Multiscale simulations reveal key features of theproton-pumping mechanism in cytochrome c oxidaseRuibin Lianga,b,c,d, Jessica M. J. Swansona,b,c,d, Yuxing Penge, Mårten Wikströmf, and Gregory A. Votha,b,c,d,1

aDepartment of Chemistry, University of Chicago, Chicago, IL 60637; bInstitute for Biophysical Dynamics, University of Chicago, Chicago, IL 60637; cJamesFranck Institute, University of Chicago, Chicago, IL 60637; dComputation Institute, University of Chicago, Chicago, IL 60637; eResearch Computing Center,University of Chicago, Chicago, IL 60637; and fHelsinki Bioenergetics Group, Programme for Structural Biology and Biophysics, Institute of Biotechnology,University of Helsinki, FI-00014 Helsinki, Finland

Edited by Richard Eisenberg, University of Rochester, Rochester, NY, and approved May 25, 2016 (received for review February 9, 2016)

Cytochrome c oxidase (CcO) reduces oxygen to water and uses thereleased free energy to pump protons across the membrane. Wehave used multiscale reactive molecular dynamics simulations toexplicitly characterize (with free-energy profiles and calculatedrates) the internal proton transport events that enable protonpumping during first steps of oxidation of the fully reduced en-zyme. Our results show that proton transport from amino acidresidue E286 to both the pump loading site (PLS) and to the binu-clear center (BNC) are thermodynamically driven by electron trans-fer from heme a to the BNC, but that the former (i.e., pumping) iskinetically favored whereas the latter (i.e., transfer of the chemicalproton) is rate-limiting. The calculated rates agree with experi-mental measurements. The backflow of the pumped proton fromthe PLS to E286 and from E286 to the inside of the membrane isprevented by large free-energy barriers for the backflow reac-tions. Proton transport from E286 to the PLS through the hydro-phobic cavity and from D132 to E286 through the D-channel arefound to be strongly coupled to dynamical hydration changes inthe corresponding pathways and, importantly, vice versa.

cytochrome c oxidase | proton-pumping mechanism | reactive moleculardynamics | bioenergetics | proton transport

Cytochrome c oxidase (CcO) (Fig. 1) catalyzes the reductionof O2 to H2O and couples the free energy of this exergonic

reaction to the pumping of protons across the membrane, creating atransmembrane proton electrochemical gradient that drives, for ex-ample, ATP synthesis (1–3). During each reaction cycle eight pro-tons are taken up from the negatively charged inside (N-side) of themembrane and either react with oxygen (referred to as “chemical”protons below) or are pumped to the positively charged outside(P-side) of the membrane (referred to as “pumped” protons below).In aa3-type CcO, the D-channel is responsible for uptake of all fourpumped protons and at least one out of four chemical protons (4, 5).Protons on the N-side are taken into D-channel via the amino acidresidue D132 at the channel entrance, and then transferred to res-idue E286 in the middle of the membrane (4, 5). By Grotthussshuttling through the water molecules in the hydrophobic cavity(HC) above E286, each proton is either transferred to react withoxygen in the binuclear center (BNC), consisting of heme a3 and theCuB complex, or transferred to the pump loading site (PLS) andthen further released to the P-side of the membrane (Fig. 1).Despite decades of study, the CcO proton-pumping mechanism

is still incompletely understood at the atomistic level. For example,controversy remains regarding how the internal proton transport(PT) events are coupled with electron transfer (ET) (3, 6–16), whatfeatures enable pumping while preventing proton backflow fromthe P-side to the N-side (3, 6, 10, 11, 15, 17, 18), and how hydrationinfluences PT through the HC and D-channel (19–26). Recentcomputational work proposed a stepwise pumping mechanism inwhich an excess proton is first transported from E286 to theD-propionate on heme a3 (PRDa3) through a poorly hydratedHC, followed by an increase in the HC hydration (24). However,as we have recently reported (27), the migration of a hydratedexcess proton can strongly and dynamically influence its solvation

