title: A method to calculate binding equilibrium concentrations in the allosteric ternary complex model that supports ligand depletion.
abstract: 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 K(A) and K(B), the cooperativity factor α, and the total concentrations [R](T), [A](T) and [B](T).
authors.affiliation: Research and Development Information Systems, Amgen, Inc., Thousand Oaks, CA 91320-1799, USA. gilles.gnacadja@gmail.com
authors.forename: Gilles
authors.initials: G
authors.lastname: Gnacadja
mesh_terms: D000465:Algorithms; D001667:Binding, Competitive; D007700:Kinetics; D008024:Ligands; D008956:Models, Chemical; D010600:Pharmacology / Q000379:methods; D013816:Thermodynamics
chemical_list: D008024:Ligands