Chemical structures representation topological descriptors

Carhart et al. [15] described a generalized structural descriptor called an atom pair which is defined in terms of the atomic environments of, and shortest path separation between, all pairs of atoms in the topological representation of a chemical structure. A similar descriptor has been suggested by Klopman [16]. More recently, Judson [20] described a more sophisticated approach to analyze structural feature of molecules for structure-activity studies. 

The importance of methods to predict log P from chemical structure was described in Chapter 14, which is focused on fragment- and atom-based approaches. In this chapter property-based approaches are reviewed, which comprise two main categories (i) methods that use three-dimensional (3D) structure representation and (ii) methods that are based on topological descriptors. 

Topological parameters were the first molecular descriptors that could be calculated for any chemical structure (other than obvious parameters such as molecular weight, atom counts, etc.) all that was required for their computation was a standard two-dimensional (2-D) representation of a chemical structure. The best known topological parameters are the molecular connectivity indices first described by Randic and investigated extensively by Hall and Kier et al. Molecular connectivity descriptors have since been used by chemists in the construction of QSAR models for many types of biological properties, especially applications in the environmental area. The reason for such heavy application in environmental studies is because these data sets often contain diverse sets of compounds, and as just mentioned, topological descriptors can be computed for any structure. 

In actual applications of MSA, many different types of representations are utilized to compute molecular similarities [41, 52-54]. Johnson [55] has provided a detailed discussion of the manifold types of mathematical spaces and their associated representations. The information contained in the representations is usually in the form of molecular or chemical features called descriptors that are derived from the structural and chemical properties of molecules. Descriptors ate nominally classified as ID (one-dimensional), 2D, or 3D. ID descriptors are usually associated with whole molecule properties such as molecular weight, logP, solubility, number of hydrogen bond donors, nnmber of rotatable bonds, and so on. 2D descriptors are associated with the topological strnctnre of molecules as typically depicted in chemists drawings. Such depictions show the atoms, the bonds connecting them, and in some cases include stereochemical features, but they do not explicitly depict the 3D structures of molecules. 3D descriptors, as their name implies, are associated with the 3D structures of molecules. Todeschini and Consonni [56] have compiled an extensive reference containing many of the descriptors used in chemical informatics applications. 

Molecular connectivity is a topological descriptor, that is to say it is calculated from a two-dimensional representation of chemical structure. All that is required in order to calculate molecular connectivity indices for a compound... 

This chapter focuses on step 3. For step 1, descriptors may include property values, biological properties, topological indexes, and structural fragments. The performance of these descriptors and forms of representation have been analyzed by Brown and Brown and Martin. Similarity searching for step 2 has been discussed by Downs and Willett characteristics of various similarity measures have been discussed by Barnard, Downs, and Willett. " For step 4, little has been published specifically about visualization and analysis of results for chemical data sets. Flowever, most publications that focus on implementing systems that utilize clustering do provide details of how the results were displayed or analyzed. 

Another class of struaural descriptors is the topological indices, which are derived from molecular structures represented as graphs. The molecule 2-methylbutane is shown below in two representations in the usual chemical stick figure drawing and as a graph. In the graphic representation, eadi atom is a node or vertex without elemental identification and each bond is an edge. 

This study demonstrated the development of linear model equations that relate NMR chemical shift data to atom-based struaural properties for a set of methyl-substituted norboman-2-ol compounds. The models were used to simulate chemical shift data for both the reference and prediction compounds. These simulated spectra provide excellent representations of the actual measured spectra. The new torsional descriptors proved valuable in the discrimination of the geometric structural environments of topologically identical carbon atoms for all six atom subsets. This allowed accurate identification of all 42 simulated spectra when compared with measured spectra. Therefore, speara can also be simulated for those mono-, di-, and trimethyl compounds for which measured NMR spectra do not currently exist. The accuracy of those simulations should approximate that of the simulated spectra for the 10 prediction compounds in this smdy. 

---