Descriptor linear molecular

Fig. 4.4 Li near versus treelike molecular descriptors Linear descriptors represent the occurrence of certain features like fragments or paths, the relative arrangement gets lost. Treelike descriptors represent the building blocks of the molecule as well as their relative arrangement.

In the present work, we will use a relatively low level of theory to derive 32 weakly correlated molecular descriptors, each based on the subdivision and classification of the molecular surface area according to three fundamental properties contribution to ClogP, molar refractivity, and atomic partial charge. The resulting collection will be shown to have applicability in QSAR, QSPR, and compound classification. Moreover, the derived 32 descriptors linearly encode most of the information of a collection of traditional mathematical descriptors used in QSAR and QSPR. 

Introduction from Linear to Non-linear Molecular Descriptors... 

In order to calculate a physicochemical property, the structure of a molecule must be entered in some manner into an algorithm. Chemical structure notations for input of molecules into calculation software are described in Chapter 2, Section VII and may be considered as either being a 2D string, a 2D representation of the structure, or (very occasionally) a 3D representation of the structure. Of this variety of methods, the simplicity and elegance of the 2D linear molecular representation known as the Simplified Molecular Line Entry System (SMILES) stands out. Many of the packages that calculate physicochemical descriptors use the SMILES chemical notation system, or some variant of it, as the means of structure input. The use of SMILES is well described in Chapter 2, Section VII.B, and by Weininger (1988). There is also an excellent tutorial on the use of SMILES at www.daylight.com/dayhtml/smiles/smiles-intro.html. 

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]. 

These results show that pattern recognition can be used as an effective tool to characterize polycyclic aromatic hydrocarbon carcinogens. Using a set of only 28 molecular structure descriptors, linear discriminants can be found to correctly dichotomize 191 out of 200 randomly selected PAH s. This same set of 28 descriptors supports a linear discriminant function that has an average predictive ability of over ninety percent when subjected to randomized predictive ability tests. 

The simplest structural descriptors are just the number of carbon atoms, or molecular weight, that is linearly related to the increase in gas chromatographic retention among a homologous series of compounds. This simple relationship led to the development of the Kovits retention index scale. A linear relationship between Kovits retention index and carbon number for homo-logues has been shown to hold for a number of chemical groups. Molar volume, molar refractivity, and molecular polarizability are other simple descriptors of molecular bulk that have been used in QSRR studies. 

The problem addressed by the GFA is the development of accurate QSAR models that are assumed to be linear combinations of a set of features chosen from a given larger set. The given set of features could be basic molecular descriptors, principal components or complex non-linear functions of the molecular descriptors. Typically, molecular descriptors could be hydrophobicity measures, partition coefficients etc. The higher-level features which are functions of the molecular features are called basis functions. The effectiveness of the models is measured by their ability to capture parsimoniously the dependence of the desired activity on an extracted set of relevant basis functions. 

Platts, J. A., Abraham, M. H., Butina, D., Hersey, A. Estimation of molecular linear free energy relationship descriptors by group contribution approach. 2. Prediction of partition coefficient. J. Chem. Inf. Comput. Sci. 2000, 40, 71-80. 

Valko et al. [37] developed a fast-gradient RP-HPLC method for the determination of a chromatographic hydrophobicity index (CHI). An octadecylsilane (ODS) column and 50 mM aqueous ammonium acetate (pH 7.4) mobile phase with acetonitrile as an organic modifier (0-100%) were used. The system calibration and quality control were performed periodically by measuring retention for 10 standards unionized at pH 7.4. The CHI could then be used as an independent measure of hydrophobicity. In addition, its correlation with linear free-energy parameters explained some molecular descriptors, including H-bond basicity/ acidity and dipolarity/polarizability. It is noted [27] that there are significant differences between CHI values and octanol-water log D values. 

Because of the large number of chemicals of actual and potential concern, the difficulties and cost of experimental determinations, and scientific interest in elucidating the fundamental molecular determinants of physical-chemical properties, considerable effort has been devoted to generating quantitative structure-property relationships (QSPRs). This concept of structure-property relationships or structure-activity relationships (QSARs) is based on observations of linear free-energy relationships, and usually takes the form of a plot or regression of the property of interest as a function of an appropriate molecular descriptor which can be calculated using only a knowledge of molecular structure or a readily accessible molecular property. 

As described earlier, Henry s law constants can be calculated from the ratio of vapor pressure and aqueous solubility. Henry s law constants do not show a simple linear pattern as solubility, Kqw or vapor pressure when plotted against simple molecular descriptors, such as numbers of chlorine or Le Bas molar volume, e.g., PCBs (Burkhard et al. 1985b), pesticides (Suntio et al. 1988), and chlorinated dioxins (Shiu et al. 1988). Henry s law constants can be estimated from ... 

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