Electron Bifurcation: Thermodynamics and Kinetics of Two-Electron

Sep 6, 2017 - National Renewable Energy Laboratory, Golden, Colorado 80401, United ... the standpoint of energy conservation and electron delivery yie...
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Electron Bifurcation: Thermodynamics and Kinetics of Two-Electron Brokering in Biological Redox Chemistry Peng Zhang,*,† Jonathon L. Yuly,‡ Carolyn E. Lubner,§ David W. Mulder,§ Paul W. King,§ John W. Peters,∥ and David N. Beratan*,†,‡,⊥ †

Department of Chemistry and ‡Department of Physics, Duke University, Durham, North Carolina 27708, United States National Renewable Energy Laboratory, Golden, Colorado 80401, United States ∥ Institute of Biological Chemistry, Washington State University, Pullman, Washington 99163, United States ⊥ Department of Biochemistry, Duke University, Durham, North Carolina 27710, United States §

CONSPECTUS: How can proteins drive two electrons from a redox active donor onto two acceptors at very different potentials and distances? And how can this transaction be conducted without dissipating very much energy or violating the laws of thermodynamics? Nature appears to have addressed these challenges by coupling thermodynamically uphill and downhill electron transfer reactions, using two-electron donor cofactors that have very different potentials for the removal of the first and second electron. Although electron bifurcation is carried out with near perfection from the standpoint of energy conservation and electron delivery yields, it is a biological energy transduction paradigm that has only come into focus recently. This Account provides an exegesis of the biophysical principles that underpin electron bifurcation. Remarkably, bifurcating electron transfer (ET) proteins typically send one electron uphill and one electron downhill by similar energies, such that the overall reaction is spontaneous, but not profligate. Electron bifurcation in the NADH-dependent reduced ferredoxin: NADP+ oxidoreductase I (Nf n) is explored in detail here. Recent experimental progress in understanding the structure and function of Nf n allows us to dissect its workings in the framework of modern ET theory. The first electron that leaves the two-electron donor flavin (L-FAD) executes a positive free energy “uphill” reaction, and the departure of this electron switches on a second thermodynamically spontaneous ET reaction from the flavin along a second pathway that moves electrons in the opposite direction and at a very different potential. The singly reduced ET products formed from the bifurcating flavin are more than two nanometers distant from each other. In Nf n, the second electron to leave the flavin is much more reducing than the first: the potentials are said to be “crossed.” The eventually reduced cofactors, NADH and ferredoxin in the case of Nf n, perform crucial downstream redox processes of their own. We dissect the thermodynamics and kinetics of electron bifurcation in Nf n and find that the key features of electron bifurcation are (1) spatially separated transfer pathways that diverge from a two-electron donor, (2) one thermodynamically uphill and one downhill redox pathway, with a large negative shift in the donor’s reduction potential after departure of the first electron, and (3) electron tunneling and activation factors that enable bifurcation, producing a 1:1 partitioning of electrons onto the two pathways. Electron bifurcation is found in the CO2 reducing pathways of methanogenic archaea, in the hydrogen pathways of hydrogenases, in the nitrogen fixing pathway of Fix, and in the mitochondrial charge transfer chain of complex III, cytochrome bc1. While crossed potentials may offer the biological advantage of producing tightly regulated high energy reactive species, neither kinetic nor thermodynamic considerations mandate crossed potentials to generate successful electron bifurcation. Taken together, the theoretical framework established here, focusing on the underpinning electron tunneling barriers and activation free energies, explains the logic of electron bifurcation that enables energy conversion and conservation in Nf n, points toward bioinspired schemes to execute multielectron redox chemistry, and establishes a roadmap for examining novel electron bifurcation networks in nature.

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reduction potential range of −300 to +300 mV, couples reducing equivalents produced by ET from a quinol to a Rieske FeS cluster and a b-type heme.4 Flavin-based electron bifurcation, the focus of this Account, occurs at much more negative potentials (typically in the +100 to −500 mV range).

