Redox-Coupled Protonation of Respiratory Complex I: The Hydrophilic Domain

Abstract

Respiratory complex I, NADH:ubiquinone oxidoreductase, is a large and complex integral membrane enzyme found in respiring bacteria and mitochondria. It is responsible in part for generating the proton gradient necessary for ATP production. Complex I serves as both a proton pump and an entry point for electrons into the respiratory chain. Although complex I is one of the most important of the respiratory complexes, it is also one of the least understood, with detailed structural information only recently available. In this study, full-finite-difference Poisson-Boltzmann calculations of the protonation state of respiratory complex I in various redox states are presented. Since complex I couples the oxidation and reduction of the NADH/ubiquinone redox couple to proton translocation, the interaction of the protonation and redox states of the enzyme are of the utmost significance. Various aspects of complex I function are presented, including the redox-Bohr effect, intercofactor interactions, and the effects of both the protein dielectric and inclusion of the membrane.

Introduction

Respiratory complex I (NADH/ubiquinone oxidoreductase) is a large L-shaped membrane-bound enzyme found in mitochondria and respiring bacteria (1,2). Although complex I has been known for some time (3), it remains poorly understood. The enzyme can be roughly divided into two domains, or arms: the membrane-bound hydrophobic domain and the hydrophilic domain, which extends into the mitochondrial matrix. The mitochondrial enzyme consists of ∼45 subunits with a mass of ∼980 kD (4–6), whereas complex I from prokaryotes consists of a highly conserved catalytic core comprised of 14 subunits with a mass of ∼550 kD (7). As such, bacterial complex I is often considered a minimal model for respiratory complex I (8). NADH produced from the citric-acid cycle within mitochondria is oxidized by complex I, which then transfers two electrons from NADH over ∼100 Å to quinone (Q) in the lipid bilayer. In this way, complex I introduces electrons into the respiratory chain, where they are eventually used to reduce molecular oxygen to water via complex IV (cytochrome c oxidase). Complex I utilizes energy from the NADH/quinone redox couple (Eq. 1) (9) to translocate four protons (2H⁺/electron) (10) across the inner mitochondrial membrane from the mitochondrial matrix (low H⁺ concentration) to the intermembrane space (high H⁺ concentration), generating in part the proton gradient utilized in the production of ATP by ATP-synthase (complex V) (for recent reviews, see Hirst (11), Sharma et al. (12), and Zickermann et al. (13)):

$$\text{NADH}+\text{Q}+{\text{H}}^{+}{+4\text{H}}_{\text{in}}^{+}\stackrel{\text{complex}\text{I}}{\rightleftarrows }{\text{NAD}}^{+}+{\text{QH}}_2+{4\text{H}}_{\text{out}}^{+}.$$ (1)

The recent x-ray crystal structure of the hydrophilic domain of complex I (Fig. 1) from the bacteria Thermus thermophilus has revealed the location of all of the electron transfer cofactors (14). These include flavin mononucleotide (FMN); two binuclear iron-sulfur clusters (Fe₂S₂), N1a and N1b; and seven tetranuclear iron-sulfur clusters (Fe₄S₄), N2, N3, N4, N5, N6a, N6b, and N7. Each FeS cluster is in turn ligated by four cysteine residues, except for cluster N5, which has a histidine residue in place of one cysteine ligand. The resulting redox states of the clusters are then 2⁻/3⁻ for the oxidized and reduced states, respectively. FMN initially accepts two electrons from NADH as hydride; electrons are then transferred one at a time to a chain of seven iron-sulfur clusters spanning the enzyme, and eventually terminating with quinone (NADH→FMN-N3-N1b-N4-N5-N6a-N6b-N2→Q). The conserved binuclear iron-sulfur cluster, N1a, is offset from the main electron pathway, and its function is unclear. The nonconserved tetranuclear cluster, N7, is only found in certain bacteria, and due to its distance from all other cofactors is not thought to be involved in electron transfer. A detailed scheme of how electrons tunnel along the chain of seven FeS clusters from FMN to N2 was recently revealed by Hayashi and Stuchebrukhov (15) (Fig. 1).

