Hansch Analysis and Classical QSAR

Numerous schemes have been explored in an effort to correlate the effects of modifying chemical substituents on a patent structure with their effects on the target property. That attributed to Professor Corwin Hansch of Pomona College, the most prevalent and easiest to understand, is based on ideas derived from physical organic chemistry. The basic problem can be illustrated using an HlV-1 protease inhibitor as an example. 

In performing a QSAR study, the data are assembled into a table (matrix) of numbers in which each row represents the data for a compound and each column a physicochemical property, often referred to as a descriptor. The first column after the compound identifier is usually reserved for the measured target property. A statistical procedure [e.g., multiple linear regression (MLR), multivariate analysis, neural networks] is then used to find a relationship between the observed measurement with some combination of the properties represented in the subsequent columns. Considering the three properties discussed above, a classical QSAR equation has the following form  

There exist many other possible candidates for descriptors, including molar refractivity (MR), pK s, molecular volume, surface area, and connectivity indices. Correlations among the descriptors pose a problem in this field of science because the statistical methodology assumes that each column represents an independent variable. This problem is addressed using multivariate 

The choice of vertices is established through an optimization procedure, which maximizes the fit of the correlation Eq. [2] for the model. For example, the target property of a molecule can be explained as  

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