Cross-Validated R2 Guided Region Selection for CoMFA Studies

Abstract

The Comparative Molecular Field Analysis (CoMFA) [ 1 ] approach was introduced in 1988. Since then, it has rapidly become one of the most widely used tools for threedimensional quantitative structure–activity relationship (3D QSAR) studies. Over the years, this approach has been applied to a wide variety of receptor and enzyme ligands (recently reviewed by Cramer et a l . [2] and Thibaut [3]). Undoubtedly, the further development of this method is of great importance and interest to many scientists working in the area of rational drug design. CoMFA methodology is based on the assumption that since, in most cases, the drug-receptor interactions are noncovalent, the changes in the biological activities or binding affinities of sample compounds correlate with changes in the steric and electrostatic fields of these molecules. In a standard CoMFA procedure, all molecules under investigation are structurally aligned first, and the steric and electrostatic fields around them are then sampled with probe atoms, usually sp carbon with +1 charge, on a rectangular grid that encompasses aligned molecules. The results of the field evaluation in every grid-point for every molecule in the dataset are placed in the CoMFA QSAR table which, therefore, contains thousands of columns. The analysis of this table by the means of standard multiple regression is practically impossible; however, the application of special multivariate statistical analysis routines, such as partial least squares (PLS) analysis and cross-validation ensures the statistical significance of the final CoMFA equation [ 1 ] . A cross-validated R (q) which is obtained as a result of this analysis serves as a quantitative measure of the predictability of the final CoMFA model. The statistical meaning of the q is different from that of the conventional R: the q value greater than 0.3 is considered significant [4]. Despite obviously successful and growing application of CoMFA in molecular design, several problems intrinsic to this methodology have persisted. Studies done by us [5] and others [1,6–9] revealed that CoMFA results can be extremely sensitive to a number of factors such as alignment rules, overall orientation of aligned compounds, lattice shifting, step size and the probe atom type. The problem of three-dimensional alignment has been the most notorious among others. Even with the development of automated and semiautomated alignment protocols, such as Active Analog Approach [10,11] and DISCO [12], and the opportunity to use, in some cases, the structural information about the target receptor [6,13], there is generally no standard recipe to align all molecules under consideration in a unique and unambiguous fashion. Our recent QSAR analysis of 60 acetylcholinesterase inhibitors is particularly illustrative with respect to