Adsorption of a single protein interacting with multiple ligands: Inner radial humps in the concentration profiles induced by non-uniform ligand density distributions

The dynamic behavior of the concentration profiles of a single protein in the pore solution and the adsorbed phase is studied in different adsorbent media when the spatial density distribution of the immobilized ligands is either uniform or non-uniform and at the same time the single protein is forming one-site and two-site adsorbate-ligand complexes with the immobilized monovalent ligands. The competition for the formation of one-site and two-site interaction complexes leads to the formation of inner radial humps in the concentration profiles of the two-site adsorbate-ligand complex in adsorbent particles having either uniform or non-uniform spatial ligand density distributions. The results show that inner radial humps in the concentration profiles of the adsorbed protein (total concentration of adsorbed protein by one-site and two-site interactions) occur only in adsorbent media whose spatial ligand density distributions are non-uniform and have maxima or minima occurring in radial positions located between the center and the outer Surface of the particles. The non-uniform spatial ligand density distributions satisfying this property provide the cause for the occurrence of inner radial hut-lips in the concentration profiles of a single adsorbed protein, while the multi-site adsorption interactions affect the magnitude and the rate of propagation of the inner radial humps in the concentration profiles of the single adsorbed protein. It is also demonstrated that adsorbent media having certain non-uniform functional forms of spatial distribution in the density of immobilized ligands could provide more efficient adsorption of a protein than an adsorbent medium whose spatial distribution of the density of immobilized ligands is uniform. Furthermore, the results in this study suggest the type of information that could be obtained from finite bath experiments and could be used to (i) determine whether multi-site adsorbate-ligand complexes are formed during the adsorption of a single adsorbate and (ii) select between alternative adsorbent media the adsorbent particles that could provide the highest overall adsorption rate for a given adsorbate of interest. The results clearly indicate that it is very important to study the dynamic behavior of an adsorption system having a non-uniform spatial ligand density distribution and where the values of the pH and ionic strength are such that the electrophoretic effects are active.