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. 2012;7(5):e36973.
doi: 10.1371/journal.pone.0036973. Epub 2012 May 22.

Inferring biological structures from super-resolution single molecule images using generative models

Suvrajit Maji  1 , Marcel P Bruchez
Affiliations

Inferring biological structures from super-resolution single molecule images using generative models

Suvrajit Maji et al. PLoS One. 2012.

Abstract

Localization-based super resolution imaging is presently limited by sampling requirements for dynamic measurements of biological structures. Generating an image requires serial acquisition of individual molecular positions at sufficient density to define a biological structure, increasing the acquisition time. Efficient analysis of biological structures from sparse localization data could substantially improve the dynamic imaging capabilities of these methods. Using a feature extraction technique called the Hough Transform simple biological structures are identified from both simulated and real localization data. We demonstrate that these generative models can efficiently infer biological structures in the data from far fewer localizations than are required for complete spatial sampling. Analysis at partial data densities revealed efficient recovery of clathrin vesicle size distributions and microtubule orientation angles with as little as 10% of the localization data. This approach significantly increases the temporal resolution for dynamic imaging and provides quantitatively useful biological information.

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Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. Structural mask for simulated data.
(A) Lines and Circles, cropped image in the yellow rectangle box is shown in Figure 2. (B) lines only (C) circles only.
Figure 2
Figure 2. Representative linear and circular structure reconstruction.
Column (A) Mask (B) outlier noise density 0 (C) outlier noise density 0.005 (D) outlier noise 0.02. Position noise is 5 pixels with data density of 15% for all cases here.
Figure 3
Figure 3. Reconstruction measure using Structural Similarity Index CW-SSIM.
A total of 100 random simulations were performed at each data density and at outlier noise densities of 0, 0.005 and 0.02. Top row is for lines and bottom row is for circles. Column (A) Position noise of 0 pixel. (B) Position noise of 5 pixels. (C) Position noise of 10 pixels. Reconstruction measure for all the noise densities are shown in Figure S2.
Figure 4
Figure 4. Parallel line reconstruction.
Reconstruction measure using Structural Similarity Index CW-SSIM (top row) and resolution, calculated as the minimum inter line distance (bottom row) at indicated outlier noise densities. A total of 100 random simulations were performed at each data density. Column (A) Position noise of 0 pixel. Column (B) Position noise of 2 pixels.
Figure 5
Figure 5. Single molecule localized data of clathrin (red) and tubulin (green).
Top row is the plotted positions from both channels. Scale bar is 500 nm. Second row is the representative reconstructed structures from both channels, overlaid on the data (A) 10% data (B) 50% data. (C) 100% data. Third row is the histogram of orientation angle of the reconstructed line segments and the bottom row is the histogram of the diameters of the reconstructed circles.
Figure 6
Figure 6. Illustration of working principle of the Hough Transform for lines.
(A) Parametric normal form line passing through a point (50, 50) (B) Hough matrix parameter space with sinusoidal line corresponding to (50, 50). (C) 2 additional points added to (A). (D) Sinusoidal curves intersect for the three collinear points. One peak in the Hough space corresponds to one line in the image.
Figure 7
Figure 7. Illustration of working principle of the Hough Transform for circles.
(A) Hough accumulator space for a circle (a,b,r) when the radius r is unknown. The scanning circles in the parameter space are on the cone surface in the 3-d space. (B) 5 points on a circle (100, 100, 50). (C) Circles in the Hough accumulator space corresponding to each of the input points in (B). (D) 20 points on a circle (100, 100, 50). (E) Circles in the Hough accumulator space corresponding to each of the input points in (D). The intersecting peak represents the center of the circle we are searching.
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References

    1. Abbe E. Beitrage zur Theorie des Mikroskops und der mikroskopischen Wahrmehmung. Archiv für Mikroskopische Anatomie. 1873;9:412–420.
    1. Hell SW, Wichmann J. Breaking the Diffraction Resolution Limit by Stimulated-Emission - Stimulated-Emission-Depletion Fluorescence Microscopy. Optics Letters. 1994;19:780–782. - PubMed
    1. Rust MJ, Bates M, Zhuang XW. Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM). Nature Methods. 2006;3:793–795. - PMC - PubMed
    1. Betzig E, Patterson GH, Sougrat R, Lindwasser OW, Olenych S, et al. Imaging intracellular fluorescent proteins at nanometer resolution. Science. 2006;313:1642–1645. - PubMed
    1. Hess ST, Girirajan TPK, Mason MD. Ultra-high resolution imaging by fluorescence photoactivation localization microscopy. Biophysical Journal. 2006;91:4258–4272. - PMC - PubMed

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