R-factors

A systematic comparison of two sets of data requires a numerical evaluation of their likeliness. TOF-SARS and SARIS produce one- and two-dhnensional data plots, respectively. Comparison of sunulated and experimental data is accomplished by calculating a one- or two-dimensional reliability (R) factor [33], respectively, based on the R-factors developed for FEED [34]. The R-factor between tire experimental and simulated data is minimized by means of a multiparameter simplex method [33]. 

Traditionally, least-squares methods have been used to refine protein crystal structures. In this method, a set of simultaneous equations is set up whose solutions correspond to a minimum of the R factor with respect to each of the atomic coordinates. Least-squares refinement requires an N x N matrix to be inverted, where N is the number of parameters. It is usually necessary to examine an evolving model visually every few cycles of the refinement to check that the structure looks reasonable. During visual examination it may be necessary to alter a model to give a better fit to the electron density and prevent the refinement falling into an incorrect local minimum. X-ray refinement is time consuming, requires substantial human involvement and is a skill which usually takes several years to acquire. 

Jack A and M Levitt 1978. Refinement of Large Structures by Simultaneous Minimization of Energy and R-factor. Acta Crystallographica A34 931-929. 

G1 as s CO de b Thei mal stress resist ance °c Strain, °C Anne alia °C Soften in °c Workin °C Knoo P hardn ess, HKio 0 Den sity, g/c 3 m Youn g s mod ulus, GPa Poiss on s ratio 25° C 25 0° C 350 °C Powe r factor, % Diele ctric const ant Loss factor, % Refrac tive index... 

Insulation material R-Factor 7 R-Value 5.3 for thickness in cm 3.5 1.8 Relative cost... 

R-Factor data for phenoHc suppHed by Manvike source for all other R-factors is The Dow Chemical Company. Units of R-factor are (W-cm)/hm -K (= 1.4 Btu-in./h-sq ft°F). R-Value per cm of thickness is the R-factor. R- and R-factors can vary with age and use conditions. Values shown are averages obtained from lab samples. 

R = factor for electrical relaxation D = dielectric constant of medium F = factor for size of spheres and = zeta potential. 

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. 

To measure the goodness of fit, and to quantify the structural determination, a reliability (i -factor) comparison is used. In comparing the data and simulation of the experiment for many trial structures, a minimum R factor can be found corresponding to the optimal structure. In this way atomic positions can be determined in favorable cases to within a few hundredths of an A, comparable to the accuracy achieved in Low-Energy Electron Diffraction (LEED). 

When automated searches are implemented, the LEED I-V calculation and the R factor comparison are called by the master search program either as subroutines or as separate programs through the operating system. The LEED I-V calculations are... 

Solution Calculate the R factor and determine the tracer requirements from Table 10-46. 

From Table 10-46 it can be determined that the calculated R factor of 6.96 is less than that of 7 shown for one -in. O.D. tracer on a 3-in. line using 1 V2 -in. insulation. Thus, a single /g -in. O.D. tracer is satisfactory. 

The permutations of 0[H] have a special effect on the rows of the matrix (1.37) if a permutation moves an element of one row into another row, then the permutation moves all the elements of the one row into the other row. The rows of (1.37) are imprimitive domains of 0[H]. The permutations of 0[H] which leave the r imprimitive domains invariant (the gross permutation of which is the identity) form a subgroup it has order it is the direct product H xHxHx...xH with r factors and is a normal subgroup of C [H], with factor group. 

Bromodeboronation has acquired a particular significance in recent theories of electrophilic substitution and briefly this has arisen since it was supposed to have a very high r factor relative to its p factor in a Yukawa-Tsuno analysis. (For a fuller discussion see ref. 729). It had been suggested729 that some of the rate coefficients determined for the reaction (Table 254) may be in error due to concurrent bromodeprotonation, and a reinvestigation730 of this possibility has revealed a number of points ... 

The titration method used is, in our experience, incapable of detecting a difference between a reaction rate of this speed or one a hundred times slower, since it takes a minimum of 45 sec to obtain the first reading. Since this is the major point on which the high r factor was based, the arguments following from it are no longer tenable. 

Energy minimization methods that exploit information about the second derivative of the potential are quite effective in the structural refinement of proteins. That is, in the process of X-ray structural determination one sometimes obtains bad steric interactions that can easily be relaxed by a small number of energy minimization cycles. The type of relaxation that can be obtained by energy minimization procedures is illustrated in Fig. 4.4. In fact, one can combine the potential U r) with the function which is usually optimized in X-ray structure determination (the R factor ) and minimize the sum of these functions (Ref. 4) by a conjugated gradient method, thus satisfying both the X-ray electron density constraints and steric constraint dictated by the molecular potential surface. 

Figure 1.15. Student s f-distiibutions for 1 (bottom), 2, 5, and 100 (top) degrees of freedom /. The hatched area between the innermost marks is in all cases 80% of the total area under the respective curve. The other marks designate the points at which the area reaches 90, resp. 95% of the total area. This shows how the r-factor varies with /. The t-distribution for / = 100 already very closely matches the normal distribution. The normal distribution, which corresponds to t(f = o), does not depend on/.

In several programs subroutine PROBAB is used to find the probability p that the result is due to chance alone if a Student s r-factor and the number of measurements is known. 

Brunger AT, Kuriyan J, Karpins M. Crystallographic r-factor refinement by molecular dynamics. Science 1987 235 458-60... 

Phosphorylative inactivation of aminoglycosidic antibiotics by Escherichia coli carrying R factor, H. Umezawa, M. Okanishi, S. Kondo, K. 

Borel, R, Factors affecting intestinal absorption of highly lipophilic food microconstituents (fat-soluble vitamins, carotenoids and phytosterols), Clin. Chem. Lab. Med., 41, 979, 2003. 

Bauer, D. C., Browner, W. S., Cauley, J. A., Orwoll, E. S., Scott, J. C., Black, D. M., Tao, J. L., Cummings, S. R., Factors associated with appendicular bone mass in older women. The study of osteoporotic fractures research group, University of California, San Francisco., Annals of Internal Medicine, 118, 741, 1993. 

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