Application of the linear free energy principle for derivation of nonlinear quantitative structure-activity relationships. A steady-state kinetic model

All the quantitative structure-activity relationships (QSAR) which so far have been practically observed can be simple interpreted within the framework of kinetic formalism. Based on the assumption that the drug action can be modeled by the steady-state kinetic scheme which includes only reactions of the f'trst order, and the rate constants of all the elementary reactions can be formally described by means of linear free energy relationships (LFER), an algorithm for the derivation of nonlinear QSA relationships is proposed. It is shown that all the possible rate equations for the kinetic schemes of a given complexity can be subdivided into a limited number of classes according to the type of concentration polyhedron. Namely, if one assumes that the kinetic scheme includes no more than n species, then there exist p(n) 1 general rate equations. Based on such classification, the possibility of f'mding the necessary QSA relationship proceeding only from the experimental data on the final biological responses is discussed.