Numerical simulation of the chromatographic process for direct ligand-macromolecule binding studies

A numerical simulation of the direct zonal liquid chromatographic method is described for studying the binding of a ligand to a macromolecule by quantification of the interacting species present in a sample at equilibrium. The algorithm accounts for both the kinetic exchanges in solution and the dispersion effects depicted by the Fick law. Dimensionless variables are used for the concentrations which are expressed as a function of the equilibrium constant, KD. The free ligand concentration was varied in the injected samples from 0.1 to 20 KD, while that of the macromolecule was kept constant. An apparent binding isotherm was obtained from the total ligand chromatogram generated by the simulation run, when the amount emerging at almost column dead volume is plotted against that eluting at the free ligand retention time. As a continuous dissociation of the complex may occur during its migration, the apparent binding curve and the theoretical binding isotherm coincide at extremely low dissociating rates. At larger dissociation rates (0.001 s(-1) < kd <0.1 s(-1), for a first peak eluting in 1 min) the simulations were used to test various chromatographic conditions. The flow rate (or column volume) is the major effect which influences the on-column dissociation process as an exponential decay was found when the apparently bound fraction is plotted against the analysis time. The apparent equilibrium coefficient is close to the theoretical one for a binding curve generated with an initial solution containing a relatively low total concentration of binding sites (< or = KD). The apparent stoichiometric term is largely underestimated as its value decreases exponentially at increasing dissociation rates. An extrapolation at extremely short analysis times could be used to determine the stoichiometric coefficient characterizing the binding interaction.