Abstract

Estimating the location of single molecules from microscopy images is a key step in many quantitative single molecule data analysis techniques. Different algorithms have been advocated for the fitting of single molecule data, particularly the nonlinear least squares and maximum likelihood estimators. Comparisons were carried out to assess the performance of these two algorithms in different scenarios. Our results show that both estimators, on average, are able to recover the true location of the single molecule in all scenarios we examined. However, in the absence of modeling inaccuracies and low noise levels, the maximum likelihood estimator is more accurate than the nonlinear least squares estimator, as measured by the standard deviations of its estimates, and attains the best possible accuracy achievable for the sets of imaging and experimental conditions that were tested. Although neither algorithm is consistently superior to the other in the presence of modeling inaccuracies or misspecifications, the maximum likelihood algorithm emerges as a robust estimator producing results with consistent accuracy across various model mismatches andmisspecifications. At high noise levels, relative to the signal from the point source, neither algorithm has a clear accuracy advantage over the other. Comparisons were also carried out for two localization accuracy measures derived previously. Software packages with user-friendly graphical interfaces developed for single molecule location estimation (EstimationTool) and limit of the localization accuracy calculations (FandPLimitTool) are also discussed.

© 2009 Optical Society of America

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2008 (3)

X. S. Xie, P. J. Choi, G. W. Li, N. K. Lee, and G. Lia, "Single-molecule approach to molecular biology in living bacterial cells," Annu. Rev. Biophys. 37, 417-444 (2008).
[CrossRef]

B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy," Science 319, 810-813 (2008).
[CrossRef]

J. S. Biteen, M. A. Thompson, N. K. Tselentis, G. R. Bowman, L. Shapiro, and W. E. Moerner, "Super-resolution imaging in live Caulobacter crescentus cells using photoswitchable EYFP," Nat. Methods. 5, 947-949 (2008).
[CrossRef]

2007 (3)

B. Zhang, J. Zerubia, and J. C. Olivo-Marin, "Gaussian approximations of fluorescence microscope point-spread function models," Appl. Opt. 46, 1819-1829 (2007).
[CrossRef]

J. H. Kim and R. G. Larson, "Single-molecule analysis of 1D diffusion and transcription elongation of T7 RNA polymerase along individual stretched DNA molecules," Nucleic Acids Res. 35, 3848-3858 (2007).
[CrossRef]

W. E. Moerner, "New directions in single-molecule imaging and analysis," Proc. Natl. Acad. Sci. U.S.A. 104, 12596-12602 (2007).
[CrossRef]

2006 (4)

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, "Ultra-high resolution imaging by fluorescence photoactivation localization microscopy," Biophys. J. 91, 4258-4272 (2006).
[CrossRef]

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," Science 313, 1642-1645 (2006).
[CrossRef]

M. J. Rust, M. Batest, X. Zhuang, "Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM)," Nat. Meth. 3, 793-796 (2006).
[CrossRef]

S. Ram, E. S. Ward, and R. J. Ober, "A stochastic analysis of performance limits for optical microscopes," Multidim. Syst. Sign. Process. 17, 27-57 (2006).
[CrossRef]

2005 (2)

P. H. M. Lommerse, B. E. Snaar-Jagalska, H. P. Spaink, and T. Schmidt, "Single-molecule diffusion measurements of H-Ras at the plasma membrane of live cells reveal microdomain localization upon activation," J. Cell. Sci. 118, 1799-1809 (2005).
[CrossRef]

S. Ram, E. S. Ward, and R. J. Ober, "How accurately can a single molecule be localized in three dimensions using a fluorescence microscope?" Proc. SPIE. 5699, 426-435 (2005).