environment, thus drawing into question this prior view of therole of solvation during PT through the HC.To address these questions, we have carried out extensive

multiscale reactive molecular dynamics (MS-RMD) (28–33)free-energy simulations to study the proton-pumping mechanismin CcO. Quantum-mechanical forces from targeted quantummechanics/molecular mechanics (QM/MM) calculations arebridged, in a multiscale fashion via a variational mathematicalframework, into the reactive molecular dynamics (MD) algo-rithm to describe the dynamics of the system nuclei, thus in-cluding chemical bond breaking and making. In this way, weexplicitly simulate PT between proton binding sites, includingGrotthuss shuttling of the excess proton(s) through residues andintervening water molecules.We focus in this work on the transitions where the PM state of

the binuclear site (called PM′ herein, where heme a and CuA arereduced) reacts further by receiving an electron from heme a,because it is representative of how PT and ET are coupled in thenative catalytic cycle, and there is extensive experimental in-formation to which we can compare our computational results. Inthe flow-flash experiments, oxidation of the four-electron reducedCcO begins with O2 binding to the BNC (see refs. 3 and 34 forreview). Three electrons and one proton from the BNC are thenconsumed during O–O bond scission (35, 36). The subsequent ETfrom heme a to BNC generates the PR state, followed by protonuptake at the BNC from N-side bulk to form the F state. InternalPT from E286 to the PLS occurs with the same time dependenceas ET (6), and a proton is pumped to the P-side on the sametimescale as the PR → F transition. We simulate the internal PTevents (excluding proton uptake and release) after O–O bondscission, including the state just before ET (herein denoted PM′)

Significance

The long-studied proton-pumping mechanism in cytochrome coxidase (CcO) continues to be a source of debate. This workprovides a comprehensive computational characterization of theinternal proton transport dynamics, while explicitly includingGrotthuss shuttling, that lead to both pumping and catalysis. Fo-cusing on the first steps of oxidation of the fully reduced enzyme,our results show that the transfer of the pumped and chemicalprotons are thermodynamically driven by electron transfer, andexplain how proton back-leakage is avoided by large back-leakbarriers and kinetic gating. This work also explicitly characterizesthe coupling of proton transport with hydration changes in thehydrophobic cavity and D-channel, thus advancing our under-standing of proton transport in biomolecules in general.

Author contributions: R.L., J.M.J.S., Y.P., M.W., and G.A.V. designed research; R.L., J.M.J.S.,and Y.P. performed research; R.L., J.M.J.S., Y.P., M.W., and G.A.V. analyzed data; and R.L.,J.M.J.S., M.W., and G.A.V. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. Email: gavoth@uchicago.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1601982113/-/DCSupplemental.

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(see SI Appendix, Table S1, for detailed definition on the states).Our results show that both PT events (E286 to the PLS and E286to the BNC) are driven by ET from heme a to the BNC. Thetransfer of the pumped proton is kinetically favored while that ofthe chemical proton is rate limiting. These results also explain howCcO prevents the decoupling of pumping from the chemical re-action with kinetic gating. Given the computational accuracy andefficiency of the MS-RMD methodology (33), a critical compo-nent of our results is the explicit characterization of the couplingbetween PT and hydration changes in both the HC and D-channel.Finally, we present results that argue against the possibility of E286being biprotonated during the pumping process.

