Predicting equilibrium constants for ion exchange of proteins - a colloid science approach

A mathematical model for predicting the equilibrium constants (K-eq) of ion exchange of proteins has been developed. The model is based on a description of the colloidal interactions between a protein molecule and a charged surface within an electrolyte solution. The electrostatic interactions are quantified using a solution of the non-linear Poisson-Boltzmann equation obtained by a finite element technique combined with a Newton sequence and an automatic adaptive mesh refinement incorporating error estimation. London-van der Waals' interactions are calculated using an unretarded Hamaker constant. The approach enables a priori prediction of K-eq, for protein ion exchange in terms of protein size, protein zeta potential (and hence pH), ion-exchanger zeta potential and electrolyte concentration. All of these parameters are readily quantified. The distance of closest approach (z(0)) between protein and ion exchanger must also be specified. For ion exchange of bovine serum albumin (BSA), there was good agreement between theory and experiment for the variation of K-eq, with pH with a constant value of z(0). This confirms the predictive capability of the approach developed. Good agreement between theory and experiment for the variation of K-eq with ionic strength could be obtained if z(0) was allowed to vary with ionic strength. Overall, this fundamental approach has promise to become a general method of predicting K-eq, for protein ion exchange. (C) 1998 Elsevier Science B.V. All rights reserved.