Residual R factor

In general, the R factor is between 0.15 and 0.20 for a well-determined protein structure. The residual difference rarely is due to large errors in the model of the protein molecule, but rather it is an inevitable consequence of errors and imperfections in the data. These derive from various sources, including slight variations in conformation of the protein molecules and inaccurate corrections both for the presence of solvent and for differences in the orientation of the microcrystals from which the crystal is built. This means that the final model represents an average of molecules that are slightly different both in conformation and orientation, and not surprisingly the model never corresponds precisely to the actual crystal. 

The residues R (mgkg ) of imibenconazole and the metabolite imibenconazole-debenzyl (calculated as imibenconazole by conversion factor) are calculated from the following equations ... 

The amount of tebuconazole residue (R) is calculated by applying the response factor (RF) to a standard (std) calibration curve. Calculations are performed using the instrument software using the following equation ... 

The unit cell is tetragonal, with a = b = 10.7 A (1.07 nm) and c = 16.1 A (1.61 nm). The amylose helix is left-handed, with four D-glucose residues per turn. Both ions are located in a water-like environment. The atoms 0-2, 0-3, and 0-4 from D-glucose residues on adjacent chains coordinate around K+. The R factor is 41%. 

The space group is P2i2i2 . The unit cell is pseudotetragonal, with a = b = 19.17 A (1.917 nm), and c = 24.39 A (2.439 nm), with two antiparallel chains per cell. The amylose chain is a left-handed 6(—1.355) helix, with three turns per crystallographic repeat. One molecule of dimethyl sulfoxide for every three D-glucose residues is located inside the helix. An additional 4 molecules of dimethyl sulfoxide and 8 of water are located in the interstices. The interstitial dimethyl sulfoxide is the source of additional layer-lines that are not consistent with the 8.13 A (813 pm) amylose repeat. The overall R factor is 35%, and, for the layer lines with amylose contribution alone, it is 29%. 

The x is best when the differences between theory and experiment are normally distributed and when the variance a is correctly estimated. The optimum has a value close to unity, y smaller than 1 indicates an overestimation of the variance. On the other hand, a is not needed for the evaluation of R-factor, which measures the residual difference in percentage. 

Waller factor, AEr correction of threshold energy and R factor residual factor. ... 

In using cross-validation it is essential to avoid, or at least minimize, bias to the free R factor itself. In the era of emerging automated procedures for modelling and refinement a frequent mistake is to set aside a fraction of reflections for minimization of the residual in reciprocal space and, at the same time, to use all data for computation of electron density and model rebuilding. Since local adjustment of the model in real space is equivalent to global phase adjustment in reciprocal space, the free reflection set becomes biased towards the current model and loses its validation credibility. 

The residual index, or R factor, gives a measure of the difference between the observed and calculated structure factors and therefore of how well the structure has refined. It is defined as... 

Using the two-chain unit-cell,3 with a = 0.817 nm, b = 0.785 nm, c = 1.034 nm, andy = 96.38°, the modified intensity-data of Mann and coworkers,37 and several residue-geometries, the structure of native ramie cellulose was refined. The resulting R factors were 15.8%, 18.5%, and 17.5% for, the antiparallel, parallel-up, and parallel-down models, respectively. A temperature factor of 0.23 nm2 was necessary in order to obtain a good fit with the observed data. It was suggested that the antiparallel packing of the chains cannot be discounted for cotton and ramie celluloses. 

Normally, if the assumed model for a crystal structure has an R value of 0.5 and resists attempts to refine to a lower residual, then the model structure is rejected as false, and a new model is tried until a fit between the observed and calculated structure factors yields an acceptable residual (R < 0.25). (Other models were tried for this complex, but they either gave Fourier maps which were uninterpretable or they converged to the present model). However, the normal crystal structure is solved with data obtained from crystals which have dimensions of the order of 0.1 mm. In the crystals available for this experiment, two of the dimensions were of the order of 0.01 mm. Thus, long exposures were required to give a small number of relatively weak diffraction spots. (Each Weissenberg photograph was exposed for five days with Cuka radiation 50 kv., 20 ma. loading, in a helium atmosphere). 

The progress of iterative real- and reciprocal-space refinement is monitored by comparing the measured structure-factor amplitudes IFobsl (which are proportional to (/obs ) /2) with amplitudes IFca(c I from the current model. In calculating the new phases at each stage, we learn what intensities our current model, if correct, would yield. As we converge to the correct structure, the measured Fs and the calculated Fs should also converge. The most widely used measure of convergence is the residual index, or R-factor (Chapter 6, Section V.E). 

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