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A pairwise distance distribution correction (DDC) algorithm to eliminate blinking-caused artifacts in SMLM

Nature Methods volume 18, pages 669–677 (2021)Cite this article

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Abstract

Single-molecule localization microscopy (SMLM) relies on the blinking behavior of a fluorophore, which is the stochastic switching between fluorescent and dark states. Blinking creates multiple localizations belonging to the same fluorophore, confounding quantitative analyses and interpretations. Here we present a method, termed distance distribution correction (DDC), to eliminate blinking-caused repeat localizations without any additional calibrations. The approach relies on obtaining the true pairwise distance distribution of different fluorophores naturally from the imaging sequence by using distances between localizations separated by a time much longer than the average fluorescence survival time. We show that, using the true pairwise distribution, we can define and maximize the likelihood, obtaining a set of localizations void of blinking artifacts. DDC results in drastic improvements in obtaining the closest estimate of the true spatial organization and number of fluorescent emitters in a wide range of applications, enabling accurate reconstruction and quantification of SMLM images.

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Fig. 1
Fig. 2: Comparison of four different thresholding methods with DDC on five spatial distributions (randomly distributed, small clusters, dense clusters and parallel filaments and intersecting filaments).
Fig. 3
Fig. 4: Application of DDC to experimentally measured spatial distributions of AKAP79 and AKAP150.
Fig. 5: Application of DDC to experimentally measured spatial distributions of dynein.
Fig. 6

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Data availability

The data in this paper are shown in the main figures and Extended Data figures. All raw data for each of the simulation systems (Figs. 1 and 2) are also included at https://github.com/XiaoLabJHU/DDC. Source data are provided with this paper. All other data are available upon request. The complete package of DDC (data, code, user guide) is available for download at https://github.com/XiaoLabJHU/DDC (there are no access restrictions).

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Acknowledgements

This work was supported by the NIH (5T32GM007231, C.H.B.; F31GM115149-01A1, M.W.; R01 GM086447; and R01 DK073368 and R35CA197622, J.Z.) and the NSF (MCB1817551), a Johns Hopkins Discovery Award, a Hamilton Innovation Research Award (J.X.), NIGMS/NIH (R01GM112008, J.X. and X.C.; R35GM127075, X.C.; and R01GM133842, M.L.) and the Howard Hughes Medical Institute (55108512, X.C.).

Author information

Authors and Affiliations

  1. Department of Biophysics and Biophysical Chemistry, Johns Hopkins School of Medicine, Baltimore, MD, USA

    Christopher H. Bohrer, Xinxing Yang, Xiaoli Weng, Ryan McQuillen & Jie Xiao

  2. Department of Biophysics, Johns Hopkins University, Baltimore, MD, USA

    Christopher H. Bohrer & Elijah Roberts

  3. Department of Physiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA

    Shreyasi Thakur & Melike Lakadamyali

  4. Department of Pharmacology, University of California San Diego, San Diego, CA, USA

    Brian Tenner, Brian Ross & Jin Zhang

  5. Department of Biology, Johns Hopkins University, Baltimore, MD, USA

    Matthew Wooten & Xin Chen

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Contributions

C.H.B., conceptualization, discovery and development of theory, software, data collection, data analysis, writing (original draft, review and editing); X.Y., experimental data collection, data analysis, writing (review and editing), project guidance; S.T., experimental data collection, data analysis; X.W., experimental data collection, data analysis; B.T., experimental data collection, data analysis, writing (review and editing); R.M., development of the user guide, software, writing (review and editing); B.R., experimental data collection, data analysis; M.W., experimental data collection, writing (review and editing); X.C., project guidance, funding acquisition, writing (review); J.Z., project guidance, funding acquisition, writing (review); E.R., project guidance, writing (review); M.L., experimental conceptualization, funding acquisition, writing (review and editing); J.X., conceptualization, project guidance, writing (original draft), supervision, funding acquisition, project administration, writing (review and editing).

Corresponding author

Correspondence to Jie Xiao.

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The authors declare no competing interests.

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Peer review information Rita Strack was the primary editor on this article and managed its editorial process and peer review in collaboration with the rest of the editorial team. Nature Methods thanks Paolo Annibale, Sebastian Malkusch, and the other, anonymous reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Photokinetic Models.

The two kinetic models used to simulate blinking, (a) 2 dark state and (b) 1 dark state. The transition probabilities per frame are shown in the figure.

Source data

Extended Data Fig. 2 Converging of Pairwise distance distributions.

The pairwise distance distributions for both photo-kinetic models shown in Extended Data Figure 1 and 6 molecular assemblies. Note here that the axis is no longer log scale as in the main text and the true pairwise distance distribution is shown as black dots.

Source data

Extended Data Fig. 3 Matching the true pairwise distance distribution.

An illustration of the pairwise distance distributions at a certain frame difference, Δn, before and after being corrected with DDC. When the likelihood is maximized all of the pairwise distance distributions will match the true pairwise distance distribution. [The true pairwise distance distribution is shown as black dots.].

Source data

Extended Data Fig. 4 Toy model illustration for inner workings of DDC.

