answer 2 c ass 2

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A rotary molecular motor that can work at near

100% efciency

Kazuhiko Kinosita Jr1,2*, Ryohei Yasuda2, Hiroyuki Noji2 and Kengo Adachi2,3

1Department of Physics, Faculty of Science and Technology, Keio University, Hiyoshi, Kohoku-ku, Yokohama 2 23- 8522, Japan2Core Research for Evolutional Science and Technology Genetic Programming Team 13, Teikyo University Biotechnology Center 3F,

Nogawa, Miyamae-ku, Kawasaki 216- 00 01, Japan3Department of Physics, Faculty of Science, Kanazawa University, Kakuma-machi, Kanazawa 920-11, Japan

A single molecule of F1-ATPase is by itself a rotary motor in which a central g-subunit rotates against asurrounding cylinder made ofa3b3-subunits. Driven by the three bs that sequentially hydrolyse ATP, themotor rotates in discrete 1208steps, as demonstrated in video images of the movement of an actin lament

bound, as a marker, to the central g-subunit. Over a broad range of load (hydrodynamic friction againstthe rotating actin lament) and speed, the F1motor produces a constant torque of ca. 40pNnm. Thework done in a 1208step, or the work per ATP molecule, is thus ca. 80 pN nm. In cells, the free energy ofATP hydrolysis is ca. 90 pN nm per ATP molecule, suggesting that the F1motor can work at near 100%eciency. We conrmed in vitro that F1indeed does ca. 80 pN nm of work under the condition where thefree energy per ATP is 90 pN nm. The high eciency may be related to the fully reversible nature of theF1motor: the ATP synthase, of which F1is a part, is considered to synthesize ATP from ADP and phos-phate by reverse rotation of the F1 motor. Possible mechanisms of F1 rotation are discussed.

Keywords:molecular motor; F1-ATPase; ATP synthase; energy conversion eciency

1. INTRODUCTION

Molecular motors generate movement and force betweentwo cellular components. Linear motors produce move-ment along a lamentous structure; for example, myosinalong an actin lament (Goldman 1998; Suzuki et al.1998; Dominguez et al. 1998; Kitamura et al. 1999),kinesin (Block 1998; Lohman et al.1998; Mandelkow &

Johnson 1998) and dynein (Shingyojiet al.1998) along amicrotubule, and RNA polymerase along DNA (Gelles &Landick 1998;Wanget al.1998). Known linear motors aredriven by free energy obtained from nucleotide hydrolysis.Usually, the molecule that contains the hydrolysis site(s),

excluding the lament, is called a motor and the lamentis regarded as a track, although the lament is likely toalso play an active role in producing force and movement(Kinosita 1998; Kinosita et al. 1998).

In the case of myosin, large-amplitude bending(conformational change) occurs when it binds ATP(Suzukiet al.1998; Dominguezet al. 1998), suggesting thatthe reversal of the bending upon release of the hydrolysisproducts may directly drive an actin lament. Thermo-dynamics of actomyosin ATPase (Taylor 1979), however,indicates that much of the free energy of ATP hydrolysisis used in the unbinding of myosin from actin. Thus,

rebinding by actin is likely to be the source of the pullingforce, at least by reinforcing the reversal of the myosinbending. Whether myosin bound to actin in fact under-goes a large-amplitude bending and, if so, whether thebending produces sucient force to drive actin, are yet to

be seen. The observation that myosin made several 5-nmsteps on actin upon hydrolysis of only one ATP molecule(Kitamura et al. 1999) is not readily explained by a simplebending model. Kinesin is likely to `walkon a microtubuleusing its two globular ATPase domains as `feet. Even so,whether the force is generated when a `leg is bent forward,or when a detached `foot is bound to the microtubule, isstill an open question. A key to understanding themechanism of linear motors is to detect their nucleotide-dependent conformational changes while they are boundto the substrate lament, but decisive experiments havenot been done.

Two rotary molecular motors are known to date. One

is the bacterial agellar motor that rotates a agellumusing proton ow through the motor as the energy source(DeRosier 1998). The other is the FoF1-ATP synthase(Boyer 1993, 1997, 2000; Junge et al. 1997; Kinosita et al.1998, 2000; Kinosita 1999; Kagawa 1999), whichcomprises two rotary motors, one driven by proton ow(Fomotor) and the other by ATP hydrolysis (F1motor), inone molecule.

The mechanisms of the proton-driven motors, whetheragellar or of ATP synthase, are less clear compared tomyosin and kinesin, because structural details have notbeen elucidated. It is of interest to note that, at least

conceptually, these proton-driven motors could operatewithout major conformational changes in either the rotoror stator: electrostatic force from moving protons couldproduce torque if the geometry of proton channels aredesigned appropriately (Luger 1977).

Large-amplitude bending occurs in the ATP-driven F1-motor of the ATP synthase (Abrahams et al. 1994). The

Phil. Trans. R. Soc. Lond. B (2000) 35 5, 473^489 473 2000 The Royal Society

*Author for correspondence.

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bending has been shown in a functional motor complexcontaining both the rotor and stator, and thus thisbending is likely to contribute directly to torque genera-tion. Unlike linear motors that undergo alternate bindingand unbinding to and from the substrate laments, therotor and stator stay together in rotary motors. Theanalysis of the molecular mechanism of the F1 motor may,in this sense, be simpler, and is expected to revealprecisely how the energy of ATP hydrolysis can beconverted to torque. (Note that, if linear motors producemovement by bending, as in the lever-arm model formyosin, the direct outcome of nucleotide hydrolysis istorque rather than vectorial force.)

2. ATP SYNTHASE AND ROTATIONAL CATALYSIS

(a) ATP synthase: a reversible molecular machine

ATP synthase is ubiquitous from bacteria to plants andanimals. It is a membrane-spanning enzyme thatproduces ATP using proton ow across the membrane. Inanimals, ATP synthase resides in the inner mitochondrialmembranes where an electrochemical gradient of protons,high on the outside of mitochondria, is generated by therespiratory chain of enzymes. An active researcherproduces his or her bodyweight of ATP in one day.

As shown in gure 1, the ATP synthase consists of amembrane-embedded portion Fo and a protrudingportion F1, and thus is also called FoF1-ATP synthase.When protons ow through Fo from top to bottom, ingure 1, ATP is synthesized in F1. The synthase is acompletely reversible molecular machine in that, whenATP is hydrolysed in F1, protons are pumped back, frombottom to top, against an electrochemical gradient. How,then, is the proton ow through Fo coupled to thesynthesis^hydrolysis of ATP in F1?

(b) Boyers proposal: two rotary motors with a

common shaft

Boyer proposed that the coupling is mechanical (Boyer& Kohlbrenner 1981): Fois a motor, or turbine, driven bythe proton ow, and F1is another motor driven by ATPhydrolysis. The two have a common shaft. Proton owfrom top to bottom in gure 1 drives the shaft in a uniquedirection, say clockwise. ATP hydrolysis in F1drives the

shaft in the opposite direction, counterclockwise. Whenthe free energy obtained from the downward ow ofprotons is greater than the free energy of ATP hydrolysis,the Fo motor rotates the common shaft in its genuinedirection. The F1motor is forced to rotate in its reversedirection, and thus ATP is synthesized in its catalyticsites. If the energy obtained from ATP hydrolysis ishigher, the F1 motor gains control and protons arepumped out.

