Quantitative structure-activity relationship Hansch equations

The fundamental assumption of SAR and QSAR (Structure-Activity Relationships and Quantitative Structure-Activity Relationships) is that the activity of a compound is related to its structural and/or physicochemical properties. In a classic article Corwin Hansch formulated Eq. (15) as a linear frcc-cncrgy related model for the biological activity (e.g.. toxicity) of a group of congeneric chemicals [37, in which the inverse of C, the concentration effect of the toxicant, is related to a hy-drophobidty term, FI, an electronic term, a (the Hammett substituent constant). Stcric terms can be added to this equation (typically Taft s steric parameter, E,). 

Hansch analysis Hansch analysis is a common quantitative structure-activity relationship approach in which a Hansch equation predicting biological activity is constructed. The equation arises from a multiple linear regression analysis of both observed biological activities and various molecular property parameters (Hammett, Hansch, and Taft parameters). 

Quantitative structure-activity relationship (QSAR) (Hansch and Klein, 1986 Hansch and Leo, 1995) represents an attempt to correlate structural descriptors of compounds with activities. The physicochemical descriptors include numerical parameters to account for electronic properties, steric effect, topology, and hydrophobicity of analogous compounds. In its simplest form, the biochemical activities are correlated to the numerical substituent descriptors of analogous compounds tested by a linear equation such as... 

Quantitative structure—activity relationships have been established using the Hansch multiparameter approach (14). For rat antigoiter activities (AG), the following (eq. 1) was found, where, as in statistical regression equations, n = number of compounds, r = regression coefficient, and s = standard deviation... 

Extensive efforts have been made to develop quantitative structure/activity relationships (QSARs) that predict membrane transport (16, 17). Particularly extensive use has been made of log P (log solvent/water partition coefficient values) and the Hansch equation (Equation 14.3) ... 

Hansch and Caldwell have analyzed the quantitative structure/activity relationships (QSAR) of a series of amphetamine and 2-phenethylamine analogs, to discern the role of steric and hydrophobic aryl substituents on the inhibition of 5-HT uptake (142). From the biological data of 19 compounds, including those in Table 15.13. and some additional analogs, the following equation was derived for inhibition of uptake activity, where C is the IC concentration, MR4 is the molar refrac-tivity value of the aryl substituent scaled by 0.1, and 7T3 is the hydrophobicity of the meUi substituent on the aryl ring ... 

Quantitative structure-activity relationships QSAR. The QSAR approach pioneered by Hansch and co-workers relates biological data of congeneric structures to physical properties such as hydrophobicity, electronic, and steric effects using linear regression techniques to estimate the relative importance of each of those effects contributing to the biological effect. The molecular descriptors used can be 1-D or 3-D (3D-QSAR). A statistically sound QSAR regression equation can be used for lead optimization. 

BR is the relative biologic activity under investigation, for example the molar EDr>o or the percent response at a given dose. Log P is the logarithm of the octanol-water partition coefficient, a is the approprite Hammett signa constant (electronic in nature), and Es is the Taft steric parameter. With the important demonstration by Hansch that the partition coefficient is often an additive constitutive property, all of the physical parameers may be obtained from the literature. A second important contribution by Hansch is the recognition that the use of statistical techniques is essential to the analysis of quantitative structure-activity relationships. To develop an equation such as that above, one feeds the... 

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. 

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,... 

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. 

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). 

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