Modeling hindered diffusion of antibodies in agarose beads considering pore size reduction due to adsorption

The aim of this study is to model, describe and predict the mass transfer of IgG as a function of the agarose concentration in the protein A stationary phase, taking into account the influence of adsorption on the pore size. Therefore, particle size distribution, bed and bead porosities were examined by light microscopy, pressure-flow behavior and iSEC. Three agarose protein A stationary phases (2 wt%, 4 wt%, 6 wt%) were investigated. The pore size decreased from 116 nm for 2 wt% to 54 nm for 6 wt% and the porosity for the target molecule IgG was reduced by 25%. A shrinking core model approach was used to assess the influence of IgG adsorption on the pore size of the stationary phase and the diffusivity of IgG. Due to IgG adsorption, the pore diameter reduced by 24 nm, which is approximately two times its hydrodynamic diameter. Effective pore diffusivities of IgG were obtained by fitting the general rate model to breakthrough curves. They were in the range between 3.96·10^-12m²/s and 6.5·10^-12m²/s, decreasing as the agarose concentration increased. The DBC_1% has a maximum for the 4 wt% agarose gel, showing optimal tradeoffs between accessibility, specific surface and diffusive mass transfer for IgG. A simple geometrical model was developed to describe the change in pore and filament diameters due to adsorption. The diffusion measured in protein A agarose beads can be described by a modification of the Ogston model. This enables the diffusion measured in protein A agarose networks to be predicted.