Phosphate release coupled to rotary motionof F1-ATPaseKei-ichi Okazakia,b,c and Gerhard Hummera,b,1

aDepartment of Theoretical Biophysics, Max Planck Institute of Biophysics, 60438 Frankfurt am Main, Germany; bLaboratory of Chemical Physics, NationalInstitute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892; and cDepartment of Pure and Applied Physics,Waseda University, Tokyo 169-8555, Japan

Edited by J. Andrew McCammon, University of California, San Diego, La Jolla, CA, and approved August 28, 2013 (received for review March 21, 2013)

F1-ATPase, the catalytic domain of ATP synthase, synthesizes mostof the ATP in living organisms. Running in reverse powered by ATPhydrolysis, this hexameric ring-shaped molecular motor formed bythree -dimers creates torque on its central -subunit. This re-verse operation enables detailed explorations of the mechano-chemical coupling mechanisms in experiment and simulation.Here, we use molecular dynamics simulations to construct a rstatomistic conformation of the intermediate state following the 40substep of rotary motion, and to study the timing and molecularmechanism of inorganic phosphate (Pi) release coupled to the ro-tation. In response to torque-driven rotation of the -subunit inthe hydrolysis direction, the nucleotide-free E interface formingthe empty E site loosens and singly charged Pi readily escapesto the P loop. By contrast, the interface stays closed with doublycharged Pi. The -rotation tightens the ATP-bound TP interface,as required for hydrolysis. The calculated rate for the outward re-lease of doubly charged Pi from the E interface 120 after ATPhydrolysis closely matches the 1-ms functional timescale. Con-versely, Pi release from the ADP-bound DP interface postulatedin earlier models would occur through a kinetically infeasible in-ward-directed pathway. Our simulations help reconcile conictinginterpretations of single-molecule experiments and crystallographicstudies by clarifying the timing of Pi exit, its pathway and kinetics,associated changes in Pi protonation, and changes of the F1-ATPasestructure in the 40 substep. Important elements of the molecularmechanism of Pi release emerging from our simulations appear tobe conserved in myosin despite the different functional motions.

F1-ATPase (F1), the catalytic domain of FoF1-ATP synthase, isa rotary molecular motor that reversibly interconverts ATPhydrolysis free energy and mechanical work associated with therotation of the central stalk (1). The minimal functional F1consists of a hexameric ring formed by three -subunit dimers,with the rod-like -subunit located at its center (2). The rotationof the -subunit is tightly coupled to the reactions in the threecatalytic sites located at the interfaces and hosted mainly bythe -subunits. As a result, F1 is a unique reversible motor thatrotates by converting ATP hydrolysis energy at high efciency(35) and, conversely, synthesizes ATP from ADP and inorganicphosphate (Pi) by forced rotation of in the reverse direction (6,7). The three nucleotide-binding sites are in different phases ofcatalysis, reecting the asymmetric structure of the -subunit.Correspondingly, the -subunits hosting the catalytic interfacesare in different conformational states, empty (E), ATP-bound(TP), and ADP+Pi-bound (DP), as seen in crystal structures (2).They communicate through the -subunit or directly withinthe 33 ring (8, 9) and cooperatively drive the rotation ofthe -subunit.Single-molecule experiments have shown that the -subunit

rotates in 120 steps (4). Distinct substeps of 80 and 40 (10) aredriven by ATP binding plus ADP release, and ATP hydrolysisplus Pi release, respectively (1013). We thus expect two meta-stable conformations of F1, one before the 80 substep (bindingdwell) and the other before the 40 substep (catalytic dwell) (14,15) (Fig. 1A). Most crystal structures correspond to the catalytic

dwell state (1, 1419), with the F1 conformation of the bindingdwell state still elusive (16).The transition from the catalytic dwell to the binding dwell

involves Pi release, but the release site and the exact timing in thefull cycle remain controversial. In most kinetic models of F1 (1),but not all (20), Pi is assumed to exit rst, followed by ADPrelease. This order appears to be consistent with kinetic (21) andstructural studies (22) showing all three sites occupied by nu-cleotide (22); by contrast, the single-molecule experiments ofWatanabe et al. (13) and structural studies of yeast F1 (23)suggest that ADP is released before Pi. With -rotation stalled inthe catalytic dwell state by magnetic tweezers, the hydrolysisreaction was found to be reversible without excess Pi in solution(13), suggesting that Pi is released at 320, i.e., from the E site(13, 24) (where ATP binding denes 0; Fig. 1A).Here, we reconcile these conicting interpretations by de-

