Method for Determination of Association and Dissociation Rate Constants of Reversible Bimolecular Reactions by Isothermal Titration Calorimeters

The rate law equation for reversible bimolecular reactions, which are describable by association and dissociation rate constants (<i>k</i><sub>1</sub> and <i>k</i><sub>-1</sub>), is not solvable to a plain formula under stoichiometric reaction conditions. Therefore, it is a general technique to observe such reactions under pseudo first-order conditions, which make the reactions a single-exponential process, and enable us to determine <i>k</i><sub>1</sub> and <i>k</i><sub>-1</sub> without any complicated iterative computations needed to analyze the same reactions under stoichiometric reaction conditions. However, the accelerated reaction rates under pseudo first-order conditions are not always favorable to the physicochemical tools employing a slow or medium response time, such as thermal analysis instruments. In this study, we have developed a simple non-iterative analytical method to determine <i>k</i><sub>1</sub> and <i>k</i><sub>-1</sub> of reversible bimolecular reactions under stoichiometric conditions on the basis of experimental data of isothermal titration calorimetry (ITC), which is generally used to determine thermodynamic parameters rather than kinetic constants. Our method is principally based on the general principle of chemical bindings caused along with the titration processes, that is, the chemical relaxation kinetics, which had been hitherto considered in the analysis on the ITC data.