1. Protein Structure Determination
Part 1 --
X-ray Crystallography

4. The method
FT-1 FT
Crystals
X-rays
Atoms

5. microscope versus diffractometer
wavelength ≈ size of cell
transmitted light
lenses
2D image
measures relative absorbance
image composed of pixels
sample is thin section
wavelength ≈ size of atom
scattered light
no lenses possible
0D images, 3D construction
measures relative e-density
composed of structure factors (waves)
sample is thick crystal

6. Experimental setup
X-ray detector
X-ray source
beam stop

7. Dimensions X-ray detector X-ray beam Beam width: ~0.20 mm
Crystal thickness: mm

8. X-ray detector
Unit cell: ~100Å = mm

9. Typical protein molecule: ~30Å = 0.000003 mm

10. Dimensions C-C bond distance: 1.52Å N O CH3 C C
Wavelength of Cu K X-rays: Å

11. Dimensions N O CH3 C C Angle of incidence=: 0-90°
Bragg plane separation distance (resolution): Å

12. X-rays see e- as if they were standing still.
Dimensions C
Carbon atom C
amount an electron
moves in one xray cycle
X-rays see e- as if they were standing still.

13. Electromagnetic spectrum
Wavelength of X-rays used in crystallography: 1Å - 3Å (Å = 10-10m) most commonly 1.54Å (Cu )
Frequency = c/ =(3x108m/s) /(1.54x10-10m) ≈ 2x1018 s-1

14. oscillating e- scatter X-rays
…in all direction.
oscillation e-
emission

15. Reflection planes The “amplitude” of scattering is measured.
The amplitude is proportional to the differences of e- density in the direction of “reflection planes”
The orientation and separation of reflection planes is determined by the directions of the incoming and scattered rays.

16. 10K+ reflections
Moving the X-rays and the detector gives a new set of planes.
Changing the angle of reflection changes the spacing (resolution).

17. X-ray diffractometer

18. Reconstruction of e- density
The density at every point in the crystal is calculated by summing over all of the density waves.

19. Topics covering in this course
Crystal growth
Diffraction theory
Symmetry
Experimental methods
Interpretation of data
Software

20. Equations you will need to know
Euler's theorem
Bragg's law
Reciprocol space
Symmetry
Fourier transform
Inverse Fourier transform

21. How to know that you know
all terms defined
physical/geometric interpretation

22. Supplementary reading
Matrix algebra
“An Introduction to Matrices, Sets and Groups for Science Students”
by G. Stephenson ($7.95)
Wave physics
“Physics for Scientists and Engineers” by Paul A. Tipler
Protein structure
“Introduction to Protein Structure”-- by Carl-Ivar Branden and John Tooze
“Introduction to Protein Architecture : The Structural Biology of Proteins” -- by Arthur M. Lesk

23. Materials Gale Rhodes “Crystallography Made Crystal Clear”
3rd Ed. Academic Press
graph paper
straight edge
protractor
compass
calculator w/trig functions