INTRODUCTION

Electron bifurcation couples exergonic and endergonic chemical reactions from a two-electron donor to two widely separated one-electron acceptors, while limiting energy dissipation as heat. Indeed, Peter Mitchell proposed electron bifurcation to explain the Q-cycle of respiration catalyzed by the cytochrome bc1 complex, and bifurcation is employed by bacterial and archaea as well.1−3 The Q cycle, operating in the © 2017 American Chemical Society

Received: June 30, 2017 Published: September 6, 2017 2410

DOI: 10.1021/acs.accounts.7b00327 Acc. Chem. Res. 2017, 50, 2410−2417

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Accounts of Chemical Research Electron bifurcation was recently described as the “third mode” of energy transduction in biology, complementing substratelevel phosphorylation and ET-linked phosphorylation.5 The recruitment of coupled uphill and downhill redox reactions in one protein is remarkable from both thermodynamic and kinetic perspectives. We will scrutinize the logic and control of these novel ET reactions. Electron bifurcation in flavoproteins was proposed when it was found that some anaerobic microorganisms couple the oxidation of NAD(P)H (E′0 = −320 mV) to the reduction of ferredoxin (E′0 typically ∼ −500 mV).6,7 This seemingly uphill thermodynamic reaction is overcome by coupling the reaction to the reduction of crotonyl CoA (E0′ = −10 mV). Soon after the discovery of flavin-based electron bifurcation, it was found that an unusual type of [FeFe]-hydrogenase couples the reduction of protons (to generate hydrogen gas, E0′ = −420 mV) to the endergonic oxidation of NADH and the concomitant exergonic oxidation of ferredoxin.8 Other bifurcating enzymes balance electron flow associated with the pyridine nucleotide pool (NAD(P)H). For example, NADHdependent reduced ferredoxin:NADP+ oxidoreductase I (Nf n) controls the relative amounts of NADH and NADPH present, and is thus a key regulator in the balance of catabolism and anabolism.9−11 Other examples of bifurcation include H2− and formate-dependent reduction of heterodisulfides coupled to ferredoxin reduction in methanogenesis,1,12 coupled NADPH oxidation and ferredoxin reduction to drive formate production in formate dehydrogenases,13 coupled exergonic electron flow from reduced ferredoxin to NAD+ with the endergonic reduction of NAD+ by lactate in lactate dehydrogenase, and coupled NADH oxidation to reduce quinone and ferredoxin in the Fix protein.14,15 These reactions are remarkable in their ability to couple thermodynamically downhill and uphill redox reactions, triggered by an obligate two-electron donor. The unifying feature of electron bifurcating flavoproteins is the presence of numerous electron-transfer cofactors (e.g., FeS clusters, flavins) on two spatially separated electron-transfer pathways that diverge from the bifurcating flavin.10,11 Interestingly, it has been found that the two one-electron reduction potentials of the bifurcating flavin are crossed.11 That is, the reduction potential of the singly oxidized flavin is much more negative than the reduction potential of the fully reduced flavin.16 Removing the second electron is more favorable thermodynamically than removing the first one. Therefore, the flavin anionic semiquinone state, ASQ (the singly oxidized donor), is energized in the bifurcating Nf n protein. We will explore whether or not this crossed potential landscape of Nf n is a necessary general feature to enable effective electron bifurcation.17 Electron bifurcation directs each electron on a different physical pathway, and this outcome could be realized via conformational gating, free energy control, or electron tunneling control. In the cytochrome bc1 complex, ET gating is proposed to involve conformational and/or redox mechanisms. In a conformational gating model, the second electron is prevented from entering the thermodynamically favorable, higher potential chain by a conformational change that moves the acceptor FeS cluster away from the donor quinone.18 It was suggested that an analogous gating mechanism could occur in structurally characterized Nf n,10 such that the two protein subunits undergo a redox state dependent conformational change that alters the distance between the bifurcating flavin and the FeS cluster of the endergonic path, analogous to the

Rieske FeS cluster domain movements in cytochrome bc1. However, our studies of Nf n indicate that a large scale conformational change is not required to explain successful electron bifurcation in this protein.11

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THEORETICAL FRAMEWORK The transfer of one electron between donor (D) and acceptor (A) cofactors, across nanometer distances, requires that two unlikely events occur. First, polarization fluctuations of the protein, solvent and counterions must bring the donor and acceptor cofactors into near electronic energy degeneracy. This probability is given by the nuclear Franck−Condon factor. Second, an electron must shift, via quantum-mechanical tunneling, from the donor to the acceptor during the persistence of the energy-matched geometry. Electron tunneling through proteins is mediated by their bonded and nonbonded coupling pathways.19−21 Since the time scale of electronic transit between distant donor and acceptor cofactors is typically much longer than the time scale of transient D−A energy matching, long-distance biological ET is nonadiabatic.22,23 The nonadiabatic ET rate is24 kET =

