Computer-aided model analysis for ionic strength-dependent effective charge of protein in ion-exchange chromatography

Abstract

A packed-bed chromatographic model developed in this study includes adsorption isotherms considering steric mass action (SMA) as well as non-linearity in liquid/solid phases, adsorption kinetics and mass transport. For solving the nonlinear and nonequilibrium adsorption model described by a partial differential algebraic equation (PDAE) system, a fast and accurate numerical method (i.e., conservation element/solution element (CE/SE) method), is proposed. Sensitivity and elasticity of the model parameters (e.g., steric/shape factors, adsorption heat coefficient, effective protein charge, equilibrium constant, mass transfer coefficient, axial dispersion coefficient and bed voidage) are analyzed for a BSA–salt system in a low protein concentration range. Within a low concentration range of bovine serum albumin (BSA) where linear adsorption isotherms are shown, the adsorption heat coefficient, shape and steric factors have little effect on adsorption isotherms and the retention time. However, the effective protein charge which is related to pH and ionic strength affects the retention time significantly even if the change is slight. The mass transfer coefficient (i.e., adsorption rate coefficient) has an effect on the peak height of the elution curve at the same retention time. Sensitivity of the retention time to the bed voidage is relatively large, since the bed voidage changes the fluid velocity of the mobile phase. Comparing the proposed model with experimental elution curves obtained at different salt concentrations, it is proposed that the effective protein charge could depend upon the salt concentration (or ionic strength). The reason for this dependence may be a steric hindrance of protein binding sites combined with a salt shielding effect neutralizing the surface charges of the protein.