Analysis of protein purification using ion-exchange membranes

The performance of ion-exchange membranes for protein purification is analy zed using numerical solutions of different mathematical models. The models incorporate nonlinear sorption isotherms and mass-transfer coefficients bas ed on either the overall or local solid-phase and liquid-phase driving forc es. The numerical solutions are compared to analytical solutions which use overall mass-transfer coefficients only and, in general, are theoretically incorrect for nonlinear isotherms. The numerical solutions are fit to exper imental breakthrough curves from the literature. The models allow the deter mination of the rate-controlling mass-transfer phenomena and solid-phase co ncentration, and prediction of the operating and membrane-design parameters needed to obtain sharp breakthrough curves.