1. Electron crystallographic methods of solving modulated structures Electron microscopy X-ray crystallography Direct methods Pseudo translational symmetries Dealing with pseudo symmetries Two-stage image processing in Electron microscopy Translational phase ambiguity Ab initio solution of superstructures Ab initio solution of modulated and composite structures Acting as a tool of image processing Pseudo centro symmetry Enantiomorphous phase ambiguity Protein SAD/SIR phasing Protein model completion

2. 电子显微学 X - 射线晶体学 直接法 赝平移对称 处理赝对称性 两步法电子 显微学图像处理 超结构 从头求解 用于图像处理 赝中心对称 蛋白质 SAD/SIR 相位推演 蛋白质 模型完整化 电子晶体学方法 求解调制结构 从头测定调制结构 和组合结构

3. Initial phasing and Model completion of Proteins Image processing in Electron Microscopy Software Modulated and Composite structures

6. Enantiomorphous phase ambiguity resolved by the direct method Sample: ZCW; Space group: P2 1 Acta Phys. Sin. 27, 169-174 (1978) Enantiomorphous phase ambiguity resolved by the direct method Direct method result Final map a c b c b c K Before treatment After treatment

7. X-ray Crystallography Objective lens Back focal plane Image plane Object Diffraction pattern Blurred image Fourier transform Fourier transform Electron microscopy Object Patterson map Diffraction pattern Diffraction wave front

8. Object Patterson map Diffraction wave front Diffraction pattern X-ray Crystallography Multiplied with F* h Objective lens Back focal plane Image plane Object Diffraction pattern Blurred image Multiplied with a contrast transfer function Fourier transform Fourier transform Electron microscopy Structure image blurred by convoluting with the Fourier transform of a contrast transfer function Structure image blurred by convoluting with It’s inverse

9. Object Patterson map Diffraction wave front Diffraction pattern X-ray Crystallography Multiplied with F* h Objective lens Back focal plane Image plane Object Diffraction pattern Blurred image Multiplied with a contrast transfer function Fourier transform In the derivation of X-ray diffraction phases, direct methods are acting as a tool of image processing. They convert the blurred image  Patterson map  to the deblurred image  electron density map. It is reasonable to expect that direct methods can be used in high-resolu- tion electron micro- scopy as a tool of image processing. Fourier transform Electron microscopy

14.  <F ><F > F oF o A B F” F’ ””      ’’  F” F *F * Phase ambiguity intrinsic in SAD F F 

15. A B  N  FRFR FDFD FNFN  D  Phase ambiguity intrinsic in SIR DD RR RR    D NN    N

16. – SAD phase doublet

17. D – derivative, R – replacing atoms, N – native – SIR phase doublet

18. Breaking SAD/SIR phase ambiguity by direct methods

19. SAD/SIR data P + (  h ) = 1/2 End Calculate P + (  h ) E h,  ’ h,  h  Calculate m h and  h,best

21. Lysozyme Space group: P4 3 2 1 2 Unit cell: a = 78.4, c = 37.0Å Number of residues in the ASU: 129 Resolution limit: 2.01Å; Multiplicity: 47.2 Anomalous scatterer: S (10 ) X-rays: Cr-K  = 2.291Å,  f ” = 1.14 Bijvoet ratio: / = 2.4% Data provided by Prof. Isao Tanaka and Dr. Nobuhisa Watanabe

22. Azurin Space group: P4 1 22 Unit cell: a = b = 52.65, c = 100.63Å Number of residues in the ASU: 129 Resolution limit: 1.9Å Multiplicity: 10.0 Anomalous scatterer: Cu (1) X-rays: synchrotron radiation  = 0.97Å  f” = 2.206 Bijvoet ratio: / = 1.44% Data provided by Prof. S. Hasnain

23. Xylanase Space group: P2 1 Unit cell: a = 41.07, b = 67.14, c = 50.81Å  = 113.5 o Number of residues in the ASU: 303 Resolution limit: 1.75Å; Multiplicity: 15.9 Anomalous scatterer: S (5 ) X-rays:  synchrotron radiation  = 1.488Å;  f ” = 0.52 Bijvoet ratio: / = 0.56% Data courtesy of Dr. Z. Dauter, National Cancer Institute, USA

24. Alanine racemase Space group: C 2 2 2 1 Unit cell: a = 72.68 b = 76.13, c = 136.27Å Number of residues in the ASU: 357 Resolution limit: 2.3Å Data collection range: 360 o Anomalous scatterer: Se (8), S (6), P (1) X-rays: Cr-K , = 2.291Å Bijvoet ratio: / = 2.8% Data provided by Dr. Cheng Yang

25. Alanine racemase Space group: C 2 2 2 1 Unit cell: a = 72.68 b = 76.13, c = 136.27Å Number of residues in the ASU: 357 Resolution limit: 2.3Å Data collection range: 360 o Anomalous scatterer: Se (8), S (6), P (1) X-rays: Cr-K , = 2.291Å Bijvoet ratio: / = 2.8% Data provided by Dr. Cheng Yang

26. SIR SOLVE/RESOLVE + OASIS/DM SOLVE/RESOLVE

27. SAD SOLVE/RESOLVE + OASIS/DM

28. SIR SOLVE/RESOLVE + OASIS/DM SIR SOLVE/RESOLVE SAD SOLVE/RESOLVE + OASIS/DM

29. SOLVE/RESOLVE + OASIS/DM SOLVE/RESOLVE SAD SOLVE/RESOLVE + OASIS/DM

30. 2.1Å 3.0Å 3.5Å 4.0Å