A Water Molecule Residing in the Fe_a3³⁺···Cu_B Dinuclear Center of the Resting Oxidized as-Isolated Cytochrome c Oxidase: A Density Functional Study

Abstract

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 Fe_a3³⁺ and Cu_B 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 Fe_a3 and Cu_B 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 Fe_a3³⁺ and Cu_B metal sites.

Short abstract

X-ray crystal structures have shown an extended electron density for a dioxygen species (O1−O2) bridging the Fe_a3 and Cu_B centers of the oxidized resting state of cytochrome c oxidase (CcO). Our current DFT calculations show that the observed peroxide type electron density is most likely an overlap of the electron density of a water molecule located at different positions between O1 and O2 in different CcO molecules with almost the same energy.

1. 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 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 (Fe_a3) and a Cu (Cu_B) ion. Fe_a3 and Cu_B are close to each other (∼5 Å). This Fe_a3-Cu_B active site is usually called the dinuclear (or binuclear) center/complex (DNC or BNC). In all types of CcO molecules, the iron in the Fe_a3 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 Cu_B 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 (2Cu_A), which serves as the initial site of electron entry to CcO,^6,7 and the other is also a heme, which is heme A (Fe_a) in the case of the aa₃ type of CcO or heme B (Fe_b) in the ba₃ type of CcO. Electrons transfer from cytochrome c to Cu_A, then on to heme A/B, and from there to the DNC Fe_a3-Cu_B.^8,9 The DNC structures of aa₃ and ba₃ oxidases are nearly identical.

The oxidation, spin, and ligation states of the Fe_a3 and Cu_B sites change during the catalytic cycle. Starting from the binding of O₂ with the reduced (R) DNC, several catalytic intermediates (see Figure 1) have been well characterized by resonance Raman (rR) studies.¹⁰⁻¹⁴ Very recently, we have calculated the Fe_a3–O/O–O stretching frequencies for several DNC intermediate states and compared them with the available rR data.¹⁵ When molecular O₂ binds with Fe_a3²⁺, state A[Fe_a3–O₂^•–···Cu_B⁺] is formed,^{10−14,16,17} where Fe_a3–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_H. 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[Fe_a3⁴⁺=O^2–···OH^––Cu_B²⁺]. State F[Fe_a3=O^2–···H₂O–Cu_B²⁺] is then formed when the OH^– ligand of Cu_B in P receives a proton and becomes a water ligand. Our density functional calculations reproduced the rR observed ∼20 cm^–1 shift of the Fe_a3–O stretching mode from state P[Fe_a3⁴⁺=O^2–···OH^––Cu_B] to F[Fe_a3⁴⁺=O^2–···H₂O–Cu_B].¹⁵ Therefore, it is highly likely that the H₂O ligand is still on the Cu_B²⁺ site in state F. On the basis of our energy calculations,²⁶ an F_H[Fe_a3=O^2–···Cu_B²⁺] state, where the H₂O ligand has dissociated from the Cu_B site and the O^2– on Fe_a3⁴⁺ also weakly binds with Cu_B, although not observed, may exist before the catalytically active form of the oxidized state O_H is formed by 1e^–/1H⁺ reduction of Fe_a3⁴⁺=O^2– to Fe_a3–OH^–. A very low frequency Fe_a3³⁺–OH^– stretching mode at 450 cm^–1 was observed in O_H, and our calculations have shown that this low Fe–O stretching mode can be produced by a nearly symmetrically bridged O_H[Fe_a3–OH^––Cu_B²⁺] structure with a relatively long Fe_a3–O distance near 2 Å.¹⁵

Figure 1.

A, P, F, and O_H are the catalytic intermediates that are identified by resonance Raman (rR) experiments after O₂ binding with Fe_a3²⁺ 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_H state.