Figure 1.

(A) Ribbon representation of the hydrophilic domain of complex I from T. thermophilus. The FMN and FeS cofactors are shown as van der Waals spheres. Red arrows indicate the electron tunneling pathway. (Inset) View is along the N2-N6b axis, illustrating residues that change protonation state upon reduction of N2. (B) Side view of the holocomplex. The hydrophobic domain is shown in red, and the membrane is indicated by the black lines.

The mechanism by which complex I couples the free energy derived from the NADH/quinone redox couple to proton translocation across the mitochondrial inner membrane remains unclear. Despite the available structural information, there is no apparent indication of any proton-pumping machinery within the hydrophilic domain of the enzyme. However, several subunits from the membrane-bound hydrophobic arm of complex I (Nqo12, Nqo13, and Nqo14) are homologous to known Na⁺(K⁺)/H⁺ antiporter enzymes and are probably involved in proton translocation. The recent crystal structure of the intact holocomplex has revealed that these antiporterlike subunits are located at the distal end of the hydrophobic arm and are quite distant from the hydrophilic arm and redox centers (16,17). Despite the lack of detailed information, a number of proton-pumping mechanisms have been proposed for complex I (9,18,19).

We present the results of protonation-state calculations of the oxidized and partially reduced hydrophilic domain of complex I. The calculations show that only a very small fraction of the 897 protonatable sites of the hydrophilic domain undergo significant changes in their protonation state upon partial reduction of the enzyme. Implications for proton pumping and further modeling are discussed. Further, the FeS cluster-cluster interactions and the effect of pH on the midpoint reduction potentials (redox-Bohr effect) of the FeS clusters are examined.

Materials and Methods

Model construction of the hydrophilic domain of complex I from Thermus thermophilus

The model of the hydrophilic domain of complex I was built from the 3.3-Å crystal structure of the hydrophilic domain of complex I from T. thermophilus (Protein Data Bank accession code 2FUG) (14). Unresolved and deleted residues were built in using the loopy module distributed as part of the JAKAL program (20). Hydrogens were added using the xleap module of Amber 7 followed by H-atom energy minimization with the Sander program (21). Mulliken partial atomic charges for FMN and the oxidized and reduced iron-sulfur clusters were determined at the Hartree-Fock 6-31G^∗ level of theory using the GAUSSIAN-03 program (22). Although we do not expect this level of theory to accurately represent the FeS clusters, it was assumed to be a reasonable first-order approximation to the charge distribution.

In addition to calculations of the isolated hydrophilic domain, calculations including the membrane were performed. The model of the hydrophilic domain was superimposed onto the low-resolution structure of the holocomplex (Protein Data Bank accession code 3M9S) (16). The low-resolution structure of the hydrophobic domain was used to define the protein dielectric in the transmembrane region as well as to provide a reference for locating the membrane. The membrane was modeled as a 26-Å dielectric slab (23–25) located midway between the inner and outer surfaces of the hydrophobic domain (see Fig. 1).

Electrostatics calculations and Monte Carlo simulation protocols

The full-finite-difference method was employed to calculate the electrostatic terms of Eq. 3. An in-house code that relies on the Adaptive Poisson-Boltzmann Solver libraries (26) to solve the linearized Poisson-Boltzmann equation was used to perform the calculations. The code implements a unique treatment of histidine that explicitly includes both the N^δ and N^ɛ sites of histidine as titratable and can accommodate all possible charge/protonation states of the imidazole ring. A solvent dielectric of ɛ_s = 80 and ionic strength of I = 100 mM was used except where otherwise noted. A protein dielectric of ɛ_p = 4 was used. Separate calculations with protein dielectrics of 10 and 20 were also performed on the isolated hydrophilic domain for comparison. CHARMM22 (27) charges and radii were used in the electrostatics calculations. The model pK_as were the same as those presented in Bashford et al. (28), except for histidine, which was assigned model pK_as of 7 for both the N^δ and N^ɛ sites.

