Mathematical modeling of adsorption isotherms in mixed salt systems in hydrophobic interaction chromatography

Hydrophobic interaction chromatography (HIC) is often used for purifying proteins. The prediction of the adsorption equilibria in such systems is a difficult task as they depend on the pH value and the influence of the salts, which are added for controlling the solvent properties. This is especially tedious when salt mixtures are used, which can have positive or negative cooperative effects on the adsorption. A mathematical model to describe these complex effects of the salts was recently introduced by our group. In that model, the influence of the salts is described by a Taylor series expansion in the individual ion molarities. However, in our previous work, only the loading of the adsorbent at a given constant protein concentration in the liquid phase c_p = 0.01 mM was considered and correlated as a function of the salt composition at constant ionic strength. In the present study, that model is extended to other protein concentrations and it is shown that the Taylor series expansion works well for a wide range of c_p . The model parameters are found to depend on c_p , but only in a simple way. The dependence of the model parameters on c_p was correlated using a new three parameter equation. From that correlation, the loading q_p can be determined for any value of c_p . Hence, the entire adsorption isotherm is known for any salt composition. The approach is illustrated using experimental data from previous studies of our group on the adsorption of bovine serum albumin, lysozyme, polyethylene glycol, and di-PEGylated lysozyme on the mildly hydrophobic resin Toyopearl PPG-600 M. The pH values are between 4.0 and 7.0. Binary and ternary mixtures of ammonium chloride, sodium chloride, ammonium sulfate, and sodium sulfate as well as the single salts are used at overall ionic strengths between 1,500 and 4,200 mM. © 2018 American Institute of Chemical Engineers Biotechnol. Prog., 2018.