Hansch-Fujita approach

The Hansch-Fujita approach is also called the linear free-energy relationship (LFER) or extrathermodynamic approach, since most of the descriptors are derived from rate or equilibrium constants. 

Quantitative structure-activity relationships, based on the Hansch-Fujita approach (7), were analyzed for 13 compounds related to ch1 orf1uazuron (Figure 2), In the best correlation obtained (Equation 2), the only term needed to determine larvicidal activity log (I/LC90) against Spodoptera 1 i t u r a (common cutworm) is tt and the straight line obtained shows that substituents having larger 71 values show enhanced activity,... 

Thus, the Hansch-Fujita approach allows one to calculate the partition coefficient of any substituted compound knowing the partition coefficient of the parent compound (RH) and the hydrophobic constants of substituents X, (Eq. [11]) ... 

This is true in particular for the (erroneous) zero value of the hydrophobic constant of H (iTh = 0.00 by definition), the limited number of experimental log P values used to derive hydrophobic substituent constants, and the number of different tt scales needed to account for the complex electronic effects operating in polysubstituted aromatic compounds. Despite several attempts to extend the applicability of log P calculations using the Hansch-Fujita approach, for instance, by inclusion of correction factors" and better treatments of electronic effects , this approach has fallen into obso-lesence when it comes to calculating log P values. In contrast, the hydrophobic substituent constants (nx) of Table 1 continue to find use as structural parameters in some QSAR studies. ... 

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-Free-Wilsoo mixed models were also proposed [Kubinyi, 1976a] by combining the two approaches in a single model. A quadratic term accounting for hydro-phobic interactions (usually logP or n Hansch-Fujita constant) can be added to the Free-Wilson (or Fujita-Ban) model as ... 

Some of the commonly used descriptors in the Hansch-Fujita QSAR approach are as follows, ir measures the relative contribution of a substituent to lipophilicity of the compound and is defined by it = log x - log Ph, where Px is the partition coefficient, usually for an -octanol/water system, of a compound with a substituent X, and Ph is the partition coefficient of the parent compound. ir, when combined with a tt term of opposite sign, accounts for a parabolic dependence on lipophilicity. Such a situation is obtained, for instance, if there are two stages involved in producing the biological effect, and they have opposite dependencies on lipophilicity. A variety of Hammett... 

An extension of the Hansch and Fujita approach was developed to calculate the partition coefficient of peptides. Because peptides are composed of amino acids, an adaptation of Eq. [11] was proposed to link the lipophilicity of... 

The main problems with the Hansch and Fujita approach are the difficulty in treating symmetrical compounds such as biphenyH and the improper identification of ir-substituent constants with log P values. The latter problem is seen when log P values are calculated by the mere addition of substituent constants including the log Prh term in Eq. [11], thus neglecting the principle of substitution. ... 

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 ... 

Quantitative Structure-Activity Relationship (QSAR) approach was first developed by Cros (1863) and Brown and Fraser (1868). In the 1960s, C. Hansch, T. Fujita, S. M. Free Jr. and J. W. Wilson started what is now considered to be classical QSAR. A series of powerful advanced computer tools have now been introduced, increasing the capacity of QSAR. 

Roy and Leonard [183] have also presented QSAR models for the HIV-1 RT inhibitory activity of the thiazolidinones listed in Tables 16 and 17 along with some more similar analogues (Table 18) [184-187] using the hydrophobic-ity and molar refractivity, quantum chemical and topological and indicator parameters as descriptors. In this, the 3-pyridyls/phenyls (Tables 16 and 17) and 3-(pyrimidin-2-yls) (Table 18) [186] have become part of the dataset. Additionally, four compounds with the thiazolidin-4-thione nucleus have been included in the dataset. In Fujita-Ban [188] and mixed (Hansch and Fujita-Ban) approaches 7 to 17 descriptor models have been discovered for the cytopathicity effect (EC50) and cytotoxic effect (CC50) of the compounds. The following equations show the minimum descriptor models for each activity from this study. 

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. 

Derived from physical organic chemistry and the - Hammett equation, this can be considered to be the first approach to modern QSAR studies. Proposed by Hansch and co-workers in the early 1960s [Hansch et al, 1962 Hansch et al, 1963 Hansch and Fujita, 1964 Hansch et al, 1965 Hansch and Anderson, 1967 Hansch, 1969 Hansch, 1971 Hansch, 1978], it is the investigation of the quantitative relationships between... 

Hansch, Muir et al, 1963 Fujita, Iwasa et al, 1964], the QSAR/QSPR approach began to assume its modern look. 

In 1962, Hansch, Maloney and Fujita [Hansch, Maloney et al, 1962] published their study on the structure-activity relationships of plant growth regulators and their dependency on Hammett constants and hydrophobidty. Using the octanol/water system, a whole series of partition coefficients was measured and, thus, a new hydrophobic scale was introduced for describing the inclination of molecules to move through environments characterized by different degrees of hydrophilicity such as blood and cellular membranes. The delineation of Hansch models led to explosive development in QSAR analysis and related approaches [Hansch and Leo, 1995]. This approach known with the name of Hansch analysis became and it still is a basic tool for QSAR modeling. 

The Hansch approach is one of the most widely used methods for analysing structure-activity relationships when quantitative data are available. It is named after the founder of modern QSAR, Corwin Hansch (Hansch and Fujita, 1964), who suggested that the biological activity of a molecule was a function of its electronic, steric and hydrophobic properties the last most often being represented by the partition coefficient (P) between water and octanol (equation 2). 

Fujita T. The extrathermcdynamic approach to drug design. In Hansch C, ed. Comprehensive Medicinal Chemistry. New York Pergamon Press, 1990 4 497-560. 

The impact of hydrophobicity on most biological processes is of great significance as can be ascertained by the frequency of its usage in most QSAR studies. Despite the early usage by Meyer and Overton at the end of the nineteenth century, hydrophobicity eventually took its cues from the Hammett approach and finally crystallized fifty years later when the best known and now well-developed hydrophobic descriptor, log Po/w was delineated by Hansch and Fujita. 

Charton s intermolecular force equation (IMF) is the best model covering all physicochemical and physicobiochemical events (97), but it is not in general use. Hansch (98), Fujita (99) and Verloop (100) all use internally consistent variations in their own research. By any consistent approach, accidental correlations are of little concern in the analysis of statistically large (n>30) sets of well measured binding data. Even smaller sets can reliably extract the major mechanistic components provided overdescription is not attempted (less than 4 data points/variable). 

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