1. Atomic structure model
Macromolecular crystallography
Model building
X-ray
Phasing
Crystal
Diffraction pattern
Electron density map
Atomic structure model

2. What we can get from the structures of biological macromolecules?
Interaction of protein-protein or protein-biomolecule
Mechanism of enzyme
Mechanisms of biological functions
Drug design
Bases for molecular dynamics simulations, protein design and engineering

3. The History of X-Ray Crystallography in the Eyes of Nobel Prizes

4. Structures of biological macromolecules
102,863 structures ( ) are deposited in PDB
Among those, 88.7 % are X-ray crystal structures, 10.3 % are solved by NMR and 0.8 % are by EM

5. Crystallization of macromolecule (protein)

6. What really looks like inside of crystal?
3X3 2D grid of protein crystal
Black box; unit cell
Red box; asymmetric unit
Infinite extension of unit cell on XYZ axis
Empty space are filled with solvent (water)
Average solvent contents of protein crystals
; 50% more or less

7. X-ray diffraction; special case of x-ray scattering
(1 Å = m = 100 pm = 0.1 nm)
atomic distances (d): ~ 1.5 Å
Ex) visible light; nm
Maximum resolution of diffraction data can be determined by y/D (θ); dmin=mλD/ymax

8. X-ray diffraction; crystal vs diffraction pattern
2D crystal
Diffraction pattern
Reciprocal relationship
2D crystal
Fourier transform
Reciprocal relationship
Structure of molecule in crystal can be determined from diffraction pattern by Fourier transformation

9. Intensity of diffraction spot
Calculating electron density; Fourier transformation
Structure factor
Electron density
h,k,l=reciprocal lattice
x,y,z=coordinate of real space
Fourier transform
Electron density
Intensity of diffraction spot
Phase
Electron density
Now Phase problem!!!

11. Patterson function; interatomic relationship within the unit cell
Calculation of x,y,z coordinates of atoms is possible in special position of Patterson space (u,v,w), where u, v, or w has defined value (0, 1, 1/n etc. ; Harker section)
Indeed, it is possible to determine all the positions of atoms when the number of atoms are enough small and distinguishable ( < 100 and high difference in electron density)
But in case of protein, atoms are usually more than 1000 and the differences of electron densities are not distinguishable (C, N, O, S)

12. What if we can have distinguishable atoms in protein crystal?
Patterson map of heavy atom derivative
Heavy atoms such as Hg, Au, Ag, Ur Pt can bind to the protein with some degree of specificity without disturbing structure or crystal packing in certain conditions
Amplitude of heavy atom in FH can be obtained from experiment
With the known electron density and coordinate obtained from Patterson function, Phase of heavy atom can be calculated

13. Vector presentation of structure factor
FPH = FP + FH

14. Multiple isomorphous replacement (MIR)
FPH FP FH
First derivative
second derivative

15. Multiple anomalous dispersion (MAD)
incident photon with relatively low energy
incident photon with high enough energy
Anomalous scattering maximized at absorption wavelength
Synchrotron is needed for tunable wavelength
Due to the Se-methionine derivate generation by auxotroph, most of the novel structures solved recently by MAD (SAD)

16. Molecular Replacement (MR)
With using similar structure, calculating phase of unknown structure

17. How can I confirm that I solve the right structure in MR?FT + =

18. Model building and refinement

19. Resolution vs Model

20. Validation of structure
R-factor represents the ideality of the model
R-free represents the correlation of model with experimental data (electron density)

21. Validation of stereochemical ideality of model
Residues should not be in disallowed region (white) when the resolution of map is better than 3.0 A