178 5.3  X-Ray Tools

crystallize due to the requirements of added solvating detergents affecting the process. In

addition, since the scattering is due to interaction with regions of high electron density, the

positions of hydrogen atoms in a structure cannot be observed by this method directly since

the electron density is too low, but rather, need to be inferred from knowledge of typical

bond lengths. Just as important, however, is the lack of real time-​resolved information of a

biological structure—​a crystal is very much a locked state. Since dynamics are essential to

biological processes, this is a significant disadvantage, although efforts can be made to infer

dynamics by investigating a variety of different locked intermediate states using crystallo­

graphic methods. Diffusing x-​ray scattering from amorphous samples (see in the following

text) can circumvent some of the issues encountered earlier regarding the use of crystals, since

they can reveal some information about protein dynamics, albeit under nonphysiological

conditions.

5.3.3  X-​RAY DIFFRACTION BY NONCRYSTALLINE SAMPLES

X-​ray diffraction can also be performed on a powder if it is not possible to grow sufficiently

large 3D crystals. A suitable powder is not entirely amorphous but is composed of multiple

small individual crystals with a random orientation. Therefore, all possible Bragg diffractions

can be exhibited in the powder pattern. However, the relative positions and intensities of

peaks in the observed diffraction pattern can be used to estimate the interplanar spacings.

Similarly, biological fibers can be subjected to x-​ray diffraction measurements if there is suf­

ficient spatial periodicity. For example, muscle fibers have repeating subunits arranged peri­

odically in one dimension parallel to the long axis of the fiber. This approach was also used to

great effect in solving the double-​helical structure of DNA from the work of Crick, Franklin,

Wilkins, and Watson in 1953.

In small-​angle x-​ray scattering (SAXS), a 3D crystalline sample is not needed, and the

technique is particularly useful for exploring the longer scale periodic features encountered

in many biological fibers. The range of scattered angles explored is small (typically <10°)

with a typical spatial resolution of ~1–​25 nm. It is used to infer the spacing of relatively

large-​scale structures up to ~150 nm (e.g., to study periodic features in muscle fibers). The

scatter signal is relatively weak compared to higher angle scattering methods of x-​ray crys­

tallography and so a strong synchrotron beamline is generally used. SAXS does not generate

atomistic-​level structural information like x-​ray crystallography or NMR, but it can deter­

mine structures, which are coarser grained by an order of magnitude in a matter of days for

biological structures, which span a much wider range of size and mass.

SAXS is performed using an x-​ray wavelength of ~0.15 nm, directing the beam to a

solution of the biomolecular structure, and the emergent scatter angle θ and beam inten­

sity I are recorded. The magnitude of the scattering vector Q =​ (4π/​k)sin(θ/​2), the formu­

lation identical to that discussed for static light scattering previously (see Chapter 4), is

normally plotted as a function of I (Figure 5.3b) and the position and sizes and the typically

broad peaks in this curve are used to infer the size and extent of spatial periodicity values

from the sample. The same level of analysis for determining radius of gyration can also be

performed for static light scattering, also including information about the coarse shape

of periodic scattering objects in the sample, but SAXS also has sufficiently high spatial

resolution to investigate different molecular states of the same complexes, for example,

to be able to discriminate between different conformational states of the same enzyme

provided the whole sample solution is sufficiently synchronized. And, being in solution, it

also offers significant potential for monitoring time-​resolved changes to molecular struc­

ture, which 3D x-​ray crystallography cannot. The use of coherent x-​rays as available from

XFEL can generate the speckled interference patterns from SAXS investigations, which

can be used to generate phase information directly from the sample in much the same way

as for XFEL on 2D crystal arrays.

SAXS, like 3D x-​ray crystallography, utilizes elastic x-​ray photon scattering. Inelastic

scattering is also possible, for which the wavelength of the emergent x-​rays is greater than

the incident beam (i.e., the scattered beam has a lower energy). Here, some portion of the