Mathematical modeling of the batch adsorption of proteins on new restricted access media with poly(Ethylene glycol) as a semipermeable barrier using compact finite differences

In this work we describe a mathematical analysis of the batch adsorption process of several proteins using a new restricted access medium consisting of agarose beads grafted with poly(ethylene glycol) (PEG) as a semi-permeable barrier and immobilized metal ions or ion exchange groups as binding sites. The model was fitted to experimental data, allowing the estimation of the adsorption rate constant and the effective diffusivity for each protein. The model was solved using compact finite differences in a MATLAB® platform. According to the results, the presence of grafted PEG reduces the adsorption of all proteins to different extent; with high molecular weight proteins being affected the most. The model also establishes a reduction in the adsorption rate constant (which affects protein interaction with binding sites). The movement of the protein molecules in the adsorbent pores is also affected by the grafted PEG, but to a lesser extent.