All the O₂ consumed by Thermus thermophilus cytochrome ba₃ is delivered to the active site through a long, open hydrophobic tunnel with entrances within the lipid bilayer

Abstract

Cytochrome ba₃ is a proton-pumping heme-copper oxygen reductase from the extreme thermophile Thermus thermophilus. Despite the fact that the enzyme’s active site is buried deep within the protein, the apparent second order rate constant for the initial binding of O₂ to the active-site heme has been experimentally found to be 10⁹ M⁻¹s⁻¹ at 298 K, at or near the diffusion limit, and two orders of magnitude faster than for O₂ binding to myoglobin. To provide quantitative and microscopic descriptions of the O₂ delivery pathway and mechanism in cytochrome ba₃, extensive molecular dynamics simulations of the enzyme in its membrane-embedded form have been performed, including different protocols of explicit ligand sampling (flooding) simulations with O₂, implicit ligand sampling analysis and in silico mutagenesis. The results show that O₂ diffuses to the active site exclusively via a Y-shaped hydrophobic tunnel with two 25-Å long membrane-accessible branches that coincide with the pathway previously suggested by the crystallographically identified xenon binding sites. The two entrances of the bifurcated tunnel of cytochrome ba₃ are located within the lipid bilayer, where O₂ is preferentially partitioned from the aqueous phase. The largest barrier to O₂ migration within the tunnel is estimated to be only 1.5 kcal/mol, allowing O₂ to reach the enzyme active site virtually impeded by one-dimensional diffusion once it reaches a tunnel entrance at the protein surface. Unlike other O₂-utilizing proteins, the tunnel is “open” with no transient barriers observed due to protein dynamics. This unique low-barrier passage through the protein assures that O₂ transit through the protein is never rate-limiting.

Graphical Abstract

Introduction

The heme-copper oxygen reductases (HCOs) are integral membrane enzyme complexes that catalyze the exergonic reduction of O₂ to water and terminate the aerobic respiratory chains of all aerobic eukaryotes and most aerobic prokaryotic organisms.^1–9 These enzymes include the mitochondrial as well as all bacterial cytochrome c oxidases. The free energy release from the reduction of O₂ is used to generate a proton motive force across biological membranes which, in turn, drives ATP biosynthesis, as well as other energy-requiring processes.^2,10–13 The HCOs, together with closely related NO reductases (NORs), are members of the heme-copper superfamily^5,10–13 which have in common a membrane subunit (Subunit I) with a minimum of 12 transmembrane α-helical spans, which contains the bimetallic active site where O₂ (or NO) binds and is reduced to water (or N₂O). For the O₂ reductases (HCOs), the bimetallic active site consists of a heme Fe (e.g. heme a₃) and a nearby Cu atom (4–5Å distant). O₂ binds to an open axial coordination site on the reduced heme Fe and is reduced by a sequence of proton-coupled electron transfer reactions. The heme-copper active site is deeply buried within the membrane subunit but must allow rapid access for each of the substrates of the reaction.

$$4e^{-}(\mathit{cytc})+4H^{+}+O_2\to 2H_{2}O$$

The active site of many enzymes are sequestered from the bulk solution, necessitating efficient strategies by which the substrates can be delivered and products removed. These strategies include hydrophilic clefts or pores or hydrophobic tunnels or cavities which allow the substrate to diffuse towards (or products away from) the active site.^14–18 Most often the pathways are gated by protein conformational changes that may be large, as in movement of a protein domain sealing the active sites, or may be small, as in single amino acid side chain fluctuations allowing passage of a small molecule between cavities within the protein, en route to the active site.^18–20

The three substrates that must access the active site of the HCOs are O₂, protons and electrons. Electrons are delivered to the active site one at a time by a linear sequence of proton-coupled, step-wise electron transfer reactions between redox-active metal centers from the site where cytochrome c is oxidized (on Subunit II).²¹ Protons are delivered to the active site through one or two different proton-conducting channels (depending on the enzyme) that have entrances at the aqueous phase on the electrically negative side of the membrane (e.g., bacterial cytoplasm or mitochondrial matrix). Conserved polar residues as well as internal water molecules provide the continuous hydrogen-bond networks needed for the long-range (25–30Å) proton diffusion to the active site by the Grotthus mechanism.^6,7,22–25 In contrast to the electron and protons “wires”, pathways for O₂ diffusion into the active site have not been well-characterized. Hydrophobic tunnels in the X-ray structures of the aerobic respiratory heme-copper oxygen reductases,^26–32 including cytochrome ba₃ from Thermus thermophilus,^28,31,33,34 have been suggested as putative O₂ tunnels. Xenon (Xe), which has a similar size as O₂, is often used in crystallographic studies to locate hydrophobic cavities that may provide binding sites for small diatomic gas molecules, including O₂, CO, H₂ or N₂.^35–39 X-ray crystallography has located Xe binding sites in both cytochrome ba₃ ^35,40 and the aa₃-type oxygen reductase from Rhodobacter sphaeroides,²⁹ thereby identifying hydrophobic cavities that are within their putative O₂ tunnels.

Recent molecular dynamics (MD) simulations and computational analyses of the HCO from Rhodobacter sphaeroides concluded that the putative O₂ tunnel suggested by X-ray crystallography is not the primary pathway by which O₂ reaches the active site.⁴¹ Two additional pathways, which are not apparent in the static X-ray structures and may be formed transiently by protein dynamics, were suggested as more likely pathways that lead O₂ to the enzyme’s active site. Hence, what appears to be an O₂ pathway may not function as such.

In the present study, we computationally examine O₂ pathways to the active site of a different respiratory HCO, cytochrome ba₃ from the hyperthermophile Thermus thermophilus. Similar to HCO from R. sphaeroides, Xe binding sites have been identified by X-ray crystallography that align within a hydrophobic tunnel suggested to act as the O₂ pathway.^35,40 In addition apparent second order rate constant for O₂ binding to the active site from solution has been directly measured to be 1×10⁹ M⁻¹s⁻¹ at 298 K,^42,43 near the diffusion limit and far greater than found for O₂ diffusion to internal sites within other proteins, including myoglobin (1.6×10⁷ M⁻¹s⁻¹).⁴⁴ The motivation of this study is to understand how O₂ reaches the deeply buried active site of cytochrome ba₃ so rapidly.

