Isotropic B factors

Table 6.5 Ranges of f work for the various levels of theory determined after optimization of all copies of selected even-numbered residues from 2VB1. In each case, the isotropic B factors were refined after the full set of optimizations was completed. Residues marked by bold letters are problematic cases and will be discussed in more detail later...

Fig. 6.4 Rwork in per cent following optimization of all included copies of one of the seven problematic residues from 2VB1. Four levels of theory are shown. Isotropic B factors were refined in all cases. The dashed, horizontal line marks Rwork of the initial structure before optimization (13.82 %). TZ means def2-TZVP , DZ means def2-SV(P) and PDZ stands for the Pople basis set 6-3IG. The lines are drawn to better guide the eye...

Table 6.8 /fwork in P t cent for ALA32 and ALA90. First the R factors for only one representation in one of the eight sectors A-Fl of 2VBliJ are shown, then the combined expected R factor from these eight results based on the linear additive assumption and then the actually found value. The results are shown forTPSS-D3(BJ)/def2-TZVP . Isotropic B factors were optimized in each case... 

Kidera et al. have applied the normal mode refinement technique to the determination of the dynamic structures of wild-type and mutant C77A/C95A lysozyme, the mutant structure lacking a disulfide bond normally found in the wild-type structure. This disulfide bond lies in the proposed hingebending region between the two domains of lysozyme. The refinement was carried out for each structure using 1.5 A data and sought to define the influence of this disulfide bond on the dynamic structure of the protein. The dynamic structure refinement was found to result in coordinates with rms variations of 0.06 and 0.07 A for all atoms relative to the structures refined by isotropic B factor refinement for the wild-type and mutant structures, respectively. The rms difference between wild-type and mutant structures was found to be 0.24 A for all atoms with B factors less than 20. 

Isotropic temperature factors (B) are in A standard deviations are given in parentheses. 

Analysis of the spectra at different frequencies yielded the parameters D = — 2.20(5) cm-1, = 0.0(1) cm-1, and a nearly isotropic g-factor, g = 1.98(2), none of which could have been determined at X-band. Analysis was aided by the observation of different slopes of the B vs. v plots for Ams > 1 and Ams = 1 transitions. A review of advanced methods, including high-field EPR, is given in ref. 11. Various recent applications of high field and multi-frequency EPR are described in refs 19-31. 

Small molecule crystallographers are familiar with these concepts, since it is routine to measure data at low temperature to improve precision by reduction of thermal motion, and structures are often done at multiple temperatures to assess the origins of disorder in atomic positions. Albertsson et al. (1979) have reported the analysis of the crystal structure of Z)(-l-)-tartaric acid at 295, 160, 105, and 35 K. Figure 22 shows the individual isotropic. S-factors for the atoms in the structure at each of these temperatures the smooth variation of B with T is apparent. Below 105 K, B is essentially identical for all atoms and is also temperature independent the value of B = 0.7 agrees well with the expected zero-point vibradonal value. However, even for this simple structure, not all of the atoms show B vs T behavior at high temperature which extrapolates to 0 A at 0 K. 

Reflection intensity in the SAED negatives was measured with a microdensitometer. The refinement of the structure analysis was performed by the least square method over the intensity data (25 reflections) thus obtained. A PPX single-crystal is a mosaic crystal which gives an "N-pattem". Therefore we used the 1/d hko as the Lorentz correction factor [28], where d hko is the (hkO) spacing of the crystal. In this case, the reliability factor R was 31%, and the isotropic temperature factor B was 0.076nm. The molecular conformation of the P-form took after that of the P-form since R was minimized with this conformation benzene rings are perpendicular to the trans-zigzag plane of -CH2-CH2-. 

Publications of refined structures often include a plot of average isotropic B values for side-chain and main-chain atoms of each residue, like that shown in Section III.C, Fig. 8.5 b for ALBP. Pictures of the model may be color coded by temperature factor red ("hot") for high values of B and blue ("cold") for... 

FIGURE 6.22. Isotropic displacement factors for oxygen, atomic number 8. Note that the larger the value of B, the greater the falloff in intensity as a function of sinO/X. but that the values of / when sin = 0 is always 8.0. 

The scale factor K may be determined, together with the average isotropic thermal factor B, by the Wilson method.On assuming that Bj is equal to B for all the atoms, Equation (3) may be rewritten as ... 

For an isotropic refinement, four parameters per atom (three for the coordinates and one for the B factor) thus have to be optimized during the refinement process. If anisotropic B factors and occupancies are used, the number of parameters increases almost three fold and therefore overfltting can become an important problem. One way to test for overfitting is the above mentioned cross-validation using Bfree. 

Table 1. Positional parameters (x,y,z) and equivalent isotropic temperature factors (B) for fluor-, hydroxyl-, and chlorapatite. Lattice parameters are at the base of the table (from Hughes et al. 1989).

These chain perturbations are uniaxial, and not the isotropic expansion factors employed in solution theory. It should be noted that while Inoue (Section 4.7.2) found dimensions increasing as the cube root of the molecular weight, values estimated by Meier increase in a manner closer to the square root of the molecular weight, and depend upon the relative lengths of the blocks. It should be emphasized that the mutual perturbations arise from the necessity that space be filled by chains connected together such that the numbers of A and B chains per unit area of interface must be the same (Meier, 1972). 

Deviations of atomic volumes do not indicate directly that a defective protein exists because deviations in atomic volumes can be attributed to other physical phenomena. It is for this reason that the authors of PROVE correlated the atom volume deviations with crystallographic qualities of the protein X-ray structure including the resolution (lowest resolvable separation between two carbon atoms), the R-factor (measure of how well the refined structure agrees with the experimental model/electron density maps/raw data), and B-factors (isotropic temperature factor).A test set of 900 protein structures was constructed, each containing a minimum of 100 buried atoms. The resolution of the protein structures ranged from 1.0 to 3.9 A. The authors found that for high-resolution structures (1.0 to 1.6 A), the average Zrmsd was approximately 1.0. When poorer quality crystal structures were considered, the Zrmsd increased. The correlation coefficient for a plot of Zrmsd versus experimental resolution was 0.89 for all protein structures in the test set... 

---