Signal and binding. II. Converting physico-chemical responses to macromolecule-ligand interactions into thermodynamic binding isotherms.
Physico-chemical titration techniques are the most commonly used methods in characterizing molecular interactions. These methods are mainly based on spectroscopic, calorimetric, hydrodynamic, etc., measurements. However, truly quantitative physico-chemical methods are absolutely based on the determination of the relationship between the measured signal and the total average degree of binding in order to obtain meaningful interaction parameters. The relationship between the observed physico-chemical signal of whatever nature and the degree of binding must be determined and not assumed, based on some ad hoc intuitive relationship/model, leading to determination of the true binding isotherm. The quantitative methods reviewed and discussed here allow an experimenter to rigorously determine the degree of binding and the free ligand concentration, i.e., they lead to the construction of the thermodynamic binding isotherm in a model-independent fashion from physico-chemical titration curves.
Evaluating the Number of Ligand Binding Sites on Protein from Tryptophan Fluorescence Quenching under Typical Experimental Conditions
Fluorescence quenching technique is extensively applied for the characterization of intermolecular interactions in the solution that is one of the major problems in biochemistry and pharmacology. Using the Stern-Volmer equation, one can obtain a measure of binding affinity calculated under the assumption of static quenching, while the possibility to determine other binding parameters is under discussion. Several mathematical approaches are known, which allow determining the number of binding sites from fluorescence quenching curves. However, they usually require high concentrations of the ligand to obtain saturating binding curves that could be complicated in a number of experimental conditions. In this paper, we present a simple algorithm, which allows to prove that the number of binding sites in the system is equal to one or not and to verify that the quantum yield of the complex is zero. The advantage of the suggested approach is its applicability at typical conditions used in tryptophan fluorescence quenching experiments for the protein-ligand binding. A web interface for automated processing of fluorescence quenching experiments based on the suggested approach is presented.
New method for analysis of enzymatic reactions: Thermolysin-catalyzed synthesis of aspartame precursor
Aspartame is an artificial sweetener which is 200 times sweeter than sucrose. A precursor of aspartame, N-(benzyloxycarbonyl)-l-aspartyl-l-phenylalanine methyl ester (Z-APM) was synthesized and hydrolyzed with thermolysin in an aqueous monophasic system. Graphical plotting methods and/or nonlinear regression have been used to analyze enzymatic reactions because of the nonlinearity of enzymatic rate equations. There are, however, problems: the former require accurate measurement of the initial reaction rate and the latter gives no analytical information. The authors proposed a method to solve the nonlinear enzymatic rate equations with respect to the concentration of a product with the Taylor expansion, especially for the reversible Theorell-Chance mechanism (Murakami, Y., Hirata, M., and Hirata, A., J. Ferment. Bioeng., 82, 246–252, 1996). This solution, however, is complex for practical use. In this paper, a simpler solution to explain the thermolysin-catalyzed synthesis of Z-APM is obtained. New methods to determine the kinetic parameters, especially for the reversible Theorell-Chance mechanism, based on the approximated solution are proposed. The results calculated using the obtained kinetic parameters can satisfactorily explain the experimental results, which demonstrates the effectiveness of the proposed analysis. We must know the relation between the concentrations of substrates and a product, and accurately evaluate of the result obtained using Taylor expansion when we determine the kinetic parameters using our newly developed methods. The methods to determine the kinetic parameters of the reversible Theorell-Chance mechanism described in this paper is, however, expected to be applied to general enzymatic reactions.