Metalloion-ligand binding energies and biological function of metalloenzymes such as carbonic anhydrase. A study based on ab initio calculations and experimental ion-ligand equilibria in the gas phase

The known structure of carbonic anhydrase includes the structure of the act ive site, which consists of Zn2+, coordinated to three histidine (His) resi dues and a water molecule. The ligand involved in the catalysis is the wate r molecule. Using imidazole (Im) to model histidine, it is found that histi dine is the strongest bonding residue to Zn2+ of all neutral amino acid res idues. On the basis of high-level ab initio calculations, the sequential bo nd energies for one to three imidazoles attached to Zn2+ were evaluated. Th e bond energy Zn(Im)(3)(2+)- (H2O) was also determined by ab initio calcula tions and (gas phase) ion equilibria measurements. From a comparison of the free energy of stabilization of Zn2+ in the enzyme and that in aqueous sol ution, we conclude that very strongly bonding residues such as histidine ar e essential to make the Zn2+ ion in the enzyme stable, relative to the aque ous environment. The strongly bonding histidine also has another more impor tant role. Due to the very large charge transfer and polarizability energy component with such a ligand and ligand-ligand repulsion, the bonding to th e fourth, i.e., the (HO)-O-2 Ligand, is very much weakened. It is shown tha t weakening of the Zn(L)(3)(2+)-(H2O) bond energy is unfavorable, i.e., inc reases the energy required for the first step of the accepted mechanism, Zn (His)(3)OH22+ -Zn(His)(3)OH+ + H+, while the second step, Zn(His)(3)OH+ CO2 H2O/-> Zn(His)(3)(H2O)(2+) + HCO3-, is favorably affected, i.e. requi res less energy. The choice of the ligands L therefore must be such so as t o lead to a compromise between the two opposing effects. By making a semiqu antitative inclusion of the solvent effect of the protein and aqueous envir onment on the reaction free energies for the above two ionic reactions, it was possible to shaw that the "choice" of the three histidine ligands is " just right" to provide this compromise. These Ligands lead to reaction free energies that are close to zero for both reactions.