Concerted Two-Electron Reduction of Ubiquinone in Respiratory

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Concerted Two-Electron Reduction of Ubiquinone in Respiratory Complex I Published as part of The Journal of Physical Chemistry virtual special issue “Abraham Nitzan Festschrift”. Muhammad A. Hagras* and Alexei A. Stuchebrukhov* Department of Chemistry, University of California Davis, One Shields Avenue, Davis, California 95616, United States

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S Supporting Information *

ABSTRACT: Respiratory complex I catalyzes two-electron/two-proton reduction of a ubiquinone (Q) substrate bound at its Q-binding pocket; upon reduction, ubiquinole carries electrons further down the electron transport chain. The mechanism of this two-electron transfer reaction is poorly understood. Here we consider a hypothetical scheme in which two electrons transfer together with two protons in a concerted fashion. On one side, a coupled electron/proton transfer occurs from the reduced N2 FeS cluster and protonated His38 residue, respectively, while on the other side a hydrogen atom transfer occurs from the neutral Tyr87 residue, generating a tyrosyl radical. A method to evaluate the coupling matrix element that corresponds to a concerted tunneling of two electrons was developed. Overall, our calculations indicate that the concerted reaction is feasible, in which case a transient tyrosyl radical is formed during the catalytic cycle of the enzyme.

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INTRODUCTION NADH:ubiquinone oxidoreductase (complex I) is the first enzyme in the electron-transport proton-pumping respiratory chain (ETC) located in the inner-mitochondrial membrane in eukaryotes or plasma membrane in prokaryotes, which converts the free energy of redox reactions to electrochemical proton gradient across the membrane, following the fundamental Mitchell chemiosmotic principle.1−3 The created proton gradient, among other things, is driving ATP synthesis in the cell. Electron transfer in respiratory complex I occurs via a chain of redox centers, starting from a bound NADH which donates electrons to a FMN cofactor, and then across seven iron−sulfur (Fe/S) clusters (N3, N1b, N4, N5, N6a, N6b, N2) to finally reduce the bound ubiquinone (Q) molecule at the Qbinding pocket. Ubiquinone with the addition of two electrons and two protons becomes ubiquinole (QH2) and carries electrons further down the respiratory chain.4 This last step in the electron transport chain of complex I is the focus of this paper. The mechanism of the reduction of ubiquinone in the binding pocket of complex I is poorly understood.5,6 Of particular interest is the formation of the transient semiquinone radical (QH or Q−), which is expected to be formed in a stepwise reduction mechanism.7 Experimental EPR data8,9 do show radical signals; however, the functional role of these radicals remains unclear. In fact, two different radical signals have been reported, which behave differently in response to the potential on the membrane hosting the enzyme. The recent higher resolution spectra8 (Qband) of the two radicals yield their split g(x,y,z) values but are still difficult to unambiguously interpret as both are due to © 2019 American Chemical Society

semiquinones, based on other high-resolution spectra of these species.10 The true high-resolution spectra for complex I are yet to be obtained. A detailed discussion of the ambiguities of experimental data for the quinone reaction is given in ref 11. Theoretically, the reduction reaction is also unclear. The difficulty is related to the fact that the redox potential of the first electron, i.e. Q/QH pair, appears to be very low, perhaps in the region of −300 mV;12 on the other hand, the potential of the N2 cluster, an immediate donor of electrons is much higher (between −80 and −180 mV13); thus, the semiquinone formation is uphill in energy. It is usually assumed that both electrons are coming from the FeS chain, which is partially reduced14 under normal physiological conditions; thus, the second electron should come again from N2 after its rereduction by an electron from another iron−sulfur cluster of the chain, most likely N6a, two clusters up along the chain.4 However, the sequential reaction appears to be unlikely, i.e., too slow, due to rather long, over 30 Å, distance of the source of the second electron. The rate for the second electron arrival to N2 is expected to be of the order of 10 to 100 μs,15,16 and due to the uphill energetics of the semiquinone intermediate, which gives an additional factor of at least 102, the overall reaction appears to exceed a typical turnover time of one millisecond. The relatively low potential for the first electron is due to a low affinity of the electron forming the radical, unlike that of the second electron in the pair QH/QH2 that stabilizes the system and has the potential around +500 mV. These data Received: April 30, 2019 Revised: May 28, 2019 Published: May 29, 2019 5265