2004 (5)

K. Murase, T. Fujiwara, Y. Umemura, K. Suzuki, R. Iino, H. Yamashita, M. Saito, H. Murakoshi, K. Ritchie, and A. Kusumi, "Ultrafine membrane compartments for molecular diffusion as revealed by single molecule techniques," Biophys. J. 86, 4075-4093 (2004).
[CrossRef]

P. H. M. Lommerse, G. A. Blab, L. Cognet, G. S. Harms, B. E. Snaar-Jagalska, H. P. Spaink, and T. Schmidt, "Single-molecule imaging of the H-Ras membrane-anchor reveals domains in the cytoplasmic leaflet of the cell membrane," Biophys. J. 86, 609-616 (2004).
[CrossRef]

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

X. Qu, D. Wu, L. Mets, and N. F. Scherer, "Nanometer-localized multiple single-molecule fluorescence microscopy," Proc. Natl. Acad. Sci. U.S.A. 101, 11298-11303 (2004).
[CrossRef]

H. Park, G. T. Hanson, S. R. Duff, and P. R. Selvin, "Nanometer localization of single ReAsH molecules," J. Microsc. 216, 199-205 (2004).
[CrossRef]

2003 (2)

M. Dahan, S. Levi, C. Luccardini, P. Rostaing, B. Riveau, and A. Triller, "Diffusion dynamics of glycine receptors revealed by single-quantum dot tracking," Science 302, 442-445 (2003).
[CrossRef]

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, "Myosin V walks hand-overhand: single fluorophore imaging with 1.5-nm localization," Science. 300, 2061-2065 (2003).
[CrossRef]

2002 (1)

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

2001 (2)

J. Markham and J. A. Conchello, "Fast maximum-likelihood image-restoration algorithms for three-dimensional fluorescence microscopy," J. Opt. Soc. Am. 18, 1062-1071 (2001).
[CrossRef]

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

1997 (1)

P. J. Verveer and T. M. Jovin, "Efficient superresolution restoration algorithms using maximum a posteriori estimations with application to fluorescence microscopy," J. Opt. Soc. Am. 14, 1696-1706 (1997).
[CrossRef]

Bates, M.

B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy," Science 319, 810-813 (2008).
[CrossRef]

Batest, M.

M. J. Rust, M. Batest, X. Zhuang, "Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM)," Nat. Meth. 3, 793-796 (2006).
[CrossRef]

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," Science 313, 1642-1645 (2006).
[CrossRef]

Biteen, J. S.

J. S. Biteen, M. A. Thompson, N. K. Tselentis, G. R. Bowman, L. Shapiro, and W. E. Moerner, "Super-resolution imaging in live Caulobacter crescentus cells using photoswitchable EYFP," Nat. Methods. 5, 947-949 (2008).
[CrossRef]

Blab, G. A.

P. H. M. Lommerse, G. A. Blab, L. Cognet, G. S. Harms, B. E. Snaar-Jagalska, H. P. Spaink, and T. Schmidt, "Single-molecule imaging of the H-Ras membrane-anchor reveals domains in the cytoplasmic leaflet of the cell membrane," Biophys. J. 86, 609-616 (2004).
[CrossRef]

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," Science 313, 1642-1645 (2006).
[CrossRef]

Bowman, G. R.

J. S. Biteen, M. A. Thompson, N. K. Tselentis, G. R. Bowman, L. Shapiro, and W. E. Moerner, "Super-resolution imaging in live Caulobacter crescentus cells using photoswitchable EYFP," Nat. Methods. 5, 947-949 (2008).
[CrossRef]

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, 2378-2388 (2001).
[CrossRef]

Choi, P. J.

X. S. Xie, P. J. Choi, G. W. Li, N. K. Lee, and G. Lia, "Single-molecule approach to molecular biology in living bacterial cells," Annu. Rev. Biophys. 37, 417-444 (2008).
[CrossRef]

Cognet, L.

P. H. M. Lommerse, G. A. Blab, L. Cognet, G. S. Harms, B. E. Snaar-Jagalska, H. P. Spaink, and T. Schmidt, "Single-molecule imaging of the H-Ras membrane-anchor reveals domains in the cytoplasmic leaflet of the cell membrane," Biophys. J. 86, 609-616 (2004).
[CrossRef]

Conchello, J. A.

