Some Mathematical Points in the QSAR Modeling
Institute of Theoretical and Experimental Biophysics RAS142290 Pushchino Moscow reg. E-mail: firstname.lastname@example.org pp. (accepted)
Quantitative Structure-Activity Relationship (QSAR) has proved to be useful for estimation of biological activity of various types. The approach allows calculating activity of unstudied compound if the experimental data is available for the same activity of the series of compounds. QSAR approach is based on the assumption that substances with similar molecular structure have close properties under the same conditions. To establish the extent of molecular structure similarity one needs some quantitative measure, which is provided by so-called molecular descriptors. Various characteristics such as physical and chemical properties (either measured or calculated), mathematical constructions (for example, topological indices) may be used as molecular descriptors for the purposes of QSAR modeling. (see for detailed collection of the molecular descriptors the book by Todeschini R., Consonni V. Molecular Descriptors for Chemoinformatics; Wiley-VCH. 2009.)
Fragmental descriptors are rather simple and clear descriptors of molecular structure, since their values are equal to the counts of different atoms or chemical groups in the molecule.
The correlation relationship may be taken in the simplest mathematical form – just the sum, and its parameters are determined by the regression methods. For the modeling it is necessary to select the subset of variables from the whole pool of presented fragments, because often the experimental data are not numerous enough for corresponding parameterization of QSAR equation. The following items will be discussed in the report: 1) Algorithms of variables subset selection, which are able to explore the molecular descriptors’ space effectively; 2) The selection criteria and their effect on the QSAR models’ accuracy; 3)The prеdictive capabilities of the obtained models.
The example of the fragmental QSAR models for the 3,5-diaryl-1,2,4-oxadiazoles as apoptosis- inducers will be presented. The impact of such modeling in the design of more active compounds as potent antitumor agents will be shown.