## Quantitative study of single molecule location estimation techniques

Optics Express, Vol. 17, Issue 26, pp. 23352-23373 (2009)

http://dx.doi.org/10.1364/OE.17.023352

Acrobat PDF (284 KB)

### 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 and misspecifications. 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

## 1. Introduction

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] [PubMed]

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

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] [PubMed]

6. 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] [PubMed]

7. M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Meth. **3**, 793–796 (2006). [CrossRef]

10. 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] [PubMed]

11. 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] [PubMed]

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

14. 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]

15. 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]

16. 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]

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

17. 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] [PubMed]

17. 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] [PubMed]

9. 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] [PubMed]

10. 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] [PubMed]

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

21. 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] [PubMed]

7. M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Meth. **3**, 793–796 (2006). [CrossRef]

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

14. 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]

22. 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). [CrossRef] [PubMed]

**86**, 1185–1200 (2004). [CrossRef] [PubMed]

**86**, 1185–1200 (2004). [CrossRef] [PubMed]

14. 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]

17. 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] [PubMed]

11. 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] [PubMed]

23. “EstimationTool,” http://www4.utsouthwestern.edu/wardlab/EstimationTool.

24. “FandPLimitTool,” http://www4.utsouthwestern.edu/wardlab/FandPLimitTool.

## 2. Materials & Methods

### 2.1. Simulating single molecule images

*13*]. The equations to model the signal at any camera pixel and the equations describing the random variables denoting the various components of the signal are given in the

*Appendix A*. The mean of the signal from the point source can be described by either an Airy or a Gaussian photon distribution profile. The equations describing both photon distributions profiles are given in the

*Appendix A*. The details of how the single molecule images are generated by realizations of the Poisson and Gaussian random variables is also described in the

*Appendix A*. All calculations involved in generating the single molecule images were performed in MATLAB (The MathWorks, Natick, MA).

### 2.2. Fitting single molecule images

*Appendix B*. All calculations involved in estimating the location of a single molecule were performed in MATLAB. For all analyses, only those estimates were used for which the MATLAB optimization functions successfully completed and the estimated location coordinates were within the image (see [23

23. “EstimationTool,” http://www4.utsouthwestern.edu/wardlab/EstimationTool.

*Software*below).

### 2.3. Limit of the localization accuracy

**86**, 1185–1200 (2004). [CrossRef] [PubMed]

**17**, 27–57 (2006). [CrossRef]

**86**, 1185–1200 (2004). [CrossRef] [PubMed]

**86**, 1185–1200 (2004). [CrossRef] [PubMed]

**17**, 27–57 (2006). [CrossRef]

24. “FandPLimitTool,” http://www4.utsouthwestern.edu/wardlab/FandPLimitTool.

*Software*below).

### 2.4. Software

## 3. Results

### 3.1. Maximum likelihood estimates have the smallest standard deviation in the ideal case

*θ*:=

*x*

_{0},

*y*

_{0}) were estimated from each image while the values for the width and photon detection rate parameters were set to the values used to generate the single molecule images.

### 3.2. The standard deviations of the maximum likelihood estimates attain the limit of the localization accuracy

*Materials and Methods*), based on the theory of the Fisher information matrix and the Cramer-Rao Lower Bound, provides a lower bound on the variance of estimates obtained using any unbiased estimator [13

**86**, 1185–1200 (2004). [CrossRef] [PubMed]

### 3.3. The effect of noise on the standard deviations of estimates

*e*

^{-}and zero mean to the data used in the calculations above and again estimated the location of the single molecule using both the nonlinear least squares and the maximum likelihood (using the Gaussian noise model) estimators. Second, for a fixed background photon detection rate of 2 photons/pixel/second (total background photon count of 338 photons), we generated images of a single molecule with varying levels of Gaussian noise and used both algorithms to again estimate the location of the single molecule. Both algorithms are again able to recover the true location of the single molecule on average in both scenarios [Fig. 3(a) and 3(b)]. The results from the first approach [Fig. 3(c)] with a constant Gaussian noise of standard deviation 4

*e*

^{-}show that for low Gaussian noise levels the performance of the two estimators is almost identical to the case when there is no Gaussian noise. The results from the second approach [Fig. 3(d)] show that increasing the Gaussian noise component also causes the standard deviations of the two algorithms to converge to the PLAM. Thus, neither algorithm provides a clear accuracy advantage when analyzing data containing a large noise component. However, at low noise and signal levels, there is an appreciable difference in the accuracy of estimates from the two algorithms.

