Cytochrome aa₃ oxygen reductase utilizes the tunnel observed in the crystal structures to deliver O₂ for catalysis

Abstract

Cytochrome aa₃ is the terminal respiratory enzyme of all eukaryotes and many bacteria and archaea, reducing O₂ to water and harnessing the free energy from the reaction to generate the transmembrane electrochemical potential. The diffusion of O₂ to the heme-copper catalytic site, which is buried deep inside the enzyme, is the initiation step of the reaction chemistry. Our previous molecular dynamics (MD) study with cytochrome ba₃, a homologous enzyme of cytochrome aa₃ in Thermus thermophilus, demonstrated that O₂ diffuses from the lipid bilayer to its reduction site through a 25-Å long tunnel inferred by Xe-binding sites detected by X-ray crystallography.¹ Although a similar tunnel is observed in cytochrome aa₃, this putative pathway appears partially occluded between the entrances and the reduction site. Also, the experimentally determined second-order rate constant for O₂ delivery in cytochrome aa₃ (~10⁸ M⁻¹s⁻¹) is 10 times slower than that in cytochrome ba₃ (~10⁹ M⁻¹s⁻¹). A question to be addressed is whether cytochrome aa₃ utilizes this X-ray inferred tunnel as the primary pathway for O₂ delivery. Using complimentary computational methods including multiple independent flooding MD simulations and implicit ligand sampling calculations, we probe the O₂ delivery pathways in cytochrome aa₃ of Rhodobacter sphaeroides. All of the O₂ molecules that arrived in the reduction site during the simulations were found to diffuse through the X-ray observed tunnel, despite its apparent constriction, supporting its role as the main O₂ delivery pathway in cytochrome aa₃. The rate constant for O₂ delivery in cytochrome aa₃, approximated using the simulation results, is 10 times slower than in cytochrome ba₃, in agreement with the experimentally determined rate constants.

Table of Contents

Introduction

A-family heme-copper oxygen reductases (HCOs) including the aa₃-type cytochrome c oxidases (cytochrome aa₃) are the terminal respiratory oxygen reductases of all eukaryotes and many bacteria and archaea.^2–5 These enzymes oxidize cytochrome c and reduce O₂ to water, and use the free energy from the O₂ reduction reaction to power the biosynthesis of ATP.^6–12 The atomic structures of cytochrome aa₃ from Rhodobacter sphaeroides (R.s),^13,14 Paracoccus denitrificans¹⁵ and bovine heart mitochondria^16–19 have been determined by X-ray crystallography. The bacterial enzymes comprise 3–4 subunits (Fig. 1A), whereas the mitochondrial enzymes contain at least ten additional accessory subunits.^20,21 The smaller bacterial enzymes are widely used as models for the mitochondrial enzymes. A homologue of cytochrome aa₃ is cytochrome bo₃ of E. coli,^5,22,23 which uses ubiquinol instead of cytochrome c as the electron donor.

Figure 1.

Putative O₂ delivery pathway in HCOs. A) Location of the pathway in cytochrome aa₃. The R.s. enzyme comprises four subunits: SI (white), SII (brown), SIII (green) and SIV (not shown). SI and SII are the minimal functional units of HCOs. The O₂ reduction site is highlighted using a dashed green box. The X-ray inferred pathway, located in SI, is shown in magenta surface drawn using CAVER 3.0.⁴⁷ This structural model is from PDB 1M56.¹³ Red arrows on the right panel depict the entrances of the pathway. B–C) Projected from the top view, the putative O₂ pathway in cytochrome aa₃ is illutrated by chains of magenta balls drawn by CAVER3.0. Unoccupied spaces within the protein were visualized using the molecular surface representation in VMD with the probe radius of 1.7 Å, which is about the vdW radius of an oxygen atom. Comparison between the crystal structure with 4 subunits (B) and the one with only SI and SI subunits from PDB 2GSM¹⁴ (C) indicates that SIII does not block the TM4–5 entrance. The simulations were performed using the 2-subuit structure. D) The equivalent pathway in cytochrome ba₃ was found to bind Xe (gray balls) by X-ray crystallographic experiments^24,25 and characterized as the O₂ delivery pathway in MD simulations.¹ The structural model is from PDB 1XME²⁷ and the atom coordinates of Xe are from PDB 3BVD.²⁴ The Xe atoms are numbered according to Luna et al.²⁴

The reduction of O₂ takes place in Subunit I (SI), a 12-TM helical subunit, containing heme a and the O₂ reduction site composed of heme a₃ and Cu_B (Fig. 1A). The reaction requires four electrons and eight protons, of which four are for the reduction of O₂ and four are translocated across the membrane.

$$O_2+8H_{N,\mathit{\text{chem}},\mathit{\text{pump}}}^{+}+4e^{-}\to 2H_{2}O+4H_{P,\mathit{\text{pump}}}^{+}$$

The four electrons are provided by the sequential oxidation of four cytochrome c^red molecules by the one-electron redox center Cu_A located in the periplasmic domain of Subunit II (SII). Electrons are sequentially shuttled to heme a and then to the reduction site. All of the protons come from the N (electrically negative) side of the membrane and are transferred via two proton-conducting input channels, the D and K channels.^8,20 The D channel transfers two of the chemical protons and all of the pumped protons. It is 25–30 Å long and comprises a continuous hydrogen-bonded network formed by water molecules and conserved polar amino acids linking residue D132 (numbering for the R. sphaeroides enzyme) anchored on the surface of the N side and residue E286 located near heme a and the reduction site. The K channel, which transfers two chemical protons, begins at residue E101 in SII and includes residue K362 near the SI–SII interface. The two channels are not redundant, each providing chemical protons during different steps in the catalytic cycle. Starting with a fully reduced enzyme, the binding of O₂ to heme a₃ initiates the O₂ reduction chemistry and reaction steps associated with proton pumping. The O₂ delivery pathway, however, has not been well characterized and is the topic of the current work.

