Tables for
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. 411   | 1 | 2 |

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

D. W. J. Cruickshanka*

aChemistry Department, UMIST, Manchester M60 1QD, England
Correspondence e-mail: Full-matrix comparison with the diffraction-component precision index

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The DPI ([link] 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[link] are given in Table[link]. For concanavalin A with [B_{\rm avg} = 14.8\ \hbox{\AA}^{2}], the full-matrix quadratic ([link] 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 ([link] gives [\sigma_{\rm diff}(r) = 0.19\ \hbox{\AA}] for a carbon atom, while the DPI gives 0.22 Å.

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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)[link]; (b) Usón et al. (1999)[link].

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 ([link] 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[link] following equation ([link]. 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.

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