It is interesting to note that the DNC structure of the resting “as-isolated” oxidized (O) state is different from that of the active O_H state. O_H 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_H is delayed (or absent) during redox cycling, just after cycling from R → O_H. Given sufficient time, O_H decays to O, which is the same as the isolated oxidized (“resting”) state. The differences between O and O_H were first seen in kinetics studies using optical difference spectroscopy and electrometry to examine the 1e^– redox transitions O_H + 1e^– → E_H 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_H → E_H is very different from that of O → E, and the first gives more efficient electron transfer, ending at Cu_B, and more effective proton transfer, for both ba₃ and aa₃ type enzymes. In the kinetic experiments, to generate state E_H from O_H, the 1e^– added is injected after a timed laser flash, and the prior reaction cycle ending in state O_H 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_H → R.²⁹⁻³¹ It has also been found in aa₃ that the reduction of O_H 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_H 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 Fe_a3³⁺ and Cu_B sites in the resting “as-isolated” O state, despite various spectral and structural analyses.³²⁻⁴⁰

The electron density between Fe_a3 and Cu_B in the as-isolated oxidized aa₃ type CcOs from 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 (O₂^2–) bridges the Fe_a3 and Cu_B in the DNC. Similarly, strong electron density for a peroxide type dioxygen species (O1–O2) bridging the Fe_a3 and Cu_B DNC was also observed in the high-resolution (1.8 Å) X-ray crystal structures (PDB entries 3S8G and 3S8F) of ba₃ CcO from Tt (see Figure 2).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 Fe_a3 and Cu_B 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 Fe_a3 and Cu_B 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.

Theoretically, Kaila et al. proposed through their quantum chemical calculations that this bridging ligand in the resting oxidized DNC of 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) calculations⁴² on the ba₃ CcO from Tt on the basis of the 3S8G(37) X-ray crystal structure with O₂^2–, O₂^•–, HO₂^–, or H₂O₂ in the bridging position. These calculations have shown that the geometry optimized DNC structures with either O₂^2– 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 Fe_a3²⁺ and Cu_B sites (Fe_a3³⁺ and Cu_B 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 Fe_a3²⁺.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 Fe_a3 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–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 Fe_a3³⁺ and Cu_B 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 Fe_a3³⁺–H₂O···OH^––Cu_B/Fe_a3³⁺−OH^–···H₂O–Cu_B 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).

2. Calculation Methods

The starting geometries of the DNC model clusters 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-symmetry⁵⁰⁻⁵²/OLYP-D3(BJ)⁴⁵/TZP 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_H[Fe_a3³⁺–OH^––Cu_B] state model, we will examine whether there are H₂O/OH^– ligands or a H₂O molecule between the Fe_a3³⁺ and Cu_B sites in the resting as-isolated O state through energetic and pK_a calculations. The whole structure of our DNC model for the O_H state is shown in Figure 3. For a clearer view, the top portion of this cluster is shown in Figure 4I, and the central Fe_a3³⁺–OH^––Cu_B part of the model is given in Figure 4II. In our O_H model, the bridging OH^– is H-bonding with a water molecule, which originates from the H₂O ligand of Cu_B in the prior state F.

Figure 3.

Our whole DNC model for state O_H. Clearer views for both the top cluster and the central Fe_a3³⁺–OH^––Cu_B portion of the model are given in Figure 4I,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 1). The rest of each model is similar to what was shown in Figure 3. Legend: (II) O_H[Fe_a3³⁺–OH^––Cu_B] state; (III) Fe_a3³⁺–H₂O···OH^––Cu_B model state; (IV) Fe_a3³⁺–OH^–···H₂O–Cu_B model state; (V) Fe_a3³⁺–H₂O–Cu_B(a); (VI) Fe_a3³⁺–H₂O–Cu_B(b); (VII) Fe_a3³⁺–H₂O–Cu_B(c); (VIII) Fe_a3³⁺–H₂O–Cu_B(d). Note that structures V–VIII are four major optimized structures (see the Results and Discussion and Table 1) with very similar energies obtained by protonating the bridging OH^– ligand in O_H[Fe_a3³⁺–OH^––Cu_B] (model II).

When each model is constructed from the X-ray crystal structure 3S8G,³⁷ the C_α atoms of Tyr237, His233, His282, His283, Asp372, His376, and His384 are each replaced with a link H atom along the original C_β–C_α direction with a C_β–H_link distance of 1.09 Å. The C_β of Arg449 and C₂₂₈ of the geranyl side chain of the a₃-heme are also replaced with a H_link atom. During the geometry optimizations, except for the H_link atom on the geranyl side chain of the a₃-heme, the positions of all other H_link 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 Fe_a3³⁺ site in different spin states (low spin, intermediate spin, and high spin). Our calculations show that the intermediate-spin-Fe_a3³⁺ state is generally lower in energy than the corresponding high-spin-Fe_a3 state for each model cluster studied here. However, the rR and EPR experimental data suggest that the Fe_a3³⁺ is high spin in both the active O_H and the resting O states.^5,57 One needs more experimental data and higher-level theoretical calculations to determine whether different spin states of Fe_a3 can coexist in the O_H and the resting O states. In fact, the existence of intermediate-/low-spin-Fe_a3 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) Fe_a3³⁺ species at very low temperature (4.2 K), and the “low-spin” Fe_a3 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) Fe_a3³⁺ site is antiferromagnetically (AF) coupled with the Cu_B site and put the results of the intermediate- and low-spin-Fe_a3³⁺ states in the Supporting Information. Note that all conclusions we find for the HS-Fe_a3 states in the following section will remain the same if the Fe_a3³⁺ is in the intermediate-spin state.

