3D Reconstruction in EM

Transcription

1 3D Reconstruction in EM C.O.S. Sorzano Biocomputing Unit, CNB-CSIC Instruct Image Processing Center

2 Contents Initial volume Angular assignment 3D Reconstruction 3D Classification Resolution Amplitude correction Overfitting

3 Towards high-throughput and high-resolution C.O.S. Sorzano, J. M. de la Rosa Trevín, J. Otón, J. J. Vega, J. Cuenca, A. Zaldívar-Peraza, J. Gómez-Blanco, J. Vargas, A. Quintana, R. Marabini, J. M. Carazo. Semiautomatic, high-throughput, high-resolution protocol for three-dimensional reconstruction of Single Particles in Electron Microscopy. Nanoimaging: Methods and Protocols. Methods in Molecular Biology, 950: Eds. Alioscka Sousa, Michael Kruhlak. Humana Press. (2012)

4 Projection Matching Images

5 Projection Matching Images Initial volume

6 Projection Matching Images Initial volume Reprojections

7 Projection Matching Images Initial volume Reprojections Match

8 Projection Matching Images Initial volume Reprojections Match Reconstruct

9 Projection matching is a greedy algorithm

10 Goal function landscape min I i Pθi V V,θ 2 i 100k projections (200x200) = D!!!

11 Model bias = 1000 images Model bias=local minimum!! Shatsky, M.; Hall, R. J.; Brenner, S. E. & Glaeser, R. M. A method for the alignment of heterogeneous macromolecules from electron microscopy. J Struct Biol, 2009, 166, 67-78

12 Initial volume problem How to choose the initial volume?

13 Option 1: Filtered volume

14 Option 2: Geometrical description Bilbao-Castro, J. R.; Sorzano, C. O. S.; García, I. & Fernández, J. J. Phan3D: design of biological phantoms in 3D electron microscopy Bioinformatics, 2004, 20,

15 Option 3: Noisy blob or blob

16 Option 4: Random Conical Tilt

17 (Central Slice Theorem)

18 Option 4: Random Conical Tilt Schenk, A. D.; Castaño-Díez, D.; Gipson, B.; Arheit, M.; Zeng, X. & Stahlberg, H. 3D reconstruction from 2D crystal image and diffraction data. Methods Enzymol, 2010, 482,

19 Option 5: Computational means Common lines Stochastic Optimization

20 Option 5: Common lines

21 Option 5: Stochastic optimization min I i Pθi V V,θ 2 i = 600D Ogura, T. & Sato, C. Posterior Euler angle assignment using simulated annealing J. Structural Biology, 2006, 156,

22 Angular Assignment

23 Angular assignment: symmetry

24 Angular assignment: comparison in Real space Fourier space Wavelet space Radon space

25 Initial volume and 3D alignment methods

26 3D Reconstruction Direct Fourier methods: Fast, high resolution, need enough particles

27 3D Reconstruction Iterative methods (ART, SIRT, ): Slow, very flexible constraints, good for few particles, and incomplete angular coverages

28 3D Reconstruction Weighted BackProjection: Traditional

29 3D Reconstruction

30 3D Classification

31 3D Reconstruction+Classification You cannot reconstruct well if you have a mixture of populations You cannot classify well if images are not well aligned

32 3D Reconstruction+Classification Multireference Alignment: An experimental 2D image belongs to a single 3D volume. Maximum likelihood: All experimental 2D images belong to all 3D volumes with different probabilities. Bayesian prior: There is a prior assumption about how 3D volumes look like.

33 3D Classification Bootstrap: Choose N images randomly Construct N volumes Analyze its differences Map variance: Analyze the local variance of 3D volumes

34 3D Classification+Reconstruction

35 Resolution Fourier Shell correlation (FSC): A measure of repeatability

36 Resolution Fourier Shell correlation (FSC): Threshold: Noise correlation ½ bit

37 Resolution Spectral Signal-to-Noise Ratio (SSNR): A measure of consistency with 2D data Threshold: 1 (=0 db)

38 Resolution 3D Spectral Signal-to-Noise Ratio (VSSNR): Unser, M.; Sorzano, C. O. S.; Thévenaz, P.; Jonic, S.; El-Bez, C.; De Carlo, S.; Conway, J. & Trus, B. L. Spectral Signal-to-Noise Ratio and resolution assessment of 3D reconstructions J. Structural Biology, 2005, 149,

39 Resolution Local resolution: Kucukelbir, A.; Sigworth, F. J. & Tagare, H. D. Quantifying the local resolution of cryo-em density maps. Nat Methods, 2014, 11, 63-65

40 Resolution

41 Amplitude correction CTF groups + Wiener filtering:

42 Amplitude correction Guinier plot: B-factor Fernández, J. J.; Luque, D.; Castón, J. R. & Carrascosa, J. L. Sharpening high resolution information in single particle electron cryomicroscopy. J Struct Biol, 2008, 164,

43 Overfitting Inflated resolution!

44 Overfitting Manual picking Gold standard Remove noise anchors: +Machine learning Fourier space Real space Slow angular assignment Remove strange particles: 2D Particle screening 2D Cluster cores 3D Cluster cores 3D Jumping particles

45 Validation Validation: Angular distribution Tilt pair Fitting Henderson, R.; Chen, S.; Chen, J. Z.; Grigorieff, N.; Passmore, L. A.; Ciccarelli, L.; Rubinstein, J. L.; Crowther, R. A.; Stewart, P. L. & Rosenthal, P. B.Tilt-pair analysis of images from a range of different specimens in single-particle electron cryomicroscopy. J Mol Biol, 2011, 413, Henderson, R.; et al. Outcome of the first electron microscopy validation task force meeting. Structure, 2012, 20,

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47 Contents Initial volume Angular assignment 3D Reconstruction 3D Classification Resolution Amplitude correction Overfitting