A Water Molecule Residing in the Fea33+···CuB2+ Dinuclear Center of the Resting Oxidized as-Isolated Cytochrome c Oxidase: A Density Functional Study.

Although the dinuclear center (DNC) of the resting oxidized "as-isolated" cytochrome c oxidase (CcO) is not a catalytically active state, its detailed structure, especially the nature of the bridging species between the Fea33+ and CuB2+ metal sites, is still both relevant and unsolved. Recent crystallographic work has shown an extended electron density for a peroxide type dioxygen species (O1-O2) bridging the Fea3 and CuB centers. In this paper, our density functional theory (DFT) calculations show that the observed peroxide type electron density between the two metal centers is most likely a mistaken analysis due to overlap of the electron density of a water molecule located at different positions between apparent O1 and O2 sites in DNCs of different CcO molecules with almost the same energy. Because the diffraction pattern and the resulting electron density map represent the effective long-range order averaged over many molecules and unit cells in the X-ray structure, this averaging can lead to an apparent observed superposition of different water positions between the Fea33+ and CuB2+ metal sites.

Introduction

Cytochrome c oxidase (CcO), located in the inner mitochondrial or bacterial membrane, is the terminal enzyme in the respiratory chain that reduces O2 to n>an class="Chemical">H2O and pumps protons across the membrane to create the chemiosmotic proton gradient used by ATP synthase to synthesize ATP.[1−5] The catalytic site of CcO that binds and reduces O2 by 4e–/4H+ transfer contains a heme a3 (Fea3) and a Cu (CuB) ion. Fea3 and CuB are close to each other (∼5 Å). This Fea3-CuB active site is usually called the dinuclear (or binuclear) center/complex (DNC or BNC). In all types of CcO molecules, the iron in the Fea3 site is coordinated to heme and an axial histidine ligand (His384; residue numbers in this paper are by default for ba3 CcO from Thermus thermophilus (Tt)), while the copper in the CuB site is coordinated to three histidine ligands: His233, His282, and His283. His233 covalently links to the Tyr237 side chain. This unique cross-linked tyrosine residue takes an important role in the processes of electron/proton transfer in CcO. There are two other redox centers also present in CcO. One is a homodinuclear Cu dimer (2CuA), which serves as the initial site of electron entry to CcO,[6,7] and the other is also a heme, which is heme A (Fea) in the case of the aa type of CcO or heme B (Feb) in the ba type of CcO. Electrons transfer from cytochrome c to CuA, then on to heme A/B, and from there to the DNC Fea3-CuB.[8,9] The DNC structures of aa3 and ba3 oxidases are nearly identical.

The oxidation, spin, and ligation states of the Fea3 and CuB sites change during the catalytic cycle. Starting from the binding of n>an class="Chemical">O2 with the reduced (R) DNC, several catalytic intermediates (see Figure ) have been well characterized by resonance Raman (rR) studies.[10−14] Very recently, we have calculated the Fea3–O/O–O stretching frequencies for several DNC intermediate states and compared them with the available rR data.[15] When molecular O2 binds with Fea32+, state A[Fea33+–O2•–···CuB+] is formed,[10−14,16,17] where Fea33+–O2•− is likely in a similar bent end-on geometry as in oxymyoglobin.[15,18−20] The following characterized states are P, F, and O. State P is not a peroxide-containing compound (as implied in the notation), but one in which the dioxygen O–O bond has already been cleaved.[21−25] It can be represented as P[Fea34+=O2–···OH––CuB2+]. State F[Fea34+=O2–···H2O–CuB2+] is then formed when the OH– ligand of CuB2+ in P receives a proton and becomes a water ligand. Our density functional calculations reproduced the rR observed ∼20 cm–1 shift of the Fea3–O stretching mode from state P[Fea34+=O2–···OH––CuB2+] to F[Fea34+=O2–···H2O–CuB2+].[15] Therefore, it is highly likely that the H2O ligand is still on the CuB2+ site in state F. On the basis of our energy calculations,[26] an F[Fea34+=O2–···CuB2+] state, where the H2O ligand has dissociated from the CuB2+ site and the O2– on Fea34+ also weakly binds with CuB2+, although not observed, may exist before the catalytically active form of the oxidized state O is formed by 1e–/1H+ reduction of Fea34+=O2– to Fea33+–OH–. A very low frequency Fea33+–OH– stretching mode at 450 cm–1 was observed in O, and our calculations have shown that this low Fe–O stretching mode can be produced by a nearly symmetrically bridged O[Fea33+–OH––CuB2+] structure with a relatively long Fea3–O distance near 2 Å.[15]

Figure 1

A, P, F, and O are the catalytic intermediates that are identified by resonance Raman (rR) experiments after O2 binding with Fea32+ in the reduced (R) state. Their DNCs are likely in the forms presented above. However, the resting “as-isolated” oxidized O state is different from the active O state.

pan class="Chemical">A, P, F, and O are the catalytic intermediates that are identified by resonance Raman (rR) expn>eriments n>an class="Disease">after O2 binding with Fea32+ in the reduced (R) state. Their DNCs are likely in the forms presented above. However, the resting “as-isolated” oxidized O state is different from the active O state.

