1 / 50

X-ray Crystallography: Theory and Practice

X-ray Crystallography: Theory and Practice. October 3, 5 2006. Examples of translational symmetry. Identity operation. Two-fold symmetry operation. Three-fold symmetry operation. Four-fold symmetry operation. Six-fold symmetry operation. Screw axis = Rotational + Translational symmetry.

dannon
Download Presentation

X-ray Crystallography: Theory and Practice

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. X-ray Crystallography: Theory and Practice October 3, 5 2006

  2. Examples of translational symmetry

  3. Identity operation

  4. Two-fold symmetry operation

  5. Three-fold symmetry operation

  6. Four-fold symmetry operation

  7. Six-fold symmetry operation

  8. Screw axis = Rotational + Translational symmetry

  9. Plane groups-pmm

  10. Examples of how to define a unit cell

  11. Unit Cell Convention

  12. Symmetry symbols

  13. Crystal Systems

  14. Space groups Example from International Tables for Crystallography, Volume A

  15. Diffraction pattern of a duck

  16. A) narrow slit B) wider slit Diffraction from a slit: Illustration of reciprocal relationship

  17. Diffraction from lines: Illustration of a reciprocal lattice

  18. Optical diffraction • lattice • 1 molecule • 2 molecules • 4 molecules • row of 6 molecules • a small crystal

  19. Example of resolution

  20. Effect of series termination

  21. To see features on the order of the distance between atoms: 10-10 meters. We can’t focus enough X-rays into a small enough volume to “see” a single molecule. Even if we could, the X-rays would burn up the molecule. Why X-rays? Why crystals?

  22. Light microscopy vs. X-ray crystallography

  23. Bragg’s Law n = 2d sin • 2 is the angle between incident and reflected beams • d is the spacing between planes •  is the wavelength • n is the order of diffraction

  24. Example of X-ray diffraction from a protein crystal

  25. Precession photographs of protein crystals trp repressor, two different crystal forms

  26. Example of a reflection file H K L intensity error 0 0 12 6714.3 347.2 0 0 18 -8.9 16.3 0 0 24 979.5 62.4 0 0 30 4136.4 272.5 1 0 3 3035.4 70.2 1 0 4 0.0 0.7 1 0 5 0.1 0.6 1 0 6 838.4 20.4 1 0 7 14903.0 535.6 1 0 8 2759.4 64.7 1 0 9 1403.5 31.0 1 0 10 109.4 5.6 1 0 11 31739.5 1611.5 1 0 12 231.9 7.6 1 0 13 5433.0 94.3 1 0 14 12392.7 211.4 1 0 15 3470.8 53.1 1 0 16 37.0 5.1 1 0 17 602.4 19.7 1 0 18 154.4 6.7 ...etc.

  27. ρ(x,y,z) =1/VΣhklFhkle-2πi (hx + ky +lz) Reflection indices of experimental measurements Fhkl= |Fhkl|e2πi Φhkl Phase: must be estimated Amplitude: from experimental measurements Electron density calculation

  28. Electron density: low resolution

  29. Electron density: higher resolution

  30. X-ray vs. neutron crystallography • H/D atoms are invisible to X-rays

  31. Crystal Structure Pipeline Hypothesis Driven Target Selection Data Collection Structure Determination Publication Crystallomics Data Deposition Data Release Isolation, Expression, Purification,Crystallization

  32. Crystallization Methods

  33. Vapor diffusion

  34. Protein Crystals

  35. Crystal Mounting

  36. Sealed Tube Diffractometer Rutgers Chemistry and Chemical Biology X-ray Lab

  37. Sealed Tube Diffractometer (detail)

  38. Rotating Anode Diffractometer Rutgers/UMDNJ Macromolecular Crystallography X-ray Lab

  39. Rotating Anode Tower, Mirror Optics

  40. Rotating Anode (Copper)

  41. Synchrotron X-ray source National Synchrotron Light Source, Brookhaven National Laboratory, Long Island, NY

  42. Synchrotron Beamline Diffractometer

  43. Phasing • MIR • Molecular Replacement • MAD/SAD

  44. MIR

  45. Map fitting

  46. Resolution Redux

  47. Atomic coordinate file: X Y Z occ B ATOM 1 N GLN R 3 17.162 56.613 0.758 1.00 45.23 ATOM 2 CA GLN R 3 15.963 56.074 1.482 1.00 45.50 ATOM 3 C GLN R 3 15.837 56.582 2.910 1.00 45.28 ATOM 4 O GLN R 3 14.829 57.247 3.245 1.00 45.08 Etc… 3D: Structural Data from a crystallographic experiment

  48. Statistical Table from a crystallographic experiment

  49. Structure Validation Example: Ramachandran Plot

  50. References Bernal, Hamilton, & Ricci. Symmetry: A Stereoscopic Guide for Chemists. W. H. Freeman and Company, 1972, pp. 44-45, 48, 50, 52. Blundell, T. L. Protein Crystallography. Academic Press, 1976, pp. 84, 113-114, 118. Glusker, J. & Trueblood, K. Crystal Structure Analysis: A Primer. Oxford University Press, 1985, pp. 4-5, 12, 22, 44, 94, 200. Holmes, K.C. and Blow, D. M. The Use of X-ray Diffraction in the Study of Protein and Nucleic Acid Structures. Robert E. Kreeger Publishing Company, 1980, p. 120. http://www.bmsc.washington.edu/people/merritt/bc530/bragg/ (try the Java Applet) Macgillavry, C. Symmetry Aspects of M. C. Escher’s Periodic Drawings. Bohn, Scheltema & Holkema, Utrecht, 1976, pp. 5, 11. McPherson, A. Crystallization of Biological Macromolecules. Cold Spring Harbor Laboratory Press, 1999, pp. 164, 179, 185. Rhodes, Gale. Crystallography Made Crystal Clear. Academic Press, Inc, 1993, plate 7.

More Related