3. Results and Discussion

Our calculated energies and the main geometric and Mulliken net spin population properties of the geometry-optimized O_H[Fe_a3^HS,3+–OH–Cu_B] state and the possible O[Fe_a3^HS,3+–H₂O···OH^––Cu_B] and O[Fe_a3^HS,3+–OH^–···H₂O–Cu_B] states are given in the first three rows of Table 1. The central portions of the Fe_a3^HS,3+–H₂O···OH^––Cu_B and Fe_a3^HS,3+–OH^–···H₂O–Cu_B DNC clusters are given in Figure 4III,IV, respectively. The net spin populations from Mulliken population analysis are the main indication of the spin state for the Fe_a3³⁺ site. In the ideal ionic limit, the net unpaired spin populations for HS-Fe_a3 and Cu_B²⁺ are 5 and 1, respectively. However, because of the metal–ligand covalency, the calculated net spin magnitudes for the Fe_a3 and Cu_B²⁺ sites are smaller than their corresponding ionic limits. The opposite signs for the spin densities of Fe_a3 and Cu_B²⁺ sites indicate the AF coupling. Our calculated net spins on Fe_a3 and Cu_B²⁺ show that we obtained the HS-Fe_a3 AF-coupled to the Cu_B²⁺ state for each cluster.

Table 1. OLYP-D3(BJ) Calculated Geometrical, Energetic, and Net Spin Properties of the Optimized DNC Clusters in Fe_a3^HS,3+–OH^––Cu_B, Fe_a3^HS,3+–H₂O···OH^––Cu_B, Fe_a3^HS,3+–OH^–···H₂O–Cu_B, and Fe_a3^HS,3+–H₂O–Cu_B States^a.

	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––CuB	2.50	1.99	2.04		3.73	0.0	0		4.08	0.12	–0.39	–0.25
Fea3HS,3+–H2O···OH––CuB	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–CuB	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–CuB(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–CuB(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–CuB(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–CuB(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

^aSee Figure 4.

^bGeometries were optimized in the broken-symmetry state with high-spin (HS) Fe_a3³⁺ AF-coupled to the Cu_B site.

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

^dThe net charge of the model clusters.

^eThe pK_a(H₂O) values were calculated for the process Fe_a3^HS,3+–OH^––Cu_B → Fe_a3^HS,3+–H₂O–Cu_B(a–d).

^fThe Mulliken net spin populations on Fe_a3³⁺, O of the bridging OH^–/H₂O, Cu_B, and the heavy atoms of the Tyr237–O^– side chain (the sum total).

^gThe X-ray crystal structure.³⁷

O_H is a metastable catalytically active state, which decays to the relaxed O state when no electron transfers to the DNC. Therefore, state O is lower in energy than O_H. However, our calculations show that both the Fe_a3^HS,3+–H₂O···OH^––Cu_B and Fe_a3^HS,3+–OH^–···H₂O–Cu_B states are higher in energy (by >6 kcal mol^–1) than the Fe_a3^HS,3+–OH–Cu_B state. Further, the O···O distances (∼2.5 Å) in Fe_a3^HS,3+–H₂O···OH^––Cu_B and Fe_a3^HS,3+–OH^–···H₂O–Cu_B 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 1). Therefore, the DNC of the resting as-isolated O state is not likely in the Fe_a3^HS,3+–H₂O···OH^––Cu_B or the Fe_a3^HS,3+–OH^–···H₂O–Cu_B form.

Next, we examine whether a water molecule is preferred residing between the Fe_a3³⁺ and Cu_B sites in the as-isolated O state. We then protonated the bridging OH^– in the state O_H[Fe_a3³⁺–OH^––Cu_B], 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 Fe_a3^HS,3+–H₂O–Cu_B structures of four major optimized geometries (a–d) are shown in Figure 4V–VIII, and their main bond distances and energies are given in rows 4–7 of Table 1.

