Further examples of the DPI using R

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 18.5.7.2. Further examples of the DPI using R

D. W. J. Cruickshank^a ^*^‡

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

18.5.7.2. Further examples of the DPI using R

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Table 18.5.7.2 shows a range of examples of the application of the DPI (18.5.6.9) using R to proteins of differing precision, starting with the smallest $[d_{\rm min}]$ . In all the examples, $[N_{i}]$ has been set equal to $[n_{\rm atoms}]$ , the total number of atoms. The ninth and tenth columns show $[\langle \Delta r\rangle]$ values derived from Luzzati (1952) and Read (1986) plots described later in Section 18.5.8.

Table 18.5.7.2| top | pdf |
Examples of diffraction-component precision indices (DPIs)

Protein	$[N_{i}]$	$[n_{\rm obs}]$	$[(N_{i}/p)^{1/2}]$	$[C^{-1/3}]$	R	$[d_{\min}]$ (Å)	DPI $[\sigma (r, B_{\rm avg})]$ (Å)	Luzzati $[\langle \Delta r\rangle]$ (Å)	Read $[\langle \Delta r\rangle]$ (Å)	Reference
Crambin	447	23759	0.150	1.074	0.090	0.83	0.021	0.055		(a)
Ribonuclease MGMP	1958	62845	0.208	1.046	0.109	1.15	0.047		0.08	(b)
Ribonuclease MSA	1832	60670	0.204	1.016	0.106	1.20	0.045		0.05	(b)
TGF- $[\beta 2]$ 1TGI	948	∼14000	0.305	∼1.0	0.173	1.80	0.16	0.21	0.18	(c)
TGF- $[\beta 2]$ 1TFG	974	∼11000	0.370	∼1.0	0.188	1.95	0.24	0.23		(c)
Lactoferrin	5907	39113	0.618	1.036	0.179	2.20	0.43	0.25–0.30	0.35	(d)
Thaumatin C2	1552	4622	^†	1.10	0.184	2.60	—	0.25		(e)

References: (a) Stec et al. (1995)

; (b) Sevcik et al. (1996)

; (c) Daopin et al. (1994)

; (d) Haridas et al. (1995)

; (e) Ko et al. (1994)

^† $[(N_{i}/p)]$ negative.

The first entry is for crambin at 0.83 Å resolution and 130 K (Stec et al., 1995). Their results were obtained from an unrestrained full-matrix anisotropic refinement. Inversion of the full matrix gave s.u.'s $[\sigma_{\rm diff}(x) = 0.0096\ \hbox{\AA}]$ for backbone atoms, 0.0168 Å for side-chain atoms and 0.0409 Å for solvent atoms, with an average for all atoms of 0.022 Å. The DPI $[\sigma (r, B_{\rm avg}) = 0.021\ \hbox{\AA}]$ corresponds to $[\sigma (x) = 0.012\ \hbox{\AA}]$ , which is satisfactorily intermediate between the full-matrix values for the backbone and side-chain atoms.

Sevcik et al. (1996) carried out restrained anisotropic full-matrix refinements on data from two slightly different crystals of ribonuclease Sa, with $[d_{\min}]$ of 1.15 and 1.20 Å. They inverted full-matrix blocks containing parameters of 20 residues to estimate coordinate errors. The overall r.m.s. coordinate error for protein atoms is given as 0.03 Å, and for all atoms (including waters and ligands) as 0.07 Å for MGMP and 0.05 Å for MSA. The DPI gives $[\sigma (r, B_{\rm avg}) = 0.05\ \hbox{\AA}]$ for both structures.

The next entries concern the two lower-resolution (1.8 and 1.95 Å) studies of TGF- $[\beta 2]$ (Daopin et al., 1994). The DPI gives $[\sigma (r) = 0.16\ \hbox{\AA}]$ for 1TGI and 0.24 Å for 1TGF. This indicates an r.m.s. position difference between the structures for atoms with $[B_{i} = B_{\rm avg}]$ of $[(0.16^{2} + 0.24^{2})^{1/2} = 0.29\ \hbox{\AA}]$ . Daopin et al. reported the differences between the two determinations, omitting poor parts, as $[\langle \Delta r\rangle_{\rm rms} = 0.15\ \hbox{\AA}]$ (main chain) and 0.29 Å (all atoms).

Human diferric lactoferrin (Haridas et al., 1995) is an example of a large protein at the lower resolution of 2.2 Å, with a high value of $[(N_{i}/p)^{1/2}]$ , leading to $[\sigma (r, B_{\rm avg}) = 0.43\ \hbox{\AA}]$ .

Three crystal forms of thaumatin were studied by Ko et al. (1994). The orthorhombic and tetragonal forms diffracted to 1.75 Å, but the monoclinic C2 form diffracted only to 2.6 Å. The structures with 1552 protein atoms were successfully refined with restraints by XPLOR and TNT. For the monoclinic form, the number of parameters exceeds the number of diffraction observations, so $[(N_{i}/p)]$ is negative and no estimate by (18.5.6.9) of the diffraction-data-only error is possible. The DPI (18.5.6.9) gives 0.17 and 0.16 Å for the orthorhombic and tetragonal forms, respectively.

References

Daopin, S., Davies, D. R., Schlunegger, M. P. & Grütter, M. G. (1994). Comparison of two crystal structures of TGF-β2: the accuracy of refined protein structures. Acta Cryst. D50, 85–92.Google Scholar

Haridas, M., Anderson, B. F. & Baker, E. N. (1995). Structure of human diferric lactoferrin refined at 2.2 Å resolution. Acta Cryst. D51, 629–646.Google Scholar

Ko, T.-P., Day, J., Greenwood, A. & McPherson, A. (1994). Structures of three crystal forms of the sweet protein thaumatin. Acta Cryst. D50, 813–825.Google Scholar

Luzzati, V. (1952). Traitement statistique des erreurs dans la determination des structures cristallines. Acta Cryst. 5, 802–810.Google Scholar

Read, R. J. (1986). Improved Fourier coefficients for maps using phases from partial structures with errors. Acta Cryst. A42, 140–149.Google Scholar

Sevcik, J., Dauter, Z., Lamzin, V. S. & Wilson, K. S. (1996). Ribonuclease from Streptomyces aureofaciens at atomic resolution. Acta Cryst. D52, 327–344.Google Scholar

Stec, B., Zhou, R. & Teeter, M. M. (1995). Full-matrix refinement of the protein crambin at 0.83 Å and 130 K. Acta Cryst. D51, 663–681.Google Scholar

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