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Pattersons

Learn about the phase problem in crystallography and the methods used to solve it. Explore the different spaces of crystallography and how to create a Patterson map. Discover major phasing techniques and the importance of phases and amplitudes in crystallographic analysis.

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Pattersons

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  1. Pattersons The “third space” of crystallography

  2. The “phase problem”

  3. The “phase problem” Phases Amplitudes

  4. The “phase problem” Phases 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. scattering detector detector x-ray beam sample

  7. How to make a Patterson map: • Set all phases to zero • Square all structure factors • Calculate Fourier transform

  8. One atom in unit cell Electron density Fraction across unit cell

  9. Patterson: one atom Electron density Fraction across unit cell

  10. Patterson: one atom Electron density Fraction across unit cell

  11. Patterson: one atom Electron density Fraction across unit cell

  12. Patterson: two atoms Electron density Fraction across unit cell

  13. Patterson: three atoms Electron density Fraction across unit cell

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

  15. Patterson: five atoms Electron density Fraction across unit cell

  16. Patterson: five atoms Electron density Fraction across unit cell

  17. scattering from a structure sample detector

  18. forward Fourier Transform inverse Fourier Transform no phase Patterson map!

  19. Snapshot from single virus particle 200 nm Reconstructed image 2 keV LCLS 200 fs Mimi virus single-shot. Resolution 20nm TEM Seibert, et al. (2011). Nature470, 78-81.

  20. lysozyme: real and reciprocal

  21. forward Fourier Transform 9 atoms

  22. forward Fourier Transform 10 atoms

  23. Patterson map 10 atoms

  24. Patterson map 9 atoms

  25. Difference Patterson Still no phases!

  26. forward Fourier Transform 9 atoms

  27. Harker Section of a Patterson

  28. X-ray data are 3D!

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

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

  31. Major Phasing techniques • Molecular Replacement • Multiple Isomorphous Replacement • Anomalous Diffraction • Direct methods

  32. 2Fo-Fc maps Electron density Fraction across unit cell

  33. 2Fo-Fc maps Electron density Fraction across unit cell

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

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

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

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

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

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

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

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

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

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

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

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

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

  47. The “phase problem” Phases Amplitudes Fobs

  48. The “phase problem” Phases & Amplitudes Amplitudes Fobs-Fcalc

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