RCooke-1997-500 Myosin Molecules Per Filament

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PHYSIOLOGICAL REVIEWSVol. 77, No. 3, July 1997

Printed ill U.S .A.

Actomyosin Interaction in Striated MuscleROGER COOKE

Department of Biochemistry and Biophysics and Cardiovascular Research Institute,Univwsi ty of California, San Francisco, California

I. IntroductionII. Protein StructuresA. Structures of actin and myosinB. Structure of the actomyosin complexC. Structure of myosin complexed with nucleotidesD. Homology between myosin and microtubule motorsE. Structural similar ity between myosin and G proteinsIII . Structure and Mechanics of Different States in the Actomyosin InteractionA. Detached statesB. Nature of pre-power-stroke statesC. Release of phosphateD. Nature of post-power-stroke statesIV. The Power StrokeA. Structural changesB. Role of the two-headed structure of myosinC. EnergeticsD. SummaryV. Steady-State Mechanics of Actomyosin InteractionA. In vitro assays of filament velocitiesB. Force generation measured in vitroC. Force generated in isometric muscleD. Length of power stroke measured in vitroE. Duty cycle for active myosin headsF. Coupling between force generation and ATP hydrolysisG. Length of drag stroke measured in fibersH. Effic iency of actomyosin interactionsVI. Transients in Force After Step Changes in Fiber LengthA. Elastic elementsB. Rapid tension recoveryC. Rapid regeneration of the power strokeD. Implications of the transient experimentsVII. Conclusions

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Cooke, Roger. Actomyosin Interaction in Striated Muscle. Physiol. Rev. 77: 671-697, 1997.-The mechanics ofthe actomyosin interaction have been extens ively studied using the organized filament array of striated muscle.However, the extrapolation of these data to the events occurring at the level of a single actomyosin interaction hasnot been simple. Problems arise in part because an active fiber has an ensemble of myosin heads that are spreadout through the various steps of the active cycle, and it is likely that only a small f raction of the heads aregenerating tension at any given time. More recently , two new approaches have greatly extended our knowledge ofthe actomyosin interaction. First, the three-dimensional crystal structures of both the actin monomer and themyosin head have been determined, and these structures have been fi t to lower resolution images to give atomicmodels of the actin filament and of the actin filament decorated by myosin heads. Second, the technology to measurepicoNewton forces and nanometer distances has provided direct determinations of the force and step lengthgenerated by a single myosin molecule interacting with a single actin filament. This review synthesizes the existingmechanical data obtained from the more-organized array of the muscle fi lament with the results obtained by thesetwo technologies.

0031-9333/97 $15.00 Copyright 0 1997 the American Physio logical Society 671


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672 ROGER COOKE Volume 77I. INTRODUCTION

In spite of considerable effort, the details of the mo-lecular mechanism by which chemical energy is trans-duced into mechanical work by biological motor proteinsare not known. A complete understanding of this mecha-nism would involve resolution of the significant states inthe cycle, determination of the structures of the proteinsin these states, and measurements of the kinetics of thetransitions between them and of the free energies thatseparate them. Significant progress in this area now bringsthis goal within reach. Studies of purified proteins in solu-tion have identified many of the kinetic intermediates inthe cycle along with their associated kinetics and energet-its. Studies of kinetic processes in fibers activated or per-turbed by the release of photoactivatable substrates orproducts have shown that a similar kinetic cycle occursin activated fibers, although some of the kinetic rates andenergetic differences may be altered by the steric con-straints of the lattice. Determination of the crystal struc-tures of a portion of the myosin head complexed withnucleotides has now provided high-resolution informationon some of the conforrnational changes that occur in spe-cific steps in this cycle. These high-resolution structuraldata have been combined with lower resolution tech-niques to produce a model of the conformational changesthat lead to force generation. The model provides a frame-work for discussing the mechanical responses of skeletalfibers. The ultimate test of these models is their ability toexplain the complex physiological responses of musclefibers.Until recently, most of the information on the me-chanics of the actomyosin interaction has been obtainedfrom studies of muscle fibers. Although a variety of differ-ent muscle types have been employed, skeletal musclehas provided the optimal fibers for these investigations.One can measure the force as a function of velocity overa wide range of velocities both positive and negative. Onecan also measure the work performed as well as energyconsumed, again as a function of velocity, providing aprecise definition of the efficiency of the actomyosin inter-action. The transient responses to either force or lengthdefine important aspects of the kinetics of cross-bridgemechanical function. However, despite a wealth of dataobtained from muscle fibers, the magnitudes of a numberof fundamental parameters of the actomyosin interactionremain controversial. These include the length of thepower stroke, the maximum force exerted in a single in-teraction, the fraction of myosin heads exerting tensionat any one time, and whether the force-generating cycleis tightly or loosely coupled to ATP hydrolysis. More re-cently, assays have been developed in which the forcesand displacements generated by purified actin and myosincan be measured. The proteins are attached to substrates,microneedles. or small beads. which can both manipulate

