Equilibrium Dialysis
 
 Equilibrium dialysis is a technique for analyzing the binding of a low molecular weight ligand to a macromolecular receptor (1). Information that can be obtained from an equilibrium dialysis experiment includes the stoichiometry of the complex formed and the affinities of the interacting components (2), plus more subtle properties such as cooperativity . In the simplest form of an equilibrium dialysis experiment, receptor and ligand solutions are placed in compartments on opposite sides of a semipermeable dialysis membrane. The pore diameter of the membrane is chosen to allow passage of the ligand and prevent passage of the receptor. The ligand thus redistributes between the two compartments, whereas the receptor stays in its own compartment. If the receptor binds the ligand, an excess of ligand begins to accumulate in the receptor compartment. When equilibrium is reached, two conditions are met, as long as there is no nonideality in the system: (1) the free ligand concentration is equal on both sides of the membrane and (2) the ligand in the receptor compartment is partitioned between free and receptor-bound form according to the equilibrium constant for the receptor–ligand interaction. The total ligand concentration on each side of the membrane is measured after equilibration, as is the receptor concentration, if necessary. The excess ligand concentration on the receptor side is attributed to its binding to the receptor. This basic experiment is repeated for a series of receptor and ligand concentrations. Pairs of bound and free ligand concentrations may then be analyzed by a graphical method, such as a Scatchard Plot, or fit by least squares to a binding equation to derive the relevant parameters of the receptor–ligand interaction (3).
 The primary advantage of equilibrium dialysis over other techniques for measuring ligand-binding equilibrium constants is that equilibrium dialysis does not rely on assumptions that a measured property, for example, a spectral change, correlates linearly with receptor occupancy. Development of microdialysis cells and of dialysis membranes made from purified material with well-defined molecular weight cutoffs have eliminated many artifacts once associated with equilibrium dialysis. Persisting sources of error include aggregation of the ligand, which will retard or prevent its passage through the dialysis membrane, adsorption of ligand or receptor to the membrane, and changes in volume and concentration resulting from an osmotic imbalance at the start of the experiment.
 The assumption that the free ligand concentration is equal on both sides of the membrane at equilibrium is not always valid. Most proteins and all nucleic acids are charged; thus these macromolecules accumulate a set of neutralizing counterions. A ligand of opposite charge can act as a neutralizing counterion, resulting in an imbalance between free ligand concentrations in the receptor and ligand compartments of an equilibrium dialysis experiment. This imbalance, known as the Donnan effect (4), does not reflect a biologically specific ligand–receptor interaction, but occurs with whatever counter-ion is available, as a consequence of maintaining the overall electrical neutrality of the solution. The practical impact of the Donnan effect is to give spurious evidence of an association between a ligand and receptor of opposite charge. Even if a ligand is uncharged, changes in ionic strength or pH due to redistribution of buffer ions may still interfere indirectly with an experiment. The magnitude of the Donnan ratio (an ion's concentration in the receptor compartment divided by its concentration in the ligand compartment) is greatest at high receptor
concentration and low ionic strength. For example, 100 µM receptor containing 10 charges in the presence of 1 mM NaCl will yield a Donnan ratio of 1.5, meaning that a monovalent ligand will appear to be 50% enriched in the receptor compartment. If the receptor concentration is lowered to 1 µM, or the salt concentration raised to 100 mM, the Donnan ratio drops to 1.005. Although simple addition of salt essentially eliminates the Donnan effect as an interfering factor in equilibrium dialysis, the added ions may distort the experiment in a different way, by competing with the ligand for association with charged groups in the receptor binding site. An alternative to using high salt concentration is to measure the Donnan ratio directly and apply a correction factor (5).
References
1. I. M. Klotz, F. M. Walker, and R. B. Pivan (1946) J. Am. Chem. Soc. 68, 1486–1490. 
2. H. N. Eisen and F. Karush (1949) J. Am. Chem. Soc. 71, 363–364. 
3. J. E. Fletcher and A. A. Spector (1968) Comput. Biomed. Res. 2, 164–175. 
4. F. G. Donnan (1911) Z. Elektrochem. 17, 572. 
5. P. Suter and J. P. Rosenbusch (1977) Anal. Biochem. 82, 109–114.