Abstract
Abstract 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.
Highlights
The mathematical description of the batch protein adsorption phenomenon is always required since it allows estimating the adsorption rate constant, the effective diffusivity, the maximum protein capacity, and the desorption equilibrium constant for a particular protein with a particular adsorbent
The maximum protein adsorption capacity and desorption equilibrium constant can be estimated from adsorption isotherms, while the adsorption rate constant and the effective diffusivity must be determined from kinetic adsorption studies
The adsorption of proteins was evaluated with the systems iminodiacetic acid (IDA)-Cu(II), PEG5-IDACu(II)L, and PEG5-IDACu(II)H
Summary
The mathematical description of the batch protein adsorption phenomenon is always required since it allows estimating the adsorption rate constant, the effective diffusivity, the maximum protein capacity, and the desorption equilibrium constant for a particular protein with a particular adsorbent. The maximum protein adsorption capacity and desorption equilibrium constant can be estimated from adsorption isotherms (equilibrium data), while the adsorption rate constant and the effective diffusivity must be determined from kinetic adsorption studies These parameters allow describing and elucidating the interaction between the target protein and the adsorption sites, but can help characterize column chromatographic experiments (Sharma and Agarwal, 2002; Gutierrez et al, 2007). In the same way, Arnold et al (1985) presented a model that considers all the mass transfer resistance associated only to pore diffusion These last two models, as a result of their simplicity, permit one to obtain an analytical solution of the batch adsorption process; not quite general
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