A previous MD study from this laboratory with a B-family HCO, cytochrome ba₃ from Thermus thermophilus¹ demonstrated that O₂ diffuses from the lipid bilayer to the reduction site through a hydrophobic tunnel that is the same as that defined by Xe-binding sites observed in the crystal structure of the protein (Fig. 1D).^24,25 This tunnel is also apparent in the absence of bound Xe in all of the available crystal structures of cytochrome ba₃.^26–28 The O₂ delivery pathway in cytochrome ba₃ has two entrances enabling O₂ access to the protein from the lipid bilayer. Both entrances begin at SI-lipid interfaces (Fig. 1D); one (termed TM1–3) is spanned by TM1, TM2 and TM3 helices, and other (termed TM4–5) is spanned by TM4 and TM5 helices. This structural feature is a “static” tunnel and is referred to as the “X-ray inferred” pathway.

An equivalent tunnel with the same two entrances (Fig. 1A–C) is observed in the crystal structures of the A-family oxygen reductases including cytochrome aa₃ from different sources.^{13,19,24,29–31} However, in the A-family enzymes, these tunnels appear to be partially occluded (Fig. 1B–C), consistent with the experimental apparent second order rate constant for O₂ diffusion from the aqueous solution to the reduction site of cytochrome aa₃ (10⁸ M⁻¹s⁻¹) being 10 times slower than for cytochrome ba₃.^32,33

The A-family oxygen reductases have a 7-TM helical subunit III (SIII) that is not present in cytochrome ba₃ or other B-family HCOs, and the TM4–5 entrance of the putative O₂ pathway in SI is adjacent to SIII. However, there are no data that indicate a functional role of SIII in O₂ delivery to the reduction site that might result from its proximity to the tunnel entrance. Although the elimination of SIII has deleterious effects, the A-family enzymes remain functional.^8,34–37 X-ray structures of A-family HCOs without SIII indicate no structural perturbations to SI or SII or to the O₂ pathways^{14,15,38–40} (Fig. 1B–C).

Two MD studies have, however, reached opposite conclusions about the use of the X-ray inferred tunnel by O₂ to reach the reduction site in the A-family HCOs. An early (1998) MD study by the Schulten group⁴¹ applied the locally enhanced sampling (LES) technique⁴² to simulate O₂ diffusion in cytochrome aa₃ oxygen reductases from P. denitrificans (P.d) and bovine. They observed an O₂ molecule initially placed at the reduction site exiting via the entrance of the X-ray inferred tunnel in each case. However, these LES simulations⁴¹ were performed in vacuum and lasted only several picoseconds. Because LES accelerates O₂ diffusion by softening interactions between O₂ and its surroundings, it might not correctly capture the dynamics that are functionally relevant for O₂ delivery.

More recently, an MD study of the A-family R.s. cytochrome aa₃ by Oliveira et al⁴³ probed the O₂ delivery pathway by performing five 100-ns flooding simulations, in which multiple copies of O₂ were explicitly included and simulated with the rest of the system (i.e. protein, lipids, water and ions). Unlike LES, flooding simulation is based on equilibrium, conventational simulations with no perturbation and rescaling of interactions between atoms in the system. However, no O₂ entry was observed during these simulations. They performed energy estimations using the implicit ligand sampling (ILS) technique, a post-simulation analysis used in probing high affinity O₂ sites,⁴⁴ and the results suggested two alternate dynamically formed tunnels as preferred O₂ pathways over the X-ray inferred tunnel.

Experimental mutagenesis data which support the use of the X-ray inferred tunnel as the O₂ delivery pathway in the A-family HCOs are based on amino acid residues, such as V279 of P.d. cytochrome aa₃⁴⁵ and V287 of E. coli cytochrome bo₃⁴⁶ (equivalent to V287 R.s. cytochrome aa₃), that are located very close to the reduction site rather than within the tunnel. Also, although an X-ray crystallographic experiment detected two Xe binding sites in the R.s. enzyme,¹³ those sites are located near the entrances of the pathway and therefore do not necessarily define a clear pathway for O₂ delivery.

Since the two previous MD simulations for O₂ diffusion to the reduction site of A-family oxygen reductases arrived at different conclusions, the present study re-examines the issue by independently performing both ILS analyses and an extended set of flooding simulations of the diffusion of O₂ to the reduction site of the R.s. cytochrome aa₃. The X-ray model used for the simulations includes SI and SII (Fig. 2). To improve the statistics on the O₂ delivery pathways compared to previous studies, twenty independent flooding simulations with different starting points were performed and each was extended to 150 ns. ILS analyses were performed on an independent 200-ns MD simulation. The results clearly show that the only pathway used by O₂ to reach the reduction site is the X-ray inferred tunnel, similar to what has been shown for the B-family cytochrome ba₃ from T. thermophilus (T.t.¹ Constrictions along the pathway result in a rate of O₂ delivery that is at least 10 times slower than the rate observed^32,33 and calculated¹ for cytochrome ba₃.

Figure 2.