It is interesting to note that the DNC structure of the resting “as-isolated” oxidized (O) state is difn>an class="Chemical">ferent from that of the active O state. O is a metastable catalytically active state, which decays to the relaxed lower-energy O state when a one-electron (1e–) transfer to the DNC in O is delayed (or absent) during redox cycling, just after cycling from R → O. Given sufficient time, O decays to O, which is the same as the isolated oxidized (“resting”) state. The differences between O and O were first seen in kinetics studies using optical difference spectroscopy and electrometry to examine the 1e– redox transitions O + 1e– → E in comparison to O + 1e– → E.[9,27] In the next step to regenerate R, one more electron is added to the active site, and a proton may move into the active site region to protonate an OH– (if needed). The observed kinetics of O → E is very different from that of O → E, and the first gives more efficient electron transfer, ending at CuB, and more effective proton transfer, for both ba3 and aa3 type enzymes. In the kinetic experiments, to generate state E from O, the 1e– added is injected after a timed laser flash, and the prior reaction cycle ending in state O is also started by a laser flash in the CO-inhibited R state,[28] synchronized with a pulse of molecular oxygen.[27] Overall, the full 2e– reduction of O → R is much slower than that of O → R.[29−31] It has also been found in aa3 that the reduction of O is coupled to proton translocation, while the reduction of O is not.[29−31] From these variations in kinetics, some significant structural differences between O and O are expected, but these specific differences are not at all evident. It has been a hot topic in the past 30 years and is still under debate which species bridges the Fea33+ and CuB2+ sites in the resting “as-isolated” O state, despite various spectral and structural analyses.[32−40]

The electron density between Fea3 and CuB in the as-isolated oxidized aa3 typn>e CcOs from n>an class="Species">Paracoccus denitrificans (Pd) and Rhodobacter sphaeroides (Rs) was originally interpreted as a H2O and an OH– ligand.[33,34] Later, on the basis of the high-resolution X-ray crystal structures of the oxidized CcO’s from Pd (PDB code 3HB3, 2.25 Å resolution)[35] and from bovine heart (PDB code 2ZXW, 1.95 Å resolution),[36] two research groups have independently proposed that a peroxide dianion (O22–) bridges the Fea3 and CuB in the DNC. Similarly, strong electron density for a peroxide type dioxygen species (O1–O2) bridging the Fea3 and CuB DNC was also observed in the high-resolution (1.8 Å) X-ray crystal structures (PDB entries 3S8G and 3S8F) of ba CcO from Tt (see Figure ).[37] Further, the peroxide type species in the resting oxidized DNC was also observed by the X-ray free-electron laser (XFEL) experiment (1.9 Å resolution).[38] Different groups reported slightly different O1–O2 distances of around 1.5–1.7 Å. Recently, Andersson et al. reported a radiation-damage-free oxidized ba3 CcO structure (2.3 Å resolution) at room temperature, in which a single hydroxide or a water molecule resides between the Fea3 and CuB sites.[39] However, the very recent low-dose high-energy X-ray data analysis on the oxidized-resting bovine heart CcO again showed the peroxide-type electron density between the Fea3 and CuB sites.[40]

Figure 2

Dinuclear center (DNC) of the X-ray crystal structure 3S8G of ba3 CcO from Thermus thermophilus (Tt).[37] (A) The electron density map adapted with permission from Figure 5 of ref (37). Copyright © 2011 Tiefenbrunn et al. (B) The ball and stick structure of this DNC in a different orientation.

Dinuclear center (pan class="Chemical">DNC) of the X-ray crystal structure 3S8G of n>an class="Chemical">ba3 CcO from Thermus thermophilus (Tt).[37] (A) The electron density map adapted with permission from Figure 5 of ref (37). Copyright © 2011 Tiefenbrunn et al. (B) The ball and stick structure of this DNC in a different orientation.

Theoretically, Kaila et al. proposed through their quantum chemical calculations that this bridging ligand in the resting oxidized DNC of n>an class="Species">bovine heart CcO is dioxygen (O2), which may be reduced to superoxide (O2•–) in the X-ray beam.[41] However, their calculated O–O distances of 1.29–1.32 Å for O2 or O2•– bridges are much shorter than the apparent O–O distances observed in the X-ray structures. Further, we are not aware of any experimental evidence favoring the presence of molecular oxygen (O2) between the oxidized Fe3+ and Cu2+ metal centers. If the affinity of O2 binding with Fe3+ and Cu2+ is low, the O–O species with high occupancy observed in the X-ray crystal structures cannot be molecular O2. We have therefore also performed density functional theory (DFT) calculations[42] on the ba3 CcO from Tt on the basis of the 3S8G(37) X-ray crystal structure with O22–, O2•–, HO2–, or H2O2 in the bridging position. These calculations have shown that the geometry optimized DNC structures with either O22– or O2•– as the bridging species would have large structural discrepancies in comparison with the X-ray crystal structure.[42] When H2O2 was put in between the Fea32+ and CuB+ sites (Fea33+ and CuB2+ metal sites were assumed to be reduced in the X-ray beam),[37] the O–O bond broke during the geometry optimizations regardless of the spin state of Fea32+.[42] Also, it is well-known experimentally that, in the oxidized resting O state in ba3, the dinuclear center is closed and reacts only very slowly with Fea3 ligands, including H2O2. (The aa3 enzyme shows more access to H2O2 in state O.) The dinuclear site in ba3 only opens up for binding of H2O2 and reaction after a single-electron photoactivated injection into the enzyme.[43,44] The presence then of H2O2 or related species within the active site of the oxidized resting O state in ba3 would be unexplained, aside from possible radiation-induced reactions.

