Editing X-ray crystallography (section)

=== Initial phasing ===
{{further|Phase problem}}

The intensity of each diffraction 'spot' is proportional to the modulus squared of the [[structure factor]]. The structure factor  is a [[complex number]] containing information relating to both the [[amplitude]] and [[Phase (waves)|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:
* '''''[[Ab initio]]'' phasing''' or '''[[Direct methods (crystallography)|direct methods]]'''&nbsp;– 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&nbsp;Å (140&nbsp;[[picometre|pm]]), [[Direct methods (crystallography)|direct methods]] can be used to obtain phase information, by exploiting known phase relationships between certain groups of reflections.<ref>{{cite journal |vauthors=Hauptman H |date=October 1997 |title=Phasing methods for protein crystallography |journal=Current Opinion in Structural Biology |volume=7 |issue=5 |pages=672–680 |doi=10.1016/S0959-440X(97)80077-2 |pmid=9345626}}</ref><ref>{{cite journal |vauthors=Usón I, Sheldrick GM |date=October 1999 |title=Advances in direct methods for protein crystallography |journal=Current Opinion in Structural Biology |volume=9 |issue=5 |pages=643–648 |doi=10.1016/S0959-440X(99)00020-2 |pmid=10508770 |doi-access=free}}</ref>
* '''[[Molecular replacement]]'''&nbsp;– 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.<ref name="Taylor">{{cite journal |vauthors=Taylor G |date=November 2003 |title=The phase problem |journal=Acta Crystallographica. Section D, Biological Crystallography |volume=59 |issue=Pt 11 |pages=1881–1890 |bibcode=2003AcCrD..59.1881T |doi=10.1107/S0907444903017815 |pmid=14573942 |doi-access=free}}</ref>
* '''[[Anomalous X-ray scattering]]''' (''[[Multi-wavelength anomalous dispersion|MAD]] or [[Single wavelength anomalous dispersion|SAD phasing]]'')&nbsp;– the X-ray wavelength may be scanned past an absorption edge{{efn|The absorption edge is originally known from [[X-ray absorption spectroscopy]]. See {{cite web |title=X-ray Anomalous Scattering |url=http://skuld.bmsc.washington.edu/scatter/ |website=skuld.bmsc.washington.edu}} for a guide to anomalous scattering.}} 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.<ref>{{cite journal |vauthors=Ealick SE |date=October 2000 |title=Advances in multiple wavelength anomalous diffraction crystallography |journal=Current Opinion in Chemical Biology |volume=4 |issue=5 |pages=495–499 |doi=10.1016/S1367-5931(00)00122-8 |pmid=11006535|doi-access=free }}</ref>
* '''Heavy atom methods''' ([[multiple isomorphous replacement]])&nbsp;– If electron-dense metal atoms can be introduced into the crystal, [[Direct methods (crystallography)|direct methods]] or [[Patterson function|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.<ref name="Taylor" />