The average protonation state of the enzyme was determined by metropolis Monte Carlo (MC) (29) and parallel tempering (PT) (30) simulations performed by another in-house code. All MC simulations were performed at 300 K in the pH range 0–14. For complex I, 100,000 equilibration sweeps (MC steps/site) were performed, followed by 50,000 production sweeps. In addition, single and double MC moves were allowed to overcome poor sampling of highly correlated sites. PT simulations were performed for the oxidized and N2-reduced oxidation states of complex I at temperatures of 300, 350, 400, 450, 500, 600, 700, 800, and 1000 K and consisted of 10⁶ equilibrium and 5 × 10⁶ production MC steps with 50,000 PT moves. In all cases, the protonation state of each site considered was determined to a precision of σ ≤ 0.02 protons.

Results and Discussion

Isoelectric point of oxidized and partially reduced hydrophilic domain of complex I

The isoelectric point (PI) of a protein is the pH at which the protein has zero net charge. In this context, the PI and associated charge-versus-pH curve serves as a metric for the global titration behavior of the enzyme (Fig. 2). Complex I is a very basic protein; its PI was determined to be 10.35 and 10.38 for the hydrophilic-domain and holocomplex models respectively. This result is in good agreement with proteomic analysis of the enzyme from bovine heart mitochondria, in which isoelectric focusing 2D electrophoresis experiments revealed that several of the complex I subunits have PI values near or above pH 10 (6). This finding is significant in terms of molecular modeling, since the hydrophilic domain of complex I will have a considerable, positive net charge at pH 7. The average total charge of the enzyme (including cofactor charges) at neutral pH was calculated as 73.2 e⁻. The nominal model, where all titrating sites are treated as unperturbed (i.e., ${\text{pK}}_{\text{a}}^{\text{prot}}={\text{pK}}_{\text{a}}^{\text{aq}}$) and noninteracting, often used to estimate protein PI values, is disastrously inaccurate in the case of the hydrophilic domain of complex I. The nominal model predicts an acidic PI of 6.55 and an average net charge of −19.0 e⁻ at pH 7 (Fig. 2). At neutral pH, the total charge predicted by the nominal model differs from the value calculated via the F/FDPB method by 92 e⁻. When preparing structures for molecular dynamics it is common to further assume that histidine residues are in the neutral protonation state at pH 7, despite the fact that histidine would typically titrate near this pH. This last assumption pushes the standard-state charge down to −50.0 at neutral pH, a difference of 123 e⁻.

Figure 2.

Total enzyme charge versus pH for various models, including the hydrophilic domain (solid line), holocomplex (short-dashed line), and null models (long-dashed line). The square point represents the standard-state charge (null model with neutral histidines) at pH 7.

Upon reduction of the FeS clusters, there is little to no shift observed in the global titration curve and PI value (data not shown). Proton uptake is independent of which FeS cluster is reduced. As each FeS cluster is reduced, a cloud of ionizable residues in the vicinity of the site is seen to undergo protonation state changes as if the protons are following the electron through the chain of cofactors. However, the calculations represent equilibrium protonation states, and as such, electron transfer through complex I may occur on timescales that prevent relaxation of the protein's protonation state in response to reduction. It is known that the highest-potential terminal FeS cluster N2 is reduced within ∼90 μs (31). The electron's residence time on N2 is probably much more significant than that for any of the other FeS clusters, and so it may be reasonable to assume that only N2 is able to interact appreciably with ionizable residues. This assumption is supported by the fact that N2 has a pH-dependent midpoint reduction potential, and by evidence from crystals of the reduced enzyme that N2 undergoes a change in its coordination, with one cysteine ligand dissociating upon N2 reduction (18).