the proteins and measure the forces and displacementsgenerated by them. Here the force and displacement pro-duced by single motors acting on single actin filamentseliminate many of the ambiguities of the fiber systemwhere one can measure only the properties of a largeensemble.In this review I first discuss the protein structures ofactin and myosin and their relationship to other proteins,the kinesin family of motors and the G proteins, withwhich they share structural homology. The structural datalead to models of the conformational changes occurringin the cycle, which are combined with biochemical datato provide a model of the active cycle and the force-pro-ducing power stroke. The mechanical data obtained from Ithe more-organized array of the muscle filament are syn-thesized with measurements of single motor mechanicsand discussed in terms of the framework of this model.The data most pertinent to defining the mechanism of

force generation are reviewed, and studies of a numberof other aspects of muscle physiology, activation, fatigue,etc., are not considered.II . PROTEIN STRUCTURES

The structures of actin and myosin have recentlybeen reviewed and are only briefly described below (20,36, 58, 117, 120, 130). Here I concentrate on models oftheir interaction derived from these structures, leadingto a synthesis of these models with the mechanical dataobtained from striated muscle.A. Structures of Actin and Myosin

The crystal structure of the actin monomer, com-plexed with another molecule to prevent polymerization,was first obtained by Holmes and co-workers (75). Twoadditional structures of actin complexed with other pro-teins have now been obtained with no substantial differ-ences between the three structures (96, 128). The atomicstructure of the actin monomer was fit into a model ofthe F-a&in filament using X-ray diffraction patterns ofactin filaments aligned in capillaries as a constraint (59,88). The actin monomer consists of four subdomains witha tightly bound nucleotide inserted into a central cleft inthe molecule. In the filament model, subdomains 3 and 4form the core of the filament, while subdomains 1 and 2project toward the periphery. Subdomain 1 contains sitesfor interaction with the myosin head as determined bycross-linking and mutagenesis (99, 135). The inner twosubdomains are connected to the outer two by only twopolypeptide strands, suggesting possible flexibility withinthe actin monomer. Several investigators have postulatedthat conformational changes within the actin filament playa maior role in the generation of force (128). Although it


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FIG. 1. A stereo view of myosin head is shown with structural elemen ts discus sed in text highlighted. Modemyosin head was derived from published coordinates of three polypeptide chain s determined by Rayment et al.Catalytic domain is at top of figure with neck extending downward. Long a-helix that comp rises core of neck regionis shown in blue. This helix ends at residue 770 on its catalytic region end, which has been tentatively identified as thefulcrum. Its distal end is at residue 843, where it conne cts to the rod. In this view of the head, the rod would extendapproximately vertically into plane of paper, and power stroke would pull rod directly toward viewer. Loc ation ofregion that is homo logous to switch I, residues 235-245, is shown in yellow. Ap proximate position of nucleotide wasmodeled in by homology with p21-ras by Dr. Michael Lorenz, and it is seen below and slightly to left of region highlightedin yellow. Region analogou s to switch II of G proteins is shown in orange, starting with residue 466, adjacent tonucleotide, and ending with residue 506 at end of a highly conserved helix. Highlighted in pink is helix containing 2reactive cysteines, which is observed to move in crystal structures of myosin bound to ADP . AIFa or to ADP . V,, residues689-708, running from right to left (37, 131). Actin site cleft can be seen at top of catalytic domain with approximatelocation of region that binds actin, highlighted in green (residues 547-572), just to left of it. Additiona l regions ofmyosin, compo sed of disordered loops, extending out above top of structure, are also thought to interact with actin,not highlighted During power stroke, ca talytic domain of myosin is thought to remain attached to thin filament viagreen region with approximately same orientation, while neck region swings through an arc, translating rod as describedabove. Several regions of chain that were not seen in crystal structure, presumably becau se they were disordered, havebeen added to structure shown here. Thes e include a loop, 204-216 seen extending above top of structure, and NHL-terminal of regulatory light chain 1- 19, modeled as an a-helix.

