X-Ray Defraction Method for Determining the Three-Dimensional Structure of a Protein

The spacing of atoms in a crystal lattice can be determined
by measuring the locations and intensities
of spots produced on photographic film by a beam of
x rays of given wavelength, after the beam has been
diffracted by the electrons of the atoms. For example,
x-ray analysis of sodium chloride crystals shows that
Na and Cl ions are arranged in a simple cubic lattice.
The spacing of the different kinds of atoms in
complex organic molecules, even very large ones such
as proteins, can also be analyzed by x-ray diffraction
methods. However, the technique for analyzing crystals
of complex molecules is far more laborious than
for simple salt crystals. When the repeating pattern of
the crystal is a molecule as large as, say, a protein, the
numerous atoms in the molecule yield thousands of
diffraction spots that must be analyzed by computer.
The process may be understood at an elementary
level by considering how images are generated in a
light microscope. Light from a point source is focused
on an object. The light waves are scattered by the object,
and these scattered waves are recombined by a
series of lenses to generate an enlarged image of the
object. The smallest object whose structure can be
determined by such a system—that is, the resolving
power of the microscope—is determined by the
wavelength of the light, in this case visible light, with
wavelengths in the range of 400 to 700 nm. Objects
smaller than half the wavelength of the incident light
cannot be resolved. To resolve objects as small as proteins
we must use x rays, with wavelengths in the
range of 0.7 to 1.5 Å (0.07 to 0.15 nm). However, there
are no lenses that can recombine x rays to form an
image; instead the pattern of diffracted x rays is collected
directly and an image is reconstructed by mathematical
techniques.
The amount of information obtained from x-ray
crystallography depends on the degree of structural
order in the sample. Some important structural parameters
were obtained from early studies of the diffraction
patterns of the fibrous proteins arranged in
fairly regular arrays in hair and wool. However, the orderly
bundles formed by fibrous proteins are not
crystals—the molecules are aligned side by side, but
not all are oriented in the same direction. More detailed
three-dimensional structural information about
proteins requires a highly ordered protein crystal. Protein
crystallization is something of an empirical science,
and the structures of many important proteins
are not yet known, simply because they have proved
difficult to crystallize. Practitioners have compared
making protein crystals to holding together a stack of
bowling balls with cellophane tape.
Operationally, there are several steps in x-ray
structural analysis (Fig. 1). Once a crystal is obtained,
it is placed in an x-ray beam between the x-ray source
and a detector, and a regular array of spots called

 flections is generated. The spots are created by the
diffracted x-ray beam, and each atom in a molecule
makes a contribution to each spot. An electron-density
map of the protein is reconstructed from the overall
diffraction pattern of spots by using a mathematical
technique called a Fourier transform. In effect, the
computer acts as a “computational lens.” A model for
the structure is then built that is consistent with the
electron-density map.
John Kendrew found that the x-ray diffraction
pattern of crystalline myoglobin (isolated from muscles
of the sperm whale) is very complex, with nearly
25,000 reflections. Computer analysis of these reflections
took place in stages. The resolution improved at
each stage, until in 1959 the positions of virtually all
the non-hydrogen atoms in the protein had been determined.
The amino acid sequence of the protein, obtained
by chemical analysis, was consistent with the
molecular model. The structures of thousands of proteins,
many of them much more complex than myoglobin,
have since been determined to a similar level
of resolution.
The physical environment within a crystal, of
course, is not identical to that in solution or in a living
cell. A crystal imposes a space and time average
on the structure deduced from its analysis, and x-ray
diffraction studies provide little information about molecular
motion within the protein. The conformation
of proteins in a crystal could in principle also be affected
by non physiological factors such as incidental

protein-protein contacts within the crystal. However,
when structures derived from the analysis of crystals
are compared with structural information obtained by
other means (such as NMR ), the
crystal-derived structure almost always represents a
functional conformation of the protein. X-ray crystallography
can be applied successfully to proteins too
large to be structurally analyzed by NMR.