J. Markham and J. A. Conchello, "Fast maximum-likelihood image-restoration algorithms for three-dimensional fluorescence microscopy," J. Opt. Soc. Am. 18, 1062-1071 (2001).
[CrossRef]

Dahan, M.

M. Dahan, S. Levi, C. Luccardini, P. Rostaing, B. Riveau, and A. Triller, "Diffusion dynamics of glycine receptors revealed by single-quantum dot tracking," Science 302, 442-445 (2003).
[CrossRef]

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," Science 313, 1642-1645 (2006).
[CrossRef]

Duff, S. R.

H. Park, G. T. Hanson, S. R. Duff, and P. R. Selvin, "Nanometer localization of single ReAsH molecules," J. Microsc. 216, 199-205 (2004).
[CrossRef]

Forkey, J. N.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, "Myosin V walks hand-overhand: single fluorophore imaging with 1.5-nm localization," Science. 300, 2061-2065 (2003).
[CrossRef]

Fujiwara, T.

K. Murase, T. Fujiwara, Y. Umemura, K. Suzuki, R. Iino, H. Yamashita, M. Saito, H. Murakoshi, K. Ritchie, and A. Kusumi, "Ultrafine membrane compartments for molecular diffusion as revealed by single molecule techniques," Biophys. J. 86, 4075-4093 (2004).
[CrossRef]

Girirajan, T. P. K.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, "Ultra-high resolution imaging by fluorescence photoactivation localization microscopy," Biophys. J. 91, 4258-4272 (2006).
[CrossRef]

Goldman, Y. E.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, "Myosin V walks hand-overhand: single fluorophore imaging with 1.5-nm localization," Science. 300, 2061-2065 (2003).
[CrossRef]

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, 2378-2388 (2001).
[CrossRef]

Ha, T.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, "Myosin V walks hand-overhand: single fluorophore imaging with 1.5-nm localization," Science. 300, 2061-2065 (2003).
[CrossRef]

Hanson, G. T.

H. Park, G. T. Hanson, S. R. Duff, and P. R. Selvin, "Nanometer localization of single ReAsH molecules," J. Microsc. 216, 199-205 (2004).
[CrossRef]

Harms, G. S.

P. H. M. Lommerse, G. A. Blab, L. Cognet, G. S. Harms, B. E. Snaar-Jagalska, H. P. Spaink, and T. Schmidt, "Single-molecule imaging of the H-Ras membrane-anchor reveals domains in the cytoplasmic leaflet of the cell membrane," Biophys. J. 86, 609-616 (2004).
[CrossRef]

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," Science 313, 1642-1645 (2006).
[CrossRef]

Hess, S. T.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, "Ultra-high resolution imaging by fluorescence photoactivation localization microscopy," Biophys. J. 91, 4258-4272 (2006).
[CrossRef]

Huang, B.

B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy," Science 319, 810-813 (2008).
[CrossRef]

Iino, R.

K. Murase, T. Fujiwara, Y. Umemura, K. Suzuki, R. Iino, H. Yamashita, M. Saito, H. Murakoshi, K. Ritchie, and A. Kusumi, "Ultrafine membrane compartments for molecular diffusion as revealed by single molecule techniques," Biophys. J. 86, 4075-4093 (2004).
[CrossRef]

Jovin, T. M.

P. J. Verveer and T. M. Jovin, "Efficient superresolution restoration algorithms using maximum a posteriori estimations with application to fluorescence microscopy," J. Opt. Soc. Am. 14, 1696-1706 (1997).
[CrossRef]

Kim, J. H.

J. H. Kim and R. G. Larson, "Single-molecule analysis of 1D diffusion and transcription elongation of T7 RNA polymerase along individual stretched DNA molecules," Nucleic Acids Res. 35, 3848-3858 (2007).
[CrossRef]

Kusumi, A.