Protonation-state changes of the hydrophilic domain of complex I upon partial reduction

Complete, or nearly complete, proton uptake by the hydrophilic domain of complex I accompanies the reduction of individual FeS clusters. Table 1 lists the change in total charge and total protonation of the enzyme upon individual reduction of each FeS cofactor in the electron tunneling pathway for both models studied. A $\Delta \langle {\text{n}}_{\text{Tot}}\rangle$of 1.0 in Table 1 would correspond to exactly one additional proton and a $\Delta q_{Tot}$ of zero, since one proton and one electron have been added to the system. Reduction of N2 is accompanied by uptake of ∼0.82 and 0.74 protons for the hydrophilic-domain and holocomplex models, respectively. It is interesting that the reduction of N6a is accompanied by an uptake of 1.29 protons for both models.

Table 1.

Change in total charge/number of protons upon FeS cluster reduction at pH 7

Reduced cluster	Hydrophilic domain				Holocomplex
	ɛp = 4		ɛp = 20		ɛp = 4
	ΔqTot.	Δ<nTot.>	ΔqTot.	Δ<nTot.>	ΔqTot.	Δ<nTot.>
N3	−0.05	0.95	−0.11	0.89	−0.20	0.80
N1b	0.07	1.07	−0.39	0.61	−0.38	0.62
N4	0.00	1.00	−0.04	0.96	−0.17	0.83
N5	0.12	1.12	−0.02	0.98	0.07	0.71
N6a	0.29	1.29	−0.09	0.91	0.29	1.29
N6b	−0.01	0.99	−0.09	0.91	−0.06	0.94
N2	−0.18	0.82	−0.16	0.84	−0.26	0.74
N6b, N2	−0.11	1.89			−0.24	1.76
Average		1.01		0.87		0.85

Table 2 lists the ionizable residues, which change their protonation state by 10% (±0.1 protons) or more upon reduction of N2. For the isolated hydrophilic domain, five residues change protonation state significantly in response to reduction of N2, whereas only four sites change protonation state in the holocomplex model. From Table 2, we see that these residues account for increases of 0.31 and 0.58 protons out of the 0.82 and 0.84 proton totals for the hydrophilic-domain and holocomplex models. For the hydrophilic domain, proton uptake is occurring primarily via very small protonation-state changes among a very large number of residues, in a sense smearing the proton over many ionizable sites. Of course, this is not desirable in terms of a proton-pumping mechanism, and it may indicate that this function is indeed relegated primarily to the hydrophobic arm of complex I. However, the holocomplex model is focusing many more of the protonation-state changes into only a couple of residues. It is interesting to note that ₄His-170 shows opposite behavior in the two models. In the hydrophilic-domain model, ₄His-170 partially deprotonates in response to the increased protonation of ₄His-169, which is adjacent to N2, whereas in the holocomplex model, ₄His-169 remains protonated in both the oxidized and reduced enzyme.

Table 2.

Residues exhibiting a change in the average per-residue protonation, Δ<n>, exceeding ±0.10 protons upon reduction of FeS cluster N2 at pH 7, ɛ_p = 4

Residue	Subunit	Hydrophilic domain	Holocomplex
4Arg-409 (C-terminus)	Nqo4, 49 kDa	0.28	/
4Asp-94	Nqo4, 49kDa	/	0.33
4Hisɛ-63	Nqo4, 49 kDa	−0.24	/
4Hisδ-169	Nqo4, 49 kDa	0.28	/
4Hisδ-170	Nqo4, 49 kDa	−0.14	0.25
6Asp-128	Nqo6, PSST	0.13	0.12
9Glu-106	Nqo9, TYKY	/	−0.12