termining the kinetics of Pi release from the E site and the DPsite with atomistic molecular dynamics simulations. These sim-ulations also allow us to explore the coupling between the 40substep and Pi release, and to examine the underlying molecularmechanisms. F1 has been studied by molecular simulations atvarious levels of resolution, including quantum chemical calcu-lations of ATP hydrolysis (2527), all-atom simulations of con-formational changes in the -subunit (28, 29), of ATP release(30), of uctuations in the complex (31, 32), and of -rotation(33, 34), as well as coarse-grained simulations of -rotation (3537). As in experiment and in earlier simulations (33), we applyexternal torque to modulate the rates of the functional processes,including Pi release.We rst characterize the molecular motions of F1 during the

40 substep in atomically detailed simulations. By rotating the

Signicance

F1-ATPase is the catalytic domain of FoF1-ATP synthase, therotary molecular motor at the core of the energy transductionmachinery in all of life. We use atomistic molecular dynamicssimulations to study a key event in its catalytic cycle, the re-lease of inorganic phosphate (Pi) produced by the hydrolysis ofATP. We determine the timing, kinetics, and molecular mech-anism of Pi release and clarify its role in torque generation.We also obtain an atomically detailed structure of a crystallo-graphically unresolved intermediate formed after the 40substep. Our results help reconcile conicting interpretationsof earlier biochemical, crystallographic, and single-moleculestudies; shed light on the functional requirements of efcientATP synthesis; and establish connections to other motors suchas myosin.

Author contributions: K.-i.O. and G.H. designed research; K.-i.O. performed research; K.-i.O.contributed new reagents/analytic tools; K.-i.O. and G.H. analyzed data; and K.-i.O. and G.H.wrote the paper.

The authors declare no conict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. E-mail: gerhard.hummer@biophys.mpg.de.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1305497110/-/DCSupplemental.

1646816473 | PNAS | October 8, 2013 | vol. 110 | no. 41 www.pnas.org/cgi/doi/10.1073/pnas.1305497110

-subunit with the help of a newly developed exible rotormethod, we show how the -angle and the protonation state of Pi(i.e., HPO4

2 or H2PO4) affect the conformation of -dimers

and the stability of Pi binding in the E site. We then estimaterates of Pi release from the E site and from the DP site with thehelp of metadynamics simulations (38). From the simulationsand by relating the calculated rates to experiment, we determinethe timing, pathway, and charge state dependence of Pi release.Finally, we show that key elements of Pi release appear to beconserved in myosin, despite the different functional motions.

ResultsRotation of and Conformational Response of -Dimers. In all-atom explicit-solvent simulations of the F1 motor, the -anglewas rotated in the hydrolysis direction with an angular velocity of1/ns by the newly developed exible rotor method (Methods,Fig. S1, and Movie S1). The angular velocity may seem higherthan in experiment. However, the millisecond timescale of F1rotation in experiment mainly reects the catalytic dwell waitingfor hydrolysis and Pi release. The rotary motion during the 40substep transition should thus be much faster, yet it has not beenmeasured without load to the best of our knowledge. Forstructurally more complex transitions like protein and RNAfolding, transition path times have been measured in the low-microsecond range, many orders of magnitude faster than thecorresponding mean rst-passage times of (un)folding (39, 40).With the -subunit allowed to twist freely in our simulations, theangle of its core lagged behind the average, while the protrudedpart moved ahead (Fig. 2B). This twisting in response to torquereects both on the torsional stiffness of and on the frictionexperienced by the core part due to its tight interactions with the33 ring. The enhanced rotation of the protruded part (orfoot) seen here is consistent with large variations in its rota-tional angle in crystal structures (22, 41) and the low torsionalstiffness of the -rotor (42). Importantly, despite the twisting the-subunit remains structurally intact, as indicated by root-mean-square deviations (RMSDs) of

region. This motion of Pi was tightly coupled to the loosening ofthe interface conformation of E (Fig. 5A) and was not observedin the free simulation without torque (Fig. S3C). The observedcoupling supports the earlier suggestion that Pi binding is regu-lated by the E interface conformation, as inferred from a com-parison of different F1 structures (43). The transient structure at3.5 ns is shown in Fig. 4B, with ARG373 and LYS162 co-ordinating Pi. The so-called Arg-nger, ARG373, seems to playa role of guiding Pi to the P loop. In fact, ARG373 remainedcoordinated to Pi even as Pi moved toward the P loop (Fig. 4A,green line). Pi stayed at the P loop for the rest of the trajectory,frequently interacting with ARG373. The rapid escape of Pi fromthe E site to the P loop during the 40 substep, as probed in thetorque simulations, is consistent with the dramatic increase in therate of Pi release between 320 and 360 reported from exper-iment (24). By contrast, the doubly charged Pi remained quite