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provided that the quantum coupling for a concerted transition is strong enough, so that the reaction is kinetically competitive. The present paper makes an estimate for such a coupling in a specific example of quinone reduction in complex I. It is interesting that some experimental studies of another enzyme of the electron transport chain, complex III, suggest that oxidation of quinones may occur via a similar concerted reaction, i.e. in a reaction reversed in the direction to one considered here.19,20 A tyrosyl radical considered here is not an unusual intermediate in redox biochemistry; in particular, one most relevant example is provided by the redox cycle of complex IV of ETC, where a tyrosine residue donates one of the four electrons for oxygen reduction.5,21 The other two wellknown examples are photosystem II and ribonucleotide reductase. However, we need to mention that in complex I, the experimental situation with tyrosine 87 in the binding pocket, Figure 1, is also controversial. There was one report22 in the past that the mutation of this highly conserved residue resulted in almost complete loss of activity of the enzyme when a close analogue of ubiquinone Q10 was used as a substrate, which would indicate the expected importance of Tyr87; however, the mutated enzyme appeared to function normally with some other (Q1, Q2)22 substrates. If so, then it is not clear which group provides the second proton for the reduction. Under these circumstances, it is particularly interesting to consider the possible role of Tyr87, the very presence of which at exact place in the binding pocket where it can potentially facilitate the quinone reduction invites exploration of various possibilities, including one considered in this paper. The study of N2 Fe4S4 cluster spin states shows energetically favorable electron localization on the lower two iron centers, mainly due to the tandem Cys45 and Cys46 residues, which facilitate tunneling between N2 and the quinone, as shown in Figure 1. The coupling between Tyr and the quinone is also strong due to close distance. The Tyr residue can therefore also donate a proton. The second proton is coming from His38 residue, see Figure 1, which is presumed to act as a rotating proton shuttle23,24 between the quinone headgroup and an aspartic acid, which acts as a step-stone for proton delivery, and is located nearby (not shown in Figure 1). The mobility of His residue is supported by our molecular dynamic simulations. Thus, it appears the binding pocket of quinone, Figure 1, is built perfectly to catalyze the quinone redox reaction. To estimate the rate of a concerted reaction, a method to compute the coupling matrix element that corresponds to a concerted tunneling of two electrons was developed.19 The contribution of protons to the reaction rate was evaluated using methods discussed in ref 18. Overall, our calculations indicate that the concerted reaction is feasible, in which case a transient tyrosyl radical is formed during the catalytic cycle of the enzyme.

can be rationalized based on bond energies of the quinones and refer to neutral species. However, there are other reports that the first electron potential is −37 mV and the second −235 mV,17 with similar data in ref 7. Thus, the experimental situation with redox potentials and overall reaction mechanism is unsettled. Given the experimental uncertainties with the sequential reaction, it is of interest to explore a theoretical possibility of a concerted two-electron/two-proton reaction, where the second electron is coming from the tyrosine residue located in the binding pocket of quinone, while the first one is from the N2 FeS cluster, as usually assumed, as shown in Figure 1.

Figure 1. Structure of the binding site, and main cofactors of the ubiquinone reduction reaction. For clarity, UQ1 is shown instead of UQ10. It is proposed Tyr87 donates hydrogen atom, generating (transient) tyrosyl radical. Second electron is coming from N2 cluster, and additional proton is transferred from His38. A red dashed arrow shows the first ET pathway while the green dashed arrow shows the second ET pathway.

In such a reaction, the tyrosine residue donates both an electron and a proton in a way of a hydrogen atom transfer (HAT), a process in which a tyrosyl radical is generated. Eventually the tyrosyl radical is reduced, and the radical generated−not a semiquinone but a tyrosyl−is of transient nature. Such a concerted two-electron tunneling reaction is of practical interest as it provides the solution to the high-energy semiquinone intermediate which is to be formed in certain cases; in a concerted reaction, such an intermediate is avoided. Theoretically, such concerted reactions are of special interest, as they involve electronic states coupled by two-electron tunneling. In fact, what we propose can be described as a two-electron PCET reaction. Indeed, a proton-coupled ET, PCET,18 is usually considered when the sequential ET/PT or PT/ET reaction has a high barrier. The concerted PCET is a way to avoid the high-energy intermediate. Here we essentially suggest the same. Assuming that the first reduction (PCET1) is uphill in energy, the concerted reaction (2×PCET) can indeed avoid the barrier in a way similar to the usual one-electron PCET,

