Macromolecular crystallography
X-ray
Crystal
Model
building
Phasing
Diffraction
pattern
Electron density
map
Atomic structure
model
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
The History of X-Ray Crystallography in the Eyes of Nobel Prizes
http://www.ibric.org/myboard/print.php?Board=report&id=2311
Structures of biological macromolecules
102,863 structures (2014. 8. 26) 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
Crystallization of macromolecule (protein)
What really looks like inside of crystal?
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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 Å
Ex) 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
Diffraction pattern
2D crystal
Reciprocal
relationship
Fourier transform
2D crystal
Reciprocal
relationship
Structure of molecule in crystal can be determined from
diffraction pattern by Fourier transformation
Calculating electron density; Fourier transformation
Structure factor
Electron
density
h,k,l=reciprocal lattice
x,y,z=coordinate of real space
Electron
density
Fourier transform
Intensity of
diffraction
spot
Phase
Electron density
Now Phase problem!!!
Patterson function; interatomic relationship within the unit cell
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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)
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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)
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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
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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
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Amplitude of heavy atom in FH can be
obtained from experiment
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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
First derivative
FP
FH
second derivative
Multiple anomalous dispersion (MAD)
incident photon with relatively low energy
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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
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R-factor represents the ideality of the model
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R-free represents the correlation of model with experimental data (electron density)
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Validation of stereochemical
ideality of model
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Residues should not be in
disallowed region (white)
when the resolution of map is
better than 3.0 A