Introduction to Cryo Electron Microscopy/Tomography

Transcription

1 Introduction to Cryo Electron Microscopy/Tomography Ricardo Miguel Sánchez Loayza Max Planck Institute for Biophysics - Kudryashev Group Goethe Universität - Visual Sensorics and Information Processing

2 Overview - CryoEM/CryoET CryoEM/ET: What and Why? Image Formation CryoEM: Single Particle Analysis CryoET: Subtomogram Averaging

3 CryoEM/ET: What and Why?

4 What is Cryo-electron Microscopy/Tomography? Techniques used to produce high resolution 3D maps. ( 2 Å or 0.2 nm). Tools used by biophysicists (structural biology) to obtain 3D density maps and estimate the atomic model of biological samples: Get atomic model. Multiple comformations (How it works) Drug design. Cryo: The sample is frozen. Electron: A electron microscope is used. Microscopy: 1 frame por sample. Tomography: Sequence of frames per sample.

5 Why CryoEM/ET? Near atomic resolution. Close to native state sample. Easy sample preparation (Compared to crystallography) New method (2012) 1 : Most of available programs are experimental. Not all issues are solved (efficiently). 1 S. Scheres, RELION: Implementation of a bayesian approach to cryoem structure determination. 2012

6 Example 1 Figure: Example of high resolution map (2.3 Å or 0.23 nm) 2 of the p97 hexameric ATPase in three different conformations. 2 S. Banerjee et al., 2.3 Å resolution map cryo-em structure of human p97 and mechanism of allosteric inhibition. 2016

7 Example 1 Figure: Atomic model fitted and measured motion.

8 Example 1 Figure: Schematic of the two-step sequence involved in p97 activation resulting from the sequential binding of ATP γ S.

9 Example 2 Figure: Example of low resolution map ( 15 Å or 1.5 nm) 3 of different conformations of the P-glycoprotein. 3 G. Frank et al., Cryo-EM Analysis of the Conformational Landscape of Human P-glycoprotein (ABCB1) During its Catalytic Cycle. 2016

10 Example 2 Figure: Atomic model (obtained with crystallography) fitted into the different 3D maps.

11 Example 2 Figure: Schematic of hp-gp at major steps during the ATPase reaction cycle.

12 Example 3 - Enzymes Figure: Example of 3D maps of 20 aminoacids and their atomic model. The resolution of each 3D map is 1.8 Å (0.18 nm) 4. 4 S. Subramaniam et al., Resolution advances in cryo-em enable application to drug discovery. 2016

13 Resolution in Structural Biology Figure: Structures to study in biology and how to sample them.

14 Electron Microscope source C1 C2 condenser aperture condenser system sample holder sample objective lens objective aperture projector system imaging Figure: Scheme of a modern Electron Microscope.

15 Electron Microscope: Source High coherence of electron beam. Acceleration voltage: 300 kv. Wavelength: 0.02 Å (2 pm). Figure: Field emission tip.

16 Electron Microscope: Lenses Uses magnetic field to change the trajectory of the electron. Equivalent to light microscope lenses. Low magnification (50x). Figure: Magnetic lens.

17 Electron Microscope: Detector Figure: Direct detector allowed the Resolution Revolution. Gatan K2 Summit detector: 400 fps, 1.06Å pixel size, 8k 8k images.

18 Electron Microscope: Sample holder Figure: Sample holder of Titan KRIOS electron microscope.

19 Sample Preparation! Get a Biochemist. Get sample of protein. Put sample on grid. Plunge freeze it!. Put grid in microscope. Take images.??? Profit.

20 Sample preparation! Figure: Sample too thick.

21 Sample preparation! Figure: Sample too thin.

22 Sample preparation! Figure: Bad luck.

23 Sample preparation! Figure: Sample perfect.

24 Record a micrograph! Figure: Reference molecule (Defocus: 70nm).

25 Record a micrograph! Figure: Recorded micrograph.

26 Record a micrograph! Figure: Filtering?.

27 Image Formation

28 Sample interaction with electron beam. Figure: Radiation destroys the sample. Limits the electron dose (25 e /Å 2 ).

29 Sample interaction with electron beam. Figure: The sample modifies the phase of the electron beam, not its amplitude.

30 Sample interaction with electron beam: Defocus. Figure: Electron beam interaction with sample. Figure: Changing the image plane adds extra phase shift.

31 Sample interaction with electron beam: Defocus. Figure: Defocus and the Contrast Transfer Function (CTF)

32 Image formation model ( ) I(x, y) = I rn + I dc + Poiss Φ e F 1 {F{Ψ exit }CTF (q)mtf (q)} Where I rn is the detector s readout noise, I dc is the dark current, Φ e is the electron flux, and Poiss(A) returns a random number from a Poisson distribution with expected value A 5. 5 M. Vulović, Image Formation modeling in Cryo-Electron Microscopy. 2013

33 Record a micrograph (again)! Figure: Reference molecule with 2000nm of defocus.

34 Record a micrograph (again)! Figure: Imaged molecule with 2000nm of defocus.

35 Record a micrograph (again)! Figure: Imaged molecule filtered

36 Remember: Radiation damage Figure: 3D maps of the same helix for different frames 6. 6 T. Grant, Measuring the optimal exposure for single particle CryoEM using 2.6 Å reconstruction of rotavirus VP

37 CryoEM: Single Particle Analysis

38 Single Particle Analysis (SPA) Goal: Generate High Resolution 3D map from Noisy Micrographs. How: Get orientation of each particle on the micrographs. Assumptions: Rigid protein. Homogeneity. No preferential orientation (Fourier space fully sampled). A lot of data: Millions of small images ( pixels, typically).

