The Link to X-Ray Protein Crystallography

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Anomalous Dispersion (SAD, MAD)

As in isomorphous replacement, the complexity of the phase problem is reduced by determining the position of a few heavy atoms with direct methods. To get the information about the positions within one single crystal anomalous scattering (or dispersion) of heavy atoms can be used. If the wavelenth of the X-ray corresponds to a transition between different electron shells of the atom, there will be a modification of the phase. This anomalous scattering results in effects in the diffraction pattern that can be distinguished from the rest (e.g. unequal amplitudes of the Fridel pairs). The atoms don't need to be as large as for isomorphous replacement and typically proteins are used where methionine is replaced by selenomethionine. Generally data is collected at the peak (λ1) for single anomalous dispersion (SAD) and additionally at inflection (λ2) and remote (λ3, 4) for multiple anomalous dispersion (MAD).

The total scattering factor of an atom is a combination of different contributions. The normal scattering factor (f°) is independent of the wavelength and is what contributes to the normal diffraction. The anomalous scattering factors (f’, f”) change with the wavelength. At high and low wavelenth these are negligable but with a tunable wavelenth they can be optimised to have a maximal anomalous signal. For a SAD experiment f” is maximised.

A SAD experiment can be illustrated using the Argand diagramme to draw a Harker construction. As in an isomorphous replacement the structure factors of the light atom structure (FP) and the contribution of the heavy atoms add up to give the structure factor of the whole structure (FH). As we measure at λ1 the the heavy atom contribution is decomposed into the normal component (FHf°) and the anomalous component (FHf”) which is perpendicular to the previous and always positive. This anomaly results in a breakdown of symmetry of the Friedel pairs (i.e. F+PH does not equals F-PH) (left figure). This anomaly allows to determine the heavy atom substructure using direct methods. By a taking the reverse phase of the Friedel mate (F-PH*) we can rearrange the illustration and get the two anomalous heavy atom contributions (F+H, F-H*) (middle figure). As in isomorphous replacement circles can be drawn around the ends of both structure factors taking the amplitudes of anomalous Friedel pair (F+PH, F-PH*) which then allows to determine the phase (right figure).

The Link to X-Ray Protein Crystallography

A. Crystal Production

B. Data Collection

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C. Structure Solution

Anomalous Dispersion (SAD, MAD)

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