Mathematical modeling of elution curves for a protein mixture in ion exchange chromatography applied to high protein concentration

Abstract

Protein elution curves in ion exchange chromatography (IEC) were simulated with a rate model. Three pure proteins and their mixture were used (alpha-lactalbumin, BSA, and conalbumin) under different operational conditions. The anionic matrix Q-Sepharose FF was used packed in a 1 mL column. A high protein concentration (37.5 mg/mL of total protein injected into the column) was used in order to extend the utility of the model. Mass transfer parameters were calculated using empiric correlations, where the axial dispersion was negligible (Pe > 300) and the mass transfer was controlled by the intraparticle diffusion (Bi > 10). The model assumes a modulator-eluite relationship were the equilibrium constant of the Langmuir isotherm was a function of salt concentration. Adsorption kinetic parameters were estimated from experimental data. The parameters for pure proteins were determined, and elution curves for changes in flow rate, ionic strength gradient, concentration, and sample size were predicted by the model. Then the kinetic parameters of the mixture were determined under the same operational conditions and some of the parameters had to be modified to take into account effects such as protein-protein interactions, competition, and displacement. Experimental elution curves obtained for changes in operational conditions such as flow rate and ionic strength gradient were simulated by the rate model for the protein mixture with a relative error in retention time of visible peaks <5%. IEC operational conditions and the peak fraction collection can be selected using a cost function of the production process which considers yield, purity, concentration, and process time that are obtained from simulations. Operational conditions that gave the minimum cost were selected. Simulations allows to diminish experimental time and cost.