Quantum Calculations of Electron Tunneling in Respiratory Complex

Subscriber access provided by UNIV OF LETHBRIDGE

Article

Quantum Calculations of Electron Tunneling in Respiratory Complex III Muhammad Hagras, Tomoyuki Hayashi, and Alexei A Stuchebrukhov J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b09424 • Publication Date (Web): 27 Oct 2015 Downloaded from http://pubs.acs.org on November 1, 2015

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Quantum Calculations of Electron Tunneling in Respiratory Complex III Muhammad A. Hagras, Tomoyuki Hayashi and Alexei A. Stuchebrukhov*

Department of Chemistry, University of California One Shields Avenue, Davis, California 95616

Keywords: Electron tunneling, bc1 complex, respiratory chain proteins, concerted electron transfer, electron gating.

ABSTRACT:

The most detailed and comprehensive up to date study of electron transfer reactions in the

respiratory complex III of aerobic cells, also known as bc1 complex, is reported. In the framework of the tunneling current theory, electron tunneling rates and atomistic tunneling pathways between different redox centers were investigated for all electron transfer reactions comprising different stages of proton-motive Q-cycle. The calculations reveal that complex III is a smart nano-machine, which under certain conditions undergoes conformational changes gating electron transfer, or channel electrons to specific pathways. One-electron tunneling approximation was adopted in the tunneling calculations, which were performed using hybrid Broken-Symmetry (BS) unrestricted DFT/ZINDO levels of theory. The tunneling orbitals were determined using an exact bi-orthogonalization scheme that uniquely separates 1

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 42

pairs of tunneling orbitals with small overlaps out of the remaining Franck-Condon orbitals with significant overlap. Electron transfer rates in different redox pairs show exponential distance dependence, in agreement with the reported experimental data; some reactions involve coupled proton transfer. Proper treatment of a concerted two-electron bifurcated tunneling reaction at the Qo site is given.

1. Introduction

Electron transfer occurs in many biological systems which are imperative to sustain life; oxidative phosphorylation in prokaryotes and eukaryotes, and photophosphorylation in photosynthetic and plant cells are well-balanced and complementary processes. Investigating electron transfer in those natural systems provides detailed knowledge of the atomistic events that lead eventually to production of ATP, or harvesting light energy. Ubiquinol:cytochrome c oxidoreductase complex (also known as bc1 complex, or respiratory complex III) is a middle player in the electron transport proton pumping orchestra, 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 chemiosmotic principle discovered by Peter Mitchell

1-2

. In humans, the mal-

functioned bc1 complex plays a major role in many neurodegenerative diseases, stress-induced aging, and cancer development, because it produces most of the reactive oxygen species, which are also involved in cellular signaling 3-5. The mitochondrial bc1 complex, shown in Figure 1, has an intertwined dimeric structure comprised of 11 subunits in each monomer, but only three of them have catalytic function, and those are the only domains found in bacterial bc1 complex. The core subunits include: Rieske domain, which incorporates iron-sulfur cluster [2Fe-2S]; trans-membrane cytochrome b domain, incorporating low-potential heme group (heme bL) and high-potential heme group (heme bH); and cytochrome c1 domain, containing heme

ACS Paragon Plus Environment

Page 3 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


c1 group and two separate binding sites, Qo (or QP) site where the hydrophobic electron carrier ubihydroquinol QH2 is oxidized, and Qi (or QN) site where ubiquinone molecule Q is reduced 6-9.

Figure 1. Bc1 complex (front view on the left, and rotated 45o counterclockwise on the right) created by superposition of three PDB structures: 3CX5, 1BE3 and 1NTZ, showing all 4 redox centers in each monomer: [2Fe-2S] cluster in the proximal (FeSb) (PDB 3CX5) and distal (FeSc) (PDB 1BE3) docking sites, whose movement is indicated by the double-headed hashed arrow; heme c1 in light green; heme bL in dark blue, and heme bH in dark purple. Also shown is heme c of cytochrome c carrier protein; ubiquinol (UQH2) shown in magenta (PDB 1NTZ) occupies Qo site in place of the inhibitor SMA, shown in light blue (PDB 3CX5). Ubiquinone (UQ), also in magenta, occupies Qi site. On the right, the protein core is exposed revealing two binding sites and the internal network of redox centers with their mutual edge-to-edge distances (for clarity, SMA is removed in the right structure). Distances with hashed lines were extracted from Ref. 10.

Electrons and protons in the bc1 complex flow according to the proton-motive Q-cycle proposed by Mitchell, which includes a unique electron flow bifurcation at the Qo site. At this site, one electron of a bound QH2 molecule transfers to [2Fe-2S] cluster of the Rieske domain, docked at the proximal docking 3 Environment ACS Paragon Plus


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 42

site, and another electron transfers to heme bL , which subsequently passes it to heme bH , and finally to Q or SQ molecule bound at the Qi-site

11-15

. Rieske domain undergoes a domain movement ~ 22 Å to

bind atthe distal docking site, where [2Fe-2S] cluster passes its electron to heme c1, which in turn passes it to heme c of the water-soluble cytochrome c carrier

8, 16

(which shuttles it to cytochrome c oxidase,

complex IV). The enzyme turnover takes two Q-cycles to collectively pump 4 protons to the membrane positive-side, uptake 2 protons from the negative-side, reduce two cytochrome c molecules, oxidize two ubiquinol molecules and reduce one ubiquinone molecule. In addition, under certain conditions electrons can flow between monomers: from heme bL of one monomer to heme bL of the other17-20. In this paper, we examine the electron tunneling pathways21-22 between different intra-monomeric and inter-monomeric redox centers of bc1 complex, including its electron carriers - ubiquinol, ubiquinone, and cytochrome c molecules, using the well-studied coarse-grained interatomic method of the tunneling current theory

23-25

. Recently, this theory successfully described electron tunneling in respiratory com-

plex I 26 and was applied to a model system of heme bL → heme bH redox pair 27. In different X-ray crystal structures of bc1 complex, some key residues of electron tunneling pathways were observed in different conformations; here we examine their relative importance in modulating electron transfer and propose a possible gating mechanism of the Q-cycle. One of the central themes of the study is intermonomeric electron transfer that has been the focus of a recent intense debate in the field

20, 28-30

. Here

we provide atomistic details of the electron transfer, and discuss the possible roles of inter-monomeric electronic communication in bc1 complex. Proper treatment of a concerted two-electron bifurcated tunneling reaction at the Qo site is given. In short, we address three fundamental issues in bc1 complex: bifurcated electron-transfer reaction, electron gating and inter-monomeric electron transfer, and extensive study of the tunneling pathways for the different redox pairs of the enzyme. Broken-Symmetry unrestricted hybrid DFT method is applied to calculate the multi-electronic diabatic donor and acceptor states 31-32, in conjunction with ZINDO method to describe the multi-electronic structure of redox centers that are utilized in the subsequent calculations of electron tunneling pathways, similarly as was done recently 26 for complex I. 4 Environment ACS Paragon Plus

Page 5 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2. Methods

Here we summarize the methods of this study. All the illustrative materials regarding methods are collected in the Supporting Information (SI).

2.1 System preparation Different X-ray crystal structures of bc1 complex were utilized to study one or more redox pair systems. If the structure with appropriate bound redox cofactor is not available, we construct a model using available similar structures. Thus, QH2 molecule extracted from 1NTZ structure was superposed on the distal Qo-subsite bound-SMA molecule in 1PPJ structure and the generated system was used to study electron transfer between ubiquinol at the distal Qo-subsite and both [2Fe-2S] cluster and heme bL. In addition, SQ molecule was also superposed on the proximal Qo-subsite bound-MYX molecule in 1SQP structure to study electron transfer between SQ in the proximal Qo-subsite and heme bL. Native bovine bc1 structure (1BE3 in PDB) was used to study electron transfer between [2Fe-2S] and heme c1, while yeast bc1 structure (3CX5 in PDB) was employed to examine electron pathways between heme c1 and cytochrome c. 1NTZ and 1NTK structures were used to study electron transfer between intramonomeric heme bL and heme bH and 1BE3 and 1NTZ structures for inter-monomeric heme bL ↔ heme bL redox pair. 1NTZ structure was used for heme bH → SQ system. Missing residues were added using BALL 33 library module of our Integrated Tunneling Environment (ITE) program; hydrogen atoms were added and then energy minimized while keeping the heavy atoms fixed in space by using GROMACS package 34-35 and Amber 03 force field 36-37. Dowser program was employed to add internal water molecules with default settings

38

. Conservation analysis was accomplished by superposing cytochrome b

unit belonging to different species: bos taurus (native: 1BE3, 1NTM, 1L0N; QH2/Q-bound: 1NTZ; SMA/ANY-bound: 1PPJ), saccharomyces cerevisiae (SMA/Q-bound: 1KB9), rhodobacter capsulate (SMA-bound: 1ZRT), rhodobacter sphaeroides (SMA/ANY-bound: 2QJP), paracoccus denitrificans 5 Environment ACS Paragon Plus


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 42

(SMA-bound: 2YIU) and Bacillus anthracis (native: 3HIJ). Structural superposition was achieved in Chimera program

39

using default settings for Needleman-Wunsch algorithm with BLOSUM-62. The

residue conservation parameters were computed using AL2CO sequence conservation score with a modified Henikoff-Henikoff frequency estimation scheme and entropy-based conservation measure 40.

2.2 Pruning To accomplish multi-electronic BS-DFT/ZINDO calculation, the size of the system should be reduced to a range of ~1000 atoms. Since electron tunneling occurs locally, via intervening residues in the region of shortest distance between donor and acceptor, such a reduction is possible. The reduction is achieved by protein pruning 25. To this end, various bc1 redox pairs were extracted from the corresponding PDB file in a spherically-capped tube of 20Å radius, with the ends centered at each redox center. The broken C-termini were capped with –NHCH3 groups and N-termini capped with –COCH3 groups. Further reduction was achieved by using the algorithm of Ref. 41, implemented in our ITE program. Final pruning is accomplished by probing one amino acid at a time where we retained all the residues whose contributions are greater than 1%. Different pruned systems range in size of ~ 500-1500 atoms.

