Crystal Diffraction pattern

Electron density map

Atomic structure model

X-ray PhasingModel

building

Macromolecular crystallography

What we can get from the structures of biological macromolecules?

1. Interaction of protein-protein or protein-biomolecule

2. Mechanism of enzyme

3. Mechanisms of biological functions

4. Drug design

5. Bases for molecular dynamics simulations, protein design and engineering

http://www.ibric.org/myboard/print.php?Board=report&id=2311

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

102,863 structures (2014. 8. 26) are deposited in PDBAmong those, 88.7 % are X-ray crystal structures, 10.3 % are solved by NMR and 0.8 % are by EM

Structures of biological macromolecules

Crystallization of macromolecule (protein)

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

X-ray diffraction; special case of x-ray scattering

X-rays: 0.1 Å < λ < 1000 Å (1 Å = 10-10 m = 100 pm = 0.1 nm)atomic distances (d): ~ 1.5 ÅEx) visible light; 400 - 700 nm

Maximum resolution of diffraction data can be determined by y/D (θ); dmin=mλD/ymax

X-ray diffraction; crystal vs diffraction pattern

2D crystal Diffraction pattern

2D crystal Fourier transform

Reciprocal relationship

Reciprocal relationship

Structure of molecule in crystal can be determined from diffraction pattern by Fourier transformation

Calculating electron density; Fourier transformation

Intensity of

diffraction spot

Electron density

Structure factor

Electron density

Electron density

Phase

Fourier transformh,k,l=reciprocal latticex,y,z=coordinate of real space

Now Phase problem!!!

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)

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

Vector presentation of structure factor

FPH = FP + FH

Multiple isomorphous replacement (MIR)

FPH FP FH

First derivative second derivative

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)

Molecular Replacement (MR)

• With using similar structure, calculating phase of unknown structure

How can I confirm that I solve the right structure in MR?

+ =

FT

Model building and refinement

Resolution vs Model

Validation of structure

• R-factor represents the ideality of the model

• R-free represents the correlation of model with experimental data (electron density)

• 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