. Express16(18), 14064–14075 (2008).
[CrossRef] [PubMed]

2006

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3(10), 793–796 (2006).
[CrossRef] [PubMed]

2004

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J.86(2), 1185–1200 (2004).
[CrossRef] [PubMed]

2002

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J.82(5), 2775–2783 (2002).
[CrossRef] [PubMed]

2001

M. K. Cheezum, W. F. Walker, and W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J.81(4), 2378–2388 (2001).
[CrossRef] [PubMed]

1986

Abraham, A. V.

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3(10), 793–796 (2006).
[CrossRef] [PubMed]

Berglund, A. J.

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Chao, J.

Cheezum, M. K.

M. K. Cheezum, W. F. Walker, and W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J.81(4), 2378–2388 (2001).
[CrossRef] [PubMed]

Chromy, B. A.

T. A. Laurence and B. A. Chromy, “Efficient maximum likelihood estimator fitting of histograms,” Nat. Methods7(5), 338–339 (2010).
[CrossRef] [PubMed]

Churchman, L. S.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods7(5), 377–381 (2010).
[CrossRef] [PubMed]

Cook, P. R.

A. Papantonis, J. D. Larkin, Y. Wada, Y. Ohta, S. Ihara, T. Kodama, and P. R. Cook, “Active RNA polymerases: mobile or immobile molecular machines?” PLoS Biol.8(7), e1000419 (2010).
[CrossRef] [PubMed]

M. Xu and P. R. Cook, “Similar active genes cluster in specialized transcription factories,” J. Cell Biol.181(4), 615–623 (2008).
[CrossRef] [PubMed]

Dabauvalle, M.-C.

A. Löschberger, S. van de Linde, M.-C. Dabauvalle, B. Rieger, M. Heilemann, G. Krohne, and M. Sauer, “Super-resolution imaging visualizes the eightfold symmetry of gp210 proteins around the nuclear pore complex and resolves the central channel with nanometer resolution,” J. Cell Sci.125(3), 570–575 (2012).
[CrossRef] [PubMed]

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Flyvbjerg, H.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods7(5), 377–381 (2010).
[CrossRef] [PubMed]

Fuchs, J.

P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, “Online image analysis software for photoactivation localization microscopy,” Nat. Methods6(10), 689–690 (2009).
[CrossRef] [PubMed]

Guilford, W. H.

M. K. Cheezum, W. F. Walker, and W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J.81(4), 2378–2388 (2001).
[CrossRef] [PubMed]

Hedde, P. N.

P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, “Online image analysis software for photoactivation localization microscopy,” Nat. Methods6(10), 689–690 (2009).
[CrossRef] [PubMed]

Heilemann, M.

A. Löschberger, S. van de Linde, M.-C. Dabauvalle, B. Rieger, M. Heilemann, G. Krohne, and M. Sauer, “Super-resolution imaging visualizes the eightfold symmetry of gp210 proteins around the nuclear pore complex and resolves the central channel with nanometer resolution,” J. Cell Sci.125(3), 570–575 (2012).
[CrossRef] [PubMed]

S. Wolter, M. SchãœTtpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc.237(1), 12–22 (2010).
[CrossRef] [PubMed]

M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl.47(33), 6172–6176 (2008).
[CrossRef] [PubMed]

Hess, H. F.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Holden, S. J.

S. J. Holden, S. Uphoff, and A. N. Kapanidis, “DAOSTORM: an algorithm for high- density super-resolution microscopy,” Nat. Methods8(4), 279–280 (2011).
[CrossRef] [PubMed]

Ihara, S.

A. Papantonis, J. D. Larkin, Y. Wada, Y. Ohta, S. Ihara, T. Kodama, and P. R. Cook, “Active RNA polymerases: mobile or immobile molecular machines?” PLoS Biol.8(7), e1000419 (2010).
[CrossRef] [PubMed]

Joseph, N.

