Chromatographic and Electrophoretic Methods for the Determination of Binding Constants for Dye-Protein Complexes

Moment analysis for reaction kinetics of intermolecular interactions

Moment equations were developed on the basis of the principle of relativity for analyzing elution peak profiles measured by ACE to analytically determine the association (k_a ) and dissociation (k_d ) rate constants of intermolecular interactions. Basic equations representing the mass balance, mass transfer rate, and reaction kinetics in ACE system in a Galilean coordinate system S were transformed to those in another coordinate system S', which imaginarily moved with respect to S. Moment equations for ACE peaks in S' in the time domain were derived from the analytical solution of the modified basic equations in the Laplace domain. Moment equations for ACE peaks in S were derived from those in S' by the inverse Galilean transformation. The moment equations were used for analyzing some ACE data previously published to determine k_a and k_d values. It was demonstrated that the moment equations were effective for extracting the information about affinity kinetics of intermolecular interactions from the elution peak profiles measured by ACE. The moment equations were also used to discuss the influence of mass transfer and reaction kinetics on ACE peak profiles. Some results of the numerical calculations are also indicated in Supporting Information.