X-ray absorption spectroscopy is particularly useful for investigating the electronic structure and local environment of the metals in metalloproteins (1). It is not limited by the physical state of the sample (e.g., gel, crystal, tissue) and, unlike X-ray crystallography, the entire structure of a crystalline molecule need not be determined to understand the local structure of the metal site. Obtaining data from light atoms, however, is very difficult. Atoms lighter than sulfur cannot be studied routinely because high vacuum is required. Most of the work reported to date has been with samples containing transition-metal ions. An intense, tunable X-ray source is required, and making measurements at a synchrotron facility must be done on a competitive basis. The ideal sample has a volume of 20 to 100 |il and a concentration of at least 1 mM. It must be maintained at low temperature while the data are being collected, so as to minimize radiation damage.
Like visible photons, X rays are absorbed by matter according to the Beer-Lambert law (see Spectroscopy) and cause changes in the energy levels of the electrons of the absorbing atom. Because the energies of X-ray photons are considerably greater than those of visible light, however, the electrons affected are those in the lower shells, principally the K- and L-shell electrons. Therefore, X rays whose energies are near those of the atomic or molecular energy levels of the metal can be used to probe the electronic structures of the metal sites. The edge region of the absorption spectrum in the top panel of Fig. 1 contains information relating to the valence state and coordination geometry of the absorbing metal atom and the chemical identities of the neighboring atoms.
Figure 1. X-ray absorption data fora) Data collected as fluorescence (F) normalized by the initial intensity I0. (b) EXAFS data derived from the data in (a) after subtracting a background, corresponding to the metal ion without neighbors, and multiolving bv the factor k:\ where k is proportional to
. (c) Fourier transformation of the EXAFS data in (b), showing the coordination shells around the Zn2+ ion. The first shell contains four imidazole N atoms at 2.40 A, and the higher shells contain the other C and N atoms of the imidazole rings.
When the X-ray energy exceeds the ionization potential or threshold of the metal, which is the energy at which the inner shell electrons are promoted to the continuum, the absorption spectrum is characterized by an oscillatory structure (top panel of Fig. 1) at energies greater than the absorption edge, which is known as the extended X-ray absorption fine structure (EXAFS). This structure results from interference in the ejected photoelectron wave from the metal atom and the photoelectron wave backscattered from neighboring atoms. This interference phenomenon provides a very precise measurement of the distance to the neighboring atoms (typically ± 0.02 A). In addition, the EXAFS oscillations contain information relating to the number of neighboring atoms of a limited range in atomic number (rows in the periodic table can generally be distinguished). Because this ejected photoelectron wave is spherical, the position in three dimensions is lost on average. In a simplified form, an equation describing these oscillations can be written as where k is the wave vector, which is related to the X-ray energy, c is the oscillatory part of the X-ray
absorption spectrum, Nis the number of neighbors at distance r, A(k) is the backscattering amplitude, which depends on the chemical identity of the neighboring atoms, and a(k) is the phase shift due to the potentials of both the absorbing metal and the neighboring atoms. The summation is over all coordination shells j, but in reality data can be collected only at distances less than about 5 A for biological samples. The previous equation is written in this interference form to facilitate describing the data analysis necessary to determine the structural parameters.
Although X-ray absorption can be measured by observing either the transmission of X rays through the sample or the fluorescence emitted as a result of absorption, the latter is used almost exclusively for biological samples, because of its enhanced sensitivity. To obtain information about the number and average distances of the neighboring atoms, the data must be analyzed to isolate these parameters in the previous equation. Figure 1 shows the results for Zn (imidazole) J during each step of the analysis. First, a simple linear background is subtracted from the data to normalize to zero the data below the edge region (top panel). Then, a background resembling the spectrum of the metal without neighbors (ie, a free atom) is subtracted, the energy scale is converted to wave numbers (A-1), and the data are multiplied by k3. The results are displayed in the middle panel of Fig. 1. Now, the _y-axis corresponds to the left side of the previous equation. Fourier transformation is used to isolate the contributions of the individual coordination shells, which converts the x-axis to r + a(k). This is similar to a radial distribution function that describes the radial electron density around the absorbing metal set at the origin. The first peak of the bottom panel of Fig. 1 is the first coordination shell, and those at greater x-axis values are further from the metal. The x-axis can be converted to r if one knows the chemical identity of the scatterers in each shell. For example, the average distance of the first shell peak is r + a(k) = 1.52 A. It is composed of four nitrogen atoms, however, and it is known from investigating model compounds of known structure that a(k) = 0.88 A for Zn-N coordination. This makes the average distance of those four nitrogen ligands 2.40 A, with an estimated error of ±0.02 A. Using model compounds, one can also determine that there are four nitrogen ligands in the first coordination shell. A more elaborate analysis, considering the higher shells of scattering atoms, would also lead to the conclusion that the ligands are imidazole. This example illustrates the need for model compound data or theoretical determination of the amplitudes and phases for each chemical type of ligand.
This example also demonstrates one limitation of EXAFS. In the absence of information about the metal-coordination environment, the data simply give an average of the number of ligands and their distances. In the best of circumstances without other biophysical or biochemical information, this method can determine only the difference between elements in the rows of the periodic table (e.g., C/N/O, S/Cl, or Se). Additional limitations occur as a result of uncertainties in the data analysis. For example, it is rarely possible to distinguish between one and two coordinated histidine residues in the presence of thiol group ligands without further information (such as knowledge of the protein primary structure). Rigorous analysis of X-ray absorption data for a complex coordination environment (e.g., metal clusters) in proteins can be impossible without methods to isolate each metal site, for example, by metal substitution.