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods7(5), 373–375 (2010).
[CrossRef] [PubMed]

Kapanidis, A. N.

S. J. Holden, S. Uphoff, and A. N. Kapanidis, “DAOSTORM: an algorithm for high- density super-resolution microscopy,” Nat. Methods8(4), 279–280 (2011).
[CrossRef] [PubMed]

Kasper, R.

M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl.47(33), 6172–6176 (2008).
[CrossRef] [PubMed]

Kodama, T.

A. Papantonis, J. D. Larkin, Y. Wada, Y. Ohta, S. Ihara, T. Kodama, and P. R. Cook, “Active RNA polymerases: mobile or immobile molecular machines?” PLoS Biol.8(7), e1000419 (2010).
[CrossRef] [PubMed]

Krohne, G.

A. Löschberger, S. van de Linde, M.-C. Dabauvalle, B. Rieger, M. Heilemann, G. Krohne, and M. Sauer, “Super-resolution imaging visualizes the eightfold symmetry of gp210 proteins around the nuclear pore complex and resolves the central channel with nanometer resolution,” J. Cell Sci.125(3), 570–575 (2012).
[CrossRef] [PubMed]

Larkin, J. D.

J. D. Larkin, N. G. Publicover, and J. L. Sutko, “Photon event distribution sampling: an image formation technique for scanning microscopes that permits tracking of sub-diffraction particles with high spatial and temporal resolutions,” J. Microsc.241(1), 54–68 (2011).
[CrossRef] [PubMed]

A. Papantonis, J. D. Larkin, Y. Wada, Y. Ohta, S. Ihara, T. Kodama, and P. R. Cook, “Active RNA polymerases: mobile or immobile molecular machines?” PLoS Biol.8(7), e1000419 (2010).
[CrossRef] [PubMed]

Larson, D. R.

D. R. Larson, “The economy of photons,” Nat. Methods7(5), 357–359 (2010).
[CrossRef] [PubMed]

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J.82(5), 2775–2783 (2002).
[CrossRef] [PubMed]

Laurence, T. A.

T. A. Laurence and B. A. Chromy, “Efficient maximum likelihood estimator fitting of histograms,” Nat. Methods7(5), 338–339 (2010).
[CrossRef] [PubMed]

Liddle, J. A.

Lidke, K. A.

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods7(5), 373–375 (2010).
[CrossRef] [PubMed]

Lindwasser, O. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Lippincott-Schwartz, J.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Löschberger, A.

A. Löschberger, S. van de Linde, M.-C. Dabauvalle, B. Rieger, M. Heilemann, G. Krohne, and M. Sauer, “Super-resolution imaging visualizes the eightfold symmetry of gp210 proteins around the nuclear pore complex and resolves the central channel with nanometer resolution,” J. Cell Sci.125(3), 570–575 (2012).
[CrossRef] [PubMed]

McClelland, J. J.

McMahon, M. D.

Mortensen, K. I.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods7(5), 377–381 (2010).
[CrossRef] [PubMed]

Mukherjee, A.

M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl.47(33), 6172–6176 (2008).
[CrossRef] [PubMed]

Nienhaus, G. U.

P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, “Online image analysis software for photoactivation localization microscopy,” Nat. Methods6(10), 689–690 (2009).
[CrossRef] [PubMed]

Ober, R. J.

Ohta, Y.

A. Papantonis, J. D. Larkin, Y. Wada, Y. Ohta, S. Ihara, T. Kodama, and P. R. Cook, “Active RNA polymerases: mobile or immobile molecular machines?” PLoS Biol.8(7), e1000419 (2010).
[CrossRef] [PubMed]

Olenych, S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Oswald, F.

P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, “Online image analysis software for photoactivation localization microscopy,” Nat. Methods6(10), 689–690 (2009).
[CrossRef] [PubMed]

Papantonis, A.

