Secondary Superposition

There have been many attempts to formulate a procedure to avoid it and both a posteriori and a priori schemes are available. The counterpoise approach (CP) (Boys and Bemardi, 1970) and related methods are the most conunon a posteriori procedures. Although this technique represents the most frequently employed a posteriori procedure to estimate this error, several authors have emphasised that the method introduced by Boys and Bemardi does not allow a clear and precise determination of the BSSE. The addition of the partner s functions introduces the "secondary superposition error" a spurious electrostatic contribution due to the modification of the multipole moments and polarizabilities of the monomers. This is particularly important in the case of anisotropic potentials where these errors can contribute to alter the shape of the PES and the resulting physical picture (Xantheas, 1996 and Simon et al., 1996). 

In the previous chapters our attention was paid mainly to the study of the figure of the earth and with this purpose in mind we represented the total field as a sum of the normal and secondary fields. In this chapter, we will discuss a completely different application of the gravity method, related to exploration geophysics, in which the gravitational field is measured in order to study lateral changes of the density near the earth s surface. By analogy, we also represent the gravitational field as a superposition of two fields ... 

Superposition of residues 83 to 248 of the family of structures is shown in Figure 9 viewed along the long axis of the catalytic helix. Residues 249 to 255 are disordered and therefore are not shown. In Figure 10 ribbon drawings of two views of the molecule are shown, one from above the (3-sheet and the other from below the Si subsite. The secondary structure of sfSTR consists of a five stranded [. -sheet with four parallel strands and... 

The crystal structure of MPT synthase and the simultaneously determined NMR structure of the MoaD-related ThiS protein involved in thiamine biosynthesis [37] unambiguously demonstrated the evolutionary relationship between a subset of enzymes involved in the biosynthesis of S-containing cofactors (e.g. Moco, thiamine and certain EeS-clusters) and the process of ubiquitin activation. MoaD displays significant structural homology to human ubiquitin (Figure 3.3B and C), resulting in a superposition with a root mean square (rms) deviation of 3.6 A for 68 equivalent Ca atoms out of 76 residues in ubiquitin. The key secondary structure... 

Fig. 4. Stereoviews of TmCsp. (A) Stereoview of a superposition of the backbone atoms of the 21 accepted structures of TmCsp. (B) Stereoview of a representative ribbon diagram of TmCsp. The secondary-structure elements are indicated. (C) Stereoview of the solution NMR structure of TmCsp (rotated ribbon diagram). Location of a possible peripheral ion cluster. Reprinted from Eur. J. Biochem., Vol. 268, W. Kremer, B. Schuler, S. Harrieder, M. Geyer, W. Gronwald, C. Welker, R. Jaenicke and H. R. Kalbitzer, Solution NMR structure of the cold-shock protein from the hyperthermo-philic bacterium Thermotoga maritima , pp. 2527-2539, Copyright 2001, with permission from Blackwell Science.

The sequence conservation is reflected in a highly conserved secondary and tertiary structure that is most clearly illustrated in the three-dimensional superposition of C atoms. Ignoring the C-terminal domains of PVC and HPII, the deviation of C atoms in a superposition of HPII with PVC, BLC, PMC, and MLC results in root mean square deviations of 1.1,1.5,1.6, and 1.5 A for 525, 477, 471, and 465 eqiuvalent centers, respectively (83). In other words, there is very little difference in the tertiary structure of the subunits over almost the complete length of the protein. The large and small subunits are shown in Fig. 8 for comparison. 

An example of the features of the spectrum of secondary electrons emitted in H° impact on water molecules from the work of Bolorizadeh and Rudd [67] is shown in Fig. 16. Compared to the simple spectrum of electrons emitted by proton impact shown as the solid line in Fig. 16 the spectrum from H° impact has an additional peak centered at an electron energy of approximately 82 eV. This broad peak is from the superposition of the spectrum of electrons stripped (elastically scattered) from the projectile on the spectrum of electrons ejected from the target. Because the stripped projectile electrons originate as bound electrons in the rest frame of the moving projectile, their laboratory energy is given approximately hy W = meE jM and the width of the peak is determined by the Compton profile of electrons in the projectile frame, but also transformed to the laboratory frame-of-reference. The results shown in Fig. 16 clearly illustrate that the cross-sections for... 