Finally, our previous calculations indicated that the O1–n>an class="Chemical">O2 species observed in the DNC of the X-ray crystal structure was best represented as HO2–, which may be a product of the photoreaction of the H2O/OH– ligands with 2e– transfer to the adjacent oxidized Fea33+ and CuB2+ sites in the X-ray beam.[42] However, in evaluating the most likely and unlikely physical explanation for the observed electron density map, we need to take into account that the operating physical mechanism will produce atomic structures that represent both a spatial and time average over billions of enzyme molecules. While some effects due to the X-ray irradiation may be observable with careful attention to the time course, these effects are not likely to be dominant when they are averaged over billions of structural sites. Indeed, as we now show in the Results and Discussion, our current calculations demonstrate that the Fea33+–H2O···OH––CuB2+/Fea33+−OH–···H2O–CuB2+ type structures are also unlikely to represent the resting state of the DNC, and the observed O1–O2 peroxide type electron density between the two metal centers is most likely the overlap of electron densities of single water molecules positioned somewhere between O1 and O2 in different DNCs with almost the same energy. The effective electron density averaging occurs because of the long-range averaging over molecular subunits in Fourier (reciprocal) space converted back to real coordinate space (Cartesian space).

Calculation Methods

The starting geometries of the pan class="Chemical">DNC model clusten>an class="Species">rs studied in this paper were established on the basis of the Cartesian coordinates of the ba3 CcO X-ray crystal structure 3S8G.[37] All calculations were performed using the DFT dispersion-corrected OLYP-D3(BJ)[45] functional implemented within the ADF2017 software package.[46−48] Goerigk et al. assessed 217 variations of dispersion-corrected and -uncorrected density functional approximations and carried out a detailed analysis to identify reliable approaches based on the analysis of the GMTKN55 benchmark database for general main-group thermochemistry, kinetics, and noncovalent interactions.[49] Their studies have shown that OLYP-D3(BJ) is one of the best three GGA functionals overall, outperforming all dispersion-corrected meta-GGAs except for SCAN-D3(BJ).[49]

Our geometry optimization calculations were performed using the broken-symmetry[50−52]/OLYpan class="Chemical">P-D3(BJ)[45]/TZn>an class="Chemical">P plus COSMO[15,26,53−56] solvation model methodology. The inner cores of C(1s), N(1s), and O(1s) were treated by the frozen core approximation.

Starting from the active O[pan class="Chemical">Fea33+–OH––n>an class="Chemical">CuB2+] state model, we will examine whether there are H2O/OH– ligands or a H2O molecule between the Fea33+ and CuB2+ sites in the resting as-isolated O state through energetic and pKa calculations. The whole structure of our DNC model for the O state is shown in Figure . For a clearer view, the top portion of this cluster is shown in Figure I, and the central Fea33+–OH––CuB2+ part of the model is given in Figure II. In our O model, the bridging OH– is H-bonding with a water molecule, which originates from the H2O ligand of CuB in the prior state F.

Figure 3

Our whole DNC model for state O. Clearer views for both the top cluster and the central Fea33+–OH––CuB2+ portion of the model are given in Figure I,II, respectively.

Figure 4

A closer look at the top (I) and the central (II–VIII) portions of the DNC model clusters studied here (see Table ). The rest of each model is similar to what was shown in Figure . Legend: (II) O[Fea33+–OH––CuB2+] state; (III) Fea33+–H2O···OH––CuB2+ model state; (IV) Fea33+–OH–···H2O–CuB2+ model state; (V) Fea33+–H2O–CuB2+(a); (VI) Fea33+–H2O–CuB2+(b); (VII) Fea33+–H2O–CuB2+(c); (VIII) Fea33+–H2O–CuB2+(d). Note that structures V–VIII are four major optimized structures (see the Results and Discussion and Table ) with very similar energies obtained by protonating the bridging OH– ligand in O[Fea33+–OH––CuB2+] (model II).

Our whole pan class="Chemical">DNC model for state O. Clearer views for both the topn> cluster and the central n>an class="Chemical">Fea33+–OH––CuB2+ portion of the model are given in Figure I,II, respectively.

