Abstract

Deep learning-based data analysis methods have gained considerable attention in all fields of science over the last decade. In recent years, this trend has reached the single-molecule community. In this review, we will survey significant contributions of the application of deep learning in single-molecule imaging experiments. Additionally, we will describe the historical events that led to the development of modern deep learning methods, summarize the fundamental concepts of deep learning, and highlight the importance of proper data composition for accurate, unbiased results.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2020 (2)

A. Gidon, T. A. Zolnik, P. Fidzinski, F. Bolduan, A. Papoutsi, P. Poirazi, M. Holtkamp, I. Vida, and M. E. Larkum, “Dendritic action potentials and computation in human layer 2/3 cortical neurons,” Science 367(6473), 83–87 (2020).
[Crossref]

L. Möckl, A. R. Roy, P. N. Petrov, and W. E. Moerner, “Accurate and rapid background estimation in single-molecule localization microscopy using the deep neural network bgnet,” Proc. Natl. Acad. Sci. U. S. A. 117(1), 60–67 (2020).
[Crossref]

2019 (12)

L. Möckl, P. N. Petrov, and W. E. Moerner, “Accurate phase retrieval of complex point spread functions with deep residual neural networks,” Appl. Phys. Lett. 115(25), 251106 (2019).
[Crossref]

J. C. Xu, G. G. Qin, F. Luo, L. N. Wang, R. Zhao, N. Li, J. H. Yuan, and X. H. Fang, “Automated stoichiometry analysis of single-molecule fluorescence imaging traces via deep learning,” J. Am. Chem. Soc. 141(17), 6976–6985 (2019).
[Crossref]

T. Kim, S. Moon, and K. Xu, “Information-rich localization microscopy through machine learning,” Nat. Commun. 10(1), 1996 (2019).
[Crossref]

E. Hershko, L. E. Weiss, T. Michael, and Y. Shechtman, “Multicolor localization microscopy and point-spread-function engineering by deep learning,” Opt. Express 27(5), 6158–6183 (2019).
[Crossref]

C. Belthangady and L. A. Royer, “Applications, promises, and pitfalls of deep learning for fluorescence image reconstruction,” Nat. Methods 16, 1215–1225 (2019).
[Crossref]

E. Moen, D. Bannon, T. Kudo, W. Graf, M. Covert, and D. Van Valen, “Deep learning for cellular image analysis,” Nat. Methods 16, 1233–1246 (2019).
[Crossref]

N. Granik, L. E. Weiss, E. Nehme, M. Levin, M. Chein, E. Perlson, Y. Roichman, and Y. Shechtman, “Single-particle diffusion characterization by deep learning,” Biophys. J. 117(2), 185–192 (2019).
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2018 (11)

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2017 (8)

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2016 (3)

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Y. Shechtman, L. E. Weiss, A. S. Backer, M. Y. Lee, and W. E. Moerner, “Multicolour localization microscopy by point-spread-function engineering,” Nat. Photonics 10(9), 590–594 (2016).
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Y. Shechtman, S. J. Sahl, A. S. Backer, and W. E. Moerner, “Optimal point spread function design for 3D imaging,” Phys. Rev. Lett. 113(13), 133902 (2014).
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2012 (4)

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, “Simultaneous, accurate measurement of the 3d position and orientation of single molecules,” Proc. Natl. Acad. Sci. U. S. A. 109(47), 19087–19092 (2012).
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H. L. D. Lee, S. J. Sahl, M. D. Lew, and W. E. Moerner, “The double-helix microscope super-resolves extended biological structures by localizing single blinking molecules in three dimensions with nanoscale precision,” Appl. Phys. Lett. 100(15), 153701 (2012).
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2011 (1)

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2006 (3)

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Figures (9)

Fig. 1.
Fig. 1. A simple Perceptron and the problem of linear separation. A) A simple Perceptron with two inputs a1 and a2 and the associated weights w1 and w2. B) Linear separation of the OR operator (green line). C) The XOR operator is not linearly separable.
Fig. 2.
Fig. 2. Number of publications found on Pubmed when searching for “neural network(s)” (black line) or “deep learning” (dashed grey line) per year.
Fig. 3.
Fig. 3. Building blocks of convolutional NNs and key mathematical concepts. A) Key mathematical operations executed in NNs: Fully-connected node, convolution, 2 × 2 MaxPooling (top to bottom). Note that activation is also performed for the convolution operation. B) Common activation functions and their definition. C) A simplified convolutional NN. The input image is passed to multiple (in this case: two) convolutional layers. After this, a 2 × 2 MaxPooling is performed, followed by flattening into a one-dimensional vector (which has, in this case, 50 elements). One fully-connected layer follows before the final layer returns the output (in this case: two scalars).
Fig. 4.
Fig. 4. Key concepts of training a NN. A) Loss. The loss function (here MSE) is a metric for the deviation of the prediction of the NN from the (known) ground truth. B) Gradient descent. The loss is reduced with respect to variation of all trainable parameters of the NN. C) Backpropagation. Each trainable parameter is iteratively adjusted backwards through the NN.
Fig. 5.
Fig. 5. Modern NN architectures relevant for image analysis in single-molecule experiments. A) Convolutional neural net (ConvNet). B) Residual net (ResNet). C) Encoder-decoder architecture. D) U-net. E) Inception architecture. F) Generative adversarial network. Note that all depicted network types exhibit considerable variations in the exact architecture, e.g. number of layers or layer sequence.
Fig. 6.
Fig. 6. The four scenarios for the relationship between data analyzed and data returned by an algorithm. Data can be within the input space of the algorithm and be mapped within the result space (i) or outside the result space (ii). Conversely, data can be not within the input space and mapped within the result space (iii) or outside the result space (iv).
Fig. 7.
Fig. 7. Influence of covering the sample space. A) Binary masks of squares, circles, rectangles, and triangles and sparse sampling of the masks (sampling rate: 10-20%). B) Output of four NNs trained on either squares, circles, rectangles, or triangles when the sparse square, circle, rectangle, or triangle dataset is supplied as input. C) Output of a NN that was trained on all four shapes when the four sparse datasets are supplied as input.
Fig. 8.
Fig. 8. Phase retrieval of a general PSF with a residual network. A) The predicted Zernike coefficients (teal) match the ground-truth Zernike coefficients (black) very well. B) Correspondingly, the retrieved PSFs (bottom line) match the input PSF (top line) throughout the whole focal range.
Fig. 9.
Fig. 9. Estimation of arbitrary structured background from images of various PSFs. Shown are the probability density function of the PSF (i.e. the noise-free, theoretical PSF), the PSF with background, the true underlying background in the PSF image, the prediction of BGnet, and the background-corrected PSFs, using either the true or the predicted background. Scale bar: 500 nm (open aperture PSF), 1 µm (other PSFs).

Tables (4)

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Table 1. Glossary of key concepts

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Table 2. Presented methods in section 5.2

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Table 3. Presented methods in section 5.3

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Table 4. Presented methods in section 5.4

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