Several of the residues listed in Table 2 are strictly conserved among species, and various mutagenesis experiments have shown that these residues are important for complex I activity and stability. For a review of mutagenesis data, see Sazanov (33). In the hydrophilic-domain model, we observe partial proton transfer from the surface residue, ₄Arg-409 (C-terminus), to nearby ₄His-63 accompanied by proton transfer from ₄His-170 to ₄His-169 near N2, representing possible endpoints in a proton transfer chain leading to N2. These residues are connected through numerous protonatable sites. Mutagenesis of these sites results in reduced, but not abolished, enzymatic function. One possible conclusion is that the proton pathway leading to N2 is redundant. Alteration of the protein dielectric through the inclusion of the membrane and transmembrane segments significantly alters the resultant protonation patterns, further suggesting multiple proton pathways linking N2 to the protein surface.

The redox-Bohr effect

It has been known for some time that FeS cluster N2 is a redox-Bohr active cofactor, that is, the apparent midpoint reduction potential (${\text{E}}_{\text{m}}^{\prime }$) of N2 is pH-dependent. The FeS redox centers interact electrostatically with each other and with ionizable residues. The cluster-cluster interactions perturb the intrinsic E_m of a given cluster as a result of the redox state of the other FeS clusters, giving rise to the apparent midpoint reduction potentials observed in experiments. The apparent midpoint reduction potential of redox center I, ${\text{E}}_{\text{m},\text{I}}^{\prime }$, can be expressed as the intrinsic midpoint reduction potential plus a shift in redox potential associated with site-site interactions (34,35),

$${\text{E}}_{\text{m},\text{I}}^{\prime }{=\text{E}}_{\text{m},\text{I}}^{\text{intr}}-\langle {\Delta \text{E}}_{\text{m},\text{I}}\rangle .$$ (2)

Charges resulting from deprotonation of acidic or protonation of basic residues can shift the ${\text{E}}_{\text{m}}$, and hence the pH of a given redox center as a result of the protonation state. The midpoint reduction potential shift is then calculated as

$$\langle {\Delta \text{E}}_{\text{m},\text{I}}\rangle =\frac{1}{\text{F}}\sum _{\nu =1}^{\text{N}}{\text{W}}_{\text{I}\nu }\left(\langle {\text{n}}_{\nu }^{\text{red}}\rangle -\langle {\text{n}}_{\nu }^{\text{ox}}\rangle \right),$$ (3)

where W_Iν is the interaction energy between sites, and $\langle {\text{n}}_{\nu }^{\text{red}}\rangle$and $\langle {\text{n}}_{\nu }^{\text{ox}}\rangle$ are the average protonation/redox state of site ν when redox site I is reduced and oxidized, respectively. ${\Delta \text{E}}_{\text{m}}$ calculated as a function of pH for cluster N2 is presented in Fig. 3.

Figure 3.

Redox-Bohr effect associated with terminal FeS cluster N2. Solid squares are the measured apparent midpoint reduction potentials,${\text{E}}_{\text{m}}^{\prime }$, for Y. lipolytica. The solid and dashed curves are the calculated shift in midpoint reduction potential, ΔE_m, for the hydrophilic domain and holocomplex models, respectively. Solid circles represent the ΔE_m of the hydrophilic domain model when the protonation state of ₄His-169 is held fixed.

