Significant Change in Electronic Structures of Heme Upon Reduction

Apr 16, 2009 - Sanban-cho, Tokyo 102-0075, Japan; Graduate School of Pure and Applied Sciences, UniVersity ...... (b) The RCSB Protein Data Bank (PDB:...
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Significant Change in Electronic Structures of Heme Upon Reduction by Strong Coulomb Repulsion between Fe d Electrons Katsumasa Kamiya,*,†,‡ Shuji Yamamoto,§,# Kenji Shiraishi,‡,§,| and Atsushi Oshiyama‡,⊥ Institute of Picobiology, Graduate School of Life Science, UniVersity of Hyogo, 3-2-1 Koto, Kamigori, Ako, Hyogo, 678-1297, Japan; CREST, Japan Science and Technology Agency, Sanban-cho, Tokyo 102-0075, Japan; Graduate School of Pure and Applied Sciences, UniVersity of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8571, Japan; Center for Computational Sciences, UniVersity of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8577, Japan; Department of Applied Physics, School of Engineering, The UniVersity of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan ReceiVed: October 23, 2008; ReVised Manuscript ReceiVed: February 20, 2009

We report total-energy electronic-structure calculations based on the density functional theory performed on a low-spin heme. We have found that the high-lying occupied and low-lying unoccupied states having Fe d and/or porphyrin π orbital character are significantly rearranged upon the reduction of the heme. An analysis of these states shows that the remarkable elevation of the Fe d levels takes place due to the strong Coulombic repulsion between accommodated d electrons. Due to a peculiarity of the heme, this elevation could be controlled by lower-lying empty porphyrin π states, leading to electron transfer from Fe d orbitals to the porphyrin π ones in order to reduce the Coulomb-energy cost. This self-limiting mechanism provides a natural explanation not only for the present calculated results, but also for general electron delocalization appearing under various physiological conditions, regardless of the types of the hemes. 1. Introduction Hemes are ubiquitous prosthetic groups of proteins, participating in a wide variety of physiological functions, such as the transport or storage of dioxygen, electron transport, and the oxidization of organic compounds,1 by taking the reduced (electron captured) or oxidized (electron released) form. The heme consists of a porphyrin ring with Fe at the center and, as typical in proteins, the iron coordinates to one or two additional axial ligands below and above the porphyrin plane. Depending on the number and field strength of the ligands, the reduced and oxidized hemes typically exhibit low-spin and high-spin states. The six-coordinated heme formed by two axial ligands with strong field strengths, such as imidazole, represents a lowspin state, i.e., S ) 0 (reduced) or S ) 1/2 (oxidized), while the five coordinated heme formed by one axial ligand shows a high-spin state, S ) 2 (reduced) or S ) 5/2 (oxidized). The hemes are known to display characteristic electron localization or delocalization in response to reduction. In fact, the location of the surplus charge upon reduction has been extensively investigated, both experimentally2-4 and theoretically,5-7 for several representatives of low-spin iron-porphyrin complexes. Electron spin resonance (ESR) and nuclear magnetic resonance (NMR) measurements performed on low-spin iron-porphyrin derivatives have indicated that an unpaired electron is localized mainly at the central iron. Yet it is also * To whom correspondence should be addressed. Tel:+81-791-580347. E-mail: [email protected]. † Institute of Picobiology, Graduate School of Life Science, University of Hyogo. ‡ CREST, Japan Science and Technology Agency. § Graduate School of Pure and Applied Sciences, University of Tsukuba. | Center for Computational Sciences, University of Tsukuba. ⊥ Department of Applied Physics, School of Engineering, The University of Tokyo. # Present address: Core Technology Center, Covalent materials, Co., Ltd., 30 Soya, Hadano, Kanagawa, 257-8566, Japan.

