Hansch-Fujita method

The Hansch-Fujita method, the Free-Wilson theory (described by Craig in Chapter 8), and the molecular orbital theory (described by Kier, Chapter 15) have greatly increased our understanding of the mode of action of many biological chemicals. It has also improved our ability to predict the activity of a variety of chemicals against plant and insect pests and certain pathogenic organisms. 

The Hansch-Fujita method is a classical QSAR technique with traditional statistics, which constructs the quantitative relationship between physico-ehemical descriptors of substituents and biological activities by using classical regression analysis. 

In organic chemistry, decomposition of molecules into substituents and molecular frameworks is a natural way to characterize molecular structures. In QSAR, both the Hansch-Fujita " and the Free-Wilson classical approaches are based on this decomposition, but only the second one explicitly accounts for the presence or the absence of substituent(s) attached to molecular framework at a certain position. While the multiple linear regression technique was associated with the Free-Wilson method, recent modifications of this approach involve more sophisticated statistical and machine-learning approaches, such as the principal component analysis and neural networks. ... 

Hansch C, Fujita T. p-o-ix Analysis method for the correlation of biological activity and chemical structure. J Am Chem Soc 1964 86 1616-26. 

Hansch, C. Fujita, T. (1964) p-u-jr Analysis. A Method for the Correlation of Biological Activity and Chemical Structure. Journal of the American Chemical Society, 85, 1616-1626. 

The second extrathermodynamic method that we discuss here differs from Hansch analysis by the fact that it does not involve experimentally derived substitution constants (such as o, log P, MR, etc.). The method was originally developed by Free and Wilson [29] and has been simplified by Fujita and Ban [30]. The subject has been extensively reviewed by Martin [7] and by Kubinyi [8]. The method is also called the de novo approach, as it is derived from first principles rather than from empirical observations. The underlying idea of Free-Wilson analysis is that a particular substituent group at a specific substitution site on the molecule contributes a fixed amount to the biological activity (log 1/C). This can be formulated in the form of the linear relationship ... 

Attempts to quantitatively relate chemical structure to biological action were first initiated in the 19th century, but it was not until the 1960s that Hansch and Fujita devised a method that successfully incorporated quantitative measurements into SAR determinations (see section 4.4). The technique is referred to as QSAR (quantitative structure-activity relationships). One of its most successful uses has been in the development in the 1970s of the antiulcer agents cimetidine and ranitidine. Both SARs and QSARs are important parts of the foundations of medicinal chemistry. 

The epoch of QSAR (Quantitative Structure-Activity Relationships) studies began in 1963-1964 with two seminal approaches the a-p-7i analysis of Hansch and Fujita " and the Free-Wilson method. The former approach involves three types of descriptors related to electronic, steric and hydrophobic characteristics of substituents, whereas the latter considers the substituents themselves as descriptors. Both approaches are confined to strictly congeneric series of compounds. The Free Wilson method additionally requires all types of substituents to be suflficiently present in the training set. A combination of these two approaches has led to QSAR models involving indicator variables, which indicate the presence of some structural fragments in molecules. 

The large number of methods used to calculate log P values have been elegantly reviewed by Leo. The method proposed in 1964 by Fujita, Iwasa and Hansch used values for the parent molecule and values for substituents gathered by analysis of thousands of values of log P for homologous and other series. In this method of substituents log P is considered to be an additive-constitutive free-energy-related property, where one can define Ft for substituent X as the difference between the log P values for the parent solute and the compound with the substituent ... 

Early QSAR studies were mainly focused on analyzing the effect of aromatic substituents on activity in congeneric compound series using substituent constants to describe the steric, electronic and lipophilic characteristics of the substituents. Hansch and Fujita proposed a method to describe quantitatively relationships between biological activity and chemical descriptors. This can be expressed as follows ... 

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