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

International Tables for Crystallography (2012). Vol. F, ch. 11.4, p. 285   | 1 | 2 |

Section Beam–2θ

Z. Otwinowski,a* W. Minor,b D. Boreka and M. Cymborowskib

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: Beam–2θ

| top | pdf |

The description of generalized multiple-axis goniostats introduced a conceptual change in the DENZO coordinate system. The data-collection axis can be oriented in any direction, so in principle rotx, roty and rotz no longer need to be defined relative to the data-collection axis. However, to keep the useful correlations between refinable parameters (for example, crystal rotz and detector rotz are typically close to 100% correlated), one real and two virtual goniostats are used simultaneously in DENZO. Refinable crystal parameters (crystal rotx, roty, rotz) are still defined, as in the past, by the data-collection axis and the beam. This means that the directions of rotations defined by fit crystal rotx, roty and rotz do not rotate around the data-collection axis as the program advances from one image to another. This coordinate system changes with the change in direction of the data-collection axis. The crystal orientation is defined by three constant, perpendicular axes, which do not have to be aligned with the physical crystal goniostat. However, the so-called 2 theta rotation has a fixed axis, and, if it exists, it defines the DENZO coordinate system together with the beam axis. Thus, the current coordinate system in DENZO should be called beam–2θ. Fortunately for the user, the conversions between different coordinate systems are handled transparently. For example, the refined change in the crystal orientation is converted from the refined axes goniostat to the crystal-orientation goniostat. The movements of the physical goniostat are converted into appropriate changes in the diffraction pattern. The physical goniostat appears only to describe the data collection and, optionally, to calculate the physical goniostat angles needed to produce particular crystal alignments.

The DENZO coordinate system (Gewirth, 2003[link]) is used in the definition of crystal goniostats, 2θ goniostat and polarization. The curvature of cylindrical detectors and Weissenberg coupling are described in this coordinate system as well.

This discussion of the coordinate systems shows that the conceptual complexity of the program description can be compatible with – or even lead to – simplicity in the use of the program. The success of data analysis does not require a full understanding of the relations between internal DENZO goniostats and the coordinate systems when using the programs. The reason for this complexity was to create a simple pattern of correlations between crystal and detector parameters in DENZO refinement. This in turn allows for simple and easy-to-understand control of the refinement process and simplifies problem diagnostics. For example: the definition of refined crystal rotx as rotation around the data-collection axis makes the spindle and shutter problems manifest only as fluctuations of crystal rotx. Constant nonzero values of refined shifts between frames of crystal roty and rotz are a sign of misalignment of the data-collection axis. Although the program compensates for this misalignment with changes in crystal orientation, this introduces a small error in the Lorentz factor (which will be, to a good approximation, compensated for in scaling). The nature of these problems is such that they do not result in a complete failure of the experiment, but they do have an impact on the quality of the result. It is up to the experimenter and the instrument manager to assess the significance of these indications.


Gewirth, D. (2003). HKL Manual. 6th ed. HKL Research, Charlottesville, USA.

to end of page
to top of page