K. Murase, T. Fujiwara, Y. Umemura, K. Suzuki, R. Iino, H. Yamashita, M. Saito, H. Murakoshi, K. Ritchie, and A. Kusumi, "Ultrafine membrane compartments for molecular diffusion as revealed by single molecule techniques," Biophys. J. 86, 4075-4093 (2004).
[CrossRef]

Larson, D. R.

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

Larson, R. G.

J. H. Kim and R. G. Larson, "Single-molecule analysis of 1D diffusion and transcription elongation of T7 RNA polymerase along individual stretched DNA molecules," Nucleic Acids Res. 35, 3848-3858 (2007).
[CrossRef]

Lee, N. K.

X. S. Xie, P. J. Choi, G. W. Li, N. K. Lee, and G. Lia, "Single-molecule approach to molecular biology in living bacterial cells," Annu. Rev. Biophys. 37, 417-444 (2008).
[CrossRef]

Levi, S.

M. Dahan, S. Levi, C. Luccardini, P. Rostaing, B. Riveau, and A. Triller, "Diffusion dynamics of glycine receptors revealed by single-quantum dot tracking," Science 302, 442-445 (2003).
[CrossRef]

Li, G. W.

X. S. Xie, P. J. Choi, G. W. Li, N. K. Lee, and G. Lia, "Single-molecule approach to molecular biology in living bacterial cells," Annu. Rev. Biophys. 37, 417-444 (2008).
[CrossRef]

Lia, G.

X. S. Xie, P. J. Choi, G. W. Li, N. K. Lee, and G. Lia, "Single-molecule approach to molecular biology in living bacterial cells," Annu. Rev. Biophys. 37, 417-444 (2008).
[CrossRef]

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," Science 313, 1642-1645 (2006).
[CrossRef]

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," Science 313, 1642-1645 (2006).
[CrossRef]

Lommerse, P. H. M.

P. H. M. Lommerse, B. E. Snaar-Jagalska, H. P. Spaink, and T. Schmidt, "Single-molecule diffusion measurements of H-Ras at the plasma membrane of live cells reveal microdomain localization upon activation," J. Cell. Sci. 118, 1799-1809 (2005).
[CrossRef]

P. H. M. Lommerse, G. A. Blab, L. Cognet, G. S. Harms, B. E. Snaar-Jagalska, H. P. Spaink, and T. Schmidt, "Single-molecule imaging of the H-Ras membrane-anchor reveals domains in the cytoplasmic leaflet of the cell membrane," Biophys. J. 86, 609-616 (2004).
[CrossRef]

Luccardini, C.

M. Dahan, S. Levi, C. Luccardini, P. Rostaing, B. Riveau, and A. Triller, "Diffusion dynamics of glycine receptors revealed by single-quantum dot tracking," Science 302, 442-445 (2003).
[CrossRef]

Markham, J.

J. Markham and J. A. Conchello, "Fast maximum-likelihood image-restoration algorithms for three-dimensional fluorescence microscopy," J. Opt. Soc. Am. 18, 1062-1071 (2001).
[CrossRef]

Mason, M. D.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, "Ultra-high resolution imaging by fluorescence photoactivation localization microscopy," Biophys. J. 91, 4258-4272 (2006).
[CrossRef]

McKinney, S. A.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, "Myosin V walks hand-overhand: single fluorophore imaging with 1.5-nm localization," Science. 300, 2061-2065 (2003).
[CrossRef]

Mets, L.

X. Qu, D. Wu, L. Mets, and N. F. Scherer, "Nanometer-localized multiple single-molecule fluorescence microscopy," Proc. Natl. Acad. Sci. U.S.A. 101, 11298-11303 (2004).
[CrossRef]

Moerner, W. E.

J. S. Biteen, M. A. Thompson, N. K. Tselentis, G. R. Bowman, L. Shapiro, and W. E. Moerner, "Super-resolution imaging in live Caulobacter crescentus cells using photoswitchable EYFP," Nat. Methods. 5, 947-949 (2008).
[CrossRef]

W. E. Moerner, "New directions in single-molecule imaging and analysis," Proc. Natl. Acad. Sci. U.S.A. 104, 12596-12602 (2007).
[CrossRef]

Murakoshi, H.

