DOI: 10.1038/s41598-017-00622-w. Analyzing Single Molecule Localization Microscopy Data Using Cubic Splines

Analyzing Single Molecule Localization Microscopy Data Using Cubic Splines

10.1038/s41598-017-00622-w

Crossref journal-article

Springer Science and Business Media LLC

Scientific Reports (297)

Abstract

AbstractThe resolution of super-resolution microscopy based on single molecule localization is in part determined by the accuracy of the localization algorithm. In most published approaches to date this localization is done by fitting an analytical function that approximates the point spread function (PSF) of the microscope. However, particularly for localization in 3D, analytical functions such as a Gaussian, which are computationally inexpensive, may not accurately capture the PSF shape leading to reduced fitting accuracy. On the other hand, analytical functions that can accurately capture the PSF shape, such as those based on pupil functions, can be computationally expensive. Here we investigate the use of cubic splines as an alternative fitting approach. We demonstrate that cubic splines can capture the shape of any PSF with high accuracy and that they can be used for fitting the PSF with only a 2–3x increase in computation time as compared to Gaussian fitting. We provide an open-source software package that measures the PSF of any microscope and uses the measured PSF to perform 3D single molecule localization microscopy analysis with reasonable accuracy and speed.

Bibliography

Babcock, H. P., & Zhuang, X. (2017). Analyzing Single Molecule Localization Microscopy Data Using Cubic Splines. Scientific Reports, 7(1).

Authors 2

Hazen P. Babcock (first)
Xiaowei Zhuang (additional)

