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1 Introduction

The CuA site functions as an electron transfer intermediate in cytochrome c oxidase (CcO), the terminal electron acceptor in aerobic respiration [1–6]. The geometrical and electronic properties of the CuA site in CcO have been studied by X-ray crystallography, electron paramagnetic resonance (EPR), X-ray absorption (XAS), resonance Raman (rR), extended X-ray absorption fine structure (EXAFS), magnetic circular dichroism (MCD), and nuclear magnetic resonance (NMR) spectroscopies, as well as by density functional theory (DFT), suggesting that the CuA site adopts a characteristic molecular structure [7–21].

The X-ray crystallographic structures of CcO revealed that the CuA site contains two copper ions bridged by two cysteinyl thiolate groups, and that each copper ion is coordinated equatorially with a histidine residue and axially with either a methionine residue or a carbonyl group of the polypeptide backbone (Fig. 30.1b) [7]. The Cu–Cu distance is remarkably short enough to allow the formation of a direct bond between the two copper ions. An EXAFS and parallel MCD studies supported the occurrence of direct Cu–Cu bonding in the CuA site [8, 9]. The reduced CuA site has a Cu1+–Cu1+ core, which is oxidized by one electron. EPR studies demonstrated that the CuA site is a completely delocalized mixed-valence Cu1.5+–Cu1.5+ species [10–14]. Many synthetic modeling studies also elucidated the important structural features for electronic and functional properties of the CuA site [15–17]. Tolman and collaborators synthesized a model complex [15, 16]. The complex shows a mixed-valence oxidized state, as well as the CuA site, but has a longer Cu–Cu distance of 2.9 Å, which implies no direct Cu–Cu bond interaction [15]. XAS and absorption spectra of the synthetic model suggested stronger superexchange interactions via the bridging thiolate groups but a weaker Cu–Cu electronic coupling [16]. On the other hand, a combination of rR and XAS of the CuA site showed that both the direct Cu–Cu interaction and the superexchange interactions via the Cu–S bonds contribute to the electronic coupling between the two copper ions [10]. DFT calculations also revealed that the mixed-valence synthetic model has a singly occupied πu redox active molecular orbital (RAMO), while that the oxidized CuA site shows a completely delocalized σu* ground state, in which an unpaired electron occupies the σu* RAMO, as illustrated in Fig. 30.2 [10, 16, 18–21]. The completely delocalized σu* RAMO produces the stronger electronic coupling between two copper ions, which provides a strongly stabilized and delocalized electronic structure. This electronic structure greatly contributes to maintain the CuA site delocalized in the low-symmetry protein environment. Olsson and Ryde also conducted DFT calculations on the CuA site, concluding that the delocalization of the unpaired electron causes the lowering of the reorganization energy in the mixed-valence oxidized state [19]. The complete delocalization of an unpaired electron and the small reorganization energy result in the rapid electron transfer rates.

Fig. 30.1
figure 1

The X-ray crystallographic structure of cytochrome c oxidase (CcO) (a) and the CuA site (b) (PDB ID: 1V54)

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Fig. 30.2
figure 2

Schematic pictures of the σu* and πu redox active molecular orbitals (RAMOs) (a) and the σu* and πu states (b)

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Our ultimate goal is to elucidate the origin of the characteristic electronic structure of the transition metal centers in proteins and its regulation by a protein environment. As shown in our recent studies [22–29], we have found that the protein environment enhances the intrinsic abilities of the cofactor. Thus, our computation suggests that a study of the intrinsic electronic structure of the cofactor is essential to understand the function of metalloproteins. For example, the redox reaction of heme a itself causes the charge transfer from the Fe ion to the heme propionate, and the surrounding protein environment enlarges the charge transfer in CcO [22, 23]. We also reported the protein activation of the electronic asymmetry of a special pair cation radical in the photosynthetic reaction center [24] and the increased reactivities of hemerythrin and hemocyanin, by the surrounding protein residues [25–27].

