Intermonomer electron transfer in the bc₁ complex dimer is controlled by the energized state and by impaired electron transfer between low and high potential hemes

Abstract

The cytochrome bc₁ complex (commonly called Complex III) is the central enzyme of respiratory and photosynthetic electron transfer chains. X-ray structures have revealed the bc₁ complex to be a dimer, and show that the distance between low potential (b_L) and high potential (b_H) hemes, is similar to the distance between low potential hemes in different monomers. This suggests that electron transfer between monomers should occur at the level of the b_L hemes. Here we show that although the rate constant for b_L → b_L electron transfer is substantial, it is slow compared to the forward rate from b_L to b_H, and the intermonomer transfer only occurs after equilibration within the first monomer. The effective rate of intermonomer transfer is about 2-orders of magnitude slower than the direct intermonomer electron transfer.

1. Introduction

1.1. The cytochrome bc₁ complex in respiratory and photosynthetic electron transport

Cytochrome (cyt) bc complexes (Complex III in mitochondria) occupy the central position in the energy transducing membranes of mitochondria, bacteria and chloroplasts (the related cyt b₆f complex), as well as many archaea, and the evolutionary homology of the bc complex among these groups is well established [1]. The functional core of all bc₁ complexes comprises 3 catalytic subunits that contain all the redox active centers, with a variable number of additional, non-redox active polypeptides. There are four identifiable redox centers and at least two quinone-binding sites. Two b-type hemes have relatively low redox mid-point potentials (E_m). Cyt c₁ and the Rieske iron-sulfur protein (ISP) are the high potential components of this complex. The two known quinone binding sites are center “o” (or Q_o site), where oxidation of ubiquinol provides reducing equivalents to the complex, and center "i" (hence Q_i site), where ubiquinone is reduced (reviewed in [1–5]).

1.2. The bc₁ complex as a functional dimer

Cyt bc₁ complexes are organized as dimers both in detergent solution (see, e.g., [6,7]) and in crystals [8–13], and it is now generally accepted that the dimer is the functional form. Strong implication of a functional role for the dimer comes from three sources: (i) the ISP is oriented so that its functional globular domain is associated with one b-subunit, while the transmembrane helix is associated with the other b-subunit, across the symmetry axis; (ii) the two “i” sites share a common volume from which quinone and quinol exchange with the larger membrane pool; (iii) the proximity of the low potential b_L hemes in each monomer strongly suggests the occurrence of intermonomer electron transfer (Fig. 1).

Figure 1.

A - Cytochrome b dimer with 4 hemes. Distances are between the nearest edges of each porphyrin macrocycle. The figure was prepared in VMD [35] using file 2A06.pdb. B - Intermonomer electron transfer (shown by dashed arrow) occurs after equilibration within the first monomer via equilibrium constant K_bLbH for electron transfer between hemes b_L and b_H, and K_bHQ, for electron transfer from b_H to Q_i. This scheme shows only the case when, initially, there is no semiquinone at the Q_i site. The value of 0.5 ms shown for the intrinsic monomer-monomer electron transfer is based on the assumption that λ =1 eV.

The X-ray structures show that various specific inhibitors bind to both monomers, in a seemingly symmetrical fashion [14], and the only direct evidence suggesting any non-equivalence of the two monomers comes from the co-crystal structure of Lange and Hunte [15], in which cyt c is bound to only one cyt c₁ in each dimer. Nevertheless, there are numerous observations, especially involving inhibitor actions at substoichiometric titres, that have suggested functional asymmetry.

Several models for a functional role of the two monomers within a dimer have been suggested, beginning with the pioneering work of de Vries [16–19]. De Vries proposed a double Q cycle in which the two monomeric halves of the enzyme act cooperatively to complete the catalytic cycle [16]. Similarly, Gopta et al. [18] proposed a dimeric Q-cycle where the energetically unfavorable oxidation of the first ubiquinol molecule by one of the bc₁ monomers is driven by the energetically favorable oxidation of the second ubiquinol by the other monomer. Nieboer and Berden [17] explained their titration of the steady-state activity of mitochondrial ubiquinol-cyt c oxidoreductase with combinations of antimycin, myxothiazol and DCCD (N, N '-dicyclohexylcarbodiimide) by assuming that the bc₁ complex is a functional dimer, consisting of “electrically interacting protomers”. Gutierrez and Trumpower [19] observed that one molecule of stigmatellin per dimer completely inhibits bc₁ complex activity (see, however, [20]). The results indicated an anticooperative interaction between monomer sites, and the authors proposed a half-of-the-sites reactivity for the bc₁ complex. Schmitt and Trumpower [21] had earlier suggested a half-of-the-sites reactivity with respect to cyt c, consistent with the structural findings of Lange and Hunte [15] for the bc₁-cyt c co-crystals.