References 24 Referenced 93

Huang, B., Wang, W., Bates, M. & Zhuang, X. Three-Dimensional Super-Resolution Imaging by Stochastic Optical Reconstruction Microscopy. Science 319, 810–813 (2008). (10.1126/science.1153529) / Science by B Huang (2008)
Pavani, S. R. P. et al. Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function. Proc Natl Acad Sci USA 106, 2995–2999 (2009). (10.1073/pnas.0900245106) / Proc Natl Acad Sci USA by SRP Pavani (2009)
Shechtman, Y., Steffen, J. S., Backer, A. S. & Moerner, W. E. Optimal Point Spread Function Design for 3D Imaging. Physical Review Letters 113, 1–5 (2014). (10.1103/PhysRevLett.113.133902) / Physical Review Letters by Y Shechtman (2014)
Jia, S., Vaughan, J. C. & Zhuang, X. Isotropic three-dimensional super-resolution imaging with a self-bending point spread function. Nature Photonics 8, 302–306 (2014). (10.1038/nphoton.2014.13) / Nature Photonics by S Jia (2014)
Juette, M. F. et al. Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples. Nature Methods 5, 527–529 (2008). (10.1038/nmeth.1211) / Nature Methods by MF Juette (2008)
York, A. G., Ghitani, A., Vaziri, A., Davidson, M. W. & Shroff, H. Confined activation and subdiffraction localization enables whole-cell PALM with genetically expressed probes. Nature Methods 8, 327–333 (2011). (10.1038/nmeth.1571) / Nature Methods by AG York (2011)
Mlodzianoski, M. J., Juette, M. F., Beane, G. L. & Bewersdorf, J. Experimental characterization of 3D localization techniques for particle-tracking and super-resolution microscopy. Optics Express 17, 8264–8277 (2009). (10.1364/OE.17.008264) / Optics Express by MJ Mlodzianoski (2009)
Liu, S., Kromann, E. B., Krueger, W. D., Bewersdorf, J. & Lidke, K. A. Three dimensional single molecule localization using a phase retrieved pupil function. Optics Express 21, 29462–29487 (2013). (10.1364/OE.21.029462) / Optics Express by S Liu (2013)
Nelder, J. A. & Mead, R. A simplex method for function minimization. The Computer Journal 7, 308–313 (1965). (10.1093/comjnl/7.4.308) / The Computer Journal by JA Nelder (1965)
Hanser, B. M., Gustafsson, M. G. L., Agard, D. A. & Sedat, J. W. Phase retrieval for high-numerical-aperture optical systems. Optics Letters 28, 801–803 (2003). (10.1364/OL.28.000801) / Optics Letters by BM Hanser (2003)
Hanser, B. M., Gustafsson, M. G. L., Agard, D. A. & Sedat, J. W. Phase-retrieved pupil functions in wide-field fluorescence microscopy. Journal of Microscopy 216, 32–48 (2004). (10.1111/j.0022-2720.2004.01393.x) / Journal of Microscopy by BM Hanser (2004)
Stetson, P. B. DAOPHOT: A Computer Program for Crowded-Field Stellar Photometry. Publications of the Astronomical Society of the Pacific 99, 191–222 (1987). (10.1086/131977) / Publications of the Astronomical Society of the Pacific by PB Stetson (1987)
Holden, S. J., Uphoff, S. & Kapanidis, A. N. DAOSTORM: an algorithm for high-density super-resolution microscopy. Nature Methods 8, 279–280 (2011). (10.1038/nmeth0411-279) / Nature Methods by SJ Holden (2011)
Tahmasbi, A., Ward, E. S. & Ober, R. J. Determination of localization accuracy based on experimentally acquired image sets: applications to single molecule microscopy. Optics Express 23, 7630–7652 (2015). (10.1364/OE.23.007630) / Optics Express by A Tahmasbi (2015)
Kirshner, H., Vonesch, C. & Unser, M. Can localization microscopy benefit from approximation theory? 2013 IEEE 10th Internation Symposium on Biomedical Imaging, 588–591 (2013). (10.1109/ISBI.2013.6556543)
Anton, H. & Rorres, C. Elementary linear algebra with applications (Wiley, 1987).
Jones, E., Oliphant, T. & Peterson, P. SciPy: Open source scientific tool for Python, www.scipy.org (2001).
Babcock, H. P., Sigal, Y. M. & Zhuang, X. A high-density 3D localization algorithm for stochastic optical reconstruction microscopy. Optical Nanoscopy 1 (2012). (10.1186/2192-2853-1-6)
Laurence, T. A. & Chromy, B. A. Efficient maximum likelihood estimator fitting of histograms. Nature Methods 7, 338–339 (2010). (10.1038/nmeth0510-338) / Nature Methods by TA Laurence (2010)
Marquardt, D. W. An algorithm for Least-Squares Estimation of Nonlinear Parameters. Journal of the Society for Industrial and Applied Mathematics 11, 431–441 (1963). (10.1137/0111030) / Journal of the Society for Industrial and Applied Mathematics by DW Marquardt (1963)
Carlini, L., Holden, S. J., Douglass, K. M. & Manley, S. Correction of a Depth-Dependent Lateral Distortion in 3D Super-Resolution Imaging. Plos One e0142949, 1–15 (2015). / Plos One by L Carlini (2015)
Proppert, S. et al. Cubic B-spline calibration for 3D super-resolution measurements using astigmatic imaging. Optics Express 22, 10304–10316 (2014). (10.1364/OE.22.010304) / Optics Express by S Proppert (2014)
Single-Molecule Localization Microscopy & Software Benchmarking. http://bigwww.epfl.ch/smlm/ (2017).
Storm-Analysis, Zhuang lab STORM movie analysis code. https://github.com/ZhuangLab/storm-analysis (2017).

Dates

Type	When
Created	8 years, 4 months ago (March 28, 2017, 9:54 a.m.)
Deposited	2 years, 8 months ago (Dec. 22, 2022, 10:20 p.m.)
Indexed	2 weeks, 4 days ago (Aug. 6, 2025, 8:48 a.m.)
Issued	8 years, 4 months ago (April 3, 2017)
Published	8 years, 4 months ago (April 3, 2017)
Published Online	8 years, 4 months ago (April 3, 2017)

Funders 0

None

BibTeX

@article{Babcock_2017, title={Analyzing Single Molecule Localization Microscopy Data Using Cubic Splines}, volume={7}, ISSN={2045-2322}, url={http://dx.doi.org/10.1038/s41598-017-00622-w}, DOI={10.1038/s41598-017-00622-w}, number={1}, journal={Scientific Reports}, publisher={Springer Science and Business Media LLC}, author={Babcock, Hazen P. and Zhuang, Xiaowei}, year={2017}, month=apr }

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