International
Tables for
Crystallography
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. 408   | 1 | 2 |

Section 18.5.4.2. Unrestrained inversion for an immunoglobulin

D. W. J. Cruickshanka*

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

18.5.4.2. Unrestrained inversion for an immunoglobulin

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Sheldrick has provided the results of the unrestrained lower-resolution refinement of a single-chain immunoglobulin mutant (T39K) with 218 amino-acid residues, with data to 1.70 Å refined isotropically (Usón et al., 1999[link]). Fig. 18.5.4.3[link] shows [\sigma_{\rm diff}(r)] versus [B_{\rm eq}] for the fully occupied protein atoms. Superposed on the data points are least-squares quadratic fits. In a first very rough approximation for [\sigma_{\rm diff}(x_{i})] suggested later by equation (18.5.6.3)[link], the dependence on atom type is controlled by [1/Z_{i}], the reciprocal of the atomic number. Sheldrick found that a [1/Z_{i}] dependence produced too little difference between C, N and O. The proportionalities between the quadratics for [\sigma (r)] in Figs. 18.5.4.1[link] and 18.5.4.3[link] are based on the reciprocals of the scattering factors at [\sin \theta /\lambda = 0.3\ \hbox{\AA}^{-1}], symbolized by [Z_{i}^{\# }]. For C, N and O, these are 2.494, 3.219 and 4.089, respectively. For potential use in later work, the least-squares fits to the [\sigma (r_{i})Z_{i}^{\# }] in Å are recorded here as [\eqalignno{ 0.11892 &+ 0.00891B + 0.0001462B^{2}, &(18.5.4.2a)\cr 0.01826 &+ 0.001043B + 0.0002230B^{2} \hbox{ and } &(18.5.4.2b)\cr 0.00115 &+ 0.004414B + 0.0000214B^{2} &(18.5.4.2c)\cr}] for the immunoglobulin (unrestrained), concanavalin A (unrestrained) and concanavalin A (restrained), respectively.

[Figure 18.5.4.3]

Figure 18.5.4.3 | top | pdf |

Plot of [\sigma_{\rm diff}(r)] versus [B_{\rm eq}] from an unrestrained full matrix for immunoglobulin mutant (T39K) with 1.70 Å data. Carbon black, nitrogen blue, oxygen red.

As might be expected from the lower resolution, the lowest [\sigma_{\rm diff}(r)]'s in the immunoglobulin are about six times the lowest [\sigma_{\rm diff}(r)]'s in concanavalin. But at B = 50 Å2, the immunoglobulin curve for carbon gives [\sigma_{\rm diff}(r) = 0.37] Å, which is only 50% larger than the concanavalin value of 0.25 Å.

Fig. 18.5.4.4[link] shows [\sigma_{\rm diff}(l)] versus [B_{\rm eq}] for the immunoglobulin. Note that the lowest immunoglobulin unrestrained [\sigma_{\rm diff}(l)] is about 0.06 Å, which is three times the 0.02 Å [\sigma_{\rm geom}(l)] bond restraint.

[Figure 18.5.4.4]

Figure 18.5.4.4 | top | pdf |

Plot of [\sigma_{\rm diff}(l)] versus average [B_{\rm eq}] from an unrestrained full matrix for immunoglobulin mutant (T39K) with 1.70 Å data. C—O black, C—N blue, C—O red.

References

First citationUsón, I., Pohl, E., Schneider, T. R., Dauter, Z., Schmidt, A., Fritz, H.-J. & Sheldrick, G. M. (1999). 1.7 Å structure of the stabilized REIV mutant T39K. Application of local NCS restraints. Acta Cryst. D55, 1158–1167.Google Scholar








































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