Results and DiscussionTransport of the Pumped Proton and Hydration of the HC. We havesimulated PT to the PLS and the BNC focusing on coupled hy-dration changes. Starting with PT from E286 to the PLS, we cal-culated two-dimensional potentials of mean force (2D PMFs) inthe PM′ state (before ET) and PR state (after ET) during thePM′ → PR → F transition (SI Appendix, Fig. S3 A and B). The col-lective variables used to define these 2D PMFs are (i) the progress ofthe excess proton center of excess charge (CEC) through the HC(horizontal axis) and (ii) the degree of hydration of the HC (verticalaxis). The 2D PMFs and minimum free-energy pathways traced outfrom those 2D PMFs (black lines in SI Appendix, Fig. S3 A and B)verify that, as the proton moves from E286 to PRDa3, the HCbecomes more hydrated (increasing from 6 to 10 waters in ourchosen hydration “box,” which also includes approximately 2 wa-ters outside of the traditionally defined interheme region). WhenE286 is protonated, the HC favors a low hydration state (approx-imately four waters in the interheme region) (SI Appendix, Fig.S6A). As the excess proton moves to the water above E286 (SIAppendix, Fig. S6B), the PRDa3 side chain rotates down to interactwith the positive charge (CEC). This weakens the interactionsbetween PRDa3 and nearby W172 and R481, allowing more watermolecules to enter the HC. The hydration level in HC reaches itsmaximum just before (PM′), or as (PR), PRDa3 is protonated (SIAppendix, Fig. S6C). The PRDa3 then rotates from downward toupward orientation through the transition state (SI Appendix, Fig.

S6D). Subsequently, the proton moves to the A-propionate onheme a3 (PRAa3) (SI Appendix, Fig. S6E).The 1D free-energy curves in Fig. 2A are plotted from the

minimum free-energy pathways traced out from the 2D PMFs.These free-energy curves describe the dominant activated reactiveenergetics for the water-mediated transport of the pumped protonin the PM′ and PR states, revealing several important findings.First, the free-energy minimum on PRAa3 in the pumping PMF ofthe PR state suggests that PRAa3 is the major PLS, in agreementwith previous work (37, 38). It is interesting to note that, in ba3-type CcO, PRAa3 is also suggested to be the PLS (39). However,PRDa3 is still actively involved in the pumping process because itshuttles the proton from E286 to the PLS (breaking its salt bridgeto R481 and hydrogen bond with W172), as suggested by Wikströmet al. (40) and Yamashita and Voth (13). Second, PT from E286to the PLS is thermodynamically unfavorable by ∼8 kcal/mol inthe PM′ state, but favorable by 3 kcal/mol in the PR state (Fig.2A). Thus, ET to the BNC provides a thermodynamic drivingforce for PT to the PLS. Combined with the experimental resultsshowing that ET is not complete without PT to the PLS in theE286Q mutant (35), one might conclude that ET to the BNC andPT to the PLS are coupled, each driving the other to its thermo-dynamically favored state during PM′ → PR transition.

Transport of the Chemical Proton. Focusing next on the transfer ofthe chemical proton, we calculated similar 2D PMFs for PT fromE286 to the BNC in PM′ and PR states, both with and without thePLS (PRAa3) protonated (SI Appendix, Fig. S4 A–D). The 1Dcurves traced along the minimum free-energy pathways (Fig. 2B)show that PT from E286 to the CuB-bound hydroxide in the BNC isthermodynamically unfavorable by more than 10 kcal/mol in thePM′ state, but favorable by ∼5 kcal/mol in the PR state. This sug-gests that ET from heme a to BNC also provides a thermodynamicdriving force for the PT from E286 to the BNC (i.e., the formationof the F state) that leads to the chemical reaction. This conclusionis independent of the protonation state of the PLS (Fig. 2B) andthe hydration level in the HC (SI Appendix, Fig. S4 A–D).The molecular mechanism of PT from E286 to the BNC in the

