Modeling the performance of protein-A affinity columns using asymptotic solutions

Protein-A affinity columns are routinely used for the capture of monoclonal antibodies from cell culture media. In process optimization studies mathematical models are often used to predict the performance of chromatography columns. In this work we report the ability of two asymptotic solutions of rigorous mathematical models to predict the dynamic loading capacities of protein-A affinity columns. The analytical solutions, predicated on two different intraparticle diffusion mechanisms (surface diffusion and homogeneous diffusion), were used to analyze published data over a wide range of column residence times. It was found that the asymptotic solution of the homogeneous diffusion model under predicted experimental dynamic loading capacities measured at low column residence times. The limiting solution of the surface diffusion model also failed to describe the same set of data. Caution is thus recommended in the use of such asymptotic solutions for process design or optimization.