stably bound in the initial position and maintained interactionswith its coordinating residues throughout the trajectory (Fig. 4C).With two negative charges, the doubly charged Pi was, in effect,trapped by the four positively charged residues in its immedi-ate surrounding, holding the interface tight during the torquesimulations.We also studied the dependence of the Pi binding stability in

the E site on the direction of -rotation. The singly charged Pi,with the -subunit rotated in the synthesis direction, stayed at theinitial position for the rst 30 ns (Fig. 5C, Left). After movingtransiently to the P loop, Pi returned back to the initial positionat around 70 ns and remained there. These motions suggest thatPi binding in the E site is more stable when is rotated in thesynthesis direction than in the hydrolysis direction. This in-creased stability would be important for ATP synthesis, whereADP should bind into the E site already occupied by Pi (seebelow). The loosening of the interface in response to-rotation in the hydrolysis direction, and the tightening in thesynthesis direction (Fig. 5B), are likely the main factors changingthe Pi binding stability. The doubly charged Pi (Fig. 5C, Right)stayed at the initial position, independent of the direction of the-rotation, and maintained tight interactions with the E residues.As a direct demonstration of the coupling between Pi release

and -rotation, three independent 40-ns free simulations withouttorque were conducted: (i) without Pi, and with (ii) singly and(iii) doubly charged Pi in the E site (Fig. S3D). The resulting-angles are distributed narrowly around 85 with doubly chargedPi, with a wider distribution for singly charged Pi indicatinga looser -shaft. Importantly, after doubly charged Pi was re-leased, indeed rotated by 10 in the hydrolysis direction (Fig.S3E). These free simulations thus further support the hypothesisthat release of doubly charged Pi from the E site drives -rotationin the hydrolysis direction.

Metadynamics Simulation of Pi Release from the E Site and DP Site. Piexits the E site (at 320) and DP site (at 200) on entirely dif-ferent pathways according to the metadynamics (38) simulations(Fig. 6A). From the E site, singly and doubly charged Pi bothescaped outward via a transient intermediate at the P loop,consistent with the escape route of H2PO4

in the torque sim-ulations. In the DP site, this outward path is blocked by ADP,forcing Pi instead to escape inward and exit at the central hole ofthe ring subunits (Table S1). This alternate pathway was con-rmed by separate simulations with a different metadynamicshill height (0.2 kcal/mol) and for a different F1 structure witha slightly open DP site [Protein Data Bank (PDB) ID code 4asu;Fig. S4].

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(Left) andHPO4

2 (Right) in the E site. Red,green, and blue points corre-spond to that starts from E,TP, and DP, respectively,and purple points correspondto X-ray crystal structures (43).The arrows indicate directionsof -motion in response to-subunit rotation in the hydrolysis direction. (B) Conformational change of TP in response to 30 rotation of the -subunit during the trajectory with HPO42.The snapshot at 30 ns is colored as in Fig. 1B, and the reference structure at 0 ns is colored in cyan. Only the C-terminal domains of are shown for the 0-nsconformation, and the -hairpin and the C-terminal helix are shown for the -subunit. (C) Conformational change of E in response to 30 rotation of the-subunit during the trajectory with H2PO4. The snapshots at 30 and 0 ns are shown as in B.

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and HPO42 are shown in red and blue, respectively.

The distance between H2PO4 and the C atom of ARG373 is plotted in

green. (B) Pi (H2PO4) migration toward the P loop at 3.5 ns (Upper) and 39

ns (Lower). (C) Tightly bound Pi (HPO42) at 20 ns (details as in Fig. 1C).