A closer look at the top (I) and the central (II–VIII) portions of the pan class="Chemical">DNC model clusten>an class="Species">rs studied here (see Table ). The rest of each model is similar to what was shown in Figure . Legend: (II) O[Fea33+–OH––CuB2+] state; (III) Fea33+–H2O···OH––CuB2+ model state; (IV) Fea33+–OH–···H2O–CuB2+ model state; (V) Fea33+–H2O–CuB2+(a); (VI) Fea33+–H2O–CuB2+(b); (VII) Fea33+–H2O–CuB2+(c); (VIII) Fea33+–H2O–CuB2+(d). Note that structures V–VIII are four major optimized structures (see the Results and Discussion and Table ) with very similar energies obtained by protonating the bridging OH– ligand in O[Fea33+–OH––CuB2+] (model II).

Table 1

OLYP-D3(BJ) Calculated Geometrical, Energetic, and Net Spin Properties of the Optimized DNC Clusters in Fea3HS,3+–OH––CuB2+, Fea3HS,3+–H2O···OH––CuB2+, Fea3HS,3+–OH–···H2O–CuB2+, and Fea3HS,3+–H2O–CuB2+ Statesa

	geometry (Å)								net spinf
structureb	Fe–N(H384)	Fe–O	Cu–O	O···O	Fe···Cu	Ec	Qd	pKa(H2O)e	Fea3	O(Fe)/O(Cu)	CuB	Y237
Fea3HS,3+–OH––CuB2+	2.50	1.99	2.04		3.73	0.0	0		4.08	0.12	–0.39	–0.25
Fea3HS,3+–H2O···OH––CuB2+	2.18	2.17	1.95	2.50	4.78	6.3	0		4.08	0.08/–0.16	–0.50	0.11
Fea3HS,3+–OH–···H2O–CuB2+	2.28	1.98	2.13	2.45	4.64	6.6	0		4.12	0.20/–0.03	–0.39	–0.36
Fea3HS,3+–H2O–CuB2+(a)	2.11	2.39	2.94		4.98	–1.5	1	12.1	4.11	0.04	–0.24	–0.62
Fea3HS,3+–H2O–CuB2+(b)	2.12	2.47	2.77		4.90	–1.6	1	12.2	4.10	0.04	–0.25	–0.61
Fea3HS,3+–H2O–CuB2+(c)	2.06	3.55	2.21		4.73	–1.2	1	11.9	4.06	–0.01	–0.36	–0.36
Fea3HS,3+–H2O–CuB2+(d)	2.09	3.26	2.20		4.73	–0.9	1	11.7	4.09	–0.02	–0.35	–0.44
3S8Gg	2.22	2.39	2.25	1.52	4.92

See Figure .

Geometries were optimized in the broken-symmetry state with high-spin (HS) Fea33+ AF-coupled to the CuB2+ site.

Calculated broken-symmetry state energies (offset by −26336.6 kcal mol–1).

The net charge of the model clusters.

The pKa(H2O) values were calculated for the process Fea3HS,3+–OH––CuB2+ → Fea3HS,3+–H2O–CuB2+(a–d).

The Mulliken net spin populations on Fea33+, O of the bridging OH–/H2O, CuB2+, and the heavy atoms of the Tyr237–O– side chain (the sum total).

The X-ray crystal structure.[37]

When each model is constructed from the X-ray crystal structure 3S8G,[37] the Cα atoms of Tyr237, n>an class="Chemical">His233, His282, His283, Asp372, His376, and His384 are each replaced with a link H atom along the original Cβ–Cα direction with a Cβ–Hlink distance of 1.09 Å. The Cβ of Arg449 and C228 of the geranyl side chain of the a3-heme are also replaced with a Hlink atom. During the geometry optimizations, except for the Hlink atom on the geranyl side chain of the a3-heme, the positions of all other Hlink atoms are fixed. Note that, in order to avoid the energy difference caused by the different H-bonding patterns, the two water molecules HOH604 and HOH608 above the O1–O2 species found in the 3S8G X-ray crystal structure are not included in our current models. We have geometry-optimized our DNC model clusters with the Fea33+ site in different spin states (low spin, intermediate spin, and high spin). Our calculations show that the intermediate-spin-Fea33+ state is generally lower in energy than the corresponding high-spin-Fea33+ state for each model cluster studied here. However, the rR and EPR experimental data suggest that the Fea33+ is high spin in both the active O and the resting O states.[5,57] One needs more experimental data and higher-level theoretical calculations to determine whether different spin states of Fea33+ can coexist in the O and the resting O states. In fact, the existence of intermediate-/low-spin-Fea3 states in the resting O DNCs may be temperature-dependent, since Mössbauer spectroscopy experiments on Tt ba3(58) and c1aa3(59) have shown the coexistence of different high-spin and “low-spin” (which might also be intermediate-spin according to the isomer shift and quadrupole splitting values) Fea33+ species at very low temperature (4.2 K), and the “low-spin” Fea33+ species changes to high spin as the temperature is increased above 190 K.[58] These spin states may exhibit spin crossover, which depends on a sensitive balance between the respective energies and entropies. For simplicity, we will present our calculated results in which the high-spin (HS) Fea33+ site is antiferromagnetically (AF) coupled with the CuB2+ site and put the results of the intermediate- and low-spin-Fea33+ states in the Supporting Information. Note that all conclusions we find for the HS-Fea33+ states in the following section will remain the same if the Fea33+ is in the intermediate-spin state.

