The study of multiple polymerization equilibria by glass bead exclusion chromatography with allowance for thermodynamic non-ideality effects

Two related aspects are explored of the frontal exclusion chromatography of proteins employing controlled-pore glass beads as the stationary phase. First, it is shown theoretically that, despite the absence of osmotic shrinkage effects previously encountered with Sephadex matrices, the experimentally measurable partition coefficient of a single non-associating solute will be dependent on its concentration due to the differing ratios of activity coefficients in mobile and stationary phases at different total concentrations. The effect is demonstrated with results obtained using ovalbumin in phosphate buffer of pH 7.4, and is Shown to be consistent (up to a solute concentration of 5 $\text{g}\text{litre}$) with theoretical prediction formulated in terms of a single virial coefficient. Secondly, it is shown for self-associating systems that it is possible to determine the monomer concentration as a function of total concentration, provided the stationary phase is selected to ensure exclusion of all oligomeric species except monomer: the relation derived for this purpose accounts for the concentrationdependence of the partition coefficient of monomer, again as a first approximation involving one virial coefficient. Such information on the monomer concentration permits elucidation of the polymerization characteristics of the system in terms of the types of species present and the relevant equilibrium constants. The feasibility of the method, its likely sources of error and the relative contribution of the non-ideality effect are investigated using bovine glutamate dehydrogenase (up to a total concentration of 5.4 $\text{g}\text{litre}$) in phosphate buffer of pH 6.9. This system was selected since comparison was possible with results obtained by other methods, which have established the enzyme polymerization pattern as an isodesmic indefinite self-association. The isodesmic equilibrium constant of 1.5 ± 0.3 $\text{litre}\text{g}$ found in this work is in reasonable agreement with previous findings.