<P> The data collected from a diffraction experiment is a reciprocal space representation of the crystal lattice . The position of each diffraction' spot' is governed by the size and shape of the unit cell, and the inherent symmetry within the crystal . The intensity of each diffraction' spot' is recorded, and this intensity is proportional to the square of the structure factor amplitude . The structure factor is a complex number containing information relating to both the amplitude and phase of a wave . In order to obtain an interpretable electron density map, both amplitude and phase must be known (an electron density map allows a crystallographer to build a starting model of the molecule). The phase cannot be directly recorded during a diffraction experiment: this is known as the phase problem . Initial phase estimates can be obtained in a variety of ways: </P> <Ul> <Li> Ab initio phasing or direct methods--This is usually the method of choice for small molecules (<1000 non-hydrogen atoms), and has been used successfully to solve the phase problems for small proteins . If the resolution of the data is better than 1.4 Å (140 pm), direct methods can be used to obtain phase information, by exploiting known phase relationships between certain groups of reflections . </Li> <Li> 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 . </Li> <Li> 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 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 . </Li> <Li> 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 MAD 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 MAD phasing with selenomethionine . </Li> </Ul> <Li> Ab initio phasing or direct methods--This is usually the method of choice for small molecules (<1000 non-hydrogen atoms), and has been used successfully to solve the phase problems for small proteins . If the resolution of the data is better than 1.4 Å (140 pm), direct methods can be used to obtain phase information, by exploiting known phase relationships between certain groups of reflections . </Li> <Li> 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 . </Li>

Who took the picture using x ray crystalography to show that dna was a double helix in structure