Inhibitor titration curves have frequently been taken to indicate interactions or cooperativity within the bc₁ complex (see, e.g., [17,22,23]). However, there are other possible sources of such titration behavior (see, e.g., [23–25]). Bechmann et al. [23] suggested that the S-shaped dependence of many apparently high affinity inhibitors of the bc₁ complex was due to their fast movement between binding sites in the dimer and a large partition coefficient between lipid and water. They also considered fast electron transfer between monomers in a dimer, but regarded this as less probable.

1.3. “Cross-dimer” (monomer-to-monomer) electron transfer

The correlation between the rate of electron transfer and distance between the cofactors (see, e.g., [26]) strongly supports the likelihood of effective electron sharing between monomers, via the b_L hemes, during bc₁ complex turnover [27]. At the same time, the symmetry of the complex has confounded the measurement of this electron transfer. In general, two different approaches have been used to date to try to elicit evidence for it, but there is still no unequivocal demonstration.

The first method, which predates the structural knowledge, is the creation of heterogeneity in the dimer by binding specific inhibitors sub-stoichiometrically and measuring the electron-transfer characteristics in such inhibitor-induced “heterodimers” (see, e.g., [17,19,28,29]). The classic difficulty with this approach is the statistical creation of distinct populations of bc₁ dimers with 0, 1 and 2 sites blocked (see, e.g., [17]). This creates the possibility for alternative explanations of any observed effect, especially in the case of steady-state rate measurements, where multiple turnovers of both Q_i and Q_o sites are needed. These include the well-known Kröger-Klingenberg effect [25] (a reflection of the two-substrate nature of the bc₁ complex), the possibility of fast intermonomer inhibitor exchange [23], number heterogeneity in the distribution of bc₁ complexes (and reaction centers) in natural vesicles [30,31], rate limitation in quinone delivery (especially detergent solubilized, isolated bc₁ complex), and modified kinetics and thermodynamics of artificial quinones.

A second approach has been to try to augment or diminish the direct intermonomer electron transfer rate by modifying the protein medium between the b_L hemes [32]. However, if what we know about electron transfer is even half right, this is doomed to failure – the hemes are sufficiently close that even putting a vacuum between them would be unlikely to modify the rate enough to make a noticeable difference.

2. Hypothesis

Rate-distance correlations based on established theory [33,34] predict a substantial b_L-b_L electron transfer rate, but the b_L-b_H electron transfer is expected to be ~2 orders of magnitude faster. We therefore suggest that net monomer-monomer electron transfer (MET) occurs only after pre-equilibration of the electron within one monomer (b_L↔b_H↔Q_i). This results in an effective rate of transfer that is 2 orders of magnitude slower than the direct process, under uncoupled conditions. However, the b_L↔b_H equilibrium constant is sensitive to the membrane potential. Thus, as the membrane potential builds up, the population of reduced b_L increases and the net rate of MET also increases. In effect, direct intermonomer electron transfer (without pre-equilibration of the electron within one monomer) is observed only under conditions when b_L-b_H electron transfer is impaired, and there is no significant electron transfer between monomers under uncoupled conditions, or in isolated bc₁ complexes, when the reaction is activated by ubiquinone.

3. Discussion

3.1. Estimation of b_L-b_L and b_L-b_H electron transfer rates from rate-distance correlation

The rate of electron transfer between electron carriers in proteins decreases exponentially with distance (see, for example, [26,33,34,36–38]). The logarithm of the rate constant, k, of intraprotein electron transfer between two electron carriers with edge-to-edge distance r can be described by the following equation:

$${log}_{10}k=15-\sigma r-\gamma {(\mathrm{\Delta }{G}^0+\lambda )}^2/\lambda$$ (1)

