Linear free-energy related model

At the time that the basic formulation and testing of the mathematical models of quantitative structure-activity correlations were being made, another type of approach, the linear free-energy related model, was introduced (2). Using the basic Hammett equation (22, 36) for the chemical reactions of benzoic acid derivatives (Equation 12), several investigators attempted quantitative correlations between physicochemical properties... 

More recent efforts have been concerned with attempts to correlate structure with activity, utilizing minor modifications of the linear free-energy related models (4, 5, 6, 8, 83). Although the basic transport and... 

The combination of quantum mechanical calculations and the linear free-energy related model has been used recently by several investigators in drug activity studies—i.e., a variety of indices obtained from the quantum chemical calculations has been utilized in these correlations (4, 8, 114). For example, Neely and co-workers obtained excellent correlations between the energy of the highest occupied molecular orbital, a relative measure of the ability of a molecule to donate an electron to an acceptor molecule, of a series of imidazolines and their analgetic potencies (115). 

Linear Free-Energy-Related Model - On the other hand, more emphasis has been placed on the correlation of observed biological activity with measured physicochemical parameters of related compounds than in previous years. Hansch has given the historical development of the use of substituent constants and certain physicochemical parameters in quantitative structure-activity studies of biochemical systems. Specifically, he has dealt with the dependence of biological activity of drug molecules upon partitioning properties, electronic parameters, and steric effects. "... 

Clayton and Purcell " have reported a comparison of the predictive utility of the mathematical model of Free and Wilson and the linear free-energy-related model of Hansch. In the study of butyrylcholinesterase-inhibitory potencies of 6 members of a homologous series of 1-decyl-3-carbamoylpiperi-dines, the free-energy-related model gave better correlations of molecular structure with biochemical activity than did the mathematical model. ... 

QSAR methodology, as it is applied nowaday.s, started in 1964, when Hansch and Fujita published a linear free-energy related model (extrathermodynamic model mo.st often called Hansch analysis) to correlate biological activities with physicochemical properties (equation 2). ... 

As an illustration of PLS regression (PLSl) we reconsider the inhibitory potencies of oxidative phosphorylation of 11 doubly substituted salicylanilides [ 17] in Table 37.1. An extended Hansch model is defined by the linear free energy relation ... 

The term F2/CsRT is obtained from the constant capacitance model (Chapter 3.7). Fig. 4.6 gives a plot of the linear free energy relation between the rate constants for water exchange and the intrinsic adsorption rate constant, kads. 

Using predictive models for measuring environmental chemodynamics of organic pollutants in complex mixtures requires literature data on partition coefficient values. In some cases the values cited are not strictly experimental, being derived from linear free energy relations, while in others wide variations are reported in experimental values. The main problem is how one should evaluate which values are correct. Thus, Table 2 provides some basis to discriminate between reported values of partition coefficients, as well as predictive equations for partition coefficient calculations [21,62,65-85]. 

Platts et al. [39] reported linear free energy relation (LEER) models of the equilibrium distribution of molecules between blood and brain, relating log BB values to fundamental molecular properties, such as hydrogen-bonding capability, polarity/polarizability, and size. They used the following modified form of Abraham s general Eq. 46 ... 

Recently, Riviere and Brooks (2007) published a method to improve the prediction of dermal absorption of compounds dosed in complex chemical mixtures. The method predicts dermal absorption or penetration of topically applied compounds by developing quantitative structure-property relationship (QSPR) models based on linear free energy relations (LFERs). The QSPR equations are used to describe individual compound penetration based on the molecular descriptors for the compound, and these are modified by a mixture factor (MF), which accounts for the physical-chemical properties of the vehicle and mixture components. Principal components analysis is used to calculate the MF based on percentage composition of the vehicle and mixture components and physical-chemical properties. 

Figure 2. Sorption edge of Fe on ferrihydrite, data from Liger et at. (1999), model with surface complexation constants estimated from linear free energy relation fLFERj and model optimized on the data of Liger et al.

In this chapter we provide a historical perspective of the development of the field of computational toxicology. Beginning from the similarity-based grouping of elements into the periodic table, the chapter presents a chronology of developments from the simple observations of qualitative relations between structure and toxicity through LFER (linear free energy related) and QSAR (quantitative structure activity relationship) models, to the current... 

Within the context of this model, c and f are adjustable constants that vary from polymer to polymer. The ratio f /c is a crude measure of the average interchain separation. As polymer chain stif ess increases and free volume decreases, c should increase (20), and as fractional free volume increases, /c should increase. This theory is based on four hypotheses (1) the solution-di sion mechanism (equation 2) governs gas transport (2) diffusion obeys an Arrhenius expression (equation 8) (3) the linear free energy relation (equation 12) is valid and (4) the effect of penetrant size on activation energy is given by equation 13. 

The underlying concept of all QSAR analyses is the additivity of substituent group contributions to biological activity values in the logarithmic scale. This additivity comes from the fact that QSAR models are linear free-energy related. All... 

The second aspect is more fundamental. It is related to the very nature of chemistry (quantum chemistry is physics). Chemistry deals with fuzzy objects, like solvent or substituent effects, that are of paramount importance in tautomerism. These effects can be modeled using LFER (Linear Free Energy Relationships), like the famous Hammett and Taft equations, with considerable success. Quantum calculations apply to individual molecules and perturbations remain relatively difficult to consider (an exception is general solvation using an Onsager-type approach). However, preliminary attempts have been made to treat families of compounds in a variational way [81AQ(C)105]. 

In a stndy of retention of aromatic carboxylic acids under IPC conditions, linear free energy relationships were observed between the capacity factors and the extraction eqnilibrinm constants of benzoic acid and naphthalene carboxylic acid. The capacity factor of benzene polycarboxylic acids was directly related to then-association constants and qnatemary ammonium ions calculated on the basis of an electrostatic interaction model [27,28],... 

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