distributed over the porphyrin ring to some extent.2-4 These are supported quantitatively by quantum chemical calculations.5-7 The physiological importance of such electron localization or delocalization stems from recent X-ray crystallography and Raman spectroscopy measurements8 performed on cytochrome c oxidase (CcO), which is the proton-pumping enzyme functioning at the final stage of aerobic cellular respiration process. The high-resolution X-ray structures have indicated that the periphery of low-spin heme (so-called heme a) is located at a proton entry site for proton pumping reaction. The Raman spectroscopy has shown the effect of the central iron reduction on the bond stretching at the periphery via the porphyrin π-electron system, suggesting that charge delocalization in the heme a might be related to the proton-transfer process. However, despite the extensive experimental and theoretical outcome about electron localization or delocalization in hemes, the fundamental roles of the electron interaction in Fe d orbitals and of their hybridization with π orbitals of the surrounding porphyrin are still far from being unraveled. Density functional theory (DFT)9,10 provides a computationally efficient approach, as indicated by its successful application to a variety of biological systems.11-13 Application to the iron-porphyrin complexes requires special care,5,6,14-21 however, due to the fact that electron correlation effects would be crucial to describe the nature of transition metal complexes, and the exchange-correlation functional in the practical DFT calculations is approximated, like the generalized gradient approximation (GGA).22 Overall, the DFT with GGA can provide a good description of the atomic structures and electron distributions for low-spin hemes, whereas it is sometimes less reliable for high-spin hemes. Regarding the low-spin case, the recent DFTGGA calculations have yielded comparable results for spin and charge distributions to those obtained from experiments or coupled-cluster calculatons.5,7 Nonetheless, it should be noted that the description of low-spin systems might require a linear

10.1021/jp809405s CCC: $40.75  2009 American Chemical Society Published on Web 04/16/2009

Change in Electronic Structures of Heme combination of determinants. One approach to this issue in the DFT framework is to use spin-density functional theory,23,24 yielding broken symmetry solutions in order to provide the best single determinantal representation of the states possible. Nevertheless, the broken symmetry solutions are not always an eigenfunction of the square of the total spin, leading to spin contamination. In the case of the low-spin heme a (S ) 1/2), it has been reported that the calculated is at most a value of 0.78, being comparable with the ideal value of 0.75.5 All of these studies of the low-spin heme a have thus corroborated the capability of describing the nature of the heme a by the DFT-GGA. The purpose of the present study is to characterize the rearrangement of electronic structures of hemes upon reduction and investigate the underlying mechanisms of the electron localization or delocalization via DFT calculations. We focus on heme a in the bovine CcO, which is a low-spin, imidazoleligated cofactor of the enzyme. It takes reduced and oxidized forms with the singlet (S ) 0) and doublet (S ) 1/2) spin states, respectively, being responsible for electron transfer process. Considering the physiological importance of the electron delocalization in the heme, the investigation into the mechanisms of such delocalization is imperative to understand the physiological roles of the heme. The present DFT calculations show that one electron reduction of heme a leads to electron transfer from Fe to the periphery of the porphyrin and the axial ligands. We have found that the calculated spin density differences between the reduced and oxidized forms exhibit a spherical exclusion area around Fe for both the majority and minority spins. This peculiar shape of the exclusion area reflects a significant reorganization of the electron states in response to the reduction of the heme. Namely, comparison with the electronic structures of the reduced and oxidized forms provides a clear indication that the occupation of an Fe d orbital by an additional electron leads to the strong elevation of all of the d levels due to the strong Coulombic repulsion between accommodated d electrons. Yet this elevation is suppressed when the elevated d level becomes close to the levels of the lower-lying empty π states of the surrounding porphyrin, thereby resulting in the strong d-π mixing. This leads to the transfer of electrons with both spins from Fe d orbitals to the porphyrin π states. This mechanism is also validated in another type of low-spin heme, such as heme b, being characterized as a general feature in low-spin hemes. The self-limiting mechanism that we have found here thus provides a perspicuous explanation for the observed spin-independent rearrangement pattern of the density differences, and, furthermore, the mechanism sheds new light on how electron delocalization generally appears under various physiological conditions, irrespective of the types of the hemes. 2. Computational Details The present heme a model system, as shown in Figure 1, has been extracted from fully reduced bovine CcO crystal structure,25 including the heme a and its two axial ligands, His61 and His378, both represented by a 4-ethylimidazole. The hydroxyfarnesylethyl chain, which does not participate in the π-conjugated group, has been replaced with a hydroxyethyl group in order to reduce the computational cost. H atoms have been added to the system to satisfy the atomic valency. The system has been placed in an orthorhombic supercell of sizes a ) 16.35 Å, b ) 16.93 Å, and c ) 21.43 Å, being an isolated macromolecule separated from its periodically repeated images by a minimum distance of 6 Å. The model obtained in this way

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Figure 1. The heme a model system used in this work. Here and in the following figures, the color code for the atoms is gray for C, white for H, red for O, blue for N, and green for Fe.