Flooding simulations of O₂ diffusion in the membrane-embedded cytochrome aa₃. A) An example taken from one of the simulation illustrating the number of O₂ molecules (N_O2) localized in the membrane and in the aqueous solution. At the beginning of the simulation, 70 O₂ molecules were placed in the membrane and 60 in the aqueous solution. After reaching the equilibrium, ~110 O₂ molecules localized in the membrane and ~20 localized in the aqueous solution. B) Snapshots taken from one of the simulations illustrating the starting (left) and equilibrium points. Helices shown in white belong to SI, while ones shown in brown belong to SII. Lipid molecules are shown in orange sticks.

Methods and Materials

System preparation

The membrane-embedded model of R.s. cytochrome aa₃ was prepared using the 2.0-Å crystal structure (PDB 2GSM) as the protein model. The structure comprises SI (catalytic subunit), which binds low-spin heme a, high-spin heme a₃ and Cu_B cofactors, SII, which binds the Cu_A complex, and 282 water molecules. Hydrogen atoms were added using PSFGEN in VMD.⁴⁸ Histidine residues except H102, H333, H334, H411, H419 and H421 of SI were in the HSE tautomeric form (N_ε atom of the imidazole ring carrying proton). H102 and H421 are ligated to the Fe atom of heme a, H284, H333 and H334 are ligated to Cu_B, H419 is ligated to the Fe atom of heme a₃, and H411 forms a hydrogen bond with the propionate A of heme a₃. The carboxylate side chain of residue E286, for which pK_a has been experimentally estimated to be >9,⁴⁹ was assigned to be protonated.

The first principal axis of the protein was aligned with the z axis (membrane normal) using the OPM (Orientations of Proteins in Membranes) database.^50,51 The protein was then inserted into a patch of POPE (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine) bilayer. Lipids that overlapped the protein were removed, keeping 132 lipids in the periplasmic and cytoplasmic leaflets. The membrane-embedded enzyme complex was then solvated with water. Water molecules that were in the membrane (−18 < z < 18), except those from the crystal structure, were removed, keeping 20,637 water molecules. Finally, 0.2 M NaCl (78 Na⁺ and 79 Cl⁻ ions) was added to neutralize and ionize the system, resulting in a fully solvated model of 104,710 atoms.

The CHARMM22 force field with ϕ/ψ corrections^52,53 was used to describe the protein and the heme cofactors, CHARMM36⁵⁴ for the lipids, and the TIP3P model⁵⁵ for water molecules. The cofactors were treated in the reduced state. The partial charge of 0.383 was used for Cu_B according to Hofacker and Schulten.⁴¹ The vdW parameters of Cu with ε = 0.19 kcal/mol and R_min =1.4 Å were from Fuchs et al.⁵⁶ The force field parameters for the hydroxyethylfarnesyl side chain, attached to the porphyrin ring of hemes a and a₃, were not available in the CHARMM force field library; they were constructed by analogy using parameterized alcohol, aldehyde, alkene, and alkane fragments;⁵⁷ the complete structure of the hemes with the atomic partial charges is shown in Fig. S1. For the Cu_A complex, the partial charges of its Cu atoms and its ligated amino acids were assigned according to Hofacker and Schulten.⁴¹

Simulation protocols

MD simulations performed to prepare the systems consisted of the following steps: (1) 0.5-ns melting of lipid tails during which only the lipid tails were allowed to move in order to achieve better packing of lipids around the inserted protein; (2) 0.5-ns simulation with restraints (k = 1 kcal/mol/Ų) applied to heavy atoms of the protein and cofactors (all lipid atoms and water moving) and with harmonic potentials (k = 0.1 kcal/mol/Ų) applied to keep water out of the membrane; (3) 0.5-ns simulations with only backbone atoms of the protein and heavy atoms of the cofactors restrained (k = 1 kcal/mol/Ų); (4) 1-ns simulation with only C_α atoms of the protein and heavy atoms of the cofactors restrained; and (5) 20-ns unrestrained relaxation. Energy minimization (1,000 steps) was performed at the beginning of Steps 1, 2 and 3 using the conjugate gradient algorithm. To maintain the ligation of Cu_B to H284, H333 and H334 and thereby the structure of the reduction site, the His-Cu_B, and heme a₃ Fe-Cu_B connections were described by bonded interactions (k =200 kcal/mol/Ų for bonds and k =50 kcal/mol/rad² for angles).

All simulations were performed using NAMD2⁵⁸ with a time step of 2 fs and with the periodic boundary condition (PBC). All bonds involving hydrogen atoms were kept rigid using the SHAKE algorithm.⁵⁹ To evaluate long-range electrostatic interactions in PBC without truncation, the particle mesh Ewald (PME) method⁶⁰ with a grid density of 1/ų was used. The cutoff for van der Waals interactions was set at 12 Å. All of simulation steps except the melting of lipid tails (Step 1) were performed in a flexible cell, which allows the system to change its dimensions independently as an NPT ensemble. The temperature was maintained at 310 K by Langevin dynamics⁶¹ with a damping coefficient γ of 1 /ps. The Nosé-Hoover Langevin piston method^61,62 with a piston period of 200 fs was used to maintain the pressure at 1 atm.

Production runs

The production runs consist of a 200-ns apo simulation performed in the absence of O₂ molecules (used for ILS analysis and starting flooding simulations), and a set of twenty 150-ns flooding simulations in which a large number of O₂ molecules were added. The apo simulation started from the 20-ns time point of the relaxation simulation. The set of twenty flooding simulations started from snapshot taken at different time points from the 200-ns apo simulation described above: 4 snapshots (at 25-ns, 100-ns, 150-ns, and 200-ns time points, respectively) were selected from the apo simulation and each one were used to seed 5 indepedent simulations, resulting in an ensemble of twenty simulations.