Results and Discussion

Our calculated energies and the main geometric and Mulliken net spin population properties of the geometry-optimized O[Fea3HS,3+–OH–n>an class="Chemical">CuB2+] state and the possible O[Fea3HS,3+–H2O···OH––CuB2+] and O[Fea3HS,3+–OH–···H2O–CuB2+] states are given in the first three rows of Table . The central portions of the Fea3HS,3+–H2O···OH––CuB2+ and Fea3HS,3+–OH–···H2O–CuB2+ DNC clusters are given in Figure III,IV, respectively. The net spin populations from Mulliken population analysis are the main indication of the spin state for the Fea33+ site. In the ideal ionic limit, the net unpaired spin populations for HS-Fea33+ and CuB2+ are 5 and 1, respectively. However, because of the metal–ligand covalency, the calculated net spin magnitudes for the Fea33+ and CuB2+ sites are smaller than their corresponding ionic limits. The opposite signs for the spin densities of Fea33+ and CuB2+ sites indicate the AF coupling. Our calculated net spins on Fea33+ and CuB2+ show that we obtained the HS-Fea33+ AF-coupled to the CuB2+ state for each cluster.

Geometries were optimized in the broken-symmetry state with high-spin (HS) pan class="Chemical">Fea33+ n>an class="Disease">AF-coupled to the CuB2+ site.

The net charge of the model clustepan class="Species">rs.

The pKa(pan class="Chemical">H2O) values were calculated for the process n>an class="Chemical">Fea3HS,3+–OH––CuB2+ → Fea3HS,3+–H2O–CuB2+(a–d).

The Mulliken net spin populations on pan class="Chemical">Fea33+, O of the bridging OH–/n>an class="Chemical">H2O, CuB2+, and the heavy atoms of the Tyr237–O– side chain (the sum total).

O is a metastable catalytically active state, which decays to the relaxed O state when no electron transpan class="Chemical">fen>an class="Species">rs to the DNC. Therefore, state O is lower in energy than O. However, our calculations show that both the Fea3HS,3+–H2O···OH––CuB2+ and Fea3HS,3+–OH–···H2O–CuB2+ states are higher in energy (by >6 kcal mol–1) than the Fea3HS,3+–OH–CuB2+ state. Further, the O···O distances (∼2.5 Å) in Fea3HS,3+–H2O···OH––CuB2+ and Fea3HS,3+–OH–···H2O–CuB2+ structures are ∼1 Å longer than the apparent O1–O2 distance found from the 3S8G X-ray crystal structure (see the last row of Table ). Therefore, the DNC of the resting as-isolated O state is not likely in the Fea3HS,3+–H2O···OH––CuB2+ or the Fea3HS,3+–OH–···H2O–CuB2+ form.

Next, we examine whether a pan class="Chemical">water molecule is pren>an class="Chemical">ferred residing between the Fea33+ and CuB2+ sites in the as-isolated O state. We then protonated the bridging OH– in the state O[Fea33+–OH––CuB2+], kept the H-bonding H2O molecule, and optimized the structure. We find that, by modification of the position of the proton added to the bridging OH– or the orientation of the H-bonding H2O molecule, the geometry optimizations will end in different minima with different Fe–O, Cu–O, and Fe···Cu distances, but with very similar energies. The central Fea3HS,3+–H2O–CuB2+ structures of four major optimized geometries (a–d) are shown in Figure V–VIII, and their main bond distances and energies are given in rows 4–7 of Table .