Boyers idea came from the analysis of the chemicalreaction in the F1part. The F1portion can be isolated insolution, and then it only hydrolyses ATP. Hence, the

isolated enzyme is called F1-ATPase. The F1-ATPaseconsists of ve types of subunits in the stoichiometry ofa3b3gde (in bovine mitochondrial F1, dand eare, respec-tively, called e and OSCP). a3b3g-subunits suce forATPase activity (and for rotation, as shown in 3(a)).Each b-subunit contributes one catalytic site for thesynthesis^hydrolysis of ATP (the catalytic site resides at

the interface between a b-subunit and an a-subunit, andis in part contributed from residues of a ). In addition,three non-catalytic nucleotide-binding sites exist, one oneach a, but we ignore these non-catalytic sites in most ofthis review. Now, Boyer and others have found that thethree catalytic sites are completely equivalent in steady-state ATP hydrolysis by F1-ATPase or in steady-state ATPsynthesis^hydrolysis by the whole ATP synthase. Theg-subunit, a single-copy subunit, was known to be indis-

pensable for the catalysis, but its amino-acid sequenceindicated that its structure could not possess threefoldsymmetry. Then, for the asymmetrical g-subunit tointeract with the three b-subunits impartially, it had torotate. The rotation could be either unidirectional or to-and-fro uctuation, but there should have been no limitin the rotational angle.

(c) Support for the rotational catalysis model

That a subunit in a compact, functional protein mole-cule could slide against other subunits over innite angleswas certainly a revolutionary idea. Textbooks teach that

protein subunits are held against each other by lock-and-key mechanisms, which would not readily allow mutualsliding.There were few believers, until a three-dimensionalstructure of F1-ATPase was solved by Walker and collea-gues (Abrahams et al. 1994). In the structure, which werefer to as the `Walker structure in this review, a3b3hexamer formed an orange-shaped cylinder, and part of

474 K. Kinosita Jr and others Rotary molecular motor near 100 % eciency

Phil. Trans. R. Soc. Lond. B (2000)

proton

outside

mitochondrial

inner membrane

inside

ADP+Pi

ATPa

a a

a

b

b

b bg

ATP

ADPnone

F1

Fo

Figure 1. A schematic view of ATP synthase (Kinosita et al.1998). The magenta rod at the centre represents the commonshaft (theg-subunit). In a currently popular but unprovenview, the orange cylinder in the membrane rotates togetherwith theg-shaft and the grey part serves as the stator. The

bottom diagram shows a top view of the F1part with catalyticnucleotides as found in the crystal (Abrahamset al.1994).

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the g-subunit, in the form of a coiled coil of two a-helices, penetrated the centre of the cylinder (d- and e-subunits were not resolved). The interface between thecentral g-subunit and surrounding a3b3-subunits wasmostly hydrophobic, suggesting that the g-shaft mightrotate in the oily sleeve. Moreover, the three catalyticsites were lled with dierent nucleotides, one withAMPPNP (an analogue of ATP), the second with ADP,and the third with none, in a clockwise order whenviewed from the top of gure 1 (see the bottom of the

diagram). If this arrangement represents an active inter-mediate during hydrolysis, the arrangement in the nexthydrolysis step would be ADP, none and ATP. The side ofthe g-subunit that tends to face the ATP-carrying b-subunit would thus rotate counterclockwise.

The Walker structure strongly supported Boyers rota-tional catalysis model; the g-subunit would constitute a

part of the common shaft of the two motors. The high-resolution structure immediately suggested experimentsthat would conrm the rotation of the g-subunit againstthe a3b3cylinder. One strategy was to cross-link a parti-cular residue on g to one of the three bs. Then the linkwas cut and the enzyme was allowed to catalyse ATPhydrolysis (F1preparation; Duncan et al.1995) or synth-esis (whole ATP synthase; Zhou et al. 1997). After that,the residue was again cross-linked to a b-subunit. Thesecond cross-linking was found to be to any of the threeb-subunits, indicating that the residue on the g-subunitfaced all three b-subunits equally during catalysis. Inexperiments where catalysis was not allowed between thetwo cross-linking treatments, the second target was thesame as the rst one. In another set of experiments(Sabbert et al.1996; Hsler et al.1998), a uorescent dyewas attached to the g-subunit. Time-resolved polarization

Rotary molecular motor near 10 0% eciency K. Kinosita Jr and others 475


Figure 2. (a) The experimental system for the observation of the rotation of F 1-ATPase. The space-lling model of F1(blue,a;green,b; magenta, g) is from Abrahamset al.(1994), actin lament (orange) from Holmeset al.(1990), and streptavidin (brown)from Livnahet al.(1993). Streptavidin has four strong binding sites for biotin, and the actin lament is heavily decorated withbiotin. There is, however, only one biotin on g. Presumably, free rotation between streptavidin and g is prevented by sterichindrance. The diameter of the grey disk, representing the surface to which the three b-subunits are bound through histidinetags, isca.22 nm. (b) Sequential images, at 33 ms intervals, of a rotating actin lament (Nojiet al.1997). The average rate ofrotation was 1.3revs1. Bar, 5 mm.

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measurement showed that the uorophore changed itsorientation over many degrees when the enzyme under-went an ATP hydrolysis reaction. In one study (Hsler etal.1998), the uorophore appeared to adopt three distinctorientations. These experiments together indicated thatthe g-subunit indeed rotates in the a3b3 cylinder, butwhether the rotation occurs in a unique direction wasunanswered.The answer came from direct imaging of therotation under a microscope, as described in the nextsection.

(d) Foawaits more experiments

Relatively little is known about the Fo motor. Aprevailing view for bacterial synthase (Junge et al.1997;Fillingame et al. 1998; Oster & Wang 2000) is that 12c-subunits in the membrane form a cylinder that isattached to g and together constitute the common shaft.The d-subunit of F1 and ab2-subunits of Fotogether consti-tute the stator (the grey part in gure 1), which isattached to the a3b3hexamer through d. The a-subunit inthe membrane apposes the c12 cylinder. Protons owthrough the interface between the a-subunit and thec12-subunits and rotate c12 against a. Recent electronmicrographs (Boekema et al. 1997; Wilkens & Capaldi1998) of ATP synthase show a thin, second stalk at aposition corresponding to the grey stator in gure 1. Onediculty in this view is that the a3b3hexamer should, ontime-average, be threefold symmetrical, yet there is onedb2a stator attached to it. Also, the c12cylinder is presum-ably 12-fold symmetrical, whereas g needs to be rmlyattached to c12 but lacks its symmetry. These may not beserious problems, but certainly detract from the eleganceof Boyers proposal.

3. IMAGING F1 ROTATION

(a) A huge tag revealed rotation in a single F1molecule

To prove that F1-ATPase is a rotary motor that consis-tently rotates in a unique direction, and to investigate thedetails of the rotational characteristics, we imaged therotation of single F1 molecules under a microscope (Nojietal.1997; Yasuda et al. 1998). A subcomplex of F1, a3b3g(hereafter we refer to this subcomplex simply as F1)

derived from a thermophilic bacterium, was xed on aglass surface, or on a submicrometre-sized plastic beadsitting on a glass surface, through histidine residues engi-neered at the bottom of the b-subunits. A micrometre-long actin lament was attached, through biotin^streptavidin links, to the protruding portion of g abovethe a3b3 hexamer (gure 2a). The actin lament wasuorescently1 labelled, and observed under a uorescencemicroscope. When ATP was infused into the observationchamber, the lament began to rotate, as shown ingure 2b.

Only a few per cent of the actin laments in the obser-

vation chamber rotated, but those that rotated did so inthe counterclockwise direction, as predicted from theWalker structure. This suggests that a structure similar tothe Walker structure, in which rotation was inhibited forcrystallization, appears as an active intermediate in therotational kinetics. Some laments made hundreds ofrevolutions without noticeable reversal.

Most of the laments did not rotate, but there arereasons for this. First, the laments are likely to stick onthe surface, because the height of F1 is only ca.10nm,whereas the actin laments were 1 mm or longer. It wouldbe dicult for F1 to keep the lament level. Indeed,putting F1 on a 0.2-mm bead helped to increase thenumber of rotating laments. However, the increase wasnot dramatic because we could not control the position ofF1such that it would be precisely at the top of the bead.Second, F1-ATPase tends to be inhibited by its reactionproduct, MgADP (see 4(b)). Third, protein moleculeson a surface are often damaged or denatured. In fact, themajor job of single-molecule researchers is to nd anappropriate surface for the protein of interest, a `missionimpossible if none of the molecules are to be sacriced.