Previous studies have characterized mutants that place bulky residues within the putative O₂ tunnel that reduce the apparent rate constant 5-fold,³³ supporting the X-ray observed tunnel as a functional O₂ pathway in cytochrome ba₃. Short (1 ns) MD simulations concentrating on the dynamics and stability of O₂ at Xe binding sites of the X-ray tunnel indicated that O₂ can rapidly move between individual Xe sites within the hydrophobic tunnel.³³ In the present study, extensive MD simulations (repeated 50-ns simulations with multiple copies of O₂) as well as implicit ligand sampling (ILS)⁴⁵ are used to characterize the energetics of O₂ partitioning within the protein and the trajectories of O₂ molecules starting outside the protein and reaching the active site. The all-atom MD was performed using the entire 3-subunit protein embedded in a lipid bilayer and surrounded by a bulk aqueous solution. The study demonstrates that the substrate O₂ utilizes the X-ray Xe-bound hydrophobic tunnel as the pathway for reaching the active site. Furthermore, unlike other proteins, such as myoglobin or the R. sphaeroides HCO, the O₂ pathway in cytochrome ba₃ is static and does not seem to be affected by protein dynamics. The highest free energy barrier for O₂ to diffuse through the identified O₂ pathway is calculated to be 1.5 kcal/mol. Cytochrome ba₃, therefore, appears to have evolved so that the transit time of O₂ through the 25-Å long hydrophobic tunnel is never rate-limiting. Under 298 K, the enzyme is limited by the rate of chemical catalysis (k_cat ≈10² s⁻¹) at O₂ concentration above 0.1 μM, and would be limited by the rate of O₂ reaching the entrances of the O₂ pathway when O₂ concentration is below 0.1 μM. At physiological conditions (343–363 K) where the organism (T. thermophilus) grows, the enzyme velocity may be limited by the rate of O₂ reaching the pathway’s entrances.

Materials and Methods

Construction of the membrane-embedded cytochrome ba₃ model

MD simulations were performed on a membrane-embedded model of the cofactor-bound cytochrome ba₃ complex constructed using the crystal structure of the enzyme from T. thermophilus HB8 strain (PDB entry 1XME)⁴⁶ inserted into a hydrated and ionized patch of POPE (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine) bilayer. The crystal structure contains three subunits (I, II and IIa), 75 water molecules, heme b, active-site heme a₃, three copper ions (Cu_B and dicopper Cu_A) cofactors. The membrane-embedded cytochrome ba₃ was constructed using VMD.⁴⁷

The cofactor-bound cytochrome ba₃ complex was embedded in a patch of POPE membrane by aligning the center of transmembrane regions of its subunits I, II and IIa with the midpoint of the membrane. Lipids that overlapped the protein were removed, keeping 98 lipids in the periplasmic leaflet and 92 lipids in the cytoplasmic leaflet. The membrane-embedded cytochrome ba₃ was then solvated with water. Water molecules that were in the membrane were removed, keeping 15,177 water molecules. Finally, 0.2M NaCl (26 Na⁺ and 33 Cl⁻ ions) was added to neutralize and ionize the complex, resulting in a fully solvated model of approximately 85,000 atoms.

Simulation protocols

MD simulations 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. In order to maintain the ligation of Cu_B to H233, H282 and H283, the His-Cu_B connections were described as bonds with k =65 kcal/mol/Ų for the bonds and k =30 kcal/mol/rad² for the angles involving the His-Cu_B bond.

All simulations were performed using NAMD2⁴⁸ with a time step of 2 fs. The periodic boundary conditions (PBC) were used throughout the simulations. All bonds involving hydrogen atoms were kept rigid using the SHAKE algorithm.⁴⁹ To evaluate long-range electrostatic interactions in PBC without truncation, the particle mesh Ewald (PME) method⁵⁰ with a grid density of 1/ų was used. The cutoff for van der Waals interactions was set at 12Å. All of simulation steps except the melting of lipid tails (Step 1) were performed in a flexible cell, which allows the membrane-embedded cytochrome ba₃ model to change its dimensions independently, and were performed under NPT ensemble. The temperature was maintained at 310K by Langevin dynamics⁵¹ with a damping coefficient γ of 1/ps. The Nosé-Hoover Langevin piston method^51,52 with a piston period of 200 fs was used to maintain the pressure at 1 atm.

The CHARMM22 force field with ϕ/ψ corrections^53,54 was used to describe the protein and heme cofactors, and CHARMM36⁵⁵ was used to describe the lipids. The TIP3P model⁵⁶ was used as the water model. All cofactors were treated in the reduced state. The force field parameters for the hydroxyethylfarnesyl side chain of the active-site heme cofactor (heme a₃), which were not available in the CHARMM force field library, were constructed by analogy using parameterized alcohol, alkene, and alkane fragments.⁵⁷ The parameters for the copper ions were those previously used by Hofacker and Schulten.⁵⁸ A harmonic potential (k=400 kcal/mol/Ų) was used for the N_ε-C_ε bond of the His-Tyr (H233–Y237) crosslink.⁵⁹

Analyses were performed mainly with VMD⁴⁷ and MATLAB. The pore profile for O₂ pathway was calculated using the MolAxis program,⁶⁰ which was previously used to probe for tunnels in several proteins.^61,62

Production runs

The final frame of wild-type cytochrome ba₃ from the 20-ns relaxation simulation was used as the starting configuration for the explicit ligand sampling simulations (ELS, aka flooding simulations^63,64 ) in which O₂ molecules were added, for the continued 50-ns simulation in the absence of O₂ (apo), and for in silico mutagenesis.

Explicit ligand sampling (ELS) simulations

Long simulations

To probe for O₂ delivery pathways of cytochrome ba₃ and characterize O₂ delivery process, 100 O₂ molecules, corresponding to 0.21M [O₂] calculated with respect to the total simulation box volume of 790,000ų, were added to the equilibrated membrane-embedded enzyme model. This O₂ concentration is 161-fold higher than the saturated O₂ concentration in water at ambient conditions. This high O₂ concentration was introduced to maximize the sampling of O₂ delivery pathways in the protein within limited timescale (tens of nanoseconds). Three independent simulation systems were designed in which O₂ molecules were initially distributed in the membrane and aqueous phases at different ratios: 70:30, 100:0 and 0:100. Each system was visually inspected to ensure that the added O₂ molecules do not overlap with atoms of other molecules, and was then simulated for 50 ns (Fig. 1a). As all three simulation systems showed that approximately 80 of 100 O₂ molecules localized in the membrane after reaching a steady distribution (Fig. 1b), the 70:30 ratio system was repeated two more times, resulting in a total of 5×50 ns simulations. Repeated simulations are to improve statistics and provide more accurate descriptions of thermodynamic properties associated the O₂ delivery. To identify O₂ delivery pathways, a 3D density map representing the O₂ occupancy profiles was calculated using the Volmap tool in VMD. Using equilibrated fractions (last 40 ns) of the MD trajectories, the map was projected as a free-energy (ΔG_i,sol) map, which describes the energetics of O₂ insertion.

