Abraham’s descriptors

While these models have clear physical meaning and are easily interpretable, their disadvantage is the requirement to experimentally determine some descriptors. There are, however, possible solutions to this problem. Recently methods to calculate Abraham s descriptors directly from 2D molecular structure were proposed [40]. SPARC uses fragment contributions to predict solubility of new molecules. In this case, nevertheless, these methods can have the same problems as other fragmental methods. 

As the solute descriptors (E, S, A, B and V) represent the solute influence on various solute-solvent phase interachons, the regression coefficients e, s, a, h and V correspond to the complementary effect of the solvent phases on these interactions. As an example, consider the product aA in Eq. (4). Since A is the H-bond acidity of the solute, a is the H-bond basicity of the system. In other words, the intermolecular forces discussed in Sections 12.1.1.2 and 12.1.1.3 are present in all Abraham s log P factorization equations, with the exception of those interactions involving ions. This is the reason why Abraham s equahons are valid for neutral species only. 

We have not yet introduced the influence of the presence of point charges on the lipophilicity of a chemical. Nevertheless, Sections 12.1.1.2 and 12.1.1.3 do warn that the lipophilic behavior of an ionized molecule might be very different from that of its parent neutral compound. Indeed, in order to investigate the balance of forces governing the lipophiUcity of ionized species we must do without Abraham s equations, since they do not exist when ions are considered. Recently, Abraham et al. also demonstrated what had long been perceived intuitively - descriptors for ions are not the same as those for nonelectrolytes [12]. 

Abraham s solute descriptors to yield a predictive regression equation. Further, the solute dipolarity/polarizability, hydrogen bond acidity, and hydrogen bond basicity were found to favor blood and solute size favor brain. 

For modeling the BBB penetration, authors used Abraham s data set of 57 compounds as the training set. The test set consisted of 13 compounds, 7 of which were taken from Abraham s data set and 6 from the data set of Lombardo and workers. In addition to the lipoaffinity descriptor, the other descriptors used by them include molecular weight and TPSA. Two models were developed one based on stepwise MLR and the other one based on ANN. To test the performance of different descriptors, they first carried out a simple LR of the 55 training set compounds (two outliers were removed) using TPSA as the only descriptor (Eq. 41). The equation was comparable to Clark s model (Eq. 33). 

Abraham s data set of 57 compounds was selected as training set for log BB prediction. The test set contained the 13 compounds used by Clark and Liu et al. A three-component model was built from the atom type descriptors, and it estimated the data set of 57 compounds with an r2 = 0.897, q2 = 0.504, and RMSEE = 0.259. The relatively lower q2 resulted from the small size of the data set. Totally, 94 different atom types were identified for the 57 compounds, and half of these atom types occurred only once or twice through the whole data set. When the compounds containing these atom types were left out in cross-validation, the contribution of these atom types could not be predicted accurately, since they did not appear in the training set. After... 

Hydrogen bonding descriptors, in particular, the ability of an atom in a given environment to be a donor Hd) and acceptor Ha) of a hydrogen bond characterized by the Abraham s constants. " ... 

Hydrogen bonding (nnmber of H-bond donors or acceptors, Abraham s a and 3 descriptors, PSA, etc.)... 

This equation is based on Abraham s solvation equation which uses five molecular descriptors excess molar refraction (F), solute polarity/polarizability (S), McGowan characteristic volume (V), solute overall acidity (A) and basicity (B). The steric (size/shape) descriptors E, S and V have a positive effect on oral absorption, while the descriptors related to H-bonding, A and B, have a negative effect. The model accounts for 74% of the variance (r ) in the data and the predictions have a 14% standard error (i). This is nearly as good as it gets, since the experimental biological variance is ca. 15%. 

Abraham-Klamt descriptors Linear Solvation Energy Relationships Abraham s general equation —> Linear Solvation Energy Relationships absolute hardness quantum-chemical descriptors ( hardness indices) absorption parameter property filters ( drug-like indices)... 

The solute descriptors are required in the system coefficient approach. The solute descriptors can be found in Abraham s databases for many compounds. Commercial software (Absolv Pharma Algorithms, Ontario, Canada) is also available for estimating the values of the solute descriptors from the struemre of the compounds. Experimental determination of the solute descriptors is best carried out through the use of multiple water/solvent partition coefficients (Abraham et al., 1999). However, it is difficult to determine the water/solvent partition coefficients using the traditional hquid-hquid extraction, which involves tedious manual operation, compheated sample handhng, and emulsion problems. 