### 3.4. The maximum likelihood estimator is less sensitive to the relative location of the point source within the pixel

*nm*in the object space starting from the left edge of the center pixel and moving toward the right edge of the center pixel of the image array. The single molecule images were generated using both pixelated Airy and Gaussian profiles. The location of the single molecule was estimated from each image using both the nonlinear least squares and maximum likelihood estimators, again assuming the absence of model misspecifications. Both algorithms are again able to recover the true location of the single molecule on average. However, examining the standard deviations of the estimates from both algorithms, we see that while the maximum likelihood algorithm attains the PLAM irrespective of the position of the point source, the accuracy of the nonlinear least squares estimator deteriorates the further away from the center of the pixel the point source is located. Thus the maximum likelihood algorithm again achieves the best possible accuracy in this scenario.

### 3.5. The maximum likelihood estimator is less sensitive to misspecifications of the width parameter

22. 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). [CrossRef] [PubMed]

*λ*=520

*nm*, imaged through an objective of numerical aperture

*n*=1.3 and magnification

_{a}*M*=100, acquired on a camera with pixel size 13

*µm*×13

*µm*. We then fit these image profiles using an Airy PSF with the same experimental and imaging conditions while floating the location coordinates and the width parameter. The theoretical value for the width parameter, given by 2

*πn*/λ, is 15.7

_{a}*µm*

^{-1}. However, at just 200

*nm*defocus, the value for the width parameter of the Airy profile was estimated at 6.53

*µm*

^{-1}, approximately half of the true value.

*µm*

^{-1}. However, if the operational numerical aperture was 1.2, the true value of the width parameter would be 14.5

*µm*

^{-1}. Thus, variations in the experimental properties of optical components along with the possibility of the sample being out of focus can lead to large deviations in the width parameter.

### 3.6. Model mismatch has different effects on the performance of the two algorithms

*α*, using criteria based on the nonlinear least squares and the maximum likelihood function [see Appendix B, Eqs. (8) and (6)]. Both criteria produced similar results. From them, we determined that for a Gaussian profile that best approximates an Airy profile with width parameter

*α*, the associated Gaussian width parameter

*σ*can be calculated by the approximation

*σ*≈1.323/

*α*which is in agreement with the results published previously [13

**86**, 1185–1200 (2004). [CrossRef] [PubMed]

27. 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] [PubMed]

*σ*=1.323/

*α*to estimate the single molecule location coordinates. In this scenario, the values for the other parameters, e.g. photon detection rate, were fixed to the values used to generate the single molecule images. In the second scenario, we simulated multiple sets of one thousand images using Airy pixelated profiles for a fixed value of the expected number of photons at the detector plane, and again fit them with Gaussian pixelated profiles to estimate the single molecule location coordinates. However, for each set of images, we deliberately misspecified the width parameter of the Gaussian profile being fit by a certain amount. The values for the photon detection rate and background parameters were again fixed to the values used to generate the single molecule images. Images were fit using both the nonlinear least squares and maximum likelihood estimators.

### 3.7. Two analytical approaches predict different localization accuracies

**86**, 1185–1200 (2004). [CrossRef] [PubMed]

**17**, 27–57 (2006). [CrossRef]

**82**, 2775–2783 (2002). [CrossRef] [PubMed]

*x*denotes the standard deviation of the single molecule location estimates, s denotes the standard deviation of the Gaussian image profile that is assumed to describe the image of the single molecule, a the length of a pixel of the detector in the object space (pixels are assumed to be square),

