94 INSTRUMENTAL METHODS
refi nements can yield R - factors in the range of 10 – 20%. An example taken
from reference 11 is instructive. In a refi nement of a papain crystal at 1.65 - Å
resolution, 25,000 independent X - ray refl ections were measured. Parameters
to be refi ned were the positional parameters ( x , y , and z ) and one isotropic
temperature factor parameter ( B ) for each of the 2000 nonhydrogen atoms in
the molecule. Four times 2000 yields 8000 parameters. With 25,000 measure-
ments the ratio of observations to parameters is slightly more than 3, a poor
(low) overdetermination. Incorporating bond length and angle data from the
known dimensions of small molecules increases the number of “ observations. ”
Another technique, called “ solvent fl attening, ” which adjusts for disordered
solvent molecules in the channels between protein molecules, is imposed. In
all cases, because protein structures are large and complex, their refi nement
is a large project computationally requiring fast computers and application of
fast Fourier transform methods. Application of refi nement to the papain struc-
ture would probably result in anR - factor of about 16% (usually reported as
a decimal, i.e., R = 0.16). Application of refi nement methods cannot completely
rule out wrong interpretations of electron density maps and consequent
entirely or partially incorrect protein structures. A number of checks for gross
errors are available including stereochemistry checks for detailed analysis of
protein geometry. One of these, PROCHECK, 17a,b information at the website
http://www.biochem.ucl.ac.uk/ ∼ roman/procheck/procheck.html , conducts a
detailed analysis of all geometric aspects of proteins using data extracted from
the Cambridge Crystallographic Data Centre ( http://www.ccdc.cam.ac.uk ) for
bond lengths, angles, and planarity in peptide structures. For torsion angles,
PROCHECK uses comparison data from high - resolution protein structures in
the Protein Data Bank (PDB; http://www.rcsb.org/pdb/home/home.do ).
The hardware necessary for collection of X - ray diffraction data includes an
X - ray source and X - ray detector. Most commonly in research laboratories, the
X - ray radiation is emitted from a copper source, Cu K α radiation, with a
wavelength of 1.5418 Å. X - ray sources include sealed X - ray tubes and the
more powerful, more usual system for small proteins, a tube with a rotating
anode — that is, a rotating anode generator. Protein crystallography benefi ts
from use of the rotating anode tube because the X rays emitted are of
higher intensity. The rotating anode generator requires maintenance of high
vacuum.
The most powerful X - ray source, a particle accelerator such as a synchro-
tron, also called a storage ring, requires the construction of a large and expen-
sive facility. Extremely high - intensity, collimated synchrotron radiation is of
value when collecting data from weakly diffracting crystals as well as proteins
consisting of more than 150 – 200 amino acid residues. A synchrotron is essen-
tially an accelerator that takes stationary charged particles, such as electrons,
and drives them to velocities near the speed of light. Strong magnets arranged
in particular arrays force electrons to travel around a circular storage ring,
tangentially emitting electromagnetic radiation and, consequently, losing
energy. This energy is emitted in the form of light and is known as synchrotron