2π ⟨|HDA|2 ⟩FC ℏ

(1)

where ⟨|HDA|2⟩ is the thermally averaged D−A coupling and FC is the Franck−Condon factor. In the Marcus high-temperature limit:25 FC =

1 exp[− (ΔG + λ)2 /(4λkT )] 4πλkT

(2)

Square barrier tunneling models approximate the pathwaymediated coupling as26 0 2 ⟨|HDA|2 ⟩ = |HDA | exp[−βRDA ]

(3)

|H0DA|

is the D−A contact coupling and β is an electron tunneling-decay factor.26 β depends on the energetic proximity of the redox active cofactor states to those of the intervening protein, the tunneling pathway structure, and the pathway thermal fluctuations.19−21,24,27,28 There are four exponentially sensitive control knobs for ET: ΔG, λ, β, and RDA. Typical values of λ in proteins range from 0.2 to 1.5 eV.25,27 The reaction is activationless when −ΔG ≈ λ, and its rate is limited by electron tunneling. When −ΔG > λ, the reaction is “inverted,” and the rate decrease as −ΔG grows larger. Average tunneling decay values for proteins (β) range from 1.0 to 1.4 Å−1.19−21,26 As such, changing the ET distance by a few angstroms will change the rate by an order of magnitude. Electron bifurcation appears to have evolved tunneling interactions and reaction free energies in order to realize a 1:1 yield ratio and to dissipate relatively little free energy in the process. Our aim is to describe how this superb level of function is achieved. The Marcus expression (eq 2) applies to both uphill and downhill ET reactions, and the ET rate ratios satisfy detailed balance. For example, uphill ET with ΔG = +0.2 eV, λ = 1 eV, a contact electronic coupling of 0.1 eV and β = 1.0 Å−1 will have a rate of ∼108 s−1, while the corresponding downhill reaction with ΔG = −0.2 eV will proceed with a rate of ∼1011 s−1. Bifurcated ET from a doubly reduced donor, D=, produces two spatially separated acceptor cofactors, A−1 and A−2 . The ET rates to form A−1 and A−2 are governed by eqs 1−3. In particular, 2411

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Figure 1. (Left) Structure and positioning of the cofactors in Pyrococcus furiosus Nfn. Pf Nfn is a heterodimer composed of the 31 kDa Nfn-S and 53 kDa Nfn-L domains. Nf n-S contains S-FAD and a [2Fe-2S]. Nf n-L contains the site of electron bifurcation, L-FAD, and two [4Fe-4S] clusters.11 Fd is believed to bind near the distal [4Fe-4S] cluster of Nfn-L. NADH and Fd thus serve as the terminal electron acceptors. Edge-to-edge distances between cofactors are given in Å. (Right) Redox potential (E) landscape for Nfn. Note that the first electron flows uphill over 14 Å, and the second electron flows further downhill, on a different physical pathway, to an acceptor 7 Å from L-FAD. Typical tunneling distance decay factors and biological reorganization energies allow understanding of the 1:1 partitioning of electrons along the two pathways, enabled by a first left (red), then right (blue) bifurcation mechanism. We refer to the Nf n mechanism as “up/down,” as the first and second bifurcating ET steps (from the respective pathways) are endergonic and exergonic, respectively. Figure 1 (left) is adapted with permission from ref 11. Copyright 2017 Macmillan Publishers.