2.3 BS-DFT/ZINDO Calculations The tunneling calculations were done as described in 26-27. The initial guess molecular orbitals (MOs) were generated using unrestricted Broken-Symmetry (BS) B3LYP method of Gaussian 09 package

42

,

employing ZINDO basis set for valence electrons and pseudo-potentials for core electrons. The pruned systems were partitioned into donor, bridge, and acceptor(s) fragments of different charges and spin multiplicities, and consequently the tunneling electron was localized either on the donor or the acceptor site. The computed initial-guess MOs were then utilized in a subsequent BS-ZINDO calculation to obtain the corresponding BS donor and acceptor diabatic ground states,

| Ψ D 〉 = | ϕ1,Dσ ,..., ϕ ND,σ 〉, | Ψ A 〉 = | ϕ1,Aσ ,..., ϕ NA,σ 〉

6 Environment ACS Paragon Plus

(1)

Page 7 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The Hartree-Fock approximation assumed above, was validated in our recent study 27. To simplify the tunneling calculation, the reduction from a fully multi-electronic picture to a one-electron approximation was accomplished by using bi-orthogonalization scheme of corresponding orbitals, as described in Ref. 23-24. The donor and acceptor orbitals with smallest overlap, and hence with most significant change during the tunneling transition, represent the tunneling pair of the one-electron approximation; the remaining corresponding (core) orbitals experience only relatively small change in the tunneling transition, with almost unit overlap, and contribute to the tunneling matrix element via the electronic FranckCondon factor 27. The transformed corresponding orbitals have the following form,

| Ψ'D 〉 = | ξ1,Dα ,...,ξlD,α ,ξ1,Dβ ,..., ξtD,β 〉 , | Ψ'A〉

= | ξ1,Aα ,...,ξlA,α ,ξ1,Aβ ,..., ξtA,β

(2)

〉

〈 Ψ 'D | Ψ 'A 〉 = 〈ξiD,σ | ξ jA,σ 〉 = δ ij siσ

(3)

σ The product of the overlaps si of the core orbitals forms the electronic Franck-Condon factor

l

t

i

j ≠t

∏ siα ∏ s βj , where we assume that the tunneling electron has a β-spin, and the tunneling orbital index “t” is the last one of the β-spin orbitals. The donor and acceptor tunneling orbitals exhibit expected localization on the donor and acceptor sites; this is probed with the atomic population analysis, using Pt ,a = ∑ Ct 2,v , where Ct ,v is the expansion ν ∈a

coefficient ν of orbital ‘t’. Figure S1A shows atomic populations of the tunneling orbitals for heme bL → heme bH redox system; characteristically, the donor tunneling orbital is localized on the donor site (heme bL) with an exponential decaying tail towards the acceptor site (heme bH), while the acceptor tunneling orbital is localized on the acceptor site with a decaying tail towards the donor site. Figure S1B shows the atomic populations of the two pairs of donor/acceptor tunneling orbitals for the bifurcated electron transfer reaction at Qo site. The α-spin donor/acceptor tunneling orbitals are employed for electron transfer between QH2 and FeS and β-spin donor/acceptor tunneling orbitals for electron transfer 7 Environment ACS Paragon Plus


Page 8 of 42

between QH2 and heme bL. As shown in Figure S1B, the α-spin and β-spin donor tunneling orbitals are

1 2 localized on QH2 molecule while the α-spin acceptor tunneling orbital is localized on [2Fe-2S] cluster 3 4 5 site and β-spin acceptor tunneling orbital on heme bL. 6 7 The overlap values for the donor and acceptor (corresponding) tunneling orbitals for different redox 8 9 systems of Qo site reactions are tabulated in Table 1; in different systems, the overlap of tunneling orbit10 11 12 als ≤ 4.80 × 10-3, while the smallest overlaps of the core orbitals are 0.48 and 0.54 (for heme bL → heme 13 14 bH (PDB: 1NTK) and heme c1 → heme c transfer), and the remaining values > 0.9. The dramatic differ15 16 ence in the overlap values of the tunneling and the core orbitals is the basis for one-electron approxima17 18 19 tion 24. The core orbitals contribute via electronic Franck-Condon factors 27 (for Qo-site reactions, eFC 20 21 factors are listed in Table 1), and range between 0.23 and 0.91 in our calculations. The overall picture 22 23 24 supports the one-electron approximation. 25 26 27 28 Table 1. Tunneling calculation results for the different generated QH2 → [2Fe2S] systems, QH2 → HbL 29 30 31 systems and concerted [2Fe-2S] ← QH2 → HbL systems. 32 33 34 Redox System 35 36 〈 Flux 〉 (b) Glu271 37 TMO ∆G0 His161 (b) eFC kET (s-1) 38 Overlap (eV) -1 Donor Acceptor protonation protonation (cm ) 39 40 state state 41 42 Concerted reactions 43 44 45 FeS 3.10 × 10-4 0.65 2.03 × 10+3(a) 2+ 46 QH 2 → QH 2 Imm Glu 47 Heme bL 1.78 × 10-5 0.64 2.35 × 10+1(a) +1.29 2.46 × 10-19 48 49 FeS 4.80 × 10-3 0.75 3.65 × 10+3(a) 50 QH 2 → Q -0.22 1.92 × 10+4 Imm → His Glu → Glu -6 (a) 51 Heme bL 3.49 × 10 0.75 8.24 52 53 Sequential reactions 54 55 QH → QH • FeS Imm → His Glu1.07 × 10-4 0.90 3.91 × 10+1 0.06 1.22 × 10+8 2 56 57 •+ FeS Imm Glu1.12 × 10-4 0.91 1.05 × 10+2 0.728 1.26 58 QH 2 → QH 2 59 60


Page 9 of 42 -

The Journal of Physical Chemistry •

QH → QH FeS His Glu 9.28 × 10 0.90 9.24 × 10 -0.23 9.81 × 10 1 2 3 QH - → QH • FeS Imm Glu 7.53 × 10-5 0.90 1.15 × 10+2 -0.23 1.53 × 10+11 4 5 QH • → Q FeS Imm → His Glu 3.77 × 10-4 0.89 3.21 × 10+2 -0.79 2.29 × 10+13 6 7 8 QH 2d → QH • Heme bL Imm 0.53 2.48 × 10+1 0.51 7.26 × 10+1 Glu- → Glu 1.75 × 10-5 9 10 QH •d → Q Heme bL His 0.83 1.29 -0.28 3.05 × 10+7 Glu- → Glu 4.78 × 10-6 11 12 • 13 Q•− Heme bL His Glu 6.29 × 10-6 0.89 1.75 × 10+1 -0.24 3.93 × 10+9 p → Qp 14 15 (a) The two rows appearing for each ET correspond to two channels of the concerted reaction, with 16 values of overlaps st1 and st2 , and fluxes Ft1 and Ft2 appearing in eq. (12). (b). The tunneling matrix el17 ement TDA = eFC × 〈 Flux 〉 , see eq. (9). 18 19 20 21 22 To further characterize molecular orbitals of the system, we examined their delocalization lengths 23 24 evaluated by the participation ratio (PR) 26, 43, 25 26 27 1 Li = n (4) 28 2 2 29 ( Pi , a ) 30 r a∈r 31 32 33 Here Pi , a is the atomic population for orbital ‘i’ of atom ‘a’ found in bridge residue ‘n’. As shown in 34 35 Figure S2, for the heme systems (HbL → HbH, Hc1 → Hc and HbL ↔ HbL), the valence band extends 36 37 38 up to a Fermi level ~ -8 eV and the conduction band starts at ~ -4 eV resulting in the energy gap ≅ 4 eV. 39 40 In the hybrid [2Fe-2S] → heme c1 system, the Fermi level reduces to ~ -12 eV with the energy gap ≅ 6 41 42 43 eV. In the electron transfer systems between QH2 (occupies the distal Qo subsite 44-46) and either [2Fe44 45 2S] or HbL , the Fermi level is at ~ -6 to -5 eV, while the occupied band starts at -2 to 2 eV with an en46 47 ergy gap of 4-7 eV. For systems with the smallest edge-to-edge tunneling distance, namely SQ (occupy48 49 50 ing the proximal Qo subsite 44-46) → HbL and HbH → Q, the Fermi level drops to ~ -14 eV while the 51 52 conduction band starts at ~ -8 to -10 eV , forming an energy gap ≅ 4-6 eV. The occupied orbitals show 53 54 a significant delocalization in general; for example, the orbitals of the heme systems at -28±4 eV are 55 56 57 delocalized over 25 bridge residues, for [2Fe-2S] → heme c1 at -29 ±3 eV over 30 bridge residues, for 58 59 QH2 reactions at -26±4 eV over 25 bridge residues and for the shortest tunneling reactions at -33±3 eV 60 -

-5

∑∑


+1

+10


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 42

over 25 bridge residues. This is remarkable, as it shows the delocalized nature of all electrons in proteins and explains why electrons can freely move in proteins over long distances. We also examined the atomic contributions of different fragments (donor, acceptor and bridge) to molecular orbitals of the heme bL → heme bH redox system evaluated as,

∑P = ∑P

i,a

Pi , f

a∈ f

(5)

i, a

a

Here Pi , f is the normalized contribution of fragment ‘f’ (donor, acceptor or bridge) to the biorthogonalized molecular orbital ‘i’ and Pi , a is the atomic contribution of atom ‘a’. As shown in Figure S3 the donor and acceptor tunneling orbitals are typically located in the energy gap of the bridge. This picture supports the tunneling mechanism of the reactions, or super-exchange, with no significant participation of the bridge-localized orbitals.

