GRID partial least squares

Partial Least Squares (PLS) regression (Section 35.7) is one of the more recent advances in QSAR which has led to the now widely accepted method of Comparative Molecular Field Analysis (CoMFA). This method makes use of local physicochemical properties such as charge, potential and steric fields that can be determined on a three-dimensional grid that is laid over the chemical stmctures. The determination of steric conformation, by means of X-ray crystallography or NMR spectroscopy, and the quantum mechanical calculation of charge and potential fields are now performed routinely on medium-sized molecules [10]. Modem optimization and prediction techniques such as neural networks (Chapter 44) also have found their way into QSAR. 

Due to the large number of descriptors (commonly 15 000-20 000 for each field), multivariate regression analysis is usually performed by partial least squares regression (PLS), with or without —> variable selection. Alternatively to grid-based QSAR models, —> similarity/diversity between molecules can be measured by comparing their interaction fields. 

Ordinary Least Square regression (OLS), also called Multiple Linear Regression (MLR), is the most common regression technique used to estimate the quantitative relationship between molecular descriptors and the property. Partial Least Squares (PLS) regression is widely applied especially when there are a large number of molecular descriptors with respect to the number of training compounds, as it happens for methods such as GRID and CoMFA. 

The last step in a CoMFA study is a partial least squares (PLS) analysis (chapter 5.3) to determine the minimal set of grid points which is necessary to explain the biological activities of the compounds. Most often good to excellent results are obtained. However, the predictive value of the model must be checked by cross-validation if necessary, the model is refined and the analysis is repeated until a model of high predictive ability is obtained. 

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