International
Tables for Crystallography Volume F Crystallography of biological macromolecules Edited by M. G. Rossmann and E. Arnold © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. F. ch. 18.5, pp. 411412
Section 18.5.7.3. Examples of the DPI using R_{free}^{a}Chemistry Department, UMIST, Manchester M60 1QD, England 
As in the case of monoclinic thaumatin, for lowresolution structures the number of parameters may exceed the number of diffraction data. To circumvent this difficulty, it was proposed in Section 18.5.6.3 to replace by and R by in a revised formula (18.5.6.10) for the DPI. Table 18.5.7.3 shows examples for some structures for which both R and were available. The second row for each protein shows the alternative values for , and the DPI from (18.5.6.10).
References: (a) Deacon et al. (1997); (b) Tickle et al. (1998a); (c) Kobe & Deisenhofer (1995); (d) Cohen et al. (1996).
^{†} negative.

For the structures with , the DPI is much the same whether it is based on R or .
Tickle et al. (1998a) have made fullmatrix error estimates for isotropic restrained refinements of γBcrystallin with and of βB2crystallin with . The DPI calculated for the two structures is 0.14 and 0.25 Å with R in (18.5.6.9), and 0.14 and 0.22 Å with in (18.5.6.10). The fullmatrix weighted averages of for all protein atoms were 0.10 and 0.15 Å, for only mainchain atoms 0.05 and 0.08 Å, for sidechain 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) with , the number of reflections is only just larger than the number of parameters, so that is very large, and the DPI with R gives an unrealistic 1.85 Å. With , .
The HyHEL5–lysozyme complex (Cohen et al., 1996) had . Here the number of reflections is less than the number of parameters, but the formula gives .
References
Cohen, G. H., Sheriff, S. & Davies, D. R. (1996). Refined structure of the monoclonal antibody HyHEL5 with its antigen hen eggwhite lysozyme. Acta Cryst. D52, 315–326.Google ScholarKobe, B. & Deisenhofer, J. (1995). A structural basis of the interactions between leucinerich repeats and protein ligands. Nature (London), 374, 183–186.Google Scholar
Tickle, I. J., Laskowski, R. A. & Moss, D. S. (1998a). Error estimates of protein structure coordinates and deviations from standard geometry by fullmatrix refinement of γB and βB2crystallin. Acta Cryst. D54, 243–252.Google Scholar