The pH dependence of FeS cluster N2 was first observed by Ohnishi in 1980 (36). The authors reported a midpoint reduction potential pH dependence of −60 mV/pH for N2 in the pH range 6.5–8.5. More recently, Brandt et al. (37) examined the redox-Bohr effect in complex I from Yarrowia lipolytica in the pH range 5.5–8.5. Similar results were obtained, and the pH dependence was reported as −36 mV/pH. The experimental data from Zwicker et al. (37) were digitized for the purpose of comparison (Fig. 3). As can be seen from Fig. 3, the calculated curve for the hydrophilic-domain model is shifted to slightly higher pH than the experimental data. The minimum slope obtained was approximately −20 mV/pH, indicating that the calculated value is less sensitive to pH changes than the measured ${\text{E}}_{\text{m}}^{\prime }$. At acidic pH, there is a clear plateau in the ${\text{E}}_{\text{m}}^{\prime }$-versus-pH curve, leading to ΔE_m(acid) = −86 mV. At pH values >9, the ${\text{E}}_{\text{m}}^{\prime }$ of N2 continues to drop until it finally levels off at a pH of ∼12.5. At this extreme pH, we obtain ΔE_m(base) = −222 mV. Of course, this pH is well outside the pH range where complex I is expected to be stable. As noted in Zwicker et al. (37), E_m values measured at pH 5 and 9 were anomalous, indicating problems with protein stability, thus providing a general pH range over which complex I is stable. If we truncate our data at the upper pH limit of 9 and fit it to a Nernstian curve, we obtain E_m(base) = −158 mV. It is important to note that we have plotted ${\Delta \text{E}}_{\text{m}}$ against the experimentally measured ${\text{E}}_{\text{m}}^{\prime }$. Complex I from different species exhibit different ${\text{E}}_{\text{m}}^{\prime }$ values, so any vertical alignment of the calculated and experimental data is coincidental.

By measuring the apparent midpoint reduction potential of N2 in a mutant complex I in which His-226 of the 49-kDa subunit of the Y. lipolytica-derived enzyme (₄His-169 in T. thermophilus) was substituted with methionine, Brandt et al. (37) demonstrated complete loss of redox-Bohr activity associated with N2 in the studied pH range. As shown in Fig. 3, when MC simulations are performed with the protonation state of ₄His-169 fixed, the midpoint reduction potential of N2 becomes pH-independent, indicating that ₄His-169 is responsible for the observed effect. The $\Delta E_m$ for the holo-complex model (Fig. 3) is pH independent stemming from the fact that ₄His-169 is protonated in both the reduced and oxidized enzyme in this pH range.

FeS cluster-cluster interactions

In a previous study, we calculated the cluster-cluster interaction energies for all of the FeS cofactors of complex I with various protein dielectrics in the absence of any explicit protein charges (34). Values obtained with ɛ_p = 20 were subsequently used to fit the experimentally determined redox titration curves (39) within the framework of a fully interacting model of the electron transfer pathway through the enzyme (35). From this analysis, statistically meaningful E_m values were obtained. A suitable fit of the experimental data was not possible using the calculated N2-N6b interaction energy. When this value was included as an adjustable parameter and optimized along with the cluster E_m values, a significantly increased value of 71 ± 14 or 96 ± 26 mV (depending on the N6a/N6b assignment) was obtained (35), compared to the calculated value of 27 mV (34) (Table 3).

Table 3.

Calculated cluster-cluster interaction energies, ΔE_m(mV), for different models

Cluster couple	Hydrophilic domain	Holocomplex	Protein as dielectric∗
	ɛp = 4	ɛp = 4	ɛp = 4, 20
(N6a, N6b)	83	87	123, 31
(N6a, N2)	(1, 5)†	5	21, 7
(N6b, N2)	(18, 47)	51	109, 27
(N6b, N2) Best fit‡			71 ± 14/96 ± 26

^∗Values taken from Couch et al. (34).

^†Values in parentheses indicate nonequivalent interactions (see text).

^‡Values taken from Medvedev et al. (35).

