Full-matrix comparison with the diffraction-component precision index

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. 411 | 1 | 2 |

Section 18.5.7.1. Full-matrix comparison with the diffraction-component precision index

D. W. J. Cruickshank^a ^*^‡

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

18.5.7.1. Full-matrix comparison with the diffraction-component precision index

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The DPI (18.5.6.9) with R was offered as a quick and rough guide for the diffraction-data-only error for an atom with $[B = B_{\rm avg}]$ . The necessary data for the comparison with the two unrestrained full-matrix inversions of Section 18.5.5 are given in Table 18.5.7.1. For concanavalin A with $[B_{\rm avg} = 14.8\ \hbox{\AA}^{2}]$ , the full-matrix quadratic (18.5.4.2b) gives 0.033 Å for a carbon atom and the DPI gives 0.034 Å for an unspecified atom. For the immunoglobulin with $[B_{\rm avg} = 26.8\ \hbox{\AA}^{2}]$ , the full-matrix quadratic (18.5.4.2a) gives $[\sigma_{\rm diff}(r) = 0.19\ \hbox{\AA}]$ for a carbon atom, while the DPI gives 0.22 Å.

Table 18.5.7.1| top | pdf |
Comparison of full-matrix $[\sigma (r, B_{\rm avg})]$ with the diffraction-component precision index (DPI)

Protein	$[(N_{i}/p)^{1/2}]$	R	$[d_{\min}\ {(\hbox{\AA})}]$	DPI $[\sigma (r, B_{\rm avg})\ {(\hbox{\AA})}]$	Full-matrix $[\sigma_{\rm diff}(r, B_{\rm avg})\ {(\hbox{\AA})}]$	Reference
Concanavalin A	0.148	0.128	0.94	0.034	0.033	(a)
Immunoglobulin	0.476	0.156	1.70	0.221	0.186	(b)

References: (a) Deacon et al. (1997)

; (b) Usón et al. (1999)

For these two structures, the simple DPI formula compares surprisingly well with the unrestrained full-matrix calculations at $[B_{\rm avg}]$ .

For the restrained full-matrix calculations on concanavalin A, the quadratic (18.5.4.2c) with $[B = B_{\rm avg}]$ gives $[\sigma_{\rm res}(r) = 0.028\ \hbox{\AA}]$ for a carbon atom, which is only 15% smaller than the unrestrained 0.033 Å. This small decrease matches the discussion of $[\sigma_{\rm res}(r)]$ and $[\sigma_{\rm diff}(r)]$ in Section 18.5.4.1 following equation (18.5.4.1). But that discussion also indicates that for the immunoglobulin, the restrained $[\sigma_{\rm res}(r, B_{\rm avg})]$ , which was not computed, will be proportionaly much lower than the unrestrained value of $[\sigma_{\rm diff}(r, B_{\rm avg}) = 0.19\ \hbox{\AA}]$ , since the restraints are relatively more important in the immunoglobulin.

References

International Tables for Crystallography (2006). Vol. F. ch. 18.5, p. 411