The method of frontal polyhedra for conformationally-nonrigid molecules. Quantitative structure—Activity relationship in the series of baker triazines—Dihydrofolate reductase inhibitors

Abstract

There are many approaches to establishing the quantitative relationship between chemical structure and biological activity (QSAR) of substances. The two key steps, which are common for all these methods, consist in representing a given structure by a set of descriptors and constructing a mathematical model-the fimction of descriptors approximating variations of the activity. The chemical structure can be described in greater or less detail using specially introduced indicator variables, physicochemical constants of the substituents [I], and various topological indices [3][4][5]. As a rule, the mathematical model has the form of a regression equation, offering a very useful empirical relationship. The main difficulty of this classical approach is to properly select the regressors, providing for the "best" model, from a huge variety of known descriptors. The standard procedure of the stepby-step regression analysis has certain limitations of a statistical character [6,7]. There were attempts to obtain the best approximating functions using non-traditional methods [8-I0] and pattern recognition algorithms [1,2].In recent years, considerable effort has been devoted toward directly taking into account the three-dimensional (3D) structure of molecules using special databases [11,12] and computer programs [13 -15]. The 3D approaches offer the most explicit implementation of the well-known hypothesis that the biological effect arises due to a ligand-receptor interaction of the "key-lock" type. A systematic analysis of the published data allows the 3D-QSAR methods to be subdivided into the following major groups. The first group con-" sists of methods proceeding directly from the structure of the receptor [16,17]. This approach is usually hindered by the lack of data on the spatial structure of the receptors involved. In this case researchers may define a set of points in space (pseudoreceptor) on the basis of conformational analysis of the compounds (ligands) studied [18][19][20]. The structural correspondence between ligands and receptor is characterized by quantities reflecting the energy of the ligand-receptor in-I I. I. Polzunov Altai State Technical University, Bamaul, Russia. 147 teraction, which are used in constructing the mathematical QSAR model. Another group includes "indirect" methods of 3D-QSAR analysis, in which assessment of the fitting of ligands to receptors is replaced by determination of the similarity between ligands, involving a procedure of optimum matching of three-dimensional molecular models. The characteristics of the resulting "supermolecule" [21 -24] or lattice [25] constructed in this way serves as a basis for the subsequent description of relationships between the structure and biological activity. Ligands studied by methods of indirect 3D-QSAR analysis must have close shapes and dimensions, since only this will lead to a unique determination of the supermolecule. Representing the imaginary receptor by a set of points also implies certain spatial resemblance between the objects studied, al...

A new paradigm for pattern recognition of drugs

“…There are many alternative variations of these methods, such as neural network, discriminant analysis, cluster analysis, etc. [1,[3][4][5][6]. Most of the research results obtained by the specific methods describing various kinds of biological activity allow one to identify the molecular fragments most often found in drugs.…”

“…Pattern recognition methods are used for analysis and prediction of biological activity of drugs [e.g., [1][2][3]. There are many alternative variations of these methods, such as neural network, discriminant analysis, cluster analysis, etc.…”