Linear additive structure-activity relationships

By its definition the Free Wilson analysis is limited to linear additive structure-activity relationships (its application to nonlinear relationships and the combination with Hansch analysis to a mixed approach are described in chapter 4.3). A detailed discussion of the scope and limitations of the Free Wilson model is given in refs. [390, 391] some applications are discussed in chapter 8. 

More recently (2006) we performed and reported quantitative structure-activity relationship (QSAR) modeling of the same compounds based on their atomic linear indices, for finding fimctions that discriminate between the tyrosinase inhibitor compounds and inactive ones [50]. Discriminant models have been applied and globally good classifications of 93.51 and 92.46% were observed for nonstochastic and stochastic hnear indices best models, respectively, in the training set. The external prediction sets had accuracies of 91.67 and 89.44% [50]. In addition to this, these fitted models have also been employed in the screening of new cycloartane compounds isolated from herbal plants. Good behavior was observed between the theoretical and experimental results. These results provide a tool that can be used in the identification of new tyrosinase inhibitor compounds [50]. 

The concept of the similarity of molecules has important ramifications for physical, chemical, and biological systems. Grunwald (7) has recently pointed out the constraints of molecular similarity on linear free energy relations and observed that Their accuracy depends upon the quality of the molecular similarity. The use of quantitative structure-activity relationships (2-6) is based on the assumption that similar molecules have similar properties. Herein we present a general and rigorous definition of molecular structural similarity. Previous research in this field has usually been concerned with sequence comparisons of macromolecules, primarily proteins and nucleic acids (7-9). In addition, there have appeared a number of ad hoc definitions of molecular similarity (10-15), many of which are subsumed in the present work. Difficulties associated with attempting to obtain precise numerical indices for qualitative molecular structural concepts have already been extensively discussed in the literature and will not be reviewed here. 

In addition, traditional quantitative structure-activity relationship (QSAR) models were reported. Gozalbes et al. attempted to predict the blood-brain barrier permeabilities of four arylacetamides using linear discriminant analysis [65], while Medina-Franco et al. discriminated between active and inactive BCG compounds using two-dimensional (2D) and three-dimensional (3D) structural-similarity methods [66]. 

A useful technique for analyzing structure-activity relationships which has come into use within the past five or so years is that pioneered by Corwin Hansch (19). Its underlying concept is that the relative biological activity of a derivative depends on the difference in hydrophobic, electronic, or steric factors between the derivative and the parent compound. The contribution of each effect to activity is assumed to be independently additive so that one has a linear free energy relationship. Equations of the form below are expected ... 

The study of structure-reactivity relationships by the organic chemist Hammett showed that there is often a quantitative relationship between the two-dimensional structure of organic molecules and their chemical reactivity. Specifically, he correlated the changes in chemical properties of a molecule that result from a small change in its chemical structure that is, the quantitative linear relationship between electron density at a certain part of a molecule and its tendency to undergo reactions of various types at that site. For example, there is a linear relationship between the effea of remote substituents on the equilibrium constant for the ionization of an acid with the effect of these substituents on the rate or equilibrium constant for many other types of chemical reaction. The relative value of Hammett substituent constants describes the similarity of molecules in terms of electronic properties. Taft expanded the method to include the steric hindrance of access of reagents to the reaction site by nearby substituents, a quantitation of three-dimensional similarity. In addition, Charton, Verloop, Austel, and others extended and refined these ideas. Finally, Hansch and Fujita showed that biological activity frequently is also quantitatively correlated with the hydrophobic character of the substituents. They coined the term QSAR, Quantitative Structure-Activity Relationships, for this type of analysis. 

Lipophilicity in particular, as reflected in partition coefficients between aqueous and non-aqueous media most commonly water (or aqueous buffer) and Z-octanol,has received much attention [105,141,152,153,176,199,232,233]. Logic )W for the octanol-water system has been shown to be approximately additive and constitutive, and hence, schemes for its a priori calculation from molecular structure have been devised using either substituent tt values or substructural fragment constants [289, 299]. The approximate nature of any partition coefficient has been frequently emphasized and, indeed, some of the structural features that cause unreliability have been identified and accommodated. Other complications such as steric effects, conformational effects, and substitution at the active positions of hetero-aromatic rings have been observed but cannot as yet be accounted for completely and systematically. Theoretical statistical and topological methods to approach some of these problems have been reported [116-119,175,289,300]. The observations of linear relationships among partition coefficients between water and various organic solvents have been extended and qualified to include other dose-response relationships [120-122,160,161,299-302]. 

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