In the optimized structure Fea3HS,3+–n>an class="Chemical">H2O–CuB2+(a) (Figure .V), the H2O molecule binds with the Fea33+ site with Fe-O distance of 2.39 Å. In Fea3HS,3+–H2O–CuB2+(b) (Figure VI), the H2O molecule is in between Fea33+ and CuB2+ and does not bind with either site (with Fe–O and Cu–O distances of 2.47 and 2.77 Å, respectively). Although structurally different, both structures are essentially at the same energy. In structures Fea3HS,3+–H2O–CuB2+(c) (Figure VII) and Fea3HS,3+–H2O–CuB2+(d) (Figure VIII), the H2O molecule binds with the CuB site (with Cu–O distances of 2.21 and 2.20 Å, respectively) in different orientations. In Fea3HS,3+–H2O–CuB2+(c), the H2O molecule tilts up and has an H-bonding interaction with one of the N atoms of the heme ring; in Fea3HS,3+–H2O–CuB2+(d), however, the H2O simply moves closer to CuB2+ starting from the bridging position. Fea3HS,3+–H2O–CuB2+(c) and Fea3HS,3+–H2O–CuB2+(d) also have nearly the same energy. In fact, all four Fea3HS,3+–H2O–CuB2+(a–d) structures are close in energy, with a maximum difference of 0.7 kcal mol–1. Since these four structures have one more proton than the O[Fea3HS,3+–OH––CuB2+] state, in order to compare the energetic stabilities, we calculated the pKa of the H2O molecules in the four Fea3HS,3+–H2O–CuB2+(a–d) structures using the equation[26,42,60,61]where E(A–) and E(AH) are the calculated total energies of the deprotonated (A–, here O[Fea3HS,3+–OH––CuB2+]) and protonated (AH, here the four Fea3HS,3+–H2O–CuB2+(a–d)) states. In ADF, the “total energy” of the system is defined relative to a sum of atomic fragments (spherical spin-restricted atoms). The calculated gas-phase energy of a proton E(H+) is therefore relative to a spin-restricted hydrogen atom. ΔGsol(H+,1 atm) is the solvation free energy of a proton at 1 atm pressure. We use the “best available” experimental value of –264.0 kcal mol–1 for this term, on the basis of an analysis of cluster-ion solvation data.[62−65] For E(H+), here we take the empirically corrected values 293.1 kcal mol–1 (i.e., 12.71 eV) for OLYP based on experimental standard hydrogen electrode energy and the proton solvation free energy (see Appendix in ref (60)). The translational entropy contribution to the gas-phase free energy of a proton is taken as –TΔSgas(H+) = –7.8 kcal mol–1 at 298 K and 1 atm pressure.[66] (5/2)RT = 1.5 kcal mol–1 includes the proton translational energy (3/2)RT and PV = RT.[66] The term ΔZPE is the zero-point energy difference for the deprotonated state (A–) minus the protonated state (AH), and it was estimated as ΔZPE = −7.7 kcal mol–1 for OH–/H2O by only optimizing the geometries (and then performing frequency calculations) of an OH– and an H2O molecule within the COSMO solvation model.

The calculated pKas of the pan class="Chemical">H2O molecule in each of the n>an class="Chemical">Fea3HS,3+–H2O–CuB2+(a–d) states are also given in Table . They are between 11.7 and 12.2, indicating that the Fea3HS,3+–H2O–CuB2+(a–d) states are energetically much more stable than the O[Fea3HS,3+–OH––CuB2+] state. We therefore speculate that it is a water molecule between the Fea33+ and CuB2+ sites in the resting as-isolated O state. However, an extended electron density, which was interpreted as a dioxygen molecule, was observed between Fea33+ and CuB2+ in the DNC of the X-ray crystal structures.[35−37] Since our initial geometries of our DNC model structures are constructed on the basis of the Cartesian coordinates of the X-ray crystal structure 3S8G,[37] to compare our optimized structures Fea3HS,3+–H2O–CuB2+(a–d) with 3S8G, we superimpose the Cartesian coordinates of the central portions of the five structures together. The overlapped structures are shown in Figure with two orientations: A and B. The colors of the atoms in the different structures are as follows: 3S8G, silver; Fea3HS,3+–H2O–CuB2+(a), orange; Fea3HS,3+–H2O–CuB2+(b), purple; Fea3HS,3+–H2O–CuB2+(c), blue; Fea3HS,3+–H2O–CuB2+(d), green.

Figure 5

Overlap of the central portions of the following DNC structures (see Table ): silver, 3S8G X-ray crystal structure; orange, Fea3HS,3+–H2O–CuB2+(a); purple, Fea3HS,3+–H2O–CuB2+(b); blue, Fea3HS,3+–H2O–CuB2+(c); and green, Fea3HS,3+–H2O–CuB2+(d). (A) and (B) are the views of this overlap from two different angles. For clarity, the H-bonding water molecules and the hydrogen atoms are not shown.

Overlap of the central portions of the following pan class="Chemical">DNC structures (see Table ): n>an class="Chemical">silver, 3S8G X-ray crystal structure; orange, Fea3HS,3+–H2O–CuB2+(a); purple, Fea3HS,3+–H2O–CuB2+(b); blue, Fea3HS,3+–H2O–CuB2+(c); and green, Fea3HS,3+–H2O–CuB2+(d). (A) and (B) are the views of this overlap from two different angles. For clarity, the H-bonding water molecules and the hydrogen atoms are not shown.

During our geometry optimizations, the CuB site and its ligands move slightly more than the heme-n>an class="Chemical">Fea3 site. Now focusing on the positions of the central oxygen atoms, we do see that the four O atoms in the optimized structures align with the 3S8G O1–O2 directions very well. The orange and purple O atoms are close to the O1 position in 3S8G, the blue O atom is near O2, and the green O atom is in about the middle between O1 and O2. This supports our proposal that the electron density around O1–O2 in the X-ray crystal structures represents the overlap of the electron density of one water molecule that is in different positions along O1–O2 in different CcO molecules in a crystal.