A. Papantonis, J. D. Larkin, Y. Wada, Y. Ohta, S. Ihara, T. Kodama, and P. R. Cook, “Active RNA polymerases: mobile or immobile molecular machines?” PLoS Biol.8(7), e1000419 (2010).
[CrossRef] [PubMed]

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Publicover, N. G.

J. D. Larkin, N. G. Publicover, and J. L. Sutko, “Photon event distribution sampling: an image formation technique for scanning microscopes that permits tracking of sub-diffraction particles with high spatial and temporal resolutions,” J. Microsc.241(1), 54–68 (2011).
[CrossRef] [PubMed]

Ram, S.

Rieger, B.

A. Löschberger, S. van de Linde, M.-C. Dabauvalle, B. Rieger, M. Heilemann, G. Krohne, and M. Sauer, “Super-resolution imaging visualizes the eightfold symmetry of gp210 proteins around the nuclear pore complex and resolves the central channel with nanometer resolution,” J. Cell Sci.125(3), 570–575 (2012).
[CrossRef] [PubMed]

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods7(5), 373–375 (2010).
[CrossRef] [PubMed]

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3(10), 793–796 (2006).
[CrossRef] [PubMed]

Sauer, M.

A. Löschberger, S. van de Linde, M.-C. Dabauvalle, B. Rieger, M. Heilemann, G. Krohne, and M. Sauer, “Super-resolution imaging visualizes the eightfold symmetry of gp210 proteins around the nuclear pore complex and resolves the central channel with nanometer resolution,” J. Cell Sci.125(3), 570–575 (2012).
[CrossRef] [PubMed]

S. Wolter, M. SchãœTtpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc.237(1), 12–22 (2010).
[CrossRef] [PubMed]

M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl.47(33), 6172–6176 (2008).
[CrossRef] [PubMed]

SchãœTtpelz, M.

S. Wolter, M. SchãœTtpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc.237(1), 12–22 (2010).
[CrossRef] [PubMed]

Schüttpelz, M.

M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl.47(33), 6172–6176 (2008).
[CrossRef] [PubMed]

Seefeldt, B.

M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl.47(33), 6172–6176 (2008).
[CrossRef] [PubMed]

Smith, C. S.

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods7(5), 373–375 (2010).
[CrossRef] [PubMed]

Sougrat, R.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

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S. J. Holden, S. Uphoff, and A. N. Kapanidis, “DAOSTORM: an algorithm for high- density super-resolution microscopy,” Nat. Methods8(4), 279–280 (2011).
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A. Papantonis, J. D. Larkin, Y. Wada, Y. Ohta, S. Ihara, T. Kodama, and P. R. Cook, “Active RNA polymerases: mobile or immobile molecular machines?” PLoS Biol.8(7), e1000419 (2010).
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S. Wolter, M. SchãœTtpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc.237(1), 12–22 (2010).
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M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3(10), 793–796 (2006).
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M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl.47(33), 6172–6176 (2008).
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[CrossRef] [PubMed]

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J.82(5), 2775–2783 (2002).
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J. Cell Biol.

M. Xu and P. R. Cook, “Similar active genes cluster in specialized transcription factories,” J. Cell Biol.181(4), 615–623 (2008).
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J. Cell Sci.

A. Löschberger, S. van de Linde, M.-C. Dabauvalle, B. Rieger, M. Heilemann, G. Krohne, and M. Sauer, “Super-resolution imaging visualizes the eightfold symmetry of gp210 proteins around the nuclear pore complex and resolves the central channel with nanometer resolution,” J. Cell Sci.125(3), 570–575 (2012).
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J. Microsc.

