Redox center models

In the reaction mechanism of cytochromec oxidase, four redox centers are involved. The re-duction of molecular oxygen to water takes place in the binuclear center where the electrons and protons are delivered for oxygen reduction and four protons are translocated across the inner-mitochondrial membrane, a process which results in a membrane electrochemical

pro-ton gradient. The propro-ton translocation is coupled with the electron transfer which makes the reaction difficult to study. To incorporate the redox centers to the protein, the redox centers were considered for the quantum chemical calculations to get the charges with different ox-idized and reduced states as well these models were used for the DFT calculations to obtain the gas phase and solvation energies. The models used for the redox centers are described below. DFT calculations were also performed in non-redox-active centers (Mg²⁺ and Ca²⁺) to obtain partial atomic charges.

MODEL FOR Cu_A CENTER. TheCu_A center contains two copper ions (see Figure 6.3) and are bridged by two cysteins sulfur atoms. The two copper ions of theCuAcenter are coordinated by two His, one Met, a backbone carbonyl oxygen of Glu, and two bridging Cys residues. The ligated cysteins were simplified as methyl thiolates. The histidines were modeled by the methyl imidazoles. The backbone carbonyl oxygen of Glu was included in the model compound. The amino acid side chains were cut at the Cαatom and their Cβatoms were fixed in their crystal structure positions. The initial coordinates were obtained from the crystal structure of R.

sphaeroides. All the hydrogens were added usingbabelprogram. TheCuA center model was used to obtain the charges for the calculations. The charges were obtained for both reduced and oxidized states ofCuAcenter.

Cu_A

M263

C256

C252

E254 H260 H217

Figure 6.3. The model compound ofCuA centerThe cysteins are simplified as methyl thiolates. The histidines are modeled by methyl imidazole.

MODEL FOR HEME a Hemea center is with two histidine residues as axial iron-ligands (see Figure 6.4). The histidine residues were modeled by methyl imidazole. The heme propionates were cut off and substituted by hydrogen atoms. The hydrophobic hydroxyethyl-farnesyl group was truncated next to the hydroxyl group. The calculations were performed both in the reduced and in the oxidized state.

heme a

H421

H102

Figure 6.4. The model compound of hemea. The histidines coordinating the iron are modeled by methyl imidazole. The hydrophobic hydroxyethyl-farnesyl group was truncated next to the hydroxy group. The heme propionates were cut off and substituted by hydrogen atoms.

MODEL FOR CuB CENTER. The model for theCuB center consists of Cu ion, methylimidazole model for coordinating histidines 284, 333, and 334 and the tyrosine 288 was modeled by methyl group (see Figure 6.5). The fourth coordination was modeled withH2O molecule and a hydroxyl group. The calculations were performed both in the reduced and the in the oxidized state.

Cu_B

H284 Y288

+2/+1

H333

H334

Figure 6.5. The model compound ofCuBcenter. The histidines coordinating the copper ion are modeled by methyl imidazole. The cross linked tyrosine 288 is replaced by methyl group. The fourth coordination is theH2O molecule. The proton binding sites are indicated by white spheres.

MODEL FOR HEMEa3 CENTER. The model for the hemea3center consists of the hemea3 and a axial histidine which was modeled by methylimidazole (see Figure 6.6). The sixth coordi-nation was modeled with H2O molecule (Fe^III-H2O and Fe^II-H2O), hydroxyl group (Fe^III-OH and Fe^II-OH), oxo-ferryl (Fe^IV=O) and ligand unbound state (Fe^IIIand Fe^II). The hydrophobic hydroxyethyl-farnesyl group was truncated next to the hydroxyl group. The hemea3 center was optimized both in oxidized and reduced states with all ligands mentioned above.

His419

heme a₃

Figure 6.6. The model compound of hemea3 center. The histidines coordinating the iron are modeled by methyl imidazole. The hydrophobic hydroxyethyl-farnesyl group was truncated next to the hydroxyl group. The heme propionates were cut off and substituted by hydrogen atoms. TheH2O molecule is considered in the six coordination position is shown.

The proton binding sites are indicated by white spheres.

6.3 D ENSITY F UNCTIONAL CALCULATIONS

The DFT calculations [81, 172] were performed to obtain partial atomic charges of the re-dox centers Cu_A, heme a, heme a₃ and Cu_B respectively. For redox centers Cu_A, heme a and heme a3 the Perdrew-Wang 91 (PW91) calculations were performed with ADF 2004.01 [173] program. The partial atomic charges of Cu_B center were obtained by B3LYP method using 6-31G* basis sets usingGAUSSIAN 03program. The DFT calculations were performed on the oxidized states of Cu_A and heme a. Following seven states were considered for heme a3: aqua ferric state (Fe^III-H2O, charge=+1, S=5/2), aqua ferrous state (Fe^II-H2O, charge=0, S=2), hydroxyl state (Fe^III-OH, charge=0, S=5/2 and Fe^II-OH, charge=-1, S=2), oxo-ferryl state (Fe^IV=O, charge=0, S=2) and ligand unbound states (Fe^III, charge=+1, S=5/2 and Fe^II, charge=0, S=2). The local density approximation (LDA) for exchange and correlation are based on the parametrization of Vosko, Wilk and Nausair [84]. The Perdrew-Wang 91 (PW91) [86]

exchange and correlation functionals were used for the generalized gradient approximation (GGA). The numerical integration scheme used in this calculation was Voronoi polyhedron method developed by te Velde et al. with the accuracy parameter ACCINT set to its default value. A set of tripleζSlater type orbital (STO) was employed with single polarization function.

The inner core shells were treated by the frozen core approximation. All the calculations were

done with a spin-unrestricted scheme. The optimization were performed by the quasi Newton method and the Hessian was updated with the Broyden-Fletcher-Goldfarb-Shanno strategy.

The distributions of partial atomic point charges were computed by fitting the molecular elec-trostatic potentials calculated by ADF 2004.01 program [173]. The programchargefitwas used to obtain point charges which is based on CHELPG algorithm [174]. The net charge of the molecule and the three Cartesian dipole moment components from PW91 calculations were adopted as constraints for the chargefit. Point charges were then computed by determining the electrostatic potential, how well the point charges effectively reproduce the electrostatic potential. The ESP charges were calculated on the cubic grid with uniform spacing of 0.2 and 3 ˚A outer boundary around each atom of the molecule. The atoms were assigned the Bondi values of 1.7 for carbon, 1.2 for hydrogen, 1.55 for nitrogen, 1.5 for oxygen, 1.3 for iron and 1.8 for sulfur. To minimize the uncertainties in the fitting procedure the single value decom-position (SVD) method [209] was used to obtain a model with stable atomic charges. Partial atomic charges for the amino acids are taken from the CHARMM22 parameter set. The partial atomic charges for all the redox centers were derived from PW91 calculations. In addition to atomic coordinates and atomic charges, electrostatic calculations require radii. The radii used were taken from Bondi [175].

All microscopic states ofCuBcenter were optimized with hybrid density functional calculations (B3LYP) using 6-31G* basis sets. The geometry optimizations were performed usingGAUSSIAN 03program. The single point calculations were performed on the optimized structures of the CuB center using B3LYP/6-31G*/PCM level. The electrostatic potential obtained from C-PCM self-consistent reaction field were fitted by Merz-Kollman method to obtain the point charges.