Theory for electrostatic interaction chromatography of proteins.

A simple theoretical framework for the effect of the eluting salt concentration on the retention factor of proteins in ion-exchange chromatography under conditions of linear elution is described. It is based on the solution of the linearized Poisson-Boltzmann equation for two oppositely charged planar surfaces in contact with a salt solution. The theory predicts a linear relation between the logarithmic retention factor and the reciprocal square root of the ionic strength of the eluent in the salt concentration range used in linear elution chromatography. A large body of retention data obtained in ion-exchange chromatography of proteins over a wide range of experimental conditions was plotted as ln k' vs 1/square root of I, where k' and I are the retention factor and ionic strength, respectively. The plots are linear or nearly so, as predicted for a moderate salt concentration range by the theory. From the slope of such plots the characteristic charges of the proteins were estimated by using only fundamental physicochemical constants. The chromatographically measured protein charges compare well to those obtained from titrimetric experiments at the same pH, although certain deviations are noted. The theoretical approach presented here offers a more realistic treatment of the ion-exchange chromatography of proteins than the stoichiometric displacement model and can serve as a convenient framework for the analysis of retention data.