New insights in the mathematical modelling of membrane affinity chromatography

Membrane affinity chromatography is an innovative technique that stands out among the cutting edge bioseparation technologies. Membrane chromatography separations are not limited by diffusion, as it is the case for the majority of chromatographic resins, and therefore are exceptionally well suited for purifying large bio-molecules such as immunoglobulin G. The modelling of such processes is of particular interesting view of the implementation of this technique for large scale applications. Indeed, the development of accurate and predictive models for membrane chromatographic operations is an imperative need that is not yet completely resolved. In this work we present and validate an effective mathematical model for membrane affinity chromatography. The model includes convection, dispersion and an appropriate set of kinetic equations to simulate the adsorption, washing and elution steps. The model also considers the extra column contributions to band spreading due to dead end volumes and mixing effects. Model validation is achieved by comparing simulation results with an extensive set of experimental data obtained using different affinity membranes; the experimental system considered is the primary capture of IgG from a cell culture supernatant. The good agreement of the model predictions with experimental data for the different supports considered demonstrates the accuracy of the model to describe all the relevant transport mechanisms involved. A comparison with other mathematical models taken from the literature is presented underlying the theoretical differences. Furthermore, the different models are used in order to generate simulations that scale-up membrane chromatographic modules. This study highlights the advantages in the predictive capabilities when using the proposed model.