Class2 d
- 1. 2D Classification 3D Initial model Christos Gatsogiannis 30. January 2019
- 2. Tissues Cells Organelles Macro(molecules) 1mm 100μm 10μm 1μm 100nm 10nm 10 Å 1 Å LM Electron tomography SAXS Electron crystallography & single particle TEM X-ray crystallography NMR http://gem.loria.fr/gEMfitter/
- 3. TRPV1 (2013, Liao et al., Nature)TRPV1 (2008, Moiseenkova-Bell et al., PNAS) Electron cryo Microscopy The END of “Blob”-ology!
- 6. Tissues Cells Organelles Macro(molecules) 1mm 100μm 10μm 1μm 100nm 10nm 10 Å 1 Å LM Electron tomography SAXS Electron crystallography & single particle TEM X-ray crystallography NMR http://gem.loria.fr/gEMfitter/
- 7. • correct for motion • estimate CTF • Particle picking • 2D Classification • Get Initial Model • 3D Refinement • 3D Variability • 3D Heterogeneity analysis • Local Resolution/Filtering
- 8. from projection images...to an initial model.. to a refined 3D structure 7 We need: • different views • average many images
- 9. Initial Assumption: All particles have the same structure and are linked by 3D rigid body transformations (Frank, 1996)
- 10. Status quo 9 CTF Picking Extraction • Stack of extremely noisy particles – low signal-to-noise ratio (SNR) • Difficult/impossible to • assess data set quality and homogeneity • do ab-initio 3D reconstruction ➜ Need to improve SNR
- 15. Improving SNR by averaging 14 Avg. 1 Avg. 10 Avg. 100 Avg. 1000 Avg. 10000 Average of many images of the same view of an identical object Closer to reality Shift and rotate every particle to match reference = 2D Alignment x y α Different measures for similarity of pairs ex. cross-correlation (CCC) or sum of squared errors (SSE) In a model world
- 16. Close to reality Improving SNR by averaging 15 Avg. 1 Avg. 10 Avg. 100 Avg. 1000 Avg. 10000 Average of many images of the same view of an identical object In a model world Too noisy to use as reference ➜ use average of all particles instead Iterate 2D alignment until result converges x y α Iteration 1Iteration 3Iteration 2
- 21. K-means clustering 1. User provides number of expected clusters 2. Splits data set randomly into K cluster 3. Calculates average image per cluster ➜ new center location K=3 Initialization steps 20
- 22. K-means clustering 4. Finds out which center it is closest to each point (MRA) 5. Calculates new average of all images belonging to one cluster 6. Repeat 4-5. until result converges K=3 Iterations 21
- 23. K-means clustering 4. Finds out which center it is closest to each point (MRA) 5. Calculates new average of all images belonging to one cluster 6. Repeat 4-5. until result converges K=3 Iterations 22
- 25. Weaknesses of K-means K-Means clustering is a good algorithm because it is simple and fast. However, it is not perfect… 24 The number of clusters is a critical parameter and can affect results considerablyNeed to guess the number of clusters K Results dramatically depend on the initialization. The algorithm may be trapped in the local optimum ➜ Model bias problem Sensitive to initial condition Not robust to outliers Data points far from the centroid may pull the centroid away from the center - Weakness of arithmetic mean ➜ Especially problematic for preferred orientations Limited to circular clusters of similar size K-means can hardly handle clusters of variable size/density
- 26. K=5 25
- 28. ISAC What can ISAC do better to overcome problems of K-means? 27 – Iterative stable alignment and clustering Need to guess the number of clusters K Sensitive to initial condition Not robust to outliers Limited to circular clusters of similar size Ask for number of images per group instead ➜ Equal-Size K-means Run 2D clustering mutiple times starting from different inital conditions ➜ Keep reproducible classes only Mutliple 2D alignments within each cluster to identify heterogenous clusters and outliers, which have high variation in alignment results ➜ Keep stable classes only Reject too small clusters typical for outliers and limit maximum size
- 31. Data assessment Quality of data set? ➜ Details of classes, contamination, preferred orientations? Information about protein ➜ Shape, oligomer, symmetry, heterogeneity? Cleaning of data set for 3D refinement + higher SNR for initial 3D model 30
- 32. 31 Movie from Chen et al. (2017) Nature Commun.
- 34. Ψ,Θ,Φ (Psi,Theta,Phi) 33 x,y - shifts
- 35. I need to get me one of them starting models! 34 How is a structure obtained from images of its 2D projections? This need to be initialized somehow Two possibilities: 1. We know the structure from previous work (boring…) 2. We produce a rough estimate of the structure from the data without using the 3D refinement algorithm. Image from Cheng et al. (2015) Cell 161: 438 – 449
- 36. How to overcome a greedy algorithm – Stochastic Hill climbing 35 Image from Cheng et al. (2015) Cell 161: 438 – 449 Image modified from Pujani et al. (2013) Nature Methods 14:290 – 296 If ccf is bigger than before then take it and stop lookingRandomize order
- 37. The original concept - PRIME 36 Elmlund et al. (2013) Structure 21:1299 – 1306 Image from Cheng et al. (2015) Cell 161: 438 – 449 If ccf is bigger than before then take it and stop lookingRandomize order
- 38. Stochastic hill climbing – When things go awry 37 In some nice cases But sometimes...
- 39. Stochastic hill climbing meets genetic algorithm 38 What‘s a genetic algorithm? An optimization technique inspired in natural selection. Initialize population Stop condition? Mutate and crossover Final result Evaluate fitness SelectionYes No
- 40. How is this implemented? The idea behind VIPER 39 Slide from Pawel Penczek This can be used to calculate an alignment accuracy
- 41. 40 Slide from Pawel Penczek Generation 1 Six independent stochastic hill climbing runs Start for generation 2 (Here’s the genetic algorithm’s turn) Generation 2 How is this implemented? The idea behind VIPER
- 42. 41 Slide from Pawel Penczek How is this implemented? What does the R in RVIPER stand for? What do you get in the end? Sorted errors main0??: Full reproducible run run0??: individual VIPER run
- 43. RVIPER Reproducible initial 3D model
- 45. Another important requirement: even angular coverage, without major gaps.
- 46. What to do after running RVIPER 45 Handedness: You hav a 50% chance of getting the right handedness from a VIPER run. It should not matter for further image processing.
- 47. „Possible explanations for intermodel variations include the model resolution, different handedness of the electron density maps, rotational freedom of the NP molecules, and source of RNP samples (viral particles versus cells).“
- 48. Filter the reference at the proper resolution!
- 49. Defocus 1.0 μm 1.1 MDA EMD-2984 -nice distribution -collect small dataset -high defocus! -high dose! -state of the art picking -check quality of class averages Defocus 1.15 μm 464 kDa
- 51. Separate the sheeps from the goats! Avoid assumptions!
- 52. 51