Protein separation by ion exchange chromatography: A model for gradient elution

Abstract

Many chromatographic separations involve two stages: (1) an attachment or adsorption step in which solutes to be recovered in purified form are attached to the column matrix, and (2) a change in a property of the solvent, with time, to detach and elute a solute as a separated band. The change of eluant property with time is frequently either a linear gradient or a sequence of (discontinuous) step changes. ' Adsorption, ion exchange, affinity, and hydrophobic chromatography are usually effected by this procedure. For example, in the second stage the solvent composition, ionic strength, or pH may be changed as a function of time. If the solvent property varies linearly with time at the column entrance, then, at constant flow rate, a linear gradient progresses through the column.The output response of the column will depend not only on the type of gradient, but also on the adsorption isotherm. For affinity adsorption the isotherm is strongly irreversible,2 but for ion exchange the isotherm is linear for a range of concentration^.^-^ In the present work, we consider the case of a linear isotherm.Gradient elution is an example of a class of programming and elution techniques used in chromatographic processes. We have applied differential moment theories to study temperature programming,6 velocity programming,' and stationary spatial temperature gradient processes.* These studies considered variation of a property of the column system with either time or column position. Our objective here is to apply this method to more general gradient elutions, where column properties change simultaneously with time and position in the column.Yamamoto and co-worker~~,~ have investigated, theoretically and experimentally, gradient elution in ion exchange chromatography of proteins. By applying a continuousflow plate theory, they considered the effect of linear and stepwise increases of ionic strength on elution characteristics (peak position and width). While their results for the retention time (first moment) are identical to those of the present work, the approach to band-broadening , based on a plate theory, required some simplifying assumptions. co-workers convincingly demonstrate how a simple analysis of small scale experiments can guide the design and operation of large-scale separations of proteins by ion exchange chromatography.33439 There is obvious value in extending and improving these ideas, for example a fundamental treatment of transport phenomena in the column, and by generalizing the technique to other chromatographic separations.In this communication, we 1) extend for the first time the moment theory to gradient elution in ion exchange chromatography; 2) consider linear, exponential, and step gradients; and 3) relate retention time (first moment) and band spreading (second moment) to separation efficiency for gradient elution processes. MODEL FOR GRADIENT ELUTIONThe analysis proposed here generalizes earlier reports ,6-8 which involved column properties varying only as a function of time (temperature or flow program...

Rate parameters and gradient correlations for gradient‐elution chromatography

“…However, the plate model required some simplifying assumptions, which limits its effectiveness. Kang and McCoy (1989) improved the studies just mentioned by a fundamental treatment of the transport phenomena in an ion-exchange column. A rate model of material balance was applied to the mobile phase and the method of moments was used to solve the model.…”

Mathematical Modeling and Scale-up of Liquid Chromatography

“…The theoretical basis of gradient elution in nonlinear chromatography has not been well established [47]. Because of the complications involved in the modeling of gradient elution, very few existing models considered mass transfer resistance or kinetic resistance, although some considered axial dispersion [47,[96][97][98]. Existing mathematical models in the literature for gradient elution were reviewed by Gu et al [99].…”

Modeling of gradient elution in multicomponent nonlinear chromatography

“…Because of the complications involved in the modeling of gradient elution processes, very few existing models considered mass transfer resistances (Furusaki et al, 1987) or the kinetic resistances (Pitts, 1976), although some considered axial dispersion (Pitt, 1976;Furusaki et al, 1987;Antia and Horvath, 1989;Kang and McCoy, 1989). Table 1 is a summary of some existing mathematical models in the literature for gradient elution.…”