K. Murase, T. Fujiwara, Y. Umemura, K. Suzuki, R. Iino, H. Yamashita, M. Saito, H. Murakoshi, K. Ritchie, and A. Kusumi, "Ultrafine membrane compartments for molecular diffusion as revealed by single molecule techniques," Biophys. J. 86, 4075-4093 (2004).
[CrossRef]

Murase, K.

K. Murase, T. Fujiwara, Y. Umemura, K. Suzuki, R. Iino, H. Yamashita, M. Saito, H. Murakoshi, K. Ritchie, and A. Kusumi, "Ultrafine membrane compartments for molecular diffusion as revealed by single molecule techniques," Biophys. J. 86, 4075-4093 (2004).
[CrossRef]

Ober, R. J.

S. Ram, E. S. Ward, and R. J. Ober, "A stochastic analysis of performance limits for optical microscopes," Multidim. Syst. Sign. Process. 17, 27-57 (2006).
[CrossRef]

S. Ram, E. S. Ward, and R. J. Ober, "How accurately can a single molecule be localized in three dimensions using a fluorescence microscope?" Proc. SPIE. 5699, 426-435 (2005).

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

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," Science 313, 1642-1645 (2006).
[CrossRef]

Olivo-Marin, J. C.

Park, H.

H. Park, G. T. Hanson, S. R. Duff, and P. R. Selvin, "Nanometer localization of single ReAsH molecules," J. Microsc. 216, 199-205 (2004).
[CrossRef]

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," Science 313, 1642-1645 (2006).
[CrossRef]

Qu, X.

X. Qu, D. Wu, L. Mets, and N. F. Scherer, "Nanometer-localized multiple single-molecule fluorescence microscopy," Proc. Natl. Acad. Sci. U.S.A. 101, 11298-11303 (2004).
[CrossRef]

Ram, S.

S. Ram, E. S. Ward, and R. J. Ober, "A stochastic analysis of performance limits for optical microscopes," Multidim. Syst. Sign. Process. 17, 27-57 (2006).
[CrossRef]

S. Ram, E. S. Ward, and R. J. Ober, "How accurately can a single molecule be localized in three dimensions using a fluorescence microscope?" Proc. SPIE. 5699, 426-435 (2005).

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

Ritchie, K.

K. Murase, T. Fujiwara, Y. Umemura, K. Suzuki, R. Iino, H. Yamashita, M. Saito, H. Murakoshi, K. Ritchie, and A. Kusumi, "Ultrafine membrane compartments for molecular diffusion as revealed by single molecule techniques," Biophys. J. 86, 4075-4093 (2004).
[CrossRef]

Riveau, B.

M. Dahan, S. Levi, C. Luccardini, P. Rostaing, B. Riveau, and A. Triller, "Diffusion dynamics of glycine receptors revealed by single-quantum dot tracking," Science 302, 442-445 (2003).
[CrossRef]

Rostaing, P.

M. Dahan, S. Levi, C. Luccardini, P. Rostaing, B. Riveau, and A. Triller, "Diffusion dynamics of glycine receptors revealed by single-quantum dot tracking," Science 302, 442-445 (2003).
[CrossRef]

Rust, M. J.

M. J. Rust, M. Batest, X. Zhuang, "Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM)," Nat. Meth. 3, 793-796 (2006).
[CrossRef]

Saito, M.

K. Murase, T. Fujiwara, Y. Umemura, K. Suzuki, R. Iino, H. Yamashita, M. Saito, H. Murakoshi, K. Ritchie, and A. Kusumi, "Ultrafine membrane compartments for molecular diffusion as revealed by single molecule techniques," Biophys. J. 86, 4075-4093 (2004).
[CrossRef]

Scherer, N. F.

X. Qu, D. Wu, L. Mets, and N. F. Scherer, "Nanometer-localized multiple single-molecule fluorescence microscopy," Proc. Natl. Acad. Sci. U.S.A. 101, 11298-11303 (2004).
[CrossRef]

Schmidt, T.