PM′ and PR states is depicted in SI Appendix, Figs. S8 and S9. Notethat, in the PM′ state, the waters between protonated E286 and theBNC (not shown in configurations A and B) are only transientlysampled, which is in line with the water gate mechanism discussedin refs. 20 and 22. First, the side chain of protonated E286 rotatestoward the BNC (configurations A, B, and C). The rotationcontributes to part of the reaction barrier due to intramolecularstrain and disruption of the optimal solvation configuration inthe HC. Then E286 deprotonates (x ’ 5–6 Å) and transfers theproton to the water molecule between E286 and BNC to form thetransition state (configurations D). This is the most narrow regionthat the proton passes through, with a single water molecule hy-drogen bonded to E286, the backbone carbonyl of G283, and CuB-OH. Thus, the free-energy barrier is due to electrostatic repulsionfrom the BNC (much larger for PM′ than for PR), a frustratedwater network, and a confined charge distribution as the protonsqueezes through this narrow pass. Finally, the combination of theexcess proton and CuB-OH completes the chemical reaction toform the F state. The reduced electrostatic repulsion from BNCafter ET makes the chemical PT reaction faster and more favor-able in PR state than in PM′ state.

Rates of the Pumped and Chemical Proton Transport Events.Analysisof the rates (Table 1; reported as time constants, i.e., the inverse ofrate constants) for PT to the PLS and BNC in the PM′ and PRstates provides deeper mechanistic insight into the proton-pumpingmechanism during the PM′→ PR → F transition. Before ET (in thePM′ state), PT from E286 to the PLS is kinetically possible withinthe experimentally determined A → PR transition [∼25 to 50 μs(17, 41)], but the rate for reverse PT (PLS to E286) outcompetesthat of the forward PT and also the reprotonation of E286 throughD-channel (Tables 1 and 2). Thus, PT to the PLS is minimal beforethe ET. In the same state, it is kinetically prohibitive to transfer the

Fig. 1. Illustration of the simulation setup for the full CcO from R. sphaer-oides in a membrane and surrounded by water. The D- and K-channels, as wellas metal centers, key residues, and internal water molecules are depicted.

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chemical proton from E286 to the BNC, which would short-circuitpumping if it were to happen before PT from E286 to the PLS (22).In contrast, after ET (in the PR state) proton backflow from thePLS to deprotonated E286 is slower than the reprotonation ofE286 through the D-channel (Tables 1 and 2). This allows timelyreprotonation of E286 and prevents the proton loaded at PLS fromleaking back to E286 and subsequently being consumed at theBNC. Thus, full loading of the PLS is achieved only with ET. Thereverse is also true considering the experiments in ref. 35. There-fore, we conclude that PT to PLS and ET to BNC gradually driveeach other to completion.Moreover, the ET also facilitates the PT from E286 to the BNC

(Table 1) by reducing the reaction barrier in PR state. (Fig. 2B).We note that the PT to PLS is still faster than PT to the BNC evenafter the ET (Table 1, PR state), which again prevents the above-mentioned short-circuiting issue. Our calculated rate for transfer

of the chemical proton in PR state is in quantitative agreementwith the experimental PR → F transition rate (6, 17) (Table 1,compare the calculated time constant for E286→ BNC in PR statewith protonated PLS to the experimental time constant for PR → Ftransition), and is slower than the PT to PLS (Table 1) and PTfrom D132 to E286 in D-channel (Table 2). Therefore, we con-clude that the PT from E286 to the CuB-bound hydroxide in theBNC is the rate-limiting step for the PR → F transition.

Comparison with Proposed Mechanisms. Our thermodynamic andkinetic results build upon the previously proposed mechanismbased on the orientation and connectivity of water chains in theHC (6, 15, 20, 22). In this mechanism, PT from E286 to the PLSand ET from heme a to the BNC are tightly coupled to each otherand occur in concerted fashion during the PM′ → PR transition.The short-circuiting (i.e., premature PT to BNC before PT to PLS)

