Structure-activity methods multiple parameter

Odor and taste quality can be mapped by multidimensional scaling (MDS) techniques. Physicochemical parameters can be related to these maps by a variety of mathematical methods including multiple regression, canonical correlation, and partial least squares. These approaches to studying QSAR (quantitative structure-activity relationships) in the chemical senses, along with procedures developed by the pharmaceutical industry, may ultimately be useful in designing flavor compounds by computer. 

The basic principles on which the Hansch multiple parameter method for structure-activity correlation depends are described. These are compared with the basic features of the Free-Wilson method for assigning additivity constants to structural features of related compounds. An example is given for which the two methods of analysis have led to similar structure-activity relationships. Factors which determine the particular method to use in a new situation are discussed. The Free-Wilson method is presented in considerable operational detail with special emphasis on the detection and avoidance of situations which lead to singularity problems in solution of the matrix. Favorable analyses, which result in additivity constants that can be correlated with known physical constants, may lead to predictions for new compounds not covered in the original matrix. 

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. 

Another classical measure of the molecular geometry of substituents is the Verloop steric parameter. This is calculated from bond angles and atomic dimensions— primarily the lengths of substituent groups and several measures of their width. Trivial as this may sound, the consideration of molecular bulk is an important and often neglected factor in making multiple quantitative correlations of structure and pharmacological activity. Balaban et al. (1980) devised several related methods that are still in use today. 

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. 

Besides stepwise multiple linear regression (MLR) analysis, other methods used for deriving QSAR models were E-state modeling [168], kNN based COMBINE [173] and VALIDATE [I8I], The VALIDATE method makes use of 3D-coordinates of known ligand-receptor complexes to calculate physicochemical parameters. It was one of the very few studies where QSAR was part of the design and synthetic efforts [181]. Several statistical techniques such as stepwise regression, EA-MLR, PCRA and PLS analysis were applied in a recent study [194] to identify the structural and physicochemical requirements for HIV protease inhibitory activity. 

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