Linear free-energy relation relationships

The concept of the similarity of molecules has important ramifications for physical, chemical, and biological systems. Grunwald (7) has recently pointed out the constraints of molecular similarity on linear free energy relations and observed that Their accuracy depends upon the quality of the molecular similarity. The use of quantitative structure-activity relationships (2-6) is based on the assumption that similar molecules have similar properties. Herein we present a general and rigorous definition of molecular structural similarity. Previous research in this field has usually been concerned with sequence comparisons of macromolecules, primarily proteins and nucleic acids (7-9). In addition, there have appeared a number of ad hoc definitions of molecular similarity (10-15), many of which are subsumed in the present work. Difficulties associated with attempting to obtain precise numerical indices for qualitative molecular structural concepts have already been extensively discussed in the literature and will not be reviewed here. 

The Tafel relationship as expressed in eqns. (82b) and (83b) is a linear free energy relation of the rate coefficient of a net electrode reaction (neglecting the back reaction). From eqn. (78)... 

These efforts were guided by the study of quantitative structure-activity relationships (QSAR) following the Hansch approach. In this method linear free-energy related and other electronic, hydrophobic, and steric substituent constants are used for a quantitative analysis of the possible ways in which substituents may modulate bioactivity in a congeneric series. In the QSAR studies of benzoylphenyl ureas the electronic Hammett a-constants and the hydro-phobic Hansch n-constants were used. To measure the steric influences, steric substituent constants of a new type (B1,B2,B3,B4, and L) were applied which had recently been introduced by us and which give improved correlations in comparison with the steric Es constants used in the literature hitherto (21, 22). The constants B- toBj are measures of the widths of substituents in four rectangular directions. The L-constant accounts for the length of a substituent ... 

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. 

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... 

RP-LC, multivariate analysis methods such as principle component analysis (PCA) and nonlinear mapping (NML), or comparative molecular field analysis (CoMFA) approaches and linear free energy-related (LFER) equations have been used to derive structure-retention relationships in chiral chromatography [16-18]. 

Due to the relationship between biological activity and the free energies of binding (or partitioning) also the terms extrathermodynaraic relationships or linear free energy-related approach are used for quantitative structure-activity relationships, especially Hansch analysis. 

Finally, it is interesting to note that the free energy relationships elicited in this work might have quite general implications for other enzyme reactions. In fact, the validity of such relationships in enzymes and solutions can be examined by computer simulation methods as has been illustrated in several preliminary studies from this laboratory [9,12b]. It appears that polar sites in enzymes obey to some extent the linear response approximation (the system polarisation is proportional to the applied local field) and therefore follow linear free energy relations. 

A quantitative treatment of surfactant solubility has been successfully made empirically using linear free energy relationships. An important relation is that for the linear free energy of transfer of alkanes to water [23] ... 

Since AG and AG are combinations of enthalpy and entropy terms, a linear free-energy relationship between two reaction series can result from one of three circumstances (1) AH is constant and the AS terms are proportional for the series, (2) AS is constant and the AH terms are proportional, or (3) AH and AS are linearly related. Dissection of the free-energy changes into enthalpy and entropy components has often shown the third case to be true. °... 

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]. 

The Hammett equation is the best-known example of a linear free-energy relationship (LFER), that is, an equation which implies a linear relationship between free energies of reaction or activation for two related processes48. It describes the influence of polar meta-or para-substituents on reactivity for side-chain reactions of benzene derivatives. 

Therefore, reaction series with constant entropy have been accorded great significance and have been investigated thoroughly. The condition in eq. (8) was even considered necessary for any linear free energy relationship to hold (16). However, as experimental data accumulated and precision improved, it was clear that for many theoretically important reaction series, this condition is not fulfilled (1, 17). It was also proved that a LFER can hold if entropy is not constant, but linearly related to enthalpy (18, 19). The linear equation... 

It should be emphasized that the above equations, which relate reaction temperatures to calculated reactant or product energies, are equivalent to the more conventional linear free energy relationships, which relate logarithms of rate constants to calculated energies. It was felt that reactant temperatures would be more convenient to potential users of the present approach -those seeking possible new free radical initiators for polymerizations. 

The above Hansch equations are also generally referred to as linear free energy relationships (LFER) as they are derived from the free energy concept of the drug-receptor complex. They also assume that biological activity is linearly related to the electronic and lipophilic contributions of the various substituents on the parent molecule. 

Significance of the Br nsted Slope in Electron Transfer. Linear free energy relationships have been extensively studied for electron transfer and related reactions in both inorganic and organic systems. For highly endergonic reactions, the Br0nsted slope a is close to unity. In many cases, however, the more or... 

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