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METHODS In this study, we examined the two-electron tunneling transition and the corresponding electron tunneling pathways25,26 from the reduced N2 cluster and neutral tyrosine residue to a bound Q molecule at the Q-binding pocket of complex I shown in Figure 1. N2 cluster is a tetranuclear Fe/S cluster (4Fe−4S) which under physiological conditions has two redox states with formal iron valences (+3, +3, +2, +2) for oxidized and (+3, +2, +2, +2) for reduced states.27 The N2 cluster high-spin iron centers are antiferromagnetically 5266

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eventually they relate this picture to the rate of electron transfer reaction by the Marcus−Levich−Dogonadze equation: ÄÅ É 2 ÅÅ (ΔG + λ)2 ÑÑÑ 2π ⟨TDA ⟩ 0 Å ÑÑ Å kET = expÅÅ− ÑÑ ÅÅÅ ÑÑÑ ℏ 4πλkBT λ k T 4 B (4) Ç Ö

coupled, and its electronic structure is characterized by many quasi-degenerate electronic states.28 We applied the brokensymmetry (BS) density functional theory (DFT) method,29 as implemented in Gaussian 09 package,30 to calculate the desired initial guess molecular orbitals (MOs), which are then utilized in semiempirical ZINDO (Gaussian 09 package) electronic structure calculations to obtain the multielectronic diabatic donor and acceptor states and the corresponding coupling matrix element of the two-electron tunneling transition. The semiempirical ZINDO method utilized in our calculations was previously validated and applied successfully to produce accurate electronic spectra of polynuclear transition metal complexes comparable to time-dependent DFT (TDDFT), but at a much lower computational cost.31 It is also known to predict reliably the electronic spin states as compared to DFT.32 Previously, ZINDO method was extensively used in calculations of electron transfer in organometallic complexes33 and various respiratory chain protein complexes.16,19,34 Generally, ZINDO has been shown empirically to be valuable in treating extended molecular systems, and so its use here is appropriate. According to electron tunneling theory,35−37 the tunneling matrix element is related to quantum mechanical transition flux between the initial and final states across the dividing surface S‡:

∫∂Ω

TDA = −ℏ

(d s ⃗ ·J ⃗ )

D

Here λ is the reorganization energy, ΔG0 is the free energy change (−ΔG0 is the driving force), TDA (or modified coupling VDA if protons are involved, as discussed later) is the coupling matrix element discussed above, and the brackets stand for the statistical averaging over possible variations in the transition state configuration of the system that occur along the dynamic trajectory of the system, or different states involved in the reaction. eq 2 gives the general multielectronic description the transition flux (or current) J(⃗ r⃗) as a matrix element of a oneelectron operator j ⃗ ̂ ( r ⃗) between the multielectronic donor and acceptor diabatic states |D⟩ and |A⟩. The two states |D⟩ and |A⟩ are nonorthogonal, as they belong to two different Hamiltonians, D and A, and thus, ⟨A|D⟩ ≠ 0. The calculation of such matrix elements is done by using corresponding orbitals.38−42 Namely, when the donor and acceptor states are represented by single-determinant many-electron wave functions, a set of corresponding orbitals can be introduced by appropriate unitary transformation of the original HF canonical MO’s of both states, |ΨD⟩ = |φ1DμφND⟩

(1)

Here TDA is the coupling matrix element, J⃗ is the electronic transition flux, and ∂ΩD is the dividing surface between the donor and acceptor complexes, located in regions ΩD and ΩA, respectively. In addition to the coupling matrix element, the spatial distribution of flux J(⃗ r⃗)carries information about how the charge redistribution actually occurs in space, i.e. describes tunneling pathways. The tunneling calculations involve two (nonorthogonal) diabatic electronic states |D⟩ and |A⟩, corresponding to localized charge on the donor and on the acceptor respectively, and the transition flux J(⃗ r⃗) is the matrix element between states A and D of the current density operator: J ⃗ ( r ⃗) = −i⟨A|j ⃗ ̂ ( r ⃗)|D⟩

|ΨA⟩ = |φ1AμφNA⟩

so that the overlap matrix of |ΨD⟩and |ΨA⟩ is diagonal: = δijsi. In the basis of corresponding molecular orbitals, the matrix element for current assumes a particularly simple form: jij zyz 1 J ⃗ ( r ⃗) = jjj∏ sjzzz∑ Ji ⃗ ( r ⃗) jj zz s k j { i i Ji ⃗ ( r ⃗) =

∑ a ∈ΩD, b ∈ΩA

(6)

