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Hydrophobic interaction chromatography (HIC) is often used for purifying proteins. A mathematical model to describe the complex effects of salts on the adsorption equilibria in HIC has recently been introduced by our group. It describes not only the influence of single salts, but also salt mixtures, in which cooperative effects may occur. The influence of the salts is thereby modeled with a Taylor series expansion in the individual ion molarities. In the present study, the model of the adsorption equilibrium is coupled with a lumped kinetic model of the adsorption kinetics to obtain a model of the elution of proteins in HIC adsorption columns. The column model is tested using experimental data on the adsorption of bovine serum albumin (BSA) and lysozyme (LYS) on the mildly hydrophobic resin Toyopearl PPG-600M at pH 7. The studied salts are ammonium chloride, sodium chloride, ammonium sulfate, and sodium sulfate as well as binary and ternary mixtures of them. The parameters of the lumped kinetic model are protein-specific and were fitted to the elution profiles of the single proteins in presence of single salts. The model was then used to predict the elution profiles of BSA and LYS solutions containing both proteins, for single salts as well as for binary and ternary salt mixtures. Both isocratic and gradient elution were studied. Furthermore, the model was applied to identify the optimal overall ionic strength for the separation of the two proteins by isocratic elution and the optimal linear gradient of the salt concentration in a multicriteria approach where the conflicting goals are high separation yield and low elution volume.
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