Chemical graph theory descriptor

Studies using the theory of Quantitative Structure-Activity Relationships (QSAR) are intended to suggest mathematical models capable of estimating the relevant properties of interest, especially when those cannot be experimentally determined for some reason. Such studies rely on the basic assumption that the structure of a compound completely determines its properties, which can therefore be translated into the so-called molecular descriptors. These parameters are calculated through mathematical formulae derived from several theories, such as Chemical Graph Theory, Information... 

Based on the use of chemical graph theory as described above, various indexes of molecular structure have been developed. These indexes may all be termed topological indexes. In the molecular connectivity method, indexes have been developed to characterize various aspects of molecular structure. The kappa shape indexes were developed so that shape measures could be directly entered in QSAR analyses. Each of these indexes characterizes the whole molecule with respect to one or more aspects of structure. In chemistry it is also of interest to characterize the skeletal atoms. In this final section we review briefly an investigation of the skeletal atoms as vertexes in the molecular graph as a basis for an atom descriptor. 

Single parameters incorporating connectivity are used principally in two different areas the analysis of structural and dynamic properties of molecules in conformations with conserved architecture, and molecular similarity analyses based on chemical graph theory. The descriptors used in these two areas differ conceptually, and their natures must be clarified from the start. 

Todeschini R, Consonni V (2009) Molecular descriptors for chemical informatics, vol 1, Alphabetical Listing. Wiley-VCH, Weinheim Topliss JG, Costello RJ (1972) J Med Chem 15 1066 Trinajstic N (1992) Chemical graph theory. CRC Press, Boca Raton... 

The two matrix representations of the protein segments, the amino acid adjacency matrix and the decagonal isometries matrix, are derived from the sequence information alone. As has been demonstrated, mathematical descriptors, dependent on the sequence information alone, have successfully revealed the underlying characteristics and patterns of given sequences. Their numerical nature also makes them easier to incorporate into a mathematical model. In addition, as has been well illustrated in chemical graph theory, when considering characterization of molecules, one can... 

To overcome this weakness, we are developing a quantitative structure-activity strategy that is conceptually applicable to all chemicals. To be applicable, at least three criteria are necessary. First, we must be able to calculate the descriptors or Independent variables directly from the chemical structure and, presumably, at a reasonable cost. Second, the ability to calculate the variables should be possible for any chemical. Finally, and most importantly, the variables must be related to a parameter of Interest so that the variables can be used to predict or classify the activity or behavior of the chemical (j ) One important area of research is the development of new variables or descriptors that quantitatively describe the structure of a chemical. The development of these indices has progressed into the mathematical areas of graph theory and topology and a large number of potentially valuable molecular descriptors have been described (7-9). Our objective is not concerned with the development of new descriptors, but alternatively to explore the potential applications of a group of descriptors known as molecular connectivity indices (10). 

The class of the empirical descriptors is a fuzzy, not well-defined class. In principle, empirical descriptors are those not defined on the basis of a general theory such as, for example, quantum chemistry or graph theory. Rather they are defined by practical rules derived from chemical experience, e.g. considering specific or local structural factors present in the molecules, often sets of congeneric compounds. As a consequence, in most cases, empirical descriptors represent limited subsets of compounds and cannot be extended to classes of compounds different from those for which they were defined. Empirical descriptors have not to be confused with experimentally derived descriptors even if it is well known that several of them are empirically derived. 

Mathematics and statistics, graph theory, computational chemistry and molecular modelling techniques enable the definition of a large number of theoretical descriptors characterizing physico-chemical and biological properties, reactivity, shape, steric hindrance, etc. of the whole molecule, molecular fragments and substituents. 

Indeed, molecular descriptors are based on several different theories, such as quantum-chemistry, information theory, organic chemistry, graph theory, and so on, and are used to model several different properties of chemicals in scientific fields such as toxicology, analytical chemistry, physical chemistry, and medicinal, pharmaceutical, and environmental chemistry. 

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