2.4 Tunneling current calculation Since the ZINDO canonical MOs are represented in a basis set which is orthogonalized (using Löwdin-orthogonalization 47 or other schemes) and therefore delocalized over many atoms, the localized atomic picture of inter-atomic tunneling currents in a tunneling transition is lost in this basis set. To conduct the tunneling current calculations, the atomic basis set localization needs therefore to be restored. By introducing the localized atomic basis set and the Mulliken type coarse-graining of the tunneling current, the tunneling transition flux is expressed in terms of the interatomic currents, which (approximately27) has the following form 24, 48:

J ab = ∏ siα ∏ s βj ∑∑ ( Hνµ − E0 Sνµ )(θ µν − θνµ ) i

j ≠t

(6)

ν ∈a µ∈b

Here ν and µ are the atomic orbitals of atoms a and b ; θνµ = Aν Dµ where D µ and Aν are the expansion coefficients of the donor and acceptor tunneling orbitals, respectively; H νµ and Sνµ are core Hamiltonian and overlap matrix, and E0 is a tunneling orbital energy defined by, 10 Environment ACS Paragon Plus

Page 11 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


E0 = ∑ Dλ Fλρ Dρ = ∑ Aλ Fλρ Aρ λ ,ρ

(7)

λ ,ρ

where Fλρ is the reduced Fock matrix 24. The second equality in Eq. (7) corresponds to the resonance of the donor and acceptor energies at the transition state of electron transfer reaction; in practice, the resonance is achieved by applying a static electric field mimicking the action of the polar environment and solvation effects as describe in 26-27. Eq. (6) shows that the inter-atomic currents are primarily determined by the overlap of the tails of the two tunneling orbitals. The electronic Franck-Condon factor ( ∏ siα ∏ s βj ) contributes as a uniform i

j ≠t

scaling factor for all inter-atomic currents. The total atomic current through a given atom a1,

J atot ≡

1 ∑ J a ,b , 2 b

(8)

is proportional to the probability that the tunneling electron is passing through this atom; as such, it provides a convenient way (e.g. with color gradient coding, as in Figures 2-9 of the paper) of identifying atoms that constitute the tunneling pathways. The tunneling matrix element is calculated as the total flux across the dividing surface between the donor and acceptor redox complexes (the flux theorem 25),

TDA = − h ∑∑ J ab

(9)

a ∈ S b∉ S

Here, the summation of interatomic tunneling currents between atoms ‘a’ on one side, denoted as ‘S’ side, of the dividing surface and atoms ‘b’ on the other side 49. The inter-atomic tunneling currents provide an internal assessment of the quality of calculation as a measure of conservation of the total tunneling flux between the donor and acceptor redox centers. An example is shown in Figure S4 for a model heme c1 → heme c system. The flux is approximately conserved along the whole tunneling pathway especially in the middle part, between donor and acceptor, as it should 23; to account for small variations,

1

The currents are real valued, and the sign of the current, positive or negative, describes the direction – in or out of the atom. The absolute values in Eq. (8) and the factor of one half give the total current flowing through the atom. 11 Environment ACS Paragon Plus


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 42

we compute the tunneling matrix element as an average over the middle region. All the studied systems behave in a similar manner.

2.5 Electron transfer rates Electron transfer rates between different redox pairs are calculated using Marcus’ theory 50:

2π k ET = h

 ( ∆G 0 + λ )2  〈TDA2 〉 exp  −  4λ k BT  4πλ k BT 

(10)

In bc1 complex, the reorganization energy typically is in the range of 0.7 – 1.0 eV 51-52 ; we have used a value of 0.7 eV in our calculations. The driving forces vary significantly for different redox pairs; they are summarized in Tables 1 - 3 (see also supporting Table S1). The electronic factor in Marcus’ formula, the mean square tunneling matrix element, was computed as described above using the tunneling flux formalism.

3. Results and Discussion 3.1 Bifurcated reaction [2Fe-2S] ← QH2 → Heme bL at Qo site Different schemes were reported in the literature

45-46, 53-55

for the electron transfer reaction at the Qo

site, which we categorize into three groups that emphasize spatial, temporal, and chemical aspects of the reaction. Spatial group emphasizes the importance of the two Qo subsites; proximal and distal one 44-45. Temporal group assumes one subsite, but discusses two possibilities: concerted vs. sequential bifurcated reactions

45, 56

. Chemical group deals with possible derivatives of ubiquinol molecule that can undergo

• electron transfer reactions, namely QH2 molecule, ubiquinol radical cation ( QH•+ 2 ), SQ radical ( QH ),

SQ anion (QH − ) and Q molecule. Presently, there is no general consensus in the field on the exact mechanism. In order to attain a better picture of the reaction at the Qo site, we calculated electron transfer rates in all those different scenarios. Different possibilities are discussed in the following subsections. 12 Environment ACS Paragon Plus

Page 13 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3.1.1 Concerted ET [2Fe-2S] ← QH2 → Heme bL reaction Here we examine a possibility discussed in the literature

56

of a concerted transfer of two QH2 elec-

trons to FeS and HbL from the distal Qo subsite; this may or may not involve proton transfers to deprotonated His161 and Glu271 (bovine sequence) residues. At Qo the QH2 molecule is hydrogen-bonded to His161 ligand of FeS cluster

57

and Glu271

58

or water molecule hydrogen-bonded to Glu271

59

. By

concerted ET here we literally mean that both electrons are dispatched from a single subsite in a single transition, as opposed to two sequential transitions from one subsite, or using two subsites for two sequential electrons. In such a concerted reaction, for both electrons we consider a single donor electronic state of QH2 and a single acceptor state, in which two electrons are transferred to FeS and HbL. In this sense, the transfer of both electrons can be considered literally concerted, with one rate constant for the reaction. Such a two-electron transfer reaction is fundamentally different from a sequential transfer of two electrons from a single site, involving two different transition state nuclear configurations, and two corresponding rate constants. Although it should be mentioned that in a special case of a sequential two-step reaction, in which one step is much faster than the other, the apparent kinetics is indistinguishable from a concerted two-electron transfer; however, theoretically such reactions are different. A priori it is not really clear which mechanism is realized, and the goal of this calculation to clarify this question 45, 56

.

Here, the donor and acceptor diabatic states of three redox partners (QH2, FeS, and HbL) are considered. For donor state, the whole system spin S = ½ (QH2 S = 0, FeS S = 0 and HbL S = ½); upon ET the whole spin remains the same S = ½ (QH2 S = 0, FeS S = ½ and HbL S = 0). Figure 2 shows the transition tunneling flux between QH2 and FeS and between QH2 and HbL for the computed states. As expected, the flux is approximately conserved in the intervening region for both pairs, and the stationary flux is taken for an estimate of the electronic couplings.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 42

Figure 2. Concerted bifurcated electron transfer pathways from ubiquinol molecule bound at the distal Qo subsite to both FeS cluster (top, red-color) and heme bL (lower, blue-color). The electron tunneling fluxes (log10 scale) of both simultaneous reactions are shown against center-to-center distance X between heme bL iron atom and the center of FeS cluster. The coupling matrix element is evaluated as an average flux values around X=0.2 (blue line) and X=0.8 (red line). Broken lines indicate expected neg-


Page 15 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ligible flux of the corresponding redox pair (actual data points are omitted for clarity) outside the tunneling region.

In general, the coupling matrix element TDA is related to transition fluxes between corresponding orbitals as follows: 



TDA = − h  ∏ si  ∑ 1 Fn ,  i  n sn

(11)

where si are the overlaps and Fn are the fluxes of pairs of corresponding orbitals of donor and acceptor states. If one electron is transferred, only one pair of tunneling orbitals (with small sn ) contributes, and only one term, n=t, determines the coupling. For a transition where two electrons are transferred, the coupling matrix element has the following form: 

TDA = −h 

∏

 i ≠t , t  1 2



1

 

 st1

si  st1 st2 

Ft1 +

 1 Ft2  st2 

(12)

where st1 and st2 are the overlaps for two pairs of tunneling orbitals, and Ft1 and Ft2 are two corresponding fluxes. If one or two electrons tunnel long distance (in our case, the first electron travels a moderate edge-to-edge distance of 6.8 Å yet the second electron transfers a much longer edge-to-edge distance of 12.2 Å, see Figure 1 and Figure 2), both st1 and st2 are expected to be small, and hence the coupling is proportional to (doubly) small s 2 , as opposed to a single power of s for a one-electron reaction. Therefore we expect the coupling for a concerted multi-electron tunneling reaction to be much smaller than that for the corresponding single-electron transfer reactions considered separately. As shown in Table 1, for both transitions the overlaps are very small, and essentially do not depend on whether or not the protons are transferred together with the electrons (this is not for the rate, but just for electronic coupling). The electronic Franck-Condon factors are also close in both scenarios. The “dou-



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 42

ble smallness” of the coupling introduced in the above paragraph is indeed realized here, and leads to an unusually small ET rate constant for a concerted reaction. It is interesting that individually the couplings for two single electron transfer reactions (formally considered separately) are not small. For example, the coupling between QH2 and FeS is over thousand wavenumbers. However, for individual one-electron transfer reactions, the electronic states involved are different and hence the couplings should be calculated differently (as in the next section). In case of a concerted ET, the estimate based on the above equations and data in Table 1 show that the smallness of the coupling can potentially explain experimental observation that the overall reaction rate at the Qo site is strikingly low ~ 10+3 sec-1, and indeed rate-limiting for the whole cycle, despite the short distance between the donor and the acceptor in the ET reaction. Moreover, one should also include protons, otherwise the reaction is strongly uphill and by far too slow (see “Concerted” data of Table 1). If protons are included, the driving force becomes positive, the reaction is downhill in energy, and the rate of pure ET is on the order of 10+4 sec-1. The inclusion of protons (via PCET mechanism, or sequential ET/PT or PT/ET reaction

60

) further reduce the rate, see Ref

60

and discussion below, and the reaction

can potentially be in the range of the observed 10+3 sec-1. However, before making such a conclusion, one should also consider the usual sequential one-electron reactions, and see if they can compete with a concerted reaction; this is done in the next section.