*N*the total photon count from the single molecule, and

*b*the standard deviation of the background [17

**82**, 2775–2783 (2002). [CrossRef] [PubMed]

*σ*/√

*N*, where

*N*is the expected number of collected photons and

*σ*denotes the parameter that describes the ‘standard deviation’ of the Gaussian image profile [14

**17**, 27–57 (2006). [CrossRef]

*σ*parameter should be used in the analytical expression above [17

**82**, 2775–2783 (2002). [CrossRef] [PubMed]

28. 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] [PubMed]

*α*√

*N*), with

*α*=2

*πn*/λ and

_{a}*N*the expected number of photons at the detector plane as described above. As discussed earlier, for a Gaussian profile that approximates an Airy profile, the standard deviation parameter

*σ*can be approximated by

*σ*≈1.323/

*α*. Substituting in Eq. 1 (while disregarding pixelation and noise sources), we obtain

*σ*/√

*N*=1.323/(

*α*√

*N*) for the predicted standard deviation of the location estimates. This implies that there is approximately a 30% difference in the accuracy predicted by the two analytical approaches for this particular scenario.

**82**, 2775–2783 (2002). [CrossRef] [PubMed]

## 4. Discussion

11. 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] [PubMed]

**86**, 1185–1200 (2004). [CrossRef] [PubMed]

**17**, 27–57 (2006). [CrossRef]

**86**, 1185–1200 (2004). [CrossRef] [PubMed]

**82**, 2775–2783 (2002). [CrossRef] [PubMed]

15. 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]

16. 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]

**86**, 1185–1200 (2004). [CrossRef] [PubMed]

**82**, 2775–2783 (2002). [CrossRef] [PubMed]

**82**, 2775–2783 (2002). [CrossRef] [PubMed]

23. “EstimationTool,” http://www4.utsouthwestern.edu/wardlab/EstimationTool.

24. “FandPLimitTool,” http://www4.utsouthwestern.edu/wardlab/FandPLimitTool.

23. “EstimationTool,” http://www4.utsouthwestern.edu/wardlab/EstimationTool.

24. “FandPLimitTool,” http://www4.utsouthwestern.edu/wardlab/FandPLimitTool.

## Appendix A: Simulating the single molecule images

*C*

_{1},…,

*C*}. The signal acquired at the k

_{K}*pixel is modeled as*

^{th}*θ*denotes the vector of parameters to be estimated,

*S*is a Poisson random variable denoting the signal from the single molecule detected at the

_{θ,k}*k*pixel, and

^{th}*B*is a Poisson random variable denoting the signal from the background component with mean

_{k}*b*Δ

*t*where

*b*is the rate at which photons from the background are being detected and Δ

*t*is the time interval over which the image is acquired, and

*W*is a Gaussian random variable denoting the camera noise with mean

_{k}*η*and standard deviation denoted by

_{w,k}*σ*.

_{w,k}*S*is given by

_{θ,k}*A*denotes the rate at which photons from the single molecule are being detected, Δ

*t*denotes the time interval over which the image is acquired,

*C*denotes the area of the

_{k}*k*pixel, and

^{th}*f*denotes the photon distribution profile, a probability distribution function which gives the probability of a photon being detected at a specified location [13

_{θ}**86**, 1185–1200 (2004). [CrossRef] [PubMed]

*f*is defined as

_{θ}*θ*:=(

*x*

_{0},

*y*

_{0}) is the location of the single molecule in the object space, and 1/

*α*denotes the width of the profile with

*α*:=2

*πn*/λ, where

_{a}*n*is the numerical aperture of the system, and λ is the wavelength of the light emitted by the single molecule.

_{a}*f*is defined as

_{θ}*σ*denotes the width of the Gaussian profile.

*K*pixels, leading to a set {

*µ*

_{θ,1}+

*b*Δ

*t*,…,

*µθ*,

*+*

_{K}*b*Δ

*t*} of mean pixel intensity values, which is referred to as the pixelated profile. For each image, a Poisson realization of the pixelated profile was generated. To simulate additive Gaussian noise, independent realizations of the Gaussian random variable

*W*in Eq. (2) for a fixed value of

_{k}*σ*are added to each pixel in the Poisson realization of the pixelated profile. In all calculations, a set of images refers to a set of one thousand simulated images. All calculations involved in generating the single molecule images were performed in MATLAB (The MathWorks, Natick, MA). The integration routines used to integrate the photon distribution profile function over a pixel were custom developed in MATLAB. Poisson realizations were generated using the Poisson random number generator provided with MATLAB’s Statistics Toolbox.