16470 | www.pnas.org/cgi/doi/10.1073/pnas.1305497110 Okazaki and Hummer

These two exit pathways have drastically different free-energybarriers (Fig. 6B). Escaping from the E site in the z direction,singly and doubly charged Pi face free-energy barriers of 5 and10 kcal/mol, respectively, to transition from the tightly boundstate to the P loop. The free-energy barrier for Pi to be releasedfrom the P loop into solution is 5 kcal/mol in both cases. Bycontrast, the free-energy barrier for Pi to be released from theDP site, moving along the x direction, is almost 30 kcal/mol intotal, and thus insurmountable on the functional timescale. Thishigh barrier is a result of the tight interface of the DP site, and ofADP blocking the pathway to the P loop, which effectively

prevent Pi escape to the outside (Fig. 6C). Our results are con-sistent with the interpretation of recent single-molecule experi-ments (13) of Pi being released from the E site, i.e., at 320 inFig. 1A during the catalytic dwell. The free-energy barriers wereconrmed by additional long simulations with a different pro-tocol (SI Text and Fig. S5).As listed in Table 1, the calculated timescale of 2 ms for the

release of doubly charged Pi agrees well with the 1-ms estimatefrom experiment (10, 12, 13). The mean rst-passage times werecalculated from the free-energy proles and diffusion coef-cients (SI Text, Fig. S6, and Table S2). As described above, thePi movement from the tightly bound state to the P loop is cou-pled to the global interface motion that occurred within a fewnanoseconds (Fig. 5A). This rapid conformational change pre-vents backtransfer of Pi, which is thus ignored in our timescaleestimates. Overall, our simulations suggest that doubly chargedPi is released from the E site at 320 before the 40 substep.

DiscussionWe found that Pi release from the E site is kinetically realisticand that release from the DP site is not. The calculated time of2 ms for the release of doubly charged Pi from the E sitematches the rate of Pi release during the catalytic dwell reportedfrom experiment (13). With this timescale matching also thecatalytic dwell time, Pi release could thus be rate-limiting. Ourresults suggest the need to correct earlier models in which Pi wasassumed to exit rst from the DP site, just after the hydrolysisreaction, followed by ADP release. Instead, Pi is likely releasedfrom the E site at 320 (Fig. 1A), 120 after the hydrolysis re-action, and after ADP release.Our simulation results help reconcile conicting interpretations

of earlier experiments. Shimo-Kon et al. (21) showed that Pibinding from solution inhibits ATP binding, concluding that the Esite must be devoid of Pi. However, at 320, Pi could have escapedwith a 1/ms rate and ATP rebound with an estimated on rate of1/ms at 1 mM concentration (24), making the empty E site short-lived in the cycle. Nucleotide binding to all three sites at 1 mMconcentration (21) could also explain the presence of three ADPsin a recent F1 crystal structure (22). With these ADPs not pro-duced during turnover, but likely taken up from solution (1), Piwould not be kinetically trapped in the DP and E sites. By con-trast, tightly bound Pi observed in the E site of some structures(23, 44) likely mimics a product Pi of hydrolysis before release inthe catalytic dwell. Gao et al. (20), on the basis of kinetic data onthe inhibition of ATP hydrolysis by ADP and Pi, concluded that Piis released after ADP, consistent with our calculations. We alsonote that, in the synthesis direction, preferential binding of Pi inthe empty E site is advantageous by favoring the subsequentbinding of substrate ADP (45) over the abundant but inhibitoryproduct ATP. The ADP/ATP preference with Pi bound could beprobed in experiment (21).The combination of experiment (13) and simulation suggests

that Pi is released as HPO42. According to quantum chemical

calculations, Pi is doubly protonated (singly charged) just afterhydrolysis (25). However, after ADP and Mg2+ (net charge is 1)leave the site, four positively charged residues surround Pi,shifting its pKa. This electrostatic environment would indeedfavor the loss of one proton, resulting in a singly protonated(doubly charged) Pi in the E site. Probing the pH dependence ofthe dwell time of the Pi release (or the 40 substep) could testthis hypothesis, assuming protonic equilibrium with the solvent.We also investigated the conformational changes of F1 in re-

sponse to the 40 rotation step of the -subunit, and their cou-pling to Pi release. was rotated both in the hydrolysis andsynthesis directions, for two possible protonation states of Pi inthe E site. By rotating for 40 in the hydrolysis direction relativeto the available crystal structures, we obtained a rst fully at-omistic conformation of the intermediate state following the 40substep. We found that the structure of the ATP-bound TPinterface became as tight as that of ADP+Pi-bound DP in-terface, thus facilitating hydrolysis. By comparison, the E

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Fig. 5. Interface conformation and -rotationaldirection dependence of Pibinding stability. (A) PC2 of the E site (left scale; blue) reporting on in-terface tightening, and Pi distance relative to starting conformation (rightscale; red) during the rst 10 ns of the hydrolytic torque simulation withH2PO4

. (B) PC2 of the E site in the hydrolytic (blue) and synthetic (purple)torque simulations with H2PO4

. (C) (Left) Distance of the singly charged Pifrom its starting point for the hydrolytic (red) and synthetic (green) torquesimulations. (Right) Distance of the doubly charged Pi for the hydrolytic (red)and synthetic (green) torque simulations.

