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

International Tables for Crystallography (2006). Vol. F, ch. 11.4, p. 226   | 1 | 2 |

Section 11.4.1. Introduction

Z. Otwinowskia* and W. Minorb

aUT Southwestern Medical Center at Dallas, 5323 Harry Hines Boulevard, Dallas, TX 75390-9038, USA, and bDepartment of Molecular Physiology and Biological Physics, University of Virginia, 1300 Jefferson Park Avenue, Charlottesville, VA 22908, USA
Correspondence e-mail:

11.4.1. Introduction

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X-ray diffraction data analysis, performed by the HKL package (Otwinowski, 1993[link]; Otwinowski & Minor, 1997[link]) or similar programs (Rossmann, 1979[link]; Howard et al., 1985[link]; Blum et al., 1987[link]; Bricogne, 1987[link]; Howard et al., 1987[link]; Leslie, 1987[link]; Messerschmidt & Pflugrath, 1987[link]; Kabsch, 1988[link]; Higashi, 1990[link]; Sakabe, 1991[link]), is used to obtain the following results:

  • (1) estimates of structure factors and determination of the crystal symmetry;

  • (2) estimates of the crystal unit-cell parameters;

  • (3) error estimates of the structure factors and unit cell;

  • (4) detector calibration; and

  • (5) detection of hardware malfunctions.

Other results, like indexing of the diffraction pattern, are in most cases only intermediate steps to achieve the above goals. The HKL system and other programs also have tools to validate the results by self-consistency checks.

The fundamental stages of data analysis are:

  • (1) visual inspection of the diffraction images;

  • (2) (auto)indexing;

  • (3) diffraction geometry refinement;

  • (4) integration of the diffraction peaks;

  • (5) conversion of the data to a common scale;

  • (6) symmetry determination and merging of symmetry-related reflections; and

  • (7) statistical summary and estimation of errors.

This order represents the natural flow of data reduction, but quite often these steps are repeated based on information obtained at a later stage.

The three basic questions in collecting diffraction data are:

  • (1) whether to collect;

  • (2) what to collect; and

  • (3) how to collect and analyse the data.

These questions and steps (1)[link]–(7)[link] of data analysis are intimately intertwined.

Data analysis makes specific assumptions which the collected data must, or at least should, satisfy. However, the experimenter can verify whether the data satisfy those assumptions only by data analysis. This circular logic can be broken by an iterative process. On-line data analysis provides immediate feedback during data collection and can remove the guesswork about whether, what and how from the process. The description of data analysis and algorithms that follows will make frequent references to the assumptions about the data and offer guidelines on how to make the experiment fulfil these assumptions.

This article uses the HKL package coordinate system to describe data algorithms and analysis. However, as most equations are written in vector notation, they can be easily adapted to conventions used in other programs.


Blum, M., Metcalf, P., Harrison, S. C. & Wiley, D. C. (1987). A system for collection and on-line integration of X-ray diffraction data from a multiwire area detector. J. Appl. Cryst. 20, 235–242.
Bricogne, G. (1987). The EEC cooperative programming workshop on position-sensitive detector software. In Proceedings of the Daresbury study weekend at Daresbury Laboratory, 23–24 January, edited by J. R. Helliwell, P. A. Machin and M. Z. Papiz, pp. 120–146. Warrington: Daresbury Laboratory.
Higashi, T. (1990). Auto-indexing of oscillation images. J. Appl. Cryst. 23, 253–257.
Howard, A., Nielsen, C. & Xuong, Ng. H. (1985). Software for a diffractometer with multiwire area detector. Methods Enzymol. 114, 452–472.
Howard, A. J., Gilliland, G. L., Finzel, B. C., Poulos, T. L., Ohlendorf, D. H. & Salemme, F. R. (1987). The use of an imaging proportional counter in macromolecular crystallography. J. Appl. Cryst. 20, 383–387.
Kabsch, W. (1988). Evaluation of single-crystal X-ray diffraction data from a position sensitive detector. J. Appl. Cryst. 21, 916–924.
Leslie, A. G. W. (1987). Profile fitting. In Proceedings of the Daresbury study weekend at Daresbury Laboratory, 23–24 January, edited by J. R. Helliwell, P. A. Machin and M. Z. Papiz, pp. 39–50. Warrington: Daresbury Laboratory.
Messerschmidt, A. & Pflugrath, J. W. (1987). Crystal orientation and X-ray pattern prediction routines for area-detector diffraction systems in macromolecular crystallography. J. Appl. Cryst. 20, 306–315.
Otwinowski, Z. (1993). Oscillation data reduction program. In Proceedings of the Daresbury CCP4 study weekend. Data reduction and processing, edited by L. Sawyer, N. Isaacs and S. Bailey, pp. 56–62. Warrington: Daresbury Laboratory.
Otwinowski, Z. & Minor, W. (1997). Processing of X-ray diffraction data collected in oscillation mode. Methods Enzymol. 276, 307–326.
Rossmann, M. G. (1979). Processing oscillation diffraction data for very large unit cells with an automatic convolution technique and profile fitting. J. Appl. Cryst. 12, 225–238.
Sakabe, N. (1991). X-ray diffraction data collection system for modern protein crystallography with a Weissenberg camera and an imaging plate using synchrotron radiation. Nucl. Instrum. Methods A, 303, 448–463.

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