In the previous studies [20, 21], the electronic structures of various models of the CuA site have been examined by using the DFT methods to elucidate what are required and sufficient to form the characteristic σu* ground state of the CuA site. We first explored the electronic structure of the Cu2S2 core model, which consists of two copper ions and two deprotonated Cys residues [20]. Our computation of the oxidized Cu2S2 core model revealed that the πu state is more stable than the σu* state, even in the short Cu–Cu distance. An addition of the coordinating ligands to Cu2S2 core model leads to the σu* ground state, due to electrostatic and orbital interactions between the core and the ligands, and implies that not only the direct Cu–Cu interaction but also the electrostatic and the orbital interactions by ligand coordination are responsible for the stabilization of the σu* state rather than the πu state in the CuA site. We next examined the effects of each coordinating ligand on the electronic structures of the CuA site through DFT calculations [21]. His ligation provides both strong orbital and electrostatic interactions to the Cu2S2 core, dominating both stabilization of the σu* ground state and regulation of the ionization potential of the CuA site. The coordination of the peptide carbonyl group electrostatically affects the ionization potential. Weak orbital and electrostatic interactions by the Met coordination are influential to the stabilization of the σu* ground state.

In the present study, we address the origin of the strong delocalized character of the oxidized σu* ground state in the CuA site, using the DFT method (the M06 exchange–correlation functional). In particular, we have examined the RAMOs, spin density distribution, and Mulliken atomic spin and charge densities of the models of the CuA site in the σu* and πu states. Our computation demonstrates that the direct Cu–Cu bond and the ligand coordination lead to the strong and robust delocalization over the Cu2S2 core in the CuA site even with the structural deformation of the Cu2S2 core. It indicates that the CuA site has a character of “flexible electron mediator.” This character is also found in heme a [23], implying that the robustness to the structural distortion is required to transition metal cofactors involved in biological electron transfer.

2 Computational Procedure

2.1 Model Construction

The models for the oxidized CuA site were constructed with the three-dimensional atomic structure of fully oxidized bovine heart CcO at the 1.8 Å resolution (PDB ID: 1V54), while the reduced CuA site was modeled with fully reduced bovine heart CcO at the 1.9 Å resolution (PDB ID: 1V55). Bovine heart CcO is dimerized, and each monomer consists of 13 subunits. Subunit II, which is represented by chain B and O in PDB data of bovine heart CcO, contains the CuA site. Since the Cu–Cu distances of chain B and O are quite different from each other, the 1V54B, 1V54O, 1V55B, and 1V55O models were built for the CuA site in the chain B and O of the oxidized and reduced CcO, respectively, as illustrated in Fig. 30.3a. The geometrical parameters of two copper ions, the bridging Cys residues, Cys196 and Cys200, and the coordinating amino acids, His161, Glu198, His204, and Met207, were employed for the construction of the models. In the models, each Cα atom of His161, Cys196, Cys200, His204, and Met207 was replaced with an H atom, and Glu198 was replaced with N-methyl acetamide. We classified the models into the core, His161, Glu198, His204, and Met207 parts, according to the Cu2S2 core and the coordinating ligands, as illustrated in Fig. 30.3b. The positions of the hydrogen atoms were optimized, while the heavy atoms were fixed to the positions in the corresponding X-ray structure.

Fig. 30.3
figure 3

Models of the CuA site, the 1V54B, 1V54O, 1V55B, and 1V55O models (a), and the classification of the models into the core, His161, Glu198, His204, and Met207 parts, according to the Cu2S2 core and the coordinating ligands (b)

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2.2 Quantum Chemical Calculations

All quantum chemical calculations were performed on the models with the Gaussian 09 program packages [30]. In the previous study [20], we assessed the validity of exchange–correlation functionals of DFT (BHandHLYP [31], B3LYP [32], BLYP [33, 34], PW91 [35], PBE0 [36], and M06 [37]) in comparison to the coupled cluster (CC) methods [38] and demonstrated that the M06 exchange–correlation functional [39] can be regarded as a reliable method to examine the electronic structure of the Cu2S2 core. The M06 exchange–correlation functional was employed for the investigation of the electronic structures of the CuA site. We used the Wachters + f basis sets for copper ions [40] and the Pople’s 6-311++G(df,pd) basis sets for other atoms [41, 42]. The environmental effect inside the protein was computed with PCM using UAKS cavity [43, 44] with a dielectric constant of 4.0 [45, 46]. The accuracy of PCM heavily depends on the use of proper boundary conditions on the surface of the cavity containing solutes. In the present study, the UAKS cavities were used in the PCM calculations since it provides reliable solvation energies for many molecules and ions [44].