contributions for the two-electron oxidation−reduction couple (EOX/HQ). The bifurcating site was further investigated in a transient absorption spectroscopic experiment where the electron transfer rate between L-FAD and the proximal [4Fe4S] cluster was measured (from the lifetime of the L-FAD ASQ intermediate). Using this rate, the distance between the two cofactors (measured from the structure), the potential of the proximal [4Fe-4S] cluster, and empirical ET rate laws, the oneelectron couple of L-FAD was estimated, EOX/ASQ = −911 mV. The potential of the other one-electron couple of L-FAD was then calculated to be EASQ/HQ = +359 mV.11 We focus our theoretical analysis on the bifurcation steps involving L-FAD (denoted D) and its two closest iron−sulfur clusters, [2Fe-2S] (A1) and [4Fe-4S] (A2). The kinetics of bifurcation are D=A1A2 ⇌ D−A1−A2 ⇌ DA1−A2−. Further downstream ET reactions are believed to be one-electron transfer events that are kinetically uncoupled from the early steps. The protein is not believed to perform multicenter coherent ET because of the very large distances between the cofactors. Interestingly, the ET steps on the first electron’s pathway are endergonic overall, while the steps on the second electron’s pathway are exergonic overall. The coexistence of the two redox chains ensures the overall spontaneity (ΔG < 0) for electron delivery to the terminal acceptors in Nf n, NAD+ and ferredoxin (see Figure 1). The two-electron reduced HQ state (D=) of L-FAD delivers one electron to a [2Fe-2S] cluster (A1) about 14 Å away, leaving L-FAD in the singly oxidized ASQ state. Transfer from L-FAD to the [2Fe-2S] cluster, rather than to the closer [4Fe4S] cluster (A2), is favored because transfer to the A2 species would involve an uphill step on the scale of +0.96 eV (the Marcus activation factors for these competing steps are assessed below). In the second ET step, an electron moves from the energized L-FAD ASQ to the closer [4Fe-4S] cluster (A2). The free energy changes for the first and second ET steps from LFAD are approximately ΔG1 = +0.28 eV and ΔG2 = −0.19 eV, respectively.11 The electron moving along the first pathway must climb uphill to reduce NAD+: while disfavored, this reaction is not forbidden.

we focus on how the corresponding Franck−Condon and tunneling factors enable (1) the generation of ET products A−1 and A−2 in a 1:1 ratio and (2) a small net free energy dissipation (−ΔG) for the overall reaction D=A1A2 → DA−1 A−2 . These characteristics of electron bifurcation are discussed in the context of Nf n below.

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ELECTRON BIFURCATION IN NADH-DEPENDENT REDUCED FERREDOXIN: NADP+ OXIDOREDUCTASE (Nf n) The source of the bifurcating flavin’s electrons in Nf n is NADPH, which delivers two electrons to the flavin adenine dinucleotide (L-FAD) through a bimolecular reaction. Electron bifurcation in Nf n (Figure 1) then proceeds from the doubly reduced L-FAD in sequential one-electron transfer steps. The first electron transfers 14 Å to the [2Fe-2S] cluster, and the second electron transfers 7 Å to the [4Fe-4S] cluster.11 The two electron L-FAD donor changes from its doubly reduced hydroquinone (HQ) form to its singly oxidized ASQ form in the first ET step, and then to its doubly oxidized (OX) form. The one-electron reduction potential landscape, inferred from experimental data,11 is shown in Figure 1. As not every potential indicated in this figure is directly measured (or computed from simulation), this landscape should be viewed as a first draft. The energy landscape for flavin-based electron bifurcation in Nf n is derived from integrated spectroscopic and electrochemical experiments. Oxidation−reduction peaks at Em8 = −718 mV and at −513 mV were obtained by square wave voltammetry (SWV) measurements, were consistent with EPR spectroscopic experiments, and the values were assigned to the proximal and distal [4Fe-4S] clusters, respectively, on the pathway to ferredoxin. In contrast to these low potential iron− sulfur clusters, the [2Fe-2S] cluster on the NADH pathway was reported to have a relatively high (positive) reduction potential of Em8 = +80 mV.29 SWV revealed a broad peak at −276 mV that was assigned as the average of both L-FAD (the bifurcating site, located in the large (L) Nf n subunit) and S-FAD (the accessory flavin, located in the small (S) Nf n subunit) 2412

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ET reaction to flow to A1 is estimated to be −0.99 eV, while flow of the second electron to A2 is estimated to be −0.19 eV).

ELECTRON TRANSFER TIMING AND BRANCHING RATIOS The viability of sending the bifurcating flavin’s electrons along two spatially separated pathways is understood in the context of modern ET theory. The D=A1A2 → D−A−1 A2 reaction has a smaller activation free energy than does the competing strongly uphill D=A1A2 → D−A1A−2 reaction (see Figure 2b). The Marcus

