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Reply to ‘Impact of optical aberrations on axial position determination by photometry’

Nature Methods volume 15, pages 990–992 (2018)Cite this article

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Franke and van de Linde reply — Gaussian fitting is a widely used and fundamental tool in single-molecule localization microscopy (SMLM), but the extraction of intensity from experimental data can be challenging1. We appreciate the thorough work of Rieger and colleagues in proposing the principal role of small optical aberrations, present in any state-of-the-art microscope, in the model mismatch between commonly used Gaussian point-spread function (PSF) fitting for SMLM and the experimental PSF, even in focus2. In our original paper1, the simulated emission profile of an emitter was based on the experimental examination of a ‘spot’, as there is no obvious distinction between the tail of the spot and the continuum of the detector. We agree that any aperture-based concept will not be able to capture the total number of photons arriving on the detector, as the probability of detecting photons far away from the molecule’s center of mass is not zero (Supplementary Fig. 1). Moreover, in an experimental situation—that is, in the presence of potentially inhomogeneous background—one cannot distinguish between singular photons arriving micrometers away from their respective centers of origin and those from other emitting objects. Nevertheless, we have observed that TRABI enables accurate determination of the photon number along an increased axial range from the most relevant part of this pattern (i.e., the spot), in contrast to Gaussian fitting1.

In our original work we derived the full width at half-maximum (FWHM) from single-molecule measurements and used a radius exceeding 1.86 × FWHM for experimental data (Supplementary Fig. 1). Expansion of the aperture for an isolated emitter might result in the capture of more than 95% of the detected photons, but intensity estimation will be impaired by typical single-molecule densities in real experiments owing to overlapping apertures. The marginal fraction of intensity from peripheral photons, which do not contribute to the spot, might cease to be extractable and come to constitute part of the background. As shown by Rieger and colleagues, fitting of a full vectorial PSF model to experimental bead data is superior to Gaussian fitting and yields different photon numbers than photometry. The actual TRABI approach was not used in their study, as the background was determined in the periphery of nonblinking individual beads, thus resembling aperture photometry1,2. Certainly, the practical implication—for example, the use of the vectorial fit to gain axial information—would be of great interest, as was shown in a similar manner by fitting of cubic spline interpolated PSF models3.

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Fig. 1: 3D TRABI imaging of a DNA origami sample consisting of two binding sites separated by 80 nm.

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Data are available from the authors upon reasonable request.

References

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Acknowledgements

We are grateful to M. Sauer for support and D. Helmerich for technical assistance. We also thank R. Thorsen, S. Stallinga and B. Rieger for discussion.

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Authors and Affiliations

  1. Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany

    Christian Franke

  2. Department of Physics, University of Strathclyde, Glasgow, UK

    Sebastian van de Linde

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Correspondence to Christian Franke or Sebastian van de Linde.

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The authors filed a patent with Carl Zeiss Microscopy GmbH (No. 10 2016 014 133.6).

Integrated supplementary information

Supplementary Figure 1 Theoretical emission profile and experimental spot.

a) Simulated areal Airy-PSF emission pattern of 2,500 photon counts distributed over 10 × 10 µm² without background (FWHM = 340 nm). Inverted image with ≥2 photon count per pixel (N px) saturation. Inset shows unsaturated partial image of the boxed region at the same scale, indicated in red. b) Top: representative experimental single-molecule image of Cy5 molecules under dSTORM conditions; middle: same region in saturation, experimental TRABI radius is shown as solid circle (0.865 µm), 1.86 × FWHM radius is shown as dashed circle (0.632 µm); bottom: intensity profile in black as indicated in the top panel, the background mean and s.d. from five consecutive frames is shown in gray and light gray, respectively. Scale bars, a) 5 µm, b) 2 µm.

Supplementary Figure 2 3D intensity-based biplane imaging of the DNA origami sample.

a) Representative part of a DNA-PAINT image. The numbers in nanometers reflect the calculated length of the selected nanoruler. b) Axial localization precision of BP-TRABI, s.d. of Gaussian fit = 17.2 nm (FWHM = 40.5 nm). c) Axial distance of the two spots, Gaussian fit yields 52.3 ± 16.5 nm (mean ± s.d.), median = 51.4 nm. d) Distribution of the calculated nanoruler length, Gaussian fit yields 74.8 ± 13.2 nm (mean ± s.d.), median = 75.5 nm. e) The absolute z-position of all localizations (black) and the nanoruler length (blue) as function of the distance from the center of the field of view (mean and s.d.). First and last data points are affected by a reduced sample size (Supplementary Table 1). Three independent fields of view (34 µm × 34 µm) were conflated for data analysis. n = 383 single spots comprising 40,091 individual localizations for b)- e) Scale bar, a) 2 µm.

Supplementary Figure 3 3D classical biplane imaging of the DNA origami sample.

a) Axial localization precision of BP-FWHM, s.d. of Gaussian fit = 26.8 nm (FWHM = 63.1 nm). b) Axial distance of the two spots, Gaussian fit yields 53.1 ± 15.6 nm (mean ± s.d.), median = 52.8 nm. d) Distribution of the calculated nanoruler length, Gaussian fit yields 75.8 ± 11.8 nm (mean ± s.d.), median = 75.5 nm. d) The absolute z-position of all localizations (black) and the nanoruler length (blue) as function of the distance from the center of the field of view (mean and s.d.). First and last data points are affected by a reduced sample size (Supplementary Table 1). Three independent fields of view (34 µm × 34 µm) were conflated for data analysis. n = 353 single spots comprising 41,928 individual localizations.

Supplementary Figure 4 Field-dependent nanoruler length of different 3D methods in comparison.

a) BP-TRABI (black, n = 383 single spots comprising 40,091 individual localizations) versus TRABI (blue, n = 222 single spots comprising 18,232 individual localizations). b) Classical biplane imaging (BP-FWHM, black, n = 353 single spots comprising 41,928 individual localizations) versus TRABI (blue). Displayed are mean value and s.d. (Supplementary Table 1).

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Supplementary Figs. 1–4, Supplementary Table 1 and Supplementary Methods

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Franke, C., van de Linde, S. Reply to ‘Impact of optical aberrations on axial position determination by photometry’. Nat Methods 15, 990–992 (2018). https://doi.org/10.1038/s41592-018-0228-3

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