_{w,k}## Appendix B: Fitting single molecule images

*z*

_{1},…,

*z*denotes the single molecule image data, and

_{K}*µ*denotes the mean pixel intensity as given by Eq. (3). MATLAB’s lsqnonlin function from the Optimization Toolbox was used to perform the nonlinear least squares minimization.

_{θ,k}*z*

_{1},…,

*z*denotes the single molecule image data,

_{K}*µ*+

_{θ,k}*b*Δ

*t*denotes the mean pixel intensity, and

*σ*and

_{w,k}*η*denote the standard deviation and mean of the Gaussian noise component respectively [14

_{w,k}**17**, 27–57 (2006). [CrossRef]

23. “EstimationTool,” http://www4.utsouthwestern.edu/wardlab/EstimationTool.

## Acknowledgements

## References and links

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. |

2. | W. E. Moerner, “New directions in single-molecule imaging and analysis,” Proc. Natl. Acad. Sci. U.S.A. |

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. |

4. | 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. |

5. | 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. |

6. | 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. |

7. | M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Meth. |

8. | B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science. |

9. | S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. |

10. | 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. |

11. | M. K. Cheezum, W. F. Walker, and W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. |

12. | S. M. Kay, |

13. | R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. |

14. | S. Ram, E. S. Ward, and R. J. Ober, “A stochastic analysis of performance limits for optical microscopes,” Multidim. Syst. Sign. Process. |

15. | J. Markham and J. A. Conchello, “Fast maximum-likelihood image-restoration algorithms for three-dimensional fluorescence microscopy,” J. Opt. Soc. Am. |

16. | 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. |

17. | R. E. Thompson, D. R. Larson, and W.W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. |

18. | A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science. |

19. | X. Qu, D. Wu, L. Mets, and N. F. Scherer, “Nanometer-localized multiple single-molecule fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. |

20. | H. Park, G. T. Hanson, S. R. Duff, and P. R. Selvin, “Nanometer localization of single ReAsH molecules,” J. Microsc. |

21. | 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. |

22. | 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. |

23. | “EstimationTool,” http://www4.utsouthwestern.edu/wardlab/EstimationTool. |

24. | “FandPLimitTool,” http://www4.utsouthwestern.edu/wardlab/FandPLimitTool. |

25. | M. Born and E. Wolf, |

26. | P. Torok and F.-J. Kao, |

27. | B. Zhang, J. Zerubia, and J. C. Olivo-Marin, “Gaussian approximations of fluorescence microscope point-spread function models,” Appl. Opt. |

28. | 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. |

29. | S. Zacks, |

**OCIS Codes**

(100.2960) Image processing : Image analysis

(180.2520) Microscopy : Fluorescence microscopy

**ToC Category:**

Image Processing

**History**

Original Manuscript: June 1, 2009

Revised Manuscript: October 31, 2009

Manuscript Accepted: December 2, 2009

Published: December 7, 2009

**Virtual Issues**

Vol. 5, Iss. 1 *Virtual Journal for Biomedical Optics*

**Citation**

Anish V. Abraham, Sripad Ram, Jerry Chao, E. S. Ward, and Raimund J. Ober, "Quantitative study of single molecule location estimation techniques," Opt. Express **17**, 23352-23373 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-23352

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### References

- 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] [PubMed]
- W. E. Moerner, "New directions in single-molecule imaging and analysis," Proc. Natl. Acad. Sci. U.S.A. 104, 12596-12602 (2007). [CrossRef] [PubMed]
- 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] [PubMed]
- 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]
- 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] [PubMed]
- 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] [PubMed]
- M. J. Rust, M. Batest, X. Zhuang, "Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM)," Nat. Meth. 3, 793-796 (2006). [CrossRef]
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