Equilibrium in the protein-immobilized-ligand-soluble-ligand system: estimation of dissociation constants of protein-soluble-ligand complexes from binding-inhibition data.

The equilibrium in the protein-immobilized-ligand-soluble-ligand system was examined theoretically and the equations found were used for determination of dissociation constants of protein-soluble-ligand complexes (K). These constants can be obtained from the s/b vs C plot [s/b = ratio of soluble and bound forms of the protein at equilibrium established in the presence of the soluble ligand (concn C)], which is linear if: (1) the concns of the complexes are much lower than the total concns of the immobilized and soluble ligands, and (2) if multiple interactions of an n-valent protein with the immobilized ligand essentially do not occur (i.e. the binding to the immobilized ligand is monovalent). The effect of violation of condition (1) is examined by computation simulation and is shown to be manifested as a non-linearity of the plot. Heterogeneity of the immobilized ligand (arising, for example, from the immobilization procedure) is predicted to have no effect on the K-values obtained. A more complex linear equation applicable principally for determination of K under more general conditions was also found. The conditions are defined under which the C50-values (i.e. concns of a series of ligands inhibiting the binding to an immobilized ligand by 50%) can be directly used for comparison of dissociation constants. The use of the s/b vs C plot was tested experimentally: transferrin, several glycoproteins or synthetic carbohydrate-containing copolymers were immobilized by adsorption in the wells of polystyrene microculture plates and thus served as immobilized ligands. Solutions of 125I-labelled ligand-binding proteins (lectins or monoclonal antibodies binding transferrin) were incubated in these ligand-coated wells in the presence of various amounts of soluble ligands (carbohydrates or transferrins): after equilibrium establishment the s/b values were determined and plotted against C and the values of K were obtained as the intercept of the plot with the abscissa. The method appears to be experimentally simple and the K-values of the lectin-sugar and monoclonal antibody-antigen complexes agree well with those determined by other methods.