Crystallographic residual

The structure was refined by block-diagonal least squares in which carbon and oxygen atoms were modeled with isotropic and then anisotropic thermal parameters. Although many of the hydrogen atom positions were available from difference electron density maps, they were all placed in ideal locations. Final refinement with all hydrogen atoms fixed converged at crystallographic residuals of R=0.061 and R =0.075. 

Subsequently, the baboon a-lactalbumin structure was refined at 1.7-A resolution by Acharya et al. (1989). Using the structure of domestic hen egg white lysozyme as the starting model, preliminary refinement was made using heavily constrained least-squares minimization in reciprocal space. Further refinement was made using stereochemical restraints at 1.7-A resolution to a conventional crystallographic residual of 0.22 for 1141 protein atoms. 

When the crystallographic residual (a quantitative measure of the degree of match between experimental and simulated diffraction data, in the zeolite case powder diffraction data) was added to the energy expression the number of hypothetical but inappropriate structural models was dramatically reduced [36]. The next step which, althoiigh seemingly obvious at the time,... 

Crystals of the seven-methionine variant were obtained using 2 M phosphate solutions, pH 6.7, and were found to be isomorphous with wild-type lysozyme (Weaver and Matthews, 1987). A data set to 1.9A resolution, 92% complete was measured. The structure was refined to a crystallographic residual of 15.2% with bond lengths and angles within O.ISA and 3.0° of ideal values and found to be similar to wild-type. The root-mean-square discrepancy of the main-chain atoms within the C-terminal domain was 0.20A. The Xi and Xi values of the mutant side-chains were similar to those in wild-type except at position 153 where Xi changed by 92° and avoided a steric clash (Table III). Thus, each of the substituted methionines essentially traces the path of... 

The crystallographic residual E ay The most common form of E ay consists of the crystallographic residual, defined as the sum over the squared differences between the observed ( Fo6s( )l) nd calculated ( f coic( ) ) structure factor amplitudes ... 

The crystallographic residual (Eq. 2) only incorporates information about the amplitudes of the observed reflections. A penalty term ( phase restraints ) [23] based on the difference between observed phases and those calculated from the model can be added to the residual ... 

In general, the improvement of the electron density map achieved in simulated annealing refinement is a consequence of conformational changes distributed throughout the molecule. This is a reflection of the fact that the first derivatives of the crystallographic residual (Eq. 1) with respect to the coordinates of a particular atom depend not only on the coordinates of that atom and its neighbors but also on the coordinates of all other atoms including solvent atoms in the crystal structure. 

The initial model is never the best obtainable but, in order to improve it, we need to know how to assess and compare its correctness. By far the best-known and most widely used measure is the crystallographic residual or //-factor ... 

X,R represent the set of atomic positions and vibrational parameters, respectively. Fobs and ivaic are respectively the observed and calculated structure factor amplitudes. R is the crystallographic residual between Fobs and Fcak-... 

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