Zonal rate model for stacked membrane chromatography part II: Characterizing ion‐exchange membrane chromatography under protein retention conditions

Abstract

The Zonal Rate Model (ZRM) has previously been shown to accurately account for contributions to elution band broadening, including external flow nonidealities and radial concentration gradients, in ion-exchange membrane (IEXM) chromatography systems operated under nonbinding conditions. Here, we extend the ZRM to analyze and model the behavior of retained proteins by introducing terms for intra-column mass transfer resistances and intrinsic binding kinetics. Breakthrough curve (BTC) data from a scaled-down anion-exchange membrane chromatography module using ovalbumin as a model protein were collected at flow rates ranging from 1.5 to 20 mL min(-1). Through its careful accounting of transport nonidealities within and external to the membrane stack, the ZRM is shown to provide a useful framework for characterizing putative protein binding mechanisms and models, for predicting BTCs and complex elution behavior, including the common observation that the dynamic binding capacity can increase with linear velocity in IEXM systems, and for simulating and scaling separations using IEXM chromatography. Global fitting of model parameters is used to evaluate the performance of the Langmuir, bi-Langmuir, steric mass action (SMA), and spreading-type protein binding models in either correlating or fundamentally describing BTC data. When combined with the ZRM, the bi-Langmuir, and SMA models match the chromatography data, but require physically unrealistic regressed model parameters to do so. In contrast, for this system a spreading-type model is shown to accurately predict column performance while also providing a realistic fundamental explanation for observed trends, including an observed increase in dynamic binding capacity with flow rate.

Zonal rate model for axial and radial flow membrane chromatography. Part I: Knowledge transfer across operating conditions and scales

“…ZRM (Francis et al, 2011, 2012) has been developed for quantitatively analyzing the impact of radially inhomogeneous flow distributions on measured chromatograms under non‐binding and binding conditions for axial flow configurations. The concept of the ZRM is to virtually partition the hold‐up volumes before and behind the membrane as well as the membrane stack itself into different zones.…”

“…A detailed description of the ZRM for different axial flow configurations has been published earlier (Francis et al, 2011, 2012; von Lieres et al, 2010). Figure 3a illustrates the modeling approach for a configuration with three virtual zones for the hold‐up volumes before and behind the membrane stack as well as for the membrane stack itself.…”

“…In Equation (1), c and q are the solute concentrations in the mobile and stationary phases, respectively, v is the flow velocity, D a is the dispersion coefficient, and ∂ q /∂ t denotes the rate of adsorption or desorption of solute molecules to or from the membrane surface. The stationary phase concentration is accounted for per unit volume of solid membrane, and the dispersion coefficient has been shown earlier to contribute negligibly to the total system dispersion (Francis et al, 2011, 2012). The binding of solute molecules will be discussed in Binding Kinetics Section.…”

“…A recent study of the Hubbuch group provides evidence for the existence of different binding orientations of lysozyme on ion‐exchange beads (Florian Dismer, 2007). In a comparative study of different binding models in membrane chromatography (Francis et al, 2011), the spreading model has been found to be most suitable for quantitatively describing the adsorption of ovalbumin on a modified polyethersulfone (PES) membrane with cationic groups. The shape of BSA, which is used in the present study, has been reported as a cigar shaped ellipsoid (7 nm × 4 nm× 4 nm) (Kim, 2002).…”

“…The protein molecules are transferred across a thin film layer and immediately bound to the adsorption sites. There is no mass transfer limitation due to pore diffusion, and film diffusion can be neglected in many cases (Dimartino et al, 2011; Francis et al, 2011; Frey et al, 1992; Gerstner et al, 1992; Shiosaki et al, 1994). Due to smaller bed height, membrane chromatography has lower pressure drops and can consequently be operated at higher flow rates.…”