The use of molecular descriptors

We recall from Section 2.6 that a molecular descriptor D comes from a mapping D on the set of labeled molecular graphs that is invariant under relabeling of a graph s nodes. In formal terms, if M = (e, C, y) e M , we require that D M) = D nM), for each relabeling n S . This gives rise to two molecular descriptors D and D with the values 

Following a refresher on descriptors below, we will introduce a particularly flexible type of molecular descriptors in Subsection 7.2.2, the substructure counts. These are defined by a molecular substructure and return simply how many times a substructure is contained in a molecular graph (i.e. the occurrence) as the descriptor value. 

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A variety of different compound selection methods have been developed. These techniques are dependent on the use of molecular descriptors which are numerical values that characterize the properties of molecules. In addition, many compound selection methods are based on quantifying the degree of similarity or dissimilarity of compounds based on molecular descriptors. This requires the use of similarity or distance coefficients. 

Jantschi, L. and Bolboaca, S. (2007) Results from the use of molecular descriptors family on structure-property/activity relationships. Int. J. Mol Scl, 8, 189-203. 

Since the definition of chemical reference spaces very much depends on the choice of molecular descriptors, we begin the description with a brief overview of some commonly used types of descriptors, as summarized in Table 1. 

A major practical issue affecting MP calculations is caused by use of correlated molecular descriptors. During subsequent MP steps, exact halves of values (and molecules) are only generated if the chosen descriptors are uncorrelated (orthogonal), as shown in Fig. 1A. By contrast, the presence of descriptor correlations (and departure from orthogonal reference space) leads to overpopulated and underpopulated, or even empty, partitions (see also Note 5), as illustrated in Fig. ID. For diversity analysis, compounds should be widely distributed over computed partitions and descriptor correlation effects should therefore be limited as much as possible. However, for other applications, the use of correlated descriptors that produce skewed compound distributions may not be problematic or even favorable (see Note 5). 

Molecular descriptors and chemical spaces. The majority of chemoinformatics methods depend on the generation of chemical reference spaces into which molecular data sets are projected and where analysis or design is carried out. The definition of chemical spaces critically depends on the use of computational descriptors of molecular structure, physical or chemical properties, or pharmacophores. Essentially, any comparison of molecular characteristics that goes beyond simple structural comparison requires the calculation of property values and the application... 

Although there is a strong negative correlation between partition coefficient and aqueous solubility (Hansch et al., 1968 Chiou et al., 1977), and a strong positive correlation between % and molecular volume (Dearden et al., 1988), the use of the partial least squares (PLS) method in this study allows the simultaneous use of intercorrelated descriptors. Nevertheless, the use of four descriptors to model the bioconcentration factor of only 11 compounds contravenes the Topliss and Costello (1972) rule, and renders the QSAR of dubious validity. 

TTie structural features are represented by molecular descriptors, which are numeric quantities related directly to the molecular structure rather than physicochemical properties. Examples of such descriptors include molecular weight, molecular connectivity indexes, molecular complexity (degree of substitution), atom counts and valencies, charge, molecular polarizability, moments of inertia, and surface area and volume. Once a set of descriptors has been developed and tested to remove interdependent/collinear variables, a linear regression equation is developed to correlate these variables with the retention parameter of interest, e.g., retention index, retention volume, or partition coefficient The final equation includes only those descriptors that ate statistically significant and provide the best fit to the data. For more details on QSRR and the development and use of molecular descriptors, the reader is referred to the literature [188,195,198,200-202 and references therein]. 

On the basis of the origin of molecular descriptors used in calculations, QSAR methods can be divided into three groups. One group is based on a relatively small number (usually many times smaller than the number of compounds in a data set) of physicochemical properties and parameters describing,for example, hydrophobic, steric, and electrostatic effects. Usually, these descriptors are used as independent variables in multiple regression approaches (18) Jn the literature, these methods are typically referred to as Hansch analysis (8).These types of descriptors and corresponding linear optimization methods used in traditional QSAR analyses are discussed extensively in the chapter by Celassie (7) and therefore is not reviewed here. 

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