3.1.2 Sequential ET reactions 3.1.2.1 QH2 derivatives → [2Fe-2S] redox system As described by Crofts et al. 44-45 and Berry et al. 46, the ET reaction between the ubiquinol molecule and FeS occurs only when the ubiquinol molecule is bound at the distal Qo-subsite and hydrogenbonded to both His161 ligand of [2Fe-2S] cluster, which exists in imidazolate form, and the deprotonated Glu271 (or to water molecule). Therefore we examined sequential ET reactions with different possible ubiquinol variants at the distal Qo subsite. These include: for the first electron, coupled ET-PT and


Page 17 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


simple ET from QH2 molecule; and for the second electron, ET from SQ anion and ET-PT from SQ radical. As listed in Table 1, simulating electron transfer in the four systems considered yield much higher ET rates compared to the experimentally measured one of ~ 10+3 sec-1 , and hence ET per se cannot be ratelimiting, even if protons are included in calculating the driving force. The ET rate in the QH 2 / QH •2+ → FeS redox system is the slowest one; however, without transferring a proton, the rate is actually much too slow to explain the experiment, and hence this is not what occurs in the enzyme. It is worth noticing that the tunneling flux in the QH 2 / QH •2+ → FeS redox system is one order of magnitude lower than in the concerted reaction, yet the overall coupling and the rate is higher. This occurs because in the concerted reaction, the coupling includes additional small (overlap) factor due to the second tunneling electron. Thus the rate of a single electron transfer to FeS is faster than the concerted reaction with two electrons. However, by itself the rate of a single electron transfer from QH2 to FeS (when the proton transfer is included in the driving force) is still much higher than the experimental value 10+3 sec-1. This indicates that the time-scale of the reaction is limited not by the electron transfer per se, but by some other factor. There are at least two possibilities. One is that the transition state of the reaction is very specific (e.g. due to the need to pass a proton to His161), and the reaction is limited by an additional free energy barrier crossing – in which the system spends most of the time finding the appropriate binding configuration (which is assumed in our calculations). Another possibility is that the proton transfer to His161 occurs simultaneously with the electron by the PCET mechanism 60; in PCET reactions, the effective coupling is always reduced by the coupled proton, thus the ET reaction alone can only provide the lower boundary of the rate (i.e. the rate of PCET is always smaller than ET alone, Ref. 60). In this case, there is a need for a special configuration as well, to reach a state of a favorable (shorter) distance for proton tunneling (in configurations of known crystal structures, the tunneling distance is exceedingly long – in excess of 1Å, see Table S2 in SI). There are other possibilities involving protons, i.e. sequential trans17 Environment ACS Paragon Plus


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 42

fers ET/PT or PT/ET. In all such cases, compared with pure ET, the reaction rate is significantly reduced by the coupled proton 60. Therefore it appears possible that the slow reaction in Qo site can be due to a sequential reaction, but with a coupled proton transfer using either PCET mechanism, or sequential ET/PT or PT/ET mechanism. (Obviously, to decipher the exact mechanism further specific study is needed.) Furthermore, as will be shown below, the second reaction in the sequential scenario is much faster than the first one, and hence the kinetics of such a sequential two-electron reaction should be indistinguishable from the true concerted one. For this reason, we will call such type of reaction quasi-concerted, as opposed to a true concerted reaction considered previously. In the literature, there is no clarity on this distinction, and there are claims favoring concerted reaction 53, 56, 61 over a sequential one without clearly distinguishing them. As displayed in Figure 3A, for QH 2 / QH • → FeS ET reaction, primary electron pathway occurs through a hydrogen bond between the ubiquinol -OH group and Nε atom of His161 ligand with a through-space jump of 1.7Å, which proves that this hydrogen bond is important for both proton and electron transfer. Interestingly, the transfer of the second electron from the SQ radical to oxidized [2Fe2S] cluster with His161 in imidizolate form produces a much higher tunneling flux than in the reaction of the first electron and consequently a larger electron transfer rate. However, such a reaction would be unproductive (the second electron should go to heme bL according to the Q-cycle mechanism) and hence this reaction must be avoided – obviously by quickly sending electron to heme bL; indeed the rate of electron transfer to heme bL is very fast, on order of 10+9 as will be shown in the next subsection. Yet, if the second electron is transferred to FeS cluster, we find the same electron transfer pathway is utilized as indicated in Figure 3B (the more intense color corresponds to higher coupling for this ET reaction).


Page 19 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 3. Electron tunneling pathway between A. ubiquinol molecule, B. SQ molecule bound at the distal Qo subsite and [2Fe-2S] cluster. Partial participation of Tyr278 phenol group in the secondary ET pathway is shown. The hydrogen atom incorporated in hydrogen-bonding between ubiquinol/semiquinone and His161 ligand of FeS is placed midway between them. Primary pathway through-space jumps are indicated by solid dark blue arrows, while the secondary pathway jumps are in dashed arrows (ranging in colors from dark to light blue based on distance). Center-to-center distance in angstrom is indicated by double-headed arrow. Through-space jump distances in angstrom are shown next to their corresponding arrows.

3.1.2.2 Ubiquinol/SQ → heme bL redox system As shown in Table 1, three electron transfer schemes were examined: 1) transfer of the first electron between the bound ubiquinol molecule at the distal Qo subsite to the oxidized heme bL, 2) transfer of the second electron from SQ radical at the distal subsite, and 3) transfer of the second electron from the SQ 19 Environment ACS Paragon Plus


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 42

anion at proximal Qo subsite to the oxidized heme bL , as proposed by Crofts et al. 44-45. The heme moiety is a low-spin system, exhibiting spin S = ½ for the oxidized state and spin S = 0 for the reduced state. The spin state of the bound ligand (ubiquinol/ubisemiquinone/ubiquinone) will be either spin S = 0 or spin S = ½ opposite to the spin of the oxidized heme bL molecule to acquire the lowest energy BS state with total spin S = 0. As shown in Figure 4A, for the transfer of either the first or the second electron, the primary pathway is dominated by hydrogen bonds; a hydrogen bond between the –OH group of the QH2 or SQ• molecule and the deprotonated carboxylate group of Glu271 of the highly conserved –PEWY- loop

62

and a hy-

drogen bond from the deprotonated carboxylate group of Glu271 to a conserved structural water molecule. In case of the absence of the water molecule the highly conserved Tyr131 residue plays an important role in electron transfer as a conducting residue in the secondary electron pathway with an equal total through-space distance of 7.5 Å as in the primary electron pathway but in two longer energypenalized jumps compared to three shorter energy-favorable jumps in the primary electron pathway. Calculating the electron transfer rate of the first case yields a value of 7.26 × 10+1 sec-1 which is much lower than the experimental measured value ~ 10+9 sec-1. In contrast, simulating ET from QH • bound at the distal subsite, the pathway shown in Figure 4B, produces an ET rate of ~10+7 much closer to the experimental one. This is in support of our quasi-concerted ET mechanism, in which the first ET QH2-FeS is rate-limiting, and the second ET QH• - HbL is much faster.


Page 21 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4. Electron tunneling pathway between A. ubiquinol molecule, B. SQ molecule bound at the distal Qo subsite and heme bL (and weakly hydrogen-bonded to protonated His161). A conserved water molecule is involved in the primary ET pathway while Tyr131 residue is part of the secondary pathway of which only its phenol group is shown. The hydrogen atom incorporated in hydrogen-bonding between ubiquinol/semiquinone and Glu271 is placed midway between them.

Finally, examining Crofts et al. proposal of the SQ intermediate movement closer to heme bL at the proximal end of Qo pocket, we found as predicted by Crofts that the calculated ET rate = 2 × 10+9 sec-1, in close agreement with the experimental one. Since the transfer between the two subsites occurs on the ns time-scale

45

, the reaction with the second electron dispatched from the proximal site can be also

characterized as quasi-concerted. The pathway for this transition is displayed in Figure 5. It is interesting to notice that the tunneling electron prefers to tunnel in the primary pathway with a through-space gap of 2.5Å (with an atomic coupling constant of 4.71 × 10+1 cm-1) rather than to travel a 2-3Å throughbond distance in the secondary pathway with a shorter through-space gap of 2.3Å (with an atomic cou-



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 42

pling constant of 7.31 cm-1). Such a reaction still can be classified as quasi-concerted since the rate for the second electron transfer is much faster than for the first electron transfer.

Figure 5. Electron tunneling pathway between SQ in the proximal Qo subsite and heme bL, where Tyr131 is involved in the ET primary and secondary pathways.

Summarizing this section, we find that the reaction at the Qo site – bifurcated transfer of two electrons of ubiquinol to [2Fe-2S] cluster of Rieske protein and to heme bL of cytochrome b domain - occurs either in concerted or quasi-concerted fashion. In practice, there is no difference in the apparent kinetics of these two reactions. However, the molecular mechanisms in the two cases are different. In the concerted case the overall small rate is due to the smallness of the electronic coupling for a coherent two22 Environment ACS Paragon Plus

Page 23 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


electron tunneling transition. In the quasi-concerted case, the first ET to FeS cluster is rate-limiting, due to a specific transition state configuration, most likely to pass a proton to His161; the difficulty finding this transition state configuration apparently determines the overall slow time-scale of the reaction 10+3 sec-1. Alternatively, the transition of the first electron is accompanied by the proton, and the reaction is of PCET type, with the effective coupling reduced by the proton

60

. The atomistic details of electron

tunneling pathways were resolved in a rigorous manner, displayed in Figures 2-5. Before we conclude, it is appropriate to mention some proposals of the reaction at the Qo site in the light of our calculations. Characteristically, experimental data alone do not allow for unambiguous conclusions about the mechanism of the reaction. Thus, Brandt and Okun measured the activation barrier for the proton transfer between QH 2 /QH •- and His161 to be ~ +40 kJ/mol

63

and proposed that step

(proton first) to be rate-limiting, responsible for the measured activation barrier (32 – 65 kJ/mol)

64-65

.

However, the electronic coupling in this proposal remains uncertain, so as the absolute rate. In the “proton-gated charge transfer” mechanism of Brandt 44, 63, or similar model of Link 66 , the electron transfer occurs from a deprotonated QH- anion; presumably, the proton transfers to deprotonated His161, as suggested by Crofts et al. 58. Our calculation shows instead that the ET is from a neutral QH2, but the low experimental rate ~10+3 is possibly due to concerted transition of two electrons. This is in agreement with that no stable SQ intermediate detected at Qo site and the net exergonic character of the overall reaction 67. Another possibility is that subsequently to the first electron transfer, the downhill proton transfer occurs (instantaneously on the time-scale of ET) from the generated QH •+2 to the hydrogen• bonded His161 ligand of [2Fe-2S], since pK of QH •+ 2 /QH < 1

69

68

and that of reduced [2Fe-2S] is > 12

. It is also possible, and even more likely, that the transfer of the proton occurs simultaneously with

the electron by the PCET mechanism (Ref.