where r is in Angstroms, σ is a “length constant” commonly taken to be equal to 0.6 Å⁻¹ [34], but which may have some dependence on the packing density of a protein [34,38]; ΔG⁰ is the standard reaction free energy in eV; λ is the reorganization energy in eV. In classical Marcus theory [33], the value of γ is given by F/(4RT·ln10) = 4.2 (at T = 298 K), where F is the Faraday constant, R is the gas constant, and T is the absolute temperature. Moser et al. [34] consider γ as an empirical term and obtained a value of 3.1 from best fits to large data collections, thereby possibly accommodating some quantum contributions. For the bc₁ complex, all parameters, except the reorganization energy, are known for both b_L-b_L and b_L-b_H electron transfer. The edge-to-edge distance between low-potential hemes estimated from X-ray structural analysis of the bovine bc₁ complex with resolution 2.1 Å is 14.3 Å, while the edge-to-edge distance between b_L and b_H in one monomer is 12.0 Å [14]. Following accepted practices, we refer to “edge-to-edge” distances, taken between the macrocycle pi-electron systems of the hemes [38,39]. The standard reaction free energy, ΔG⁰, is 0 for b_L-b_L electron transfer and approx. −0.1 eV for b_L-b_H electron transfer.

For λ=1 eV, equation 1 yields an intrinsic time of ~0.5 ms and ~5 μs for electron transfer between b_L-b_L and b_L-b_H, respectively. The two orders of magnitude difference between rates of b_L-b_H and b_L-b_L electron transfer leads to the predominant reduction of b_H in the same monomer. The absolute values of these rates are very sensitive to uncertainties in the parameters, but the relative rates are much less so.

3.2. The ratio of b_L-b_H to b_L-b_L electron transfer rates is large and almost independent of the reorganization energy

Using Eq. 1 one can estimate the ratio of b_L-b_H to b_L-b_L electron transfer rates, k_bLbH/k_bLbL. While the precise values of the reorganization energy are unknown, the difference Δλ=λ_bLbH - λ_bLbL is expected to be small. For Δλ=0, Figure 2 shows that the ratio of b_L-b_L and b_L-b_H electron transfer rates is ~10² and is almost independent of the reorganization energy. The two orders of magnitude difference in the b_L-b_L and b_L-b_H electron transfer rate constants leads to the dominant reduction of heme b_H first, i.e., the branching ratio, P = k_bLbL/(k_bLbL+k_bLbH), is small (see below). Therefore, we can assume that the equilibrium between b_L and b_H within one monomer is established before any significant electron exchange between monomers takes place.

Figure 2.

The dependence of the ratio of the intrinsic rate constants for b_L-b_L and b_L-b_H electron transfer on the reorganization energy, calculated from Eq. 1 for Marcus and Moser-Dutton treatments. The edge-to-edge distance between low-potential hemes was assumed to be 14.3 Å, while the edge-to-edge distance between b_L and b_H in the same monomer was taken as 12.0 Å [14]. The standard reaction free energy, ΔG⁰, is 0 for b_L-b_L electron transfer and ~ −0.1 eV for b_L-b_H electron transfer. It is assumed that λ_bLbH = λ_bLbL.

3.3. The apparent time of monomer-monomer electron transfer

It is straightforward to estimate the apparent rate of single electron transfer between monomers, k^app (assuming that there is no more than one electron in either monomer of the dimer). The net rate of electron transfer is determined by the population of b_L- and the intrinsic b_L - b_L electron transfer rate. Since the forward rates within a monomer are clearly fast, the electron is initially in quasi-equilibrium within one monomer:

Here K_bLbH is the equilibrium constant of electron transfer between b_L and b_H hemes; K_bHQ, is the equilibrium constant of electron transfer from b_H heme to Q_i; k_bLbL is the intrinsic rate constant for direct electron transfer between b_L hemes (see also Fig. 1).

In this case the apparent rate constant of the MET can be approximated by the product of the intrinsic rate constant of the electron transfer between b_L hemes and the quasi-equilibrium relative population of reduced b_L in the monomer, k^app ≈ k_bLbL{Q_ib_Hb_L⁻}. According to Scheme 1 the fraction of reduced b_L is:

Scheme 1

$$\left\{Q_i{b}_H{b_L}^{-}\right\}=1/(1+K_{\mathit{bLbH}}(1+K_{\mathit{bHQ}}))$$ (1)

The observed time for the “leaking” of electrons from the first to the second monomer is given by:

$${\tau }^{\mathit{app}}\equiv 1/k^{\mathit{app}}\approx {\tau }_{\mathit{bLbL}}(1+K_{\mathit{bLbH}}(1+K_{\mathit{bHQ}}))$$ (3)

The equilibrium constant K_bLbH for one-electron transfer from b_L to b_H, measured in the presence of myxothiazol and antimycin, is equal to ~20 in the absence of Δψ [40]. However, it is known that myxothiazol shifts the redox potential of b_L by ~ 20 mV [41]. Thus, the value of 15–25 for the equilibrium constant K_bLbH determined in the presence of myxothiazol [40] should correspond to a value of 30–50 in the absence of myxothiazol. In all further calculations we will assume that K_bLbH=40 in the absence of myxothiazol.

