Based on Atom Coordinates

The most simple way is using the same single atom properties as for the topological autocorrelation descriptors. The distance now is not measured as the number of bonds between the two atoms in consideration, but as the real distance between the atoms. The distances are assigned to classes (e.g., distance between 0.1 nm and 0.2 nm) in order to get a limited number of descriptors (e.g., 20), and the coefficient is calculated for each class [87]. 

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The bond order results of Table 2 reflect again the general picture based on atom coordination. Bonds between doubly coordinated oxygen, 0(2), and each of their two vanadium neighbors result in bond order values close to 1, sugges-... 

Fig. 7. Three-dimensional structure of the photosynthetic reaction center of Rps. viridis. The a-helices are drawn as cylinders and the cofactors by black rectangles (in perspective). See text for other details. Adapted from the original color drawing by Prof. Jane Richardson of Duke University, based on atomic coordinates provided by Deisenhofer, Michel and Huber. Cf. the broad view of the Rp. viridis reaction-center model on the book cover and side view in Color Plate 1.

Abstract The present knowledge of protein science includes information on amino acid sequence and 3D structure in terms of precise models on the atomic level. Recourse to the respective databanks and advanced computer programs allows a series of molecular features to be calculated. Application of analytical surface calculation programs (SIMS, MSRoU) based on atomic coordinates or the coordinates of gravity centers of amino acids allows precise molecular dot surfaces to be calculated, in addition to numerical data for anhydrous molecular surface and anhydrous molecular volume. Usage of in-house hydration programs (HY-DCRYST, HYDMODEL) permits the putative localization of individual water molecules on the protein envelope to be addressed explicitly. To estimate the overall values of protein volume and hydration, simple approximations based on the amino acid composition and characteristic numbers for the constituents can be used. Derivation of secondary... 

Atoms not explicitly included in the trajectory must be generated. The position at which an atom may be placed is in some sense arbitrary, the approach being analogous to the insertion of a test particle. Chemically meaningful end states may be generated by placing atoms based on internal coordinates. It is required, however, that an atom be sampled in the same relative location in every configuration. An isolated molecule can, for example, be inserted into... 

Methods of decomposing the nonbonded force evaluation fall into two classes, spatial decomposition [15] in which atoms and their interactions are divided among processors based on their coordinates, and force-matrix decomposition [16] in which the calculation of the interaction between a pair of atoms is assigned to a processor without considering the location of either atom (Fig. 1). Spatial decomposition scales better to large numbers of... 

The geometry of the coordination compounds can be similarly predicted based on the coordination number of the central atom. Coordination numbers 2 and 3 are both relatively rare and give linear and planar or pyramidal geometries, respectively. The most important coordination numbers are 4, 5 and 6 with the latter being the most important one as nearly all cations form 6-coordinate complexes. Table 2.4 shows the geometries corresponding to the commonest coordination numbers in biological systems. 

Wyckoff et al. (62) have provided a preliminary coordinate list of all nonhydrogen atoms in RNase-S. Along with the list is a series of notations on the quality of the map and the fit of the atomic model to the electron density contours. The following comments concerning group accessibilities are based on this coordinate list, but detailed interpretations must be made with caution in view of the uncertainties in many parts of the structure. 

This section presents the structure of the boron hybrides and is arranged in accordance with the relationship defined by Wade s Rules and expressed by Williams and Rudolph. Thus for the boranes containing six or more pairs of skeletal bonding electrons, the relationship between the structures of the closo-, nido-, arachno-and hypho-species is described. In cases where the parent borane does not exist, examples from heteroboranes with the correctly predicted structure based on Williams coordination number pattern recognition theory (CNPR) of borane structures will be described 70. Treated separately will be mono- and diborane species and also species with more than 12 boron atoms. Although there have been several reviews on the structures of the boranes in recent years none have used the current approach89. ... 

Recognized characters are then grouped to form words based on their coordinates. This method combines characters lying next to each other but also considers vertical relationships to handle vertically oriented atom labels. 