For clarity, the pan class="Chemical">water molecule that has an H-bonding interaction with the ligand n>an class="Chemical">H2O in each of the four geometry-optimized structures is not shown in Figure . In 3S8G, a water molecule (HOH608) was seen 3.01 Å above the position of O2. Therefore, HOH608 may have an H-bonding interaction with the H2O ligand in a position as in Fea33+–H2O–CuB2+(c) (Figure VII). No other H2O molecules were identified within the H-bonding distances around O1–O2 in 3S8G. This means that not all CcO molecules in the crystal have an H2O molecule H-bonding to the H2O ligand, and even if there is an H-bonding H2O molecule in some of the CcO DNCs, the H-bonding patterns and the positions of the H-bonding H2O molecules may differ; therefore, they may not be identified in the X-ray crystal structure.

Since it is not clear whether there is an H-bonding pan class="Chemical">H2O molecule in the n>an class="Chemical">DNC of the O state, we removed the H-bonding H2O from the Fea3HS,3+–H2O–CuB2+(a–d) structures and optimized the geometries again. The central portions of the corresponding optimized structures (S) are given as S1–S4 in Figure , respectively. Their main bond distances and the calculated energies are given in Table .

Figure 6

Structures (S) S1–S4 (see Table ): the central portions of the optimized geometries after removing the H-bonding H2O molecule from the Fea3HS,3+–H2O–CuB2+(a–d) structures (see Figure V–VIII). S5 is a constrained geometry optimized structure with a fixed Fe–O distance at 2.39 Å. (A) and (B) show the overlap of S1–S5 with the X-ray crystal structure 3S8G in two different viewing angles (see also Figure ).

Table 2

Geometry Optimized Fea3HS,3+–H2O–CuB2+ DNC Structures and Energies, in Which No Water Molecule H-Bonding to the H2O Liganda

	distance (Å)
structureb	Fe–O	Cu–O	Fe···Cu	Ec (kcal/mol)
S1	2.61	2.82	5.03	1.4
S2	2.97	2.52	4.98	0.3
S3	3.54	2.29	4.76	0.0
S4	3.07	2.41	4.87	0.6
S5d	2.39	2.81	4.91	0.8

See Figures and 7.

Geometries (S1–S5) were optimized in the broken-symmetry state with high-spin Fea33+ AF-coupled to the CuB2+ site.

Calculated broken-symmetry state energies (offset by –26004.7 kcal mol–1). Note that Fea33+ and CuB2+ are very weakly coupled. The F-coupled calculations on these structures yield essentially the same energy as the corresponding broken-symmetry state.

The Fe–O distance was fixed at 2.39 Å during this geometry optimization.

Figure 7

Overlap of the structures S1–S5 (also see Table and Figure ) with the electron density map that was reconstructed from the X-ray crystal structure 3S8G data file.

Geometries (S1–S5) were optimized in the broken-symmetry state with high-spin pan class="Chemical">Fea33+ n>an class="Disease">AF-coupled to the CuB2+ site.

Calculated broken-symmetry state energies (offset by –26004.7 kcal mol–1). Note that pan class="Chemical">Fea33+ and n>an class="Chemical">CuB2+ are very weakly coupled. The F-coupled calculations on these structures yield essentially the same energy as the corresponding broken-symmetry state.

The pan class="Chemical">Fe–O distance was fixed at 2.39 Å during this geometry opn>timization.

Structures (S) S1–S4 (see Table ): the central portions of the optimized geometries pan class="Disease">after removing the H-bonding n>an class="Chemical">H2O molecule from the Fea3HS,3+–H2O–CuB2+(a–d) structures (see Figure V–VIII). S5 is a constrained geometry optimized structure with a fixed Fe–O distance at 2.39 Å. (A) and (B) show the overlap of S1–S5 with the X-ray crystal structure 3S8G in two different viewing angles (see also Figure ).

Without the H-bonding pan class="Chemical">H2O molecule, the binding of the n>an class="Chemical">H2O ligand with the two metal sites, especially with the Fea33+ site, are weakened. For instance, from Fea3HS,3+–H2O–CuB2+(a) to S1, the H2O dissociates from the Fea33+ site (from an Fe–O distance of 2.39 Å) and moves to about the middle between Fea33+ and CuB2+ (Fe–O, 2.61 Å; Cu–O, 2.82 Å). S1 has the longest calculated Fea33+ and CuB2+ distance of 5.03 Å. S3 differs from the Fea3HS,3+–H2O–CuB2+(c) structure with slightly elongated Cu–O and Fe–Cu distances. S2 and S4 look very similar and have almost the same energy, but with different Fe–O, Cu–O, and Fe–Cu distances. The calculated energies among S2–S4 are within 1 kcal mol–1. Although S1 has the highest calculated energy, it is only 1.4 kcal mol–1 higher than S3. Further, to see how high the energy would be if the H2O molecule is close to the Fea33+ site as in the structure Fea3HS,3+–H2O–CuB2+(a), we reoptimized the geometry of S1 with a fixed Fe–O distance at 2.39 Å. The constraint optimized structure is also shown in Figure as S5, and its geometric and energetic properties are also given in Table . It turned out that the calculated energy of S5 is very close to those of S2 and S4 and is only 0.8 kcal mol–1 higher than that of S3. Because of the very similar energies, in principle, the structures S1–S5 may coexist in the DNCs of different CcO molecules.