ℏ (φ D∇φi A − φi A∇φi D) 2m i

(7)

In this picture, each electron undergoes an independent transition from the initial to final state orbital,φDi → φAi , with the corresponding flux given by eq 7. The total current is naturally the sum of currents between corresponding orbitals, one pair of orbitals per electron. Corresponding orbitals resembles normal modes of molecular vibrations. They are also closely related to Dyson orbitals.43 Notice that each one-electron term Ji⃗ (r⃗) has a weight factor, which is the Franck−Condon overlap of the initial and final state, in which one pair of orbitals (and one electron) is excluded:

(2)

The formulation is the same for a one-electron or multielectronic description of the system. In order to describe the tunneling pathways in terms of chemical structure, the so-called interatomic currents Jab are introduced, which are coarse-grained currents flowing between atoms. The total current through an atom is proportional to the probability that the tunneling electron will pass through this atom during the tunneling jump, thus the concept allows one to determine the atoms of the molecular structure that are involved in the tunneling transition. Moreover, interatomic currents Jab are also connected to the coupling matrix element in a way similar to that of spatial flux J,⃗ namely TDA = −ℏ

(5)

⟨φAi |φDj ⟩

FC(i) = ⟨A|D⟩(i) =

∏ sj j≠i

(8)

⟨φAj |φDj ⟩.

were sj = Naturally, in a tunneling transition, all electrons undergo change of state, even if only a single charge is transferred; however, typically only a few pairs of orbitals with smallest overlaps si contribute significantly to total current, as in the case discussed in this paper. This drastically simplifies the multielectronic picture of the transition. In practice, only one or two (as in this paper) orbitals undergoes significant “relocation” in space, from the donor to

Jab (3)

where the sum of interatomic currents crossing the dividing surface is calculated, instead of the surface integral in eq 1. Both interatomic currents Jab and current density J(⃗ r⃗) provide full information about the tunneling process, and 5267

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Here, the lowest energy oxidized (4 in total) and reduced (3 in total) spin states were chosen as suitable candidates to probe the electron transfer reactions (Figure 2). Out of the 12

the acceptor, and naturally the overlap for such a pair(s) is very small, as only far tails of such orbitals overlap. All other orbitals remain pinned down to same bond or group of atoms and change very little in response to a transferred charge, so that the overlaps for such orbitals are close to unity. Accordingly, one (or two, as in this paper) pair of tunneling orbitals contributes mostly to total current. This allows introducing an effective one-electron picture of the transition: ij yz j z ℏ J ⃗ ( r ⃗) = jjj∏ sjzzz (φtD∇φt A − φt A∇φtD) jj zz 2m k j≠t {

(9)

Hence the coupling matrix element takes the following form: OTE TDA = TDA FC(t )

(10)

where FC(t ) =

∏ sj = ⟨core(A)|core(D)⟩ (11)

j≠t 44

is the electronic Franck−Condon factor, OTE TDA =−

ℏ2 2m

∫∂Ω

D

and

(φtD∇φt A − φt A∇φtD) d s ⃗

(12)

is a Koopmans-type, one tunneling electron (OTE) approximation for the coupling matrix element. Since the exchange effects are taken into account in HF Hamiltonian, the OTE approximation can also describe the hole transfer.37,40,45 The reduction to a one-tunneling-electron picture described above allows for an obvious generalization when two (or more) electrons tunnel in concert. In case of two tunneling electrons, as in this paper, only two overlaps are small, and hence, two pairs of corresponding orbitals contribute to the coupling matrix element. The resulting formula utilized in this paper is given in the results section below, together with a modification due to participation of protons. The integrated flux through a dividing surface will be denoted as total flux F.

Figure 2. Relative electronic energies of the different N2 cluster oxidized (total spin = 0 in red and spin = 1 in green) and reduced spin electronic states (total spin = 1/2 in blue). The spin configuration of N2 cluster is shown for the lowest energy spin states (red arrow represents ferrous center and green arrow represents ferric one). Tandem cysteine residues are represented by two-connected yellow circles. Allowed combinations of reduced and oxidized spin states during ET reaction are indicated by hashed arrows.