Flooding simulations

Flooding simulations were carried out to probe potential O₂ delivery pathways and the dynamics associated with the O₂ delivery process. To maximize the sampling of O₂ delivery pathways within a limited timescale (150 ns), 130 O₂ molecules, corresponding to a concentration of 210 mM with respect to the volume of the simulation box, were added to the equilibrated structure of the membrane-embedded cytochrome aa₃. At the start of the simulation, 70 O₂ molecules were placed in the membrane and 60 molecules in the aqueous phas generating a concentration of 185 mM in the aqueous phase with all O₂ molecules occupying space outside the protein (Fig. 2). Twenty 150-ns simulations, adding upto a total of 3,000 ns, were carried out to probe for potential O₂ pathways. The simulated O₂ molecules are described by the standard CHARMM force field.⁵² The partial charges for the oxygen atoms of O₂ are +0.021 and −0.021, respectively. Its intramolecular interactions are described by the bond distance of 1.23 Å and the spring constant of 600 kcal/mol/Ų. The vdW parameters of the oxygen atoms are with ε = −0.12 kcal/mol and R_min =1.7 Å. We note that the O₂ model with the partial charges of ±0.021 and the one with the partial charges of 0 used in the ILS calculations, in which no electrostatic terms are included, show negligible differences in O₂ solvation in the aqueous solution and O₂ partitioning in the membrane (Fig. S3–S4 and Table S1). Moreover, it is important to note that although the phrase “O₂ ligand for heme” is tagged in the CHARMM topology file containing both O₂ and hemes, these charges of ±0.021 are far away from the strongly polarized O₂ molecule when ligated to the heme iron. A calculation by Daigle et al⁶³ showed that oxygen atoms of an O₂ molecule ligated to heme are strongly polarized with the partial charges of −0.18 and −0.32, clearly indicating that the slightly charged model (±0.021) used in the flooding simulations is not representing a heme-bound O₂. The very small charges of ±0.021 used in the present study (and in other simulation studies^64,65) are used to take into account a portion of the polarization that O₂ would experience when it approaches to strongly charged portions of the protein. In such cases, the rotation of O₂ can orient the small introduced dipole with the surrounding field, thereby giving a small portion of polarization effects.

To identify whether O₂ delivery events took place during the simulations, we used the 6-Å distance cutoff from Cu_B as the criterion. Then, we obtained the identity of the delivered O₂ molecules and examined the simulation trajectories whether they were indeed localized in the reduction site.

Implicit ligand sampling (ILS)

Complementary to the flooding simulations in which ligand diffusion is explicitly probed, ILS was employed to identify potential regions and pathways for O₂ insertion that may not be sufficiently sampled by flooding simulaitons. ILS calculates ligand-interaction energies (E_i) in any position inside the protein over an ensemble of protein conformations and ligand orientations,⁴⁴ which estimate a 3D free energy map of inserting an O₂ molecule at position i (ΔG_i).

$$\mathrm{\Delta }{G}_i=-\mathit{\text{RT}}\text{ln}\frac{p_i}{p_0}=-\mathit{\text{RT}}\text{ln}\frac{<e^{-E_i/\mathit{\text{RT}}}>}{p_0}$$

where p₀ (in vacuum) = 1 and p_i is the probability of inserting an O₂ molecule at position i.

Following the assumption that small, hydrophobic gases weakly interact with proteins and therefore do not affect the protein structure and dynamics, the 200-ns apo trajectory (10,000 frames) was analyzed for O₂ pathways. O₂ molecules were sampled in a 55 × 50 × 75 ų grid with spacing of 1 Å, covering the entire cytochrome aa₃ enzyme. Ten orientations of O₂ were sampled in each subgrid, which contained 3×3×3 interaction sites. The solvation free energy of O₂ (ΔG_sol) was used as the reference for calculating the partitioning free energy of O₂ (ΔG_i,sol).

$$\mathrm{\Delta }{G}_{i,\mathit{\text{sol}}}=\mathrm{\Delta }{G}_i-\mathrm{\Delta }{G}_{\mathit{\text{sol}}}$$

ΔG_sol was independently calculated over a 30×30×30 ų using of NaCl solution ILS and free-energy perturbation (FEP).⁶⁶ Both techniques yield ΔG_sol values of 2.1 kcal/mol, which is consistent to a previous calculation by Cohen et al.⁴⁴

Results and Discussion

O₂ delivery pathway to the reduction site

To unequivocally probe for pathways used by O₂ to diffuse to the reduction site of cytochrome aa₃, flooding simulations with 130 O₂ molecules were performed. Twenty simulations were performed using different starting points taken from the equilibrated system of the apo simulation: at t = 25 ns, 100 ns, 150 ns or 200 ns. The O₂ molecules were initially placed outside the protein, 70 molecules in the membrane and 60 molecules in the aqueous solution. Each simulation lasted 150 ns, but it took only ~20 ns to achieve steady distributions of O₂ in both the membrane and aqueous phases (Fig. 2), where ~110 O₂ molecules resided in the membrane and ~20 resided in the aqueous solution. In 15 of 20 simulations, O₂ molecules were observed to enter the reduction site; the number of this event ranged from 1 to 7 with an average of 2 events per simulation, corresponding to an average of O₂ entry in every 75 ns. Based on the 6-Å distance cutoff from the center of Fe of heme a₃ and Cu_B, the residence times of O₂ in the reduction site ranged from ~1 ns to ~90 ns (Fig. 3).