60

). Quasi-concertedly, the second electron and a proton

transfer from the formed QH• to HbL and to Glu271, respectively, with a calculated rate constant in good agreement with the measured one.



Page 24 of 42

The energetics of different possible routes of the overall reaction FeS3+/3+|QH2|Glu-|HbL3+ ⇒

1 2 FeS2+/3+H|Q|GluH|HbL2+ in Qo is summarized in Table 2 and Table S1. 3 4 5 6 7 Table 2. The energetics data of different reactions in Qo site. 8 9 10 Redox System 11 12 0 0 ∆Gelec His161 Glu271 13 ∆G proton 14 (mV) Acceptors protonation protonation 15 Donor (mV) 16 17 state state 18 19 Imm → His Glu0 289.9 QH2 → QH •− FeS 3+ / 3+ HbL 3+ 20 21 •− His Glu-230.0 0 HbL 3+ QH → QH • FeS 3+ / 3+ → FeS 3+ / 2+ 22 23 •+ Imm Glu728.0 0 24QH2 → QH2 FeS 3+ / 3+ → FeS 3+ / 2+ HbL 3+ 25 26 •+ QH QH • Glu0 -668.6 Imm → His FeS 3+ / 2+ HbL 3+ 27 2 → 28 Imm → His Glu60.0 0 29QH2 → QH • HbL 3+ FeS 3+ / 3+ → FeS 3+ / 2+ 30 31QH • → Q •− His Glu- → Glu 0 -47.3 FeS 3+ / 2+ HbL 3+ 32 33 •− • His Glu -240.0 0 FeS 3+ / 2+ HbL 3+ → HbL 2+ 34 Q → Q 35 • His Glu- → Glu -280.0 0 FeS 3+ / 2+ HbL 3+ → HbL 2+ 36 QH → Q 37 38 QH2 → Q 0 Imm → His Glu- → Glu -220.0 FeS 3+ / 3+ → FeS 3+ / 2+ HbL 3+ → HbL 2+ 39 40 Based on the values in Table S1 within ≈ ±30mV of assumed experimental uncertainty 70. (a). Meas41 ured based on Brandt and Okun 63. ND; not-determined. E‡ for the ET reaction = (∆G0 + λ)2/4λ based on 42 the energy-gap law of Marcus theory 50, 71 and assuming E‡ ≈ ∆G‡ 72. ∆G0 for proton transfer = 43 44 2.303kT(pKdonor – pKacceptor) based on BrØnsted relationship 73. 45 46 47 48 3.2 High-potential redox chain: [2Fe-2S] → heme c1 → heme c redox chain 49 50 The subsequent steps immediately following the reduction of [2Fe-2S] cluster appear to involve con51 52 formational change, but the details are ill-defined. There is a range of possibilities including an instant 53 54 55 detachment of the Rieske domain from the proximal docking site (FeSb interface), or undocking only 56 57 after re-oxidation of heme bL or/and heme bH 54. Whatever the sequence of these intermediate steps, 58 59 60


E‡ (kJ/mol)

40.0(a) 7.6 70.3 ND 20.0 ND 7.3 6.1 7.9

Page 25 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


upon reduction, the iron-sulfur domain eventually undergoes significant domain movement of ~22 Å, to dock at the distal docking site (FeSc interface) 16, 74 , closer to heme c1 redox center. It is from this distal docking site an electron of FeS center is further transferred to heme c1. Here we consider details of this reaction. As already mentioned, the reduced FeS cluster contains two anti-ferromagnetic coupled high-spin iron ions. Furthermore, as a whole, the reduced FeS cluster (spin S = ½) is antiferromagnetically coupled to the oxidized heme c1 iron atom with spin S = ½, yielding spin S = 0 for the whole system in the lowest energy BS donor diabatic state. In the acceptor diabatic state all the redox complexes have spin S = 0. The donor and acceptor states were determined for a configuration in which the Rieske domain is docked at the distal docking site and the pathways were studied in the usual manner. As displayed in Figure 6A, the primary pathway for the electron transfer between [2Fe-2S] cluster and heme c1 occurs through a hydrogen bond between the Hε atom of the neutral His161 ligand of FeS cluster and the Oδ of the propionate group in the heme c1 complex. The secondary electron transfer pathway runs through a highly conserved structural water molecule, and spans double through-space distance as compared to the primary pathway. Subsequently, the electron is passed from the reduced heme c1 to the oxidized heme c of the docked water- soluble electron-carrier cytochrome c. Here we find electrons tunnel only via a single, direct heme-to-heme primary pathway, as shown in Figure 6B 51, 75.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 42

Figure 6. Electron tunneling pathways in the high-potential chain. A. Between reduced [2Fe-2S] cluster docked at the distal surface and heme c1 redox center. B. Between the subsequently reduced heme c1 and heme c in the water-soluble cytochrome c electron carrier.

3.3 Low-potential redox chain One of the two electrons originally carried by the ubiquinol molecule, relays at heme bL and has two distinct paths to go further: 1) intra-monomer route, and 2) inter-monomer route. By comparing differ26 Environment ACS Paragon Plus

Page 27 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ent native, ligand- and inhibitor-bound structures, we have discovered different conformations of some key residues that appear to regulate electron transfer passage in both routes via modulating the corresponding electron transfer rates. We postulate that those key residues act as internal switches shunting the electron at heme bL to either pathway based on the circumstantial demand of the enzyme. Below, we will discuss details of each route, and the conditions under which one pathway dominates the other.

3.3.1 Intra-monomeric heme bL → heme bH → Q redox chain In this route, electron is transferred from heme bL to heme bH of the same monomer. The center-tocenter tunneling distance is about 20 Å. We first examined bovine bc1 structure PDB 1NTK, in which Qo is unoccupied and the inhibitor ANY occupies Qi site. The details of tunneling pathway are shown in Figure 7A. In that structure, the computed tunneling flux at the intervening Phe90 residue is found to be surprisingly low (indicated in Figure 7A by the low red color density on that residue), indicating that this residue acts as a bottleneck for the transfer. As listed in Table 3, the resulting rate of electron transfer was found to be only 2.06 × 10+2 sec-1, which is below enzyme’s turnover and both experimental estimate (> 1.6 × 10+5 sec-1) 65 and that calculated with Moser-Dutton empirical formula (6.72 × 10+5 sec-1) 10, 52, 76

.

Table 3. Calculation results for different redox systems in bc1 complex.

Redox Pair

2 〈 TDA 〉

(cm-2) FeS ← QH2 → HbL

∆G0 (eV)

kET(d) (s-1)

FeS → Heme c1

kET (s-1) (QH2 → FeS ) 1.65 × 10+3(a)65

1.53 × 10-3

-0.22

1.92 × 10+4

2.42 × 10+2

-0.24

3.93 × 10+9

0.053

+5

(concerted)

Q•− p → Heme bL

Experimental

5.56

6.33 × 10


( QH •d → HbL)>1.27 × 10+9(a)65 > 1.27 × 10+9(a) 65 > 10+5(a)65, 6.0-8.0 × 10+4(a) 77-78,


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 42

1.6 × 10+4(b)77 8.0 × 10+4(a)79, Heme c1 → Heme c

1.30 × 10+1

-0.002

4.51 × 10+6

6.0 × 10+4(b) 80, 1.4 × 10+4(c)81

→ Heme bH Heme bL 

7.20 × 10

OFF → Heme bH Heme bL 

-2

+5

> 1.65 × 10+5(a) 65,

-0.13

2.41 × 10

6.17 × 10-5

-0.13

2.06 × 10+2

NDE

OFF → Heme bL Heme bL 

0.0

0.0

0.0

NDE

 → Heme bL Heme bL ON

1.53 × 10-2

0.0

5.10 × 10+3

~ 10+3 20, 83

Heme bH → Q

5.16 × 10+5

0.03

9.47 × 10+10

> 1.65 × 10+3(a) 65

ON

1.0 × 10+4(a)82

a. Bc1 complex in Rhodobacter sphaeroides; b. Bc1 complex in Bos taurus.; c. Bc1 complex in Saccharomyces cerevisiae; d. ET rates were calculated according to eq. (10) with reorganization energy λ = 0.7 eV and 〈 T 〉 and ∆G0 as listed in second and third columns. NDE, Not Detected Experimentally. 2

DA

On the other hand, in the native ligand-bound structure of bc1 complex (1NTZ in PDB where QH2 molecule occupies Qo site and Q occupies Qi site), the calculated rate is much higher and equals to 2.41 × 10+5 sec-1, in perfect agreement with experiment. In this structure, the key residue Phe90 turns out to

be in a different conformation, which regulates the passage of the electron. As displayed in Figure 7B, the calculated atomic tunneling flux shows a dramatically higher density on Phe90. Based on these calculations, we speculate that Phe90 plays the role of an internal switch modulating the electron transfer passage. The switch appears to be regulated by the ligand binding at the Qo site. We symbolize the conformational state of Phe90 of higher electron transfer rate as ONLH, and that of lower electron transfer rate as OFFLH.


Page 29 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 7. Calculated electron tunneling pathway between heme bL and heme bH in two X-ray bc1 crystal structures (PDB 1NTK in A and 1NTZ in B). A. resiude Phe90 exists in OFFLH conformation. B. resiude Phe90 exists in ONLH conformation.

3.3.2 Inter-monomeric heme bL ↔ heme bL redox system The second path for the electron on heme bL is to hop to heme bL of the other monomer, via center-tocenter distance of 20.7-21.3 Å. In Figure 8 we show the calculated inter-monomeric electron transfer pathways in the native (PDB: 1BE3), and ligands-bound bc1 complex (PDB: 1NTZ). Here, it appears there is another internal switch, namely the bridging dimeric Phe183 twin. The Phe183 pair turns out to 29 Environment ACS Paragon Plus


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 42

exist in two different conformations: one as an edged T-shaped structure of the Phe183 pair, with a total through-space jump distance of 8.1Å between the edges of the porphyrin rings and the closest edge-toedge distance between of the aromatic rings of the Phe183 pair (Figure 8A); the other conformation is such that the aromatic rings of the Phe183 pair are parallel-like, with 9.9Å total through-space jump distance (Figure 8B) 84-85.

