Extrathermodynamic methods

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 ... 

Extrathermodynamic methods represent powerful tools for the evaluation of single-ion solvation quantities, but the available data are rather low in accuracy. Accurate knowledge of solubility and salt activity coefficients is highly desirable. Estimation of liquid-liquid junction potentials (particularly at nonaqueous-aqueous electrolyte... 

Since the extrathermodynamic method investigates correlation between thermodynamic properties, the appropriate physical property is the relative free energy of the above equilibrium. Hence logP is used to express this physical property, known as hydrophobicity (or lipophilicity). 

Another method for studying solvent effects is the extrathermodynamic approach that we described in Chapter 7 for the study of structure-reactivity relationships. For example, we might seek a correlation between og(,kA/l ) for a reaction A carried out in a series of solvents and log(/ R/A R) for a reference or model reaction carried out in the same series of solvents. A linear plot of og(k/iJk ) against log(/ R/ linear free energy relationship (LFER). Such plots have in fact been made. As with structure-reactivity relationships, these solvent-reactivity relationships can be useful to us, but they have limitations. 

We have seen that physical properties fail to correlate rate data in any general way, although some limited relationships can be found. Many workers have, therefore, sought alternative measures of solvent behavior as means for correlating and understanding reactivity data. These alternative quantities are the empirical measures described in this section. The adjective empirical in this usage is synonymous with model dependent this is. therefore, an extrathermodynamic approach, entirely analogous to the LFER methods of Chapter 7 with which structure-reactivity relationships can be studied. 

Two types of methods are used to measure activity coefficients. Potentiometric methods that measure the mean activity coefficient of the dissolved electrolyte directly will be described in Section 3.3.3. However, in galvanic cells with liquid junctions the electrodes respond to individual ion activities (Section 3.2). This is particularly true for pH measurement (Sections 3.3.2 and 6.3). In these cases, extrathermodynamical procedures defining individual ion activities must be employed. 

We conclude this section by a few general remarks about extrathermodynamic approaches. These quantitative methods involve empirical approaches that cannot be derived strictly from thermodynamic theory. They are widely used to predict and/ or to evaluate partition constants and/or partition coefficients (see Box 3.2 for nomenclature) of organic compounds. There are many situations in which some of the data required to assess the partitioning behavior of a compound in the environment are not available, and, therefore, have to be estimated. For example, we may need to know the water solubility of a given compound, its partition coefficient between natural organic matter and water, or its adsorption constant from air to a natural surface. In all these, and in many more cases, we have to find means to predict these unknown entities from one or several known quantities. 

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. 

Kubinyi, H. (1990). The Free-Wilson Method and its Relationship to the Extrathermodynamic Approach. In Quantitative Drug Design. Vol. 4 (Ramsden, C.A., ed.), Pergamon Press, Qxford (UK), pp. 589-643. 

The reactivity of molecules represents their ability to undergo certain interactions. In the extrathermodynamic approach, the reactivity characteristics of molecules are described as changes in the reactivity of a reference molecule upon substitution. It is known from chemistry, however, that molecular interactions are determined by properties of the entire molecule. Quantum chemistry offers the means of obtaining molecular properties from first principles of physics and chemistry the quantum chemical computation methods are now able to predict good relative values of physicochemical properties that can be determined by experiment either with great difficulty or only by inference. 

The Hansch method (114) relates the observed biological activity to extrathermodynamic parameters (see above, section A) that are assumed to represent the electronic, steric and hydro-phobic properties of the compounds responsible for the biological... 

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. 

We discussed the extrathermodynamic relationships that provide a common basis for most of the parameters used in QSAR. We have presented a critical analysis of the empirical framework for the derivation of these parameters and a rationale for choosing them. The analysis of the physicochemical basis of the parameters and of the methods shows the caution needed in interpreting molecular mechanisms from QSAR correlations. 

Kubinyi, H. The Free-Wilson method and its relationship to the extrathermodynamic approach. In Comprehensive Medicinal... 

Trasatti [2] has described the methods used to estimate the absolute electrode potential on the basis of suitable extrathermodynamic assumptions. The method presented here is the one which gives an estimate which can be related to the potential scale used by physicists. Moreover, the resulting estimates of the absolute values of the standard electrochemical potential are based on experimentally measured quantities. The analysis is illustrated here for cell (9.3.30), which contains a hydrogen electrode. An air gap is introduced into the cell, so that the solutions surrounding each electrode are separated. The resulting cell is... 

The discussed calculation procedure is not based on any extrathermodynamic assumptions and therefore the inaccuracy of the result obtained is determined only by the experimental errors of measuring a work function and the Volta potential difference. Furthermore, from the solvent surface potential x determined by any estimation method we can find the ideal solvent-electron interaction energy Vq = U — ex . Unlike U , V, is not a strictly thermodynamic quantity and the inaccuracy in determining it, besides experimental errors, is caused by the inaccuracy of model assumptions made for estimating x -... 

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. 

Kubinyi H. The Free-Wilson method and its relationship to the extrathermodynamic approach. In Ramsden CA, ed. Quantitative Drug DesignHansch C, Sammes PG, Taylor JB, eds. Comprehensive Medicinal Chemistry. The Rational Design, Mechanistic Study and Therapeutic Application of Chemical Compounds 1990 Vol. 4. Oxford Pergamon Press, 1990 589-643. 

Mathematical analysis of the extrathermodynamic relationships exemplified by Hansch and Free-Wilson equations is done by the statistical method of regression analysis, the least-squares fit. With the aid of computers the best fit of a large amount of data to the... 

The second method (GC), based on structure dependence, is an outgrowth of the extrathermodynamic approach outlined in Chapter 2 and encompasses a whole range of properties. Starting from zero or first-order approximations, these methods have been developed over the years to remarkably high levels of precision. 

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