Extrathermodynamic parameters

Many reaction obey equation 55 (90) implying that the steric effect can be treated as an extrathermodynamic parameter. 

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... 

Several attempts have been made (217, 218, 219, 220) to establish the relationship between the extrathermodynamic approach of Hansch (114) and the mathematical approaches (198, 212, 213, 215, 216). The numerical equivalence and the theoretical interrelation between the two approaches derives from the assumption that the contributions of the individual substituents to the biological activity is represented as a weighted sum of several physicochemical properties (e.g., the extrathermodynamic parameters in the Hansch equation) as expressed in equation 103... 

Using the principle of additivity of extrathermodynamic parameters (see section A), we can sum the same parameters for various substituents at different position and write... 

Even the combination of extrathermodynamic parameters with similarity matrices, leading to a mixed Hansch analysis/molecular similarity approach, seems to be reasonable and should be further investigated. 

The corresponding three-dimensional grid plots for the S-values [derived according to Eq. (5)] of these two polypeptides as the temperature and j/ values were systematically varied are shown in Fig. 26a-d. In each case, the S values for polypeptides 1 and 2 were derived by regression analysis methods from the gradient of the experimental plots of log k, vemus i/> at the specified j/ and T values with the regression eoefficients >0.9985. In turn, the S value of a peptide or protein in the presence of an RPC sorbent can be related [16,20,211,212] to extrathermodynamic parameters, such as the accessible molecular surface area, A/l, ui, through the expression... 

This classification is extrathermodynamic because it does not take into account the division between the enthalpic and entropic components of the binding free energy. - Such neglect is tolerable in the present context for two reasons. First, many if not all the forces listed in Figure 1 contain both components, and their interpretation in terms of enthalpy and entropy is a different issue altogether. And second, lipophilicity is also an extrathermodynamic parameter, and can be interpreted as such. 

The discussion in Section 7.1 should prepare us to expect deviations from such a simple relationship as the Hammett equation if the reaction being correlated differs greatly from the standard reaction. When this happens we have two choices (within this extrathermodynamic approach) We can select a different standard reaction, or we can increase the number of parameters. 

Now, it can be postulated that solvolysis rate should be a function of two properties of the solvent one is its ionizing power, and the other is its nucleo-philicity. An SnI process should be promoted by high ionizing power, and an Sn2 process by high solvent nucleophilicity. At this point, we are ready to bring the extrathermodynamic approach to bear on this problem. This was initiated by Grun-wald and Winstein, who defined a solvent ionizing power parameter Y by... 

It follows that for a special value of one parameter, the observed value of y is independent of the second parameter. This happens at Ii= a2/ai2 or I2 = -ai/ai2 any of these values determines y= a -aia2/ai2, the so called isoparametrical point. The argument can evidently be extended to more than two independently variable parameters. Experimental evidence is scarce. In the field of extrathermodynamic relationships, i.e., when j and 2 are kinds of a constants, eq. (84) was derived by Miller (237) and the isoparametrical point was called the isokinetic point (170). Most of the available examples originate from this area (9), but it is difficult to attribute to the isoparametrical point a definite value and even to obtain a significant proof that a is different from zero (9, 170). It can happen—probably still more frequently than with the isokinetic temperature—that it is merely a product of extrapolation without any immediate physical meaning. 

The next step in the development of the extrathermodynamic approach was to find a suitable expression for the equilibrium constant in terms of physicochemical and conformational (steric) properties of the drug. Use was made of a physicochemical interpretation of the dissociation constants of substituted aromatic acids in terms of the electronic properties of the substituents. This approach had already been introduced by Hammett in 1940 [14]. The Hammett equation relates the dissociation constant of a substituted benzoic acid (e.g. meta-chlorobenzoic acid) to the so-called Hammett electronic parameter a ... 

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 ... 

