Nonequilibrium capillary electrophoresis of equilibrium mixtures, mathematical model

We recently introduced a new electrophoretic method, nonequilibrium capillary electrophoresis of equilibrium mixtures (NECEEM). NECEEM provides a unique way of finding kinetic and equilibrium parameters of the formation of intermolecular complexes from a single electropherogram and allows for the use of weak affinity probes in protein quantitation. In this work, we study theoretical bases of NECEEM by developing a mathematical model for the new method. By solving a system of partial differential equations with diffusion in linear approximation, we found the analytical solution for concentrations of components involved in complex formation as functions of time from the beginning of separation and position in the capillary. The nonnumerical nature of the solution makes it a powerful tool in studying the theoretical foundations of the NECEEM method and modeling experimental results. We demonstrate the use of the model for finding binding parameters of complex formation by nonlinear regression of NECEEM electropherograms obtained experimentally.