In gure 2b, the actin lament rotates around its centre,like a propeller. The propeller rotation shows that thewhole g-subunit slides against the a3b3stator over unlim-ited angles. It is not a fake rotation one could make, forexample, by holding an end of a rod over ones head andtwisting ones wrist without changing the grip. If one holdsthe middle of a long rod, one cannot rotate it without occa-sional releases. Thus, the propeller rotation of the actinlament cannot be made by torsion within the g-subunit.The g-subunit has to be separate from the a3b3 cylinderand truly rotate against the hexamer. Also, the propellerrotation cannot be supported by two or more F1 molecules.Thus, F1-ATPase is a rotary motor made of a single mole-cule. Its size being ca.10 nm, the F1-ATPase is the smallestrotary motor known. Counterclockwise rotation has alsobeen demonstrated for F1from Escherichia coli (Omote etal.1999; Noji et al.1999) and chloroplast (Hisabori et al.1999).

Of the ve kinds of subunit in F1, a3b3gsuce for rota-tion. Cross-linking studies (Aggeler et al.1997) have indi-cated that eis probably a part of the rotor and dbelongsto the stator. When an actin lament was bound to einstead of g, the lament also rotated counterclockwise,although the rotary speed was somewhat lower (Kato-Yamadaet al. 1998).

(b) Stepping rotation

When ATP concentration was reduced, the rotationbecame stepwise, as shown in gure 3. The step size of

1208 is consistent with, though not a necessary conse-quence of, the basic threefold symmetry of the a3b3stator.We have been unable to resolve sub-steps at the highesttemporal resolution, of 5 ms, achieved so far. Note thatthe motor made a clear back-step at ca. 45 s in gure 3. Amolecular machine must occasionally make mistakes. The1208 steps have also been conrmed in F1without actin(K. Adachi, unpublished data), by attaching a uorophoreon g and observing the polarization of the uorescencefrom the single uorophore under a microscope (Saseet al.1997; Ha et al. 1998). Thus, stepping is not an artefactcaused by friction between the actin lament and the

stator cylinder with pseudo-threefold symmetry.

4. THE KINETICS OF ATP HYDROLYSIS

The hydrolysis kinetics of F1-ATPase is complicated,because of the presence of three catalytic sites (and threenon-catalytic sites that also bind a nucleotide), and of the

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MgADP inhibition. It is dicult to extract a unied viewfrom the literature, partly because the eect of the (almostinevitable) MgADP inhibition on the experimental results

is often ignored or not mentioned. The description below isan arbitrary selection from the literature. For comprehen-sive reviews, see Boyer (1993, 1997, 2000).

(a) Three modes of hydrolysis reaction

At extremely low ATP concentrations, at most onecatalytic site of F1 is lled with a nucleotide. Under thisuni-site regime, ATP and its hydrolysis products are inequilibrium in the catalytic site, and the products arevery slowly released into the medium (gure 4). For mito-chondrial F1, Cunningham & Cross (1988) describe theuni-site kinetics as

F1 ATPk1 610

6 M1 s1 k14 7106 s1

F1 ATPk 2 12 s

1 k2 24 s1

F1 ADPPik3 410

3 s1 k355106M1 s1

F1ADP Pik 4 410

3 s1 k4 4106 M1 s1

F1 ADP Pi

k1/k1 K151012 M1,

k2/k2 K2 80:5,k3/k3 K348 10

2 M,k4/k4 K4 10

9 M,

where Pi is inorganic phosphate, k+iand ki are forwardand backward rate constants, and Ki k+i/ki are theequilibrium constants. Unlike myosin (Taylor 1979), the

rates of ADP and phosphate releases from F1appear tobe similar, and thus phosphate release does not neces-sarily precede the release of ADP. A more recent study(Milgrom et al.1998) indicates that the rates of productrelease (k+3 and k+4) are an order of magnitude higherand K2 is about 0.8. The rate of ATP binding to asecond catalytic site (at a higher ATP concentration) issimilar to k

+1

above (Cross et al. 1982). Thus, uni-sitecatalysis is expected when free ATP concentration isbelow 1nM. Uni-site catalysis has been reported to takeplace even when rotation of g is prohibited (Garc|a &Capaldi 1998). This, however, does not necessarilyexclude the possibility that rotation might still accom-pany uni-site catalysis.

Binding of a second ATP greatly promotes the rate ofhydrolysis on the rst site and particularly the rates ofproduct release from the rst site (Boyer 1993, 1997). Thepositive cooperativity in catalysis and negative coopera-tivity in nucleotide binding result in an increase in theoverall hydrolysis rate by a factor of more than 103. Atsubmicromolar ATP concentrations, hydrolysis occurs inthe bi-site mode where, at most, two catalytic sites arelled with a nucleotide (gure 4). Our result in gure 3,the observation of rotation at 20 nM ATP, then indicatesthat bi-site hydrolysis accompanies rotation.

At higher ATP concentrations, it has often beensuggested that hydrolysis proceeds in the tri-site modewith a moderate acceleration from the bi-site mode. Oneindication has been that the hydrolysis rate over submi-cromolar to millimolar ATP concentrations, above theuni-site range, cannot be described by simple Michaelis^Menten kinetics (see, for example, dashed line ingure 6) and requires two sets of Michaelis parameters,one presumably corresponding to a second site and theother to the third site. The claim of acceleration is basedon an approximately tenfold dierence in the values ofVmax. Unlike the transition from uni-site to bi-site wheredoubling ATP concentration more than doubles thehydrolysis rate, however, the acceleration to tri-site is notreadily apparent in raw data. The deviation from asimple kinetics is not large (see the example in gure 6),and is variable depending on preparations, possibly dueto variability in the degree of MgADP inhibition.Milgrom et al. (1998) have reported that, when care was

taken to avoid inhibition, one set of parameters(Km 130 mM and Vmax700 s

1 for mitochondrial F1at25 8C) suced for the description of the multi-sitekinetics up to 1mM ATP. Thus, F1-ATPase may not adoptthe tri-site mode. Strong support for tri-site catalysis hascome from the measurement of site occupancies throughthe nucleotide-induced quenching of tryptophans in thecatalytic sites (Weberet al. 1993). The interpretation of theuorescence signal, however, is not absolutely unambig-uous (Milgromet al. 1998).

Because the rotation ofghas been demonstrated in thebi-site regime, we think that the bi-site mode is funda-

mental at least for the mechanism of rotation. Bi-sitehydrolysis in ATP synthase pumps protons (Muneyuki &Hirata 1988).

(b) MgADP inhibition

Figure 5 shows typical time-courses of ATP hydrolysisat three ATP concentrations. The a3b3g subcomplex of

Rotary molecular motor near 100 % eciency K. Kinosita Jr and others 477


Figure 3. Stepping rotation of F1at 20 nM ATP (Yasudaet al.1998). Inset shows the trace of the centroid of the actinlament.

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bacterial origin used to demonstrate the g rotation wassuspended in solution without attaching actin. Theamount of ATP hydrolysed was estimated by regeneratingATP by pyruvate kinase and coupling the reaction to theoxidation of NADH by lactate dehydrogenase (Kato et al.1995). As seen, the rate of hydrolysis gradually decreasedto less than half the initial value. This is the so-calledMgADP inhibition, where the hydrolysis productMgADP is tightly bound to a catalytic site and inhibits

further turnover of the enzyme (Boyer 1997, 2000).The inhibition does not proceed to completion,

because slow binding of ATP to non-catalytic sites tendsto displace the tightly bound MgADP in the catalyticsite. Under certain conditions, the hydrolysis kineticsbecomes tri-phasic: full activity in the initial phaseslows down due to the inhibition, and then followspartial recovery toward an intermediate hydrolysis rate(e.g. 60 mM in gure 5). In a mutant where ATPbinding to the non-catalytic sites was prohibited, therewas no recovery and the inhibition proceeded tocompletion (Matsui et al.1997). In the assay in gure 5,

the hydrolysis products were immediately convertedback to ATP. If ATPase kinetics is measured without aregeneration system by, for example, chromatographicassay of ATP and ADP, the enzyme is more severelyinhibited (E. Muneyuki, personal communication).Thus, a small amount of MgADP in the mediumpromotes the inhibition.