Figure 8. Electron tunneling pathway between the inter-monomeric heme bL ↔ heme bL in ubiquinolbound bc1 structure (A. PDB: 1NTZ) and in native bc1 structure (B. PDB: 1BE3). A. The Phe183 twin 30 Environment ACS Paragon Plus

Page 31 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


shows a displaced parallel orientation (ONLL). B. The conformation of Phe183 twin is close to the edged T-shaped one (OFFLL). Electron pathways are double-headed due to the symmetry of inter-monomeric heme bL ↔ heme bL redox system and hashed for clarity.

We designate the edged T-shaped conformation of the Phe183 twin as OFFLL and the parallel-like conformation as ONLL. Despite the longer overall through-space distances, we observed a significant and nicely behaved tunneling flux for the ONLL conformation, with corresponding ET rate of 5.10 × 10+3 sec-1, and irregular tunneling flux behavior in the OFFLL conformation, indicting low transfer rate, as shown in Figure 8 and listed in Table 3 (see upcoming paper for a complete study of the internal switches). The inter-monomer electron transfer in bc1 complex gained a considerable attention recently, and is under vigorous debate; the opinions range from completely favoring 20, 30, 83 or conditional acceptance 17, 19, 30, 86

, to its complete rejection

28

. Our findings add new twist to the debate. Based on our tunneling

calculations, as summarized in Table 3, we conclude that inter-monomeric heme bL electron transfer can occur with greater probability only in one out of the four possible scenarios, namely in ONLL-OFFLH state, since the inter-monomer heme bL electron transfer rate is much faster (in ONLL state), by about one order of magnitude, than the heme bL → heme bH transfer in the OFFLH state. On the other hand, when Phe90 is in the ONLH state, no inter-monomeric tunneling flux can be observed whatever the conformation of Phe183 side chain is. In one case, namely (OFFLH-OFFLL), the probability to tread either route is comparable but the rate is very small; we speculate that such particular case does not happen in practice. To address this issue and other questions, a detailed study of the internal switches is reported elsewhere.

3.3.3 Heme bH → Q redox system



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 42

Tunneled through either inter- or intra-monomeric route, the electron traversing the low-potential pathway ultimately reaches its final destination at the Qi site. The final step, ET from the reduced heme bH to Q or SQ molecule bound at Qi is considered next. As shown in Figure 9, the primary electron transfer pathway manifests the shortest through-space distance of 2.7Å; the next in significance, secondary electron transfer pathway involves a comparable distance of 2.9Å. In addition, there are other possible secondary pathways of longer distance, which taken together with the first two form a “cat claw” multi-branched pathway for the electron transfer. The unusual branched structure of the tunneling pathway is due to parallel orientation and close proximity of the donor propionate group and the acceptor planar quinone ring. The rate is listed in Table 3.

Figure 9. Electron tunneling pathway between heme bH and ubiquinone bound at Qi site. The primary pathway (visualized as solid arrow) is the shortest in distance; secondary pathways comparable in 32 Environment ACS Paragon Plus

Page 33 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


distance (visualized as dashed arrows) are also accessible, forming collectively with the primary pathway a “cat claw” pathway for the electron transfer.

4. Conclusions In this paper, using rigorous quantum mechanical calculations we examined the atomistic details of the tunneling pathways and the rates of all electron transfer reactions in bc1 complex. For the first time, we simulated proper concerted bifurcated reaction at the Qo site, and its sequential alternatives. Our calculation shows that the reaction occurs either in proper concerted fashion with simultaneous transfer of two electrons, or in equivalent quasi-concerted sequential manner, in which the rate- limiting transfer of the first electron to high-potential chain is followed by a much faster second electron transfer to the low potential chain. The apparent kinetics of the two types of reactions are indistinguishable from each other. In both cases, the participation of protons is needed. Since pure electron transfer is much slower for simultaneous tunneling of two electrons than the tunneling of a single electron, the sequential ET reaction appears to be more likely scenario. The exact mechanism of proton coupling in the reaction requires further detailed study. We concluded that the expected ~10+9 sec-1 ET rate for QH• → HbL occurs in a quasi-concerted manner while QH• is either still bound at the distal end of the Qo pocket or when QH• moves to the proximal end. The difference between the two cases was found to be inconsequential for the Q-cycle. Many conserved electron-conducting residues or water molecules were identified in the tunneling pathways, such as the water molecule in the primary pathway between QH2d and HbL, or Tyr131, Phe90 and Phe183 residues as shown in Figure S5, which summarizes differences in various 10 structures. Tyr131 is an important residue for conducting tunneling electrons between the Qo site and HbL, while Phe90 and Phe183 residues were postulated to play a role of internal switches shunting the tunneling electron into a certain pathway depending on the ligand binding status of the enzyme. The calculations show dramatic ET rate change due to switching between the ON and OFF conformations. Such a change 33 Environment ACS Paragon Plus


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 42

could not be detected with the empirical Moser-Dutton approach, which downplays the atomic details of the intervening medium in a tunneling reaction. In Figure 10 we have summarized different tunneling ET reactions in one round of a Q-cycle. The cycle can be formally started from the native bc1 configuration (1BE3) where Phe90 and Phe183 are both in the OFF conformation, as shown in Figure 10A. Upon binding of QH2, the conformation of those two internal switches changes (as seen in 1NTZ structure) and the concerted bifurcation reaction proceeds from the distal domain of the Qo site as displayed in Figure 10B. The electron of HbL relays at HbH to finally reduce Q molecule bound at Qi site while FeS domain undergoes major domain movement, transferring the other electron to heme c1 and further to mobile electron carrier cytochrome c, as shown in Figure 10C and D.

Figure 10. Summary of electron tunneling pathways in one half of the Q-cycle. A. The relative positions and orientations of the key participants in different electron transfer reactions in the native bc1 structure 34 Environment ACS Paragon Plus

Page 35 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(1BE3 in PDB). B. Binding of both QH2 (magenta in color, 1NTZ) and SMA (blue in color, 3CX5) at the distal Qo subsite and binding of Q (magenta in color, 1NTZ) at the Qi site are displayed. The concerted bifurcation reaction is portrayed as red color gradient for ET reaction from QH2 to FeS and blue color gradient for ET reaction from QH2 to HbL. In addition, the switch of the conformation of the two internal switches is shown; C. The tunneling pathway of the second electron is shown, from QH • at the proposed proximal Qo subsite to HbL (through Tyr131) and then to HbH (through Phe90 at ONLH), and finally to Q molecule at the Qi site. For clarity, the overall tunneling pathway is visualized using dark red-to-yellow color gradient. Domain movement of FeSb cluster is indicated as hashed arrows. D. Tunneling pathway of the first electron transferred from FeSc to relay at Hc1 and end finally at the heme c of cytochrome c electron carrier.

As displayed in Figure S6A, the scatter plot of log10 of the calculated ET rates using the tunneling current theory against the edge-to-edge distances for the 7 redox systems in bc1 complex shows a reasonable linear trend, approximated - for the concerted reaction at the Qo site - by the line with the slope of 0.30. Such a low slope value compared to a typical value of -0.6 reported for proteins

87

is due to the

unconventional nature of the bifurcated ET reactions, in which a slow rate-determining ET reaction of ~ 10+3 sec-1 occurs along a short edge-to-edge distance (6.8Å), while a fast ET reaction of ~ 10+9 sec-1 occurs along a long edge-to-edge distance of 12.2Å. However, if we assume a sequential mechanism (where QH• bound at the proximal subsite and hence the edge-to-edge distance is only 5.9Å), thereby eliminating one of the atypical ET reactions, the slope of the best-fit line becomes -0.52 in close agreement to the typical -0.6 value, as shown in Figure S6B. In both cases, the best-fit line slopes of the empirical Moser-Dutton model are significantly lower (-0.02 and -0.31). Finally, comparing the calculated ET rates using the tunneling current theory with the measured ET rates for all 6 redox reactions (excluding HbH/Q reaction due to the lack of accurate experimental value),



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 42

we find a reasonable agreement, Table 3. Quantitatively, the linear regression best-fit line in the theory vs experiment data set has the slope of +0.92, as displayed in Figure S6C.

Supporting Information Experimental data on the redox potentials and pK values for the different redox centers in bc1 complex are listed in Table 1; the distances between QH2 hydroxyl oxygen atoms and both His161 and Glu271 residues in different X-ray crystal structures are tabulated in Table 2; atomic population of the donor and acceptor tunneling orbitals for the pruned heme bL → heme bH system and the bifurcated electron transfer reaction in heme bL ← QH2 → [2Fe-2S] system are shown in Figure S1. Figure S2 displays the delocalization lengths of different bi-orthogonalized MO’s over the bridge residues against the corresponding orbital energies, Figure S3 shows the normalized atomic contribution for different fragments (donor, acceptor and bridge) in the heme bL → heme bH system, Figure S4 shows the total electron tunneling flux of heme c1 → heme c redox system, Figure S5 displays the conservation pattern for key residues in ET reactions in bc1 complex and Figure S6 shows the scatter plot of log10 of the calculated ET rate constants for all 7 redox systems against the edge-to-edge distance (using the distal SQ/HbL ET rate constant value in A and the proximal one in B), and also displays the scatter plot of log10 of the calculated ET rate constants against log10 of the experimentally measured ET rate constants in C.

Acknowledgements

This work has been supported by NIH grant M054052.

Abbreviations


Page 37 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Q or UQ, ubiquinone; QH2 or UQH2, ubiquinol; SQ, ubisemiquinone; SMA, stigmatellin; ANY, antimycin; ET, electron transfer; PT, proton transfer; PCET, proton coupled electron transfer; BS, BrokenSymmetry; eFC, electronic Franck-Condon.

