Tools for Deriving a Quantitative 3D-QSAR Model

Having determined the conformations and alignments of the molecules under investigation, one can begin to derive the 3D-QSAR model. As stated, this is done in a statistical manner, and several major approaches have been advanced over the years. 

The method of multiple linear regression analysis derives a least-squares fit of the predictor (independent) variables, molecular properties in this case, to biological activity. Usually the investigator examines the effect of including or not including particular variables. Although this approach is often used in 3D-QSAR, we will not discuss it further because it is already well documented.  

For statistical reasons, multiple regression analysis cannot be used for 3D-QSAR methods that consider many more 3D descriptors than compounds or for which the descriptors are mutually correlated. The alternative strategies described next can be used to find a quantitative model in such situations. As will be seen, cross-validation is an important technique for assessing the robustness of a proposed model. 

PLS can be used to explain biological potency when a relatively large number of intercorrelated descriptors are used in the analysis. -  

The PLS algorithm decomposes the matrix of properties, called the X matrix, as a product of two matrices T (scores) and B (loadings) plus the matrix E of the errors (Eq. [1]). 

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