Data-model refinement

Otwinowski, Z.; Minor, W.

doi:10.1107/97809553602060000677

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

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International Tables for Crystallography (2006). Vol. F. ch. 11.4, pp. 229-230 | 1 | 2 |

Section 11.4.5.3. Data-model refinement

Z. Otwinowski^a ^* and W. Minor^b

^a UT 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: zbyszek@mix.swmed.edu

11.4.5.3. Data-model refinement

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The parameters of the data model can be classified into four groups:

(1) Those refinable from self-consistency of the data by a (nonlinear) least-squares method.
(2) Parameters that can be determined from internal self-consistency of the data, but for which least squares is not implemented. For example, error-estimate parameters are in this category.
(3) Parameters that have to be established in a separate experiment, e.g. pixel sensitivity from flood-field exposure.
(4) Parameters that are obtained from hardware description.

The least-squares method is based on minimization of a function that is a sum of contributors of the following type: $[(\hbox{pred} - \hbox{obs})^{2}/\sigma ^{2} = \chi^{2}, \eqno(11.4.5.1)]$ where pred is a prediction based on some parameterized model, obs is the value of this prediction's measurement and $[\sigma^{2}]$ is an estimate of the measurement and the prediction uncertainty. DENZO has the following least-squares refinements:

(1) refinement of unit-cell vectors in autoindexing;
(2) refinement of background and background slope; and
(3) refinement of crystal orientation, unit cell, mosaicity, beam focus and position, detector orientation and position, and geometrical distortions that are parameterized differently for different detectors.

SCALEPACK can refine the following parameters by least-squares methods:

(1) unit cell, crystal orientation and mosaicity, including changes of these parameters during an experiment;
(2) goniostat internal alignment angles;
(3) crystal absorption, using spherical harmonics (Katayama, 1986; Blessing, 1995) expansion of the absorption surface;
(4) uniformity of exposure, including shutter timing error;
(5) correction to the Lorentz factor resulting from a misalignment of the spindle axis;
(6) reproducible wobble of the rotation axis resulting from a misalignment of gears in a spindle assembly;
(7) non-uniform smooth detector response, for example, resulting from decay of the image-plate signal during scanning; and
(8) other factors contributing to scaling resulting from a slow fluctuation of beam intensity, change in exposed volume, overall crystal decay and resolution-dependent crystal decay.

References

Blessing, R. H. (1995). An empirical correction for absorption anisotropy. Acta Cryst. A51, 33–38.Google Scholar

Katayama, C. (1986). An analytical function for absorption correction. Acta Cryst. A42, 19–23.Google Scholar

International Tables for Crystallography (2006). Vol. F. ch. 11.4, pp. 229-230