Figure 3.

Access of O₂ to the reduction site during 150-ns timespan of the simulations quantified by the distance between an O₂ molecule and the binuclear center (denoted as BNC) of the reduction site (O₂-cat) as the function of simulation time. Each panel represents one of the 15 simulations in which O₂ delivery took place. In relation to Table 1, panels A–D denote Sims. 1A–D, panels E–H denote Sims. 2A–D, panels I–K denote Sims. 3A and 3D–E, and panels L–O denote Sims. 4A–B and 4D–E. Each line corresponds to the trajectory of an individual O₂ molecule diffusing into the reduction site (shaded green), defined by the proximity of <6 Å from the centers of mass between the Fe atom of heme a₃ and Cu_B. The dashed line in each panel indicates the location of the main bottleneck, corresponding to the kinetic barrier region separating the reduction site from the rest of the O₂ delivery pathway, where O₂ resided very transiently while diffusing towards the reduction site.

O₂ molecules that reached the reduction site were identified and their diffusion dynamics was visually examined in order to locate the O₂ delivery pathways. Their trajectories are shown in Fig. 4; each colored line represents an individual O₂ molecule. The results of flooding simulations showed that the delivered O₂ molecules enter the reduction site via a pathway, which contains three entry branches (entrances) accessible from the membrane. One of the entrances begins at a lipid-protein interfacial region formed by TM1, TM2 and TM3 (TM1–3) helices, one begins at the TM4–TM5 (TM4–5) interface, and one begins at the TM5–TM6 (TM5–6) interface. In some of the simulations, O₂ is observed to enter via all three entrances, while in others, the entries occur via only one or two entrances (Fig. 4). The location of the pathway in cytochrome aa₃ is similar to the one previously defined for O₂ delivery in cytochrome ba₃, which resembles a Y-shaped tunnel (shown in Fig. 1C). The O₂ delivery pathway in cytochrome ba₃¹ corresponds to a two-branched hydrophobic tunnel as was also determined to bind Xe by X-ray crystallography.^24,25 The TM1–3 entrance of cytochrome aa₃ is equivalent to Branch A of cytochrome ba₃, so it is referred to as Branch A. The TM4–5 entrance is equivalent to Branch B, so it is referred to as Branch B. The TM5–6 entrance was not found in cytochrome ba₃ and is denoted as Branch C.

Figure 4.

O₂ access routes. The trajectories of the delivered O₂ molecules into the reduction site during each of the 15 simulations are illustrated by line traces with different colors. O₂ molecules enter the X-ray inferred pathway via three membrane-accessible branches, denoted as “A”, “B” and “C”. Branch A originates at TM1, TM2 and TM3. Branch B originates at TM4 and TM5 which is adjacent to SIII. Branch C, which was previously unknown, originates at TM5 and TM6. In some of the simulations, O₂ were found entering via all 3 branches, whereas in others, they entered via only 1 or 2 of the branches were visited by O₂. In relation to Table 1, panels A–D denote Sims. 1A–D, panels E–H denote Sims. 2A–D, panels I–K denote Sims. 3A and 3D–E, and panels L–O denote Sims. 4A–B and 4D–E.

Comparisons of O₂ delivery pathways in cytochrome aa₃ and cytochrome ba₃

The slower O₂ delivery rate in cytochrome aa₃ (1×10⁸ M⁻¹s⁻¹) compared to the one in cytochrome ba₃ (1×10⁹ M⁻¹s⁻¹)^32,33 is probably due to the presence of diffusions barriers within the protein. However, the inability to observe O₂ delivery in some of the flooding simulations makes it difficult to compare our current results with cytochrome aa₃ and our previous ones with cytochrome ba₃ using the results of flooding simulations. Therefore, ILS analyses were performed to calculate thermodynamically favorable O₂ regions within cytochrome aa₃. The results of ILS were used to map out potential O₂ delivery pathways, which were then compared to the pathways obtained from the flooding simulations and to the results of cytochrome ba₃ obtained from our previous study.¹ The comparison between cytochrome aa₃ and cytochrome ba₃ is shown in Fig. 5A–B as 3D free energy isosurfaces, in which the colored surfaces represent free energy states of O₂ insertion.

Figure 5.

Potential O₂ pathways predicted by ILS. A) Equivalent regions to the O₂ delivery pathway of cytochrome aa₃. Red isosurfaces correspond to ΔG of ~-3.3 kcal/mol. Magenta isosurfaces correspond to ΔG ~-1.8 kcal/mol. Discontinuous gaps between the isosurfaces indicate unfavorable O₂ insertion regions, correlated with hindrances along the pathway. Constricting residues are labeled; E286 (not shown) is located below F282 and G283. B) The entire pathway of cytochrome ba₃ is highly favorable for O₂. The ILS results of cytochrome ba₃ were obtained by analyzing the simulation trajectories for our previous study.¹ C) Other potential O₂ delivery pathways in cytochrome aa₃. Pink surfaces correspond to ΔG of +1 kcal/mol. The O₂ pathway, highlighted in dashed red box, is the only region extending all the way from the membrane to the reduction site. The alternate pathways proposed by Oliveira et al⁴³ start in between TM7 and TM8 and in between SII (brown), TM8 and TM9.

