Theoretical determination of the standard reduction potential of plastocyanin in vitro

Quantum chemical QM/MM calculations have been performed on the copper-containing blue protein plastocyanin that is involved in the photosynthetic electron transfer. Crystallographic coordinates of the non-hydrogen atoms in the oxidized and reduced forms of poplar plastocyanin were obtained from the Protein Data Bank. The present work required calculations on the oxidized form that has a molecular structure independent of pH, and the reduced form with different structures at pH values 3.8 and 7. At pH 7, both the oxidized and reduced forms of the protein have distorted tetrahedral geometry for the copper-containing active site, the Cu atom being coordinated to two histidine, one cysteine, and one methionine residues. At pH 3.8, the active site of the reduced species is trigonally coordinated to one histidine, one cysteine, and one methionine residues. To optimize the geometry of the system while retaining the constraints of the protein backbone, the ONIOM methodology was adopted so as to treat the active site by the DFT-B3LYP method using the 6-31G basis set, whereas the geometries of the nearby residues as well as six neighboring water molecules were optimized by the MM/UFF method. Then atomic charges for the atoms of the protein (apart from those in the active site) were determined from DFT calculations separately for each amino acid residue using the STO-3G basis set. The atomic charges of the water molecules were computed by the DFT/6-31G(d) method. Finally, the electronic energies were recalculated by the ONIOM technique where the DFT-optimized active site was again treated at the 6-31G level of theory, whereas the rest of the protein, along with the solvent molecules near the active site, were treated by the Amber force field method using the calculated DFT charge on each atom. This treatment effectively allowed us to retain the steric constraints offered by the protein backbone during the optimization process, as well as the effects arising from the interaction of the protein dipoles and the bare charges on the protein with the atomic charges in the complex, thereby accommodating all electronic interactions such as charge-charge, charge-dipole, dipole-dipole, etc. The thermal energies of various oxidized and reduced forms were computed for a slightly simplified model of the active site (the part optimized in ONIOM) by using the DFT-B3LYP methodology. The effective radius of the globular protein plastocyanin was determined from the crystallographic data. The stability of each species arising from its interaction with medium was determined by explicitly calculating the Born charge-dielectric (water) interaction energy and, for the solvated proton, the Debye-Huckel energy of ion-ionic atmosphere interaction. The dielectric constant of water and plastocyanin were taken as 78.5 and 8.0, respectively. The interaction with the medium and the entropy changes are found to play a critical role in determining the reduction potential. The process of reduction of plastocyanin in an aqueous medium involves a very large reorganization of water molecules, and a large entropy change that cannot be computed readily. Hence, the entropy of reduction of plastocyanin was taken from experimental data that are available for pH 7. The free energy change was calculated for the reduction of plastocyanin in water and proton in water. From these values, the standard reduction potential was determined at pH 7. The calculated potential (376 +/- 38 mV) is in excellent agreement with the observed one (379 mV) for the radius of the globular protein 22.37 +/- 0.16 Angstrom. A similar calculation leads us to predict the entropy of reduction of plastocyanin at pH 3.8