Editing Phase problem (section)

==Phase retrieval ==
{{Main|Phase retrieval}}

There are several ways to [[Phase retrieval|retrieve]] the lost phases. The phase problem must be solved in [[x-ray crystallography]],<ref name=":0" /> [[neutron crystallography]],<ref>{{Cite journal|last1=Hauptman|first1=Herbert A.|last2=Langs|first2=David A.|date=2003-05-01|title=The phase problem in neutron crystallography|journal=Acta Crystallographica Section A|volume=59|issue=3|pages=250–254|doi=10.1107/S010876730300521X|pmid=12714776}}</ref> and [[electron crystallography]].<ref name=":2">{{Cite journal|last=Dorset|first=D. L.|date=1997-03-04|title=Direct phase determination in protein electron crystallography: The pseudo-atom approximation|journal=Proceedings of the National Academy of Sciences|language=en|volume=94|issue=5|pages=1791–1794|doi=10.1073/pnas.94.5.1791|pmc=19995|pmid=9050857|bibcode=1997PNAS...94.1791D|doi-access=free}}</ref><ref name=":3">{{Cite journal|last=Dorset|first=D. L.|date=1996-05-01|title=Direct Phasing in Protein Electron Crystallography – Phase Extension and the Prospects for Ab Initio Determinations|journal=Acta Crystallographica Section A |language=en|volume=52|issue=3|pages=480–489|doi=10.1107/S0108767396001420|pmid=8694993|doi-access=free|bibcode=1996AcCrA..52..480D }}</ref><ref>{{Cite journal|last1=Henderson|first1=R.|last2=Baldwin|first2=J. M.|last3=Downing|first3=K. H.|last4=Lepault|first4=J.|last5=Zemlin|first5=F.|date=1986-01-01|title=Structure of purple membrane from halobacterium halobium: recording, measurement and evaluation of electron micrographs at 3.5 Å resolution|journal=Ultramicroscopy|language=en|volume=19|issue=2|pages=147–178|doi=10.1016/0304-3991(86)90203-2}}</ref>

Not all of the methods of [[phase retrieval]] work with every [[wavelength]] (x-ray, neutron, and electron) used in crystallography.

=== [[Direct methods (crystallography)|Direct (''ab initio)'' methods]] ===
If the crystal diffracts to high resolution (<1.2 Å), the initial phases can be estimated using direct methods.<ref name=":0" />  Direct methods can be used in  [[x-ray crystallography]],<ref name=":0" /> [[neutron crystallography]],<ref>{{Cite journal|last=Hauptman|first=H.|date=1976-09-01|title=Probabilistic theory of the structure invariants: extension to the unequal atom case with application to neutron diffraction|journal=Acta Crystallographica Section A |language=en|volume=32|issue=5|pages=877–882|doi=10.1107/S0567739476001757|bibcode=1976AcCrA..32..877H|doi-access=free}}</ref> and [[electron crystallography]].<ref name=":2" /><ref name=":3" />

A number of initial phases are tested and selected by this method. The other is the Patterson method, which directly determines the positions of heavy atoms.  The [[Patterson function]] gives a large value in a position which corresponds to interatomic vectors. This method can be applied only when the crystal contains heavy atoms or when a significant fraction of the structure is already known.  

For molecules whose crystals provide reflections in the sub-Ångström range, it is possible to determine phases by [[brute-force search|brute force]] methods, testing a series of phase values until spherical structures are observed in the resultant electron density map.  This works because atoms have a characteristic structure when viewed in the sub-Ångström range.  The technique is limited by processing power and data quality.  For practical purposes, it is limited to "small molecules" and peptides because they consistently provide high-quality diffraction with very few reflections.

=== [[Molecular replacement]] (MR) ===
Phases can also be inferred by using a process called [[molecular replacement]], where a similar molecule's already-known phases are grafted onto the intensities of the molecule at hand, which are observationally determined.  These phases can be obtained experimentally from a homologous molecule or if the phases are known for the same molecule but in a different crystal, by simulating the molecule's packing in the crystal and obtaining theoretical phases.  Generally, these techniques are less desirable since they can severely bias the solution of the structure.  They are useful, however, for ligand binding studies, or between molecules with small differences and relatively rigid structures (for example derivatizing a small molecule).

=== [[Isomorphous replacement]] ===

==== ''[[Multiple isomorphous replacement]] (MIR)''  ====
''[[Multiple isomorphous replacement]] (MIR)'', where heavy atoms are inserted into structure (usually by synthesizing proteins with analogs or by soaking)

=== Anomalous scattering ===

==== ''[[Single-wavelength anomalous dispersion]]'' (SAD). ====

==== ''[[multi-wavelength anomalous dispersion|Multi-wavelength anomalous dispersion (MAD)]]'' ====
A powerful solution is the ''[[multi-wavelength anomalous dispersion]]'' (MAD) method. In this technique, atoms' inner electrons{{clarify|reason=Which atoms? Special new atoms that are introduced?|date=July 2016}} absorb X-rays of particular wavelengths, and reemit the X-rays after a delay, inducing a phase shift in all of the reflections, known as the ''[[anomalous dispersion]] effect''. Analysis of this phase shift (which may be different for individual reflections) results in a solution for the phases. Since X-ray fluorescence techniques (like this one) require excitation at very specific wavelengths, it is necessary to use [[synchrotron radiation]] when using the MAD method.