Editing X-ray crystallography (section)

=== Model building and phase refinement ===
[[File:Helix electron density myoglobin 2nrl 17-32.jpg|thumb|Structure of a protein alpha helix, with stick-figures for the covalent bonding within electron density for the crystal structure at ultra-high-resolution (0.91&nbsp;Å). The density contours are in gray, the helix backbone in white, sidechains in cyan, O atoms in red, N atoms in blue, and hydrogen bonds as green dotted lines.<ref>From PDB file 2NRL, residues 17–32.</ref>]] [[File:Fitting a model into electron density.gif|thumb|3D depiction of electron density (blue) of a ligand (orange) bound to a binding site in a protein (yellow).<ref>{{cite web |title=Garman lab: Interconversion of lysosomal enzyme specificities – Proteopedia, life in 3D |url=http://proteopedia.org/wiki/index.php/Garman_lab:_Interconversion_of_lysosomal_enzyme_specificities |access-date=2018-11-28 |website=proteopedia.org |archive-date=2018-11-28 |archive-url=https://web.archive.org/web/20181128212454/http://proteopedia.org/wiki/index.php/Garman_lab:_Interconversion_of_lysosomal_enzyme_specificities |url-status=live }}</ref> The electron density is obtained from experimental data, and the ligand is modeled into this electron density.]]
{{further|Molecular modelling{{!}}Molecular modeling}}

Having obtained initial phases, an initial model can be built. The atomic positions in the model and their respective [[Debye-Waller factor]]s (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 are carried out. This iterative process continues until the correlation between the diffraction data and the model is maximized. The agreement is measured by an [[R-factor (crystallography)|''R''-factor]] defined as

:<math>R = \frac{\sum_{\text{all reflections}} \left|F_\text{obs} - F_\text{calc} \right|}{\sum_{\text{all reflections}} \left|F_\text{obs} \right|},</math>

where ''F'' is the [[structure factor]]. A similar quality criterion is ''R''<sub>free</sub>, which is calculated from a subset (~10%) of reflections that were not included in the structure refinement. Both ''R'' factors depend on the resolution of the data. As a rule of thumb, ''R''<sub>free</sub> should be approximately the resolution in angstroms divided by 10; thus, a data-set with 2&nbsp;Å resolution should yield a final ''R''<sub>free</sub> ~ 0.2. Chemical bonding features such as stereochemistry, hydrogen bonding and distribution of bond lengths and angles are complementary measures of the model quality. In iterative model building, it is common to encounter phase bias or model bias: because phase estimations come from the model, each round of calculated map tends to show density wherever the model has density, regardless of whether there truly is a density. This problem can be mitigated by maximum-likelihood weighting and checking using ''omit maps''.<ref name="pmid25554228">{{cite journal |last1=Lamb |first1=AL |last2=Kappock |first2=TJ |last3=Silvaggi |first3=NR |date=April 2015 |title=You are lost without a map: Navigating the sea of protein structures. |journal=Biochimica et Biophysica Acta (BBA) - Proteins and Proteomics |volume=1854 |issue=4 |pages=258–68 |doi=10.1016/j.bbapap.2014.12.021 |pmc=5051661 |pmid=25554228}}</ref>

It may not be possible to observe every atom in the asymmetric unit. In many cases, [[crystallographic disorder]] smears the electron density map. Weakly scattering atoms such as hydrogen are routinely invisible. It is also possible for a single atom to appear multiple times in an electron density map, e.g., if a protein sidechain has multiple (<4) allowed conformations. In still other cases, the crystallographer may detect that the covalent structure deduced for the molecule was incorrect, or changed. For example, proteins may be cleaved or undergo post-translational modifications that were not detected prior to the crystallization.