Models for Protein Adsorption Capacity and Competition

Single Component Adsorption. The specific mechanisms by which large macromolecular proteins contact and adsorb to a solid surface are varied and generally highly complex. Depending on the choice of protein, adsorbent, and solution properties, the surface attachment mechanism may be driven by several different general types of interactions, such as ion exchange, affinity (protein-ligand reaction), less-specific hydrophilic, hydrophobic, van der Waals, or hydrogen bonding. In principle, the thermody-namic treatment of protein adsorption from solution could be directly analogous to that for adsorption of small nonpolar molecules from the vapor phase for which there are several well-developed surface equations of state. For such simple molecule adsorption, the adsorbent surface geometric and energetic irregularities along with specific sorbate-surface interactions are generally the chief complexities (1). For protein adsorption in practice, however, thermodynamic treatment of equilibria is severely limited by the additional complexities arising from specific solvent-protein interactions, protein conformational variations both in solution and on the adsorbent surface, and frequent multipoint attachment configurations.

As a consequence of the somewhat intractable experimental and mathematical complexities, most models used for protein adsorption equilibria are simple empirical or semitheoretical models that are useful according to their goodness-of-fit to the experimental data. The semitheoret-ically based Langmuir adsorption isotherm given by q = qm C/(KD + C

where q is quantity adsorbed per unit of adsorbent, C is concentration of protein in solution, qm is maximum quantity adsorbed at high C, and KD is the disassociation or binding constant has been frequently fitted to protein adsorption data with adequate correlation. Although the physical assumptions underlying the development of this model are not followed by protein adsorption via ion exchange (2), the model nonetheless has provided a good fit if salt concentration-dependent parameters are used. For example, Weaver and Carta (3) fitted data for lysozyme on POROS 50 HS (a macroporous resin based on styrene-divinyl benzene copolymer) and on S-Hyper D-M (polystyrene-coated silica filled with functionalized poly-acrylamide hydrogel), both of which possess strong cationic functionality. In their studies, the fitted values for qm ranged from 109 to 262 mg/cm3, and disassociation constants ranged from 5.3 X 10"3to2.6 X 10"1 mg/cm3. The isotherms displayed classical protein adsorption characteristics; the nearly rectangular-shaped isotherms indicative of highly favorable adsorption at low salt concentration moderated to an almost linear-shaped isotherm indicative of weak adsorption at high salt concentration. Numerous other ion exchange protein adsorption studies have been performed with similar relative measures of adherence to the Langmuirian behavior.

Affinity adsorption may be highly selective, depending on the specific ligand-protein interaction, which may often be driven by a combination of electrostatic, hydrophobic, or hydrogen bonding type forces. Some affinity adsorption data has been successfully correlated with simple equilibrium models, based on the assumed simple reaction

where [P] and [L] denote concentration of protein and li-gand, respectively, and from which an equilibrium constant may be defined such as

Generally, Keq is small, often ranging between 10"4 M to 10"10 M, implying that binding is nearly irreversible or that the rate constants are related by kadsorp > kdesorp. Ad sorption data for many affinity systems can also be approximated through the fitted Langmuir model, although the range of fitted constants vary widely, depending on substrate-enzyme, antigen-antibody, carrier proteinhormone, or base sequence nucleic acid interactions. As an example, Chase describes the fit of data to equation 1 above for j-galactosidase adsorbing onto monoclonal antibodies immobilized on agarose gels, where it was found that Kd and qm typically had values of 1.5 x 10"8 M and 6 x 10"9 gmol/mL, respectively (4).

Protein adsorption onto dye-ligand modified supports generally is controlled by a combination of electrostatic and hydrophobic protein-dye interactions. The Langmuir equation provides a reasonable fit to the data for many systems (5), although some data are better correlated through other models, such as the Freundlich isotherm. Typically, qm for such systems is between those observed for high capacity ion exchange and the lower capacity affinity adsorbents. There are many other protein-adsorbent systems in which adsorption is driven predominantly by nonspecific mechanisms of interaction that could be used for either batch adsorption or chromatographic separations. Some of these systems are adequately fitted by simple models, whereas others, such as those displaying sig-moidal isotherms, clearly follow more elaborate adsorption mechanisms. A listing of representative adsorption capacities for several typical types of protein-adsorbent systems is shown in Table 1.

As indicated in Table 1, the choice of adsorbent and solution conditions provide a wide range of possible adsorbent capacities and relative strengths of adsorption. The suitability of any particular adsorbent-solution system to accomplish an effective separation process, however, will depend significantly on the adsorption capacity for the protein of interest relative to other competing proteins as well as on the relative rates of protein component adsorption and desorption.

Multicomponent Adsorption. Application of adsorption models to protein mixtures has been much more limited because of several factors:

1. Limitations of applicability of the empirical or semi-theoretical models when extended to multiple adsorbing protein components

2. Limited adsorption database available for even model protein mixtures

3. The fact that industrially important separations, whether by batch adsorption or chromatographic adsorption processes, typically involve mixtures containing numerous protein components (many of which may be poorly characterized) or additional impurities that substantially confound the analysis

As an example model binary system, adsorption of mixtures of bovine serum albumin (BSA) and lysozyme on the strong cation exchanger S Sepharose FF has been studied (9). For this system, the single component isotherms were well correlated by the Langmuir equation. For the mixture data, the authors evaluated both competitive and

Table 1. Representative Capacities and Binding Constants for Protein Adsorption




qm (mg/mL)

Kd (mg/mL)

Ref. :

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