Figure 4. Three modes of ATP hydrolysis by F1-ATPase. The timing ofg rotation, and whether g rotates in the uni-site mode,

are yet to be determined. (a) Uni-site hydrolysis, [ATP]51 nM; (b) bi-site hydrolysis, [ATP] ca.1 mM; (c) tri-site hydrolysis,[ATP]4100 mM.

(b)

numberofATPhyd

rolysed

15000

10000

5000

55s1

160s1

0 0 50 300250200150100

time (s)

7000 700

600

500

400

300

200

100

0

6000

5000

4000

3000

2000

1000

0

(a) 23s1

70s1

4s1

1s1

Figure 5. Time-courses of ATP hydrolysis measured insolution at 23 8C (H. Noji, unpublished data). (a) [ATP]60 mM shown in red, [ATP] 0.6 mM shown in green;(b) [ATP] 2mM.

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Figure 6. Comparison of the hydrolysis and rotational rates(Yasudaet al.1998). The hydrolysis rateV(open circles) wasmeasured in solution, and was tted with Vkcat[ATP]/([ATP] + Khydm ), wherekcat 125s

1 and Khydm 12 mM(dashed line), or with V(kacatK

hydm

b[ATP] + kcatb[ATP]2)/([ATP]2 +Khydm

b[ATP] + KhydmaKhydm

b), wherekacat 75 s1,

kbcat 177 s1, Khydm

a 6.6 mM, andKhydmb 285 mM (dotted

line). The rotational ratev was measured by attaching a short(0.8^1.2mm) actin lament (closed circles), and was ttedwithv vmax[ATP]/([ATP] + K

rotm ) wherevmax 3.9 rev s

1

and Krotm 0.8 mM (solid line).

60

40

20

060

40

20

0 1 2 3

(a)

(b)

0 3 6 9

numberofevents

dwell time (s)

Figure 7. Histograms of dwell times between steps (Yasudaet al.1998). (a) [ATP] 20nM; (b) [ATP] 60 nM. Blacklines indicate exponential ts: constantexp(kon[ATP]t),wherekonis the rate constant for ATP binding(2.7107 M1 s1 at 20nM ATP and 2.2107 M1 s1 at60 nM) andtis the dwell time. Green and red lines show tswith two exponentials (simultaneous consumption of rapidlyand slowly bound ATP): constant {exp(kslowon [ATP]t)exp(krapidon [ATP]t)}, wherek

rapidon was xed at

1.0108 M1 s1 (green lines) and 2.5108 M1 s1 (redlines).

10

1

0.1

0 1 2 3 4

actin length (mm)

rotationalrate(rps)

2 mM

20 mM

0.6 mM

0.2 mM

0.06 mM

0.02 mM

2 mM

Pi 0.1mM

Pi 10 mM Figure 8. Load (actin length) and ATPdependence of the average velocity ofrotation (Yasudaet al.1998). ATPconcentrations are shown in the key. ADPand phosphate concentrations were notcontrolled, except for the + symbols forwhich [ATP] 2mM and [ADP] 10 mM.Lines are calculated as 1/(3t1208), wheret1208 tATP + tstepis the time per 1208step,

tATP is the ATP cycle time at no load esti-mated from gure 6, and tstep (2/3)/N,whereN40pN nm andis the frictioncoecient in equation (1). It is likely thattATP is overestimated by ca.30% because ofthe MgADP inhibition, and thus the calcu-lated velocities (lines) at low [ATP] areunderestimated by the same proportion.

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The MgADP inhibition would economize bypreventing futile consumption of ATP in cells, but it is anuisance for researchers analysing the ATPase kinetics.Unless tightly bound nucleotides are completely removedfrom F1-ATPase prior to measurement, which is not oftenthe case, the preparation will contain an unknownamount of inhibited enzyme, possibly most of the mole-cules. Results on such a preparation, or on the `steady-stateATPase, have to be interpreted with caution.

The Walker structure is probably an MgADP-inhibitedform (Abrahams et al.1994). As already pointed out, thefact that the arrangement of nucleotides in this structureis consistent with the sense of observed rotation suggeststhat the Walker structure resembles an active intermediatethat appears during rotation. An attempt to `freeze F1-ATPase in this structure by cross-linking supported thisview (Tsunoda et al. 1999). Presumably, the inhibitedstructure represents one of the most stable forms of thisenzyme, and is separated by a relatively small activationbarrier from the major kinetic pathway of the hydrolysisreaction. In this regard, it is worth noting that MgADPinhibition does not operate during synthesis (Boyer 1997,2000), and synthesis renders inhibited enzyme back to aform capable of hydrolysis (Galkin & Vinogradov 1999).Free energy obtained by clockwise rotation of g will liftthe enzyme from the bottom of the potential well back tothe major pathway, or to a possibly dierent path for thesynthesis.

(c) Three ATP molecules per turn

The rate of ATP hydrolysis and the rate of g rotationare compared in gure 6 (Yasuda et al.1998). The hydro-lysis rate was measured as the initial rate (gure 5), and isdivided by three to facilitate the comparison. Therotational rate was measured with an actin lament oflength 0.8^1.2mm. At ATP concentrations above 1 mM,the rotational rate saturated because of the frictional loadimposed on the rotating lament (see 5(a)). Below 1 mMwhere ATP binding was rate limiting, the rotational rateand one-third of the hydrolysis rate grossly agreed witheach other, suggesting that three ATP molecules areconsumed per turn.

The agreement was not perfect, a likely cause beingthe MgADP inhibition. Whereas the rotational rate in

gure 6 is the average over selected laments that rotatedvigorously and continuously without unnatural pauses,which represented at most a few per cent of the lamentson the surface, the hydrolysis rate is the ensemble averageover all enzyme molecules in the solution. Some mol-ecules in the solution may have been inhibited from thebeginning. These samples (also those shown in gure 5)contained about 0.3M of tightly bound nucleotide permole of F1, implying that 30% may well have been inhib-ited at the beginning. Also, the initial rate was measuredover the rst 3^13 s and signicant inhibition might haveoccurred during these periods.

The MgADP inhibition may also be responsible for thefailure in tting the hydrolysis rate with a simpleMichaelis^Menten kinetics (solid line in gure 6).Another possible reason is that the non-catalytic sitestend to be lled with ATP earlier at higher ATP concen-trations; the hydrolysis rate might be somewhat higherwhen the non-catalytic sites bind ATP.

(d) One ATP molecule per step

In gure 6, the rotational and hydrolysis rates areproportional to the ATP concentration in the sub-micromolar range. This suggests that, at least in thisrange, both processes are fuelled by individual ATPmolecules, not by the combination of two or more ATPmolecules. To further conrm this point, we analysed thedwell times between rotary steps at very low ATPconcentrations where 1208 steps were clearly resolved(gure 3).

Figure 7 shows histograms of the dwell times (Yasuda etal.1998). If each 1208step is driven by one ATP molecule,the histogram should be exponential, as was indeed thecase (black lines in gure 7). If, on the other hand, twoor more ATP molecules were required for each step, thehistogram would have started from the origin at thelower left, as in the green and red lines, because simulta-neous arrivals of two or more ATP molecules should be arare event. The data point to one ATP molecule per step.Experimental distinction, however, is not easy whenbinding of the rst ATP molecule is always much fasterthan the second: in this case the rise of the histogramnear the origin will be very steep (compare the green andred lines). As seen, the experimental histograms cannotexclude the two-ATP-molecule case if the rate constantfor the rst binding is much larger than 108 M1 s1. Sucha high rate (essentially diusion limited) has not beenreported for the hydrolysis kinetics of F1-ATPase, whetherfor uni-, bi-, or tri-site modes.

