Lipophilicity nonlinear

Rapid dermal absorption of trichloroethylene is evident from a study in which peak blood and exhaled air concentrations occurred within 5 minutes after a human subject immersed one hand in a solution of unspecified trichloroethylene concentration for 30 minutes (Sato and Nakajima 1978). Studies on dermal absorption of trichloroethylene in humans, as well as animals, are complicated by the fact that exposure in these studies is usually by direct contact of the skin with the undiluted chemical. Trichloroethylene is a lipophilic solvent that defats the skin and disrupts the stratum comeum, thereby enhancing its own absorption. Thus, the rate of absorption probably increases in a nonlinear fashion with greater epidermal disruption. Although the extent of absorption through the skin may be relatively modest with normal industrial use (Sato and Nakajima 1978 Stewart and Dodd 1964), there is insufficient information to evaluate the effects of chronic, low-level exposure in hiunans, especially when multiple routes may be involved. 

Schaper, K.-J., Simultaneous determination of electronic and lipophilic properties [pKa, P(ion), P(neutral)] for acids and bases by nonlinear regression analysis of pH-dependent partittion measurements, J. Chem. Res. (S) 357 (1979). 

Molecules with a large molecular weight or size are confined to the transcellular route and its requirements related to the hydrophobicity of the molecule. The transcellular pathway has been evaluated for many years and is thought to be the main route of absorption of many drugs, both with respect to carrier-mediated transport and passive diffusion. The most well-known requirement for the passive part of this route is hydrophobicity, and a relationship between permeability coefficients across cell monolayers such as the Caco-2 versus log P and log D 7.4 or 6.5 have been established [102, 117]. However, this relationship appears to be nonlinear and reaches a plateau at around log P of 2, while higher lipophilicities result in reduced permeability [102, 117, 118]. Because of this, much more attention has recently been paid towards molecular descriptors other than lipophilicity [86, 119-125] (see section 5.5.6.). The relative contribution between the para-cellular and transcellular components has also been evaluated using Caco-2 cells, and for a variety of compounds with different charges [110, 112] and sizes [112] (see Section 5.4.5). 

Among the quadratic terms, the most used is usually (logP), in order to mimic the nonlinear behaviour of the interchange between a two-phase system (e.g. aqueous/ organic system), i.e. too low or too high lipophilicity values act as a limiting factor. The most common parabolic model is specifically defined as ... 

Of course, the developed methods do not necessarily have to be based on a linear equation. For example, Artemenko et al. predicted lipophilicity using fragmental descriptors and artificial neural networks [85]. The use of linear equations nevertheless provides, an easier interpretation of calculated results that can be difficult when using nonlinear methods of data analysis. 

In 1962, Hansen [14] derived a first Hammett-type relationship between the toxicities of substituted benzoic acids and the electronic a constants of their substituents. However, later, it turned out that this was a chance correlation that only resulted from a close interrelationship between the Hammett a parameter and the lipophilicity constant % (Sec. 4 Eqs. (42) and (43)). In the same year, for the very first time, a nonlinear multiparameter equation (Eq. 6) [15] was used to describe biological activity values ... 

Free-Wilson analysis can be used for a first inspection of biological activity data [30-32]. The values of the group contributions indicate which physicochemical properties might be responsible for the variations in biological activity values and whether nonlinear lipophilicity-activity relationships are involved. Free-Wilson contributions can be derived from Hansch equations (e.g., by Eq. (18) from Eq. (14), or by Eq. (19) from Eq. (15)) [30] ... 

The parabolic Hansch model is a good approximation of observed nonlinear structure-activity relationships. However, whereas the left and right sides of a parabola are always nonlinear, many nonlinear lipophilicity relationships show linear left and right sides, as also observed for the function describing the rate constants of... 

The bilinear model, in combination with other physicochemical properties (Eq. (30)) [24,62], was the first mathematical expression to describe nonlinear lipophilicity-activity relationships, precisely and in a flexible manner. Besides pharmacokinetic properties, such as absorption, distribution, elimination, and permeation of the... 

In addition to this nonlinear relationship for the blood-brain barrier permeation of imidazolines, many other nonlinear lipophilicity relationships have been derived for buccal and gastrointestinal absorption, skin permeation, as well as blood-brain and blood-placenta barrier permeation (e.g., Eqs. (58) to (62) Fig. 7 [59,60,63,64] Barbiturates permeation through an organic membrane ... 

Figure 7 The permeation of barbiturates through an organic membrane, the gastric and intestinal absorption of carbamates, the blood-placenta transfer rate constants of various drugs, and the neurotoxicity of homologous primary alcohols, as a measure of blood-brain barrier permeation, follow nonlinear lipophilicity relationships (Eqs. (58)-(62)). (From Refs. 58,59,62,63.)...

In addition to nonlinear lipophilicity relationships for the transport and distribution of drugs, nonlinear relationships on molar refractivity are frequently observed in QSAR studies of enzyme inhibition data (provided that MR values are scaled by a factor of 0.1, as usual) [60,63,64,66-68]. Two such examples are given in Eq. (63) (Escherichia coli DHFR) and Eq. (64) (Lactobacillus casei DHFR) [101]. The differences between both models could be explained after the 3D structure of the enzyme became known. Whereas all substituents of a benzyl ring contribute to biological activities in E. coli DHFR, only the 3- and 4-substituents show up in the QSAR model for L. casei DHFR but not the 5-substituents. This results from a narrower binding pocket in L. casei DHFR a (3-branched leucine hinders the accommodation of 5-substituents, whereas a more flexible methionine in the same position of E. coli DHFR opens a wider binding pocket [101] ... 

From their QSERR they find solute lipophilicity and steric properties as being responsible for analyte retention (k ) while enantioseparation (a) varied mainly with electronic and steric properties. The main difference between the analytes is that the enantioseparation of the esters is correlated with steric parameters that scale linearly with log a while the sulfoxides scale nonlinearly (parabolic), but this may be due to a computational artifact. The 3D-QSERR derived from field analysis revealed that while superpositioning of field maps for both analytes are not exactly the same, a similar balance of physicochemical forces involved in the chiral recognition process are at play for both sets of analyes. This type of atomistic molecular modeling, then, is a powerful adjunct to the type of modeling described earlier in this chapter and will, no doubt, be used more frequently in future studies. 

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