References 1. Mitchell, P., Coupling of Phosphorylation to Electron and Hydrogen Transfer by a ChemiOsmotic Type of Mechanism. Nature 1961, 191, 144-148. 2. Mitchell, P., Chemiosmotic Coupling in Oxidative and Photosynthetic Phosphorylation. Biol. Rev. Camb. Philos. Soc. 1966, 41, 445-502. 3. Emerit, J.; Edeas, M.; Bricaire, F., Neurodegenerative Diseases and Oxidative Stress. Biomed. Pharmacother. 2004, 58, 39-46. 4. Benzi, G.; Moretti, A., Are Reactive Oxygen Species Involved in Alzheimer's Disease? Neurobiol. Aging 1995, 16, 661-674. 5. Bell, E. L.; Klimova, T. A.; Eisenbart, J.; Moraes, C. T.; Murphy, M. P.; Budinger, G. R. S.; Chandel, N. S., The Qo Site of the Mitochondrial Complex III Is Required for the Transduction of Hypoxic Signaling Via Reactive Oxygen Species Production. J. Cell Biol. 2007, 177, 1029-1036. 6. Xia, D.; Yu, C. A.; Kim, H.; Xia, J. Z.; Kachurin, A. M.; Zhang, L.; Yu, L.; Deisenhofer, J., Crystal Structure of the Cytochrome Bc1 Complex from Bovine Heart Mitochondria. Science 1997, 277, 60-6. 7. Schagger, H.; Link, T. A.; Engel, W. D.; von Jagow, G., Isolation of the Eleven Protein Subunits of the Bc1 Complex from Beef Heart. Methods Enzymol. 1986, 126, 224-37. 8. Zhang, Z.; Huang, L.; Shulmeister, V. M.; Chi, Y.-I.; Kim, K. K.; Hung, L.-W.; Crofts, A. R.; Berry, E. A.; Kim, S.-H., Electron Transfer by Domain Movement in Cytochrome Bc1. Nature 1998, 392, 677-684. 9. Iwata, S.; Lee, J. W.; Okada, K.; Lee, J. K.; Iwata, M.; Rasmussen, B.; Link, T. A.; Ramaswamy, S.; Jap, B. K., Complete Structure of the 11-Subunit Bovine Mitochondrial Cytochrome Bc1 Complex. Science 1998, 281, 64-71. 10. Moser, C. C.; Farid, T. A.; Chobot, S. E.; Dutton, P. L., Electron Tunneling Chains of Mitochondria. Biochim. Biophys. Acta 2006, 1757, 1096-109. 11. Mitchell, P., Possible Molecular Mechanisms of the Protonmotive Function of Cytochrome Systems. J. Theor. Biol. 1976, 62, 327-367. 12. Brandt, U.; Trumpower, B., The Protonmotive Q Cycle in Mitochondria and Bacteria. Crit. Rev. Biochem. Mol. Biol. 1994, 29, 165-197. 13. Crofts, A. R.; Hong, S.; Ugulava, N.; Barquera, B.; Gennis, R.; Guergova-Kuras, M.; Berry, E. A., Pathways for Proton Release During Ubihydroquinone Oxidation by the Bc(1) Complex. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 10021-10026. 14. Crofts, A. R.; Shinkarev, V. P.; Kolling, D. R.; Hong, S., The Modified Q-Cycle Explains the Apparent Mismatch between the Kinetics of Reduction of Cytochromes c1 and bH in the Bc1 Complex. J. Biol. Chem. 2003, 278, 36191-201. 15. Osyczka, A.; Moser, C. C.; Dutton, P. L., Fixing the Q Cycle. Trends Biochem. Sci 2005, 30, 176-182. 16. Crofts, A. R.; Guergova-Kuras, M.; Huang, L.; Kuras, R.; Zhang, Z.; Berry, E. A., Mechanism of Ubiquinol Oxidation by the Bc1 Complex: Role of the Iron Sulfur Protein and Its Mobility. Biochemistry 1999, 38, 15791-15806. 37 Environment ACS Paragon Plus


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 42

17. Covian, R.; Trumpower, B. L., Rapid Electron Transfer between Monomers When the Cytochrome Bc1 Complex Dimer Is Reduced through Center N. J. Biol. Chem. 2005, 280, 22732-40. 18. Gong, X.; Yu, L.; Xia, D.; Yu, C.-A., Evidence for Electron Equilibrium between the Two Hemes bL in the Dimeric Cytochrome Bc1 Complex. J. Biol. Chem. 2005, 280, 9251-9257. 19. Shinkarev, V. P.; Wraight, C. A., 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. FEBS Lett. 2007, 581, 1535-41. 20. Świerczek, M.; Cieluch, E.; Sarewicz, M.; Borek, A.; Moser, C. C.; Dutton, P. L.; Osyczka, A., An Electronic Bus Bar Lies in the Core of Cytochrome Bc(1). Science 2010, 329, 451-454. 21. Gray, H. B.; Winkler, J. R., Long-Range Electron Transfer. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 3534-3539. 22. Beratan, D. N.; Onuchic, J. N.; Winkler; Gray, H. B., Electron-Tunneling Pathways in Proteins. Science 1992, 258, 1740-1741. 23. Stuchebrukhov, A. A., Long-Distance Electron Tunneling in Proteins. Theor. Chem. Acc. 2003, 110, 291-306. 24. Stuchebrukhov, A. A., Tunneling Currents in Long-Distance Electron Transfer Reactions. V. Effective One Electron Approximation. J. Chem. Phys. 2003, 118, 7898-7906. 25. Stuchebrukhov, A. A., Toward Ab Initio Theory of Long-Distance Electron Tunneling in Proteins: Tunneling Currents Approach. Adv. Chem. Phys. 2001, 118, 1-44. 26. Hayashi, T.; Stuchebrukhov, A. A., Electron Tunneling in Respiratory Complex I. Proc. Natl. Acad. Sci. 2010, 107, 19157-19162. 27. Hagras, M. A.; Stuchebrukhov, A. A., Transition Flux Formula for the Electronic Coupling Matrix Element. J. Phys. Chem. B 2015, 119, 7712-7721. 28. Hong, S.; Victoria, D.; Crofts, A. R., Inter-Monomer Electron Transfer Is Too Slow to Compete with Monomeric Turnover in Bc(1) Complex. Biochim. Biophys. Acta 2012, 1817, 1053-1062. 29. Covian, R.; Trumpower, B. L., Regulatory Interactions in the Dimeric Cytochrome Bc(1) Complex: The Advantages of Being a Twin. Biochim. Biophys. Acta 2008, 1777, 1079-1091. 30. Lanciano, P.; Lee, D.-W.; Yang, H.; Darrouzet, E.; Daldal, F., Intermonomer Electron Transfer between the Low-Potential b Hemes of Cytochrome Bc1. Biochemistry 2011, 50, 1651-1663. 31. Becke, A. D., Density‐Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648-5652. 32. Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J., Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields. J. Phys. Chem. 1994, 98, 11623-11627. 33. Moll, A.; Hildebrandt, A.; Lenhof, H. P.; Kohlbacher, O., Ballview: A Tool for Research and Education in Molecular Modeling. Bioinformatics 2006, 22, 365-6. 34. Lindahl, E.; Hess, B.; van der Spoel, D., Gromacs 3.0: A Package for Molecular Simulation and Trajectory Analysis. J. Mol. Model. 2001, 7, 306-317. 35. Berendsen, H. J. C.; van der Spoel, D.; van Drunen, R., GROMACS: A Message-Passing Parallel Molecular Dynamics Implementation. Comput. Phys. Commun. 1995, 91, 43-56. 36. Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. M.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P. A., A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules. J. Am. Chem. Soc. 1995, 117, 51795197. 37. Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A., Development and Testing of a General Amber Force Field. J. Comput. Chem. 2004, 25, 1157-1174. 38. Gumbart, J.; Trabuco, L. G.; Schreiner, E.; Villa, E.; Schulten, K., Regulation of the ProteinConducting Channel by a Bound Ribosome. Structure 2009, 17, 1453-1464. 39. Pettersen, E. F.; Goddard, T. D.; Huang, C. C.; Couch, G. S.; Greenblatt, D. M.; Meng, E. C.; Ferrin, T. E., UCSF Chimera--a Visualization System for Exploratory Research and Analysis. J. Comput. Chem. 2004, 25, 1605-12. 38 Environment ACS Paragon Plus

