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Analyzing M odel B ias in C ryo-EM S ingle- P article I mage P rocessing Shao- Hsuan Wang

COAUTHOR. Analyzing M odel B ias in C ryo-EM S ingle- P article I mage P rocessing Shao- Hsuan Wang Institute of Statistical Science, Academia Sinica. This is a joint work with. The Nobel Prize in Chemistry 2017. Yi-Ching Yao Institute of Statistical Science, Academia Sinica

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Analyzing M odel B ias in C ryo-EM S ingle- P article I mage P rocessing Shao- Hsuan Wang

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  1. COAUTHOR Analyzing Model Bias in Cryo-EM Single-Particle Image Processing • Shao-Hsuan Wang • Institute of Statistical Science, Academia Sinica This is a joint work with The Nobel Prize in Chemistry 2017 • Yi-Ching Yao • Institute of Statistical Science, Academia Sinica • Wei-Hau Chang • Institute of Chemistry, Academia Sinica • I-Ping Tu • Institute of Statistical Science, Academia Sinica NEWS for developing cryo-electron microscopy(Cryo-EM)

  2. Henderson R. (2013). Avoiding the pitfalls of single Particle Cryo-electron microscopy: Einstein from noise

  3. Model Bias Experiment Alignment using Cross Correlation(CC) Reference image • Model bias means that the final structure • is influenced by the initial model 1,000 Random images 1,000 Random images Average image

  4. Story behind the model bias experiment

  5. The questions are How does model bias happen? Can we construct a mathematical framework for model bias? Can we quantify model bias?

  6. OUTLINE Background of Cryo-EM Image Alignment and Model Bias Mathematical Framework for Model Bias Asymptotic Theory Simulation Results Overview

  7. OUTLINE Background of Cryo-EM Image Alignment and Model Bias Mathematical Framework for Model Bias Asymptotic Theory Simulation Results Overview

  8. Some proteins are thousands times smaller than a human hair Why do scientists favor Cryo-EM Human body

  9. How to solve the structures of small molecules?

  10. Why do scientists favor Cryo-EM X-ray Crystallography Crystallized Sample X-ray Electron-beam Frozen protein sample Not everything can be crystallized !!!! Cryo-EM

  11. The challenge of Cryo-EM micrograph

  12. The challenge of Cryo-EM

  13. Cryo-EM Analysis Flowchart Source: MRC Laboratory of Molecular Biology

  14. Cryo-EM Analysis Flowchart Single Particle Image Single Particle Image 2D Clustering 2D Clustering Motion、CTF Corrections Motion、CTF Corrections 3D Reconstruction 3D Reconstruction Initial Volume Initial Volume 3D Classification 3D Classification 3D Refinement 3D Refinement

  15. OUTLINE Background of Cryo-EM Image Alignment and Model Bias Mathematical Framework for Model Bias Asymptotic Theory Simulation Results Overview

  16. Image normalization

  17. Cross correlation, Similarity, and Alignment

  18. Cross correlation (CC) 2. for two normalized images 1. CC is a similarity measurement

  19. vec(X) vec(Y) X Y CC(X,Y) =

  20. X Y • Based on CC values, computers decide • whether images are similar or not Not Similar Similar • Align Y with Xmeans that rotate or • shift Y to maximize the CC(X,Y) -1.00 0.00 0.00 1.00 CC =

  21. How to remove noise from Cryo-EM images by using alignment ? micrograph

  22. Alignment and sort based on CC Reference image Average the Top m Align Average image Candidate particles Average

  23. Simplified Model Bias Experiment: 1. Set an image to be a reference image with size p 2. Generate a lot of random images which come from uniform distribution on (p-1)-dim sphere 3. No translation and rotation, compute CC between each random image and the reference 4. Sort these random images based CC values from high to low 5. Get average image of Top-m images

  24. Reference image Average The Top 100 Compute and sort based onCC Compute ?? Average image 2,000,000 Random images Average

  25. 2057of 2,000,000 images (CC > 0.03) • The first 6 largest CC values CC: .045 CC: .046 CC: .044 CC: .044 CC: .044 CC: .043

  26. 400 100 CC: 0.374 CC: 0.600 200 500 CC: 0.485 CC: 0.639 300 600 CC: 0.554 CC: 0.665

  27. Alignment and sort based on CC Reference image Average the Top m Align Average image Candidate particles Questionable!!! Average

  28. Different reference images

  29. How does model bias happen?

  30. OUTLINE Background of Cryo-EM Image Alignment and Model Bias Mathematical Framework for Model Bias Asymptotic Theory Simulation Results Overview

  31. How does model bias happen North pole Reference image Random image (p-2)-dim Equator

  32. The first m largest images

  33. The first m largest images Average

  34. Does model bias always happen when we average images ?

  35. Does model bias always happen when we average images ? m=1 m=100 m=600 m= ?

  36. Motivation ? (n , p, m) model bias

  37. OUTLINE Background of Cryo-EM Image Alignment and Model Bias Mathematical Framework for Model Bias Asymptotic Theory Simulation Results Overview

  38. Notation

  39. Model bias • We can use and to quantify • Model bias

  40. How to estimate and ?

  41. Model bias index:

  42. Example: Einstein from noise Our estimation Reference image (100 x 100) Cross Correlation (CC) function 600 CC: 0.665 Average image 2,000,000 Random images

  43. Convergence rate:

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