The equilibrium constant between b_H and quinone is ~3 (estimated from the difference in midpoint potentials of b_H /b_H⁻ (~50 pH 7) and Q/Q⁻ (~80 mV, pH 7)). If we take τ_bLbL ~0.5 ms, as estimated above for λ=1 eV, the apparent time of monomer-monomer electron transfer will be:

$${\tau }^{\text{app}}\approx 0.5(1+40\ast 4)\approx 80\hspace{0.17em}\text{ms}$$ (4)

This estimate illustrates that the apparent time of monomer-monomer electron transfer could be substantially slower than the typical turnover time of the bc₁ complex under uncoupled conditions (~1 ms when quinone pool is reduced, and ~ 10 ms when the quinone pool is oxidized). However, we should stress here that this estimate involves the absolute value of the rate constant k_bLbL, which is based on the use of the distance-rate correlation. In contrast to the ratio of rates, it is significantly dependent on the value of the reorganization energy. As a result, the apparent time of MET also depends on this unknown value (Figure 3).

Figure 3.

Dependence of the apparent time of monomer-monomer electron transfer, τ^app, on the reorganization energy, calculated from Eq. 3, with τ_bLbL calculated from Eq. 1. The equilibrium constant K_bLbH for electron transfer from b_L to b_H is equal to 40. The equilibrium constant K_bHQ, for electron transfer from b_H heme to Q_i is taken as 3; τ_bLbL =0.5 ms (see text); other parameters as for Fig. 2. Shaded area indicates the characteristic times of bc₁ complex turnover.

If the Q_i site of the initial monomer is already occupied by semiquinone, the new electron will form QH₂, which will equilibrate rapidly with the pool. A similar description of the intramonomer equilibrium is valid, but includes unbinding of QH₂. The overall equilibrium with the quinone pool will strongly deplete electrons from b_L and the net rate of intermonomer transfer by this route will be negligible, and certainly not distinguishable from diffusion of QH₂ between sites.

3.4. The transmembrane electric potential controls the monomer-monomer electron transfer

Due to the transmembrane orientation of the b_L and b_H hemes, the equilibrium constant of electron transfer between them, K_bLbH, depends on the value of the transmembrane electric potential, Δψ:

$$K_{\mathit{bLbH}}={K^0}_{\mathit{bLbH}}{e}^{-\alpha \mathrm{\Delta }\psi F/RT}$$ (5a)

Here K⁰_bLbH is the value of the equilibrium constant of electron transfer between b_L and b_H hemes at zero transmembrane potential, R is the gas constant, T is the absolute temperature, F is the Faraday constant, α is the fraction of Δψ applied between b_H and b_L. Because the center-to-center distance between b_L and b_H is about 20 Å, compared to a typical membrane thickness of 40Å, we have assumed a value of α=0.5. Structures of the bc₁ complex indicate that electron transfer between b_H heme and Q_i has little transmembrane vectoriality. However, the reaction is clearly electrogenic [42–46] and this is now ascribed to electrogenic protonation of reduced Q_i species [45,47]. Whatever the origin of the electrogenicity the equilibrium constant, K_bHQ, is also dependent on Δψ, in much the same way as for b_L-b_H electron transfer:

$$K_{\mathit{bHQ}}={K^0}_{\mathit{bHQ}}{e}^{-\alpha \mathrm{\Delta }\psi F/RT}$$ (5b)

For the sake of illustration, we will assume that the two steps - b_L-b_H and b_H-Q_i – are equally electrogenic (α=0.5 for both equilibria), which is close to relative contributions suggested for the bc₁ [43] and b₆f [46] complexes. Combining equations 3 and 5, and assuming that RT/F = 25 mV, we have:

$${\tau }^{\mathit{app}}\approx {\tau }_{\mathit{bLbL}}(1+{K^0}_{\mathit{bLbH}}{e}^{-\mathrm{\Delta }\psi /50}(1+{K^0}_{\mathit{bHQ}}{e}^{-\mathrm{\Delta }\psi /50}))$$ (6)

Equation 6 predicts that increasing Δψ, increases the population of reduced b_L and accelerates the apparent electron transfer between monomers.

