Expected profile residual

As expected, adding the contribution from the impurity phase (again as Le Bail s approximation) results in further reduction of the profile residuals, see row six in Table 7.7. The final model of this crystal structure, as determined using the combined Rietveld refinement in the two-phase approximation, is found in the data file Ch7Ex01k.inp on the CD. Structural parameters are listed in Table 7.8. 

Another group of methods for testing 3D models that implicitly take into account many of the criteria listed above involve 3D profiles and statistical potentials [87,216]. These methods evaluate the environment of each residue in a model with respect to the expected environment as found in the high resolution X-ray structures. Programs implementing this approach include VERIFY3D [216], PROSA [217], HARMONY [218], and ANOLEA [120]. 

A prior distribution for sequence profiles can be derived from mixtures of Dirichlet distributions [16,51-54]. The idea is simple Each position in a multiple alignment represents one of a limited number of possible distributions that reflect the important physical forces that determine protein structure and function. In certain core positions, we expect to get a distribution restricted to Val, He, Met, and Leu. Other core positions may include these amino acids plus the large hydrophobic aromatic amino acids Phe and Trp. There will also be positions that are completely conserved, including catalytic residues (often Lys, GIu, Asp, Arg, Ser, and other polar amino acids) and Gly and Pro residues that are important in achieving certain backbone conformations in coil regions. Cys residues that form disulfide bonds or coordinate metal ions are also usually well conserved. 

In several cases, a fit of equation (2) to the data was not statistically significant, or the residuals indicated systematic deviations due to strongly curved release profiles. Then, alternatively a fit of equation (3) was tried in order to be able to describe tendencies which occur on variation of matrix composition. In all cases the first time interval was not considered, as burst effects are to be expected which are not representative for long-term drug release. 

When the energy of residues is plotted as a function of the amino acid sequence position, we obtain an energy profile. High energies in the energy profile point to deviations from the expected energies in native proteins (Figure 11.4). 

Fig. 1.3. Paramagnetic relaxation enhancement profiles for apomyoglobin unfolded at pH 2.3 in the presence (left panels) and absence (right panels) of 8M urea. Data for spin labels attached at residues 18 and 77 is shown. The plots show the ratio of HSQC cross-peak intensity with the spin label oxidized (paramagnetic) and reduced (diamagnetic) as a function of residue number. The solid lines in the left panels represent the broadening profile expected for a random coil polypeptide. The figure is adapted from data reported in [14]. The positions of the helices in holomyoglobin are shown by the bars at the top of the figure...

Again, the degree of deactivation can be expected to depend on the temperature and conversion level, as expressed by Equations 4 and 5. Indeed, coke profiles over isothermal laboratory reactors (72) show such differences, primarily due to a reduction in hydrogen partial pressure. Metals deposition over residue catalysts beds show a decrease with conversion simply because of depletion of the reactant 2,13,14). 

The initial model of the crystal structure results in acceptable residuals without refinement of coordinates and displacement parameters of individual atoms. When the coordinates of all atoms and the overall displacement parameter were included into the least squares, the residuals further improve (row four in Table 7.14). The biggest improvement is observed in the Bragg residual, Rb, which is expected because this figure of merit is mostly affected by the adequacy of the structural model and it is least affected by the inaccuracies in profile parameters. 

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