Many-body effect determines the selectivity for Ca²⁺ and Mg²⁺ in proteins

Calcium ion is a versatile messenger in many cell-signaling processes. To achieve their functions, calcium-binding proteins selectively bind Ca²⁺ against a background of competing ions such as Mg²⁺ The high specificity of calcium-binding proteins has been intriguing since Mg²⁺ has a higher charge density than Ca²⁺ and is expected to bind more tightly to the carboxylate groups in calcium-binding pockets. Here, we showed that the specificity for Ca²⁺ is dictated by the many-body polarization effect, which is an energetic cost arising from the dense packing of multiple residues around the metal ion. Since polarization has stronger distance dependence compared with permanent electrostatics, the cost associated with the smaller Mg²⁺ is much higher than that with Ca²⁺ and outweighs the electrostatic attraction favorable for Mg²⁺ With the AMOEBA (atomic multipole optimized energetics for biomolecular simulation) polarizable force field, our simulations captured the relative binding free energy between Ca²⁺ and Mg²⁺ for proteins with various types of binding pockets and explained the nonmonotonic size dependence of the binding free energy in EF-hand proteins. Without electronic polarization, the smaller ions are always favored over larger ions and the relative binding free energy is roughly proportional to the net charge of the pocket. The many-body effect depends on both the number and the arrangement of charged residues. Fine-tuning of the ion selectivity could be achieved by combining the many-body effect and geometric constraint.