Unrestrained inversion for an immunoglobulin

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. 408 | 1 | 2 |

Section 18.5.4.2. Unrestrained inversion for an immunoglobulin

D. W. J. Cruickshank^a ^*^‡

^a Chemistry 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). Fig. 18.5.4.3 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), 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 and 18.5.4.3 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| 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 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| 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

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

International Tables for Crystallography (2006). Vol. F. ch. 18.5, p. 408