Electrostatic coupling to pH-titrating sites as a source of cooperativity in protein-ligand binding

This paper describes an alternative mechanism for the cooperative binding of charged ligands to proteins. The ligand-binding sites are electrostatically coupled to protein side chains that can undergo protonation and deprotonation. The binding of one ligand alters the protein's protonation equilibrium in a manner that makes the the binding of the second ligand more favorable. This mechanism requires no conformational change to produce a cooperative effect, although it is not exclusive of conformational change. We present a theoretical description of the mechanism, and calculations on three kinds of systems: A model system containing one protonation site and two ligand-binding sites; a model system containing two protonation sites and two ligand-binding sites; and calbindin D9k, which contains two Ca2+-binding sites and 30 protonation sites. For the one-protonation-site model, it is shown that the influence of the protonation site can only be cooperative. The competition of this effect with the anticooperative effect of ligand-ligand repulsion is studied in detail. For the two-protonation site model, the effect can be either cooperative or, in special cases, anticooperative. For calbindin D9k, the calculations predict that six protonation sites in or near the ligand-binding sites make a cooperative contribution that approximately cancels the anticooperative effect of Ca2+-Ca2+ repulsion, accounting for more than half of the total cooperative effect that is needed to overcome repulsion and produce the net cooperativity observed experimentally. We argue that cooperative mechanisms of the kind described here are likely when there is more than one ligand-binding site in a protein domain.