Protein adsorption in porous adsorbent particles: a multiscale modeling study on inner radial humps in the concentration profiles of adsorbed protein induced by nonuniform ligand density distributions.

Recently published results determined from molecular dynamics (MD) modeling and simulation studies have shown that the spatial distribution of the density of immobilized charged ligands in ion-exchange porous adsorbent particles is most likely nonuniform and the adsorbent particles also exhibit local nonelectroneutrality. In this work, the functional forms of the nonuniform spatial distributions of the density of the immobilized ligands in four different porous adsorbent media that were determined by MD studies were employed in a macroscopic continuum model describing the transport and adsorption of a single protein in the porous particles of the four different adsorbent media. The results clearly show that inner radial humps in the concentration profiles of the adsorbed protein can occur when the spatial distribution of the density of the immobilized ligands in the porous adsorbent particles is nonuniform and also has local maxima or minima along the radial direction in the particle. The results also indicate that the rate at which the equilibrium condition is approached depends significantly on the functional form of the spatial distribution of the density of the immobilized ligands. When adsorption equilibrium has been reached, the concentration profile of the adsorbed protein exhibits the shape of the spatial distribution of the density of the immobilized ligands. The results suggest that the technique of confocal scanning laser microscopy could be used to measure the concentration profile of an adsorbed protein at equilibrium and this measurement could provide the spatial distribution of the density of the immobilized ligands, and such measurements could also be used for quality control of the adsorbent medium. The results in this work have also implications in the modeling, design, analysis, and quality control of systems involving biocatalysis. Furthermore, the results clearly indicate that it is very important to study the dynamic behavior of an adsorption system having a nonuniform spatial distribution in the density of the immobilized charged ligands and where (i) both monovalent and multivalent interactions between the single charged adsorbate and the immobilized charged ligands occur and (ii) the values of the pH and ionic strength are such that the electrophoretic effects are active.