amounts to 107 atoms and has a net charge Q ) 0 and +1 for reduced and oxidized forms, respectively. All calculations have been performed in the framework of the spin-density functional theory,26 including the PerdewBurke-Ernzerhof (PBE) generalized gradient approximation on the exchange and correlation functional.27 Using different exchange-correlation functionals (the Becke-Perdew (BP),28,29 the Becke-Lee-Yang-Parr (BLYP),28,30 and the HamprechtCohen-Tozer-Handy (HCTH)31 functionals) provides nearly the same results for the rearrangement of the total electron density, the spin densities, and the electronic structures upon reduction of heme a.32 The interaction between core and valence electrons has been described by ultrasoft pseudopotentials.33 Valence electron wave functions have been expanded in a planewave basis set with a cutoff energy of 36 Ry.34 Atomic positions of the present model have been deduced from the corresponding X-ray data, although the H positions, which are unavailable there, have been determined by the geometry optimization with the forces being less than 3.6 × 10-2 eV/Å.35 A conjugated gradient minimization has been used for both the electronicstructure calculations and the geometry optimizations. 3. Results and Discussion 3.1. Rearrangement of the Total and Spin Densities upon Reduction. We start with the rearrangement of the total electron density upon reduction of heme a. Figure 2a shows the calculated density difference between the reduced and oxidized models. Blue and pink colors represent increase and decrease areas in the density upon reduction, respectively. It has been found that while the increased areas appear over the entirety of the heme, the decreased regions are observed predominantly around the central iron atom and its nitrogen ligands, leading to cancelation of the excess charge around Fe. In fact, only 10% of the net charge is detected by integration of the density difference (solid line in Figure 3) within a sphere around iron with the radius (1.97 Å) up to the nitrogen ligands. These results indicate that the reduction of heme a leads to a net electron transfer from Fe to the periphery of the porphyrin and the axial imidazoles. Figure 2, parts b and c, represents the spin density differences between the reduced and oxidized forms for the majority spin (spin-up) and minority spin (spin-down), respectively. It is clear

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Figure 3. The integrated values of the spatial distributions of some electron density differences shown in Figure 2. The labels (a-c) and (e) refer to the corresponding distributions in Figure 2. All of the integrations are performed within the sphere centered on Fe. The upper labels indicate the atoms in the porphyrin shown in the inset; the Pr, F, and V stand for the propionate, formyl, and vinyl groups, respectively. The Cδ and Hfarthest are both in the propionate.

Figure 2. Isosurface of electron density difference between reduced and oxidized forms, i.e., ∆F ) Fred - Foxi, for (a) total (∆Ftot), (b) spinup (∆Fup), and (c) spin-down (∆Fdown) electrons. (d) Isosurface of the charge-density of the oxidized LUKS state. (e) Isosurface of the spindown electron density difference subtracted with the oxidized LUKS state contribution. In each panel, blue and pink colors show positive and negative values, respectively. The isovalues are ( 0.02 (a) and ( 0.01 (b, c, d, and e) (e/Å3).

from Figure 2b that a significant rearrangement of the spin-up density takes place in response to the addition of an electron with down spin upon reduction. A large exclusion area for spinup electrons appears around Fe, characterized by a hollow oval in shape (Figure 2b). The integration of the values around the corresponding region shows that up to 40% of a spin-up electron is evacuated from the sphere with 1.26 Å of the Fe ionic radius, leading to the significant exclusion of spin-up electrons around the central iron and transfer them to the rest of the molecule (dotted line in Figure 3). In fact, it is observed in Figure 2b that the increased regions are mainly around the nitrogen ligands (along Fe-N bonds), the pyrrole carbons, the vinyl carbons, and the formyl oxygen. In the spin-down case, as shown in Figures 2c and 3 (dashed line), the excess electron with down spin is distributed almost all over the molecule. With regard to the increased regions in the density, a comparison of the distribution with that of the charge-density of the lowest unoccupied Kohn-Sham state (LUKS) of the oxidized form shows that they have similar patterns of distribution (Figure 2, parts c and d). Yet, there are some notable decreased regions in the spindown density upon the reduction of the heme a. A straightforward subtraction of the LUKS state contribution from the spindown density difference (Figure 2e) provides a clear indication that the exclusion area exists mainly around Fe. The other

Figure 4. Energy levels and characters of the higher occupied and lower unoccupied KS states for the spin-up and spin-down electrons in the oxidized heme a (labeled as Oxi up and Oxi down, respectively), and for the spin-up electrons in the reduced form (named as Red). The solid and dotted lines show the occupied and unoccupied states, respectively. The notation “P(π)” represents porphyrin π character, while the “d” is used to include several d orbital characters at once. The upper left inset shows the coordinate axes used in this work.