J. D. Larkin, N. G. Publicover, and J. L. Sutko, “Photon event distribution sampling: an image formation technique for scanning microscopes that permits tracking of sub-diffraction particles with high spatial and temporal resolutions,” J. Microsc.241(1), 54–68 (2011).
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P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, “Online image analysis software for photoactivation localization microscopy,” Nat. Methods6(10), 689–690 (2009).
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Supplementary Material (2)

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Figures (5)

Fig. 1
Fig. 1

JD localization. (a) An individual photon carries information about the probability of an emitter’s location. CM/MLS/MLE (blue) assume equal probability throughout the pixel, with zero probability elsewhere; JD localization (red) uses a normal distribution to emulate the microscope PSF (FWHM = 2.8x pixel width) which spreads beyond the pixel (shaded area). The area under both curves is equal. (b) Principles behind JD localization. Each photon represented in a pixel is treated individually (1, 2, and 3, photons indicated by x1, x2, x3), and individual probabilities of the location of the emitter, Pi (red curves) are aggregated to yield the joint probability, P, of emitter location (green). (c) Flow diagram for JD localization. Photons are attributed to each pixel dependent on intensity, and a probability distribution of the source of each photon is built using peak location (µi) and width (σi). The peak can be located at the pixel centre (left) or anywhere within or outside the pixel (right); the width can be that of the PSF (left) or any arbitrary value (e.g., as a function of distance, di, from the most intense pixel; right). Background (bkgd) noise is estimated and the influence of background photons nullified by setting σi = . Then, probabilities of individual photons are projected onto a single axis, combined to infer the probability of emitter location for that axis, and the projection and inference repeated for each axis.

Fig. 2
Fig. 2

Qualitative comparison of methods. Computer-generated images (15x15 pixels) like those illustrated were generated using 10-104 emitter photons and different numbers of background photons (i.e., b = 0 or 10 photons/pixel) to give different signal-to-noise ratios (S:N); then, the root-mean-square error of localization in one dimension (1-D RMSE in nm or pixel units) was calculated (104 localizations per data point) using the methods indicated. Photon counts (top) and S:N (bottom) are indicated in some typical images. The lower bound, LB (blue dashed line), is computed using Eq. (6) of Thompson et al. [14] and plotted here and in subsequent Figures as a reference. (a) With no background (b = 0), the ‘default’ version of JD returns the same results as CM, and both track the LB; MLS and MLE fail at low photon counts. The failure of MLS without background is examined more in Supplemental Fig. 1(b). In the presence of background (b = 10), all methods fail at low photon counts; at moderate counts, MLE performs best, and at high counts MLS is the worst as the others converge to the minimum error. (c) An ‘optimized’ version of JD increases precision at low S:N while retaining precision at high S:N. The grey region is analyzed further in Fig. 3. Arrows: conditions used in Fig. 4.

Fig. 3
Fig. 3

Tuning µi and σi to maximize localization precision near the detection limit. The 1-D RMSE in location of a point source was determined using 104 computer-generated images (15x15 pixels, 50-250 emitter photons, b = 10) per data point. JD localizations were determined by varying peak position (µi) and/or width (σi). Errors obtained using CM, MLS, and MLE, plus the lower bound (LB), are included for comparison (MLS/MLE plots smoothed by linear regression). (a) Varying µi depending on distance, di, from the most intense pixel (σi = σPSF for all distributions). Peaks of distributions are shifted towards the brightest pixel (in this example the central one) by ½ a pixel in both x- and y-dimensions. Left: cartoon illustrating how this shift applies to selected distributions (from blue curves/dots to red curves/dots). Right: JD localization yields 5% less error than CM for all S:N shown. (b) Varying σi as a function of distance, di, from the most intense pixel (as µi = pixel center for all distributions). Widths of distributions from the brightest pixel remain equal to σPSF, as those from surrounding ones expand. Left: cartoon illustrating these changes for selected distributions (from blue curves/halos to red curves/halos). Localization using JD yields up to 36% less error than CM. (c) Varying both peak position and width (as in (a) and (b), but using an x and y shift of ¼ pixel for µi). Representative images are shown (with photon counts given in white, and S:N in yellow). At this low S:N, JD localization yields less error than other methods. Arrow: condition used in Fig. 4. Error over the full range of S:N is shown in Supplemental Fig. 2. The effects of window size and offset of emitter from window center are shown in Supplemental Fig. 3.

