Ion exchange chromatography of proteins—prediction of elution curves and operating conditions. I. Theoretical considerations

Abstract

A mathematical model is proposed for the elution of proteins on ion exchange columns by a linear gradient increase and stepwise increase of ionic strength in order to predict relationships between the elution characteristics (the peak position, the peak width, etc.) and the operating conditions (the flow rate, the slope of gradient, etc). This model is in principle based on the continuous-flow plate theory, in which the protein concentration and ionic strength dependent distibution coefficient between proteins and ion exchangers and zone sperading effects are taken into consideration. The advantage of this model is its simplicity since it requires only two parameters: The distribution coefficient and the number of plates. Since the distribution coefficient of proteins depends on both the protein concentration and ionic strength of the elution buffer, the number of plates should vary with time. However, it is extremely difficult to take into consideration the time-dependent number of plates. Therefore, we assume that the number of plates is constant and related to that number derived from a mass balance model which includes longitudinal dispersion and gel phase diffusion. On the basis of these assumptions, a method for determining the number of plates by the moment method is presented. Although the dependencies of the peak position and peak width on the slope of linear gradient are predictable by numerical calculations of the present model, simpler methods for prediction of these dependencies are desirable. A graphical method is proposed for prediction of the peak position. For prediction of the peak width, an asymptotic solution is derived from a quasi-steady-state model.

Cation-exchange chromatography of monoclonal antibodies: Characterisation of a novel stationary phase designed for production-scale purification

“…The linear gradient elution model developed by Yamamoto delivers data for the prediction of protein elution behavior, as well as information about stationary phase properties and electrostatic and non-electrostatic proteinmatrix-interactions. 17,18 Linear gradient elutions were performed and analysed as described by Ishihara and Yamamoto to obtain information about the strength of protein-matrix-interactions. 16 Other important properties of chromatographic media are adsorption capacities and mass transfer characteristics.…”

Mathematical Modeling of Protein Chromatograms

“…At low protein concentration, the adsorption kinetics is computed from the value of a distribution coefficient K(I) that depends only on the ionic strength (I). Yamamoto et al proposed the following equation for the concentration of the adsorbed protein (C Ã bi ) [12,65]:…”

“…According to the plate model, the protein concentration in each plate (C bi ) is given by the following equation [12]:…”

“…There are several approaches for modeling elution curves in chromatography, however, two of them have been more commonly used: the theoretical plate model (PM) [12] and the general rate model (GRM) [13]. Both models have been applied to describe the breakthrough curves in frontal analysis [14][15][16][17][18] and to represent isocratic and gradient elution curves of a pulsed injection [19,20].…”

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“…Results from the previous investigation for were found to be 0.325 and 0.362 for modules 1 and 2, respectively . For the estimation of D ieff , Yamamoto et al (1983aYamamoto et al ( , 1983b found that (D ieff /u i ) is constant regardless of the flow rate and type of gel particles and solutes, and is a unique function of the particle size of the gel. Here, u i is the interstitial velocity in the packed bed.…”