decreased regions are found around the N ligands and the atoms at the periphery of the porphyrin ring, while the increased ones are around the formyl oxygen and the vinyl carbon (gray line in Figure 3). Interestingly, these features are the same as in the spin-up case (Figure 2b and dashed line in Figure 3), indicating the existence of the common, spin-independent feature that characterizes the rearrangement of the electron density upon the heme reduction. 3.2. Reorganization of the Electronic Structures upon Reduction. To reveal the underlying origins of the observed spin-independent characteristics, we have analyzed the higher occupied and lower unoccupied Kohn-Sham (KS) states in the oxidized and reduced heme a. The results are summarized in Figure 4. As shown in the figure, all of the KS states have an Fe d character and/or a porphyrin π character, being comparable with a general characteristic of the electronic structures of a low-spin heme. Namely, in a low-spin Fe of the heme, the degenerate d levels are split into two (dx2-y2 and dz2) and three

Change in Electronic Structures of Heme (dxy, dyz, and dzx) levels due to octahedral crystal field. The former dx2-y2 and dz2 orbitals (dσ) are unoccupied, but hybridize with occupied σ-symmetry orbitals of the porphyrin-imidazole ligand, contributing to the formation of the low-lying occupied states. The latter three orbitals are occupied, fully or partially according to its redox state, and the dyz and dzx orbitals (dπ) hybridize with occupied or unoccupied π-symmetry orbitals of the ligand, being rearranged into the bonding, the antibonding, and the nonbonding states. Hence, the Fe dπ and the porphyrinimidazole π orbitals appear in character in the higher occupied and lower unoccupied KS states. The dxy orbital, which does not have the proper symmetry to interact with the ligand π orbitals, also appears in these states as a nonbonding character. In the reduced heme a, it is found that each energy level for up and down spins is located at the same position. It has also been found from Figure 4 that the energy levels of the highest occupied KS state (HOKS) and the next two (HOKS-1 and HOKS-2) are almost degenerate and separated well from those of the HOKS-3 and HOKS-4 states. The HOKS, HOKS-1, and HOKS-2 states are characterized mainly as Fe dzx, dxy, and dyz orbitals, respectively, while the HOKS-3 and HOKS-4 states are predominately as porphyrin π states that are similar to those of the two highest occupied π states of a D4h porphyrin ring, known to be 3a2u(π) and 1a1u(π) orbitals.2 The LUKS and LUKS+1 states, however, have a character of both Fe d and porphyrin π states (Figure 4). The porphyrin π states are, in this case, characterized as the lowest unoccupied π states, i.e., 4eg(π*), of the D4h porphyrin ring2. The corresponding KS states of the oxidized form are, however, reorganized as compared to the reduced case. Actually, in the spin-up case, the energy level of the dxy-like KS state shifts down remarkably, ∼2.2 eV (Figure 4). Similarly, the energy levels of the dyz-like and dzx-like KS states become low, being closer to those of the 3a2u(π)-like and 1a1u(π)-like KS states and further to those of the 4eg(π*)-like ones. These level shifts thus lead to significant changes in an amount of hybridization of the Fe d orbitals with the porphyrin π states. As a consequence, the higher occupied KS states in the oxidized form have a character of both the Fe d and porphyrin π states, while the lower unoccupied KS states are characterized predominantly by the porphyrin π states. In the spin-down case, however, the energy level displays an intermediate feature as compared with the previous two cases (Figure 4). Although the energy levels of the dxy, dyz, and dzx-like KS states shift down, the amount of the d level shift becomes small as compared with the spin-up case, thereby displaying the small amount of the d-π hybridization. The difference in the d levels between spin-up and down cases results from the exchange splitting. In fact, spin-up polarization takes place around Fe in the oxidized heme a, as well as in many low-spin iron-porphyrin derivatives,2 reducing all of the energy levels of the KS states having d characters only for spin-up electrons. 3.3. Strong Elevation of Fe d Levels. The present calculations clearly show that the strong elevation of the Fe d level takes place upon the reduction of the heme a. It is possible, however, that this elevation is self-limited. Namely, the strong elevation (∼2.2 eV, Figure 4) of the Fe d level stops when it matches the energy level of the lowest unoccupied porphyrin π state (4eg(π*)) because of the strong d-π mixing. This is illustrated in Figure 5. In this figure, the level of the 4eg(π*) state is estimated by the calculations of porphyrin model system constructed by the removal of Fe from the present heme a model. The calculated energy level of the 4eg(π*)-like KS state