3 Results and Discussion

3.1 Redox Active Molecular Orbitals (RAMOs) of the CuA Site

We first examined the shapes and symmetries of the RAMOs of the oxidized models (the 1V54B and 1V54O models) in the σu* and πu oxidized states. The RAMOs are represented by β-LUMOs and are equivalent to the singly occupied molecular orbitals (SOMOs). Figure 30.4 illustrates the RAMOs of the 1V54B and 1V54O models in the σu* and πu oxidized states. The σu* RAMOs consist of an antibonding orbital between a dσ* orbital (d x2–y2–d x2–y2) of the Cu–Cu part and a pπ orbital (p x  + p x ) of the S–S part of the Cu2S2 core in the CuA site, as illustrated in Fig. 30.2a. On the other hand, the πu RAMOs are composed of an antibonding orbital interaction between a dπ orbital (d xy  + d xy ) of the Cu–Cu part and a pσ* orbital (p y –p y ) of the S–S part of the Cu2S2 core in the CuA site (Fig. 30.2a).

Fig. 30.4
figure 4

σu* and πu redox active molecular orbitals (RAMOs) of the 1V54B and 1V54O models of the CuA site in the gas phase. All isovalue surfaces are set at 0.03 (e/Å3)1/2. Molecular structures are shown in thin lines

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As shown in Fig. 30.4, the σu* RAMOs are delocalized on the coordinating ligands, the Nδ atoms of His161 and His204 and the Sγ atom of Met207, and exhibit antibonding orbital interactions between the Cu2S2 core and the coordinating ligands. These antibonding orbital interactions indicate the increase in the σu* RAMO energy. In contrast to the σu* RAMOs, the πu RAMOs of all of the models are almost localized on only the Cu2S2 core, showing that the ligand coordination hardly affects the orbital energy of the πu RAMOs. This difference in the orbital interactions between the Cu2S2 core and the coordinating ligands contributes to the higher orbital energy of the σu* RAMO, as compared with that of the πu RAMO, resulting in the σu* ground state of the CuA site, as illustrated in Fig. 30.5. In addition, this stronger delocalized character of the σu* RAMO of the CuA site, as compared to the πu RAMO, facilitates the overlapping of the molecular orbitals of the adjacent amino acids to accomplish the long electron transfer to heme a in CcO.

Fig. 30.5
figure 5

Schematic pictures of the orbital interactions of the σu* (a) and πu (b) orbitals of the Cu2S2 core with the His161 and His204 parts

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Although the geometrical parameters, in particular the Cu–Cu and S–S distances, are quite different between the 1V54B and 1V54O models (Fig. 30.3a), the shapes and symmetries of the σu* and πu RAMOs are equivalent to each other. This orbital similarity results in the similarity in the electronic structures between two models. It indicates that the CuA site can transfer electrons despite the distortion of the diamond core, implying that the CuA site can be regarded as a “flexible electron mediator.” This flexibility is useful for the incorporation of the CuA site to protein for electron transfer inside the protein. In the previous study [23], we exhibited that heme a in CcO can also keep the delocalized electronic structure in spite of the deformation of the porphyrin ring. These results indicate that metal cofactors, which are involved in the electron transfer in proteins, have such robustness of the delocalized state.

3.2 Spin Density Distribution of the Oxidized CuA Site

We next investigated the spin density distribution and Mulliken atomic spin densities of the 1V54B and 1V54O models in the σu* and πu oxidized states, which show the character of the mixed-valence Cu1.5+–Cu1.5+ state. Since the oxidized state of the CuA site has an unpaired electron, the spin density distribution demonstrates that the positive spin density is fully delocalized over the Cu2S2 diamond core formed by the two copper ions and Cys196 and Cys200, and that the negative spin density polarized by the positive spin density is found on the chemical bonds such as the Cu–S and Cu–Cu bonds, as shown in Fig. 30.6.

Fig. 30.6
figure 6

Spin density distribution of the 1V54B and 1V54O models of the CuA site in the σu* and πu oxidized states in the gas phase. All isovalue surfaces are set at 0.001 e/Å3. Blue and green surfaces represent positive and negative spin densities, respectively. Molecular structures are shown in thin lines

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The shapes of the spin density distribution are similar to those of RAMOs in both the σu* and πu oxidized states, respectively, indicating that the SOMO is dominant to the mixed-valence Cu1.5+–Cu1.5+ character of the CuA site. While an unpaired electron is localized on one iron ion in the Fe3+–Fe2+ mixed-valence active site of uteroferrin [29], due to the unsymmetrical coordination (class I mixed-valence state), it is fully delocalized over the Cu2S2 core of the models of the CuA site in both the σu* and πu states. This means that the oxidized CuA site is a completely delocalized (class III) mixed-valence Cu1.5+–Cu1.5+ species even in the low-symmetry environment [42], because the direct bonding character of the copper ions is caused by the strong orbital interaction, leading to the strong delocalization over the Cu2S2 core in the CuA site.

