Structure-activity extrathermodynamic

The background supporting the versatility of the Hansch approach is that it is in fact an extrathermodynamic approach to drug action. The information on the structure-activity relationship of various kinds of drugs is expressed as equations which provide a convenient way for comparative studies with simpler and similar model reactions to elucidate the mechanism of overall drug action without microscopic knowledge of complex processes occurring in vivo. 

Tihe two methods of structure-activity correlation which have received the most application in the past decade are the Hansch multiple parameter method, or the so-called extrathermodynamic approach, and the Free-Wilson, or additive model. The basic differences and similarities of these methods are discussed in this presentation. 

Thermodynamics describes the behaviour of systems in terms of quantities and functions of state, but cannot express these quantities in terms of model concepts and assumptions on the structure of the system, inter-molecular forces, etc. This is also true of the activity coefficients thermodynamics defines these quantities and gives their dependence on the temperature, pressure and composition, but cannot interpret them from the point of view of intermolecular interactions. Every theoretical expression of the activity coefficients as a function of the composition of the solution is necessarily based on extrathermodynamic, mainly statistical concepts. This approach makes it possible to elaborate quantitatively the theory of individual activity coefficients. Their values are of paramount importance, for example, for operational definition of the pH and its potentiometric determination (Section 3.3.2), for potentiometric measurement with ion-selective electrodes (Section 6.3), in general for all the systems where liquid junctions appear (Section 2.5.3), etc. 

The attempt to correlate biological activity with chemical structure in quantitative terms assumes that a functional dependence exists between the observed biological response and certain physicochemical properties of molecules. Without a mechanistic model one obtains it by an empirical correlation. A rational way to define such empirical relationships is within the extrathermo-dynamic approach (1). Although extrathermodynamic relationships... 

It thus seems appropriate to use partition coefficients between aqueous and organic phases to represent molecular properties related to the hydrophobic interactions between small molecules and the biophase. This choice is well established at the level of a second order approximation in the extrathermodynamic derivation (see section A. 3). Numerous examples (137, 138) illustrate the utility of the partition coefficient in correlations of biological activity with chemical structure. 

Statistical methods. Certainly one of the most important considerations in QSAR is the statistical analysis of the correlation of the observed biological activity with structural parameters - either the extrathermodynamic (Hansch) or the indicator variables (Free-Wilson). The coefficients of the structural parameters that establish the correlation with the biological activity can be obtained by a regression analysis. Since the models are constructed in terms of multiple additive contributions the method of solution is also called multiple linear regression analysis. This method is based on three requirements (223) i) the independent variables (structural parameters) are fixed variates and the dependent variable (biological activity) is randomly produced, ii) the dependent variable is normally and independently distributed for any set of independent variables, and iii) the variance of the dependent variable must be the same for any set of independent variables. 

In the present chapter, the relationship between the electrode potential and the activity of the solution components in the cell is examined in detail. The connection between the Galvani potential difference at the electrode solution interface and the electrode potential on the standard redox scale is discussed. This leads to an examination of the extrathermodynamic assumption which allows one to define an absolute electrode potential. Ion transfer processes at the membrane solution interface are then examined. Diffusion potentials within the membrane and the Donnan potentials at the interface are illustrated for both liquid and solid state membranes. Specific ion electrodes are described, and their various modes of sensing ion activities in an analyte solution discussed. The structure and type of membrane used are considered with respect to its selectivity to a particular ion over other ions. At the end of the chapter, emphasis is placed on the definition of pH and its measurement using the glass electrode. 

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. 

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