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Figure 5. Schematic representation of the self-limiting mechanism.

is about 0.9 eV when it is measured from that of the 3a2u(π)like KS state in the system, comparable to the difference in energy levels between the three highest d-like KS states and the 3a2u(π)-like KS state in the reduced heme a case, ∼0.8 eV (Figure 4). Alternatively, the value of the d level elevation for the addition of one electron to the isolated ferric ion (Fe3+) is estimated to be 18 eV, suggesting that the elevation is restricted to approximately 10% in the heme case. These results suggest that the elevation of Fe d level could be self-controlled by the low-lying empty π states of the surrounding porphyrin during the reduction process. The self-limiting mechanism accounts for the spin-independent feature observed in the spin density differences. As shown in Figure 2, parts b and e, the large exclusion areas for both spin-up and spin-down electrons are observed around Fe. The region is characterized by a hollow oval in shape. This peculiar shape corresponds exactly to the decrease of both the dσ and dπ occupations upon the reduction. Namely, spin-up and spin-down electrons are transferred from the dσ and dπ orbitals to the surrounding porphyrin-imidazole ligand, appearing as the rounded exclusion areas in the corresponding density differences. The “oval” shape of the area indicates that there is no contribution of the dxy orbital to the charge redistribution, consistent with the fact that this orbital does not have the proper symmetry to interact with ligand π states and, hence, the occupation of this state is not subject to the reduction. The decrease in both the dσ and dπ contributions upon the reduction results from the d level elevation. As mentioned, in a general low-spin heme, the unoccupied Fe dσ orbitals hybridize with occupied σ-symmetry orbitals of the porphyrin-imidazole ligand, while the occupied dπ orbitals are able to hybridize with occupied or unoccupied π-symmetry orbitals of the ligand, both contributing to the formation of the occupied electron states of the heme. After receiving an additional electron, all of the Fe d levels dramatically elevate. This elevation makes the energy levels of the dπ orbitals close to those of the low-lying ligand π* states and the dσ-level further to the σ-level of the ligand as compared with the oxidized case. Hence, the dσ and dπ contributions to the occupied bonding states of the heme a become small upon reduction, leading to the decrease of the occupation of these d orbitals. The present self-limiting mechanism also provides a natural explanation for electron delocalization appearing in reduction

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of a heme group. As inferred from the present work, the elevation of Fe d level takes place upon reduction of the hemes due to the strong Coulomb repulsion between electrons accommodated into Fe d orbitals. This Coulomb-energy cost is, however, reduced by the self-limiting mechanism, whereby the d level elevation and its occupation are both limited by the lowlying porphyrin unoccupied π states, leading to electron transfer from Fe d orbitals toward the electron states delocalized over the periphery of the porphyrin ring and/or the axial ligands. More qualitatively, as shown in the present heme a case, the net charge around Fe upon the reduction is eventually 10% (solid line in Figure 3), consistent with the 10% restriction of the d level elevation in the heme system as compared with the isolated Fe3+ case (see first paragraph in this subsection), suggesting that the difference in energy level between the Fe d and porphyrin π states is essentially related to the amount of electron delocalization through the self-limiting mechanism. The present scenario sheds new light on not only the fundamental roles of the Fe d and the surrounding porphyrin π orbitals in electron localization, but also why such delocalization generally appears under various physiological conditions regardless of the types of hemes. To further validate the self-limiting mechanism, we have investigated physiological effects, in terms of atomic structures, on the relation between the d level elevation and the rearrangement of the electron densities as observed in heme a. The X-ray structures of heme a25 have shown that the lengths of six Fe-N bonds are asymmetry, from 1.86 to 2.08 Å, and the formyl group is twisted, the torsion angle CRsCβsCdO ) -25°, due to the protein environment. The geometry optimizations36 performed on the present heme a model have shown that all of the six Fe-N bonds appear equivalent, 1.97 to 2.00 Å, and the torsion angle around the formyl group becomes -4°. Yet the rearrangement pattern of the total density, spin densities, and the electronic structures upon the reduction are nearly the same as those for the X-ray structure, indicating that such a physiological effect does not affect the relation between the d level shift and the rearrangement of the electron densities. Let us next remark on the DFT calculations37 performed on heme b of cytochrome b5, which is a low-spin, six-coordinated heme by two imidazole ligands (inset in Figure 6). The difference between hemes a and b is that the formyl group and the hydroxyfarnesylethyl chain are replaced with the methyl group and the vinyl group, respectively, in heme b. Furthermore, the X-ray structures of heme b38 have shown that the propionate groups and the imidazole ligands have different orientations as compared with those in heme a.39 Nevertheless, it has been found that the calculated results for heme b have been demonstrated to be nearly the same as those of heme a (Figure 6). Indeed, a distinguishing characteristic of the rearrangement of the electron densities around Fe and the strong d level elevation, ∼2.0 eV, have been found in response to one electron reduction of the heme b. These results clearly substantiate the present self-limiting mechanism and characterize it as a general feature in low-spin hemes under various physiological conditions. 3.4. Relation between the d Level Elevation and Spin Polarization. We finally discuss spin polarization observed in many low-spin iron-porphyrin derivatives. The ESR and NMR measurements have indicated that the spin density is somewhat delocalized to the porphyrin ring, yet spin-up electron is still localized mainly at the iron.2-4 These features have been also found in the present study, shown in the calculated spin density distribution of the oxidized heme a (Figure 7a). It is seen in the figure that spin-up electrons are found mainly at the central