For the scenario of one ATP molecule per step, therate constant for ATP binding is estimated from theexponential constant for the histogram: 2.7107 M1 s1

at 20 nM ATP and 2.2107 M1 s1 at 60 nM ATP.These values agree, within experimental uncertainty,with each other and also to the slope of hydrolysis rateversus ATP concentration (gure 6). Literature valuesare scattered mostly between 105 and 107 M1 s1 (bothuni-site and multi-site), and our values here belong tothe high end (possibly indicative of the absence ofMgADP inhibition).

Judging from gures 6 and 7, we are fairly sure thateach 1208 step is driven by the hydrolysis of one ATPmolecule. Of course this does not necessarily meanthat the ATP molecule just bound is hydrolysed and

released into the medium during one 1208 step: it ishighly likely that one ATP molecule is bound to acatalytic site and products are released from a dierentsite, as shown in gure 4. We are less certain aboutthe reverse statement, that each ATP hydrolysis alwaysaccompanies rotation. This is suggested by gure 6,but the hydrolysis rate in the complete absence ofMgADP inhibition might be somewhat higher than therotational rate. Futile consumption of ATP, as occursin the myosin^actin system (Huxley 1957), cannot beruled out completely.

5. MECHANICAL PROPERTIES OF THE F 1 MOTOR

(a) The actin lament is a heavy burden for F1When we observed the rotation of actin laments

attached to g, we noticed that longer laments tended torotate slower. This seemed reasonable, because the hydro-dynamic friction against a rotating lament is essentially

480 K. Kinosita Jr and others Rotary molecular motor near10 0% eciency


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proportional to the cube of its length L: the frictionaldrag coecient is given by (Huntet al.1994)

(4/3)L3/ln(L/2r) 0:447, (1)

where ( 103 N m2 s) is the viscosity of the medium,and r( 5 nm) is the radius of the lament. Equation (1)applies to a lament rotating around one of its ends; suchlaments were selected for analysis.

The rotational rate ! (in radians per second (rad s1))is related withand the torqueNof the motor by

N !. (2)

To rotate an actin lament at the observed speed, the F1motor has to produce an enormous torque. For example,an actin lament of length 1 mm rotated at 6 revs1

( 40rads1). This requires a torque of about 40 pN nm.If this torque is generated at the g^b interface at theradius of 1nm, the force that let gslide past b amounts to40pN, the largest among the forces produced by knownnucleotide-driven motors (Kinositaet al. 1998).

(b) The F1motor produces a constant torque

In gure 8, the rotational rates of actin laments thatmade at least ve continuous revolutions without unna-tural pauses are plotted against the lament length. Asseen, the data points at dierent ATP concentrations,distinguished by dierent symbols, fall approximately onthe respective smooth lines that have been calculated onthe assumption of constant torque. That is, we assumedthat (i) F1produces a constant torque of 40 pN nm irre-spective of the frictional load (actin length) or of the ATPconcentration, and (ii) the time per one-third of a revolu-tion is simply the sum of the ATP cycle time at no load(taken from gure 6) and the time needed to rotate theactin lament by 1208under the torque of 40 pN nm. Thelatterthe time needed to move the lamentwasassumed to be given by 2/3 rad( 1208) divided by!N/, where the torque N was assumed to be40 pN nm for all curves.

The fair agreement between the data and the curves ingure 8 indicates that the F1motor produces a constanttorque of 40pNnm over the range of rotational ratesbetween 0.1 and 10revs1 and over the range of ATPconcentrations b etween 20 nM and 2 mM. The slowerrate for a longer lament is explained by the higher fric-tion, and the slower rate at a lower ATP concentration isdue to the lower rate of ATP binding. The constant torqueoutput of the F1motor is contrasted with the force of themyosin^actin motor, which decreases with the slidingspeed (Huxley 1957). The bacterial agellar motorproduces a constant torque when the rotary speed is nothigh (Berg & Turner 1993). In this regard, the rotationalrates of the F1motor in gure 8 are also low compared tothe expected unloaded rate: gure 6 indicates that the

maximal rate of ATP hydrolysis in the absence of actin isabout 180 s1, implying that the maximal rotational ratewill exceed 60 rev s1 at high ATP concentrations.Indeed, recent measurements show unloaded rotation atca. 100 rev s1 at 23 8C (R. Yasuda, unpublished data). Thetorque performance at high rotational rates remains to bedetermined.

(c) The energy conversion eciency can be nearly

100%

The torque of 4 0 pN nm times the angular displace-ment of 2/3rad( 1208),ca.80 pN nm, is the mechanicalwork done in a 1208step. This value of 80 pN nm is closeto the free energy obtained from the hydrolysis of oneATP molecule under intracellular conditions: G G0+ kBTln[ADP][Pi]/[ATP], where G050pNnm isthe standard free-energy change per molecule for ATPhydrolysis at pH 7, k BT4.1pN nm is the thermal energyat room temperature, and intracellular [ATP] and [Pi]are both in the order of 103 M, giving G of100 pN nm for [ADP]10 mM and 90pNnm for[ADP]100 mM. Thus, the F1motor appears to work atan eciency close to 100%.

Most of the observations in gure 8 were made inthe presence of the ATP regenerating system, and thusthe concentrations of ADP and phosphate wereminimal, implying that jGj was much larger than80 pN nm. To conrm the high eciency, therefore, weconducted experiments in the absence of the regener-ating system, at [ATP]2 mM, [ADP]10 mM, and[Pi] at either 0.1 or 10 mM (crosses in gure 8). Calcu-lated G are 110 pNnm for [Pi]0.1mM and90pNnm for [Pi] 10 mM. As seen, the rotationalrates under these conditions are also on the red line forthe torque of 40 pN nm, indicating that the work perstep is also ca. 80pNnm. The F1 motor is made toproduce a constant work per step of ca. 80 pN nm, andit can work even when the energy supply per step is aslow as 90 pN nm.

The scatter of data in gure 8 may make the claim ofnear 100% eciency dubious. In fact, there were manymore actin laments, not shown in the gure, thatrotated with irregular intermissions and thus gave loweraverage speed. There are, however, many factors thatmay impede the lament rotation, as already discussed.Another factor that has not been mentioned is that theeective viscosity close to a surface is higher than in thebulk for which equation (1) applies (Huntet al.1994): forthe actin lament close to the surface, the eective visc-osity can be three times as high (Noji et al.1997). Of thedata points in gure 8, those that are slow may have beenaected by these impeding factors. On the other hand,

we cannot think of experimental uncertainties that wouldlead to a gross overestimation of the rotational rate, deter-mined as the average over ve or more revolutions. Actinlength determined from the uorescence image is subjectto error, but the error is relatively small for a long la-ment. In some cases, the lament was slightly curved inthe image plane, or the rotating end oated from thesurface. The curvature or inclination, however, do notaect the interpretation seriously, because they changethe eective length as a cosine of the angle; deviation by208 is noticeable, for which the ratio of the arc length toits chord is (/2)/sin(/2) 1.01 (close to 1).

We also analysed the speed of rotation in individual1208steps observed at low ATP concentrations (Yasuda etal.1998; also see 5(d)). The torque estimated from equa-tion (2) for !measured in each step averaged 44 pN nm,and hence the work per step averaged ca. 90 pNnm, inagreement with the values obtained from the rotationalrate averaged over many revolutions.

Rotary molecular motor near 100% eciency K. Kinosita Jr and others 481


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Interestingly, the occasional backward steps were asfast as forward steps, implying that the work needed toproduce the back step is also ca. 90 pN nm. Presumably, abackward step also consumes one ATP molecule. In the

bi-site catalysis (gure 4), two catalytic sites remainempty for most of the time. Binding of ATP to the wrongone of the two may well cause the backward step. Or, theback step may result from premature dissociation ofnewly bound ATP before hydrolysis.

