Modeling non-linear elution of proteins in ion-exchange chromatography

Abstract

The problem of non-linear elution of a band of protein in isocratic ion-exchange chromatography leads to a pair of coupled non-linear partial differential equations. The equilibrium may be modeled using the Steric Mass Action (SMA) model of ion exchange, which treats both the salt dependence of protein adsorption and the steric shielding present under non-linear conditions. Neglecting axial dispersion, a model of ideal chromatography is formulated that may be solved by the method of characteristics. The predictions of this relatively simple model are shown to agree with experimental results concerning the non-linear elution of cytochrome c in a strong cation-exchange column. Of particular interest is the existence of two plateaus in the solution of this problem for large injection volumes. While this result cannot be understood or predicted on the basis of the traditional Langmuir isotherm or other currently available descriptions of adsorption, the chromatographic model presented in this work makes this otherwise anomalous result clear. Further, the use of such a model during parameter estimation is discussed.