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THERMODYNAMIC EFFICIENCY OF ELECTRON BIFURCATION The thermodynamic efficiency for DA−1 A−2 production from D=A1A2 is of particular interest, since Nf n is a simple ET broker, and the second law of thermodynamics guarantees that a nonzero commission must be paid to disburse the flavin’s two electrons. Kinetic analysis of the up/down reaction scheme (Figure 2a) indicates that the D−A−1 A2 intermediate population is negligible at any time, a desirable feature that supports electron bifurcation. This feature ensures a 1:1 branching ratio of the two one-electron products at a low overall thermodynamic cost. This characteristic is independent of the ratio of the two one-electron transfer rates k1 (from D= to A1) and k2 (from D− to A2). Making the first ET step uphill may have a physiological advantage as well, namely that the buildup of the highly reducing species, D−A−1 A2 would be insignificant in an up/down free energy landscape. As such, there is never very much of the highly reducing ASQ species present when the two reduction potentials are crossed as indicated in Figure 1 (right). Additionally, there will be no reverse electron transfer from A−1 to the bifurcating flavin, even though the departure of the first electron is endergonic. Other bifurcating enzymes seem to use the up/down free energy landscape adopted by Nf n (e.g., the quinones in the bc1 complex of mitochondria4). Michaelis−Menten (steady-state) analysis can be used to compute the rate of stepwise two-electron transfer k2e through an unstable intermediate in the up/down free energy landscape (Figure 2a):

Figure 2. Three possible sequences of ET reactions in the up/down free energy landscape for bifurcated ET of Nfn. Panel a shows the functional reaction pathway that initiates electron bifurcation. (a) D=A1A2 ⇌ D−A−1 A2 ⇌ DA−1 A−2 (physiological reaction); (b) D=A1A2 ⇌ D−A1A−2 ⇌ DA−1 A−2 (swapped reaction sequence); (c) D=A1A2 ⇌ D−A−1 A2 ⇌ DA=1 A2 (double reduction of primary acceptor A1). D represents L-FAD. A1 and A2 represent the [2Fe-2S] and [4Fe-4S] iron−sulfur clusters that are 14.1 and 7 Å away from L-FAD, respectively. The reaction pathway in panel (b) is prevented by a large activation free energy barrier (ΔG≠1 ≥ 0.96 eV), and the reaction pathway in panel (c) is disfavored by the small D−/A−1 electronic coupling (over the 14 Å donor−acceptor distance) and by the large activation free energy (since ΔG2 ∼ −0.99 eV).11

k 2e =

k 2k1 ΔG k 2 + k1 exp⎡⎣ − kT1 ⎤⎦

(4)

The reverse ET rate from A−2 to D is negligible because of its large positive ΔG value, so the D−A−1 A2 concentration likely reaches a steady-state value. If the second ET step from D− is much faster than the first electron recombination rate (k2 ≫ k1 e−ΔG1/kT), the overall ET rate k2e is equal to k1. In the opposite limit, k2e grows linearly with k2 (and may lead to population accumulation of the one-electron transfer intermediate and thus lowered bifurcation efficiency). There are other plausible free energy profiles, in addition to the up/down scheme, that could produce effective electron bifurcation, and this is the subject of the next section.

factor (eq 2) thus disfavors ET to the closer A2 species by ≥ ∼ 106-fold compared to A1, despite a tunneling factor that favors transfer to A2 by about ∼104-fold.26 The significant shift in the L-FAD redox potential upon oxidation to form ASQ changes the balance of tunneling and Marcus factors for the second electron, as described below, launching it in the opposite direction from the first electron! A crucial feature of bifurcated ET in Nf n is that fully reduced L-FAD undergoes structural/solvational changes after departure of the first electron, making the second electron much more reducing. This pivot in reduction potentials strongly enhances the FC factor (eq 2) for the D−A−1 A2 → DA−1 A−2 ET reaction, avoiding the formation of the competing DA1=A2 product. The large potential swing disfavors the flow of two electrons along the first pathway by placing ET of the second electron to A1 in the very highly activated regime, and perhaps in the Marcus inverted regime. This redox potential swing, and the 7 Å shorter distance between D− and A2, directs the second electron to the second physical pathway (ΔG for the second

Electron Bifurcation in Down/Down and Down/Up Free-Energy Landscapes

There are three possible free energy landscapes for electron bifurcation from a two-electron donor. One is the up/down scenario described above, and the other two landscapes are indicated in Figure 3: down/down and down/up. The D−A−1 A2 state may lie above both D=A1A2 and DA−1 A−2 (an “up/down” landscape, described above), below both D=A1A2 and DA−1 A−2 (a “down/up” landscape), or intermediate between D=A1A2 and DA−1 A−2 (“down/down” landscape). Endergonic ET First; Exergonic ET Second (Down/Down)