possible combinations, only two pairs (O2/R3 and O3/R3) have the corresponding spin polarizations (ΔS = 0) on iron atoms for ET reaction to occur. Since ΔS = 0 during ET reaction, only specific pairs of states are possible candidates for the reduced/oxidized donor/acceptor states in the reaction, and hence, they were taken as typical representatives of all the states involved in the reaction. We picked the most stable candidate (O3/R3) to conduct our ET calculations. The energetic stability of this particular combination is attributed to the extra-delocalization of the tunneling electron through the tandem cysteine residues (cys45 and cys46) as seen by in-phase overlap of α-spin highestoccupied MO (HOMO) state and α-spin lowest-unoccupied MO (LUMO) state (Figure S2). Such stabilization is lost for other states, due to the out-of-phase overlap through the tandem cysteines. Another factor which has to be included in the analysis of ET reaction is His38 conformation relative to the Qbenzoquinone group. Histidine residue is known to function as a rotating proton shuttle.23,24 By manual rotation of the His38 imidazole ring, two initial conformations were formed: hydrogen-bonded (H-bonded) conformation with respect to benzoquinone oxygen atom and 180° rotated imidazole ring with respect to H-bonded conformation. We then run the molecular dynamics (MD) simulation. (It was formally done on the whole respiratory complex I embedded in a membrane with ubiquinone (Q6) inside its Q-binding pocket, although

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RESULTS AND DISCUSSION In electronic structure calculations, the donor and acceptor states were defined as follows. Donor state is reduced N2, reduced TyrOH, protonated His38H+, and quinone Q; the acceptor state is oxidized N2, oxidized TyrO radical tyrosyl, deprotonated (neutral) His38, and (reduced) quinol QH2. As described in the Supporting Information, the charge transfer system is reduced to a manageable size by protein pruning, and calculations were performed to find donor and acceptor electronic states, using external field to simulate resonant condition for charge transfer, keeping protons halfway between the initial and final equilibrium states. Overall, 30 (combinatorial) oxidized spin states with total spin = 0 and spin = 1, and 12 reduced spin states with total spin = 1/2 were calculated on a model system for N2 redox center (Figure S1 and Table S1). BS-ZINDO was applied to generate the correct antiferromagnetic coupling of spin states for the N2 cluster. These states exhibit characteristic quasidegeneracy; for example, within an energy window of kBT there are typically four or more states (Table S1). This high density of states indicates that in ET reaction from or to Fe4S4 clusters multiple states are typically involved. Therefore, an averaging of the (square of) coupling of different states occurs in such reactions. 5268

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Figure 3. Molecular dynamics simulation of ubiquinone bound at Q-binding pocket of respiratory complex I with two possible His38 conformations (H-bonded and Edged-T). On the right side, the simulated respiratory complex I is shown embedded in the membrane. Panels a and d show the distance (r1) for H-bonded and edged-T conformation, respectively. Panels b and e show the distance r2. Panels c and f show the distance r3. The middle panel shows the distances measured. Two different ubiquinone-6 conformations at the Q-binding pocket are shown in panels g and h. Panel g: Q6 aromatic headgroup is hydrogen-bonded to both His38 and Tyr87 residues. Panel h: Q6 aromatic headgroup is in the edged T-conformation to the His38 residue. (For additional details see the Supporting Information to this paper.)

state of a concerted reaction. The tunneling orbitals were selected using the method of corresponding orbitals, as described in refs 35−37. As shown in Figure S4, indeed for the donor tunneling orbital the α-electron is localized on N2 cluster while the β-electron is localized on Tyr87. For the acceptor tunneling orbitals, both α- and β-electrons are localized on the Q molecule. The electronic couplings and the tunneling pathways for the concerted α- and β-ET reactions were probed for four different model states: N2 at reduced/oxidized two lowest-energy spin states in combination with His38 at H-bonded and e-T conformation in each case; the reaction of largest coupling was then selected. As shown in Figure 4 (panel A), for one such reaction, in which the α-electron is initially localized on the lower right iron of N2 and His38i is in H-bonded conformation, the tunneling transition currents in α-spin span the Ala47 residue between N2 and Q and form a primary pathway with a shorter through-space jump of 2.7 Å; the secondary pathway involves an Ala44-Tyr87 link with a larger through-space jump of 3.6 Å. The corresponding transition fluxes (the total integrated flux is denoted as Fα and Fβ in eq 13) are shown in Figure 5. The fluxes are highly conserved for a midposition of the dividing surface, as expected; the conservation of flux is used an internal validation of the high-quality calculation.16 The strong coupling and the conservation of tunneling flux along the α-ET path is mainly due to a favorable in-phase overlap between the biorthogonalized donor/acceptor α-tunneling molecular orbitals (TMO) tails at the Ala47 residue (Figure S5, panel a). Similar trends in α-ET reactions but with a much lower ET probability are observed with His38 at edged-T conformation, which signify the importance of hydrogen-bonding between His38 and Q for the ET reaction to occur. For β-ET reactions, occurring between Tyr87 and Q, different reduced/oxidized spin states combinations or different His38 conformations do not significantly affect the corresponding ET flux and corresponding coupling. This is expected as such β-ET reaction is more localized between Tyr 87 and Q along the formed hydrogen-bond with

