BIOINORGANIC CHEMISTRY A Short Course Second Edition

X-RAY CRYSTALLOGRAPHY 93

synchrotron radiation. Anomalous scattering occurs when the electrons

in atoms can no longer be considered free electrons, but rather electrons

affected by the X rays themselves. The effect is negligible for light atoms

C, N, and O but becomes useful for heavier atoms (S onwards). Anoma-

lous scattering can be exploited for protein phase angle determination

by the multiple wavelength anomalous dispersion (MAD) method.

Determination of the absolute confi guration of a protein structure is also

possible.

3. The molecular replacement method assumes similarity of the unknown
   structure to a known one. This is the most rapid method but requires the
   availability of a homologous (similar) protein ’ s structure. The method
   relies on the observation that proteins that are similar in their amino
   acid sequence (homologous) will have very similar folding of their poly-
   peptide chains. This method also relies on the use of Patterson functions.
   As the number of protein structure determinations has been increasing
   rapidly, the molecular replacement method becomes extremely useful
   for determining protein phase angles.


4. The so - called direct methods rely on the principles that phase informa-
   tion is included in the intensities, that electron density is always positive,
   and that the crystal contains atoms that are or may be considered equal.
   Phase relations based on probability theory have been formulated and
   applied to clusters of refl ections. Direct methods are standard techniques
   for determining phase angles in smaller molecules ( < 100 atoms). Recent
   advances in theory by H. A. Hauptman of the Hauptman – Woodward
   Medical Research Institute and Department of Structural Biology,
   School of Medicine and Biomedical Sciences, State University of New
   York at Buffalo have allowed the structures of small proteins to be solved
   using the so - called Shake and Bake statistical method. In essence, the
   Shake and Bake method executes phase angle determination in small
   protein molecules by applying it to the strongest refl ections only. More
   information on this developing technique can be found in the reference
   18 articles and on the website http://www.psc.edu/science/Hauptman/
   Hauptman.html.

A preliminary structural model of a protein is arrived at using one of the
methods described above. Calculated structure factors, | Fcalc |, based on the
model generally are in poor agreement with the observed structure factors
|Fobs |. The agreement is represented by an R - factor defi ned as found in equa-
tion 3.11 , where k is a scale factor.

R

FkF

F

hkl

hkl

=

−

×

∑

∑

obs calc

obs

100 (3.11)

Refi nement takes place by adjusting the model to fi nd closer agreement
between the calculated and observed structure factors. For proteins the