For cytochrome ba₃, the entire O₂ delivery pathway is energetically favorable as indicated in Fig 5B by the Y-shaped red surface corresponding to ΔG of −3.3 kcal/mol. For cytochrome aa₃, the pathway identified by the flooding simulations are found to be less favorable for O₂ insertion relative to the one in cytochrome ba₃. The pathway contains several higher energy regions between the entrances and the reduction site illustrated in Fig 5A by the discontinuity of the magenta surfaces corresponding to ΔG of −1.8 kcal/mol forming diffusion barriers. Here, O₂ molecules diffusing from any of the three entrances to the reduction site encounter a barrier located in the vicinity of residues F172 and G283.

In both cytochrome aa₃ and cytochrome ba₃, the results of flooding simulations are correlated to the results of ILS calculations. In our previous study of O₂ delivery in cytochrome ba₃, although flooding simulations were performed for only 50 ns using the O₂ concentration of 210 mM, we were able to observe O₂ delivery on an average of 20 events.¹ For cytochrome aa₃, the simulations lasted much longer (150 ns), but only two delivery events occurred on the average, which represent a 30-fold decrease compared to cytochrome ba₃. Fewer O₂ delivery events indicate that the pathway in cytochrome aa₃ is less accessible to O₂ than the one in cytochrome ba₃.

The study by Oliveira et al⁴³ with the same R.s. cytochrome aa₃ presented five 100-ns flooding simulations but found no O₂ entry. These results are consistent with the present study insofar we also found free energy barriers that limit the rate of O₂ diffusion to the reduction site. Five of the 20 simulations performed in the present study exhibited no O₂ entry events while the rest observed only few events (Table 1). Based on their ILS analyses, however, Oliveira et al⁴³ concluded that O₂ prefers to use alternate pathways rather than the X-ray inferred pathway to reach the reduction site⁴³ although no passage of O₂ through such alternative pathways was observed.

Table 1.

Access of O₂ to the reduction site of cytochrome aa₃

Sim.	No. entry events	tcat (ns)	Bulk <[O2] >	tent (ns)	tcat−ent (ns)
1A	3	92.6	57 mM	2.11	90.49
1B	4	57.15	63 mM	6.84	50.31
1C	1	36.45	60 mM	2.59	33.86
1D	6	27.02	71 mM	3.28	23.74
1E	0	NA	63 mM	3.91	NA
2A	2	11.45	70 mM	1.93	9.52
2B	2	39.95	69 mM	0.34	39.61
2C	2	107.38	74 mM	0.63	106.75
2D	2	53.48	70 mM	4.38	49.1
2E	0	NA	73 mM	2.23	NA
3A	2	91.95	68 mM	1.72	90.23
3B	0	NA	74 mM	4.04	NA
3C	0	NA	70 mM	0.62	NA
3D	1	78.01	70 mM	4.38	73.63
3E	2	9.97	60 mM	1.94	8.03
4A	2	33.7	62 mM	2.5	31.2
4B	7	58.74	62 mM	0.82	57.92
4C	0	NA	64 mM	3.85	NA
4D	2	105.03	65 mM	2.26	102.77
4E	2	50.94	81 mM	2.77	48.17
Avg.	2	57	67 mM	2.7	54

t_cat is the time taken to observe the first entry event of O₂ to the reduction site. t_ent is the time taken to observe the first O₂ molecule reaching the entrance(s) of the O₂ delivery pathway. Sims 1X, 2X, 3X and 4X were prepared using the 25-ns, 100-ns, 150-ns and 200-ns equilibrated complex of the 200-ns apo simulation as the starting model.

Different free energy isosurfaces, especially the ones at higher free energy contours (e.g., at ΔG = 1 kcal/mol, shown in Fig. 5C), were used to test for the existence of potential O₂ pathways besides the X-ray inferred pathway. However, despite the free energy barriers within the X-ray inferred pathway, the results of flooding simulations show that all of the 39 O₂ molecules reaching the reduction site in cytochrome aa₃ during the flooding simulations from the solutions (Table 1) use this X-ray inferred pathway, suggesting that the X-ray inferred pathway is the primary O₂ delivery pathway in cytochrome aa₃.

Delivery rate of O₂

To directly connect the results of the present study to the ones experimentally determined from time-resolved absorption spectroscopy,^32,33 we provide an approximation of the second order rate of O₂ delivery (k_obs) to cytochrome aa₃. Since flooding simulations provide dynamic details of O₂ diffusion, the obtained data can be used to semi-quantitatively describe steps associated with O₂ delivery. The delivery of O₂ to the reduction site involves two major steps: 1) the diffusion of O₂ from the solution to the entrance(s) of the pathway and 2) the migration of O₂ from the entrance(s) to the reduction site. Assuming that the consumption of O₂ is 100% efficient once in the reduction site, k_obs can be calculated by using the following steady-state kinetics model:

$$O_2+E\underset{k_{-1}}{\overset{k_1}{\rightleftharpoons }}E(O_2)\stackrel{k_2}{\to }E{(O_2)}_{\mathit{\text{cat}}}$$

where E(O₂) is the species in which O₂ has arrived at one of the entrances and E(O₂)_cat is when O₂ is in the reduction site. k_obs is defined as:

$$k_{\mathit{\text{obs}}}=\frac{[O_2]k_1{k}_2}{[O_2]k_1+k_{-1}+k_2}.$$

k₁ is the rate constant of O₂ reaching the entrance(s) of the pathway describing the diffusion step of O₂ from the solution to the reduction site. It was calculated as the reciprocal of the product of the time taken to observe the first O₂ molecule diffusing from the solutions to the entrance(s) of the pathway during the simulation (t_ent) and the aqueous concentration of O₂ ([O₂]). The average t_ent calculated from all 20 simulations is 2.7 ns and the average [O₂] in the aqueous solution is 67 mM (Table 1), so k₁ is ~5.5×10⁹ M⁻¹s⁻¹.

