Relative weighting of diffraction and restraint terms

Cruickshank, D. W. J.

doi:10.1107/97809553602060000697

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. 18.5, p. 406 | 1 | 2 |

Section 18.5.3.3. Relative weighting of diffraction and restraint terms

D. W. J. Cruickshank^a ^*^‡

^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), it has been common (Rollett, 1970) 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) 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) 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).

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

References

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

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

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

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

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