from lower resolution structures—many of the hydro-
gen atoms, alternate conformations, and distinc-
tions between oxygen and nitrogen atoms. Direct
observation of hydrogen bonds is especially valuable
for enzymologists, as is resolving ambiguities about
the orientations of Asn, Gln, and His. As more high-
resolution structures are completed, it should be
possible to document true deviations of geometries
from the canonical values embedded in restraint
libraries. The example shown in Figure 2 illustrates
the clear definition of densities corresponding to
individual atoms and the assignments of hydrogens
from difference maps.
Displaying and Comparing
Structures
The computing power of current desktop machines
allows the non-crystallographer to display and analyze
structures that have been deposited in the Protein Data
Bank. Particularly useful features of available programs
are algorithms that align structures for comparisons of
conformations, facile analysis of noncovalent inter-
actions, routines for mutation and model building, and
the capability to generate illustrations in a variety of
styles.
SEE ALSO THE FOLLOWING ARTICLES
Imaging Methods † Protein Data Resources † Second-
ary Structure in Protein Analysis
GLOSSARY
asymmetric unit The smallest motif from which the crystal can be
generated by translation and rotation operations. The unit cell that
is repeated by translation to form the crystal may contain a number
of asymmetric units.
isomorphism When addition of a ligand or heavy atom does not alter
the scattering contribution (structure factor) of the protein atoms,
the derivative and native crystals are said to be isomorphous. Cell
dimensions are expected to be unchanged.
non-crystallographic symmetry (NCS) When the asymmetric unit
includes more than one copy of a polypeptide, the multiple copies
are related by local coordinate transformations that do not obey the
symmetries that define the space group.
structure factor A vector F with phase
a
h,k,l
whose length lFl is
the amplitude of the reflection h, k, l. The structure factor is the
resultant of summing over scattering contributions from all
the atoms in the asymmetric unit and can be calculated from the
atom parameters. Fourier transformation of the structure factors
yields the electron density.
temperature factor (displacement parameter) A measure of the
motion of an atom about its equilibrium position. Temperature
factors may be isotropic (B-values) or anisotropic. In the general
anisotropic case, six parameters are required to describe the
displacements.
FURTHER READING
Baldwin, J., and Chothia, C. (1979). Hemoglobin: the structural
changes related to ligand binding and its allosteric mechanism.
J. Mol. Biol. 129, 183–191.
Bru
¨
nger, A. T., Adams, P. D., and Rice, L. M. (1999). Annealing in
crystallography: A powerful optimization tool. Prog. Biophys.
Mol. Biol. 72, 135–155.
Carter, C. W., Jr., and Sweet, R. M. (eds.) (1997). Macromolecular
Crystallography, Parts A and B. Methods in Enzymology, Vols 276
and 277. Academic Press, San Diego.
Cruickshank, D. W. (1999). Remarks about protein structure
precision. Acta Crystallogr. D55, 583–601.
Drenth, J. (1999). Principles of Protein Crystallography. Springer-
Verlag, New York.
Garman,E.F.,andSchneider,T.R.(1997).Macromolecular
cryocrystallography. J. Appl. Cryst. 30, 211– 237.
Guex, N., and Peitsch, M. C. (1997). SWISS MODEL and the Swiss-
PdbViewer: An environment for comparative protein modeling.
Electrophoresis 18, 2714–2723.
Kleywegt, G. J. (2000). Validation of protein crystal structures. Acta
Crystallogr. D56, 249–265.
Moffat, K. (2001). Time-resolved biochemical crystallography: A
mechanistic perspective. Chem. Rev. 101, 1569–1581.
Rossmann, M. G., and Arnold, E. (eds.) (2001). Crystallography of
Biological Macromolecules, International Tables for Crystal-
lography, Vol F. Kluwer Academic Publishers, Dordrecht.
Schlichting, I., Berendzen, J., Chu, K., Stock, A. M., Maves, S. A.,
Benson, D. E., Sweet, R. M., Ringe, D., Petsko, G. A., and Sligar,
S. G. (2000). The catalytic pathway of cytochrome P450cam at
atomic resolution. Science 287, 1615–1622.
Stoddard, B. L. (2001). Trapping reaction intermediates in
macromolecular crystals for structural analyses. Methods 24,
125–138.
Stryer, L., Kendrew, J. C., and Watson, H. C. (1964). The mode of
attachment of the azide ion to sperm whole methemoglobin. J. Mol.
Biol. 8, 96 –104.
Terwilliger, T. C., and Berendzen, J. (1999). Automated
MAD and MIR structure solution. Acta Crystallogr. D55,
849–861.
BIOGRAPHY
Martha L. Ludwig is Professor of Biological Chemistry and Research
Biophysicist at the University of Michigan in Ann Arbor. She is an
X-ray crystallographer whose primary research interest is the structure
and function of enzymes that require metal- and vitamin-based
cofactors. She is a Fellow of the American Association for the
Advancement of Science and a member of the National Academy
of Sciences.
428 X-RAY DETERMINATION OF 3-D STRUCTURE IN PROTEINS