A B

DC

Fig. 2. (A) One-dimensional free-energy profiles for PT from E286 to the PLS for the PM′ (red) and PR (blue) states traced out along the minimum free-energypathways of the full 2D PMFs in SI Appendix, Fig. S3. (B) One-dimensional free-energy profiles for PT from E286 to the BNC in the PM′ state with and without a protonpreloaded in the PLS (purple and red, respectively), and the PR state (black and blue, respectively) along the minimum free-energy pathways of the 2D PMFs in SIAppendix, Fig. S4. PT to the BNC with the PLS preloaded (black curve) is the most physically relevant for the PR→ F transition. (C) Full 2D PMF for PT fromD132 to E286through the D-channel in the PR state, with a proton preloaded at the PLS. The 2D PMF is a function of the CEC coordinate through the D-channel and the waterhydration in the asparagine gate region. The strongly coupled behavior of PT and hydration in the asparagine gate region along the 1D minimum free-energy path(black line) is clearly evident. (D) One-dimensional free-energy trace for PT through the D-channel for PR (blue) and F (red) states, along the minimum free-energypathway in C and SI Appendix, Fig. S5. The statistical errors of the 1D free-energy profiles in A, B, and C are in the range of ∼0.1–1 kcal/mol. The statistical errors of the2D PMF in D are in the range ∼0.1–3 kcal/mol. In all of the plots, the positions of E286, PRDa3, PRAa3, BNC, D132, N139, S200, and S201 are labeled with text boxes.

Table 1. Calculated and experimental time constants (inverse of rate constants) of protontransport processes

State E286 → PLS, μs

E286 → BNC, μs

PLS → E286, μsDeprotonated PLS Protonated PLS

PM′ (2.6 ± 0.2) × 10−1 (4 ± 3) × 106 (7.7 ± 0.2) × 108 (1.5 ± 0.4) × 10−5

PR 2.1 ± 0.3 (3 ± 2) × 102 (1.7 ± 0.9) × 102 (1.2 ± 0.6) × 103

Exp (A → PR) 25–50Exp (PR → F) 200

Time constants for transport of the pumped proton (E286 → PLS), the chemical proton (E286 → BNC), and theback-leaked proton (PLS → E286) for the PM′ and PR states. The PT from E286 to the BNC should be comparedwith the experimental rate of the PR → F transition (see the main text). The rate constant calculations areexplained in the SI Appendix.

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is avoided by the absence of a water chain leading from protonatedE286 to BNC in the PM′ state. However, this mechanistic proposalwas based on classical nonreactive MD simulations in the absenceof a shuttling excess proton. Our results support the conclusion thatPT to the BNC is unfavorable in PM′ state, but given our treatmentof the explicit proton transport they further explain why PT to thePLS is preferred after ET occurs, a question raised but not fullyanswered in ref. 15. Moreover, our results describe the diffusive PTprocesses that influence the dynamic water environment in the HC,which in turn is strongly coupled to the PT.Our results are also in partial agreement with the mechanism

proposed by Faxén et al. (17) in which PT from E286 to the PLSoccurs during PR → F rather than PM′ → PR transition. Thismechanism was further discussed later by Lepp et al. (42), whoconcluded that the electrometric signal during PM′ → PR tran-sition is caused by the upward movement of K362 side chainrather than PT from E286 to PLS. However, it has been shownthat this electrometric signal is large enough to include both thelysine swing and the PT from E286 to PLS (15). Moreover, theelectrometric signal was shown to be lost in the E286Q mutant(35), resulting in a product that was actually no longer pure PR,but a PR/PM′ mixture with the latter dominating (see section 5.2and figure 10 in ref. 3). Based on these experimental findings, wesuggest that the coupled PT/ET process during PM′ → PR tran-sition is at present the best explanation (15).