The steady-state two-electron transfer rate (eq 4) in the down/ down scheme of Figure 3a is the same as is found in the up/ down reaction scheme of Figure 2a. Kinetic analysis of the down/down scheme indicates that the D−A−1 A2 intermediate population is negligible at any time if k2 ≫ k1. In contrast, if k2 2413

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regardless of the difference in the two one-electron transfer rates. This behavior degrades the thermodynamic efficiency of electron bifurcation because rapid reverse ET in the second ET step will always favor the one-electron transfer intermediate state. At steady state, the thermodynamically favored lowenergy intermediate state will yield less than 100% of the 1:1 bifurcated product, regardless of the reactivity of the oneelectron intermediate. This down/up pathway seems unlikely to be attractive because of its lower thermodynamic efficiency compared to the other free energy landscapes.

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CROSSED REDOX POTENTIALS AND ELECTRON BIFURCATION Crossed redox potentials have been described as a hallmark of biological electron bifurcation (more negative reduction potential for the second electron than for the first).17 When potentials are crossed (and the free energy landscape is up/ down or down/down, see Figures 2a and 3a), the population of the singly oxidized donor is negligible, and the time evolution of the state populations mimics the circumstance that would be found with a concerted two-electron step from D=A1A2 to DA−1 A−2 . Note that the one-electron intermediate population in a two-step kinetic scheme is determined by the reaction freeenergy profile, which is defined by the reduction potentials of the redox partners, ΔG = −nF(EA − ED), where n is the number of electrons, F is Faraday’s constant and EA(D) is the reduction potential of the electron acceptor (donor). Kinetically, a negligible one-electron intermediate population is always found for the up/down free energy profile (Figure 2a) and may be found for the down/down free energy profiles (Figure 3a). These free energy landscapes do not, however, require crossed-potentials to produce effective electron

Figure 3. Alternative free energy profiles for bifurcated two-electron transfer reaction mechanisms. (a) In a down/down landscape, the first and second electron transfer reactions are both exergonic. (b) In a down/up landscape, the first electron transfer reaction is exergonic and the second is endergonic. In case (b), the two-electron transfer efficiency is low.

≤ k1, substantial D−A−1 A2 density will accumulate, although a 100% 1:1 two-electron transfer product ratio can be obtained at steady state if no loss of the D−A−1 A2 population arises through competing side reactions. The down/down bifurcation scheme can produce a 1:1 branching ratio at a low overall thermodynamic cost if either (1) D− is stable (that is, the ET rate for D− → A2 is faster than other reactions that would deplete the second electron from D−) or (2) if the rate of the second ET is much faster than the rate of the first ET. Electron bifurcation in the down/down scheme is thus more constrained compared to the up/down scheme. Exergonic First; Endergonic Second (Down/Up)

Kinetic analysis of the down/up reaction scheme in Figure 3b finds that the D−A−1 A2 intermediate will always accumulate,

Figure 4. Hypothetical uncrossed two-electron bifurcation landscapes. Panels (a)−(c) show the reduction potential landscapes; Panels (d)−(f) indicate the Gibbs free energy landscapes for the nearest neighbor electron bifurcation reactions D=A1A2 ⇌ D−A−1 A2 ⇌ DA−1 A−2 (these initial steps are enclosed in the dashed boxes in (a)−(c)). The first ET pathway (in red) is overall exergonic, while the second is overall endergonic (in blue). The free energy profile for two-electron bifurcation to A1 and A2 in (f) is similar to that in the Nfn protein. 2414

