Quantitative structure-activity nonlinear models

Nonlinear Quantitative Structure-Activity Relationship Modeling For the... 

Kubinyi, H., Quantitative structure-activity relationships. IV. Nonlinear dependence of biological activity on hydrophobic character a new model, Arzneim. Forsch. (Drug Res.) 26, 1991-1997 (1976). 

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. 

Another area of molecular modeling involves development of quantitative structure-activity or structure-property relationships (QSAR and QSPR). These studies use a range of statistical methods (linear and nonlinear... 

Kubinyi H. Quantitative structure-activity relationships 7. The bilinear model, a new model for nonlinear dependence of biological activity on hydrophobic character. J Med Chem 1977 20 625-629. 

Due to the relationships between Hansch analysis and the Free Wilson model, indicator variables (chapter 3.8) have relatively early been included in Hansch analyses (e.g. [21, 427, 428]). Both models can be combined to a mixed approach, in a linear (eq. 78) and a nonlinear form (eq. 79), which offers the advantages of both, Hansch analysis and Free Wilson analysis, and widens their applicability in quantitative structure-activity relationships [22]. 

The discipline of quantitative structure-activity relationships (QSAR), as we define it nowadays, was initiated by the pioneering work of Corwin Hansch on growthregulating phenoxyacetic acids. In 1962—1964 he laid the foundations of QSAR by three important contributions the combination of several physicochemical parameters in one regression equation, the definition of the lipophilicity parameter jt, and the formulation of the parabolic model for nonlinear lipophilicity-activity relationships. 

The most, comprehensive review of quantitative structure-pharmacokinetics relationships [452] tabulates about 100 equations, including absorption, distribution, protein binding, elimination, and metabolism of drugs. Since many of these equations and those included in other reviews e.g. [472, 761]) have been derived before appropriate mathematical models for nonlinear lipophilicity-activity relationships (chapter 4.4) and for the correct consideration of the dissociation and ionization of acids and bases (chapter 4.5, especially eqs. 107—110) were available, some of the older results should be recalculated by using the theoretical models (chapters 4.4 and 4.5) instead of the empirical ones. 

Linear or nonlinear multiple regression analysis is used as a statistical tool to derive quantitative models, to check the significance of these models and of each individual term in the regression equation. Other statistical methods, such as discriminant analysis, principal component analysis (PCA), or partial least squares (PLS) analysis (see Partial Least Squares Projections to Latent Structures (PLS) in Chemistry) are alternatives to regression analysis (see Che mo me tries Multivariate View on Chemical Problems)Newer approaches compare the similarity of molecules with respect to different physicochemical or other properties with their biological activities. 

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