In the optimized structure Fe_a3^HS,3+–H₂O–Cu_B(a) (Figure 4.V), the H₂O molecule binds with the Fe_a3³⁺ site with Fe-O distance of 2.39 Å. In Fe_a3–H₂O–Cu_B²⁺(b) (Figure 4VI), the H₂O molecule is in between Fe_a3 and Cu_B²⁺ 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 Fe_a3–H₂O–Cu_B²⁺(c) (Figure 4VII) and Fe_a3–H₂O–Cu_B²⁺(d) (Figure 4VIII), the H₂O molecule binds with the Cu_B site (with Cu–O distances of 2.21 and 2.20 Å, respectively) in different orientations. In Fe_a3–H₂O–Cu_B²⁺(c), the H₂O molecule tilts up and has an H-bonding interaction with one of the N atoms of the heme ring; in Fe_a3–H₂O–Cu_B²⁺(d), however, the H₂O simply moves closer to Cu_B starting from the bridging position. Fe_a3^HS,3+–H₂O–Cu_B(c) and Fe_a3^HS,3+–H₂O–Cu_B(d) also have nearly the same energy. In fact, all four Fe_a3^HS,3+–H₂O–Cu_B(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_H[Fe_a3^HS,3+–OH^––Cu_B] state, in order to compare the energetic stabilities, we calculated the pK_a of the H₂O molecules in the four Fe_a3^HS,3+–H₂O–Cu_B(a–d) structures using the equation^26,42,60,61

1

where E(A^–) and E(AH) are the calculated total energies of the deprotonated (A^–, here O_H[Fe_a3^HS,3+–OH^––Cu_B]) and protonated (AH, here the four Fe_a3^HS,3+–H₂O–Cu_B(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. ΔG_sol(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 –TΔS_gas(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 pK_as of the H₂O molecule in each of the Fe_a3^HS,3+–H₂O–Cu_B(a–d) states are also given in Table 1. They are between 11.7 and 12.2, indicating that the Fe_a3^HS,3+–H₂O–Cu_B(a–d) states are energetically much more stable than the O_H[Fe_a3^HS,3+–OH^––Cu_B] state. We therefore speculate that it is a water molecule between the Fe_a3³⁺ and Cu_B sites in the resting as-isolated O state. However, an extended electron density, which was interpreted as a dioxygen molecule, was observed between Fe_a3³⁺ and Cu_B 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 Fe_a3^HS,3+–H₂O–Cu_B(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 5 with two orientations: A and B. The colors of the atoms in the different structures are as follows: 3S8G, silver; Fe_a3^HS,3+–H₂O–Cu_B(a), orange; Fe_a3^HS,3+–H₂O–Cu_B(b), purple; Fe_a3^HS,3+–H₂O–Cu_B(c), blue; Fe_a3^HS,3+–H₂O–Cu_B(d), green.

Figure 5.

Overlap of the central portions of the following DNC structures (see Table 1): silver, 3S8G X-ray crystal structure; orange, Fe_a3^HS,3+–H₂O–Cu_B(a); purple, Fe_a3^HS,3+–H₂O–Cu_B(b); blue, Fe_a3^HS,3+–H₂O–Cu_B(c); and green, Fe_a3^HS,3+–H₂O–Cu_B(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 Cu_B site and its ligands move slightly more than the heme-Fe_a3 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 water molecule that has an H-bonding interaction with the ligand H₂O in each of the four geometry-optimized structures is not shown in Figure 5. 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 Fe_a3³⁺–H₂O–Cu_B(c) (Figure 4VII). 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 H₂O molecule in the DNC of the O state, we removed the H-bonding H₂O from the Fe_a3^HS,3+–H₂O–Cu_B(a–d) structures and optimized the geometries again. The central portions of the corresponding optimized structures (S) are given as S1–S4 in Figure 6, respectively. Their main bond distances and the calculated energies are given in Table 2.

Figure 6.

Structures (S) S1–S4 (see Table 2): the central portions of the optimized geometries after removing the H-bonding H₂O molecule from the Fe_a3^HS,3+–H₂O–Cu_B(a–d) structures (see Figure 4V–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 7).

Table 2. Geometry Optimized Fe_a3^HS,3+–H₂O–Cu_B DNC Structures and Energies, in Which No Water Molecule H-Bonding to the H₂O Ligand^a.

	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

^aSee Figures 6 and 7.

