Publisher Summary X-ray data can be collected with zero-, one-, and two-dimensional detectors, zero-dimensional (single counter) being the simplest and two-dimensional the most efficient in terms of measuring diffracted X-rays in all directions. To analyze the single-crystal diffraction data collected with these detectors, several computer programs have been developed. Two-dimensional detectors and related software are now predominantly used to measure and integrate diffraction from single crystals of biological macromolecules. Macromolecular crystallography is an iterative process. To monitor the progress, the HKL package provides two tools: (1) statistics, both weighted (χ2) and unweighted (R-merge), where the Bayesian reasoning and multicomponent error model helps obtain proper error estimates and (2) visualization of the process, which helps an operator to confirm that the process of data reduction, including the resulting statistics, is correct and allows the evaluation of the problems for which there are no good statistical criteria. Visualization also provides confidence that the point of diminishing returns in data collection and reduction has been reached. At that point, the effort should be directed to solving the structure. The methods presented in the chapter have been applied to solve a large variety of problems, from inorganic molecules with 5 A unit cell to rotavirus of 700 A diameters crystallized in 700 × 1000 × 1400 A cell.

Processing of X-ray diffraction data collected in oscillation mode

!Received 19 December 2005; accepted 27 January 2006 "The deÞnitions for important Rietveld error indices are deÞned and discussed. It is shown that whilesmaller error index values indicate a better Þt of a model to the data, wrong models with poor qualitydata may exhibit smaller values error index values than some superb models with very high qualitydata. © 2006 International Centr e for Diffraction Data. #DOI: 10.1 154/1.2179804 $

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R factors in Rietveld analysis: How good is good enough?

Detailed practical and numerical information is provided for undertaking and evaluating absolute-structure and absolute-configuration determinations. The interpretation of numerical values of x, the Flack [Acta Cryst. (1983), A39, 876–881] parameter, and its standard uncertainty u are explained in terms of the inversion-distinguishing power. Moreover, the conditions to obtain reliable values of x(u) are detailed. Further explanatory material is provided on the use of right-handed axes, valid intensity data, the application to macromolecular structures, the dangers of polar-dispersion errors, Euclidean normalizers of space groups, the detection and reporting of molecular symmetry, enantiopurity and optical activity in solution. New CIF data names are introduced.

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Reporting and evaluating absolute-structure and absolute-configuration determinations

FIT2D is one of the principal area detector data reduction, analysis and visualization programs used at the European Synchrotron Radiation Facility and is also used by more than 400 research groups worldwide, including many other synchrotron radiation facilities. It has been developed for X-ray science, but is applicable to other structural techniques and is used in analysing electron diffraction data and microscopy, and neutron diffraction and scattering data. FIT2D works for both interactive and `batch'-style data processing. Calibration and correction of detector distortions, integration of two-dimensional data to a variety of one-dimensional scans, and one- and two-dimensional model fitting are the main uses. Many other general-purpose image processing and image visualization operations are available. Commands are available through a `graphical user interface' and operations common to certain types of analysis are grouped within `interfaces'. Executable versions for most workstation and personal computer systems, and web page documentation, are available at http://www.esrf.eu/computing/scientific/FIT2D.

FIT2D: a multi-purpose data reduction, analysis and visualization program

Full-matrix least squares is taken as the basis for an examination of protein structure precision. A two-atom protein model is used to compare the precisions of unre­strained and restrained refinements. In this model, restrained refinement determines a bond length which is the weighted mean of the unrestrained diffraction-only length and the geometric dictionary length. Data of 0.94 A resolution for the 237-residue protein concanavalin A are used in unrestrained and restrained full-matrix inversions to provide standard uncertainties σ(r) for positions and σ(l) for bond lengths. σ(r) is as small as 0.01 A for atoms with low Debye B values but increases strongly with B. The results emphasize the distinction between unrestrained and restrained refinements and between σ(r) and σ(l). Other full-matrix inversions are reported. Such inversions require massive calculations. Several approximate methods are examined and compared critically. These include a Fourier map formula [Cruickshank (1949). Acta Cryst. 2, 65–82], Luzzati plots [Luzzati (1952). Acta Cryst. 5, 802–810] and a new diffraction-component precision index (DPI). The DPI estimate of σ(r, Bavg) is given by a simple formula. It uses R or Rfree and is based on a very rough approximation to the least-squares method. Many examples show its usefulness as a precision comparator for high- and low-resolution structures. The effect of restraints as resolution varies is examined. More regular use of full-matrix inversion is urged to establish positional precision and hence the precision of non-dictionary distances in both high- and low-resolution structures. Failing this, parameter blocks for representative residues and their neighbours should be inverted to gain a general idea of σ(r) as a function of B. The whole discussion is subject to some caveats about the effects of disordered regions in the crystal.

Remarks about protein structure precision

The Subcommittee has attempted to elucidate the nature of problems encountered in the definition and use of statistical descriptors as applied to crystallography and to propose procedural improvements. The report contains (a) a dictionary of statistical terms established for use by experimentalists; (b) a description of the statistical basis for refinement procedures; (c) sections dealing with defects in the physical model used for refinement, and with the choice and significance of weighting schemes; and (d) recommendations, some of which may be readily implemented, whilst others may require a long-term effort to bring them into general use.

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B. E. Robertson

Papers

Statistical descriptors in crystallography: Report of the IUCr Subcommittee on Statistical Descriptors

Statistical Descriptors in Crystallography Report of the International Union of Crystallography Subcommittee on Statistical Descriptors