Figure 1. Partitioning profiles of O₂ in membrane.

a) Distributions of O₂ in membrane vs. aqueous phase in the protein-free system. Top panel illustrates the diffusion of O₂ molecules (shown as red balls) from the aqueous phase to the membrane. O₂ is considered to be in the membrane when either oxygen atom in the molecule is in between the C22 atoms (C_α of the palmitate’s ester) of the POPE lipids in the two leaflets (−16Å ≤ z ≤ 16Å). Partitioning free-energy profiles of O₂ calculated from ELS simulations and ILS indicate that more O₂ molecules reside in the membrane (shaded orange) than in the aqueous phase (shaded blue). b) A representative ELS simulation system in the presence of cytochrome ba₃. All systems with different initial ratio of O₂ show that O₂ is more distributed in the membrane than in the aqueous phase.

$$\mathrm{\Delta }{G}_{i,\mathit{sol}}=-\mathit{RT}ln\frac{p_i}{p_{\mathit{sol}}}$$

p_i represents the probability of finding O₂ at a site i calculated over the equilibrated trajectories. p_sol is probability of finding O₂ in the bulk aqueous solution. p_sol = 0.00035, determined from the simulation, was used as the reference for estimating partitioning free energies of O₂, as O₂ appears to distribute uniformly in the aqueous phase whereas it is heterogeneously distributed in the membrane, potentially due to various degrees of hydrophobicity in different regions of the membrane (Fig. 1a). For simulations including the protein, O₂ was considered to reach the active site of the enzyme when either one of its oxygen atoms was within 6Å of Cu_B. Their entries were confirmed by visually monitoring all delivered O₂ molecules through MD trajectories and their separation from Cu_B. For the re-entry of O₂, if O₂ first moves away from Cu_B by more than 30Å which is already outside the protein and later diffuses into the active site, we considered it as an independent (re-entry) event.

Short simulations

Once the O₂ delivery pathway was identified, the time of O₂ diffusing from outside of the protein to the active site, which can relate MD simulation results to time-resolved spectroscopic experiments, can be estimated.^42,43 To improve statistics, a set of 21 independent short (each 3–5 ns) simulations was performed. To reduce the computational costs, these new simulations were terminated once one O₂ reached the active site, which was determined by its presence within 6Å of Cu_B. They were all initiated with 90 O₂ in the membrane and 10 in the aqueous phase corresponding to the upper equilibrium ratio of 90:10 obtained from the 50-ns long simulations. A 0.5-ns pre-equilibration was then performed for each system to allow further randomizing of O₂ molecules. A different random number seed was assigned to initialize each production run. From these short simulations, the time to observe the first O₂ to reach the active site after the start of a simulation is referred to as “first entry time” or t_first. The transit time of O₂ diffusion to the entrance of the pathway (t_out→ent) and the transit time of O₂ diffusion from the entrance to the active site (t_ent→cat) can also be estimated.

Implicit ligand sampling (ILS) calculations

The implicit ligand sampling (ILS) method⁴⁵ was employed as an alternative, complementary method to the ELS simulations to characterize O₂ delivery pathways of cytochrome ba₃. ILS is a quantitative method for characterizing gas migration pathways^65–68 that might be difficult to probe with conventional MD simulations (i.e., ELS) due to limited sampling. The method is only applicable to ligands that have weak interactions with proteins. As previously described,⁴⁵ ILS calculates ligand-interaction energies (E_i) at all sites of each subgrid averaged over an ensemble of protein conformations and ligand orientations, which estimate the probability of finding a ligand in a particular subgrid (p_i) and then the free energy of inserting ligand into that subgrid (ΔG_i).

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

where p₀ (in vacuum)=1.

The apo trajectory of cytochrome ba₃, which was simulated in the absence of O₂ for 50 ns following the 20-ns relaxation simulation, was used for ILS calculations to characterize potential O₂ delivery pathway. A 60×65×85ų grid was placed on the cytochrome ba₃ complex covering portions of the membrane and aqueous phases. The grid, which defines where O₂ molecules were sampled and consists of several subgrids, was 331,500ų. Each subgrid contained 3×3×3 interaction sites. Ten orientations of O₂ were sampled in all 27 interaction sites of a subgrid over 5,000 frames. The solvation free energy of O₂ (ΔG_sol) was used as the reference for calculating the partitioning free energy of O₂ (ΔG_i,sol).

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

We calculated ΔG_sol using free-energy perturbation (FEP)⁶⁹ and ILS methods over a 30×30×30ų ionized water box. Both methods yielded ΔG_sol of 2.1 kcal/mol.

In silico site-directed mutagenesis

To examine the role of the identified O₂ pathway of cytochrome ba₃ in facilitating the delivery of the substrate O₂, aliphatic residues along the pathway (I78, V79, A120, A149, S150 and L200) were individually mutated to either a phenylalanine or a tryptophan. These residues were characterized as lining residues by the ELS simulations and ILS calculations of the wildtype enzyme. Four single (I78F, A120F, A149F, S150W), two double (A120F/S150W and V79F/S150W) and one triple (I78F/V79F/L200F) mutants were modeled and simulated. Each mutant was energy-minimized for 1,000 steps, and equilibrated for at least 10 ns. ILS was employed to assess the effects of the mutations by exploring the free energy of O₂ partitioning in the pathway. In addition, ELS simulations were performed to locate O₂ delivery pathways and estimate transit times of O₂ diffusion into the active site.

Simulations of O₂ in protein-free membrane

We also performed simulations of a protein-free membrane system in order to calculate the partitioning profiles of O₂ between the membrane and aqueous phases (without any perturbation caused by the protein in the lipid structure) and to compare the results with those previously obtained from experiments and MD simulations.^70–74 The protein-free membrane model was composed of 40,666 atoms (172 POPE lipids, 6,372 water molecules, 24 Na⁺, and 24 Cl⁻ ions). The 0.5-ns melting of lipid tails, 5-ns relaxation and 10-ns production simulations were performed as described above. The 10-ns production trajectory was analyzed by ILS for O₂ insertion. Then, two independent ELS simulations were performed starting from the 5-ns apo relaxation step: one with 100 O₂ initially in the aqueous phase, and one with 100 O₂ initially in the membrane. The O₂ concentration calculated with respect to the total volume of 435,000Å₃ was 0.38 M. A 0.1-ns equilibration at 400K followed by a gradual cooling from 400K to 310K with the total time of 0.2 ns was performed to allow rapid randomizing of O₂. 50-ns production simulations were performed after the cooling. The partition coefficient of O₂ was determined from the ratio of O₂ in the membrane to the aqueous phase. O₂ was considered to be in the membrane when either oxygen atom in the molecule resided between the C22 atoms (C_α of the palmitate’s ester) of the POPE lipids in both leaflets or −16Å ≤ z ≤ 16Å (Fig. 1a). With the estimated volume of the aqueous phase of 210,000ų being slightly smaller than that of the membrane, the number of O₂ residing in the aqueous phase must be multiplied by a factor of 1.1 to calculate the partition coefficient.

