Miscalculating Equilibrium Constants for Multivalent Protein Complexes: Site-Binding Concentration or Protein Molecular Concentration?

Because the authors continue to note instances in the scientific literature of failure to use the correct receptor binding site concentration for determining binding constants, herein we discuss the fundamental concepts that need to be considered to determine correct binding constants or conversely calculate accurate reactant concentrations with known equilibrium constants. We also show the derivation and analytical solutions of the cubic and quartic equations that give the exact free ligand concentration in bivalent and trivalent receptor systems at equilibrium as a function of the macroscopic equilibrium dissociation constants and the total concentrations of ligand and multivalent protein. These equations and solutions strongly reemphasize the critical dependency of deriving the correct concentrations of bound or free ligand and multivalent protein on the choice of the correct concentration basis for the multivalent protein, which is in turn dependent upon the type of equilibrium constant used. These results demonstrate the importance of choosing the proper multivalent protein concentration for the determination of either valid microscopic or valid macroscopic equilibrium dissociation constants from binding isotherms of ligand-multivalent protein complexes.