Similar to the case for Figure , in Figure A,B, we have also shown the overlap of the pan class="Chemical">DNCs of S1–S5 and the X-ray crystal structure 3S8G in two difn>an class="Chemical">ferent viewing angles. The colors of the atoms in different structures are as follows: 3S8G, silver; S1, orange; S2, purple; S3, blue; S4, green; S5, red. In the overlap structure, the H2O molecules in S1 and S5 are in the vicinity of the O1 position in 3S8G, the H2O in S3 is close to the position of O2, and the H2O molecules in S2 and S4 are located between O1 and O2. The same overlap structure is also shown in Figure , where the electron density map is reconstructed from the 3S8G data file. Again, this supports the proposal that in the resting O state the H2O molecule may reside at different positions along the O1–O2 direction between the Fea33+ and CuB2+ sites in different enzyme molecules.

Further, although the structures and energies for pan class="Chemical">Fea3HS,3+–n>an class="Chemical">H2O–CuB2+(a–d) and S1–S5 given in Tables and 2 are obtained from broken-symmetry state calculations in which the HS-Fea33+ is AF-coupled to CuB2+, the coupling between the HS-Fea33+ and CuB2+ sites appears to be very weak. Our Fea3HS,3+-CuB2+ ferromagnetically coupled (F-coupled) calculations show that each of these structures also represents an optimization-converged geometry in the F-coupled state with essentially the same energy as the corresponding broken-symmetry state. Therefore, both Fea3HS,3+-CuB2+ AF-coupled and F-coupled configurations of the DNCs may coexist in the resting O state.

Conclusions

Starting from the O[pan class="Chemical">Fea33+–OH––n>an class="Chemical">CuB2+] DNC structure of the active oxidized state CcO, where a hydroxo bridges the Fea33+ and the CuB2+ sites, we have studied the feasible DNC structures of the resting as-isolated oxidized O state. Our calculations show that the O state is not likely in the Fea33+–H2O···OH––CuB2+ or the Fea33+–OH–···H2O–CuB2+ forms, where an H2O/OH– binds with Fea33+/CuB2+ and the H2O and OH– ligands H-bond with each other, since both the Fea33+–H2O···OH––CuB2+ and the Fea33+–OH–···H2O–CuB2+ structures are higher in energy than the O[Fea33+–OH––CuB2+] state. Also, the structures of these metal bridging OH–···H2O systems show O···O distances in poor agreement with the X-ray structures of ba3 and aa3 CcOs. Further, our pKa calculations show that the bridging OH– ligand in the O[Fea33+–OH––CuB2+] state energetically prefers to be protonated at neutral pH. We therefore propose that a water molecule is between the Fea33+ and CuB2+ sites in the resting O state of CcO. Our calculations further suggest that the H2O molecule can bind with either the Fea33+ or the CuB2+ site or it can stay at various positions between the Fea33+ and CuB2+ sites with very similar energies, depending on the Fea33+–CuB2+ distance and whether or not this H2O molecule has an H-bonding interaction with another H2O molecule.

The X-ray crystal structures of the oxidized CcOs from Pd (3HB3),[35] from n>an class="Species">bovine heart (2ZXW),[36] and from Tt (3S8G and 3S8F)[37] all show that there is strong electron density for a dioxygen type species (O1–O2) bridging the Fea33+ and CuB2+ in the O state. In a crystal structure with ∼1.9 Å resolution, it is actually not possible to tell if the ∼1.5 Å apart O–O species is due to overlapping water molecules or a peroxide, as both models would produce very similar overlapping densities in comparison to the experimental electron density map. Since our initial DNC model structures were constructed on the basis of the Cartesian coordinates of the X-ray crystal structure 3S8G, we then superimposed the 3S8G DNC with several of our geometry-optimized O[Fea33+–H2O–CuB2+] structures that have different H2O positions between Fea33+ and CuB2+ and have very similar calculated energies. The overlap structures show that the H2O molecules lie between and along the O1–O2 direction in 3S8G. There are billions of CcO molecules in the crystal, and the water molecule may occupy one equilibrium position at a given time in a given DNC but different ones at other times or in other DNCs. The positions of the different water molecules may be “locked” after the crystal is rapidly frozen (normally at 100 K). However, even at 100 K, the atoms and the water molecules vibrate around their equilibrium positions. The atomic positions obtained from X-ray diffraction analysis are the averages of billions of unit cells over both time and space. Both dynamic and static disorder comparing DNCs in different CcO molecules will contribute to the X-ray structure. We therefore propose that the extended electron density between Fea33+ and CuB2+ observed in the X-ray crystal structures is the overlap of the electron density of a water molecule located at different positions in different CcO molecules in the crystals.

The change in protonation state and structure from state O to O leads to large difpan class="Chemical">ferences in the electron and proton transn>an class="Chemical">fer kinetics for the two different subsequent reaction pathways, O → E → R in comparison to O → O → E → R, with the sequence of 1e– and 1H+ transfers to the reactive oxidized Fea33+–OH––CuB2+ complex switched. The new structural analysis of state O in comparison to O provides a foundation for further exploration of these differences in kinetics.