Bilinear model, Kubinyi

Figures 7.31a-c clearly show that after some critical soy content in dodecane, Pe values decrease with increasing soy, for both sink and sinkless conditions. [This is not due to a neglect of membrane retention, as partly may be the case in Fig. 7.23 permeabilities here have been calculated with Eq. (7.21).] Section 7.6 discusses the Kubinyi bilinear model (Fig. 7.19d) in terms of a three-compartment system water, oil of moderate lipophilicity, and oil of high lipophilicity. Since lipo-some(phospholipid)-water partition coefficients (Chapter 5) are generally higher than alkane-water partition coefficients (Chapter 4) for drug-like molecules, soy lecithin may be assumed to be more lipophilic than dodecane. It appears that the increase in soy concentration in dodecane can be treated by the Kubinyi analysis. In the original analysis [23], two different lipid phases are selected at a fixed ratio (e.g., Fig. 7.20), and different molecules are picked over a range of lipophilicities.

The delineation of these models led to explosive development in QSAR analysis and related approaches. The Kubinyi bilinear model is a refinement of the parabolic model and, in many cases, it has proved to be superior (21). 

Kubinyi ( ) used distribution coefficients of the same series of compounds with his bilinear model for absorption to obtain an even closer correlation. Equation 5. pis a constant related to the model. 

We ve looked at many other analyses of "simple" processes, but my favorite is a correlation for the absorption of an acid and a base in the same equation, — not only that, but with each one at six different pH s, (Figure 2). The data are from Schurmann Turner ( ) the base is propranolol and the acid, 4-n-hexylphenylacetic. Only a single parameter is required, log D, Equation 6. Kubinyi s bilinear equation gives an even better correlation ( ), Equation 7. (This is a special version of the bilinear model which sets the coefficients of each term equal.)... 

The ascending and descending slopes are equal (== l)and linear. However, a major drawback of this model is that it forces the activity curves to maximize at logP = 0. These studies woe extended by Kubinyi, who developed the elegant and powerful bilinear model, which is superior to the parabolic model and is extensively used in QSAR studies (192). 

Besides the nonlinear models and, specifically, the parabolic model, other models were proposed for nonlinear dependence of the biological response from hydrophobic interactions. Among them, the most important are the Hansel bilinear models [Kubinyi, 1977 Kubinyi, 1979] such as ... 

Kubinyi, H. (1977). Quantitative Structure-Activity Relationships. 7. The Bilinear Model, a New Model for Nonlinear Dependence of Biological Activity on Hydrophobic Character. J.Med. Chem., 20,625-629. 

Kubinyi, H. (1977) Quantitative structure-activity relationships. 7. The bilinear model, a new model for nonlinear dependence of biological activity on hydrophobic character. J. Med. Chem.,... 

Kubinyi H. Lipophilicity and biological activity the use of the bilinear model in QSAR. In Kuchar M ed. QSAR in Design of Bioactive Compounds. Proceedings of the First International Telesymposium on Medicinal Chemistry. Barcelona Prous Science Publishers, 1984 321-346. 

The ester derivatives showed a similar relationship, the optimum log P values being 6.3 -6.7, which was higher than that of the ether derivatives. The relationship among the ILS (150 and 160%), the minimum lethal dose (MLD) and the hydrophilic coefficient of the ether series of RA-V were analyzed according to both the Hansch-Fujita and the bilinear models of Kubinyi. When the parabolic model obtained from the Hansch-Fujita equation was applied to the ILS and MLD, no significant results were obtained. 

To circumvent this problem, Bintein, Devillers and Karcher developed one of the most comprehensive models for a wide range of chemicals including many pesticides for which bioconcentration data were acquired in five families of freshwater fish. They utilized Kubinyi s bilinear model the log P values of the compounds in the dataset ranged from 1 to 9. 

The bilinear model of Kubinyi (1977, 1993) was derived from a reconsideration of the McFarland probability model and takes into account the different volumes of the aqueous and the organic target phases in biological systems ... 

Nevertheless, numerous QSARs involve other lipophilicity dependencies to model biological activity of drugs, among which Kubinyi s bilinear relationship must be quoted [338] (see Ref 109 for a review). However, the database collected by Hansch s group showed in 1993 [339] that only 15% of the biological QSARs do not imply any lipophilicity term. Hence, lipophilicity is clearly a major determinant of biological activity [340]. 

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