Here, we revisit the cluster-cluster interaction energies of select FeS centers as determined from the current fully atomistic model. Table 3 lists the cluster-cluster interaction energies, ${\Delta \text{E}}_{\text{m}}$, for various models from this and previous work. Inclusion of the enzyme protonation state can break the equivalence of interaction between clusters, since a different protonation state can result when different clusters are reduced. These nonequivalent interactions are listed in parentheses in Table 3. For the (N6b, N2) couple, the interaction energies listed in Table 3 (reported as the negative of the reduction potential) for the hydrophilic-domain model are (18, 47) mV. Here, and in a similar way throughout Table 3, the first value in parentheses corresponds to the interaction energy when the first FeS cluster of the pair (i.e., N6b) is reduced, and the second value corresponds to the interaction energy when the second FeS cluster is reduced (i.e., N2). Thus, N6b's midpoint reduction potential is shifted down 47 meV when N2 is reduced as described by Eq. 5. When N6b is reduced, however, only an additional 18 mV is required to reduce N2. A single value in Table 3 indicates equivalent interactions between the specified clusters. Inclusion of the membrane and hydrophobic domain eliminate the nonequivalence of the interaction energies. Comparison with the protein-as-dielectric model illustrates how the inclusion of protein charges results in a significant increase in electrostatic screening and an increased effective protein dielectric. Compared to the isolated hydrophilic domain, the holocomplex model exhibits larger interactions involving N2, primarily due to the inability of mobile counterions to approach N2 in this model.

Effect of protein dielectric

The effect of increasing the protein dielectric was examined for the hydrophilic-domain model. Increasing the protein dielectric from 4 to 20 reduced the PI from 10.35 to 9.15. The response of individual sites to changes in redox state and pH were also diminished with increasing dielectric. Of the sites listed in Table 2, only ₄His-169 retained a significant change in protonation state upon reduction of N2 with ɛ_p = 10, and this change was reduced to <0.1 protons when the dielectric was increased to 20. Proton uptake was also reduced, but remained above 0.85 protons even with ɛ_p = 20. In a similar way, the redox-Bohr effect was eliminated with increasing protein dielectric, as might well be expected given the individual site responses.

Characterization of protonation state dynamics

Finally, we examine the protonation-state energetics associated with reduction of FeS cluster N2. Fig. 4 illustrates the distribution of energies observed from an equilibrated MC trajectory consisting of 500,000 steps for the oxidized and reduced enzyme at pH 7; also shown is the energy distribution immediately after reduction (i.e., before protonation-state relaxation). The energy associated with the redox centers is omitted from Fig. 4. For the oxidized enzyme, 24,402 unique proton configurations were observed, whereas the trajectory of the reduced enzyme consisted of 24,364 unique configurations. As stated previously, there are ∼${10}^{270}$ possible proton configurations. Thus, the accessible phase space at 300 K is a very small fraction of the total.

Figure 4.

(A) Energy distribution obtained from MC simulation of the oxidized enzyme, showing the calculated data (solid circles) and the Gaussian best fit (solid line). (B) Energy distributions for the oxidized enzyme (solid line) immediately after N2 reduction (short-dashed line) and after the protonation state has been allowed to equilibrate to the new redox state (long-dashed line).

Due to the discrete nature of the proton configurations, we can discuss the protonation-state energetics in terms of energy levels associated with the unique configurations in analogy to quantum mechanical systems. At pH 7, complex I has a significant positive charge, so the introduction of an electron into the system should result in a lowering of the protonation-state energy irrespective of the redox energetics. Immediately upon reduction of N2, the peak in the energy distribution is shifted down in energy by ∼42 kJ/mol. Significant reordering of the energy levels is observed, as is a broadening of the distribution. After relaxation of the protonation state (both internal proton rearrangement and proton exchange with the solvent phase) in response to the reduction of N2, the peak in the energy distribution is further shifted by approximately −9 kJ/mol, for a total shift in the distribution peak of −51 kJ/mol (Fig. 4).