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Figure 6. The integrated values of the spatial distributions of electron density differences of heme b between reduced and oxidized forms, i.e., ∆F ) Fred - Foxi, for (solid line) total (∆Ftot), (dotted line) spin-up (∆Fup), and (dashed line) spin-down (∆Fdown) electrons. The corresponding curves of heme a are the same as in Figure 3 (shown by gray). All of the integrations are performed within the sphere centered on Fe. The upper labels indicate the atoms in the porphyrin as similar to Figure 3; the position of the Cmethyl atom corresponds to that of the Oformyl. The inset shows the atomic structure of the heme b model used in this work.

Figure 7. Isosurface of (a) electron spin density of the oxidized heme a and (b) the spin density subtracted with the dzx-like LUKS contribution. Blue and pink colors show the area where the spin-up or spindown polarization takes place, respectively. The isovalues are ( 0.01 (e/Å3). (c) The integrated values of the spatial distributions shown in the upper panels, referred to by the labels a and b. All of the integrations are performed within the sphere centered on Fe. The upper labels for representative atoms are the same as those in Figure 3.

iron atom, yet a notable amount is also detected at the surrounding parts of the heme molecule (blue regions). This is also shown quantitatively by integrating the spin density around Fe within the sphere of 1.26 Å radius, which yields the value of ∼85% (Figure 7c).

Change in Electronic Structures of Heme The present calculations provide a clear indication that two remarkable differences between spin-up and spin-down electron states are reflected in the relevant spatial distribution of the spin polarization. The first one obviously comes from the fact that the dzx-like KS orbital, which is the oxidized LUKS, is unoccupied in the case of spin-down electrons (Figure 4). The charge-density distribution of this state is similar to that of the spin-up polarized density (Figures 2d and 7a) where most of the excess spin-up electrons exist, indicating that the unoccupation of this state for spin-down electrons is the main contribution to the formation of the spin-up polarization. Nevertheless, a simple subtraction of the dzx-like LUKS contribution from the spin density makes it clear that there are notable spin-up electrons around Fe (Figure 7b); ∼24% is the integrated value within the sphere with the radius of 1.26 Å (Figure 7c). This is related to exactly the second difference in spin-up and spin-down electron states. As shown in Figure 4, the energy levels of the KS states having d characters are lower for spin-up electrons than those for spin-down ones due to exchange splitting. Hence, in the spin-up case, the empty dσ level is closer to occupied σ levels of the porphyrin-imidazole ligand whereas the occupied dπ level is further to the low-lying empty σ levels of the ligand, leading to electron transfer from the ligand to the iron much more than the spin-down case. The calculated spin density also shows that excess spin-down electrons along the Fe-N bonds (Figure 7, parts a and b). This is attributed to the effect of the spin-up polarization around Fe that excludes the parallel spin electrons around it. Actually, when the corresponding spin polarization disappears upon the reduction of the oxidized form, it is observed that spin-up electrons move back to the vicinity of the Fe-N bonds (Figure 2b). 4. Conclusions We have studied the reorganization of the electron states of heme a in response to reduction. We have found that the one spin-down electron reduction leads to a significant change in both spin-up and spin-down electron states of the heme, being reflected in the spin-independent rearrangement of the electron densities. Fe d and porphyrin π orbitals are primary components of the higher occupied and lower unoccupied electron states. The change in their hybridization upon reduction is found to be controlled by the remarkable elevation of Fe d levels attributed to the strong Coulombic repulsion between accommodated d electrons. The elevation could be limited by the lower-lying empty π states of the porphyrin due to the strong d-π mixing. The number of electrons accommodated into d orbitals is limited by this self-limiting mechanism in a way that both spin-up and spin-down electrons are transferred from Fe to the surrounding porphyrin-imidazole ligand, providing a perspicuous explanation for the spin-independent rearrangement pattern of the density differences. The self-limiting mechanism is also validated in heme b of cytochrome b5, being characterized as a general feature in low-spin hemes. The difference between spin-up and spin-down electron states is also reflected in the spin polarization observed in the oxidized heme a. The present calculations provide a firm theoretical framework to understand each role of the electron interaction in Fe d orbitals and of their hybridization with π orbitals of the surrounding porphyrin in response to one electron reduction of low-spin hemes. Acknowledgment. We gratefully acknowledge the fruitful discussions and precious suggestions from Y. Shigeta. A part of the work is supported by a grant-in-aid from MEXT under the Contract No. 17064002. Computations were performed on