Fig. 4
Fig. 4

Computation speeds of the different methods (expressed relative to that of MLE). The times taken by the different methods to compute 2-D localizations were determined using 104 computer-generated images (15x15, 13x13, or 10x10 pixels) using conditions at the points indicated by the arrows in Figs. 2(c) and 3(c) (either 183 photons, b = 10, and S:N = 2; or 1,000 photons, b = 10, and S:N = 10). JD was tested using both ‘optimized’ and ‘tuned’ versions. Our MLS script gave 390 localizations per second with 15x15-pixel images, which is even faster than other reports on comparable computers [7]; it was also 50-times faster than an MLE script written by others [5] but implemented by us. JD applied using the ‘optimized’ conditions was 120- to 180-times faster than MLE, and the ‘tuned’ version was 100- to 140-times faster than MLE. As expected, CM (applied with background correction) proved the fastest, but both JD versions were faster than the two iterative techniques.

Fig. 5
Fig. 5

Localization using ‘real’ images of transcription sites and microtubules in monkey cells (cos-7). (a) Nascent RNA at transcription sites. Cells expressing an EGFP gene containing an intron were fixed, and (nascent) EGFP transcripts detected using RNA FISH with probes targeting a short (sub-resolution) segment of the intron; images were collected using a wide-field microscope and CCD (90-nm pixels). One-hundred spots with S:N < 3 (histogram) were chosen manually, and four examples are shown at the top; the panels below illustrate the central 5x5 pixels in the upper panels, with 2-D localizations obtained by the different methods. As S:N decreases (left-to-right), localizations become more scattered (see Media 2 for results with all 100 spots). (b) Microtubules. Cells were fixed, microtubules indirectly immuno-labeled with Alexa 647, and a series of 30,000 images of temporally- and spatially-separated spots of one field collected using inclined illumination and an EM-CCD (155-nm pixels); 154,040 windows (11x11 pixels) containing 1 centrally-located spot were selected for analysis (using a Gaussian spot-finding algorithm). (i) Mean projection of all windows. (ii) One representative window (the histogram below illustrates the number of windows with different S:N). (iii) Individual windows were deliberately corrupted with noise (typical example and histogram shown). (iv) Mean projection of all resulting windows. Individual windows were now passed to each of the four methods, and localizations convolved with a 20-nm Gaussian intensity profile to aid visualization. (v, vi) Localizations obtained by MLS and the tuned version of JD yield roughly equivalent images. (vii) Magnified areas of the inset in (vi). Large circles in JD images contain fewer isolated results than the others, consistent with fewer mis-localizations (see also Supplemental Fig. 4(d)).

Equations (7)

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µ i =f( d i )= {   µ c + S o /C µ c S o /C   d i <0 d i >0 ,
µ i = µ c ( ( I o I R )( I o I L ) ) I o 1 ,
g( x, I i , d i )= { ( 2π σ psf 2 ) 1/2 e ( x( µ max S o ) ) 2 2 σ psf 2 ( 2π σ psf 2 ) 1/2 ( 2π σ psf 2 ) 1/2 e ( x( µ max S o ) ) 2 2 σ psf 2   x< µ max 2  S o ( 2π σ psf 2 ) 1/2  x> µ max +2  S o .
k 1 =  i N σ i 2 ,   k 2 =2 i N μ i σ i 2 ,
P(x) e 1 2 i N ( 1 σ i 2 ) [ x   i N ( μ i σ i 2 ) / i N ( 1 σ i 2 ) ] 2 ,
if σ i =σ,then μ o = 1 σ 2 i N μ i /( N σ 2 )= i N ( μ i )  N 1 .
N= i n j m I ij .

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