our problem is obviously local, and relatively short runs of several tens to a hundred nanoseconds were sufficient.) Two MD simulations were employed; each was started with one His conformation. By monitoring the important through-space distances along the MD trajectory (r1, r2, and r3; Figure 3), it is clear that His38 stays in the H-bonded conformation (r1 ∼ 1.75 Å, Figure 3 panel a) when initially started from it; thus, the Hbonded conformation is stable. Moreover, when started from a 180°-rotated H-bonded conformation (Figure S2, panel a), another metastable conformation is detected, which is the edged-T conformation (r1 ∼ 7.0 Å, Figure 3, panel d, Figure S2 panel b), but His38 quickly rolls back to the more stable Hbonded conformation (Figure S2 panel d). Hence, His38 can exist in either stable H-bonded or a metastable edged-T (e-T) conformation (Figure 3, panels g and h). The conformation of His38 has a 2-fold significance. First, His38 in H-bonded conformation can donate a proton directly to benzoquinone oxygen of ubiquinone, unlike that in e-T conformation. Second, the ubiquinone headgroup also has to assume a specific conformation with respect to Tyr87 and Ala47 for a concerted ET reaction to occur. As shown in Figure 3 (panels b, e), different conformations of His38 do not significantly affect the through-space distance between Tyr87 and Q (range ∼1.5−2.0 Å). On the other hand, the throughspace distance between Ala47 and Q (Figure 3, panels d and f) depends dramatically on the His38 conformation: ∼4.0 Å for H-bonded and ∼6.0 Å for edged-T. We therefor conclude that His38 has to be in the H-bonded conformation for an efficient ET from N2 to Q along Ala47 path (more specifically discussed below) to occur. This conformation was chosen for a subsequent electronic structure calculation. BS-ZINDO method was utilized to calculate the diabatic donor and acceptor states; in donor state, one electron is localized on N2 (α-spin state) and one on Tyr87 (β-spin), and in the acceptor state both electrons are localized on Q. In such calculations, Tyr87 hydroxyl hydrogen atom and His38 (in Hbonded conformation) amino hydrogen atom were placed midway between their corresponding residue and Q benzoquinone oxygen atoms. This is the model transition 5269

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the β-ET flux is much higher, but the corresponding overlap in α-spin is smaller, see below, thus both transitions contribute) for the H-bonded configuration, and the overlap values si of sαTMO = 5.27 × 10−4 and sβ-TMO = 5.97 × 10−3, the corresponding ET matrix element can be calculated based on the formula19 ÅÄÅ ÑÉ ij yz ÅÅ 1 1 ÑÑÑÑ jj zz Å TDA = −ℏjj ∏ si zzstαstβÅÅ Ftα + Ftβ ÑÑ jj zz ÅÅ stα stβ ÑÑÑÖ ÅÇ (13) k i ≠ tα , tβ { where tα and tβ are tunneling orbitals of α- and β-spin. In the discussion above and elsewhere, by α-ET flux Fα and β-ET flux Fβ we mean fluxes in tα and tβ tunneling orbitals. The corresponding Franck−Condon factor (FC, the product of si, i.e., overlaps of all pairs all orbitals, except for tunneling ones, tα and tβ) for α-spin = 0.893 and β-spin = 0.934, which signify minimal polarization influence on the core orbitals upon ET reaction. The total ET matrix element = 2.27 × 101 cm−1. Of course, these data should be interpreted only semiquantitatively, as only few states were probed, a specific configuration of the transition states was taken, and the contribution of the protons (see below) is not yet taken into account. With confidence, however, we take this as indicating that for a concerted two-electron tunneling transition, in which one electron tunnels to Q from N2 and another from Tyr87, the pure electronic coupling is of the order of 10−20 cm−1. The calculated ET coupling is surprisingly high, given a concerted two electron tunneling nature of the reaction (compared e.g. to other tunneling reactions in complex I16); however, this is perfectly explained by the close donor/ acceptor proximity in β-ET reaction, and the strong coupling between the Tyr87 and Q. In fact, without the second tunneling reaction, the one-electron coupling of Tyr87 and Q would place this reaction in adiabatic regime (the coupling is much higher than kBT). Given such a strong coupling, the electron tunneling reaction alone, can be, according to Marcus theory (maximum rate), as high as 1010−1011 per second. But this is only electronic part of the reaction. We now need to include (estimate) proton contribution to the reaction. In general, proton-coupled electron-transfer reactions (PCET) are much reduced in (maximum) rates, compared with uncoupled reactions, simply because the joint probability