39 Fourier Central Slice Theorem Figure: Example of 2D Central Slice Theorem 7. 7 G. Zeng, Medical Image Reconstruction: A Concept Tutorial

40 SPA: Fourier Reconstruction Figure: The fourier transform of each projection is added to the fourier transform of the volume. The reconstruced volume is reconstructed by applying the inverse fourier transform.

41 The SPA problem. Problem: Given the unknown 3D structures V 1,..., V K, and the observed images X 1,..., X N, where X n = proj(v k, φ n ). Find φ n and V n. Solution (Bayesian likelihood framework): arg max V 1,...,V K log p(v 1,..., V K X 1,..., X N ) = arg max V 1,...,V K N log n=1 K k=1 1 K p(x n, φ n V k )dφ n + log p(v 1...K ) Solve by Regularized Expectation Maximization algorithm 8. Issue: Needs an initial guess of the volume. 8 S. Scheres, RELION: Implementation of a bayesian approach to cryoem structure determination. 2012

42 The SPA problem: Overfitting Figure: Image obtained from noise by using the Mona Lisa as initial guess.

43 The SPA problem: Speed of execution Figure: Using Stochastic Gradient Descent algorithm 9. 9 A. Punjabi et al., cryosparc: algorithms for rapid unsupervised cryoem structure determination. 2016

44 The SPA problem: Speed of execution Figure: Branch and Bound: Define a inexpensive lower bound over all poses A. Punjabi et al., cryosparc: algorithms for rapid unsupervised cryoem structure determination. 2016

45 SPA: Procedure Figure: CryoEM micrograph and a particle image F. Sigworth, Principles of cryoem single particle image processing. 2016

46 SPA: Procedure Figure: Proposed SPA workflow S. Scheres, RELION: Implementation of a bayesian approach to cryoem structure determination. 2012

47 SPA: My simplified workflow Correct for particle drifting. Correct CTF. Pick particles. Get an initial model. Get orientations and 3D maps. Classify 3D maps (Heterogeneity). Refine and polish 3D maps. Get resolution. Cure cancer (or publish somewhere, at least).

48 SPA: Procedure Figure: Proposed SPA workflow S. Scheres, RELION: Implementation of a bayesian approach to cryoem structure determination. 2012

49 SPA: Observations/Problems CTF is corrected typically by phase flipping. Particle picking is done by a highly trained machine: a biophysicist. There is no reliable autopicking program. 2D classification is needed. The proper selection of the initial model is crucial. Pose/orientation estimation was slow (?). Sometimes you get scooped.

50 SPA: Local Refinement Global 3D Refinement Global Reconstruction Estimated center of subunits RSS REP (proposed) Figure: Proposed Local refinement scheme. Local 3D Refinements and Local Reconstructions

51 CryoET: Subtomogram Averaging

52 Subtomogram Averaging (StA) Goal: Generate High Resolution 3D map of a particle in situ. How: Use tomograms instead of micrographs. Limitations: Limited views, typically from 60 to +60 with steps of 2 or 3. Tomograms are huge: 8k 8k 2k (480 GB). Alignment is done with volumes, no images. No need of projection matching. Artifacts: Missing Wedge. SLOW.

53 Tomogram creation

54 Tomogram creation

55 Tomogram creation Figure: Frames need to be aligned.

56 Weighted Back Projection 1 Figure: Back Projection G. Zeng, Medical Image Reconstruction. Springer 2016.

57 Weighted Back Projection 2 Figure: Weighted Back Projection G. Zeng, Medical Image Reconstruction. Springer 2016.

58 Algebraic Reconstruction Techniques 1 Figure: Mathematical Model for ART 16 For one projection: p θ = A x 16 G. Zeng, Medical Image Reconstruction. Springer 2016.

59 Algebraic Reconstruction Techniques 2 For multiple projections: p θ1 p θ2 p θ3 p θtotal = A 1 A 2 A 3 x = A total x Underdetermined system: More variables than equations. Cannot be solved by direct algorithms. Iterative algorithms are used: Slow. Mathematical model allows constrains to the solution, like: Solution ˆx must be smooth. Highlight the edges of solution ˆx. Consider pθtotal is noisy.

60 Progressive Stochastic Reconstruction Technique 1 Figure: Graphical description of the PSRT algorithm B. Turonova, Progressive Stochastic Reconstruction Technique for Cryo Electron Tomography. Journal of Structural Biology, 2015

61 Progressive Stochastic Reconstruction Technique 2 Figure: Example of three densities. x 1 is accepted (decrease energy), x 2 is out of range, and x 3 is rejected (does not decrease energy) J. Gregson. Stochastic Tomography and ist Application in 3D imaging of Mixing Fluids

62 StA: My simplified workflow Collect RAW series. Align them using fiducials. Create full tomogram. Pick particles (cannot be avoided, yet?). Crop Subtomograms. Align subtomograms. Publish if not scooped.

63 Tilt series Alignment Figure: Gold beads picked in a tilt series.

64 Subtomogram Averaging Scheme. Figure: Scheme of the StA procedure A. Crowther, Methods in Enzymology - The Resolution Revolution: Recent Advances In CryoEM. 2016

65 StA: Observations/Problems Uses Brute Force to find orientations. Alignment of the tilt series is not accurate. Even lower electron dose than SPA: very low SNR. Low SNR: Difficult to estimate CTF and pick particles.

66 Final Remarks CryoEM is a relatively new technique with a lot of room for improvement. CryoET is even younger!. Most of the problems in CryoEM/CryoET are ill-posed. Most of the tools used in CryoEM/CryoET are based in basic ideas in image processing. Thanks.