P. H. M. Lommerse, B. E. Snaar-Jagalska, H. P. Spaink, and T. Schmidt, "Single-molecule diffusion measurements of H-Ras at the plasma membrane of live cells reveal microdomain localization upon activation," J. Cell. Sci. 118, 1799-1809 (2005).
[CrossRef]

P. H. M. Lommerse, G. A. Blab, L. Cognet, G. S. Harms, B. E. Snaar-Jagalska, H. P. Spaink, and T. Schmidt, "Single-molecule imaging of the H-Ras membrane-anchor reveals domains in the cytoplasmic leaflet of the cell membrane," Biophys. J. 86, 609-616 (2004).
[CrossRef]

Selvin, P. R.

H. Park, G. T. Hanson, S. R. Duff, and P. R. Selvin, "Nanometer localization of single ReAsH molecules," J. Microsc. 216, 199-205 (2004).
[CrossRef]

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, "Myosin V walks hand-overhand: single fluorophore imaging with 1.5-nm localization," Science. 300, 2061-2065 (2003).
[CrossRef]

Shapiro, L.

J. S. Biteen, M. A. Thompson, N. K. Tselentis, G. R. Bowman, L. Shapiro, and W. E. Moerner, "Super-resolution imaging in live Caulobacter crescentus cells using photoswitchable EYFP," Nat. Methods. 5, 947-949 (2008).
[CrossRef]

Snaar-Jagalska, B. E.

P. H. M. Lommerse, B. E. Snaar-Jagalska, H. P. Spaink, and T. Schmidt, "Single-molecule diffusion measurements of H-Ras at the plasma membrane of live cells reveal microdomain localization upon activation," J. Cell. Sci. 118, 1799-1809 (2005).
[CrossRef]

P. H. M. Lommerse, G. A. Blab, L. Cognet, G. S. Harms, B. E. Snaar-Jagalska, H. P. Spaink, and T. Schmidt, "Single-molecule imaging of the H-Ras membrane-anchor reveals domains in the cytoplasmic leaflet of the cell membrane," Biophys. J. 86, 609-616 (2004).
[CrossRef]

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," Science 313, 1642-1645 (2006).
[CrossRef]

Spaink, H. P.

P. H. M. Lommerse, B. E. Snaar-Jagalska, H. P. Spaink, and T. Schmidt, "Single-molecule diffusion measurements of H-Ras at the plasma membrane of live cells reveal microdomain localization upon activation," J. Cell. Sci. 118, 1799-1809 (2005).
[CrossRef]

P. H. M. Lommerse, G. A. Blab, L. Cognet, G. S. Harms, B. E. Snaar-Jagalska, H. P. Spaink, and T. Schmidt, "Single-molecule imaging of the H-Ras membrane-anchor reveals domains in the cytoplasmic leaflet of the cell membrane," Biophys. J. 86, 609-616 (2004).
[CrossRef]

Suzuki, K.

K. Murase, T. Fujiwara, Y. Umemura, K. Suzuki, R. Iino, H. Yamashita, M. Saito, H. Murakoshi, K. Ritchie, and A. Kusumi, "Ultrafine membrane compartments for molecular diffusion as revealed by single molecule techniques," Biophys. J. 86, 4075-4093 (2004).
[CrossRef]

Thompson, M. A.

J. S. Biteen, M. A. Thompson, N. K. Tselentis, G. R. Bowman, L. Shapiro, and W. E. Moerner, "Super-resolution imaging in live Caulobacter crescentus cells using photoswitchable EYFP," Nat. Methods. 5, 947-949 (2008).
[CrossRef]

Thompson, R. E.

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

Triller, A.

M. Dahan, S. Levi, C. Luccardini, P. Rostaing, B. Riveau, and A. Triller, "Diffusion dynamics of glycine receptors revealed by single-quantum dot tracking," Science 302, 442-445 (2003).
[CrossRef]

Tselentis, N. K.