Proton Transport Through the D-channel. The D-channel is respon-sible for transporting two protons from the N-side of the mem-brane to E286 during the PM′ → PR → F transition, one forpumping and the other for the chemical reaction. Three highlyconserved asparagine residues, N139, N121, and N207, resideroughly one-third of the way into the D-channel and form a con-stricted region (called the asparagine gate) (43). Previous non-reactive classical MD simulations have revealed a gating motion ofN139 that controls the hydration state of D-channel (25, 26).However, that work hypothesized that PT through the D-channelfollows a sequence in which the proton waits on the proton donor(D132) until a “water wire” is formed, and then rapidly dissociatesand transports through the preformed water wire to the protonacceptor (E286). As discussed above and in ref. 27, this historicallypopular depiction of PT in aqueous systems can be misleading andis inconsistent with the dynamically coupled and cooperative na-ture of the hydration environment and the excess proton migration.Here, as we did earlier for the PT in the HC, we investigate how

the motion of the excess proton is coupled to the change of thehydration level across the asparagine gate by explicitly calculatingfull 2D PMFs for PT through the D-channel in the PR and F states(Fig. 2C and SI Appendix, Fig. S5 A and B). The minimum free-energy pathways are identified on the 2D PMFs (black lines), andthe corresponding 1D traces can be compared in Fig. 2D.The D-channel PT process starts at D132 (x ’ 35 Å) and ends at

E286 (x ’ 0–5 Å). Initially, when D132 is protonated, the spacebetween N139 and N121 is narrow and dehydrated, forming aneffective gate for PT (SI Appendix, Fig. S7A). As the excess protontransitions to the water above D132, the N139 side chain rotatesand opens a pathway for solvation and PT past the asparagineresidues (SI Appendix, Fig. S7B). The transition state is reached

when the excess proton is in the middle of the asparagine gate (SIAppendix, Fig. S7C). Once the excess proton shuttles through, theasparagine gate gradually closes and becomes dehydrated again (SIAppendix, Fig. S7D). The curvy and nonhorizontal nature of theminimum free-energy pathways on the 2D PMFs (SI Appendix, Fig.S5 A and B) indicates that PT and hydration changes are stronglycoupled processes. After traversing the gate region, the excessproton proceeds to the serine zone (S200 and S201), where it formshydrogen bonds with the hydroxyl groups of the pore-lining serineresidues (x ’ 14 Å). This downhill free-energy region importantlycreates a large proton backflow barrier. Subsequently, the excessproton protonates E286 in the “down” conformation (x ’ 5 Å; Fig.2D), reaching the global free-energy minimum, and E286 rotatesup for either pumping or the chemical reaction (x ’ 1 Å; Fig. 2D).The 1D free-energy traces (Fig. 2D) reveal free-energy barriers

for the proton to pass through the asparagine gate in the D-channel.For both states, the calculated rates for forward PT (D132 to E286)are much faster than the overall PR → F transition rate (Table 2),confirming that forward PT through the D-channel is not rate-limiting in the PR → F transition. The D-channel PT rates are alsofaster than the PT backflow rates from the PLS, as discussed above,allowing for fast reprotonation of E286 before proton backflowfrom the PLS to deprotonated E286. It is plausible, based on theseresults, that the decoupling mutants, such as N139T (42) andN139D (44), disable kinetic gating by slowing down PT through theD-channel [enabling backflow from the PLS to E286 to outcompetethe reprotonation of E286 as previously suggested (3, 26, 39)], bydirectly slowing down the pumping rate (bypassing pumping alto-gether), or by lowering the backflow barriers through the D-channel.In ref. 16, an alternative biprotonated mechanism was proposed,

in which the excess proton approaches a protonated (neutral) E286through the D-channel and facilitates proton pumping through apositively charged, biprotonated E286 transition state. Our resultsshow that the self-consistent charge density functional tight-binding(SCC-DFTB) method used in ref. 16 overestimates the pKa foraspartic acid deprotonation in bulk water and that the biprotonatedE286 transition state is highly energetically unfavorable (SI Ap-pendix). These results suggest that the conclusions reached in ref.16 could, at least in part, be attributed to the SCC-DFTB methodoverestimating the proton affinity of E286 (see the SI Appendix forfurther discussion).