Results

Partitioning of O₂ between the membrane and aqueous phases

Before starting the ELS simulations on cytochrome ba₃, we determined the partition coefficient of O₂ between the membrane and aqueous phases using the protein-free membrane system (Fig. 1a). The total volume of this system, 435,000ų, consists of water and phospholipids in a volume ratio of approximately 9:10. 100O₂ molecules or 380mM [O₂] were added and allowed to distribute in the system for 50 ns. Starting with different initial distributions of the O₂ molecules in the membrane and aqueous phases (100:0 or 0:100) yielded the same equilibrium distribution within 10 ns, with approximately 85 O₂ molecules in the membrane and 15 in the aqueous phase (Supp. Fig. 1). After normalizing to the volumes of the aqueous and membrane phases, the ratio of concentrations gives a partition coefficient of 5.5 for O₂ favoring the membrane, close to the values obtained previously in a similar simulation study performed in the absence of a protein, 4.7,⁶⁵ and still comparable to the experimental value of 3.9 estimated using fluorescence quenching.⁷¹ The equilibrium profile of O₂ distribution within the membrane was also calculated independently using the ELS trajectories and ILS (Fig. 1a). The results are equivalent to those reported previously for simulations with just the aqueous solution and phospholipid⁶⁵ and also agree with experimental data using NMR and ESR.^73,74

For the membrane-embedded complex of cytochrome ba₃, the total volume of the simulation system, 790,000ų yields an O₂ concentration of 210mM (100 O₂ molecules) incorporated in the system. Similar to the system, different initial distributions of the O₂ molecules in the protein-free membrane and aqueous phases resulted in the same equilibrium distribution with approximately 80 O₂ molecules in the membrane-protein phase and 20 in the aqueous phase (Fig. 1b). Since the volume ratio of the aqueous phase to the combined membrane-protein phase is 9:7, the equilibrium concentration of O₂ in the aqueous phase has to be normalized, yielding a partition coefficient of 5.2 which is in comparable to that of the protein-free system and previous studies.^65,71

O₂ pathway to the active site

O₂ access to the active site of cytochrome ba₃ was monitored in ELS trajectories starting with 100 O₂ molecules distributed between the membrane and aqueous phases, but not within the protein. Regardless of the initial O₂ distribution, the first O₂ reached the active site in each simulation in less than 5 ns (Fig. 2). Taking together the trajectories of all five ELS simulations (250-ns total), a total of 148 O₂ molecules reached the active site, averaging to one per 1.7 ns. Of these 148 events, 26 are cases where the same O₂ molecule had two or more entries, since the simulation allowed molecules to diffuse back into the solution and return. The data are summarized in Table 1. The density map of O₂ within the protein was determined by combining the last 40 ns segments of the five simulations, and was normalized with respect to the average O₂ density in the aqueous phase. The results are displayed as a 3D isosurface image (Fig. 3) in order to facilitate comparison to the ILS results (Fig. 4).

Figure 2. Entry of O₂ into the active site observed during the ELS simulations.

Three of the five simulations are with 70 O₂ molecules initially in the membrane and 30 in the aqueous phase, one is with all 100 O₂ molecules initially in the membrane, and one with all 100 O₂ molecules initially in the aqueous phase. O₂ is considered to be the active site when it is within 6Å of Cu_B.

Table 1.

O₂ delivery events observed during the long ELS simulations

System	Delivery events	Unique delivery O2
1) 70:30	29	26
2) 70:30	34	27
3) 70:30	28	23
4) 100:0	36	28
5) 0:100	21	18
sum	122	148
average	24.4	29.6

Systems=initial O₂ mem:sol ratio. Unique delivered O₂ = number of distinguishable O₂ molecules (different ID numbers) found in the active site. Delivery events=number of O₂ delivery events observed during the 50-ns simulations. A few O₂ molecules made multiple entries to both the enzyme and active site.

Figure 3. O₂ delivery pathway of cytochrome ba₃ identified by the ELS simulations.

All images were taken from the same top view of the enzyme. a) Highly occupied O₂ regions characterized by the 3D density map calculated using the combined last 40-ns trajectories of five independent simulations. One region, which appears in a Y-shaped form, is the pathway that has been found to deliver O₂ to the active site (green-dashed box). It is connected to the membrane via two branches, which we refer to and label as Branches A and B. Red-solid isosurfaces represent O₂ partitioning free energy (ΔG_i,sol) of −3.5 kcal/mol. b) The O₂ delivery pathway. Purple-solid and red-wireframe isosurfaces correspond to ΔG_i,sol of −4.0 and −3.0 kcal/mol, respectively. c) Xe binding sites identified by X-ray crystallography.^35,40 Xe atoms were detected in a hydrophobic tunnel, displayed as a yellow-transparent surface using a probe radius of 1.8Å; they are numbered according to PDB entry 3BVD.³⁵ The O₂ delivery pathway identified in the present study (b) largely overlaps with this Xe-bound tunnel.

Figure 4. Favorable O₂ partitioning regions in cytochrome ba₃ characterized by ILS.

a) Highly probable O₂ binding regions characterized by the 3D free-energy map calculated by ILS. Red-solid and red-wireframe isosurfaces correspond to ΔG_i,sol of −3.5 and −3.0 kcal/mol, respectively. b) Region in the 3D free-energy map that is equivalent to the O₂ delivery pathway characterized by ELS: purple-solid and red-wireframe isosurfaces correspond to ΔG_i,sol of −4.0 and −3.0 kcal/mol, respectively. c) O₂ delivery pathway calculated by MolAxis⁶⁰ for the crystal structure and displayed as corridors. Green corridors represent pore radii of 1.2–3.0Å. Blue corridors represent pore radii of >3.0Å. d) Pore profiles of Branches A and B of the O₂ delivery pathway.

The ELS simulations reveal high-occupancy regions within the protein which form a Y-shaped O₂ pathway with two openings at the protein interface with lipids, pathways leading from these openings (Branches A and B, Fig. 3a) to a common branch-point, and a single pathway leading from the branch-point to the active site. The branch-point is surrounded by residues I78, A149 and L200 (Fig. 3b). The red surfaces in Fig. 3a are isosurfaces where the free energy with respect to the aqueous phase (ΔG_i,sol) is −3.5 kcal/mol. This represents favorable partitioning from the aqueous phase to these regions of about 300 folds and a 10-to-50-fold favorable partitioning of O₂ with respect to the membrane phase (depending on the location within the membrane). Fig. 3b shows the isosurfaces defining ΔG_i,sol =−3.0 (red-wireframe) and −4.0 kcal/mol (purple-solid), indicating higher and lower O₂ affinity sites along the pathway. Examination of all O₂ trajectories shows that all the O₂ reaching the active site use the Y-shaped pathway shown in Figs. 3a and b. All the O₂ comes from the lipid bilayer and through the hydrophobic tunnel to reach the active site (Supp. Fig. 2). Fig. 3c shows that the pathways correspond to the Xe binding sites observed by X-ray crystallography.^35,40 The X-ray Xe binding sites overlap with several purple isosurfaces in Fig. 3b indicating O₂ binding sites (ΔG_i,sol =−4.0 kcal/mol).

