Hammett equation biological

On the analogy of the physicochemical relation, one was led to define a biological Hammett equation which related the equilibrium constant of the drug-receptor complex to the electronic a parameters of the substituents (e.g. chlorine, bromine, methyl, ethyl, hydroxyl, carboxyl, acetyl, etc.) of the drug molecule. Since the equilibrium constant of a drug-receptor complex is reflected by the biological activity, this led to the first extrathermodynamic relationship in QS AR ... 

Tj in this biological Hammett equation stands for the activity value of the i" member of a series, Te, is the biological activity value of the ethyl compound of the same series, P is a substituent constant (corresponding to the electronic a parameter... 

The use of the Hammett equation has also been extended to several new types of applications. Since these are not germane to the subject matter of the present chapter, we wiU simply mention work on applications to ethylenic and acetylenic compounds the various applications to physical properties, such as infrared frequencies and intensities, ultraviolet spectra, polarographic half-wave potentials, dipole moments,NMR and NQR spectra,and solubility data and applications to preparative data and biological activity. 

In a parallel development, structural effects on the chemical reactivity and physical properties of organic compounds were modelled quantitatively by the Hammett equation 8). The topic is well reviewed by Shorter 9>. Hansen 10) attempted to apply the Hammett equation to biological activities, while Zahradnik U) suggested an analogous equation applicable to biological activities. The major step forward is due to the work of Hansch and Fujita12), who showed that a correlation equation which accounted for both electrical and hydrophobic effects could successfully model bioactivities. In later work, steric parameters were included 13). 

Systematic studies of the effects of structure on the biological activities of organic compounds and the analysis of the results are comprised in the term Quantitative Structure-Activity Relationships (QSAR). Many of the treatments employed in the correlation analysis of data in this field closely resemble those used for linear free-energy relationships, e.g. the Hammett equation and extensions thereof, and so the study of the biological properties of organic compounds is often regarded as a part of physical organic chemistry. In recent years, some historical study of work in... 

The correlation of biological activity with physicochemical properties is often termed an extrathermodynamic relationship. Because it follows in the line of Hammett and Taft equations that correlate thermodynamic and related parameters, it is appropriately labeled. The Hammett equation represents relationships between the logarithms of rate or equilibrium constants and substituent constants. The linearity of many of these relationships led to their designation as linear free energy relationships. The Hansch approach represents an extension of the Hammett equation from physical organic systems to a biological milieu. It should be noted that the simplicity... 

A discussion of the acceptable range of the Hammett equation, the treatment of deviations, and the meaning of the separation of interaction mechanism is of prime importance in assessing the contribution of electronic effects to biological activity. 

From the Hammett equation [Hammett, 1935, 1937], the seminal vork of Hammett gave rise to the a—p culture in the delineation of substituent effects on organic reactions, whose aim was to search for linear free energy relationships (LFER) [Hammett, 1938] steric, electronic, and hydrophobic constants were derived for several substituents and used in an additive model to estimate the biological activity of congeneric series of compounds. 

Structure/Response Correlations, Hansch analysis, Hammett equation, Free-Wilson analysis. Linear Solvation Energy Relationships, Linear Free Energy Relationships, group contribution methods, substituent descriptors, extrathermodynamic approach, and biological activity indices. 

In the following decades, various a scales were derived for different systems and several attempts were made to derive such relationships also for biological activities of organic compounds. Bruice et al. [10] formulated group contributions to biological activity values in a series of thyroid hormone analogs, which may be considered as a first Free-Wilson-type analysis. Zahradnik and Chvapil [11] and Zahradnik [12,13] tried to apply the concept of the Hammett equation also to biological data (Eq. (5)) ... 

The use of the Hammett equation was extended by Zahradnik and co-workers to relate other physicochemical parameters of homologous series of compounds to their biological activities (Equation 15) (49). In Equation 15, r is the molar concentration of the ith congener of an... 

From a cheminformatic perspective, the most important consequence of the Hammett equation is that it separates explicitly the contribution of environment from that of chemical structure in the prediction of an outcome (in this case, a reactivity property). As such, the Hammett equation represents one of the earliest attempts to predict molecular behavior on the basis of chemical structure alone. Notably, however, later investigators experienced difficulties when trying to apply Hammett-type relationships to biological systems, indicating that additional structural determinants need to be considered [32, 37]. 

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,). 

These and other investigators have shown, for many systems where a biological response can be measured quantitatively, that relative biological response can be expressed as functions of various molecular properties by using equations of the same forms as Hammett or Taft relationships ... 

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). 

Hansch et al. (9, 10) have developed linear free energy relations which can correlate biological activity and chemical structure. Equations 1 and 2, together with simplified versions, have been proposed to relate the molar concentration, Cx, of a substituted compound of a series, which all cause an equivalent biological response, to the hydrophobic bonding or partition constant, r, and the Hammett constant, [Pg.137]

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