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Fig. 6. Pi release from the E site and DP site. (A) Pathways and (B) free-energy proles of Pi release determined from metadynamics simulations ofsingly charged Pi (brown) and doubly charged Pi (yellow) from the E site, andof singly charged Pi from the DP site (green). In A, E (cyan cartoon) issuperimposed on DP (orange cartoon), and the P loops are colored in purple.ADP, Mg2+, and Pi in the DP site are shown as sticks. (C) Cut through thebinding site in the DP state, with arrows indicating exit pathways.

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interface became looser, and Pi escaped to the P loop. We expectthese structures to be representative of the conformations of thetwo sites in the binding dwell state. The DP site remains rel-atively tight and shows only a slight opening, as indicated by thedisplacement of purple and blue points in Fig. 3A. We concludethat DP motions in response to -rotation are considerablyslower than those of E and TP (16). The salt bridges between and 33 formed in the intermediate state are listed in SI Text.To test whether the intermediate state is stable without torqueapplied to , two 40-ns free simulations were conducted with thetorque switched off at 40 and 50 from the catalytic dwell, re-spectively. In both simulations, the -angle settled around 110(30 from the catalytic dwell), indicating the formation of a meta-stable state (Fig. S7A). Importantly, the torque simulations drivethe system out-of-equilibrium (as would the Fo motor in intactATP synthase). In such a nonequilibrium process, the -rotor willbe slightly over-twisted. Releasing the torque that drives the ro-tation is thus expected to result in a fast relaxation of the angle.We indeed observed a relaxation on a 5-ns timescale after re-leasing the torque at 120, close to the presumed metastableminimum (Fig. S7A, green curve). When we released the torque at130, beyond the minimum, we again saw this fast recoil, and inaddition a more gradual relaxation to a state at 110, consistentwith an overdamped, weakly driven motion in a metastable min-imum at 110. The interface conformations of E and TPrelaxed partially, but importantly in a reversible way (Fig. S7B).These interfacial motions are coupled to torque generation,

which should make it possible to probe our results by mutation.Torque generation as a result of nucleotide binding/dissociation hasbeen probed extensively by mutations of interactions (46). Bycontrast, relatively little is known about the specic mechanisms oftorque generation as a result of Pi release. The interfacial motionsseen in our simulations suggest that torque generation by Pi releaseshould be sensitive to the hydrophobic interactions betweenPHE403/PHE406 and ILE16/ILE19/LEU77, and the elec-trostatic interactions between ASP409 and ARG133, ASP411and LYS30, GLU355 and LYS11, and GLU399 and LYS18.Perturbations of these interactions by mutation should affect thecoupling between the E interface and the -subunit, and shouldthus report directly on torque generation as a result of Pi release.Remarkably, the two Pi exit pathways observed in this study

appear to be conserved in myosin, and possibly other members ofthe large family of P-loop ATPases. In particular, a so-calledback door exit pathway for Pi release has been proposed formyosin, to circumvent the front door pathway blocked by ADPin the binding pocket (47). Molecular dynamics simulationsshowed that the Pi release pathway is tightly linked to the cleft-closing motion of myosin upon binding to actin (48, 49). Theback door route dominated for an open cleft and a closedbinding site, whereas the front door and a variant of the backdoor route dominated for a closed cleft and an open binding site(49). We have a similar situation in F1, although the globalmotions are quite different. With the binding site closed (DPsite), Pi escaped via an inward route that corresponds to the backdoor in myosin (toward switch II). By contrast, with the bindingsite open (E site), we observed the outward route correspondingto the front door in myosin (Fig. S8). Despite large differences inthe global functional motions of different P-loop ATPases, localmotions during the hydrolysis cycle thus appear to be conserved.Functional requirements then dictate the dominant route of Piexit in different ATPases, and possibly also GTPases. Myosinuses both back and front doors, whereas F1 takes the front doorexclusively, as shown here.