Page 39 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


40. Pei, J.; Grishin, N. V., Al2co: Calculation of Positional Conservation in a Protein Sequence Alignment. Bioinformatics 2001, 17, 700-712. 41. Daizadeh, I.; Gehlen, J. N.; Stuchebrukhov, A. A., Calculation of Electronic Tunneling Matrix Element in Proteins: Comparison of Exact and Approximate One-Electron Methods for Ru-Modified Azurin. J. Chem. Phys. 1997, 106, 5658-5666. 42. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, et al., Gaussian 09, Gaussian, Inc.: Wallingford, CT, USA, 2009. 43. Hayashi, T.; Mukamel, S., Vibrational−Exciton Couplings for the Amide I, II, III, and A Modes of Peptides. J. Phys. Chem. B 2007, 111, 11032-11046. 44. Crofts, A. R.; Lhee, S.; Crofts, S. B.; Cheng, J.; Rose, S., Proton Pumping in the Bc1 Complex: A New Gating Mechanism That Prevents Short Circuits. Biochim. Biophys. Acta Biochim Biophys Acta 2006, 1757, 1019-34. 45. Crofts, A. R.; Barquera, B.; Gennis, R. B.; Kuras, R.; Guergova-Kuras, M.; Berry, E. A., Mechanism of Ubiquinol Oxidation by the Bc1 Complex: Different Domains of the Quinol Binding Pocket and Their Role in the Mechanism and Binding of Inhibitors. Biochemistry 1999, 38, 1580715826. 46. Berry, E. A.; Huang, L. S., Observations Concerning the Quinol Oxidation Site of the Cytochrome Bc1 Complex. FEBS Lett. 2003, 555, 13-20. 47. Löwdin, P.-O., A Quantum Mechanical Calculation of the Cohesive Energy, the Interionic Distance, and the Elastic Constants of Some Ionic Crystals. Ark. Mat. Astr. Fys. A. 1947, 35, 9. 48. Stuchebrukhov, A. A., Tunneling Currents in Long-Distance Electron Transfer Reactions. IV. Many-Electron Formulation. Nonorthogonal Atomic Basis Sets and Mulliken Population Analysis. J. Chem. Phys. 1998, 108, 8510-8520. 49. Stuchebrukhov, A. A., Tunneling Currents in Electron Transfer Reactions in Proteins. J. Chem. Phys. 1996, 104, 8424-8432. 50. Marcus, R. A.; Sutin, N., Electron Transfers in Chemistry and Biology. Biochim. Biophys. Acta 1985, 811, 265-322. 51. Lange, C.; Hunte, C., Crystal Structure of the Yeast Cytochrome Bc(1) Complex with Its Bound Substrate Cytochrome C. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 2800-2805. 52. Ransac, S.; Mazat, J.-P., How Does Antimycin Inhibit the Bc1 Complex? A Part-Time Twin. Biochim. Biophys. Acta 2010, 1797, 1849-1857. 53. Trumpower, B. L., A Concerted, Alternating Sites Mechanism of Ubiquinol Oxidation by the Dimeric Cytochrome Bc(1) Complex. Biochim. Biophys. Acta 2002, 1555, 166-73. 54. Mulkidjanian, A. Y., Ubiquinol Oxidation in the Cytochrome Bc1 Complex: Reaction Mechanism and Prevention of Short-Circuiting. Biochim. Biophys. Acta 2005, 1709, 5-34. 55. Rich, P. R., Electron and Proton Transfers through Quinones and Cytochrome Bc Complexes. Biochim. Biophys. Acta 1984, 768, 53-79. 56. Zhu, J.; Egawa, T.; Yeh, S.-R.; Yu, L.; Yu, C.-A., Simultaneous Reduction of Iron–Sulfur Protein and Cytochrome bL During Ubiquinol Oxidation in Cytochrome Bc1 Complex. Proc. Natl. Acad. Sci. 2007, 104, 4864-4869. 57. Hong, S.; Ugulava, N.; Guergova-Kuras, M.; Crofts, A. R., The Energy Landscape for Ubihydroquinone Oxidation at the Qo Site of the Bc1 Complex Inrhodobacter Sphaeroides. J. Biol. Chem. 1999, 274, 33931-33944. 58. Crofts, A. R., Proton-Coupled Electron Transfer at the Qo-Site of the Bc1 Complex Controls the Rate of Ubihydroquinone Oxidation. Biochim. Biophys. Acta 2004, 1655, 77-92. 59. Seddiki, N.; Meunier, B.; Lemesle-Meunier, D.; Brasseur, G., Is Cytochrome b Glutamic Acid 272 a Quinol Binding Residue in the Bc1 Complex of Saccharomyces Cerevisiae? Biochemistry 2008, 47, 2357-68. 60. Hammes–Schiffer, S.; Stuchebrukhov, A. A., Theory of Coupled Electron and Proton Transfer Reactions. Chem. Rev. 2010, 110, 6939-6960. 39 Environment ACS Paragon Plus


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 42

61. Snyder, C. H.; Gutierrez-Cirlos, E. B.; Trumpower, B. L., Evidence for a Concerted Mechanism of Ubiquinol Oxidation by the Cytochrome Bc1 Complex. J. Biol. Chem. 2000, 275, 13535-13541. 62. Victoria, D.; Burton, R.; Crofts, A. R., Role of the -PEWY-Glutamate in Catalysis at the Qo-Site of the Cyt Bc1 Complex. Biochim. Biophys. Acta 2013, 1827, 365-386. 63. Brandt, U.; Okun, J. G., Role of Deprotonation Events in Ubihydroquinone:Cytochrome c Oxidoreductase from Bovine Heart and Yeast Mitochondria. Biochemistry 1997, 36, 11234-11240. 64. Covian, R.; Trumpower, B. L., The Rate-Limiting Step in the Cytochrome Bc1 Complex (Ubiquinol-Cytochrome c Oxidoreductase) Is Not Changed by Inhibition of Cytochrome b-Dependent Deprotonation: Implications for the Mechanism of Ubiquinol Oxidation at Center P of the Bc1 Complex. J. Biol. Chem. 2009, 284, 14359-14367. 65. Crofts, A.; Wang, Z., How Rapid Are the Internal Reactions of the Ubiquinol:Cytochrome c2 Oxidoreductase? Photosynth. Res. 1989, 22, 69-87. 66. Link, T. A., The Role of the `Rieske' Iron Sulfur Protein in the Hydroquinone Oxidation (Qp) Site of the Cytochrome Bc1 Complex: The `Proton-Gated Affinity Change' Mechanism. FEBS Lett. 1997, 412, 257-264. 67. Brandt, U., Control of Ubiquinol Oxidation at Center P (Qo) of the Cytochrome Bc1 Complex. J. Bioenerg. Biomembr. 1999, 31, 243-50. 68. Brandt, U., Bifurcated Ubihydroquinone Oxidation in the Cytochrome Bc1 Complex by ProtonGated Charge Transfer. FEBS Lett. 1996, 387, 1-6. 69. Zu, Y.; Couture, M. M. J.; Kolling, D. R. J.; Crofts, A. R.; Eltis, L. D.; Fee, J. A.; Hirst, J., Reduction Potentials of Rieske Clusters: Importance of the Coupling between Oxidation State and Histidine Protonation State†. Biochemistry 2003, 42, 12400-12408. 70. Mao, J.; Hauser, K.; Gunner, M. R., How Cytochromes with Different Folds Control Heme Redox Potentials. Biochemistry 2003, 42, 9829-40. 71. Marcus, R. A., On the Theory of Electron‐Transfer Reactions. VI. Unified Treatment for Homogeneous and Electrode Reactions. J. Chem. Phys. 1965, 43, 679-701. 72. Devault, D., Quantum Mechanical Tunnelling in Biological Systems. Q. Rev. Biophys. 1980, 13, 387-564. 73. Kresge, A. J.; Silverman, D. N., [12] Application of Marcus Rate Theory to Proton Transfer in Enzyme-Catalyzed Reactions. In Methods Enzymol., Vern L. Schramm, D. L. P., Ed. Academic Press: 1999; Vol. Volume 308, pp 276-297. 74. Darrouzet, E.; Moser, C. C.; Dutton, P. L.; Daldal, F., Large Scale Domain Movement in Cytochrome Bc1: A New Device for Electron Transfer in Proteins. Trends Biochem. Sci 2001, 26, 445451. 75. Kokhan, O.; Wraight, C. A.; Tajkhorshid, E., The Binding Interface of Cytochrome C and Cytochrome c1 in the Bc1 Complex: Rationalizing the Role of Key Residues. Biophysical Journal 99, 2647-2656. 76. Ransac, S.; Parisey, N.; Mazat, J.-P., The Loneliness of the Electrons in the Bc1 Complex. Biochim. Biophys. Acta 2008, 1777, 1053-1059. 77. Sadoski, R. C.; Engstrom, G.; Tian, H.; Zhang, L.; Yu, C.-A.; Yu, L.; Durham, B.; Millett, F., Use of a Photoactivated Ruthenium Dimer Complex to Measure Electron Transfer between the Rieske Iron−Sulfur Protein and Cytochrome c1 in the Cytochrome Bc1 Complex. Biochemistry 2000, 39, 42314236. 78. Engstrom, G.; Xiao, K.; Yu, C.-A.; Yu, L.; Durham, B.; Millett, F., Photoinduced Electron Transfer between the Rieske Iron-Sulfur Protein and Cytochrome c1 in Therhodobacter Sphaeroides Cytochrome bc1 Complex: Effects of pH, Temperature, and Driving Force. J. Biol. Chem. 2002, 277, 31072-31078. 79. Millett, F.; Durham, B., Kinetics of Electron Transfer within Cytochrome Bc1 and between Cytochrome Bc1 and Cytochrome C. Photosynth. Res. 2004, 82, 1-16. 80. Tian, H.; Sadoski, R.; Zhang, L.; Yu, C.-A.; Yu, L.; Durham, B.; Millett, F., Definition of the Interaction Domain for Cytochrome C on the Cytochrome Bc1 Complex: Steady-State and Rapid 40 Environment ACS Paragon Plus

Page 41 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Kinetic Analysis of Electron Transfer between Cytochrome C and Rhodobacter Sphaeroidescytochrome Bc1 Surface Mutants. J. Biol. Chem. 2000, 275, 9587-9595. 81. Engstrom, G.; Rajagukguk, R.; Saunders, A. J.; Patel, C. N.; Rajagukguk, S.; MerbitzZahradnik, T.; Xiao, K.; Pielak, G. J.; Trumpower, B.; Yu, C.-A.; Yu, L.; Durham, B.; Millett, F., Design of a Ruthenium-Labeled Cytochrome c Derivative to Study Electron Transfer with the Cytochrome Bc1 Complex. Biochemistry 2003, 42, 2816-2824. 82. Shinkarev, V. P.; Crofts, A. R.; Wraight, C. A., The Electric Field Generated by Photosynthetic Reaction Center Induces Rapid Reversed Electron Transfer in the Bc1 Complex. Biochemistry 2001, 40, 12584-12590. 83. Czapla, M.; Cieluch, E.; Borek, A.; Sarewicz, M.; Osyczka, A., Catalytically-Relevant Electron Transfer between Two Hemes bL in the Hybrid Cytochrome Bc1-Like Complex Containing a Fusion of Rhodobacter Sphaeroides and Capsulatus Cytochromes b. Biochim. Biophys. Acta 2013, 1827, 751-760. 84. McGaughey, G. B.; Gagné, M.; Rappé, A. K., Π-Stacking Interactions: Alive and Well in Proteins. J. Biol. Chem. 1998, 273, 15458-15463. 85. Gervasio, F. L.; Chelli, R.; Procacci, P.; Schettino, V., The Nature of Intermolecular Interactions between Aromatic Amino Acid Residues. Proteins 2002, 48, 117-25. 86. Bechmann, G.; Weiss, H.; Rich, P. R., Non-Linear Inhibition Curves for Tight-Binding Inhibitors of Dimeric Ubiquinol-Cytochrome c Oxidoreductases. Evidence for Rapid Inhibitor Mobility. Eur. J. Biochem. 1992, 208, 315-25. 87. Lin, J.; Balabin, I. A.; Beratan, D. N., The Nature of Aqueous Tunneling Pathways between Electron-Transfer Proteins. Science 2005, 310, 1311-1313.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

TOC Image


Page 42 of 42

Quantum Calculations of Electron Tunneling in Respiratory Complex

Recommend Documents