Figure 27 shows plots of all the available EM s for closures of small- and common-sized saturated carbocycles and heterocycles by intramolecular nucleophilic displacement. Clearly, a-values as small as 0.1 would be required in order to calculate extrathermodynamically from (67) EM-values comparable to those actually observed for ring-sizes 3 and 4, and an even smaller value would be necessary for ring-size 5. This would lead to the conclusion that the effect of ring strain on cyclisation rates is insignificant. The same conclusion was recently drawn by Benedetti and Stirling (1983), based on rates and activation parameters for the cyclisation of bis-sulphonyl-stabilised carbanions to 3-, 4-, and 5-membered bis-sulphonylcyloalkanes. 

We now proceed to more complicated ionophores in order to testify the validity of this extrathermodynamic relationship and its hypothetical interpretation as an attempt to understand the nature of supramolecular interactions more generally and deeply. The thermodynamic parameters are plotted in Figures 16-19 for long glymes, (pseudo)cyclic ionophore antibiotics, lariat ethers with donating side-arm(s), and bis(crown ethers), whose structural changes upon complexation are schematically illustrated in Figure 20. 

Nevertheless the general conclusions discussed here, as well as the overall experimental design for their validation, still follow the same unifying trends. For example, linear extrathermodynamic expressions can be proposed between the free energy change of a polypeptide or protein molecule involved in such hydrophobic interactions and particular molecular property parameters %j. This relationship takes the form of... 

Having a data bank which contains extrathermodynamic equations on both pure organic reactions as well as biochemical reactions is important in gaining insight into mechanism of action as Equation 42 illustrates. The type of a constant best suited to correlate the data is important as well as the value and the sign of p. Examples in which o-+ has proved to be a better parameter than o- are also known (36). 

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. 

Therefore, knowledge of the solvent properties and ion solvation in such media is essential. Although an exact determination of the solvation energy of individual ions is not possible, extrathermodynamic assumptions have been introduced in order to estimate this parameter. These ideas will be presented before the influence of solvents on equilibrium and kinetic parameters of electrode reactions is discussed. As a basis for this discussion, a brief presentation of the properties of solvents frequently used in electrochemical experiments will be given. 

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... 

This approach to separating the different types of interactions contributing to a net solvent effect has elicited much interest. Tests of the ir, a, and p scales on other solvatochromic or related processes have been made, an alternative ir scale based on chemically different solvatochromic dyes has been proposed, and the contribution of solvent polarizability to it has been studied. Opinion is not unanimous, however, that the Kamlet-Taft system constitutes the best or ultimate extrathermodynamic approach to the study of solvent effects. There are two objections One of these is to the averaging process by which many model phenomena are combined to yield a single best-fit value. We encountered this problem in Section 7.2 when we considered alternative definitions of the Hammett substituent constant, and similar comments apply here Reichardt has discussed this in the context of the Kamlet-Taft parameters. The second objection is to the claim of generality for the parameters and the correlation equation we will return to this controversy later. 

Sometimes used as a synonym of - Hansch analysis, the extrathermodynamic approach refers to models based on empirical relationships of - physico-chemical properties with thermodynamic parameters such as free energies, enthalpies and entropies for various reactions. 

These relationships, based on thermodynamic parameters but not requiring the formal thermodynamic theory, are therefore extrathermodynamic . 

We derive the extrathermodynamic relationships as a basis for the definition and understanding of the parameters for QSAR. This derivation is similar to that of Grunwald and Leffler Cl). 

The analysis of the parameters representing the effect of the medium in terms of extrathermodynamical relations has shown (see above, section A.2) that the hydrophobic substituent constant it depends on the molecules from which it is derived. For example, hydrophobic constants derived from the octanol/water partition coefficients of aromatic molecules differ from those obtained from aliphatic molecules (112). Collander s equation (111) provides the empirical basis for the evaluation of logP values for the same molecule in different solvents. However, solvents with markedly different solvation properties (e.g., hydrogen bonding ability) do not conform to Collander s equation (see below, section C.3). 

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. 

Thermodynamic data for electrolyte solvation have been found experimentally for many different electrolytes. Ultimately, one would like to be able to analyze these results further to obtain separate contributions from the cation and anion. However, that is not possible without making an extrathermodynamic assumption. As a result, a scale of single ion solvation parameters has been defined relative to those for the H" " ion. For example, the enthalpy associated with the process... 

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