A method to calculate binding equilibrium concentrations in the allosteric ternary complex model that supports ligand depletion

The allosteric ternary complex model is frequently used in pharmacology to represent the interaction of a receptor R with two ligands A and B. Certain well-known formulas are routinely used to calculate the fractions of the receptor bound at equilibrium with A only, B only, and both A and B. However, it is often omitted that these classical formulas presume that there is no ligand depletion, i.e. that the equilibrium concentrations [A] and [B] of the ligands are well approximated by their total concentrations [A]T and [B]T. We present a calculation method which is applicable without this or any restrictions. The equilibrium concentration [R] of the receptor is implicitly characterized by an equation which is solved with a very simple convergent numerical algorithm. The concentrations [A] and [B] are given by explicit formulas in terms of [R]. The required parameters are the equilibrium dissociation constants KA and KB, the cooperativity factor α, and the total concentrations [R]T, [A]T and [B]T.

► Equilibrium concentrations are calculated without customary assumption that total receptor concentration is infinitesimal.
► An implicit formula characterizes equilibrium receptor concentration and a simple convergent algorithm calculates it.
► Two explicit formulas express equilibrium ligand concentrations in terms of equilibrium receptor concentration.
► Customary method can give substantially incorrect results when total receptor concentration is not negligible.