k₋₁ is the dissociation rate constant of O₂ from the entrance of the pathway to the membrane. It is the product of k₁ and the standard concentration (1 M) over the partitioning ratio of O₂ at the entrance and the membrane defined as P_ent,mem). P_ent,mem is inversely proportional to exponent of the substraction of ΔG_ent from ΔG_mem. ΔG_mem is ΔG of O₂ in the membrane with respect to the aqueous solution and is −2 to −1.5 kcal/mol.^1,67 ΔG_ent is ΔG of O₂ at the entrances of the pathway with respect to the aqueous solution. Because the ΔG contour with ΔG = −3.3 kcal/mol is found at all of the entrances according to ILS calculations (Fig. 5A), ΔG_ent is approximated to be −3.3 kcal/mol, indicating that O₂ is 1.3 to 1.8 kcal/mol or 10–20 folds more favored to partition at the entrance of the delivery pathway than in the membrane. Hence, k₋₁ is approximated to be ~2.8–5.5×10⁸ s⁻¹.

k₂ is the rate constant of O₂ migration from the entrance(s) to the reduction site and is the reciprocal of the time of O₂ to diffuse into the reduction site after reaching the entrance(s) of the pathway (t_cat−ent). t_cat−ent is obtain by subtracting the time taken to observe the first event of O₂ to the catalytic site or t_cat, which is ~57 ns, from t_ent. Although the average t_cat−ent is 54 ns, O₂ delivery occurred only in 15 out of 20 simulations or 75% of the total number of simulations. To account for this, the average value of t_cat−ent was scaled to 72 ns. Thus, k₂ is ~1.39×10⁸ s⁻¹.

Under physiologically relevant O₂ concentrations, it is reasonable to assume that [O₂] k₁ ≪ k₋₁ and k₂, so

$$k_{\mathit{\text{obs}}}\approx \frac{[O_2]k_1{k}_2}{k_{-1}+k_2}.$$

This leads to the estimated k_obs/[O₂] of 1.1–1.8×10⁹ M⁻¹s⁻¹, which is 8–13 fold slower than the one estimated by our previous MD study with cytochrome ba₃ (15×10¹⁰ M⁻¹s⁻¹).¹ Although this estimated k_obs/[O₂] is 10-fold faster than the experimentally determined second-order rate constant of 1×10⁸ M⁻¹s⁻¹,^32,33 the experimental rate constant was determined from the time required to convert the enzyme from the fully reduced non-O₂ bound state to the ferrous-oxy (O₂ bound) state. Hence, the experimental measurement includes the chemical ligation of O₂ to the heme a₃, the reaction that is beyond to scope of classical MD simulation. The experimental rate constant for O₂ to form the heme Fe adduct in T.t. cytochrome ba₃ is 1×10⁹ M⁻¹s⁻¹,^32,33 which is 10-fold faster than that determined for R.s. cytochrome aa₃.

The computationally estimated rate constant for O₂ delivery to the reduction site of cytochrome aa₃ is 1.1×10⁹ M⁻¹s⁻¹, which means that even when the O₂ concentration is as low as 10 µM, the rate of O₂ diffusion into the reduction site (~10⁴ s⁻¹) will be considerably faster than the rate of O₂ catalysis (k_cat~10² s⁻¹). Because of the specific pathway allowing rapid diffusion of O₂ from the membrane to the reduction site of the enzyme, the rate of catalysis will not be limited by the ambient concentration of O₂ until that concentration in solution is in the low micromolar range.

Constrictions along the O₂ delivery pathway in cytochrome aa₃

Although the O₂ delivery pathway in cytochrome aa₃ contains an additional entrance (Branch C) when compared to cytochrome ba₃, its presence probably has little or no effect on O₂ migration to the reduction site. This is concluded based on previous simulations on cytochrome ba₃ with in silico mutants designed to block the two O₂ entrances (Branches A and B in cytochrome ba₃). Those mutants, however, did not appreciably impair the passage of O₂.¹

Three O₂ entrances of cytochrome aa₃ merge at 12–15 Å distant from the reduction site. At this location, the flooding simulations identified a low O₂ sampling region, which can be seen in the left panel of Fig. 6A. The presence of this barrier region is correlated with a broad range of residence times (1–90 ns) for O₂ in the reduction site (Fig. 3). This region was also characterized by ILS calculations as a diffusion barrier for O₂. The previous study by Oliveira et al⁴³ also observed this kinetic barrier and, using a similar approach, calculated the energetic cost of ~9.5 kcal/mol for O₂ to pass through this region, thereby excluding the X-ray inferred pathway as the primary O₂ delivery pathway.⁴³ In the present study, the height of this barrier is suggested to be much smaller since O₂ molecules crossed this region in 15 of 20 150-ns simulations. These results support the role of the X-ray-inferred tunnel as the main, if not the only, pathway used for the substrate O₂ to diffuse to the reduction site.

Figure 6.

