Tables for
Volume G
Definition and exchange of crystallographic data
Edited by S. R. Hall and B. McMahon

International Tables for Crystallography (2006). Vol. G, ch. 3.6, pp. 159-160

Section Analysis of the refined structure

P. M. D. Fitzgerald,a* J. D. Westbrook,b P. E. Bourne,c B. McMahon,d K. D. Watenpaughe and H. M. Bermanf

aMerck Research Laboratories, Rahway, New Jersey, USA,bProtein Data Bank, Research Collaboratory for Structural Bioinformatics, Rutgers, The State University of New Jersey, Department of Chemistry and Chemical Biology, 610 Taylor Road, Piscataway, New Jersey, USA,cResearch Collaboratory for Structural Bioinformatics, San Diego Supercomputer Center, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0537, USA,dInternational Union of Crystallography, 5 Abbey Square, Chester CH1 2HU, England,eretired; formerly Structural, Analytical and Medicinal Chemistry, Pharmacia Corporation, Kalamazoo, Michigan, USA, and fProtein Data Bank, Research Collaboratory for Structural Bioinformatics, Rutgers, The State University of New Jersey, Department of Chemistry and Chemical Biology, 610 Taylor Road, Piscataway, New Jersey, USA
Correspondence e-mail: Analysis of the refined structure

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The data items in this category are as follows:

REFINE_ANALYZE [Scheme scheme63]

The bullet ([\bullet]) indicates a category key. The arrow ([\rightarrow]) is a reference to a parent data item.

In small-molecule crystallography, there is general agreement on the metrics that should be used to assess the quality of a structure determination, and data items in the REFINE category of the core CIF dictionary can be used to record them. For macromolecular structure determinations, no such agreement has been achieved yet and new metrics are frequently suggested as the field evolves. The REFINE_ANALYZE category can be used to record the metrics that were in common use at the time that the mmCIF dictionary was constructed; it is anticipated that new metrics will be added in future versions of the dictionary, and that some of the current metrics may fall into disuse.

Luzzati (1952[link]) devised a method for estimating the average positional shift that would be needed in an idealized refinement to reach an R factor of zero by using a plot of R factors against resolution. For some time, macromolecular crystallographers have used a modification of this approach to assess the average positional error. Recent practice has used Luzzati plots based on the free R values to yield a cross-validated error estimate. Data items are provided for recording these coordinate-error estimates and the range of resolution included in the plot (Example[link]). Related data names allow the specification of the value of [\sigma_a] used in constructing the Luzzati plot.

Example Aspects of the refinement of an HIV-1 protease structure (PDB 5HVP) described with data items in the REFINE_ANALYZE category.

[Scheme scheme65]

A general feature of introducing more parameters in the model of the structure is a reduction in the R factor, but the statistical significance of this is often obscured by the simultaneous reduction in the ratio of observations to parameters. Attempts to extend Hamilton's (1965[link]) test to macromolecular structures are usually confounded by the use of restraints. Tickle et al. (1998[link]) proposed the use of a Hamilton generalized R factor analyzed separately for reflections in the working set (those used in the refinement) and for reflections in the free set (those set aside for cross validation), and these metrics are often reported in the literature. Data items are provided for recording the Hamilton generalized R factor for the working and free set of reflections, and for the ratio of the two.

Other indicators of a successful refinement involve the relative order of the model. Data items are provided for recording the sum of the occupancies of the hydrogen and non-hydrogen atoms in the model. The number of disordered residues may also be recorded.


Hamilton, W. C. (1965). Significance tests on the crystallographic R factor. Acta Cryst. 18, 502–510.
Luzzati, V. (1952). Traitement statistique des erreurs dans la determination des structures cristallines. Acta Cryst. 5, 802–810.
Tickle, I. J., Laskowski, R. A. & Moss, D. S. (1998). Rfree and the Rfree ratio. I. Derivation of expected values of cross-validation residuals used in macromolecular least-squares refinement. Acta Cryst. D54, 547–557.

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