Figure 4. Electron tunneling flux densities of the concerted reaction N2 → Q←Tyr87. (A) α-Electron tunneling flux density at the transition state of the reaction with His38 at H-bonded conformation. Solid blue arrows indicate primary electron tunneling pathway and hashed ones indicate secondary pathway. Through-space distances (Å) are shown next to the arrows. The color intensity manifests the contribution of the corresponding atom/bond to electron transfer reaction. (B) β-Electron tunneling flux density for the same state with His38 at H-bonded conformation.

constructive overlap between biorthogonalized donor β-TMO on Tyr87 and acceptor β-TMO on Q (Figure S5, panel b). The data shown in Figures 4 and 5 are typical for a strongly coupled donor and acceptor states. We noticed that for some other pairs the coupling is much weaker, which indicates that these states do not contribute to the reaction. Thermal averaging occurring naturally in real system obviously helps the protein to find the strongly coupled states and transfer electrons with high efficiency. Thus, the high degeneracy of spin states in FeS clusters appears to play a fundamental role in such reactions. On the basis of the conserved α-ET flux (Fα = 4.21 × 1001 cm−1) and β-ET flux (Fβ = 4.60 × 1004 cm−1) (as anticipated,

Figure 5. Logarithmic plots of the α/β-electron tunneling fluxes calculated across a separating surface running perpendicular to the direct line connecting N2 FeS cluster (origin) to Q-benzoquinone oxygen atom (normalized coordinate = 1.0). Panel a shows the logarithmic fluxes of the αelectron tunneling from N2 cluster to Q for R3/O3 N2 spin states combination and different His38 conformations. Panel b shows the logarithmic fluxes of the β-electron tunneling. The black vertical arrows indicate the midpoint of the corresponding α/β-electron tunneling fluxes taken for coupling matrix element evaluation, as explained in the text. 5270

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the formally high potential prevent the described reaction from happening? To this we note that upon PCET (or rather HAT) both the proton and an electron are displaced very short distance between Tyr87 and Q, and therefore, the standard redox potential is not a reliable guide in this case. Indeed, more relevant is bond energy, as in fact an H atom is transferred. The actual precise values of redox potentials and other energetics parameters are difficult to evaluate accurately in poorly defined and fluctuating protein environments. We therefore suggest that the predicted reaction involving Tyr oxidation would be best to test experimentally. The key observation is that Tyr87 radical is formed in the reaction, which, despite its transient nature, should be possible to detect, if it indeed exists,22 as our estimate suggests.

of both proton and electron making transition at the same time is small; each probability being small, the product is even smaller. The detailed theory of such reactions is reviewed in ref 18. A good estimate of the reduction factor can be taken from the so-called nonadiabatic PCET reaction in which effective coupling for the reaction is obtained as a product of pure electronic coupling, estimated above and the Franck−Condon overlap of the protonic wave functions χH+ D/A in the donor and acceptor states: eff el V DA = ⟨χAH + |χDH + ⟩TDA

(14)