^bGeometries (S1–S5) were optimized in the broken-symmetry state with high-spin Fe_a3³⁺ AF-coupled to the Cu_B site.

^cCalculated broken-symmetry state energies (offset by –26004.7 kcal mol^–1). Note that Fe_a3³⁺ and Cu_B are very weakly coupled. The F-coupled calculations on these structures yield essentially the same energy as the corresponding broken-symmetry state.

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

Without the H-bonding H₂O molecule, the binding of the H₂O ligand with the two metal sites, especially with the Fe_a3³⁺ site, are weakened. For instance, from Fe_a3–H₂O–Cu_B²⁺(a) to S1, the H₂O dissociates from the Fe_a3 site (from an Fe–O distance of 2.39 Å) and moves to about the middle between Fe_a3³⁺ and Cu_B (Fe–O, 2.61 Å; Cu–O, 2.82 Å). S1 has the longest calculated Fe_a3³⁺ and Cu_B distance of 5.03 Å. S3 differs from the Fe_a3^HS,3+–H₂O–Cu_B(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 Fe_a3³⁺ site as in the structure Fe_a3–H₂O–Cu_B²⁺(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 6 as S5, and its geometric and energetic properties are also given in Table 2. 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 5, in Figure 6A,B, we have also shown the overlap of the DNCs of S1–S5 and the X-ray crystal structure 3S8G in two different 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 7, 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 Fe_a3³⁺ and Cu_B sites in different enzyme molecules.

Figure 7.

Overlap of the structures S1–S5 (also see Table 2 and Figure 6) with the electron density map that was reconstructed from the X-ray crystal structure 3S8G data file.

Further, although the structures and energies for Fe_a3^HS,3+–H₂O–Cu_B(a–d) and S1–S5 given in Tables 1 and 2 are obtained from broken-symmetry state calculations in which the HS-Fe_a3³⁺ is AF-coupled to Cu_B, the coupling between the HS-Fe_a3³⁺ and Cu_B sites appears to be very weak. Our Fe_a3^HS,3+-Cu_B 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 Fe_a3^HS,3+-Cu_B AF-coupled and F-coupled configurations of the DNCs may coexist in the resting O state.

4. Conclusions

Starting from the O_H[Fe_a3³⁺–OH^––Cu_B] DNC structure of the active oxidized state CcO, where a hydroxo bridges the Fe_a3³⁺ and the Cu_B 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 Fe_a3³⁺–H₂O···OH^––Cu_B or the Fe_a3³⁺–OH^–···H₂O–Cu_B forms, where an H₂O/OH^– binds with Fe_a3³⁺/Cu_B and the H₂O and OH^– ligands H-bond with each other, since both the Fe_a3³⁺–H₂O···OH^––Cu_B and the Fe_a3³⁺–OH^–···H₂O–Cu_B structures are higher in energy than the O_H[Fe_a3³⁺–OH^––Cu_B] 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 pK_a calculations show that the bridging OH^– ligand in the O_H[Fe_a3³⁺–OH^––Cu_B] state energetically prefers to be protonated at neutral pH. We therefore propose that a water molecule is between the Fe_a3³⁺ and Cu_B sites in the resting O state of CcO. Our calculations further suggest that the H₂O molecule can bind with either the Fe_a3³⁺ or the Cu_B site or it can stay at various positions between the Fe_a3³⁺ and Cu_B sites with very similar energies, depending on the Fe_a3³⁺–Cu_B 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 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 Fe_a3³⁺ and Cu_B²⁺ 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[Fe_a3³⁺–H₂O–Cu_B] structures that have different H₂O positions between Fe_a3³⁺ and Cu_B 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 Fe_a3³⁺ and Cu_B 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_H to O leads to large differences in the electron and proton transfer kinetics for the two different subsequent reaction pathways, O_H → E_H → R in comparison to O_H → O → E → R, with the sequence of 1e^– and 1H⁺ transfers to the reactive oxidized Fe_a3³⁺–OH^––Cu_B complex switched. The new structural analysis of state O in comparison to O_H provides a foundation for further exploration of these differences in kinetics.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.inorgchem.0c00724.

• Calculated low-spin-/intermediate-spin-Fe_a3³⁺ results, an analysis which corresponds to the high-spin-Fe_a3³⁺ results in Table 1, and the Cartesian coordinates of the structures given in Tables 1 and 2 (PDF)

The authors declare no competing financial interest.