(d) The torque is constant over the rotational angle

In gure 9a, individual steps for a 1-mm lamentrotating at 0.2 mM ATP are superimposed on each other.As seen in the thick cyan line showing the average, thesteps were made at an approximately constant speed from

beginning to end. The linearity is clearer in the twocurves (red and pink) showing succession of two stepsstarting at 0:33 revolutions.

The constant speed implies, according to equation(2), a constant torque over the stepping angle of 1208.The thick green line indicates that the constant torqueis about 44 pN nm. If this torque N ( 44pNnm) is

derived from an angle-dependent potential energyV():

@V/@ N, (3)

then the potential will be linearly downhill as shown ingure 9b. The depth of the potential is given by N( 44pNnm) multiplied by 2/3, or ca. 90 pN nm, inaccordance with the work per step of 80^90 pN nmabove. The fact that the F1 motor produces a constanttorque and constant work per step irrespective of theload, speed, and ATP concentration, is easily understoodif ATP binding and subsequent hydrolysis somehowproduces the rotational potential depicted in gure 9b.

Note that the chemical state of bound nucleotides

probably changes while the motor makes a 1208 step,and thus the potential in gure 9b does not necessarilycorrespond to a single chemical state. There may well beseveral chemical states during one mechanical step, eachwith a dierent potential. The experimental potentialdescribed here (gure 9b) should be regarded as aneective potential.



0.67

0.33

0.00

0.33200 100 100 2000

(a)

(b)

revolutions

time (ms)

V

00 120

q

slope: N8090pNnm

~20KBT

Figure 9. Time-courses of individual steps(Kinosita et al.2000). (a) Steps weremeasured at 0.2 mM ATP for F1bearing a1.0-mm lament. Traces for individual stepsare superimposed such that the middle ofeach step is located at time zero. Rapid

succession of two steps are seen in twotraces (red and pink). The thick cyan lineshows the average of all traces. The thickdark-green line shows a constant-speedrotation at 44 rads1, corresponding to atorque of 44 pN nm. (b) Rotational potential,V(), deduced from (a).

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The torque of 44pNnm in gure 9a is the torqueunder the bi-site condition (submicromolar ATP). Asimilar torque value of 40pNnm is deduced at 2mMATP (gure 8), which is in the putative tri-site regime.Thus, tri-site operation, if it occurs, does not add powerto this motor.

6. POSSIBLE MECHANISMS OF ROTATION

(a) Probable experimental facts about the F1motor

Before discussing the mechanism, we summarize belowprobable facts about the F1 motor. We say probable

because, in general, there are few experiments fromwhich one can draw conclusions with certainty.

(i) F1-ATPase is a rotary motor made of a single mol-ecule. The energy source is ATP.

(ii) a3b3g suce for rotation and ATP hydrolysis. g isthe rotor anda3b3hexamer is the stator.

(iii) The rotation of g is counterclockwise when viewedfrom the Foside.

(iv) The motor rotates in discrete 1208 steps, at least atlow ATP concentrations.

(v) The F1 motor is so designed as to produce aconstant torque ofca.40 pN nm over broad rangesof speed and load, and of ATP concentration.

(vi) The mechanical work done in each 1208step is alsoconstant, except for statistical variations, andamounts to 80^90 pN nm.

(vii) Hydrolysis of one ATP molecule suces for makingone step.

(viii) The energy conversion eciency approaches 100%when the free energy of ATP hydrolysis is decreasedto the intracellular level.

(ix) Bi-site catalysis supports rotation. The torque inthe bi-site regime is as high as the torque in theputative tri-site regime at high ATP concen-trations.



Figure 10. A three-pole DC motor (Kinosita et al.2000). The commutators on the shaft control the polarity of stator magnetssuch that the shaft rotate continuously counterclockwise.

(a)

(b)

bATP

ATP ADP

ATPADP

ATP ADP

bADP bempty

emptyempty

empty

a a a

g g g

Figure 11. Nucleotide-dependent conformational changes in F1(Kinositaet al.2000). (a) From the crystal structure (Abrahamset al.1994), the centralg, onebto the left ofg, and one a to the right are selected and shown. The black lines indicate therotation axis suggested by Wang & Oster (1998): the lower half of F1retains an approximate threefold symmetry around thisaxis. Nucleotides are shown in CPK colours. (b) Top view of sections of F1between the gold lines in (a).

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(x) Apparently, each step is made along a linear,downhill potential with a depth of 80^90pN nm.

(xi) Back steps occur occasionally.

(b) Analogy might help

A mechanism that is guaranteed to rotate is shown ingure 10. This direct current (DC) motor has threedriving poles in the stator part, like the F

1

motor. Themotor is powered by a unidirectional current, while ATPhydrolysis is also practically unidirectional. Continuous,counterclockwise rotation of the DC motor is assured bythe three pairs of switches on the shaft (commutators),which alternate the polarities of the stator magnets. Therotor is made of a static magnet. The DC motor operatesin the bi-site mode in that the three stator magnets neveradopt the same polarity at the same time. The DC motorbecomes a DC generator if the rotor shaft is forciblyrotated in the clockwise direction. The energy-conversioneciency of modern electrical motors is quite high, often495%. Thus, there are apparent similarities betweenthis three-pole DC motor and the F1motor. There mightbe similarities in their operational principles, too.

The driving forces in the DC motor in gure 10 are theattraction between north and south poles and therepulsion between like poles. Wang & Oster (1998)suggest that such a push^pull mechanism may alsooperate between the g- and b-subunits of the F1motor.Figure 11ashows side views of the three pairs of opposingb- and a-subunits, together with the central g, in theWalker structure. The vertical black lines show therotational axis suggested by these authors: the bottompart of the a3b3 stator has an approximate threefoldsymmetry around this axis, and thus the conformations ofb and a in the bottom do not change greatly dependingon the bound nucleotide. In contrast, in the upper partthe bs binding ATP or ADP are bent towards, and there-fore push, g, whereas the empty b retracts and pulls gtowards it. Wang & Oster (1998) suggest that, because thecentral g is slightly bent and skewed, cooperative push^pull actions of the three bs would rotate as seen ingure 11b.

(c) An F1model relying on switches

Figure 12 shows a model for F1 rotation based on the

push^pull mechanism above, a simplied version of themodel proposed by Wang & Oster (1998). The side of gthat faces the empty b in the Walker structure is desig-nated the north pole (N), and thus an empty b is thesouth pole (S). A nucleotide-carrying b is N, and repelsthe N face ofgand attracts its S face. By reciprocity, theS face of g augments the anity of opposing b for anucleotide, and the N face decreases the anity (the freeenergy is lowered when N and S oppose each other). Tomake this model rotate in a unique direction, additionalcontrol of nucleotide binding kinetics via commutators isrequired. A simple example is given in gure 12b:

binding^release of ATP is allowed for b while it is on thepink side of g, and ADP binding^release while on thegreen side. As shown in gure 12c,d, the switching ensurescounterclockwise rotation of g when ATP is hydrolysed;when the rotor is forced to rotate clockwise in thepresence of ADP (and phosphate), ATP is synthesized.(We do not distinguish ADP, ADP plus phosphate, or

phosphate alone, because the rate constants for ADP andphosphate releases are similar and because we do not yetknow which event is pivotal in producing rotation.)

More elaborate switches have been proposed byWang &Oster (1998; also see Oster & Wang 2000), and their modelcan account for many experimental observations includingthe near100% eciency and1208stepping with occasionalback steps. In their model, as with the model in gure 12,the motor tends to pause at angles of 608out of phase fromthe Walker structure (gure 12a), a prediction experimen-tally testable. How the switching action is implemented inthe protein structure is yet to be specied.