J. Phys. Chem. B, Vol. 113, No. 19, 2009 6871 the computer facilities at Academic Computing and Communications Center, University of Tsukuba, at Institute for SolidState Physics, University of Tokyo, at Research Center for Computational Science, Okazaki Research Facilities, National Institutes of Natural Sciences, and at Institute of Picobiology, Graduate School of Life Science, University of Hyogo. References and Notes (1) Messerschmidt, A.; Huber, R.; Poulos, T.; Wieghardt, K. Handbook of Metalloproteins, Volume 1; John Wiley & Sons, Ltd: West Sussex, 2001. (2) Walker, F. A. Coord. Chem. ReV. 1999, 185-186, 471–534. (3) Astashkin, A. V.; Raitsimring, A. M.; Walker, F. A. J. Am. Chem. Soc. 2001, 123, 1905–1913. (4) Astashkin, A. V.; Raitsimring, A. M.; Kennedy, A. R.; Shokhireva, T. Kh.; Walker, F. A. J. Phys. Chem. A 2002, 106, 74–82. (5) Johansson, M. P.; Sundholm, D.; Gerfen, G.; Wikstro¨m, M. J. Am. Chem. Soc. 2002, 124, 11771–11780. (6) Johansson, M. P.; Blomberg, M. R. A.; Sundholm, D.; Wikstro¨m, M. Biochim. Biophys. Acta 2002, 1553, 183–187. (7) Johansson, M. P.; Sundholm, D. J. Chem. Phys. 2004, 120, 3229– 3236. (8) Tsukihara, T.; Shimokata, K.; Katayama, Y.; Shimada, H.; Muramoto, K.; Aoyama, H.; Mochizuki, M.; Shinzawa-Itoh, K.; Yamashita, E.; Yao, M.; Ishimura, Y.; Yoshikawa, S. Proc. Natl. Acad. Sci. USA. 2003, 100, 15304–15309. (9) Hohenberg, P.; Kohn, W. Phys. ReV. 1964, 136, B864-B871. (10) Kohn, W.; Sham, L. J. Phys. ReV. 1965, 140, A1133-A1138. (11) Barone, V.; Adamo, C. J. Chem. Phys. 1996, 105, 11007–11019. (12) Boero, M.; Terakura, K.; Tateno, M. J. Am. Chem. Soc. 2002, 124, 8949–8957. (13) Kamiya, K.; Boero, M.; Tateno, M.; Shiraishi, K.; Oshiyama, A. J. Am. Chem. Soc. 2007, 129, 9663–9673. (14) Rovira, C.; Kunc, K.; Hutter, J.; Ballone, P.; Parrinello, M. J. Phys. Chem. A 1997, 101, 8914–8925. (15) Rovira, C.; Carloni, P.; Parrinello, M. J. Phys. Chem. B 1999, 103, 7031–7035. (16) Siegbahn, P. E. M.; Blomberg, M. R. A. Chem. ReV. 2000, 100, 421–437. (17) Harris, D. L. Curr. Opin. Chem. Biol. 2001, 5, 724–735. (18) Bikiel, D. E.; Boechi, L.; Capece, L.; Crespo, A.; Biase, P. M. D.; Lella, S. D.; Lebrero, M. C. G.; Marti, M. A.; Nadra, A. D.; Perissinotti, L. L.; Scherlis, D. A.; Estrin, D. A. Phys. Chem. Chem. Phys. 2006, 8, 5611–5628. (19) Ghosh, A.; Vangberg, T.; Gonzalez, E.; Taylor, P. J. Porph. Phth. 2001, 5, 345–356. (20) Scherlis, D. A.; Estrin, D. A. Int. J. Quantum Chem. 2002, 87, 158– 166. (21) Ghosh, A.; Taylor, P. R. Curr. Opin. Chem. Biol. 2003, 7, 113– 124. (22) Fiolhais, C.; Nogueira, F.; Marques, M. A Primer in Density Functional Theory; Springer-Verlag: Berlin, 2003. (23) Jones, R. O.; Gunnarsson, O. ReV. Mod. Phys. 1989, 61, 689–746. (24) Perdew, J. P.; Savin, A.; Burke, K. Phys. ReV. A 1995, 51, 4531– 4541. (25) (a) Muramoto, K.; Hirata, K.; Shinzawa-Itoh, K.; Yoko-o, S.; Yamashita, E.; Aoyama, H.; Tsukihara, T.; Yoshikawa, S. Proc. Natl. Acad. Sci. USA. 2007, 104, 7881–7886. (b) The RCSB Protein Data Bank (PDB: http://www.pdb.org/), PDB ID 2eij. (26) (a) Codes used in the present work are based on Tokyo Ab initio Program Package (TAPP); (b) Yamauchi, J.; Tsukada, M.; Watanabe, S.; Sugino, O. Phys. ReV. B 1996, 54, 5586–5603. (c) Kageshima, H.; Shiraishi, K. Phys. ReV. B 1997, 56, 14985–14992. (d) Sugino, O.; Oshiyama, A. Phys. ReV. Lett. 1992, 68, 1858–1861. (27) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865–3868. (28) Becke, A. D. Phys. ReV. A 1988, 38, 3098–3100. (29) Perdew, J. P. Phys. ReV. B 1986, 33, 8822–8824. (30) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785–789. (31) Hamprecht, F. A.; Cohen, A. J.; Tozer, D. J.; Handy, N. C. J. Chem. Phys. 1998, 109, 6264–6271. (32) These DFT calculations have been conducted by using the CarrParrinello Molecular Dynamics code (CPMD, Copyright IBM Corp. 19902006, Copyright MPI fu¨r Festko¨rperforschung Stuttgart 1997-2001.). (33) Vanderbilt, D. Phys. ReV. B 1990, 41, 7892–7895. (34) To check convergence of the parameter, we have computed equilibrium structures of formamide, FeC2, and NFeO. The differences between our calculated results and the experimental and/or theoretical available data are 0.1-1.3%, assuring required accuracy in the present calculations.