Figure 4 shows the dependence of the apparent time of electron transfer between monomers on the transmembrane electric potential. As Δψ is increased up to a high steady-state value (200–250 mV), the apparent intermonomer electron transfer accelerates by about two orders of magnitude. The absolute value of the time for MET depends significantly on the unknown reorganization energy and on γ (Fig. 4). For λ ≥ 0.7 eV, the rate under weakly coupled conditions (Δψ ≤ 70 mV) is slower than the corresponding turnover time of the bc₁ complex (approx. 1 ms). However, at larger values of Δψ, the rate of MET speeds up and the rate of turnover slows, and the two become comparable. The choice of γ is significant and, for γ = 3.1, the rate of MET at Δψ ≥ 200 mV is only slower than the coupled turnover time for rather large values of λ (≥1.35 eV). For the classical form of the Marcus equation, with γ = 4.2, the MET rate remains slower than the coupled turnover time for λ ≥ 1.0 eV.

Figure 4.

The dependence of the apparent time of electron transfer between monomers, τ^app, on the transmembrane electric potential at different value of the reorganization energy, λ, calculated from Eq. 6. Parameters used for calculation are the same as for Fig. 3. Shaded area indicates the characteristic times of bc₁ complex turnover.

In spite of the large uncertainty in the appropriate tunneling parameters for electron transfer between the b-hemes, the estimates of Fig. 4 illustrate that the apparent time of monomer-monomer electron transfer is likely to be significantly slower than the optimal turnover time of the bc₁ complex under uncoupled conditions (~1 ms when the quinone pool is well poised), and even when the quinone pool is oxidized (~ 10 ms). However, they also suggest that MET can become a significant pathway under conditions of tight coupling, when Δψ achieves maximal levels.

3.5. The transition probability for direct b_L-b_L electron transfer is small even with a fully developed transmembrane electric potential

The one-step transition probability or branching ratio,

$$\text{P}=k_{\mathit{bLbL}}/(k_{\mathit{bLbL}}+k_{\mathit{bLbH}}),$$ (7)

characterizes the fraction of complexes in which b_L-b_L electron transfer occurs instead of electron transfer to b_H. The transmembrane electric potential influences this transition probability through the electric field dependence of k_bLbH, but the large value of the ratio of the intrinsic rate constants for b_L-b_L and b_L-b_H electron transfer (Fig. 2) means that the probability remains small, even at the largest transmembrane potential. At 250 mV, the transition probability is still substantially less than 0.1 for all considered values of the reorganization energy. Thus, the main mechanism of intermonomer electron transfer necessarily involves pre-equilibration of the electron within one monomer, which is characterized by the observed (apparent) time for the “leaking” of electrons between monomers.

3.6. Direct b_L-b_L electron transfer is observed only when electron transfer between low and high potential hemes is impaired

The small branching ratio for an electron on b_L (even in the presence of a transmembrane electric potential) means that direct b_L-b_L electron transfer, without prior equilibration within the initial monomer, is significant only when forward electron transfer to b_H is impaired. This could occur when b_H heme is partially reduced (when one electron is already present within the monomer, i.e., (Q_ib_H)⁻) or fully reduced (when 2 electrons are already present within the monomer, i.e., Q_i⁻b_H⁻). In this case direct b_L-b_L electron transfer could become significant for the continued function of the complex. Such “impaired” forward electron transfer due to pre-reduction of b_H can arise from the Δψ dependence of K_bHQ in the highly coupled, energized state, but also under reducing conditions, and in inhibited states. In all other cases, the inter-monomer electron transfer occurs only after the equilibration within the monomer.

3.7. Significance

We find that although the intrinsic rate for b_L→b_L electron transfer is substantial, it is slower than the forward rate from b_L to b_H and intermonomer electron transfer occurs significantly only after equilibration within the first monomer. Under uncoupled conditions, the effective rate of MET is then about 2-orders of magnitudes slower than the direct transfer (τ^app ~10² ms under uncoupled conditions for λ=1 eV). As a result, MET is likely to be slower than the typical turnover of the bc₁ complex (1–10 ms). However, under conditions that substantially decrease the equilibrium constant of electron transfer between b_L and b_H hemes (e.g., large transmembrane electric potential, or alkaline pH), the net rate of MET can approach and exceed the “respiratory controlled” turnover time of the bc₁ complex.

