QSAR without arbitrary descriptors: the electron-conformational method

Abstract

The electron-conformational (EC) method in QSAR problems employs a unique (based on first principles) descriptor of molecular properties that incorporates the electronic structure and topology of the molecule and is presented in a digital-matrix form suitable for computer processing, the EC matrix of congruity (ECMC). Its matrix elements have clear-cut physical meanings of interatomic distances, bond orders, and atomic reactivity (interaction indices). By comparing these matrices for several active compounds of the training set a group of matrix elements is revealed that are common for these compounds within a minimum tolerance, the EC submatrix of activity (ECSA). The latter is the numerical pharmacophore for the level of activity and diversity of the tried compounds. The EC method was described in detail and used for pharmacophore identification and quantitative bioactivity prediction elsewhere. In this paper we give further general considerations of its uniqueness and emphasize its advantages as compared with traditional QSAR methods, outlining the following three novel points: (1) The unique, non-arbitrary descriptor employed in the EC method avoids the shortcomings of the arbitrary chosen descriptors and statistical estimation of their weight in the evaluation of the pharmacophore used in traditional QSAR methods. Arbitrary descriptors may be interdependent (“non-orthogonal”) and their sets are necessarily incomplete, hence they may lead to chance correlations and artifacts. The EC pharmacophore is void of these failures, thus deemed to be absolutely reliable within the accuracy of the experimental data and the diversity of the molecules used in its evaluation; (2) The tolerances in the matrix elements of the ECSA play a special role reflecting the flexibilities of the pharmacophore parameters and the dependence of the activity on the latter quantitatively; they are obtained in a minimization procedure; by increasing the tolerances one can get pharmacophores for larger intervals of activity. An advanced formula is derived for the activity as a function of the drug–receptor bonding energy which handles also the multi-conformational problem, and a regressional procedure is suggested to represent the interaction energy and the activity by the ECSA matrix elements or tolerances; (3) The possibility of bimolecular activity is discussed when a single molecule of the active compound has no pharmacophore, but the latter is present in the bimolecular structure. Examples are given from the problem of aquatic toxicity to fish.