Quantitative Structure- Activity Relationships equation

To theoretical and computational chemists, the world may seem to revolve around the Schrodinger equation, potential energy force field equations, or perhaps some quantitative structure-activity relationship equations for predicting biological activity. These various equations have been the basis of the livelihood of many a computational chemist. Interestingly, author Guillen apparently did not deem these equations to have risen to the level of having... 

Fundamental Quantum Quantitative Structure-Activity Relationships Equation... 

The fundamental assumption of SAR and QSAR (Structure-Activity Relationships and Quantitative Structure-Activity Relationships) is that the activity of a compound is related to its structural and/or physicochemical properties. In a classic article Corwin Hansch formulated Eq. (15) as a linear frcc-cncrgy related model for the biological activity (e.g.. toxicity) of a group of congeneric chemicals [37, in which the inverse of C, the concentration effect of the toxicant, is related to a hy-drophobidty term, FI, an electronic term, a (the Hammett substituent constant). Stcric terms can be added to this equation (typically Taft s steric parameter, E,). 

Linear free energy relationships, see Bronsted equation, Dual substituent parameter (equations), Hammett equation(s), Quantitative structure-activity relationships, Ritchie nucleophilicity equation... 

In 1868 two Scottish scientists, Crum Brown and Fraser [4] recognized that a relation exists between the physiological action of a substance and its chemical composition and constitution. That recognition was in effect the birth of the science that has come to be known as quantitative structure-activity relationship (QSAR) studies a QSAR is a mathematical equation that relates a biological or other property to structural and/or physicochemical properties of a series of (usually) related compounds. Shortly afterwards, Richardson [5] showed that the narcotic effect of primary aliphatic alcohols varied with their molecular weight, and in 1893 Richet [6] observed that the toxicities of a variety of simple polar chemicals such as alcohols, ethers, and ketones were inversely correlated with their aqueous solubilities. Probably the best known of the very early work in the field was that of Overton [7] and Meyer [8], who found that the narcotic effect of simple chemicals increased with their oil-water partition coefficient and postulated that this reflected the partitioning of a chemical between the aqueous exobiophase and a lipophilic receptor. This, as it turned out, was most prescient, for about 70% of published QSARs contain a term relating to partition coefficient [9]. 

For both nonspecific and structure-based approaches, physicochemical solvation parameters may be used directly, or they may be embedded in quantitative structure-activity relationships.3 This chapter starts with a review of the thermodynamic equations that may be used for a quantitative description of the free energy of solutes in fluid media. Then it provides an... 

A procedure that utilizes quantitative structure-activity relationships to assist in the characterization and design of enzyme alternative substrates, inhibitors, and effectors. In this procedure, the inhibition (or activity) results of a series of structurally related compounds are analyzed to determine the coefficients in an equation of the form ... 

The correlation of bioactivity data with Eq. 1 or some relationship derived from it results, if successful, in a correlation equation called a quantitative structure activity relationship (QSAR). 

Quantitative structure-activity relationships (QSARs) are important for predicting the oxidation potential of chemicals in Fenton s reaction system. To describe reactivity and physicochemical properties of the chemicals, five different molecular descriptors were applied. The dipole moment represents the polarity of a molecule and its effect on the reaction rates HOMo and LUMO approximate the ionization potential and electron affinities, respectively and the log P coefficient correlates the hydrophobicity, which can be an important factor relative to reactivity of substrates in aqueous media. Finally, the effect of the substituents on the reaction rates could be correlated with Hammett constants by Hammett s equation. 

Quantitative structure-activity relationship models can be used to predict kinetic rate constants for compounds similar in chemical structure under UV /TiOz photocatalytic oxidation. In formulating the Hammett correlations, the descriptors, such as on s and o, proved to be successful in deriving equations for aromatic and aliphatic compounds respectively. For the case of aromatic compounds, the ores descriptor formulated better Hammett correlations than the om descriptor. 

Hansch analysis Hansch analysis is a common quantitative structure-activity relationship approach in which a Hansch equation predicting biological activity is constructed. The equation arises from a multiple linear regression analysis of both observed biological activities and various molecular property parameters (Hammett, Hansch, and Taft parameters). 

Systematic studies of the effects of structure on the biological activities of organic compounds and the analysis of the results are comprised in the term Quantitative Structure-Activity Relationships (QSAR). Many of the treatments employed in the correlation analysis of data in this field closely resemble those used for linear free-energy relationships, e.g. the Hammett equation and extensions thereof, and so the study of the biological properties of organic compounds is often regarded as a part of physical organic chemistry. In recent years, some historical study of work in... 

Quantitative structure-activity relationship (QSAR) (Hansch and Klein, 1986 Hansch and Leo, 1995) represents an attempt to correlate structural descriptors of compounds with activities. The physicochemical descriptors include numerical parameters to account for electronic properties, steric effect, topology, and hydrophobicity of analogous compounds. In its simplest form, the biochemical activities are correlated to the numerical substituent descriptors of analogous compounds tested by a linear equation such as... 

An advantage of defining the problem in this manner is that the partition coefficient has become a central property in quantitative structure-activity relationships (QSAR) and a large data base of P values is available in the medicinal chemistry literature (22-24). In particular, if a correlation (Equation 15) between the polymer-water and octanol-water partition coefficients can be established for a series of solutes, it becomes possible to utilize log P (oc-tanol/water) value as a reference point from which to calculate the polymer-water value. 

Quantitative structure—activity relationships have been established using the Hansch multiparameter approach (14). For rat antigoiter activities (AG), the following (eq. 1) was found, where, as in statistical regression equations, n = number of compounds, r = regression coefficient, and s = standard deviation... 

Quantitative Structure Activity Relationship (QSAR) is a method that makes predictions by the quantitative description of molecular properties with the use of descriptors of the chemical structure (Dearden 2003). This means QSAR models describe the quantitative or calculated relationship between a chemical structure and their biological activity (e.g. toxicity) with the help of chemical descriptors that are generated from the molecular structure (Durham and Pearl 2001). This relationship is described in from of a mathematical equation (e.g. log 1/C = a tt + b a +. .. + const). QSAR models generally show better predictivity if all compounds of a dataset involved in the prediction are derived from a congeneric series of compounds, that means they should all act by the same mechanism of action, since the physico-chemical and structural descriptors used in the QSAR reflect the same mechanism of action. Sometimes it is difficult to determine the mechanism of action, so series of compounds involved in a QSAR model are often restricted to a given chemical class in the hope that this will ensure a single mechanism of action (Dearden 2003). 

A computational method of the structure prediction of an inhibitor is based on an analysis of the quantitative structure-activity relationship (QSAR) (Ariens, 1989 Martin et al, 1996). In this method, quantities such as volume, hydrophobicity or a number of specific groups are experimentally derived. QSAR for a given TS is a polynomial equation with n terms. Each of these terms corresponds to the number of aforementioned regions of a particular molecule under investigation. In the framework of this approach, it is necessary to define, prior to synthesis and testing, a functional relationship between molecular structure and molecular action. Then the polynomial equation can be used to predict the inhibition constant of molecules that have been not tested experimentally. 

Quantitative structure-activity relationships (QSARs) are mathematical equations produced from statistical analysis of the biological and structural data for series of compounds, where it is assumed that some degree of correla-... 

QSAR. Quantitative structure-activity relationships—the science of deriving quantitative linear or nonlinear mathematical relationships between physicochemical and topo-logical/topographical properties of chemical structures and their biological activity. Originally, regression analysis was the only tool used to derive QSAR equations. More re-... 

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