Constricting residues along the O₂ delivery pathway of cytochrome aa₃. A) Occupancy of O₂ in cytochrome aa₃ (left) vs. cytochrome ba₃ (right). Red lines are the collections of O₂ molecules partitioning in the protein during a flooding simulation (150 ns for aa₃ and 50 ns for ba₃). The results of cytochrome ba₃ were taken from the simulation trajectories performed in our previous study.¹ B) Comparison of amino acid residues lining the pathway in cytochrome aa₃ (left) and cytochrome ba₃ (right). Constricting residues, which surround the kinetic barrier region of the O₂ delivery pathway in cytochrome aa₃ are labeled in bold; their equivalences in cytochrome aa₃ are also labeled in bold.

The region that coincides with the kinetic barrier is surrounded by bulky amino acids M107, W172, F282 and E286 (Fig. 6B, left). This structural feature is common in A-family oxygen reductases. Residue M107 is within TM2, W172 is in the loop connecting TM3 and TM4, and F282 and E286 are both within TM6. W172 and F282 have been suggested to restrict the access of O₂.²⁴ In cytochrome ba₃, the equivalent region contains amino acids with smaller side chains (Fig. 6B, right), and the barrier height has been estimated to be much less, around 1.5 kcal/mol (Fig. 5C).¹ For example, M107^Rs and F282^Rs are equivalent to A77 and T231 of cytochrome ba₃, respectively. W172^Rs is equivalent to Y133 of cytochrome ba₃, and replaceing this tyrosine by a tryptophan by site-directed mutagenesis resulted in a 5-fold decrease in the O₂ delivery rate.⁶⁸ E286^Rs is the terminal amino acid of the D channel, a proton-delivery pathway that is present in the A-family HCOs but is absent in B-family HCOs;^26,69 in T.t cytochrome ba₃, it is equivalent to I235 (Fig. 6B).

The X-ray inferred pathway in cytochrome aa₃ is not a static pathway, and requires dynamics to change from a closed to an open form to allow for O₂ to migrate across the barrier (Fig. 7 and Fig. S2). Conformational dynamics of the bulky residues of cytochrome aa₃ were assessed by measuring minimum pairwise distances of F282-E286, F282-F108, W172-E286 and M107-E286 (Fig. 7A). The inuences of this dynamics on O₂ migration were examined by ILS calculations over selected periods (Fig. 7B). When the side chains of F282, E286 and M107 protrude into the pathway, they approach each other as well as F108 and W172, significantly interfering with O₂ migration. For example, during the 171–175 ns period of the 200-ns apo simulation in which all of the four distances came close to 4 Å, the free energy for O₂ to migrate through the kinetic barrier can be greater than 4 kcal/mol (Fig. 7B). As indicated in Fig. 7A, the occurrence of these conformational changes, however, is relatively infrequent and might not be observed using shorter simulation times.

Figure 7.

Conformational dynamics of constricting residues and O₂ accessibility. A) Minimum distances between lining amino acid residues during the 200-ns apo simulation. Dynamics of the residues affects O₂ passage. For example, from 171 to 175 ns (highlighted in red), the side chain of E286 comes in contact with those of W172, M107 and F108, while that of F282 comes very close to that of F108. These close contacts restrict O₂ passage. In the crystal structures, N-C_α-C_β-C_γ of F282 is ~180° which constricted the pathway; its transition to 60° increases its contact distances to E286 and F108 from 4 to 6 Å, relieving the hindrance. Residue F108 is located opposite to F282 and in cytochrome ba₃, it is equivalent to residue I78 (Fig. 6B) B) ΔG isosurface of +1 kcal/mol (pink surfaces) calculated using ILS over the period from 171 to 175 ns. The kinetic barrier is encircled in red, indicating a high energy of O₂ insertion and the blockage of O₂ passage. C) ΔG isosurface of +1 kcal/mol calculated over the entire 200-ns trajectory. Referring to Fig. 5A, ΔG of the two regions adjacent to the barrier are lower than −3.3 kcal/mol indicated in red surfaces. Hence, the ΔG barrier is greater than 4 kcal/mol when the constricting residues simultaneously form very close contacts.

Finally, it is noted that, in the A-family HCOs, both pumped and chemical protons pass from the D channel to the periplasmic surface and the reduction site via hydrogen-bonded water chains. The terminal region of the O₂ delivery pathway is also overlapped to that of the D channel. Since chemical protons and O₂ use the same delivery route to the reduction site, the presence of transiently localized water molecules may interfere with the passage of O₂. However, in the simulations performed in the present study as well as those reported in the recent study by Oliveira et al,⁴³ the region connecting the terminus of the D channel and the reduction site remained dehydrated. Therefore, we can only conclude that the observed restriction of O₂ migration is related to the presence of amino acids with bulky side chain. The transient presence of water in this region could also affect the rate of O₂ delivery in the A-family HCOs which possess the D channel.

Conclusion

This MD study characterizes the X-ray inferred tunnel as the primary delivery pathway for O₂ in R.s. cytochrome aa₃. This conclusion is opposite to the one made by Oliviera et al, likely related to shorter simulation times used in the previous study⁴³ due to slow conformational dynamics of amino acids lining the pathway. Because there are multiple constriction regions along the pathway indicated by both flooding simulations and ILS calculations, the simulation time needs to be sufficiently long to observe the migration of O₂ to the reduction site of R.s. cytochrome aa₃. We conclude that both R.s. cytochrome aa₃ and T.t. cytochrome ba₃ use similar pathways to effectively deliver O₂, and this pathway also appears to be conserved in other HCOs.