In atomic absorption, confusion seldom occurs, but the technique is still vulnerable to the superposition of two lines the line of the chosen element and a secondary line of another element. This is why it is suggested that a second measurement is performed at another wavelength. In atomic emission, this problem is more frequent because spectra are more complex. 

Exercise. Suppose there are N primary individuals, where N is random with a Poisson distribution. Each primary produces M secondaries, where M is again Poissonian. Find an expression for the distribution of the total number of individuals. Exercise. Consider a superposition of Poisson distributions ... 

As a rule the radiation effect produced by any type of emission is a superposition of direct effects of the primary radiation and of the secondary (and even tertiary) radiation the latter induces. Consequently, if the radiation effect is mostly due to the effect produced by secondary (or tertiary) emission, the latter can be used instead of the primary radiation. As concerns the structure of tracks, such a simulation will be correct if the spatial distribution of chemically active particles in the irradiated volume remains close to the one produced by the primary source. 

Figure 8 Superposition of the T. thermophilus NAD-IMDH binary complex with NAD (gray) on the E. coli NADP-IDH binary complex with NADP (black). NADP-IDH numbering is used throughout. It is noted that due to the difference of the local secondary structures, the NAD-IMDH does not have the counterpart of the Arg395 found in the NADP-IDH.

Fig. 3 Structural changes of tubulin subunits upon MT disassembly, a Structure of a 3 subunit of the T2R complex (pdb id 1SA0 [15]). The monomer is sub-divided in an N-terminal domain (blue) with bound GDP (ball-and-stick drawing, grey), the central helix H7 yellow), an intermediate domain green), and the C-terminal helices red), b Comparison of the 3 subunit conformation in the T2R complex (same color code as in a) and in a straight protofilament (nucleotide binding domain and C-terminal helix hairpin in cyan, H7 helix in salmon, intermediate domain in pink, pdb id 1JFF [70]) after superposition of the secondary structural elements of their N-terminal domain, c Schematic representation recapitulating the movements between straight and curved tubulin monomers (domains are color-coded as in a the nucleotide is depicted as a red sphere)...

Figure 46 Superposition of secondary ion mass spectrometry (SIMS) concentration data for SrO on theoretical surface diffusion curves. SrO had diffused for 473 hr at 693K. (From Ref. 145.)...

Basis set superposition error (BSSE) is a particular problem for supermolecule treatments of intermolecular forces. As two moieties with incomplete basis sets are brought together, there is an unavoidable improvement in the overall quality of the supermolecule basis set, and thus an artificial energy lowering. Various approximate corrections to BSSE are available, with the most widely used being those based on the counterpoise method (CP) proposed by Boys and Bemardi [3]. There are indications that potential energy surfaces corrected via the CP method may not describe correctly the anisotropy of the molecular interactions, and there have been some suggestions of a bias in the description of the electrostatic properties of the monomers (secondary basis set superposition errors). 

The literature is rich in examples of this upside-down minimum and the secondary maxima arising from electrode polarization40 43 . Figure 19 shows Lawless superposition of a temperature ramp, the viscosity, and the measured tan 8X for the cure of an Avco 5505 epoxy resin with parallel plates in the presence... 

Turbulent flow — arises at high Reynolds numbers and is characterized by the superposition upon the principal motion of a fluid, countless irregular and chaotic secondary components. 

Since the model is linear, the resultant prediction for the concentration of the primary or secondary pollutant at a receptor site is a linear superposition of the x s for the individual point sources. The model is optimized by a least squares criterion the nine parameter values are chosen so as to minimize E2,... 

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