Descriptors molecular connectivity

Hall, L. H., Kier, L. B. Molecular connectivity chi indices for database analysis and structure-property modeling. In Topological Indices and Related Descriptors in QSAR and QSPR, Devillers,... 

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). 

Liu and Zhong introduced a number of QSPR models based on molecular connectivity indices [151, 152], In a first iteration, the researchers developed polymer-dependent correlations descriptors were calculated for a set of solvents and models were developed per polymer type [151], Polymer classes under consideration were polystyrene, polyethylene, poly-1-butene, poly-l-pentene, poly(4-methyl-l-pentene), polydimethylsiloxane, and polyisobutylene. As the authors fail to provide any validation for their models, it is difficult to asses their predictive power. In a subsequent iteration and general expansion of this study, mixed and therefore more general models based on the calculated connectivity indices of both solvent and polymers were developed. While it is unclear from the paper which polymer representation was used for the calculation of the connectivity indices, the best regression model (eight parameter model) yields only acceptable predictive power (R = 0.77, = 0.77, s = 34.47 for the training set, R = 0.75... 

Three sets of molecular descriptors that can be computed from a molecular connection table are defined. The descriptors are based on the subdivision and classification of the molecular surface area according to atomic properties (such as contribution to logP, molar refractivity, and partial charge). The resulting 32 descriptors are shown (a) to be weakly correlated with each other (b) to encode many traditional molecular descriptors and (c) to be useful for QSAR, QSPAR, and compound classification. 

Therefore, for estimates of Kioc s it is more feasible to use compound class-specific LFERs. These include correlations of log Kioc with molecular connectivity indices (or topological indices for an overview see Gawlik et al., 1997), with log Cf (L) (analogous to Eq. 7-11), and with log Kiow. Although molecular connectivity indices or topological indices have the advantage that they can be derived directly from the structure of a chemical, they are more complicated to use and do not really yield much better results than simpler one-parameter LFERs using C (L) or Kmv/ as compound descriptors. 

Delta Value Schemes and Molecular Connectivity Indices A delta (6 or 6V) value is an atomic descriptor for nonhydrogen atoms in a molecular graph. The superscript-free delta value, <5, is defined as the number of adjacent nonhydrogen atoms of atom i ... 

In the following, compound-class-specific correlations between Kow and selected molecular descriptors such as chlorine number, molecular connectivity indices, van der Waals volume and area, molecular volume, and polarizability are reviewed. Further, the model of Bodor, Babanyi, and Wong will be introduced, which allows estimation from molecular structure input for a broad range of compounds. 

An alternative to dimension reduction is the use of composite and uncorrelated descriptors that are suitable for the design of information-rich yet low-dimensional chemical spaces. An elegant example is presented by the popular BCUT (Burden-CAS-University of Texas) descriptors (Pearlman and Smith 1998). BCUTs are a set of uncorrelated descriptors that combine information about molecular connectivity, inter-molecular distances, and other molecular properties. BCUT spaces used for many applications are typically only six-dimensional and can frequently be further reduced to 3D representations for visualization purposes by identifying those BCUT axes around which most compounds map. 

The less than satisfactory modeling of log BCF by log Kow has encouraged numerous workers to examine the potential of other descriptors to model BCF values, the most widely used of which are undoubtedly molecular connectivities. These are topological descriptors (see Chapter 5 and Kier and Flail, 1976 1986) calculated from knowledge of the bonds between atoms in a molecule, and they have been found to have wide applicability. The descriptors are information-rich, but difficulty is encountered in comprehending their physicochemical significance. Dearden et al. (1988)... 

Clearly, y encodes more relevant information (probably size) than does log Kow, which does contain a size component, but also contains hydrogen bonding and polarity/polarizability components (Dearden and Bentley, 2002). Log Kow would, however, be expected to be a better descriptor for polar chemicals. In connection with this, Gerstl and Helling (1987) commented that the ability of molecular connectivities to predict log Koc was rather limited for diverse data sets. Baker et al. (2001) included two cluster connectivity terms to improve the correlation of soil sorption of a small hydrophobic data set, yielding R2 = 0.806 and 5 = 0.302. 

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