Thus, MET allows the bc₁ complex to adapt to tightly coupled conditions, when the membrane potential can lead to partial reduction of b_H or even b_L. MET facilitates equilibrium distribution of the reducing equivalents to minimize the chance that both b hemes are reduced in one monomer. Without MET, the distribution of electrons is expected to be statistical, with the relative accumulation of singly reduced monomers in which the electron is shared between Q_i and b_H and, to a lesser extent, b_L. Intermonomer electron exchange minimizes the population of singly reduced monomers by allowing the dismutation of semiquinones in adjacent Q_i sites to disproportionate. Nevertheless, if b_H is pre-reduced in one monomer and a subsequent turnover in the same monomer produces reduced b_L, direct b_L-b_L electron transfer also comes into play. Thus, MET can “relieve” the bc₁ complex, by minimizing the chances of accumulating reduced b_L. This, in turn, decreases the probability of metastable low-potential semiquinone at the Q_o site, produced by transient oxidation of quinol by the iron sulfur center when oxidized b_L is not available to take the other electron. This is widely thought to be responsible for the production of superoxide in the bc₁ complex [48,49], and MET therefore serves to lower the propensity for superoxide production.

It has been known for some time that the bc₁ complex possesses transhydrogenase activity [50], but the mechanism is unknown. MET accounts for this activity by allowing electrons from quinol in the Q_i site of one monomer to reduce the quinone in the Q_i site of the other monomer in a dimer. Although originally demonstrated with an unphysiological quinone (duroquinone), such transhydrogenase activity of complex III could be functional in the reduction of vitamin E [51,52]. This would be important for vitamin E recycling and antioxidant protection of membrane [53,54].

MET also provides a mechanism for semiquinone dismutase activity, meaning that when two semiquinones are present in each monomer, MET allows oxidation of one semiquinone and reduction of the other and release of Q and QH₂ to the pool. This effectively restores the original Q-cycle model of Mitchell [55], in which one electron to Q_i comes via the b hemes and the other from an alternate source (a dehydrogenase, originally). According to current versions of the Q-cycle, the first turnover of the bc₁ complex, originating from quinol oxidation at the Q_o site, leads to semiquinone formation at the Q_i site. The only fate for this semiquinone in such models was waiting for the second turnover of the same Q_o site. MET provides the additional possibility of semiquinone dismutation within the bc₁ complex dimer with release of QH₂. In fact, Mitchell and Moyle [56] proposed that the bc₁ complex might function as a dimer, with Q_i- from one monomer donating to the other, by ”local electron conduction”. MET, as we envision it, is a regulated mechanism to achieve this.

Abbreviations and Notations

bc₁ complex

ubiquinol:cytochrome c oxidoreductase

b_L and b_H

low- and high-potential hemes of cytochrome b, respectively

cyt

cytochrome

E_h

redox potential of the medium

E_m

midpoint redox potential

F

the Faraday constant

ISP

Rieske iron-sulfur protein

k^app

apparent rate constant of electron transfer between monomers

K_bHQ

the equilibrium constant of electron transfer from cyt b_H to Q_i

K_bLbH

the equilibrium constant of electron transfer between b_L and b_H hemes

K⁰_bLbH

the equilibrium constant of electron transfer between b_L and b_H hemes at zero transmembrane potential

K^Δψ_bLbH

the equilibrium constant of electron transfer between b_L and b_H hemes at transmembrane potential Δψ

k_bLbH

the intrinsic rate constant of electron transfer between b_L and b_H hemes in the same monomer

k_bLbL

the intrinsic rate constant of electron transfer between b_L hemes

MET

monomer-monomer electron transfer

Q

coenzyme Q (ubiquinone)

QH₂

dihydroquinone (quinol)

Q_i site (Q_o site)

quinone reducing (quinol oxidizing) site of bc₁ complex

r

edge-to-edge distance

R

the gas constant

Rb

Rhodobacter

r_bLbH

edge-to-edge distance between b_L and b_H hemes

r_bLbL

edge-to-edge distance between b_L and b_H hemes

SQ

semiquinone

T

the absolute temperature

α

the fraction of Δψ applied between b_H and b_L

γ

the coefficient in Eq.1, equal to either 4.2, or 3.1

λ

the reorganization energy in eV

Δλ

difference of reorganization energies for the reactions b_L↔b_H and b_L↔b_L

Δψ

transmembrane electric potential

τ^app=1/k^app

apparent time of electron transfer between monomers, which takes into account the equilibration within the initial monomer

τ_bLbL

intrinsic time of electron transfer between b_L hemes

ΔG⁰

the standard reaction free energy in eV