To determine the number of active ionizable sites in the simulations, we examine the energy dependence of the density of states (for example, see Hill (40)). The probability associated with state${\stackrel{\rightharpoonup }{\text{n}}}^{\text{s}}$ is given by

$$\text{P}\left({\stackrel{\rightharpoonup }{\text{n}}}^{\text{s}}\right)\propto \text{g}\left(\text{s}\right){\text{e}}^{-\beta {\text{E}}_{\text{s}}},$$ (4)

where $\text{g}\left(\text{s}\right)$ is the density of states and β is the inverse temperature, $1/k_{B}T$. We can rewrite the density of states as an explicit function of the energy, $\text{g}\left(\text{s}\right){=\text{kE}}_{\text{s}}^{\alpha },$ where k is a constant and the exponent α is related to the degrees of freedom of the system, $\text{D}=\alpha -1$. Rewriting Eq. 4, we have

$$\text{P}\left({\stackrel{\rightharpoonup }{\text{n}}}^{\text{s}}\right)={\text{ke}}^{-\beta {\text{E}}_{\text{s}}+\alpha \text{ln}{\text{E}}_{\text{s}}},$$ (5)

where we have incorporated the partition function into k to form the equality. By fitting the probability distribution(s) in Fig. 4 to Eq. 5, the exponent α can be determined directly. However, it can be shown that α is related to the variance of the distribution by Taylor expansion of Eq. 5 to the second order, resulting in $\alpha ={\sigma }^2{\beta }^2$, where ${\sigma }^2$ is the distribution variance.

From the above analysis, it was determined that α ∼ 101. This indicates that ∼100 of the 897 ionizable sites are active during the MC simulation and account for the observed fluctuations in the energy. The standard deviations for the oxidized and reduced distributions are similar at 25.1 and 25.7 kJ/mol, respectively. From this, we find that the number of active ionizable sites is nearly constant upon reduction of N2. Fig. 5 illustrates the number of sites, ${\text{N}}_{\text{f}}$, that change protonation state, or flip, at least f times for the oxidized simulation. Nearly 400 sites flip at least once whereas one site flips a maximum of 389 times during the simulation. The curve in Fig. 5 drops off exponentially with a decay constant of ∼1/100. From this decay constant, a mean lifetime of ∼100 sites is evident.

Figure 5.

Plot of the number of residues, N_f, that change state, or flip, at least f times during the MC simulation, showing the calculated distribution (solid line) and best fit (dashed line). The distribution drops off exponentially with a decay constant of ∼0.01.

Conclusion

We have shown that respiratory complex I has a high isoelectric point for all protein dielectrics studied. At neutral pH, the enzyme exhibits a large positive charge and is very poorly modeled by the nominal model. The investigation of FeS cluster-cluster interactions has illustrated how the protein charges, in particular charges arising from the protonation/deprotonation of ionizable sites, also contribute significantly to the dielectric screening. This is achieved primarily through the dispersion of charge over many ionizable sites associated with the injection of an electron into the chain of redox centers.

The experimentally measured redox-Bohr effect was shown to be reproduced only with a low protein dielectric of 4. The FeS cluster-cluster interactions obtained at low protein dielectric best reproduce the values previously deduced from experimental results. Both quantities strongly suggest that the environment around the terminal FeS cluster N2 is indeed a low dielectric environment. This finding is consistent with the results of Medvedev et al. (35), of recent x-ray crystal structures of the intact holoenzyme that place N2 ∼30 Å from the mitochondrial membrane (16,17), and the fact that within the quinone binding site the quinone headgroup is only ∼14 Å from N2 (41), which necessitates the quinone's migration into the hydrophilic domain from the membrane.

The calculations further show that complete or near complete proton uptake is associated with partial reduction of the enzyme at pH 7. This is perhaps somewhat surprising considering the large excess of positive charge associated with the enzyme at neutral pH. We have also shown that ₄His-169 is, or can act as, the redox-Bohr group associated with N2. This result is consistent with mutagenesis experiments. Finally, we have shown that the protonation-state dynamics is dominated by only 100 of the ∼900 ionizable sites in complex I. This indicates that only a small fraction of the available phase space is accessible at room temperature, and that relatively few sites need to actually be considered.