The ILS calculations result in an energetic picture that is fully in line with ELS simulations, as shown by the free energy isosurfaces in Figs. 4a and b. Additional regions of the protein that favorably bind O₂ are also revealed by both the ELS simulations and ILS calculations, but these are isolated cavities that do not constitute a pathway. Fig. 5a shows a 2D-projection of the free energy map, which strongly supports the conclusion that no pathway other than the Y-shaped pathway is available for O₂ to reach the enzyme’s active site. The Y-shaped pathway has a radius throughout its length of at least 1.5Å (Figs. 4c and d), which is large enough for unhampered diffusion of O₂. During the simulations, no protein fluctuations of blocked or altered the pathways, and the protein structure was not altered by the presence of O₂, even at such a high concentration as 210mM (Supp. Fig. 3). The agreement of the ELS and ILS results demonstrates that the 50-ns simulations are sufficiently long for adequate sampling of O₂ diffusion throughout the protein.

Figure 5. Energetic profiles of O₂ along the delivery pathway.

a) A 2D projection of the free-energy map, calculated using MATLAB, describing the partitioning of O₂ in the enzyme and its surroundings. The map was calculated by collapsing the normalized 3D density profiles of O₂ calculated from ELS over a 50×50×30ų grid, which spans the enzyme region covering the entire O₂ delivery pathway, heme cofactors, Cu_B, and surrounding lipids. Dark colors indicate high probability O₂ regions. Light colors indicate O₂ scarce regions. b) Estimated number of O₂ binding sites along the pathway calculated by integrating O₂ probability densities (p_d) from the active site to the entrances of the pathway. c) 1D free-energy profiles of O₂ partitioning along its delivery pathway. The coordinates of O₂ that have been within 3Å of pathway’s residues are clustered into normalized O₂ density profiles with respect to the aqueous phase using the distance from the active site (d) as the reaction coordinate. d=(((x − x₀)² +(y − y₀)² +(z − z₀)²)^1/2) - 6. (x₀, y₀, z₀) is the position of Cu_B cofactor. O₂ is considered to be in the active site when it has been within 6Å of Cu_B. BP specifies intersection point of Branches A and B, referring to as “branch-point”. ΔΔG^TS–BP = +1.5 kcal/mol. The average speed of O₂ diffusion along the pathway (v₀) is 0.39 (0.29)Å/ps.

There are 7 to 8 binding sites of O₂ along the Y-shaped pathway (Figs. 3b, 5a and 5b). These sites have ΔG_i,sol values ranging from −3.5 to −4.5 kcal/mol, corresponding to dissociation constants of 0.6 to 3mM. If the concentration is 250 μM (air saturated), these data predict between 0.5 and 1 O₂ present within the pathway. Under more physiologically relevant conditions, the amount of O₂ present within the protein at equilibrium will be negligible. Figs. 3 and 5b provide more details relating the Xe binding sites^35,40 to the regions of the protein favorable for O₂ binding. The site closest to the active site coincides with Xe1 in the X-ray structure (Figs. 3b and 3c³⁵ ). The affinity for O₂ at the branch-point (BP) is most favorable and corresponds to the combination of Xe5 and Xe6 densities in the X-ray structure.³⁵ The two O₂ sites in Branch B coincide with Xe3 and Xe4. Branch A contains 3 O₂ binding sites. Two are located near the entrance of Branch A (residues V79 and A120) and are not visualized by X-ray crystallography. The third O₂ site in Branch A coincides with the region around Xe2 and Xe7. The 1D-projection free energy profiles of O₂ in Fig. 5c show the largest free-energy barrier along the Y-shaped pathway of only 1.5 kcal/mol, located at the transition from the BP to the Xe1 site, which is very close to the active site. Other free-energy barriers are all below 1 kcal/mol.

The rate of delivery of O₂ to the active site

To obtain an estimate of the rate of O₂ delivery to the active site, a series of 21 short ELS simulations (3–5 ns each) were performed to determine the time required for the first O₂ from the solution to reach the active site. This was defined arbitrarily as an O₂ molecule getting to within 6Å of Cu_B. The initial distribution of O₂ was 90 molecules in the membrane and 10 molecules in the aqueous phase, which is equivalent to an O₂ concentration of 37mM in the aqueous phase and 185mM in the membrane. Similar to the 50-ns ELS simulations, O₂ molecules were initially placed outside the protein in these short ELS simulations. In all 21 trials, O₂ diffused to the active site within the first 5 ns. In 14 trials, O₂ reaching the active site entered via Branch B and in the remaining 7 trials, through Branch A (Table 2). On the average, it took 1.7 ns for O₂ to diffuse to the immediate vicinity of Cu_B, essentially the same as observed in the 50-ns ELS simulations. Using the nominal concentration in the aqueous phase (37 mM), we may estimate an apparent second order rate constant of (1/0.037M)(1/1.7×10⁻⁹s)=1.6×10¹⁰ M⁻¹s⁻¹. This is an “apparent” second order rate constant since the O₂ molecules that reach the active site are initially within the membrane and then must pass through the protein tunnel. The apparent rate constant has been experimentally determined to be 1×10⁹ M⁻¹s⁻¹ by determining the rate of formation of the initial O₂ adduct with heme a₃, using enzymes dissolved in detergent micelles.⁴² The important point is that the calculated estimate is consistent with a remarkably rapid rate of diffusion of O₂ to reach the active site.

Table 2.

O₂ migration times estimated from the ensemble of 21 short ELS simulations

Branch	Sim.	tfirst (ns)	tent→cat	tBP →cat	tent→BP
A	7	2.1±0.9	0.7±0.2	0.4±0.2	0.3±0.3
B	14	1.5±0.7	0.6±0.2	0.4±0.3	0.2±0.2
total	21	1.7±0.8	0.6±0.4	0.4±0.3	0.2±0.2

These results are determined from the first delivered O₂ molecules in all the simulations. Sim.=number of simulations. t_first =time taken to observe the first O₂ reaching the active site after the start of a simulation. t_ent→cat =transit time of O₂ diffusion from the entrance to the active site. t_{BP →cat} =transit time of O₂ diffusion to the BP to the active site. t_ent→BP =transit time of O₂ from the entrances to the intersection point of Branches A and B.

Further insight is obtained by observing transit times for successful trajectories of O₂ for the molecule to reach the entrance of either Branch A or B, and the transit from the pathway’s entrance(s) to Cu_B (Table 2). The average time for O₂ (at 37mM) to get into the entrance of the pathway (either branch) is about t_out→ent ≈1 ns. Once at the entrance of the pathway, the average transit time to the active site (Cu_B) is t_ent→cat ≈0.6±0.4 ns. All the successful trajectories took O₂ to the BP (t_ent→BP ≈0.2 ns) and to Cu_B (t_{BP →cat} ≈0.4 ns). The fraction of O₂ molecules that started at the entrance of either Branch A or B and the went on the reach Cu_B is about 40 %. It should be noted that the time for O₂ to diffuse to the entrance of the pathway will depend inversely on O₂ concentration in the membrane, but the transit times within the O₂ pathway and the fraction of molecules that reach the active site once entering the pathway will be independent of O₂ concentration.

