Molecule Representation of Structures

D Molecule Representation of Structures Based on Electron Diffraction Code (3D MoRSE Code)... 

D-molecule representation of structures based on electron diffraction 3D-MoRSE descriptors... 

D-MoRSE 3D-Molecule Representation of Structures based on Electron diffraction descriptors... 

Many years later, it was found that this characteristic of the descriptor could be used for the correlation of biological activity and three-dimensional structure of molecules. The activity of a compound also depends on the distances between atoms (such as H-bond donors or acceptors) in the molecular structure [91]. Adaptation of the RBF function to biological activity led to the so-called 3D-MoRSE code (3D-Molecule Representation of Structures based on Electron diffraction) [92]. The method of RBF calculation can be simplified in order to derive a descriptor that includes significant information and that can be calculated rapidly ... 

To calculate 3D-MoRSE descriptors (3D-MOlecule Representation of Structures based on Electron diffraction, or simply MoRSE descriptors), Gasteiger et al. ]Schuur and Gasteiger, 1996,1997] returned to the initial I(s) curve and maintained the explicit form of the curve. As the atomic weighting scheme w, various physico-chemical properties such as atomic mass, partial atomic charges, and atomic polarizability were considered. To obtain uniform-length descriptors, the intensity distribution I(s) was made discrete, calculating its value at a sequence of evenly distributed values of, for example, 32 or 64 in the range of 1-31 A . Clearly, the more the values are chosen, the finer the resolution in the representation of the molecule. 

Figure 8.1 Schematic representation of structure of the flexible disordered caseins at a planar hydrophobic interface (a) asi-casein (b) p-casein. The solid bars denote hydrophobic regions of the molecules they do not imply rigidity. Reproduced from Home (1998) with permission.

Although the molecular orbital description of bonding has some mathematical advantages, simple valence bond representations of structures are adequate for many purposes. The structures of molecules that have only single bonds (and in some cases unshared pairs of electrons on the... 

A chemical structure is a pictorial representation of the bonding of atoms in a molecule. Chemical structures appear within text at the point at which they are discussed. Structures are numbered sequentially with either arabic or roman numerals consult the publisher s guidelines to determine if one is preferred over the other. Generally, there is no need to provide graphical representations of structures for materials that can be accurately represented on one line or in the form of text. For scientific publications, structures should be included for clarity of communication only. 

Many different structural descriptors have been developed for similarity searching in chemical databases [4] including 2D fragment based descriptors, 3D descriptors, and descriptors that are based on the physical properties of molecules. More recently, attention has focused on diversity studies and many of the descriptors applied in similarity searching are now being applied in diversity studies. Structural descriptors are basically numerical representations of structures that allow pairwise (dis)similarities between structures to be measured through the use of similarity coefficients. Many diversity metrics have been devised that are based on calculating structural (dis)similarities, some of these are described below. 

On a point of interest, the Cambridge Structural Database (8) archives crystal structure data (currently approx 153,000 small molecules) and enables searches to be performed using a graphical interface. Entries for terpenes, alkaloids, and miscellaneous natural products are identified as such, which is useful for searching these classes of compounds. The number of compounds in these three categories, with coordinates to enable 3D representation of structure, currently stands at approx 3700. 

A Fischer projection does not show the three-dimensional structure of the molecule, and it represents the molecule in a relatively unstable eclipsed conformation. Most chemists, therefore, prefer to use perspective formulas because they show the molecule s three-dimensional structure in a stable, staggered conformation, so they provide a more accurate representation of structure. When perspective formulas are drawn to show the stereoisomers in their less stable eclipsed conformations, it can easily be seen—as the eclipsed Fischer projections show—that the erythro isomers have similar groups on the same side. We will use both prospective formulas and Fischer projections to depict the arrangement of groups bonded to an asymmetric carbon. 

Note that it is important when working out possible isomers to remember the limitations of the two-dimensional representation of structures on paper. Thus the structures represented in Figures 10.21a and 10.21b are not isomers at all. In Figure 10.21a the chain appears to turn a corner on paper, but remember that, in reality, the structure around each carbon atom is tetrahedral and that there is free rotation around each bond. In Figure 10.21b, one structure is just the other turned over on the paper. It is crucial to remember that isomers are compounds with the same molecular formula but with different arrangements of atoms in the molecules. 

In the three-dimensional (3D) approach the 3D structure (see Structure Generators) of a molecule is transformed into a structure code. This is performed by regarding every atom pair in the molecule as a point scatterer and calculating the center symmetric diffraction pattern of the molecule as it would be obtained from an electron diffraction experiment. Based on these equations the 3D molecular representation of structures based on electron diffraction (3D-MoRSE) code has been developed. The 3D-MoRSE code is calculated using the equation... 

Figure 2-1. Hierarchical scheme for representations of a molecule with difFerent contents of structural information.

A major disadvantage of a matrix representation for a molecular graph is that the number of entries increases with the square of the number of atoms in the molecule. What is needed is a representation of a molecular graph where the number of entries increases only as a linear function of the number of atoms in the molecule. Such a representation can be obtained by listing, in tabular form only the atoms and the bonds of a molecular structure. In this case, the indices of the row and column of a matrix entry can be used for identifying an entry. In essence, one has to distinguish each atom and each bond in a molecule. This is achieved by a list of the atoms and a list of the bonds giving the coimections between the atoms. Such a representation is called a connection table (CT). 

A connection table has been the predominant form of chemical structure representation in computer systems since the early 1980s and it is an alternative way of representing a molecular graph. Graph theory methods can equally well be applied to connection table representations of a molecule. 

Benzene has already been mentioned as a prime example of the inadequacy of a connection table description, as it cannot adequately be represented by a single valence bond structure. Consequently, whenever some property of an arbitrary molecule is accessed which is influenced by conjugation, the other possible resonance structures have to be at least generated and weighted. Attempts have already been made to derive adequate representations of r-electron systems [84, 85]. 

Conversion in both directions needs heuristic information about conjugation. It would therefore be more sensible to input molecules directly into the RAMSES notation. Ultimately, we hope that the chemist s perception of bonding will abandon the connection table representation of a single VB structure and switch to one accounting for the problems addressed in this section in a manner such as that laid down in the RAMSES model. 

To code the configuration of a molecule various methods are described in Section 2.8. In particular, the use of wedge symbols clearly demonstrates the value added if stereodescriptors are included in the chemical structure information. The inclusion of stereochemical information gives a more realistic view of the actual spatial arrangement of the atoms of the molecule imder consideration, and can therefore be regarded as between the 2D (topological) and the 3D representation of a chemical structure. 

An alternative and much more flexible approach is represented hy the STAR file format [L48, 149, which can be used for building self-describing data files. Additionally, special dictionaries can be constructed, which specify more precisely the contents of the eorresponding data files. The two most widely used such dictionaries (and file formats) arc the CIF (Crystallographic Information File) file format [150] - the International Union of Crystallography s standard for representation of small molecules - and mmCIF [151], which is intended as a replacement for the PDB format for the representation of macromolecular structures,... 

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