ERRAT

ERRAT contains a database of acceptable nonbonded atom-atom distances. It classifies the atom-atom distances in a proposed structure and then does a statistical evaluation of those atom-atom distance interactions. The parameters used to construct the database were derived from known protein structures of varying fold classifications. The known structures used for the database were required to have a maximum resolution of 2.5 A, an R-factor less than 25%, be monomeric or homo-oligomeric, be native structures, and contain peptide bond dihedral angles 15° from ideal values based on the secondary structure. A total of 96 solved X-ray protein structures from the PDB were used as the dataset of correct protein structures. The six types of atom-atom distances were restricted to be atoms from different amino acid residues or to be atoms that interact with each other with a through-space distance no greater than 3.5 The average and standard deviation of each atom-atom distance interaction fraction (the fraction of specific atom-atom pairwise distances in a protein structure), as illustrated in Eq. [4] for CC distances 

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Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

One may also observe a transition to a type of defect-mediated turbulence in this Turing system (see figure C3.6.12 (b). Here the defects divide the system into domains of spots and stripes. The defects move erratically and lead to a turbulent state characterized by exponential decay of correlations [59]. Turing bifurcations can interact with the Hopf bifurcations discussed above to give rise to very complicated spatio-temporal patterns [63, 64]. 

Assisted model building with energy refinement (AMBER) is the name of both a force field and a molecular mechanics program. It was parameterized specifically for proteins and nucleic acids. AMBER uses only five bonding and nonbonding terms along with a sophisticated electrostatic treatment. No cross terms are included. Results are very good for proteins and nucleic acids, but can be somewhat erratic for other systems. 

Vibrational frequencies from semiempirical calculations tend to be qualitative in that they reproduce the general trend mentioned in the introduction here. However, the actual values are erratic. Some values will be close, whereas others are often too high. SAMI is generally the most accurate semiempirical... 

Some density functional theory methods occasionally yield frequencies with a bit of erratic behavior, but with a smaller deviation from the experimental results than semiempirical methods give. Overall systematic error with the better DFT functionals is less than with HF. 

Material properties can be further classified into fundamental properties and derived properties. Fundamental properties are a direct consequence of the molecular structure, such as van der Waals volume, cohesive energy, and heat capacity. Derived properties are not readily identified with a certain aspect of molecular structure. Glass transition temperature, density, solubility, and bulk modulus would be considered derived properties. The way in which fundamental properties are obtained from a simulation is often readily apparent. The way in which derived properties are computed is often an empirically determined combination of fundamental properties. Such empirical methods can give more erratic results, reliable for one class of compounds but not for another. 

Production of pentaerythritol in the United States has been erratic. Demand decreased in 1975 because of an economic recession and grew only moderately to 1980 (69). The range of uses for pentaerythritol has grown rapidly in lubricants (qv), fire-retardant compositions, adhesives, and other formulations where the cross-linking capabiUties are of critical importance. 

Consumption of propylene glycol follows an erratic pattern in the United States which reflects domestic economic conditions. Table 5 gives a breakdown by percentage for the principal uses of propylene glycol in the United States. 

Goal Production. In 1860 world coal production was 122 x 10 t/yr. Production increased to 1140 x 10 t in 1913, giving a 4.2% aimual average rate of increase. The rate has slowed and been erratic since that time. Statistical data on world coal production from 1860 to 1960 is given in Reference 81. World coal and lignite production rose to about 4.7 x 10 t in 1988 (1). 

Almost all PVC powder coatings are appHed by the fluidized-bed coating process. Although some electrostatic spray-grade formulations are available, they are very erratic in their appHcation characteristics. The resistivity of plasticized PVC powders is low compared to other powder coating materials and the appHed powder quickly loses its electrostatic charge. For the same reason, PVC powders show poor appHcation characteristics in an electrostatic fluidized bed and are seldom used in this process. 

Absorption of proteins and peptides, which has been reviewed (60), is generally low and somewhat erratic. The judicious use of absorption enhancers may be necessary and can be accomphshed in a very controUed manner in this area. The mouth is routinely exposed to a wide variety of agents of different pH and osmolarity and appears to be more robust than many other epitheha. Exposure to a wide range of pH values produced damage only at the extremes of... 

Flash points, lower and upper flammability limits, and autoignition temperatures are the three properties used to indicate safe operating limits of temperature when processing organic materials. Prediction methods are somewhat erratic, but, together with comparisons with reliable experimental values for families or similar compounds, they are valuable in setting a conservative value for each of the properties. The DIPPR compilation includes evaluated values for over 1000 common organics. Detailed examples of most of the methods discussed are available in Danner and Daubert."... 

Good management practice will hold inventories at the lowest possible levels consistent with customer satisfaction and efficient plant operation. Excessive inventories are unproductive and are an investment having httle or no rate of return. Excessive inventories should be maintained only when supphes are erratic or rising in price. Management should normally aim for a high inventoiy-turnover ratio, as given by ... 

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