In silico mutagenesis of the O₂ pathway

Seven different mutants were constructed in silico to determine their influence on the diffusion of O₂ through the Y-shaped pathway (Table 3). In each of these mutants, the native residues were replaced by a bulky side chain, namely phenylalanine or tryptophan. These residues are I78, A149, A120, S150, V79 and L200, which correspond to F67, L150, H151, L112, F68 and L202 of the bovine cytochrome c oxidase or F108, V194, A153, H195, F109 and L246 of the R. sphaeroides enzyme.

Table 3.

Alterations of O₂ access by in silico mutagenesis

Mutant	Sim	tfirst	Branch	tent→cat	tBP →cat	tent→BP
A120F	20	3.2±2.0	B	0.8±0.5	0.5±0.3	0.3±0.2
A149F	20	2.6±2.0	A/B	0.8±0.6	0.3±0.4	0.5±0.4
S150W	20	2.7±1.1	A	1.2±0.7	0.8±0.8	0.4±0.3
A120F/S150W	18	3.8±2.0	B	2.0±1.6	1.0±1.0	1.0±1.1
V79F/S150W	8	4.0±2.3	(A)/B	1.6±1.1	0.4±0.2	1.2±1.0
I78F/V79F/L200F	29	6.7±3.9	(A)/B	2.4±2.0	0.6±0.8	1.8±2.0

The results are from the short ELS simulations. Sim=number of independent simulations. Branch(es)= entrance(s) of the first observed O₂ molecule entering the active site in each simulation. In the A120F/S150W mutant, O2 delivery was observed in only 8 of its 10-ns simulations. In the V79F/S150 mutant, O2 delivery was observed in only 18 of its 20-ns simulations. In the triple mutant, O₂ delivery was observed in 29 of its 15-ns simulations. Of all repeated simulations, O₂ entry via Branch A was found only in one simulation for V79F/S150W and triple mutants.

1. I78F (Fig. 6 and Supp. Fig. 4): Although I78 is at the BP, its replacement by phenylalanine has only a modest effect on the free energy barrier of O₂ translocation along the pathway.

2. A149F (Figs. 6 and 8, and Supp. Figs. 4 and 5): A149 is located at the BP. Although its replacement by phenylalanine creates a barrier, O₂ can readily bypass it and still reach the active site via both Branches A and B. Short ELS simulations show that this mutation has only a modest effect on the transit time of O₂ to the active site.

3. A120F (Figs. 6 and 8, and Supp. Figs. 4 and 5): A120 is located within Branch A and the X-ray structure of the A120F mutant has been reported.³¹ Although the structure of this mutant perfectly aligns with the wild-type structure, the introduced phenylalanine at this position occupies the Xe2–Xe7 sites, as shown both in the X-ray structure³¹ and in the simulation (Fig. 6), and reduces O₂ diffusion through branch A. However, since Branch B is still fully functional, the net effect on the rate of O₂ diffusion to the active site is modest.

4. S150W (Figs. 6 and 8, and Supp. Figs. 4 and 5): S150 is at the entrance of Branch B. A tryptophan at this position creates a significant barrier to O₂ diffusion and reduces the radius of the pathway to below 1.2Å. However, Branch A is still fully functional, and the time required for O₂ to reach the active site is only modestly influenced.

5. A120F/S150W double mutant (Figs. 7 and 8, and Supp. Figs. 5 and 6): Ten simulations (5–10 ns each) were performed for this mutant, and O₂ was observed to reach the active site in eight of them. This mutant increases the barrier to O₂ diffusion through both Branches A and B, but the net result is only to double the average time required for the first O₂ to reach the active site during the simulations (Table 3).

6. V79F/S150W double mutant (Figs. 7 and 8, and Supp. Figs. 5 and 6): V79 is located at the entrance of Branch A, near A120. This double mutant also increases the barrier against O₂ diffusion through both Branches A and B. However, in 18 of 20 simulations (5–10 ns each), O₂ reached the active site and the time for the first O₂ was only increased by a factor of 2.

7. I78F/V79F/L200F triple mutant (Figs. 7 and 8, and Supp. Figs. 5 and 6): L200 is located near S150 at the entrance of Branch B. This triple mutant increases barriers to O₂ diffusion at the BP as well as the entrances of each branch. A total of 30 simulations ranging from 5 to 15 ns were performed and in 29 of these O₂ reached the active site. The time required for the first O₂ to reach the active site is about 4-fold greater than in the wild type (6.7 ns vs. 1.7 ns).

Figure 6. Alterations of the O₂ delivery pathway by in silico mutagenesis of pathway-lining residues to bulky substitutions.

Left panels highlight predicted O₂ binding regions calculated by ILS performed on the 10-ns of apo trajectories. The pink transparent surface indicates regions with ΔG_i,sol of −2.5 kcal/mol for O₂ binding. Right panels show the O₂ delivery pathway calculated from the equilibrated structure (at t = 10 ns) of each mutant using MolAxis.⁶⁰ Red corridors represent pore radii of <1.2Å. Green corridors represent pore radii of 1.2–3.0Å. Blue corridors represent pore radii of >3. 0Å.

Figure 8. Migration profiles of O₂ along the delivery pathway in the wild-type and mutants of cytochrome ba₃ explicitly determined from multiple short ELS simulations.

t_ent→cat is the transit time of O₂ from the entrances of the pathway to the active site. It is directly measured from the first delivered O₂ molecule in each simulation. Histograms in each plot represent t_ent→cat distribution of a mutant. The shaded curved behind the bar histogram represents t_ent→cat distribution of the wild-type enzyme, providing a direct comparison with each mutant. t_ent→cat for the wild-type is 0.6±0.4 ns.

Figure 7. Alterations of the O₂ delivery pathway upon in silico blockages of pathway’s entrances.

Double (V79F/S150W and A120F/S150W) and triple (I78F/V79F/L200F) mutants have been introduced to hinder the O₂ delivery pathway. Descriptions of left and right panels are the same as in Fig 6.

Hence, the expectation for these mutations is that the effects on the transit of O₂ through the protein will be modest. We note that the length of the simulations performed here may not be sufficient to detect potentially large conformational changes, beyond the observed local constrictions of the O₂ pathway described above. However, we also note that the crystal structures of different types of cytochrome oxidases in which the regions studied here by in silico mutagenesis show variations in their amino acid compositions, have indicated no global structural differences. Furthermore, a crystal structure of one of the mutants studied here (A120F)³¹ perfectly aligns with the wild-type structure. Based on these, we do not expect significant global structural changes in the enzyme due to the introduced mutations.