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(35) The positions of five terminal H atoms and the H in the hydroxyl group have been kept fixed, according to the CcO crystal structure. (36) The geometry optimization has been performed until the forces become less than 5.1 × 10-2 eV/Å. During the calculations, the positions of the CR atom and four terminal H atoms of the imidazole ligands and the C and H atoms in the hydroxyl group have been kept fixed, in accordance with the CcO X-ray structure. (37) The present heme b model has been constructed on the basis of the X-ray structure of the bovine cytochrome b538 in a similar manner as in the case of the heme a. An orthorhombic supercell was obtained with the following sizes: a ) 16.75 Å, b ) 17.23 Å, and c ) 20.53 Å. The DFT calculations have been performed in the plane-wave basis set with a cutoff

Kamiya et al. energy of 80 Ry by using the PBE exchange-correlation functional and Troullier-Martins norm-conserving pseudopotentials. (38) (a) Durley, R. C.; Mathews, F. S. Acta. Crystallogr. Sect. D 1996, 52, 65–76. (b) The PDB ID is 1cyo. (39) The torsion angle around the CRsCβ bond in one of the propionates is-62° in heme b, while it is-173° in heme a. Regarding the orientation of the imidazole ligands, the plane defined by the axial imidazoles is parallel to the line C11sC20 of the porphyrin (in accordance with 1-24 IUPAC numbering nomenclature) in heme b, whereas they are perpendicular each other in heme a.

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