J. S. Biteen, M. A. Thompson, N. K. Tselentis, G. R. Bowman, L. Shapiro, and W. E. Moerner, "Super-resolution imaging in live Caulobacter crescentus cells using photoswitchable EYFP," Nat. Methods. 5, 947-949 (2008).
[CrossRef]

Umemura, Y.

K. Murase, T. Fujiwara, Y. Umemura, K. Suzuki, R. Iino, H. Yamashita, M. Saito, H. Murakoshi, K. Ritchie, and A. Kusumi, "Ultrafine membrane compartments for molecular diffusion as revealed by single molecule techniques," Biophys. J. 86, 4075-4093 (2004).
[CrossRef]

Verveer, P. J.

P. J. Verveer and T. M. Jovin, "Efficient superresolution restoration algorithms using maximum a posteriori estimations with application to fluorescence microscopy," J. Opt. Soc. Am. 14, 1696-1706 (1997).
[CrossRef]

Walker, W. F.

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

Wang, W.

B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy," Science 319, 810-813 (2008).
[CrossRef]

Ward, E. S.

S. Ram, E. S. Ward, and R. J. Ober, "A stochastic analysis of performance limits for optical microscopes," Multidim. Syst. Sign. Process. 17, 27-57 (2006).
[CrossRef]

S. Ram, E. S. Ward, and R. J. Ober, "How accurately can a single molecule be localized in three dimensions using a fluorescence microscope?" Proc. SPIE. 5699, 426-435 (2005).

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

Webb, W. W.

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

Wu, D.

X. Qu, D. Wu, L. Mets, and N. F. Scherer, "Nanometer-localized multiple single-molecule fluorescence microscopy," Proc. Natl. Acad. Sci. U.S.A. 101, 11298-11303 (2004).
[CrossRef]

Xie, X. S.

X. S. Xie, P. J. Choi, G. W. Li, N. K. Lee, and G. Lia, "Single-molecule approach to molecular biology in living bacterial cells," Annu. Rev. Biophys. 37, 417-444 (2008).
[CrossRef]

Yamashita, H.

K. Murase, T. Fujiwara, Y. Umemura, K. Suzuki, R. Iino, H. Yamashita, M. Saito, H. Murakoshi, K. Ritchie, and A. Kusumi, "Ultrafine membrane compartments for molecular diffusion as revealed by single molecule techniques," Biophys. J. 86, 4075-4093 (2004).
[CrossRef]

Yildiz, A.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, "Myosin V walks hand-overhand: single fluorophore imaging with 1.5-nm localization," Science. 300, 2061-2065 (2003).
[CrossRef]

Zerubia, J.

Zhang, B.

Zhuang, X.

B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy," Science 319, 810-813 (2008).
[CrossRef]

M. J. Rust, M. Batest, X. Zhuang, "Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM)," Nat. Meth. 3, 793-796 (2006).
[CrossRef]

Annu. Rev. Biophys. (1)

X. S. Xie, P. J. Choi, G. W. Li, N. K. Lee, and G. Lia, "Single-molecule approach to molecular biology in living bacterial cells," Annu. Rev. Biophys. 37, 417-444 (2008).
[CrossRef]

Appl. Opt. (1)

Biophys. J. (6)

P. H. M. Lommerse, G. A. Blab, L. Cognet, G. S. Harms, B. E. Snaar-Jagalska, H. P. Spaink, and T. Schmidt, "Single-molecule imaging of the H-Ras membrane-anchor reveals domains in the cytoplasmic leaflet of the cell membrane," Biophys. J. 86, 609-616 (2004).
[CrossRef]

K. Murase, T. Fujiwara, Y. Umemura, K. Suzuki, R. Iino, H. Yamashita, M. Saito, H. Murakoshi, K. Ritchie, and A. Kusumi, "Ultrafine membrane compartments for molecular diffusion as revealed by single molecule techniques," Biophys. J. 86, 4075-4093 (2004).
[CrossRef]

