Molecular descriptors correlation

Degeneracy of 735 molecular descriptors as well as their pairwise correlations were estimated on the NGI database for 221,860 compounds and made available on a software module called Molecular Descriptor Correlations (MDC) [MDC - Milano Chemometrics, 2006]. 

MDC — Molecular Descriptor Correlations, Ver. 1.0, Milano Chemometrics QSAR Research Group, Univ. Milano-Bicocca, P.za. della Sdenza 1, Milano, Italy http //michem.disatunimib.it/ chm/download / molecular correlationinfo.htm. 

Molecules are usually represented as 2D formulas or 3D molecular models. WhOe the 3D coordinates of atoms in a molecule are sufficient to describe the spatial arrangement of atoms, they exhibit two major disadvantages as molecular descriptors they depend on the size of a molecule and they do not describe additional properties (e.g., atomic properties). The first feature is most important for computational analysis of data. Even a simple statistical function, e.g., a correlation, requires the information to be represented in equally sized vectors of a fixed dimension. The solution to this problem is a mathematical transformation of the Cartesian coordinates of a molecule into a vector of fixed length. The second point can... 

Tab. 5.1 Cross-correlations (expressed as r ) between popular molecular descriptors (see text).

Calculated molecular descriptors including H-bond parameters were used for QSAR studies on different types of permeabiUty. For example, the new H-bond descriptor characterizing the total H-bond ability of a compound, was successfully appUed to model Caco-2 cell permeability of 17 drugs [30]. A similar study on human jejunal in vivo permeabiUty of 22 structurally diverse compounds is described in Ref. [62]. An exceUent one-parameter correlation of human red ceU basal permeabiUty (BP) was obtained using the H-bond donor strength [63] ... 

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. 

Many groups have discussed the correlation between solubility and molecular properties [14-19], and the octanol/water partition coefficient, the molecular volume and surface area, the boiling point and charge distribution in the molecules are well-documented molecular descriptors that correlate strongly with experimental solubility. 

The VolSurf approach was used to correlate the 3D molecular descriptors by utilizing the water solubilities for as many compounds as could be found. Although over 2000 solubility values were identified, many showed contradictory results (both low and high values published). Moreover, some of the estimations had not been made by the authors and the original reference was not reported, while others were simply wrong, having not been measured under the standard conditions required. From the 2000 compounds, about 850 were carefully selected in addi-... 

In the multimedia models used in this series of volumes, an air-water partition coefficient KAW or Henry s law constant (H) is required and is calculated from the ratio of the pure substance vapor pressure and aqueous solubility. This method is widely used for hydrophobic chemicals but is inappropriate for water-miscible chemicals for which no solubility can be measured. Examples are the lower alcohols, acids, amines and ketones. There are reported calculated or pseudo-solubilities that have been derived from QSPR correlations with molecular descriptors for alcohols, aldehydes and amines (by Leahy 1986 Kamlet et al. 1987, 1988 and Nirmalakhandan and Speece 1988a,b). The obvious option is to input the H or KAW directly. If the chemical s activity coefficient y in water is known, then H can be estimated as vwyP[>where vw is the molar volume of water and Pf is the liquid vapor pressure. Since H can be regarded as P[IC[, where Cjs is the solubility, it is apparent that (l/vwy) is a pseudo-solubility. Correlations and measurements of y are available in the physical-chemical literature. For example, if y is 5.0, the pseudo-solubility is 11100 mol/m3 since the molar volume of water vw is 18 x 10-6 m3/mol or 18 cm3/mol. Chemicals with y less than about 20 are usually miscible in water. If the liquid vapor pressure in this case is 1000 Pa, H will be 1000/11100 or 0.090 Pa m3/mol and KAW will be H/RT or 3.6 x 10 5 at 25°C. Alternatively, if H or KAW is known, C[ can be calculated. It is possible to apply existing models to hydrophilic chemicals if this pseudo-solubility is calculated from the activity coefficient or from a known H (i.e., Cjs, P[/H or P[ or KAW RT). This approach is used here. In the fugacity model illustrations all pseudo-solubilities are so designated and should not be regarded as real, experimentally accessible quantities. 

A fundamental problem encountered in these correlations is the mismatch between the accuracy of experimental data and the molecular descriptors which can be calculated with relatively high precision, usually within a few percent. The accuracy may not always be high, but for correlation purposes precision is more important than accuracy. The precision and accuracy of the experimental data are often poor, frequently ranging over a factor of two or more. Certain isomers may yield identical descriptors, but have different properties. There is thus an inherent limit to the applicability of QSPRs imposed by the quality of the experimental data, and further efforts to improve descriptors, while interesting and potentially useful, may be unlikely to yield demonstrably improved QSPRs. 

P-gp substrate 22 substrates and 31 nonsubstrates 115 substrates and 157 nonsubstrates 61% substrates and 81% nonsubstrates correctly predicted. Overall accuracy 72.4% Transport Caco-2 cell line Size, shape (e.g. molecular surface and glo-bularity), hydrophilic and H-bonding related descriptors correlated positively with P-gp activity, log P0/w not significant [54]... 

Fig. 18.4 An ideal compound library. Compounds (black dots) are uniformly distributed in 2D descriptor space, a plane defined by two molecular descriptors that correlate with biological activity but not with one another. The compounds are surrounded by nonoverlapping neighborhoods (circles)...

A set of n = 209 polycyclic aromatic compounds (PAC) was used in this example. The chemical structures have been drawn manually by a structure editor software approximate 3D-structures including all H-atoms have been made by software Corina (Corina 2004), and software Dragon, version 5.3 (Dragon 2004), has been applied to compute 1630 molecular descriptors. These descriptors cover a great diversity of chemical structures and therefore many descriptors are irrelevant for a selected class of compounds as the PACs in this example. By a simple variable selection, descriptors which are constant or almost constant (all but a maximum of five values constant), and descriptors with a correlation coefficient >0.95 to another descriptor have been eliminated. The resulting m = 467 descriptors have been used as x-variables. The y-variable to be modeled is the Lee retention index (Lee et al. 1979) which is based on the reference values 200, 300, 400, and 500 for the compounds naphthalene, phenanthrene, chrysene, and picene, respectively. 

Table 14. Correlation coefficients between logiCoc and molecular descriptors of PAHs...

Russell et al. (1992) conducted a similar study using the same data set from Hine and Mookeijee (1975). They developed a computer-assisted model based on five molecular descriptors which was related to the compound s bulk, lipophilicity, and polarity. They found that 63 molecular stmctures were highly correlative with the log of Henry s law constants (r = 0.96). 

The first stage includes the selection of a dataset for QSAR studies and the calculation of molecular descriptors. The second stage deals with the selection of a statistical data analysis and correlation technique, either linear or nonlinear such as PLS or ANN. Many different algorithms and computer software are available for this purpose in all approaches, descriptors serve as independent variables and biological activities serve as dependent variables. 

---