A mathematical model for the simulation of affinity membrane chromatography process

Membrane affinity chromatography is one of the processes that are considered as a possible alternative to bead based chromatography. Membrane chromatography is not limited by diffusion as the majority of chromatographic resins and therefore it is particularly suited for purifying large bio-molecules such as high molecular mass proteins and viruses. Nevertheless, in order to promote its applications in up-scaled plants, it is imperative to develop a reliable simulation tool able to describe the process performance in a predictive way. In this work we present a mathematical model that can describe a complete affinity cycle and its chromatographic steps: adsorption, washing and elution. The mathematical formalization takes into account all the relevant mass transport and kinetics phenomena involved in the membrane affinity chromatography process, namely axial convection, longitudinal dispersion in the micro-porous matrix and affinity binding with the specific adsorption site. Further, extra-column effects in terms of mixing volumes and delay time are included in the model. The few relevant fitting parameters were derived from a calibration with an extensive set of experimental affinity cycles performed with pure IgG solutions. The affinity cycles have been carried out using different innovative affinity membranes tested under a broad spectrum of operating conditions. Model validation is then achieved by comparing simulation results with experimental data which have been obtained for the purification of immunoglobulin G from a complex feed as a cell culture supernatant. Model simulations are in good agreement with the experimental affinity cycles both in the case of pure IgG solutions and for the cell culture supernatant considered, demonstrating the accuracy of the model to describe the transport phenomena in the column and the adsorption binding mechanism.