Tables for
Volume F
Crystallography of biological macromolecules
Edited by M. G. Rossmann and E. Arnold

International Tables for Crystallography (2006). Vol. F. ch. 21.1, pp. 498-499   | 1 | 2 |

Section Local statistics

G. J. Kleywegta*

aDepartment of Cell and Molecular Biology, Uppsala University, Biomedical Centre, Box 596, SE-751 24 Uppsala, Sweden
Correspondence e-mail: Local statistics

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From a practical point of view, these are the most useful for the crystallographer who is about to rebuild a model. Examples of useful quality indicators are:

  • (1) The real-space fit (Jones et al., 1991[link]; Chapman, 1995[link]; Jones & Kjeldgaard, 1997[link]; Vaguine et al., 1999[link]), expressed as an R value or as a correlation coefficient between `observed' and calculated density. This property can be calculated for any subset of atoms, e.g. for an entire residue, for main-chain atoms or for side-chain atoms. It is best to use a map that is biased by the model as little as possible [e.g., a σA-weighted map (Read, 1986[link]), an NCS-averaged map (Kleywegt & Read, 1997[link]) or an omit map (Bhat & Cohen, 1984[link]; Hodel et al., 1992[link])]. In practice, the real-space fit is strongly correlated with the atomic temperature factors, even though these are not used in the calculations.

  • (2) The Ramachandran plot (Ramakrishnan & Ramachandran, 1965[link]; Kleywegt & Jones, 1996b[link]). Residues with unusual main-chain ϕ, ψ torsion-angle combinations that do not have unequivocally clear electron density are almost always in error. However, one should keep in mind that the error may have its origin in (one of) the neighbouring residues. For instance, if the peptide O atom of a residue is pointing in the wrong direction, the ϕ value for the next residue may be off by 150–180° (Kleywegt, 1996[link]; Kleywegt & Jones, 1998[link]).

  • (3) The pep-flip value (Jones et al., 1991[link]; Kleywegt & Jones, 1998[link]). This statistic measures the r.m.s. distance between the peptide O atom of a residue and its counterparts found in a database of well refined high-resolution structures that occur in parts of those structures with a similar local Cα backbone conformation. If the pep-flip value is large (e.g. >2.5 Å), the residue is termed an outlier, but whether it is an error can only be determined by inspecting the local density.

  • (4) The rotamer side-chain fit value (Jones et al., 1991[link]; Kleywegt & Jones, 1998[link]). This statistic measures the r.m.s. distance between the side-chain atoms of a residue and those in the most similar rotamer conformation for that residue type. A value greater than ∼1.0–1.5 Å signals an outlier. In many cases (particularly, but not exclusively, at low resolution), a non-rotamer side chain can easily be replaced by a rotamer conformation, perhaps in conjunction with a slight rigid-body movement of the entire residue or with some adjustment of the side-chain torsion angles (Zou & Mowbray, 1994[link]; Kleywegt & Jones, 1997[link]).

  • (5) Hydrogen-bonding analysis. The correct orientation of histidine, asparagine and glutamine side chains cannot usually be inferred from electron density alone. Inexperienced crystallographers can benefit from suggestions based on the analysis of hydrogen-bonding networks (Hooft et al., 1996b[link]), although every case should be examined critically (e.g. the program does not know about solvent molecules that have not yet been added to the model or that cannot be placed because of the limitations of the data; in addition, sometimes an amino group may be interacting with an aromatic side chain).

In addition to these criteria, residues with other unusual features should be examined in the electron-density maps for the crystallographer to be able to decide whether they are in error. Such features may pertain to unusual temperature factors, unusual occupancies, unusual bond lengths or angles, unusual torsion angles or deviations from planarity (e.g. for the peptide plane), unusual chirality (e.g. for the Cα atom of every residue type except glycine), unusual differences in the temperature factors of chemically bonded atoms, unusual packing environments (Vriend & Sander, 1993[link]), very short distances between non-bonded atoms (including symmetry mates), large positional shifts during refinement, unusual deviations from noncrystallographic symmetry (Kleywegt & Jones, 1995b[link]; Kleywegt, 1996[link]) etc.


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First citation Chapman, M. S. (1995). Restrained real-space macromolecular atomic refinement using a new resolution-dependent electron-density function. Acta Cryst. A51, 69–80.Google Scholar
First citationHodel, A., Kim, S.-H. & Brünger, A. T. (1992). Model bias in macromolecular crystal structures. Acta Cryst. A48, 851–858.Google Scholar
First citation Hooft, R. W. W., Sander, C. & Vriend, G. (1996b). Positioning hydrogen atoms by optimizing hydrogen-bond networks in protein structures. Proteins Struct. Funct. Genet. 26, 363–376.Google Scholar
First citation Jones, T. A. & Kjeldgaard, M. (1997). Electron density map interpretation. Methods Enzymol. 277, 173–208.Google Scholar
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First citation Kleywegt, G. J. (1996). Use of non-crystallographic symmetry in protein structure refinement. Acta Cryst. D52, 842–857.Google Scholar
First citation Kleywegt, G. J. & Jones, T. A. (1995b). Where freedom is given, liberties are taken. Structure, 3, 535–540.Google Scholar
First citation Kleywegt, G. J. & Jones, T. A. (1996b). Phi/Psi-chology: Ramachandran revisited. Structure, 4, 1395–1400.Google Scholar
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First citation Kleywegt, G. J. & Jones, T. A. (1998). Databases in protein crystallography. Acta Cryst. D54, 1119–1131.Google Scholar
First citation Kleywegt, G. J. & Read, R. J. (1997). Not your average density. Structure, 5, 1557–1569.Google Scholar
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First citation Vaguine, A. A., Richelle, J. & Wodak, S. J. (1999). SFCHECK: a unified set of procedures for evaluating the quality of macromolecular structure-factor data and their agreement with the atomic model. Acta Cryst. D55, 191–205.Google Scholar
First citation Vriend, G. & Sander, C. (1993). Quality control of protein models: directional atomic contact analysis. J. Appl. Cryst. 26, 47–60.Google Scholar
First citationZou, J. Y. & Mowbray, S. L. (1994). An evaluation of the use of databases in protein structure refinement. Acta Cryst. D50, 237–249.Google Scholar

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