The rate, in nonadiabatic limit, is proportional to square of the effective coupling, |VefDAf |2. The overlap of the vibrational protonic functions is obviously less than unity and can in practice be as small as 0.1, or even smaller,18 thus resulting in a significant reduction of rate. However, the small overlap of vibrational wave functions in the above formulation (assuming, for example, transition between two vibrational ground states, although this is not necessarily always the case46) implies that it will strongly depend on the mass, i.e., even smaller values should be expected for deuterium substitution of a proton and hence a very strong kinetic isotope effect. In practice, in many cases,18 as in this case, the strong KIE is not observed, indicating that at the transition state the two vibrational wells between which proton transfer occurs are essentially united due to the short distance between the two groups exchanging a proton; the vibrational barrier is reduced to essentially nonsignificant values, so that no proton tunneling through a vibrational barrier is involved. This, however, typically requires additional activation, to “push” the two groups exchanging the proton together, and the reaction transition state (the optimal distance between the two groups) is defined by a trade-off between this additional activation and the small overlap,18 both of which depend on the distance. In our case, the configuration that results from MD simulation is such that the two wells are not separated significantly and the overlap is of the order of 0.5 or slightly less. In our MD simulations, we could not detect activation energies that may result in additional factor of 0.5 or so, thus leaving the exact value of the reduction factor poorly defined. It is difficult to describe such reactions in proteins quantitatively accurately, as the geometry of the system is not known precisely. There are a number of energetic parameters that are difficult to evaluate accurately, and even the nature of the reaction (concerted vs sequential) is often uncertain; however, the order of magnitude can be typically predicted in a reasonably narrow range, to be of value in the discussion of experimental data.18 All of this is applicable here, and we are aware of the approximate nature of the estimate. Thus, it would be reasonable to assume the reduction factor for each proton to be of the order of 1/10, or slightly smaller; then the square of this factor becomes 1/100. Given our assumption that actually two protons will be transferred together with electrons, the overall reduction factor should be expected to be in the range 10−4−10−6, bringing the coupled two-electron two-proton transfer reaction to the range of 104− 106 per second. Thus, we expect the reduction factor due to coupled protons to be rather huge; however, the overall rate still appears to be in the physiologically meaningful range and therefore is considered as feasible. One can question the energetics of Tyr87 oxidation, for which a typical redox potential21 is on the order of 0.8 V. Can

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CONCLUSION We propose that the reaction of reduction of ubiquinone in respiratory complex I can occur via concerted two-electron two-proton transfer, one electron coming from the iron−sulfur cluster N2, and another from Tyr87, which is presumably a donor of both electron and a proton (hydrogen atom transfer, HAT). The transient tyrosyl radical is predicted to be formed in the reaction, which is reduced by the second electron eventually arriving via the iron−sulfur electron transport chain in the enzyme. The estimate, which involved an accurate electronic coupling of a concerted two-electron tunneling, and a crude evaluation of the reduction factor due to protons, suggests the reaction may occur with the rate of 104−106 per second, which would be in line with current understanding the mechanics of the enzyme chain.4 Alternatively, if electron transfers from Tyr and N2 occur sequentially (it is usually difficult to distinguish between the concerted and sequential reactions occurring in a short timewindow), then the two radicals Tyr• and SQ will be sequentially generated. One can speculate if the two different EPR signals of radicals reported in the literature are in fact due to these two species. The calculations were done using BS-ZINDO method, applying a novel theory of a concerted two-electron tunneling. The electronic structure method was successful in reproducing the antiferromagnetic coupling and the quasi-degenerate spin states of N2 cluster and in accurately capturing the overlap between the donor/acceptor tunneling orbitals for the ET reactions, as the theory of tunneling fluxes suggests. The N2 cluster in respiratory complex I is uniquely characterized by the tandem cysteine residues, which impart extra electrondelocalization, and to preferential electron localization on the two iron atoms of FeS cluster that facilitate ET between N2 and quinone. Two tunneling pathways were detected for α-electron from N2 to Q; through Ala47 or Ala44-Tyr87. On the basis of our simulations, concerted convergent ET reaction (where αelectron is transferred from N2 through Ala47 and β-electron from Tyr87) produces a conserved ET flux and requires the αelectron to be localized on the iron atom closer to Ala47. His38 conformations significantly impact the α-ET even with a fixed Q configuration, but it has a negligible effect on β-ET. An experimental test of this hypothesis is proposed, which is to look at the transient Tyr87 radical, a signature of the proposed mechanism. The proposed Tyr87 radical would parallel that formed in cytochrome c oxidase, where the catalytic center Tyr provides one of the four electrons for 5271

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The Journal of Physical Chemistry B oxygen reduction. Here a similar role is proposed for Tyr87 residue donating both electron and a proton to ubiquinone.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.9b04082.

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Molecular dynamics (MD) simulations, protein pruning, tunneling currents calculations, and additional tables and figures showing oxidized and reduced states of the N2 cluster and canonical and tunneling orbitals of the system (PDF)

AUTHOR INFORMATION

Corresponding Authors

*(M.A.H.) E-mail: [email protected]. *(A.A.S.) E-mail: [email protected]. ORCID

Muhammad A. Hagras: 0000-0002-6062-2544 Alexei A. Stuchebrukhov: 0000-0002-0673-1037 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported in part by NIH GM054052. REFERENCES

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