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, pp. 411-412   | 1 | 2 |

Section Examples of the DPI using Rfree

D. W. J. Cruickshanka*

aChemistry Department, UMIST, Manchester M60 1QD, England
Correspondence e-mail: Examples of the DPI using Rfree

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As in the case of monoclinic thaumatin, for low-resolution structures the number of parameters may exceed the number of diffraction data. To circumvent this difficulty, it was proposed in Section[link] to replace [p = n_{\rm obs} - n_{\rm params}] by [n_{\rm obs}] and R by [R_{\rm free}] in a revised formula ([link] for the DPI. Table[link] shows examples for some structures for which both R and [R_{\rm free}] were available. The second row for each protein shows the alternative values for [(N_{i}/n_{\rm obs})^{1/2}], [R_{\rm free}] and the DPI [\sigma (r, B_{\rm avg})] from ([link].

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Comparison of DPIs using R and Rfree

The second row for each protein contains values appropriate to the DPI equation ([link] using Rfree.

Protein[N_{i}][n_{\rm obs}][(N_{i}/p)^{1/2}], [(N_{i}/n_{\rm obs})^{1/2}][C^{-1/3}]R, [R_{\rm free}][d_{\min}] (Å)DPI [\sigma (r, B_{\rm avg})] (Å)Luzzati [\langle \Delta r\rangle] (Å)Read [\langle \Delta r\rangle] (Å)Reference
Concanavalin A 2130 116712 0.148 1.099 0.128 0.94 0.034 0.06   (a)
    0.135   0.148   0.036      
γB-Crystallin 1708 26151 0.297 1.032 0.180 1.49 0.14 0.16 0.12 (b)
    0.256   0.204   0.14      
βB2-Crystallin 1558 18583 0.356 ∼1.032 0.184 2.10 0.25 0.21 0.17 (b)
    0.290   0.200   0.22      
Ribonuclease A with RI 4416 18859 1.922 1.145 0.194 2.50 1.85 0.32 0.57 (c)
    0.484   0.286   0.69      
Fab HyHEL-5 with HEWL 4333 11754 1.111 0.196 2.65 0.30   (d)
    0.607   0.288   0.69      

References: (a) Deacon et al. (1997)[link]; (b) Tickle et al. (1998a)[link]; (c) Kobe & Deisenhofer (1995)[link]; (d) Cohen et al. (1996)[link].
[(N_{i}/p)] negative.

For the structures with [d_{\min} \leq 2.0\ \hbox{\AA}], the DPI is much the same whether it is based on R or [R_{\rm free}].

Tickle et al. (1998a)[link] have made full-matrix error estimates for isotropic restrained refinements of γB-crystallin with [d_{\min} = 1.49\ \hbox{\AA}] and of βB2-crystallin with [d_{\rm min} = 2.10\ \hbox{\AA}]. The DPI [\sigma (r, B_{\rm avg})] calculated for the two structures is 0.14 and 0.25 Å with R in ([link], and 0.14 and 0.22 Å with [R_{\rm free}] in ([link]. The full-matrix weighted averages of [\sigma_{\rm res}(r)] for all protein atoms were 0.10 and 0.15 Å, for only main-chain atoms 0.05 and 0.08 Å, for side-chain atoms 0.14 and 0.20 Å, and for water oxygens 0.27 and 0.35 Å. Again, the DPI gives reasonable overall indices for the quality of the structures.

For the complex of bovine ribonuclease A and porcine ribonuclease inhibitor (Kobe & Deisenhofer, 1995[link]) with [d_{\min} = 2.50\ \hbox{\AA}], the number of reflections is only just larger than the number of parameters, so that [(N_{i}/p)^{1/2} = 1.922] is very large, and the DPI with R gives an unrealistic 1.85 Å. With [R_{\rm free}], [\sigma (r, B_{\rm avg}) =0.69\ \hbox{\AA}].

The HyHEL-5–lysozyme complex (Cohen et al., 1996[link]) had [d_{\rm min} = 2.65\ \hbox{\AA}]. Here the number of reflections is less than the number of parameters, but the [R_{\rm free}] formula gives [\sigma (r, B_{\rm avg}) =0.69\ \hbox{\AA}].


First citationCohen, G. H., Sheriff, S. & Davies, D. R. (1996). Refined structure of the monoclonal antibody HyHEL-5 with its antigen hen egg-white lysozyme. Acta Cryst. D52, 315–326.Google Scholar
First citationKobe, B. & Deisenhofer, J. (1995). A structural basis of the interactions between leucine-rich repeats and protein ligands. Nature (London), 374, 183–186.Google Scholar
First citationTickle, 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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