Discussion

This study is motivated by the report of the remarkably fast rate of O₂ diffusion into the deeply buried active site of cytochrome ba₃ for T. thermophilus The experimentally determined second order rate constant at 298K for the formation of the initial complex of O₂ with the active-site heme a₃ is k¹ =1×10⁹ M⁻¹s^−1.42,43 This is ten times faster than the rate constant for the equivalent first step in the reaction of the mitochondrial cytochrome c oxidase, k¹ =1×10⁸ M⁻¹s⁻¹,^42,43 100 times faster than O₂ binding to myoglobin, k¹ =1.6×10⁷ M⁻¹s⁻¹,⁷⁵ and 100 times larger than O₂ diffusing into the diiron active site of toluene/oxylene monooxygenase hydroxylase, k¹ =2.1×10⁵ M⁻¹s^−1.76 The rate constant for CO or O₂ to reach the buried active site of NiFe hydrogenase has been measured to be 6.3×10⁷ M⁻¹s⁻¹,⁷⁷ also considerably less than cytochrome ba₃.

The first experiments to measure the diffusion of O₂ within proteins determined the rate constant for the collisional quenching by O₂ of the fluorescence of tryptophan within small soluble proteins.^78,79 The second order rate constants for this were found to be diffusion-limited, in the range of 2–8×10⁹ M⁻¹s⁻¹. Residues internally buried within the proteins that are not accessible to O₂ based on the static X-ray structures were readily quenched by collisional contact with O₂. It was estimated that O₂ could diffuse through the protein at rates that are 20–50% of the diffusion rate in water,⁷⁹ providing one of the first demonstrations of protein dynamics, necessary to allow O₂ to penetrate the protein. Although these data suggest that there may be no need for specific pathways to facilitate the diffusion of O₂ or other small, hydrophobic gases within proteins, considerable experimental and computational evidence indicates that such pathways have evolved for enzymes that use small gas molecules as substrates, e.g., nitrogenase,⁸⁰ methane monooxygenase,^81,82 laccase,^83,84 NiFe hydrogenase,^77,85 FeFe hydrogenase,^36,86 D-amino acid oxidase,⁶⁷ copper amine oxidase, ⁸⁷ myoglobin,^{45,75,88–90} hemoglobin,⁹¹ CO dehydrogenase/acetyl-CoA synthase,⁹² and heme-copper oxygen reductases, including cytochrome ba₃.^{33–35,40–43,58,93–95} There are also several examples of enzymes with multiple active sites that have molecular tunnels for delivering the product generated at one site to a second distant site where it is consumed as a substrate.¹⁵

In many cases, the gas channels include hydrophobic cavities that are identified by locating Xe binding sites using X-ray crystallography.³⁶ An important caveat is that the Xe binding sites identified crystallographically may not be functional and need not be involved in O₂ diffusion within the protein. For example, photosystem II from Thermosynechococcus elongates ⁹⁶ has 25 Xe binding sites scattered through the membrane domain of the protein, but they are clearly not involved in O₂ diffusion away from the oxygen evolving cluster. Myoglobin has 4 Xe binding sites, which may also bind O₂, but it remains unclear which, if any, of these sites are on the primary pathway for O₂ to reach the heme Fe.^75,90

Protein conformational changes are often crucial either in the transient formation of the hydrophobic cavities or in opening the passage connecting adjacent hydrophobic cavities, thus allowing passage of O₂. These are dynamic tunnels. An example of this is the pathway for CO₂ to reach the buried metal cluster where it is reduced to CO in the CO dehydrogenase/acetyl-CoA synthase.⁹² Dynamic tunnels have also been proposed for FeFe hydrogenase,^36,86 the Scarpharca dimeric hemoglobin,⁹¹ laccase,⁸⁴ and for the HCO from R. sphaeroides.⁴¹

A recent MD study in the cytochrome c oxidase from R. sphaeroides ⁴¹ concluded that the X-ray inferred tunnel is not an important route for O₂ to reach the active site and are in contrast with the finding reported here on cytochrome ba₃. The HCO from R. sphaeroides is an A-family heme-copper oxygen reductase, and crystallographic studies previously identified a putative O₂ pathway with two Xe binding sites.²⁹ This tunnel is roughly in the same location as the tunnel observed here in cytochrome ba₃, which is a B-family HCO. The functionality of the X-ray inferred tunnel in two different A-family heme-copper oxygen reductases has been tested experimentally by site-directed mutations.^94,97,98 However, these mutations are too close to the active site to allow straightforward interpretation. Using computational techniques similar to those employed in the present study, three putative O₂ pathways were suggested in the R. sphaeroides HCO,⁴¹ one corresponding to that inferred by the X-ray studies. A detailed examination of the structures of the A-family HCOs³³ as well as the MD simulations⁴¹ have revealed a constriction in the X-ray inferred tunnel that would substantially impede the passage of O₂ molecules to the active site. MD simulations did not observe any delivery event of O₂ to the active site over 100-ns periods.⁴¹ Nevertheless, free-energy profiles estimated from data generated by ILS calculations suggested two probable alternative pathways for O₂ diffusion from the solvent to the active site.⁴¹ Since the free-energy barriers of the two pathways were estimated to be 5 kcal/mol lower than the X-ray inferred tunnel, it was concluded that these alternative pathways, not observed in the static X-ray structures, are the preferred routes used in the R. sphaeroides HCO.⁴¹

In contrast, the inferred pathway from X-ray data for O₂ diffusion to the active site of cytochrome ba₃ is supported by both previous experimental data and by MD simulations, which only concentrated on the dynamics and stability of O₂ binding at individual X-ray Xe sites,^33,34 as well as the present study. The tunnel in this B-family heme-copper oxygen reductase does not have the constriction observed in the A-family enzymes.^33,35 The constriction in the A-family HCOs is due to bulky residues W172 and F282 (numbering for the R. sphaeroides enzyme) or residues W126 and F238 (numbering for the bovine enzyme), whereas the equivalent residues in the T. thermophilus enzyme are Y133 and T231. The examination of the Y133W mutant of cytochrome ba₃ showed that the second order rate constant for O₂ to diffuse to the active site is slowed down 5-fold to k₁ =2×10⁸ M⁻¹s^−1.33 Short (1 ns) MD simulations showed that there is effectively no barrier within this tunnel for O₂ diffusion.³⁴

The present study employs long ELS MD simulations (50 ns) with a model that places the entire 3-subunit cytochrome ba₃ in a lipid bilayer surrounded by an aqueous solution. By initially placing O₂ molecules outside the protein, this allows not only substrate O₂ to unequivocally search for its delivery pathways, but also to address the role of protein dynamics in modulating the X-ray inferred tunnel and to forming other alternative pathways. A sufficient number of trajectories were obtained for O₂, starting outside the protein and reaching the active site, to estimate a free energy map of O₂ within the protein based on occupancy. In addition, ILS calculations were performed to obtain an independent free energy map of O₂ in the protein. The results of both the ELS and ILS calculations are in full agreement with each other as well as previous experimental and computational studies.^33,34 The most important points are summarized below.

