title: [Analysis of some "insoluble" problems of determining the binding parameters of ligand-receptor interaction and methods of their solving].
abstract: Some problems of the estimation of the parameters of ligand-receptor interaction (affinity, rate constants, valency, etc.) were considered. It was demonstrated that not only the Scatchard plot but also Klotz plot could be used for determining the parameters of ligand-receptor interaction for two types of binding sites of different affinity. A new approach and new coordinate systems for the estimation of the parameters of ligand-receptor interaction were suggested. It was shown that for the estimation of the affinity of putative monovalent antibodies by ELISA various equations, which are more precise and convenient than the Friguet et al. equations, could be obtained by the transformation of mass action law equation. The problem solution for the estimation by ELISA the affinity of two types of bivalent antibodies with different affinity and their concentrations for the case of the mixture of these antibodies was also suggested. The application of the proposed coordinate of dilution allows to solve the problem of determination of the parameters of ligand-receptor interaction (including antigen-antibody system) for the pre-existing ligand-receptor mixture without their preliminary separation and purification. This approach is especially important for the cases when the receptor is not stable enough to be isolated in the intact form from this mixture. It was shown that the well-known phenomenon of the prozone often observed under the titration of serum antibodies by the method of agglutination may get a mathematical explanation. Analytical solution of the problem of determining the velocity constant and the amount of the end product of the first order irreversible and reversible reaction kinetics was suggested, despite the fact that the process is described by the system of irrational equations. Mehods of asymptotic solution of transcendental irrational equations which describe the dynamics of reactions which mechanisms are subject to the so-called heterogeneous, successive, or competitive models have been considered. These methods permit the finding of the reaction rate constants and the amount of the end product, if the kinetics of the transformation of either initial, or end product of the reaction is known.
authors.forename: S A
authors.initials: SA
authors.lastname: Bobrovnik
mesh_terms: D001665:Binding Sites; D007700:Kinetics; D008024:Ligands; D008962:Models, Theoretical
chemical_list: D008024:Ligands