MethodsInitial Structures. The initial structures of F1 were taken from the azide-freecrystal structure (PDB ID code 2jdi) (50). Residues 24510 were used for the-subunits, 9478 were used for the -subunits, and all residues were usedfor the -subunit. MODELER (51) was used to model structures of missingresidues. Missing residues in the -subunit were modeled according to thedicyclohexylcarbodiimide-inhibited structure (PDB ID code 1e79) (52). In theazide-free structure, the TP site and DP site bind an ATP analog (AMPPNP)and Mg2+, and the E site is empty. For the simulation system, the ATP analogin the TP site was replaced with ATP, and that in the DP site was replacedwith ADP and Pi (H2PO4

). Pi (HPO42 or H2PO4

) was modeled in the E site,representing the catalytic dwell state just after ATP hydrolysis (SI Text). Avariety of analyses (1, 1419) consistently indicate that the initial crystalstructure represents the catalytic dwell, which corresponds to a -angle of80 by denition (Fig. 1A). The half-closed structure by Menz et al. (44) wasnot used here because it possibly corresponds to an E site occupied by ADPrebound from solution at high ADP concentration, and thus would not bepart of the actual sequence of product release. Pi in the DP site was modeledas doubly protonated following the quantum chemical studies of ATP hy-drolysis in this site (25). Crystal water molecules were retained unless theyclearly overlap with replaced ligands.

Simulation Setups. The modeled F1 with crystal waters was solvated withTIP3P water (53) in a rectangular box such that the minimum distance tothe edge of the box is 11 , and neutralizedwith potassium ions. Then, 100mMKClwas added to the system. The total number of atoms is313,000 (Fig. S1). TheAmber ff99SB forceeldwas used for theprotein (54),withmodiedparametersfor KCl (55), and for ATP and ADP (56). The point charges for singly and doublyprotonated Pi were determined using Gaussian 03 (57) and the Antechambermodule of Amber (58) (SI Text). The system was energy minimized and equili-brated at isothermalisobaric (NPT) conditions with Ewald electrostatics andrestraints on all heavy atoms in the protein for 500 ps, and subsequently, withrestraints ononly C atoms for 1ns. After the equilibration, production runswereconductedwith restraints on the C atoms of the 10N-terminal residues of eachof the three -subunits, mimicking the role of His-tag anchoring in single-molecule experiments. NAMD 2.8 was used for the molecular dynamics sim-ulations with periodic boundary condition (59). Langevin dynamics with1 ps1 damping coefcient was used for temperature control at 310 K, andthe NoseHoover Langevin piston was used for pressure control at 1 atm (60).

Flexible Rotor Simulation. In the torque simulations, only the average rota-tional angle of the -subunit was restrained. As in an earlier method (61), the-subunit is allowed to twist freely, but here without arbitrary subdivisioninto slabs. We also allow free translation of its center of mass. Details of themethod and explicit expressions for the restraint forces are in SI Text.

Metadynamics Simulation of Pi Release. To enhance the sampling and estimatefree-energy proles for Pi release, metadynamics (38) simulations wereconducted using the PLUMED 1.3 plugin with NAMD (62). The relative Car-tesian coordinates x, y, and z of Pi from the binding site were used as col-lective variables (63), where the binding site was dened by the C atoms of-subunit residues 188, 256, 257, 259, and 309312, which are within 8 from Pi in the DP site. Flexible and P-loop residues are excluded. RepulsiveGaussian potentials with heights of 0.1 kcal/mol and widths of 0.6 weredeposited every 1 ps during the metadynamics simulations. The free-energyproles were calculated by a PLUMED utility, sum_hills.

ACKNOWLEDGMENTS. We thank Drs. Kazuhiko Kinosita and Hiroyuki Nojifor insightful discussions, and Drs. Edina Rosta, Fangqiang Zhu, JrgenKnger, Pilar Cossio, and Ikuo Kurisaki for technical help. This work wassupported by the Intramural Research Program of the National Institute ofDiabetes and Digestive and Kidney Diseases, National Institutes of Health andby the Max Planck Society. K.-i.O. is supported by research fellowship foryoung scientists and postdoctoral fellowship for research abroad of the JapanSociety for the Promotion of Science. The research used the high-performancecomputational capabilities of the Biowulf Linux cluster at the National Insti-tutes of Health (http://biowulf.nih.gov).

Table 1. Estimated mean rst-passage times of Pi release from the E site

Pi Tightly bound to P loop P loop to tightly bound P loop to release

H2PO4 2.4 s 0.11 s 0.34 s

HPO42 2.0 ms 0.014 s 41 s

16472 | www.pnas.org/cgi/doi/10.1073/pnas.1305497110 Okazaki and Hummer

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