(d) A switch-less F1model

The roles of the commutators in gure 10 are to alter-nate the polarities of the stator magnets, and to do so atprecise timings dictated by the rotational angle of theshaft. Unlike the magnet driven by direct current, thealternation of the polarity is inherent in the ATP-driven`magnet, where bound ATP is eventually hydrolysed andreleased, and the S state is restored spontaneously. Thus,only coordination of nucleotide kinetics among the threestator magnets needs be programmed. This could be donewithout postulating switches, as shown in gure 13, whichis one version of the general model of Oosawa & Hayashi(1986).

In gure 13, the position of the `magnetic pole in bchanges depending on the bound nucleotide. This dual-pole arrangement, combined with the higher anity fornucleotides when the pole is closer to the S face of g,ensures counterclockwise rotation in bi-site hydrolysis byinducing ATP binding primarily in the empty b in thecounterclockwise direction (gure 13c). Note that theangle dependence of the nucleotide anity is a result ofthe reaction to nucleotide-dependent push^pull action,and that this angle dependence does not require switches.An additional factor warranting correct rotation in thismodel is the higher anity for ATP than for ADP.Because ATP hydrolysis on b is reversible (the free-energydierence between b binding ATP and b bindingADP + phosphate is small), the anity for the hydrolysisproducts has to be lower in order for bto act as ATPase.In the original model of Oosawa & Hayashi (1986), near100% eciency was achieved for both hydrolysis and

synthesis.The essence of the dual-pole arrangement is that the

hydrolysis of ATP to ADP on a b-subunit produces rota-tional force, and the release of ADP tends to furtherrotateg. That is, direct rotational force, in addition to thepushing^pulling, is produced by a single b hydrolysingATP. Apparently, the Walker structure gives moreemphasis to pushing^pulling than direct rotation, but thestructure of g in the protruding portion has not beenresolved. Also, a key intermediate(s) in actual rotation,particularly the state with only one bound nucleotideamong the catalytic sites, may well have a somewhat

dierent structure. Boyer (1997, 2000) points out that theequilibrium between ATP and its hydrolysis products onbis shifted depending on whether ATP synthase is synthe-sizing or hydrolysing ATP. The switch-less model predictsthis behaviour because clockwise rotation of g shifts theequilibrium towards ATP and counterclockwise rotationtowards ADP (gure 13c,d).



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The abstract models in gures 12 and 13 might helpdissect the actual F1 motor, but they are nothing more thana guide. The magnetic representation obscures severalfactors that may be important. For example, unlike themagnets, actual g and b do not possess reectionsymmetry. The force between g and individual b musttherefore be more or less asymmetrical, favouring one rota-tional direction over the other, as modelled by the dualpoles in gure 13. Whether the rotational potential can beapproximated by a simple superposition of three pairwiseinteractions between individualband g, as implied by themagnetic representation, may also be questioned. Ingures 12 and 13, nucleotide kinetics on dierent bs arecoordinated only through the rotation ofg, butbs may alsocommunicate with each other through interveningas.

7. PROSPECTS

(a) F1When do we say we have understood the mechanism

of F1 rotation, or of molecular motors in general? TheF1-ATPase has given us the unique opportunity ofdetermining the mechanical potential that underlies theforce and movement. The potential in gure 9b, however,is an apparent one, and we do not yet know how it isformed, except for guess work. We need to, and should beable to, determine the mechanical potential for eachchemical state of the bound nucleotides. The chemicalstate, at least which of the binding sites are lled with anucleotide, could be measured with single-moleculeimaging of uorescent nucleotides (Funatsu et al.1995) orby introducing a probe uorophore within the bindingsite (Weber et al.1993). The potential could be estimatedby forcibly rotating the g-subunit, for example withoptical tweezers. As we discussed above, the potential andthe anity for nucleotides are in a sense mirror images ofeach other: if, for example, ATP binding favours acertain orientation ofg, that orientation increases the a-nity for ATP. Thus, measurement of nucleotide anityalso serves as an indirect means of estimating the poten-tial.

When we know the potentials for individual chemicalstates involved in rotation, we would like to ask how eachof them is formed. We wish to answer on the basis of the

atomic structure of the F1motor. Here, the vitally impor-tant structure is yet to be solved: the structure in whichonly one catalytic site is lled with a nucleotide, the struc-ture from which the bi-site stepping begins. Presumably,the transition from this structure to something similar tothe Walker structure drives the rotation. The key issuesare whether the two empty bs in the one-nucleotidestructure adopt the conformation of the empty b in theWalker structure, and if not, whether the b with adierent structure may contribute to the production of arotational force, perpendicular to the push^pull directionin gure 11. If the force along the direction of rotation is

absent, switches are required, and their physical constructshould be explored.

The structure ofa3b3 hexamer without g and withoutnucleotides has been solved (Shirakihara et al.1997); allthree b-subunits adopted a conformation closely resem-bling the empty b in the Walker structure. The hexamerwithout g is not stable in the presence of nucleotides. In

contrast, F1-ATPase or thea3b3gsubcomplex are not stablein the absence of nucleotides (except for those from ther-mophilic bacteria, which are relatively stable). The g-subunit appears to favour at least two bs to be in thenucleotide-binding conformation. F1 bearing only onecatalytic nucleotide is probably less stable, and thus showsa high anity for a second nucleotide. Binding of ATP tothe second site thus releases free energy that can be usedfor rotation. Because the one-nucleotide structure is prob-ably less stable, its crystallization may not be easy. Deter-mination of the structure may require indirect meanssuch as the uorescence energy transfer technique. Arecent cross-linking study has suggested that the one-nucleotide structure is dierent from the Walker structure(Tsunodaet al. 1999).

Experimental determination of mechanical potential isfeasible in the case of F1, but is not easy for linear motorssuch as myosin and kinesin that undergo attachment^detachment cycles. These latter motors may use biasedBrownian motion and selective binding as a source ofmovement and force, in addition to potential-drivenbending (Huxley 1957; Kinosita et al. 1998). Such athermal ratchet mechanism should be explored in linearmotors, not in F1 for which eciency appears to be toohigh for a thermal ratchet to be operative.

The F1 motor also oers an opportunity of demon-strating conversion of mechanical energy into chemicalenergy: mechanical synthesis of ATP by forced, clockwiserotation of g. Nowadays most people believe F1in intactATP synthase will do this, but experimental proof withisolated F1 is awaited.

(b) FoRecently, two crystal structures have been reported that

elucidate the link between gand Fo. In a crystal of yeastFoF1(Stocket al. 1999), a ring of ten (not12) c-subunits wasconnected to and e (in yeast nomenclature), as shownin gure 14a,b(part of the densities assigned to gare notshown in this gure). Much of the g-subunit was revealed(gure 14c,d) in a crystal of F1from Escherichia coli(Haus-rath et al.1999). Despite the dierences in crystal forms,the structures of g in the two crystals appear largelysimilar to each other. In particular, contact between gand the c-ring is indicated in the yeast structure, near the

putative rotation axis (black dot and line in gure 14a,b).The top of g in gure 14c,dcoincides with the contactregion.

The structure in gure 14bsuggests that, when the a3b3hexamer is xed on a surface and ATP is supplied, the c-ring and e will rotate together with . Indeed, an actinlament attached to ein F1preparation (Kato-Yamada etal.1998) or c in FoF1preparation (Sambongi et al.1999)was seen to rotate. Whether the c-ring (and e) in intactATP synthase is a rotor and rotates against its putativestator (the grey part in gure 1), however, remains to beseen. The presence of an intact stator was assumed in the

FoF1experiment (Sambongi et al.1999), but the stator didnot impede the rotation at all, and the rotation waspoorly inhibited by an Foinhibitor. In this regard, it is ofinterest to note that the yeast crystal contained only F1-subunits and c, although the `mother solution contained afull complement of FoF1 (Stock et al.1999). The putativestator appears to be quite labile in the presence of



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detergent, an indispensable component for the purica-tion of Foor FoF1.

