direct methods can be used to obtain phase information, by exploiting known phase relationships between certain groups of reflections. Molecular replacement – if a related structure is known, it can be used as a search model in molecular replacement to determine the orientation and position of the molecules within the unit cell. The phases obtained this way can be used to generate electron density maps. Anomalous X-ray scattering (MAD or SAD phasing) – the X-ray wavelength may be scanned past an absorption edge of an atom, which changes the scattering in a known way. By recording full sets of reflections at three different wavelengths (far below, far above and in the middle of the absorption edge) one can solve for the substructure of the anomalously diffracting atoms and hence the structure of the whole molecule. The most popular method of incorporating anomalous scattering atoms into proteins is to express the protein in a methionine auxotroph (a host incapable of synthesizing methionine) in a media rich in seleno-methionine, which contains selenium atoms. A multi-wavelength anomalous dispersion (MAD) experiment can then be conducted around the absorption edge, which should then yield the position of any methionine residues within the protein, providing initial phases. Heavy atom methods (multiple isomorphous replacement) – If electron-dense metal atoms can be introduced into the crystal, direct methods or Patterson-space methods can be used to determine their location and to obtain initial phases. Such heavy atoms can be introduced either by soaking the crystal in a heavy atom-containing solution, or by co-crystallization (growing the crystals in the presence of a heavy atom). As in multi-wavelength anomalous dispersion phasing, the changes in the scattering amplitudes can be interpreted to yield the phases. Although this is the original method by which protein crystal structures were solved, it has largely been superseded by multi-wavelength anomalous dispersion phasing with selenomethionine. Model building and phase refinement Having obtained initial phases, an initial model can be built. The atomic positions in the model and their respective Debye-Waller factors (or B-factors, accounting for the thermal motion of the atom) can be refined to fit the observed diffraction data, ideally yielding a better set of phases. A new model can then be fit to the new electron density map and successive rounds of refinement is carried out. This iterative process continues until the correlation between the diffraction data and the model is maximized. The agreement is