1. Protein Structure Determination Part 2 -- X-ray Crystallography

4. The method CrystalsX-raysAtoms FT FT -1

5. EM versus x-ray electron microcope resolution ≈ 1nm de Broglie wavelength of e- ≈ size of atom transmitted light lensing possible, 10 6 x mag. 2D image w/tilt measures density. sample is thin section diffractometer resolution up to 0.1nm = 1Å wavelength ≈ size of atom scattered light no lens possible 3D reconstruction measures relative e- density sample is single crystal

6. X-ray diffractometer

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

8. Dimensions X-ray beam X-ray detector Beam width: ~0.20 mm Crystal thickness: 0.10-1.00 mm

9. X-ray detector Unit cell: ~100Å = 0.00001mm

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

11. N O CH 3 CC C C-C bond distance: 1.52Å Wavelength of Cu K  X-rays: 1.5418Å Dimensions

12. N O CH 3 CC C Angle of incidence=  : 0-90° Bragg plane separation distance (resolution): 0.7-50Å Dimensions

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

14. Electromagnetic spectrum Wavelength of X-rays used in crystallography: 1Å - 3Å (Å = 10 -10 m) most commonly 1.54Å (Cu ) Frequency = c/  =(3x10 8 m/s)  /(1.54x10 -10 m) ≈ 2x10 18 s -1

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

16. 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.

17. 10K+ reflections Moving the X-rays and the detector gives a new set of planes. Changing the angle of reflection changes the spacing (resolution).

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 Bragg's law Euler's theorem Reciprocol space Symmetry Fourier transform Inverse Fourier transform

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

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

23. Materials Gale Rhodes “Crystallography Made Crystal Clear” 3rd Ed. Academic Press graph paper straight edge protractor compass calculator w/trig functions http://www.bioinfo.rpi.edu/bystrc/courses/bcbp4870/bcbp4870.html