1. The equilibrium distribution of O₂ between the membrane and aqueous phases, as well as distribution of O₂ within the membrane in the computational model are consistent with previous experimental and computational data.^73,74

2. The protein contains about 7 binding sites for O₂ corresponding generally to the Xe binding sites in the X-ray structure. At 298 K, each site has a dissociation constant for O₂ of about 1mM with respect to the concentration in aqueous solution. At 250 μM O₂, at equilibrium there will be an average of about 1 O₂ molecule present in the protein, distributed among the sites within the pathway. At 10 μM O₂, more realistic physiologically, the occupancy of each site is less than 1% (at 298 K). Hence, these binding sites do not act as a storage reservoir for O₂.

3. The average time for O₂ to reach an entrance of its delivery pathway is about 1 ns, starting with a concentration of 37mM in the aqueous phase (MD simulation condition). The first O₂ molecule to reach the pathway entrance in each simulation always originates in the lipid bilayer. Based on the concentration of O₂ in solution, the apparent second order rate constant to reach the pathway entrance is about 1.6×10¹⁰ M⁻¹s⁻¹. This compares favorably with the measured second order rate constant for the collisional quenching by O₂ of pyrene dissolved in the lipid bilayer of 1.2×10¹⁰ M⁻¹s^−1.99 When the dissolved O₂ concentration in the aqueous phase is 250 μM (air saturated water at 298 K), the rate for an O₂ molecule to reach the pathway entrance can be estimated to be (2.5×10⁻⁴ M)(1.6×10¹⁰ M⁻¹s⁻¹)=4×10⁶ s⁻¹, or about one O₂ per 250 ns.

4. The O₂ binding sites right next to the pathway entrances have binding free energies of about −1.5 to −2 kcal/mol with respect to the O₂ pool within the membrane, recalling that O₂ in the lipid is favored by about −2 kcal/mol with respect to O₂ in solution. This is equivalent to an association constant of about 20 for O₂ binding from the lipid bilayer. Since the simulated second order rate constant to reach these sites from the bilayer is 1.6×10¹⁰ M⁻¹s⁻¹, the off rate constant can be estimated to be k₋₁ =(1.6×10¹⁰/20)=8×10⁸ s⁻¹. The transit time from the pathway entrance to the active site is 0.6 ns, so the first order rate constant to transit through the pathway is k₂ =(1/6×10⁻¹⁰)=1.7×10⁹ s⁻¹. These rough estimates indicate that about half the molecules that get into the pathway make it all the way to the active site. At no point do protein conformational changes introduce any significant free energy barrier to the diffusion of O₂ within the delivery pathway.

5. We can model the steady state kinetics of collision with the active site as a two-step process: i) a reversible step to enter the pathway from the lipid, followed by ii) an irreversible step to reach the active site. The O₂ that reaches the active site is assumed in this model to be consumed with 100% efficiency.

   $$[O_2]+E\underset{k_{-1}}{\overset{[S]k_1}{\rightleftharpoons }}E(O_2)\stackrel{k_2}{\to }E{(O_2)}_{C{u}_B}$$
   The observed rate for O₂ reaching the active site in this model is given by

   $$k_{\mathit{obs}}=\frac{[O_2]k_1{k}_2}{[O_2]k_1+k_{-1}+k_2}$$
   For any reasonable value of [O₂], it is reasonable to assume [O₂]k₁ ≪ k₋₁, k₂. Then

   $$k_{\mathit{obs}}\approx \frac{[O_2]k_1{k}_2}{k_{-1}+k_2}\approx 1.5\times {10}^{10}[O_2]s^{-1}$$

   assuming k₁ =1.6×10¹⁰ M⁻¹s⁻¹, k₋₁ =8×10⁸ s⁻¹ and k₂ =1.7×10¹⁰ s⁻¹. The second order rate constant for O₂ to reach the active site is predicted to be about 1.5×10¹⁰ M⁻¹s⁻¹, which is about 15-fold larger than the measured rate constant of 1×10⁹ M⁻¹s^−1.42 The experimental measure of the second order rate constant includes the process of forming the adduct with heme a₃ at the active site, and this could be rate-limiting, explaining why the value is smaller than the rate of reaching the vicinity of the active site which is computed. In any event, the MD simulations demonstrate that diffusion through the body of the protein is not rate limiting.

6. In order for the rate of transit through the protein to be rate limiting, it would be necessary to slow the transit time to about 100 ns or k₂ =10⁷s⁻¹. This would mean adding about 3 kcal/mol to the highest energy barrier (to 4.5 kcal/mol), and would result in a second order rate constant of about 10⁸ M⁻¹s⁻¹, which is what is measured for the bovine cytochrome c oxidase and is the result of adding a constriction to the pathway in cytochrome ba₃.

7. Using the measured rate constant, 1×10¹⁰ M⁻¹s⁻¹, and assuming that the maximum rate of catalysis is k_cat ≈10² s⁻¹ O₂ reduced /sec, the enzyme will be limited by the dissolved concentration of O₂ at concentrations of less than about 10⁻⁷M (0.1 μM) at 298 K. At concentrations of O₂ greater than 0.1 μM, the chemistry of catalysis is rate limiting.

8. In the native enzyme, the highest free energy barrier is about 1.5 kcal/mol. Mutations in the pathway that slow the rate of O₂ diffusion through the protein must present a free energy barrier of at least 4 kcal/mol, which would lower the second order rate constant to about 10⁸ M⁻¹s⁻¹, which is what the Y133W must accomplish in cytochrome ba₃.³³

9. If the second order rate constant for O₂ to reach the active site were reduced to 10⁷ M⁻¹s⁻¹, similar to the value for myoglobin, the consequence would be that the concentration of O₂ would limit the turnover rate of the enzyme at 10 μM instead of 0.1 μM. This is in a range that is physiologically significant, and provides a plausible rationale for why the respiratory HCOs have evolved to allow very fast access to the enzyme’s active site. The unusual hydrophobic tunnel present in cytochrome ba₃ with a largest free energy barrier of 1.5 kcal/mol suggests that this enzyme has evolved for maximum turnover even at concentrations of its O₂ substrate down to 0.1 μM. It is noted that this enzyme from T. thermophilus normally functions at 75°C or 348 K, so conclusions about physiological relevance involve extrapolations from the simulations and experiments done at or near 25°C (298 K).

In summary, a combination of ELS MD simulations and ILS thermodynamic calculations provide a consistent explanation for the rapid kinetics of O₂ to access the active site of cytochrome ba₃: the protein has a hydrophobic, static tunnel that provides an unencumbered 25-Å pathway from the lipid bilayer to the active site, allowing the enzyme to operate at maximal velocity at O₂ concentrations as low as 0.1 μM at 298 K.

Abbreviations

HCO

heme-copper oxygen reductase

ba₃

cytochrome ba₃ oxidase

ELS

explicit ligand sampling

ILS

implicit ligand sampling