ConclusionsThe MS-RMD simulations and quantitative analysis of the explicitPT steps in CcO presented in this work, combined with previousexperimental findings (see refs. 3, 15, and 18, and referencestherein), lead us to the following conclusions regarding the mostlikely sequence of PT and ET events during the PM′ → PR → Ftransition (Fig. 3A). First, an electron is transferred from heme a tothe BNC during the 25- to 50-μs A→ PR transition, likely followingthe chemistry that occurs at the BNC (35, 36). Either coupled withthis ET event (during the PM′ → PR transition) or immediatelyafter it (during the PR → F transition), a proton is transferred froma singly protonated E286 to the PLS (PRAa3). Experimentalfindings suggest that the former (coupled PT/ET) is more likely (3,15, 35). This PT induces and is accompanied by an increase in theHC hydration from approximately four to eight waters. Second,E286 is rapidly reprotonated through the D-channel, and the HCrelaxes back to the low hydration state. Third, the uncompensatednegative charge in the BNC caused by ET triggers transfer of thechemical proton from E286 to the CuB-bound hydroxide in theBNC, forming a water molecule. Fourth, E286 is reprotonatedagain through D-channel, accompanied by partial ET from CuA toheme a and proton ejection from PLS to the P-side.Based on the above reaction sequence, we combine the PMFs

and available experimental data to estimate the free-energy dia-gram for the PM′ → F transition (Fig. 3B). Based on the experi-mental finding that ET to the BNC in the absence of PT to the PLS(E286Q mutant) results in only 30% PR formation (ref. 3, figure10), ET from heme a to BNC is estimated to be endergonic by∼0.5 kcal/mol. Therefore, starting from the PM′ state (state I,

Table 2. Calculated and experimental time constants (inverse ofrate constants) for PT in the D-channel

State D132 → E286, μs

PR (5 ± 2) × 10−1

F (2 ± 1) × 10−1

Exp (PR → F) 200

The calculated rates for PT through the D-channel (from D132 to E286) inthe PR and F states are compared to the experimental rate of the PR → Ftransition (17). The PLS is protonated in the simulation. The rate constantcalculations are described in the SI Appendix.

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0 kcal/mol), the PT from E286 to the PLS coupled with ET fromheme a to heme a3 leads to PR state (state II) with energy level of−2.9 + 0.5 = −2.4 kcal/mol. Following this, assuming the pKa ofD132 is 4.9 [raised by 1 pH unit relative to that in bulk (45), which is∼3.9 (46)], proton uptake to D132 from N-side bulk leads to state III(0.5 kcal/mol). (This step was not explicitly simulated in our work.)Then PT from D132 to E286 forms state IV (−5.6 kcal/mol). Theproton on E286 is subsequently transferred to the BNC, forming theF state (state V, −10.8 kcal/mol). The subsequent proton uptake ofD132 from N-side bulk (not explicitly simulated in our work) leads tostate VI (−7.9 kcal/mol), followed by the second reprotonation ofE286 that leads to state VII (−14.4 kcal/mol). If proton release fromthe PLS to the P-side bulk is estimated to have exergonicity of2.8 kcal/mol [not explicitly simulated in our work, but based on thePLS pKa of 5 after F-state formation and P-side pH of 7 (37)], thencompleting the A → F transition leads to state VIII with an exer-gonicity of −17.2 kcal/mol. This reflects the overall driving force forthe PM′ → F transition, and is larger than the ∼12 kcal/mol exer-gonicity estimated from experiments (3, 37). However, a recentcomputational study by Blomberg (47) indicated that the exergonicityof PM → F is ∼20 kcal/mol, in close agreement with our result.Our results show that ET from heme a to the BNC drives both