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by employing protein conformational gating. The reduction potential landscapes in Figure 4a and c are not monotonically downhill or uphill for the two spatially separated ET pathways. However, this does not influence the overall driving force for each ET chain, or the spontaneity of the electron bifurcation. The second viable uncrossed electron bifurcation mechanism does not necessarily produce a 1:1 electron transfer product ratio. Thus, a potentially less favorable down/up Gibbs free energy landscape (Figure 4e) could be used if the reduction potential landscapes for the two spatially separated ET pathways are monotonically downhill or monotonically uphill (Figure 4b). This landscape seems less favorable, in light of the disadvantages discussed above for the down/up energy landscape. However, these disadvantages may not be as serious in the case of uncrossed potentials. In the uncrossed case, the second electron donor (D−) is less strongly reducing compared to the crossed potentials case. Therefore, capture of the second electron by adventitious reactions may be of limited concern. The second electron will be slowly drained from the system, following its uphill progress (e.g., by dissociation of the terminal reduced ET product). In the case of uncrossed potentials, therefore, the down/up free energy landscape may be operative as long as the ET rate from D− to the desired electron acceptor is faster than competing side reactions. However, a slow offloading of the second electron (D−A−1 A2 → DA−1 A−2 ) will reduce the achievable electron bifurcation flux, as it will lengthen the time scale for the enzyme to complete an entire redox cycle. The most viable uncrossed potential landscape for electron bifurcation appears to be the down/down free energy landscape (Figure 4d). However, there are at least two physiological disadvantages associated with the uncrossed landscapes. If the first electron is highly reducing, the protein will need to prepare and store this reactive species at the bifurcating site. This would seem less dangerous if the initial state could be triggered suddenly (e.g., by light) and could promptly carry out its chemistry. A second drawback of uncrossed potentials is that the transfer of the second electron at A2 (along the thermodynamically uphill pathway, indicated by the blue energy levels in Figure 4) could recombine with D (reverse ET). In the case of crossed potentials, this is not an issue, since the molecular changes that produce the strongly reducing D− state eliminate the possibility of reverse ET from A−1 . Both the up/down (Figure 4f) and the down/down (Figure 4d) uncrossed landscapes suffer from the possibility of charge recombination. The effectiveness (and novelty) of the crossed-potential landscape is that the first electron’s progress is locked in by the spontaneous transfer of the second electron. Departure of the first electron in the crossed-potential scheme essentially eliminates the possibility of reverse ET to the bifurcating site. This is a novel feature of crossed potentials that produces an outcome similar to that achieved by large-scale conformational changes following ET. The slow departure of the second electron from D− in the uncrossed-potential landscape could impede the overall progress of bifurcation, delaying the regeneration of the two-electron donor D=, and the further cycling of the protein. The dual advantage of crossed potentials in minimizing the presence of a highly reactive intermediate and of avoiding back ET of the first electron may be physiologically compelling.

bifurcation based purely on thermodynamic and kinetic grounds. Why, then, might biology favor crossed potentials? Crossed potentials5,17 are well-known in Nf n, and in other proteins. While we suggest that crossed potentials are not essential on thermodynamic or kinetic grounds in order to realize electron bifurcation, crossed-potentials may have advantages. A crossed potential reaction scheme guards against the persistence of highly reactive species that could cause physiological harm, or (at best) energy dissipating side reactions. Our conclusion that crossed potentials are not essential on kinetic or thermodynamic grounds (provided that initial electron delivery to the bifurcating site is kinetically viable in the first place) is reached by recognizing that forming the two-electron product, DA−1 A−2 , in high yield and at low thermodynamic cost, is the metric for successful electron bifurcation. As well, the flavin’s redox potentials must be compatible with eventual hole filling. With these simple metrics of success, it does not matter whether the first or second redox chain is exergonic, so long as DA−1 A−2 is produced efficiently. Viable hypothetical electron bifurcation landscapes that do not employ crossed potentials are sketched in Figure 4, and these serve as intriguing targets for synthetic bioinspired electron bifurcating assemblies. In the proposed uncrossed electron bifurcation schemes, the flux along the first pathway is exergonic and the flux along the second pathway is endergonic. Assembly of such synthetic ET structures would be useful to prove that crossed potentials are not a prerequisite for effective electron bifurcation. The most significant difference between uncrossed and crossed bifurcation pathways is the difference in the reducing power of the first (D=) and the second (D−) electron donor species. In the L-FAD regulated bifurcation of Nf n, the reduction potential of OX/ASQ (D/D−) is estimated to be very strongly reducing, at a potential of −911 mV. ASQ can reduce essentially all electron acceptors that fall in the ∼2 V window exploited in bioenergetics.30 The very short lifetime of the second electron donor (D−) in a protein geometry like that found in Nf n may keep D− from donating its electron to adventitious acceptors. Protection of the D− species would be less important for uncrossed free energy landscapes, because of the decreased reducing power of D−. However, in uncrossed landscapes, the hot D= species must be protected. As such, in bioinspired uncrossed constructs, it might be useful to produce the D= species using a photochemical trigger. We now define two classes of free energy and reduction potential landscapes for electron bifurcation based on uncrossed potentials. A 1:1 two-electron transfer product (DA−1 A−2 ) ratio is deemed to be a required outcome for electron bifurcation in the case of uncrossed potentials, as it is for crossed potentials. Thus, the free-energy landscape profile must be down/down for D=A1A2 ⇌ D−A−1 A2 ⇌ DA−1 A−2 (vide supra), and this defines the first case for uncrossed electron bifurcation. The kinetics of the up/ down free energy landscape will produce a long-lived highly reducing D= species and, consequently, it may lead to the undesirable depletion of the two-electron donor, decreasing the efficiency of bifurcation. Figure 4a−f shows the reduction potentials and free energy landscapes for a two-electron bifurcation based on uncrossed potentials. The first ET reaction from the donor to A2 will be much slower than the ET reaction from the donor to A1. The second ET from the donor to A1 will be much slower than ET to A2. These rate constraints can be realized by exploiting the familiar ET distance and free energy control parameters discussed above, or 2415