Toy model illustration for inner workings of DDC (See text within SI for in depth description): a, Simple toy model with 4 true localizations and 2 repeats (color coded), with the number showing the frame of each localization (can also be used to identify each localization for this example). b, The true pairwise distance distribution (PT (Δr)) and the distribution of distances between loci given that at least one is a repeat (PR1(Δr∣Δn = 1)) for the localizations within (a) The number (and probability) for ‘small’ distances and ‘large’ distances for each distribution is above each bar, with an assigned variable (a, b, c, d) used in the calculation of the Likelihood (Lik). We also show the specific pairs of loci under the bars to illustrate how assigning a particular loci to a certain set influences the likelihood calculation. Note: for this specific example blinks only appear with Δn = 1, and hence we ignore the distributions with Δn > 1 (See text). c, Simplified illustration of how Alg. 1 and Alg. 2 work together and assign localizations as a true localization or repeat localization. Multiple steps of the MCMC are shown with different rows (1 to 3) (See Text). Alg. 1 essentially calculates the probability that a localization is a repeat (green bars), if this value is above .5 it is assigned to that set. Alg. 2 varies this calculation by a small amount each step, generating new sets d, The sets assigned in (c) lead to different likelihoods (due to the particular distribution the distance between each pair is assigned (changing (a,b,c,d), note how the specific distances between each pair change with each assigned set), when the distributions of the assigned sets match the correct distributions (those in (B)) Lik is maximized. (See text for further details).

Source data

Extended Data Fig. 5 Maximization of Likelihood Results in Correct Conformation of Localizations.

Maximization of Likelihood Results in Correct Conformation of Localizations: For 6 systems investigated within this work, we randomly varied the percentage of true localizations and calculated the log(Lik) and the image error for each conformation (See Text).

Source data

Extended Data Fig. 6 Overcounting and undercounting in individual pixels.

Overcounting and undercounting in individual pixels: Comparison of four different thresholding methods with DDC in counting the number of true localizations in individual pixels on five spatial distributions as depicted and simulated in main text Fig. 2. The y axis is the difference between the true count and the method-identified count expressed as Count-[True Count], with positive values indicating the degree of over-counting and negative values the degree of under-counting. The x-axis is the number of true counts in individual pixels. The pixel size was set to 50 nm. Note that only DDC shows consistent distributions of y values near zero at different true count values and across all five spatial patterns. [Each scatter point is colored to illustrate the estimated probability density - allowing one to visualize the regions of high density (red) and regions of low density (blue).].

Source data

Extended Data Fig. 7 AKAP scatter plots through time.

Scatter plots for a section of a cell with the localizations from AKAP79 with the color indicating the frame of the localization (Blue is early and Red is late) for the three different methodologies.

Source data

Extended Data Fig. 8 Computationally varying the label density.

a, The results of computationally varying the label density on some of the simulation systems. b, The results of computationally varying the label density on AKAP79 and AKA150. (Values greater than 1 indicate significant clustering.).

Source data

Extended Data Fig. 9 Experimental Concerns.

Image Error at different densities of localizations (a) and activation probability per frame (b). The raw data points are shown as gray points and the moving average is shown in black (Supporting Material). c, An intensity trajectory of a single mEos3.2 molecule with labels showing the definitions of Ton and Toff. d, The average Ton, Toff (per frame, frame rate 33Hz), and number of blinks for Alexa647 and mEos3.2 at different UV activation intensities (405 Power).

Source data

Extended Data Fig. 10 Varying Raw Image Error.

The raw Image Error (Not Normalized) for the uncorrected SMLM images for varying the density of the localizations and the activation energy.

Source data

Supplementary information

Supplementary Information

Supplementary Table 1, Discussion and Figs. 1–12.

Reporting Summary

Source data

Source Data Fig. 1

Data used to generate plots in Fig. 1.

Source Data Fig. 2

Data used to generate plots in Fig. 2.

Source Data Fig. 3

Data used to generate plots in Fig. 3.

Source Data Fig. 4

Data used to generate plots in Fig. 4.

Source Data Fig. 5

Data used to generate plots in Fig. 5.

Source Data Fig. 6

Data used to generate plots in Fig. 6.

Source Data Extended Data Fig. 1

Data used to generate plots in Extended Data Fig. 1.

Source Data Extended Data Fig. 2

Data used to generate plots in Extended Data Fig. 2.

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Data used to generate plots in Extended Data Fig. 3.

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Data used to generate plots in Extended Data Fig. 4.

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Data used to generate plots in Extended Data Fig. 5.

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Data used to generate plots in Extended Data Fig. 6.

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Data used to generate plots in Extended Data Fig. 7.

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Data used to generate plots in Extended Data Fig. 8.

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Data used to generate plots in Extended Data Fig. 9.

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Data used to generate plots in Extended Data Fig. 10.

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Bohrer, C.H., Yang, X., Thakur, S. et al. A pairwise distance distribution correction (DDC) algorithm to eliminate blinking-caused artifacts in SMLM. Nat Methods 18, 669–677 (2021). https://doi.org/10.1038/s41592-021-01154-y

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