The arrangement of the c-ring in gure 14a,b appar-ently poses a problem. The ring is inclined against theputative rotation axis, and the attachment to g is not atthe centre of the ring. When g rotates, the ring will makean eccentric movement. The putative stator, whilemoving the ring to rotate g, has to maintain close contactwith this eccentric ring by bending itself and/or g. Aproton channel(s) must also be secured. A hand-over-hand mechanism, like kinesin, may solve this dilemma,possibly by coordinating structural changes (Rastogi &Girvin 1999) in two or three c-subunits, such that at leastone c-subunit is tightly bound to the stator. Occasionally,

though, the grip may fail and the c-ring may swing away.Is it then ATP hydrolysis that brings the ring back to thestator surface?

If there were three stators, the c-ring would not escape,and the symmetry mismatch with the a3b3 hexamerwould also be solved. The symmetry mismatch betweenthe three stators and ten c-subunits would be advanta-

geous for c rotation. Two peripheral stalks, in addition tothe central g, have been seen in an electron micrograph

of V-type ATPase, raising the possibility of three periph-eral stalks at least for this enzyme (Boekema et al.1999).Is it not possible that FoF1 is stripped of some statorcomponents during detergent purication?

It is possible that, in intact synthase, is connected tothe centre of the c-ring. A central contact with thesymmetrical ring, however, would be more liable to slip-page than the peripheral contact in gure 14a,b. Note thatthe c-ring might be neither a rotor nor a stator: it couldrotateg by a circular or conical movement without chan-ging its orientation, like a sleeve on a crank handle.

Assignment of rotor subunits apart, the real challenge

is to demonstrate, and to elucidate the mechanism of,rotation driven by proton ow. Kaim & Dimroth (1999)have shown that proton gradient alone is not sucient forATP synthesis and that transmembrane potential isrequired. We therefore like to design an experiment inwhich individual FoF1molecules are observed while theyare exposed to an electric eld.



ATP

ATP

ADP

ADP

empty

(a)

(c)

(d)

(b)

ATPbindingand/orreleaseallowed

ADPbindingand/orreleaseallowed

thickness:

affinity for

and

e e e

e

ee

e

eeee

e eT

D

T/D

T/DT/DT/D

T/D

T/D

T/DT/DT/D

Figure 12. A simple model for the F1motor (Kinositaet al.2000). (a) The Walker structure. The g-subunit is regarded as apermanent magnet, the side ofg that faces the empty bin the Walker structure being the north pole. (b) The anity for anucleotide is higher whenb is closer to the south pole ofg (strictly, the anity for ATP is higher than that for ADP). Bindingand release of ATP and ADP are kinetically inhibited on the right- and left-hand sides, respectively. (c) Bi-site hydrolysis([ATP]40, [ADP]ca. 0). Bound ATP (T) is in equilibrium with ADP (D) and phosphate, and is released as ADP when a secondATP binds and rotatesg. (d) Bi-site synthesis ([ATP] ca. 0, [ADP]40). Forced, clockwise rotation ofg results in the uptake ofADP (and phosphate) and release of ATP.

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T D

(D)

(D)

(T)

(T) e

(a)

(c

)

(d)

(b)

ATP form: stronger

thickness:affinity for

ATP ADPand

(higher for ATP)

e e e e e e

e e e e

e

e

(D)

(D)

(D)

(T)

(T)

(T)

T(T)

TT(T)

T

T

T

DDD

D

D

D(D)

(D)

(D)

(D)

Figure 13. A switch-less model for the F1motor (Kinositaet al.2000). (a) The Walker structure. Location of the magnetic poleon b changes depending on the bound nucleotide. ATP magnet is stronger than ADP magnet, and hence, (b) the anity for ATPis higher than that for ADP (no switches on g). (c) Bi-site hydrolysis ([ATP]40, [ADP]ca.0). When only one nucleotide isbound, it is reversibly converted between ATP and ADP-phosphate. Comparison of anities suggests that the most likely way oflling a second site is binding of ATP in the b in the counterclockwise direction. (d) Bi-site synthesis ([ATP] ca. 0, [ADP]40).Wheng is forcibly rotated clockwise, the equilibrium between ATP and ADP is shifted towards ATP, which is eventually released

while ADP is newly bound in the second site.

(a) (b) (c) (d)

bADP

bADPbATP bATP bATPaADP aADP

bempty

c10

e

g g g

Figure14. Crystalstructuresof yeast F0F1 (Stock etal. 1999)andofEscherichiacoli F1 (Hausrath etal. 1999).(a, b)Topandsideviewsofthe a-carbon modelof theyeast structure. (c, d)Backbonemodelofthe E.coli structure.(d) is rotatedby 908withrespectto(c).Blackdotin(a)andblacklinesin(b^d) show theputativerotationaxis(Wang & Oster 1998).b-subunits in greenand a-subunitsincyan.

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We are grateful to Professor Masasuke Yoshida and themembers of CREST Team 13 for collaboration and discussion,and to Dr Eiro Muneyuki for many useful comments. Thiswork was supported in part by Grants-in-Aid from theMinistry of Science, Education, Sports and Culture of Japan,and a Keio University Special Grant-in-Aid. R. Yasuda was aResearch Fellow of the Japan Society for the Promotion ofScience.

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http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0028-0836^28^29396L.380[aid=534603,csa=0028-0836^26vol=396^26iss=6709^26firstpage=380,doi=10.1038/24640,nlm=9845076]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0036-8075^28^29286L.1700[aid=534457,doi=10.1126/science.286.5445.1700,nlm=10576729]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0969-2126^28^295L.825[aid=534674,csa=0969-2126^26vol=5^26iss=6^26firstpage=825,nlm=9261073]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0028-0836^28^29393L.711[aid=534715,csa=0028-0836^26vol=393^26iss=6686^26firstpage=711,doi=10.1038/31520,nlm=9641685]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0028-0836^28^29402L.263[aid=534714,csa=0028-0836^26vol=402^26iss=6759^26firstpage=263,doi=10.1038/46224,nlm=10580496]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0065-227X^28^2922L.151[aid=534390]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0027-8424^28^2996L.7780[aid=534706,doi=10.1073/pnas.96.14.7780,nlm=10393898]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0027-8424^28^2994L.10583[aid=534713,doi=10.1073/pnas.94.20.10583,nlm=9380678]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0092-8674^28^2993L.1117[aid=534459,nlm=9657145]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0028-0836^28^29393L.29[aid=534712,doi=10.1038/29908,nlm=9590688]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0036-8075^28^29282L.902[aid=534710,doi=10.1126/science.282.5390.902,nlm=9794753]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0028-0836^28^29396L.279[aid=534393,csa=0028-0836^26vol=396^26iss=6708^26firstpage=279,doi=10.1038/24409,nlm=9834036]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0021-9258^28^29274L.1[aid=534709,nlm=9867801]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0028-0836^28^29396L.380[aid=534603,csa=0028-0836^26vol=396^26iss=6709^26firstpage=380,doi=10.1038/24640,nlm=9845076]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0036-8075^28^29286L.1700[aid=534457,doi=10.1126/science.286.5445.1700,nlm=10576729]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0969-2126^28^295L.825[aid=534674,csa=0969-2126^26vol=5^26iss=6^26firstpage=825,nlm=9261073]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0027-8424^28^2994L.5646[aid=534708,csa=0027-8424^26vol=94^26iss=11^26firstpage=5646,doi=10.1073/pnas.94.11.5646,nlm=9159126]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0036-8075^28^29286L.1722[aid=534707,doi=10.1126/science.286.5445.1722,nlm=10576736]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0028-0836^28^29381L.623[aid=534672,csa=0028-0836^26vol=381^26iss=6583^26firstpage=623,nlm=8637601]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0065-227X^28^2922L.151[aid=534390]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0027-8424^28^2996L.7780[aid=534706,doi=10.1073/pnas.96.14.7780,nlm=10393898]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0028-0836^28^29386L.299[aid=534389,nlm=9069291]http://www.ingentaselect.com/rpsv/cgi-bin/linker?ext=a&reqidx=/0264-6021^28^29330L.1037[aid=534705,nlm=9480927]

answer 2 c ass 2

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