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, "Ultra-high resolution imaging by fluorescence photoactivation localization microscopy," Biophys. J. 91, 4258-4272 (2006).
[CrossRef]

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

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

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

J. Cell. Sci. (1)

P. H. M. Lommerse, B. E. Snaar-Jagalska, H. P. Spaink, and T. Schmidt, "Single-molecule diffusion measurements of H-Ras at the plasma membrane of live cells reveal microdomain localization upon activation," J. Cell. Sci. 118, 1799-1809 (2005).
[CrossRef]

J. Microsc. (1)

H. Park, G. T. Hanson, S. R. Duff, and P. R. Selvin, "Nanometer localization of single ReAsH molecules," J. Microsc. 216, 199-205 (2004).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Markham and J. A. Conchello, "Fast maximum-likelihood image-restoration algorithms for three-dimensional fluorescence microscopy," J. Opt. Soc. Am. 18, 1062-1071 (2001).
[CrossRef]

P. J. Verveer and T. M. Jovin, "Efficient superresolution restoration algorithms using maximum a posteriori estimations with application to fluorescence microscopy," J. Opt. Soc. Am. 14, 1696-1706 (1997).
[CrossRef]

Multidim. Syst. Sign. Process. (1)

S. Ram, E. S. Ward, and R. J. Ober, "A stochastic analysis of performance limits for optical microscopes," Multidim. Syst. Sign. Process. 17, 27-57 (2006).
[CrossRef]

Nat. Meth. (1)

M. J. Rust, M. Batest, X. Zhuang, "Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM)," Nat. Meth. 3, 793-796 (2006).
[CrossRef]

Nat. Methods. (1)

J. S. Biteen, M. A. Thompson, N. K. Tselentis, G. R. Bowman, L. Shapiro, and W. E. Moerner, "Super-resolution imaging in live Caulobacter crescentus cells using photoswitchable EYFP," Nat. Methods. 5, 947-949 (2008).
[CrossRef]

Nucleic Acids Res. (1)

J. H. Kim and R. G. Larson, "Single-molecule analysis of 1D diffusion and transcription elongation of T7 RNA polymerase along individual stretched DNA molecules," Nucleic Acids Res. 35, 3848-3858 (2007).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (2)

X. Qu, D. Wu, L. Mets, and N. F. Scherer, "Nanometer-localized multiple single-molecule fluorescence microscopy," Proc. Natl. Acad. Sci. U.S.A. 101, 11298-11303 (2004).
[CrossRef]

W. E. Moerner, "New directions in single-molecule imaging and analysis," Proc. Natl. Acad. Sci. U.S.A. 104, 12596-12602 (2007).
[CrossRef]

Proc. SPIE. (1)

S. Ram, E. S. Ward, and R. J. Ober, "How accurately can a single molecule be localized in three dimensions using a fluorescence microscope?" Proc. SPIE. 5699, 426-435 (2005).

Science (3)

M. Dahan, S. Levi, C. Luccardini, P. Rostaing, B. Riveau, and A. Triller, "Diffusion dynamics of glycine receptors revealed by single-quantum dot tracking," Science 302, 442-445 (2003).
[CrossRef]

B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy," Science 319, 810-813 (2008).
[CrossRef]

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," Science 313, 1642-1645 (2006).
[CrossRef]

Science. (1)

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, "Myosin V walks hand-overhand: single fluorophore imaging with 1.5-nm localization," Science. 300, 2061-2065 (2003).
[CrossRef]

Other (6)

S. M. Kay, Fundamentals of statistical signal processing (Prentice Hall, 1993).

"EstimationTool," http://www4.utsouthwestern.edu/wardlab/EstimationTool.

"FandPLimitTool," http://www4.utsouthwestern.edu/wardlab/FandPLimitTool.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, UK, 1999).

P. Torok and F.-J. Kao, Optical Imaging and Microscopy (Springer, 2003).

S. Zacks, Theory of Statistical Inference (John Wiley and Sons, 1971).

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