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

International Tables for Crystallography (2006). Vol. F. ch. 18.5, p. 406   | 1 | 2 |

Section 18.5.3.3. Relative weighting of diffraction and restraint terms

D. W. J. Cruickshanka*

a Chemistry Department, UMIST, Manchester M60 1QD, England
Correspondence e-mail: dwj_cruickshank@email.msn.com

18.5.3.3. Relative weighting of diffraction and restraint terms

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When only relative diffraction weights are known, as in equation (18.5.2.13)[link], it has been common (Rollett, 1970)[link] to scale the geometric restraint terms against the diffraction terms by replacing the restraint weights [w_{\rm geom} = 1/\sigma_{\rm geom}^{2}] by [w_{\rm geom} = S^{2}/\sigma_{\rm geom}^{2}], where [S^{2} = (\sum w_{h} \Delta_{h}^{2})/(n_{\rm obs} - n_{\rm params})] . However, this scheme cannot be used for low-resolution structures if [n_{\rm obs} \lt n_{\rm params}].

The treatment by Tickle et al. (1998a)[link] shows that the reduction [n_{\rm params}] in the number of degrees of freedom has to be distributed among all the data, both diffraction observations and restraints. Since the geometric restraint weights are on an absolute scale (Å−2), they propose that the (absolute) scale of the diffraction weights should be determined by adjustment until the restrained residual R′ (18.5.3.1)[link] is equal to its expected value [(n_{\rm obs} + n_{\rm restraints} - n_{\rm params})].

For a method of determining the scale of the diffraction weights based on [R_{\rm free}], see Brünger (1993)[link].

The geometric restraint weights were classified by the IUCr Subcommittee (Schwarzenbach et al., 1995[link]) as derived from observations supplementary to the diffraction data, with uncertainties of type B (Section 18.5.2.3)[link].

References

First citation Brünger, A. T. (1993). Assessment of phase accuracy by cross validation: the free R value. Methods and application. Acta Cryst. D49, 24–36.Google Scholar
First citation Rollett, J. S. (1970). Least-squares procedures in crystal structure analysis. In Crystallographic computing, edited by F. R. Ahmed, S. R. Hall & C. P. Huber, pp. 167–181. Copenhagen: Munksgaard.Google Scholar
First citation Schwarzenbach, D., Abrahams, S. C., Flack, H. D., Prince, E. & Wilson, A. J. C. (1995). Statistical descriptors in crystallography. II. Report of a working group on expression of uncertainty in measurement. Acta Cryst. A51, 565–569.Google Scholar
First citation Tickle, I. J., Laskowski, R. A. & Moss, D. S. (1998a). Error estimates of protein structure coordinates and deviations from standard geometry by full-matrix refinement of γB- and βB2-crystallin. Acta Cryst. D54, 243–252.Google Scholar








































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