Hansch-Fujita model

The relationships among the ILS (150 and 160%), the minimum lethal dose (MLD), and the hydrophylic coefficient of the ether series of RA-V were analyzed according to both the Hansch-Fujita model and the bilinear model of Kubinyi. When the parabolic model obtained from the Hansch-Fujita equation was applied to the ILS and MLD, significant results could not be obtained. (See Fig. 21.)... 

The Fujita-Ban model having the hydrogen substituted compound as reference compound is related to the -> Hansch linear model by the following relationship ... 

The Hansch linear model is related to the - Fujita-Ban model when, in both models, the hydrogen substituted compound is taken as the reference compound each Fujita-Ban regression coefficient b s corresponds to the Hansch equation for a single substituent ... 

In particular, the Fujita-Ban group contributions implicitly contain all the possible physico-chemical contributions of a substituent as a consequence, the Fujita-Ban models always give an upper limit of correlation which can be achieved by Hansch linear models. 

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 ... 

Well-known substituent descriptors are the substituent constants which are experimentally determined descriptors among them, - electronic substituent constants, steric substituent descriptors, and lipophilicity substituent descriptors such as - Hansch-Fujita hydrophobic constants are the most commonly used in QSAR/QSPR modelling. 

Hansch analysis tries to correlate biological activity with physico-chemical properties by linear and nonlinear regression analysis, finding property-activity relationship models. A Craig plot is a plot of two substituent parameters (e.g., Hansch-Fujita n and Hammett a values). The simplest Hansch analysis is based on the Hansch linear model [Kubinyi, 1988b], defined... 

Hansch-Fujita hydrophobic substituent constants Hansch linear model —> Hansch analysis Hansch nonlinear model —> Hansch analysis Hansch parabolic model —> Hansch analysis Harary-Balaban index —> distance matrix... 

Quantitative structure-activity relationships (QSAR), a concept introduced by Hansch and Fujita (1964) is a kind of formal system based on a kinetic model, which in turn is expressed in term of a first-order linear differential equation. Solution of the differential equation leads to a linear equation ( Hansch-Fujita equation ), the coefficients of which are determined by regression analysis resulting in a QSAR equation of a particular compound series. For a prediction, the dependent variable of the QSAR equation is calculated by algebraic operations. 

Hansch and Toshio Fujita, a postdoctoral researcher in Hansch s group, designed a parameter, ttr, to estimate the lipophilicity of an R-group.3 Hansch s parameter relies on partition coefficients to measure lipophilicity. Partition coefficients, P, are equilibrium constants describing the degree to which a molecule distributes into a biphasic mixture of two immiscible solvents. Hansch used 1-octanol and water as the model solvents because these were known to simulate the lipid membrane-cytosol interface. The partition coefficient of a molecule is defined as the ratio of a molecule s concentration in an octanol layer to its concentration in an aqueous layer (Equation 12.12). 

The classical QSAR methodology started 1964 with the publications of Hansch and Fujita (1964) and Free and Wilson (1964) and the statement of Hansch (1969) resulted from a proposal by Fujita. They proposed to combine several physiochemical parameters (tt, a), also called descriptors, in a quantitative model. This Hansch-type analysis is very flexible and describes many different kinds of biological activities, e.g. in vitro data such as enzyme inhibition (Kubinyi 2002) ... 

Hansch and Fujita used a Gaussian probability function to characterize the partitioning Step 1 and the Hammett function (log(k/k0) = pa) to describe the rate Step 2 in their model (10,12,13). By appropriate mathematical treatment, they arrived at the following general structure-activity relationship which has come to be termed the Hansch Equation. 

Model Parent Compound Series. Experimental partition coefficient data for a variety of substituted benzenes and seven other related parent compound series (phenoxyacetic acid, phenylacetic acid, benzoic acid, benzyl alcohol, phenol, aniline, nitrobenzene) were reported in 1964 by Fujita et al. (II). The ir values (see Equation 3) derived for individual substituents in each of the above-mentioned parent compound series have since been frequently used (with varying degrees of success) by many investigators to approximate tt values for the corresponding substituents in other related parent compounds for which no experimental partitioning data are available. For example, Hansch and Deutsch (26), in a correlation study of structure—activity relationships in cholinesterase inhibitors, used tr values derived for aromatic ring substituents (X) in the phenoxyacetic acid series... 

Therefore, it is difficult to define a reasonable basis for selecting any of the parent series previously examined by Fujita et al. (11) as a model for the TFMS series of the present study. Indeed, some initial Hansch analyses of our TFMS pre-emergence herbicidal activity data using Fujita s phenoxyacetic acid substituent n values produced very poor correlations. We thus deemed it prudent (if not essential) to determine experimentally w values for all substituents in the TFMS series. 

Hansch and Fujita (5) have proposed a model for biological activity which may be expressed by the following equation ... 

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. 

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. 

TABLE 6. Property-Activity Model of Hansch and Fujita (1964)... 

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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