PT events (E286 to the PLS and E286 to the BNC). Among all ofthese processes, transfer of the chemical proton from E286 tothe BNC is rate-limiting, which is in agreement with previousisotope effect studies (48, 49), and our calculated rate is in quan-titative agreement with experiments (6, 17). In this mechanism,the pathways that would decouple pumping from transfer of thechemical proton or damage the directionality of proton flow areavoided by kinetic gating in two ways. First, the fast PT from E286to the PLS precedes proton transfer to the BNC during the entirePM′→ F transition. Second, the possible proton backflow from thePLS to deprotonated E286 is avoided by fast reprotonation of

E286 through the D-pathway combined with a large barrier forproton backflow from the PLS to E286 after ET from heme a toBNC (PR state). Although PT in the D-channel is clearly coupledwith solvation changes through the asparagine gate, it is neverfound to be rate-limiting in the PM′ → F transition. Althoughnuclear quantum effects were not included in our PT simulations,they are very unlikely to change our conclusions because the ki-netic isotopic effect for PR → F transition is small (∼2.0) (48, 49),corresponding to ∼0.4 kcal/mol decrease in the chemical PT re-action barrier at room temperature. The MS-RMD simulationspresented herein thus provide a comprehensive picture of the pro-ton-pumping mechanism in CcO, the important final enzyme in therespiratory electron transfer chain. Our future work will exploreproton pumping in CcO mutants and other redox-coupled proteins.

Materials and MethodsThe full structure of CcO from Rhodobacter sphaeroides [Protein Data BankID code 1M56 (50)] was embedded in a dimyristoylphosphatidylcholine(DMPC) lipid bilayer and solvated by water molecules on each side of themembrane. MS-RMD simulations using metadynamics (MTD) (51) were per-formed to identify PT pathways (52) in both the D-channel and HC. TheFitRMD method (32, 33) was used to parameterize the MS-RMD models fromQM/MM data for protonatable sites in CcO. The MS-RMD umbrella samplingcalculations in the HC and D-channel were carried out by restraining (i) theexcess proton CEC position (see the SI Appendix for definition) along the PTpathway defined from the MTD procedure, and (ii) the water density in apredefined box (see ref. 27 for definition). Further details on simulationmethods are provided in the SI Appendix.

ACKNOWLEDGMENTS. We acknowledge Prof. Peter Brzezinski and Prof.Robert Gennis for helpful discussions and Dr. Vivek Sharma, Prof. VilleKaila, and Prof. Qiang Cui for providing equilibrated structures from theirpublished work, which were very helpful in determining the startinghydration state of the HC for our 2D PMFs. We also acknowledge Dr. J. G. Nelson

A

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Fig. 3. (A) Reaction sequence during the PM′ → F tran-sition. The redox groups and protonatable sites are la-beled. The red minus sign and various colored plus signsindicate electron and proton occupancy, respectively, inthe starting state, while arrows indicate charge migra-tion. The first, second, and third proton to travel throughthe enzyme are colored black, blue, and orange, respec-tively. The potential leakage pathways that would de-couple pumping from reaction are indicated by dashedgray arrows. (B) Free-energy diagram for the reactionsequence during the PM′ → F transition. The resting statesare described in the main text. The transition states be-tween them are labeled with “TS,” and the activationbarriers are obtained from the free-energy profiles(1D minimum free-energy traces from the 2D PMFs) in Fig.2 A, B, and D. The black numbers indicate the energylevels for each state in kcal/mol. The red numbers indicatethe time constants for the forward transitions betweenthe two neighboring resting states.

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for the initial simulation setup and helpful discussions in the early stagesof this project. This research was supported by National Institutes ofHealth Grant R01-GM053148 (to G.A.V., J.M.J.S., R.L., and Y.P.) and theSigrid Jusélius Foundation (M.W.). The researchers used computing fa-cilities provided by the Extreme Science and Engineering Discovery

Environment (XSEDE), which is supported by National Science FoundationGrant OCI-1053575, as well as from the University of Chicago Research Com-puting Center (RCC), the Texas Advanced Computing Center at the University ofTexas at Austin, and the US Department of Defense (DOD) High-PerformanceComputing Modernization Program.

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