As well as the RAMOs, the spin density distribution is delocalized on the directly coordinating Nδ and Sγ atoms of the His and Met residues in the σu* state, respectively, while it is almost localized over only the Cu2S2 diamond core in the πu oxidized state. As listed in Table 30.1, the Mulliken atomic spin densities are found on the His161, His204, and Met207 parts in the σu* oxidized CuA models, whereas most of the Mulliken atomic spin densities are found on only the core part in the πu oxidized ones. The RAMOs and spin density distribution supports the advantage of the σu* state in the electron transfer compared with the πu state.

Table 30.1 Mulliken atomic spin densities of the oxidized models (the 1V54B and 1V54 models) of the CuA site in the protein solutiona at the M06 level of theory
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The spin density distribution and the Mulliken atomic spin densities of the 1V54B model are almost same as those of the 1V54O model, indicating the robust electronic structure of the CuA site and the synthetic model complexes; see Fig. 30.6 and Table 30.1.

3.3 Mulliken Atomic Charge Density of the CuA Site

Mulliken atomic charge densities are related to the distribution of all electrons of the CuA site. The computed Mulliken atomic charge densities are summarized in Table 30.2 and show that negative atomic charges move from the coordinating His198, His204, and Glu198 parts to the core part because the coordinating parts are electron-rich due to the unsaturated bonds of the imidazole ring of the His198 and His204 parts and the peptide group of the Glu198 part. Owing to the longest coordination distance, as shown in Fig. 30.3a, the Met207 part shows the smallest charge transfer to the core part in all the coordinating parts in the oxidized state and the back charge transfer in the reduced state. As compared to the Glu198 part, the stronger charge transfer of the His parts is responsible for the equatorially coordinating lone pair of the His161 and His204 parts to the core part (Fig. 30.5) and the weak axial coordination of the Glu198 part with the longer coordination distance of 2.4 Å, as shown in Fig. 30.3a.

Table 30.2 Mulliken atomic charge densities of the oxidized models (the 1V54B and 1V54O models) and the reduced models (the 1V55B and 1V54O models) of the CuA site in the protein solutiona at the M06 level of theory
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Since the formal charges of the core part in the models of the CuA site are 1.0 and 0.0 in the oxidized and reduced states, respectively, the charge transfer of the models of the oxidized CuA site is much stronger than that of the reduced Cu A site. In the oxidized state, the charge transfer in the σu* state is stronger than that in the πu state because the σu* orbital can interact with the lone pair of the His161 and His204 parts, while the πu orbital fails to interact with them; see Fig. 30.5.

As compared with the 1V54O model, the 1V54B model provides the stronger ligand-to-core charge transfer, due to the change in the large amount of the negative charges of the His161 and His204 parts, as shown in Table 30.2. This result indicates that the stronger orbital interaction of the 1V54B model between the core and coordinating parts than the 1V54O model, resulting from the approach of the orbital energy of the RAMOs to that of the lone pair of the His part because the 0.14 Å longer Cu–Cu bond of the 1V54B model provides a weaker d–d antibonding interaction between the copper ions of the core part.

4 Concluding Remarks

By means of the M06 method with the PCM, we have explored the RAMOs, spin density distribution, and Mulliken atomic spin and charge densities of the models of the CuA site in the σu* and πu states in order to elucidate the origin of the strong delocalized character of the oxidized σu* ground state in the CuA site. We found that the fully delocalized mixed-valence Cu1.5+–Cu1.5+ state of the CuA site is because the σ- and π-type direct orbital interactions are formed between the two copper ions and because the ligand coordination stabilizes the Cu–Cu direct interaction, as shown in Fig. 30.5a. The structural variation in the Cu2S2 core of the CuA site hardly influences the shape of the RAMO and spin density distribution, because broader 3d orbitals than 2p orbitals enable the direct orbital overlap between the two copper ions even in the Cu–Cu elongation by 0.14 Å [47]. It indicates that the charge densities can be strongly delocalized over the Cu2S2 core in the redox reaction, even when the Cu2S2 core is distorted. Since the charge delocalization is related to the electron transfer of the CuA site, the CuA site can transfer electrons despite the distortion of the Cu2S2 core. It implies that the CuA site can be regarded as a “flexible electron mediator.” This flexibility is useful for the incorporation of the CuA site to protein for electron transfer inside the protein. The character of “flexible electron mediator” is found in not only heme a [23] but also the CuA site and is common to transition metal cofactors in biological electron transfer.