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Pattersons The “third space” of crystallography. The “phase problem”

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Presentation on theme: "Pattersons The “third space” of crystallography. The “phase problem”"— Presentation transcript:

1 Pattersons The “third space” of crystallography

2 The “phase problem”

3 PhasesPhases Amplitudes

4 The “phase problem” PhasesPhases Amplitudes

5 The “spaces” of crystallography Direct/real space –Distances are in Å, Angles are in degrees Reciprocal space –Distances in 1/Å, Angles are different Patterson space –Distances are in Å, Angles are in degrees –Relative distances only, origin lost –“direction” is preserved

6 detector sample detector x-ray beam scattering

7

8

9 How to make a Patterson map: 1.Set all phases to zero 2.Square all structure factors 3.Calculate Fourier transform

10 One atom in unit cell Fraction across unit cell Electron density

11 Patterson: one atom Fraction across unit cell Electron density

12 Patterson: one atom Fraction across unit cell Electron density

13 Patterson: one atom Fraction across unit cell Electron density

14 Patterson: two atoms Fraction across unit cell Electron density

15 Patterson: three atoms Fraction across unit cell Electron density

16 Patterson: three atoms Fraction across unit cell Electron density Better resolution!

17 Patterson: five atoms Fraction across unit cell Electron density

18 Patterson: five atoms Fraction across unit cell Electron density

19 scattering from a structure sample detector

20 forward Fourier Transforminverse Fourier Transform no phase Patterson map!

21 Snapshot from single virus particle TEM 2 keV LCLS 200 fs Mimi virus single-shot. 200 nm Reconstructed image Resolution 20nm Seibert, et al. (2011). Nature 470, 78-81.

22 lysozyme: real and reciprocal

23 forward Fourier Transform 9 atoms

24 forward Fourier Transform 10 atoms

25 Patterson map 10 atoms

26 Patterson map 9 atoms

27 Difference Patterson Still no phases!

28 forward Fourier Transform 9 atoms

29 Harker Section of a Patterson

30 X-ray data are 3D!

31 Patterson: five atoms + 3-fold symmetry Fraction across unit cell Electron density

32 Patterson: five atoms + 3-fold symmetry Fraction across unit cell Electron density

33 Major Phasing techniques Molecular Replacement Multiple Isomorphous Replacement Anomalous Diffraction Direct methods

34 2Fo-Fc maps Fraction across unit cell Electron density

35 2Fo-Fc maps Fraction across unit cell Electron density

36 2Fo-Fc maps Fraction across unit cell Electron density

37 2Fo-Fc maps Fraction across unit cell Electron density

38 2Fo-Fc maps Fraction across unit cell Electron density

39 2Fo-Fc maps Fraction across unit cell Electron density

40 2Fo-Fc maps Fraction across unit cell Electron density

41 2Fo-Fc maps Fraction across unit cell Electron density

42 2Fo-Fc maps Fraction across unit cell Electron density

43 2Fo-Fc maps Fraction across unit cell Electron density

44 2Fo-Fc maps Fraction across unit cell Electron density

45 2Fo-Fc maps Fraction across unit cell Electron density

46 2Fo-Fc maps Fraction across unit cell Electron density

47 2Fo-Fc maps Fraction across unit cell Electron density

48 2Fo-Fc maps Fraction across unit cell Electron density

49 The “phase problem” PhasesPhases Amplitudes F obs

50 The “phase problem” Phases & Amplitudes Amplitudes F obs -F calc

51 The “phase problem” Phases & Amplitudes Amplitudes 2F obs -F calc

52 The “phase problem” PhasesPhases Amplitudes

53 The “phase problem” Phases & Amplitudes Amplitudes 2F obs -F calc

54 The “phase problem” Phases & Amplitudes Amplitudes 2mF obs -F calc (  A weighting)

55 sample x-ray beam anomalous scattering detector

56 sample detector x-ray beam anomalous scattering

57 sample x-ray beam anomalous scattering detector

58 sample detector x-ray beam anomalous scattering

59 sample detector x-ray beam anomalous scattering

60 Harker Section of a Patterson

61 Summary Patterson = real-space representation of all information in diffraction pattern “small”, high-resolution structures solved with no phases! Difference Pattersons for finding heavy atom sites Native Patterson for symmetry

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