180 5.3  X-Ray Tools

a camera. This raw diffraction pattern is used to reconstruct the image of the sample through

a Fourier transform on the intensity data combined with computational iterative phase

recovery algorithms to recover the phase information due to the lack of sufficient coher­

ence used in synchrotron radiation. In effect, a computer performs the job of an equivalent

objective lens to convert reciprocal space data into a real space image. The main advantage of

CXDI is that it does not require lenses to focus the beam so that the measurements are not

affected by aberrations in the zone plates but rather is only limited by diffraction and the x-​

ray intensity. Although not yet a mainstream biophysical technique, the superior penetration

power of x-​rays combined with their small wavelength and thus high spatial resolution has

realistic potential for future studies of complex biological samples (see Thibault et al., 2008).

A future potential for these techniques lies in time-​resolved x-​ray imaging.

5.3.5  X-​RAY SPECTROSCOPY

An incident x-​ray photon can have sufficient energy to eject a core electron through the

photoelectric effect, resulting in the appearance of significant absorption edges in the spectra

of transmitted photons through the sample, which correspond to the binding energies for an

electron in different respective shells (K, L, M, etc.). This subatomic process can involve sub­

sequent fluorescence emission analogous to that exhibited in light microscopy (Chapter 3);

if an excited electron undergoes vibrational losses prior to returning to its ground state, it

results in radiative x-​ray fluorescence emission of a photon of slightly longer wavelength

than the incident photon. Also, when the ejection of the core inner shell electrons occurs,

it results in higher energy outer shell electrons dropping to these lower energy vacant states

with a resultant radiative emission of a secondary x-​ray photon whose energy is the difference

between the binding energies of the two electronic levels. The position and intensity of these

absorption and emission peak as a function of photon wavelength, constituting a unique fin­

gerprint for the host atom in question, and thus, x-​ray absorption spectroscopy (XAS) (also

known variously as very similar/​identical techniques of energy-​dispersive x-​ray spectroscopy,

energy-​dispersive x-​ray analysis, and simply x-​ray spectroscopy) is a useful biophysical tool

for determining the makeup of individual elements in a sample, that is, performing elemental

analysis.

X-​ray absorption spectra of relevance to biological questions can be categorized into x-​

ray absorption near edge structure, which generates data concerning the electronic “oxida­

tion state” of an atom and the spatial geometry of its molecular orbitals, and extended x-​ray

absorption fine structure, which generates information about the local environment of a

metal atom’s binding sites (for an accessible review, see Ortega et al., 2012). The penetration

of lower energy secondary x-​rays (wavelengths >1 nm) through air is significantly worse than

those of higher energy secondary x-​rays (wavelength <1 nm). This characteristic wavelength

for K-​line transitions varies as ~(Z − 1)² as predicated by Moseley’s law, and the ~1 nm cutoff

occurs at around Z =​ 12 for magnesium. Thus, most metals generate detectable secondary

x-​rays, which facilitate metal elemental analysis. Of special relevance are metal-​binding

proteins, or metalloproteins, and XAS can probe details such as the type of neighboring

atoms, how many bonds are formed between them, over what distances, and others. This is a

particularly attractive feature of the technique, since proteins containing metal ions actually

constitute more than one-​third of all known proteins.

A schematic of a typical setup is shown in Figure 5.3e, utilizing a polychromatic syn­

chrotron x-​ray source, which generates a suitably intense and collimated beam required for

XAS. Normally, hard x-​rays are used, with a monochromator then utilized to scan through

a typical wavelength range of ~0.6–​6 nm. Samples, which can include cultures of cells but

more typically consist of high concentrations (~0.5 mM) of protein, need to be cryofixed to

a glassy frozen state to stabilize thermal disorder and minimize sample radiation damage.

But measurements can at least be performed in a hydrated environment, which increases its

physiological relevance.

A standard XAS investigation measures the absorption coefficient as a function of incident

wavelength, characterized by the simple Beer–​Lambert law (see Chapter 3) from measuring