Briefly, the PSP approach heavily resides on the quantum mechanics-based COSMO-RS theory of solutions [17-22], The COSMO model belongs to the class of continuum solvation models (CSM) of quantum mechanics. For the solvation picture, it considers the molecule embedded in a conductor of infinite permittivity that screens perfectly the molecular charges on the surface of its molecular cavity. This molecular cavity is characterized by a volume, Fcogni, and a molecular surface area, The crucial information is contained in the so-called COSMO tile of each compound obtained from quantum chemical calculations at various levels of theory. COSMO tiles give the detailed surface charge distribution or the o-protile of each molecule. The o-protile may be analyzed into its moments of various orders, known as COSMOments, out of which a large number of properties may be calculated, among them the molecular descriptors of Abraham s QSPR/LSER model [23,24]. 

Among the approaches proposed so far, we recall here single-parameter models [102-111, 115, 118-120, 122, 123, 125, 126, 129], and multi-parametric correlation equations (either based on the combination of two or more existing scales or on the use of specific parameters to account for distinct types of effects) [112, 113, 116, 117, 121, 124]. Additional popular models are the Abraham s scales of solute hydrogen-bond acidity and solute hydrogen-bond basicity [127, 128], and the Catalan et al. solvatochromic scales [130,132, 133]. Methods based on quantitative stmcture-property relationships (QSPR) with solvent descriptors derived from the molecular structure [131, 134], and on principal component analysis (PCA) [135, 136] have been also proposed. An exhaustive review concerning the quantification of the solvent polarity has been recently published [138-140], including a detailed list of solvent scales, interrelations between parameters and statistical approaches. 

The coefficients of descriptors A, AB and S are not statistically significant, but the terms are left in the equation for comparison with Abraham and Le s [8] water-solubility equation, modified here to conform to the mathematical conventions used in this chapter ... 

M. H. Abraham, New solute descriptors for linear free energy relationships and quantitative structure-activity relationships, in Quantitative Treatments of Solute/Solvent Interactions, P. Politzer and J. S. Murray, eds., Elsevier, Amsterdam (1994) pp. 83-134. 

In an excellent paper, Zhao et al. [29] assembled a carefully reviewed literature set of human absorption data on 241 drugs. They showed that a linear regression model built with 5 Abraham descriptors could fit percent human absorption data reasonably well (r2 = 0.83, RMSE = 14%). The descriptors are excess molar refraction (E), polarizability (S), hydrogen bond acidity (A), hydrogen bond basicity (B), and McGowan volume (V), all related to lipophilicity, hydrophilicity, and size. In a follow-on paper, data on rat absorption for 151 drugs was collected from the literature and modeled using the Abraham descriptors [30]. A model with only descriptors A and B had r2 = 0.66, RMSE = 15%. 

Abraham et al. [2] published a number of papers in which they analyzed Young s data set using MLR and gave a general solvation equation in which various solvent-solute interactions were described by solute descriptors and equation coefficients (Eq. 16)... 

Zhao and coworkers [53] also constructed a linear model using the Abraham descriptors. The MLR model possesses good correlation and predictability for external data sets. In this equation, E is an excess molar refraction (cm3/mol/ 10.0) and S the dipolarity/polarizability, A and B are the hydrogen bond acidity and basicity, respectively, and V is the McGowan characteristic volume (cm3/ mol/100). The large coefficients of A and B indicate too polar molecules having poor absorption. 

Let us now extend our molecular descriptor model introduced in Chapter 4 (Eqs. 4-26 and 4-27) to the aqueous activity coefficient. We should point out it is not our principal goal to derive an optimized tool for prediction of yw, but to develop further our understanding of how certain structural features determine a compound s partitioning behavior between aqueous and nonaqueous phases. Therefore, we will try to keep our model as simple as possible. For a more comprehensive treatment of this topic [i.e., of so-called linear solvation energy relationships (LSERs)] we refer to the literature (e.g., Kamlet et al., 1983 Abraham et al., 1990 Abraham, 1993 Abraham et al., 1994a and b Sherman et al., 1996). 

During the last 15 years, Abraham and his co-workers have established a set of five descriptors for the general description of logarithmic partition coefficients by linear regression. Their so-called linear free energy relationship (LFER) descriptors E, S, A, B, and V are effective parameters for the polarizability, polarity, hydrogen-bond acidity and basicity, and volume of the solute molecules, respectively [113-116]. They are mainly derived from experimental refraction and partition coefficients of the solutes. 

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