The stereodrawing of morphine plotted by a computer program (41) and based on the coordinates and thermal parameters experimentally determined by X-ray analysis of a crystal of the HBr salt (42) has been oriented to show the characteristic T shape of the molecule (or ion with the protonated N) in Fig. 20(a). Naloxone, a potent narcotic antagonist, differs from morphine chemically in the substitution of an allyl chain for the methyl group on the N atom, the substitution of OH for H at C-14, the saturation of the C-7-C-8 bond, and a carbonyl oxygen at C-6 rather than a hydroxyl. The stereodrawing of naloxone in Fig. 20(b) shows that morphine and naloxone (43) have identical molecular conformations, except for atoms C-6 and C-7 in ring D. 

The described treatment has the disadvantage of being based on Cartesian coordinates, which depend on the system of axes used to localize the molecule. As an example, a methyl group can have different coordinates (CH3 in toluene or ethane), while the chemical and spectro.scopic properties of both are very similar. In order to take advantage of this chemical information, internal coordinates were introduced, which refer to chemically relevant quantities. A molecule with n atoms has 3n degrees of freedom, six of which correspond to the overall translations and rotations of the molecule. Only 3n 6 coordinates are necessary to describe the vibrational motions of the system. Five types of coordinates can be defined ... 

The direct labelling of TOPO capped semiconductor CdSe or CdSe/ZnS QDs with tetra-pyridyl substituted porphyrin (Fig. 1). Here P is based on the coordination of the pyridyl N lone pair with Zn or Cd atoms on the surface of QD. 

An atom diatom quantum program based on APH coordinates (sec Parker, G.A., Crocchianti, S., Kiel, M. (2000) Lecture Notes in Chemistry, 75, 88). 

Let us summarize the three important prerequisites for a 3D structure descriptor It should be (1) independent of the number of atoms, that is, the size of a molecule (2) unambiguous regarding the three-dimensional arrangement of the atoms and (3) invariant against translation and rotation of the entire molecule. Further prerequisites depend on the chemical problem to be solved. Some chemical effects may have an undesired influence on the structure descriptor if the experimental data to be processed do not account for them. A typical example is the conformational flexibility of a molecule, which has a profound influence on a 3D descriptor based on Cartesian coordinates. The application in the field of structure-spectrum correlation problems in vibrational spectroscopy requires that a descriptor contains physicochemical information related to vibration states. In addition, it would be helpful to gain the complete 3D structure from the descriptor or at least structural information (descriptor decoding). 

The three-dimensional model of cephalosporin (Figure 6.38, upper left) is based on Cartesian coordinates (xyz-triples) for each atom. It is usually calculated by force-field methods that take the repulsion of the atoms magnetic fields into account. 

In standard molecular mechanics methods, all atoms and bonds between atoms are explicitly defined, i.e., they are either present or not. In order to model the changes in pH, one must therefore alter the protonation states of ionizable amino acid side chains. For a decrease in pH, the relevant side chains are those of histidine, glutamate, and aspartate. Their pXa values in solution are 6.08, 4.15, and 3.71, respectively [98]. The local protein environment can, however, change the pKa of individual residues significantly. Langella et al. [99] calculated theoretical pKa values of the relevant side-chains based on the coordinates deposited for human recPrP obtained by protein NMR at pH 4.5 and pH 7.0 [39, 76]. Although differences in the local conformation of residues between the various structures lead to a... 

Aluminosilicate zeolites have anionic lattices based on 2-coordinate oxygen and 4-coordinate aluminium and silicon atoms. Each aluminium atom corresponds to a formal negative charge. One can represent the anionic lattice by the empirical formula, xSiOg.A -. In the case of ZSM-5 zeolite, x is large -mostly > 20 and possibly 20. Consequently one expects the aluminium atoms of the lattice to be well separated and to represent uniformly strong acid sites. 

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