(759c) Role of Local Metal-Site Interactions and Bulk Protein Restraints In the Thermodynamics of Zinc Binding to a Zinc-Finger Protein

To gain analytical insights into metal binding to proteins, we express the effective Hamiltonian of an ion binding site in a protein as a combination of the restraints from the protein and the instrinsic vacuum Hamiltonian of the ion bound site. The protein restraints are described by the elastic network mode and the vacuum Hamiltonian of the ion bound site is a generalized Hessian. The resultant of the addition of the two quadratic forms is recast as a pure quadratic form. The free energy of the ion bound protein is analytical. We apply our model to the zinc finger peptide. The model quantitatively captures thermodynamics of Zn²⁺ preference over its competitors Fe²⁺, Co²⁺, Ni²⁺, and Cd²⁺ in the protein binding site. We predict that a binding site with minimal protein restraints will select for  Zn²⁺ better than a zinc finger peptide over Fe²⁺ and  Ni²⁺ while the preference for Zn²⁺ over Cd²⁺ and Co²⁺ will be diminished. We show that the inspecting the interplay between the instrinsic modes of vibrations of the the ion-site cluster  and the restraints from the proteins provides a platform for completely analytical and rigorously thermodynamic design principles for metalloproteins.