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COHERENT TWO-ELECTRON BIFURCATION? Electron bifurcation in Nf n is believed to proceed through single-electron steps, each with a well-defined rate that satisfies detailed balance. This kind of mechanism is expected for long distance ET with large reorganization energies and slower rates (time scales of 0.5 ms and 10 ps for ET from L-FAD to the two adjacent iron sulfur clusters11), and is supported by the experimental detection of redox intermediate species. The potential competition between coherent and stepwise incoherent two-electron transfer is a topic of current interest. Recent studies have identified reaction coordinates and tunneling mechanisms for coherent two-electron transfer reactions, including the definition of multielectron coupling pathways and their interferences, mechanisms for decoherence, schemes for multiple-carrier trafficking, and the competition among sequential and concerted mechanisms.31−35 Assuming that other bifurcated ET reactions involve similar DA distances and reorganization energies, it seems unlikely that multielectron coherence effects will play a substantive role.

John W. Peters is Professor and Director of Institute of Biological Chemistry at Washington State University, and directs the US DOE Energy Frontier Research Center on Biological Electron and Catalysis (BETCy). David N. Beratan is the R.J. Reynolds Professor of Chemistry, Professor of Physics, and Professor of Biochemistry at Duke.

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ACKNOWLEDGMENTS P.Z., J.L.Y., C.E.L, D.W.M, P.W.K., J.W.P., and D.N.B. were supported by the Biological and Electron Transfer and Catalysis EFRC (BETCy), an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences under Award # DE-SC0012518. C.E.L., D.W.M., and P.W.K. were supported by the US Department of Energy under Contract No. DE-AC36-08-GO28308 with the National Renewable Energy Laboratory.

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SUMMARY AND CONCLUSIONS We have established a language to categorize electron bifurcation in terms of three possible free energy (and redox potential) landscapes. We find that the up/down landscape of Nf n and the down/down landscape can produce effective electron bifurcation. Moreover, the population of the reactive intermediate D−A−1 A2 can be made very small, causing the reaction to impersonate a two-electron concerted process. Our structural and kinetic analysis of Nf n does not seem to require large-scale conformational gating to enable electron bifurcation, although conformational gating assists electron bifurcation in mitochondrial complex III. We also showed that crossed reduction potential landscapes (i.e., high potential first/low potential second) are not essential to accomplish electron bifurcation, although crossed potentials present practical advantages. Uncrossed potentials (i.e., low potential first/high potential second) are viable for electron bifurcation, provided that the highly reactive low potential species is not at risk of causing reductive damage or otherwise leading to energy wasting redox chemistry.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Carolyn E. Lubner: 0000-0003-1595-4483 Paul W. King: 0000-0001-5039-654X David N. Beratan: 0000-0003-4758-8676 Notes

The authors declare no competing financial interest. Biographies Peng Zhang is Research Assistant Professor of Chemistry at Duke. Jonathon L. Yuly is a graduate student in Physics at Duke. Carolyn E. Lubner is a Staff Scientist at NREL. David W. Mulder is a Staff Scientist at NREL. Paul W. King is a Staff Scientist at NREL. 2416

DOI: 10.1021/acs.accounts.7b00327 Acc. Chem. Res. 2017, 50, 2410−2417

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