nlikely that actin is a completely passive partnerinteraction, there has been no definitive evidence neck region thatconformational changes within actin play a major role inthe generation of force. A variety of spectroscopic probeshave reported changes in the structure of actin upon inter-action with myosin, but none of these appears to be large,nor are they identified with force generation (reviewedef. 27).The structure of the myosin head (Sl), determinedby Rayment and Holden (117) is shown in Figure 1.The mvosin head consists of a large globular catalvtic

the rod. The catalytic domain is composed entirely ofthe myosin heavy chain. The myosin heavy chain thenextends in a single a-helix from the catalytic domain tothe rod, a distance of 85 A. The a-helix, shown in bluein Figure 1, forms the core of the neck region and isstabilized by two light chains, light chain 1 adjacent tothe catalytic domain and the regulatory light chain closeto the junction with the rod. The light chains are mem-bers of the calmodulin family. and they wrap aroundYv 1 Iain that contains the sites for binding both actin the helix forming a structure that is similar to th


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674 ROGER COOKE Volume 77calmodulin interacting with one of its targets. At oneend, the helix connects to the rod, which transmitsforce from the head to the core of the thick filament.At the other end, the helix extends into the catalyticdomain for a distance of -10 A (see Fig. 1). The regionwhere the helix terminates within the catalyt ic regionhas been tentatively identif ied as the point about whichthe neck rotates and has been designated as the ful-crum (142, 149). The nucleotide pocket is a shallowdepression near the center of the catalytic domain alittle closer to the neck region than to the distal tip ofthe molecule. A prominent cleft bisects the catalyticdomain, with its wide end close to the region that bindsto actin and its narrow end adjacent to the phosphatebinding site of the nucleotide pocket. This actin sitecleft divides the catalytic domain into two regions,known as the upper and lower regions, with a majorportion of the binding site for actin located on the lower(in Fig. 1, the lower region is shown on the left frontwith the actin binding site highlighted in green). As dis-cussed in section ILT, these upper and lower regionshave counterparts in the homologous structures of theG proteins, which are associated with nucleotide-in-duced conformational changes.

B. Structure of the Actomyosin ComplexThe atomic structure of the myosin head was docked

onto a model of the F-actin filament using low-resolutionstructural data obtained from three-dimensional recon-structions of electron micrographs of the actomyosincomplex (101, 118, 127). When the two proteins were fittogether using this approach, there were def inite stericclashes between the two structures. One method of allevi -ating these conflicts was to assume that the actin site clefton myosin was more closed in the complex. This cleftcould thus provide a route of communication betweenactin binding sites and the nucleotide site. Due to thecomplexity of the structures and the requirement for con-formational changes within them, the exact details of theinteraction cannot be determined. However, the regionsinvolved as well as some likely interactions can be sur-mised. The major site of interaction is centered on a helix-loop-helix motif in the lower portion of the catalytic do-main (shown in green in Fig. 1). These structures haveexposed hydrophobic residues that are positioned to in-teract with hydrophobic regions in the subdomain 1 ofactin, and mutagenesis of two of these residues severelyinhibits the actomyosin interaction (107). Several chargedgroups on the subdomain 1 of actin have also been identi-fied as participating in the interaction (99, 100). Additionalcontacts are provided by interactions of several loops inthe myosin structure adjacent to the region above (4).In particular, a disordered section of positively charged

polypeptide chain that connects the upper and lower sec-tions of the catalytic domain is positioned to interact withthe negatively charged NHz-terminal of actin. Such an in-teraction could be a part of a weak bond between actinand myosin, thought to occur before the formation ofthe stronger more stereospecific bond formed during thepower stroke (99, 135). Essentially, this bond could helpdock myosin on actin. The region of interaction withactin is connected directly to the vicinity of the fulcrumby a very long and highly conserved helix (residues 475-506, shown in orange in Fig. 2). This helix is thought tobe involved in nucleotide-induced conformationalchanges, as discussed in section TIC. Although a numberof observations have shown that conformational changesoccur in both proteins upon formation of their complex,the exact nature of these changes and their role in forcegeneration remain unknown (reviewed in Ref. 17). Thespectra of fluorescent nucleotides suggest that actin bind-ing does not produce a gross change in the conformationof the nucleotide site (41).

Approximately 750- 1,000 A of the myosin surface isinvolved in the interface of the rigor complex, which is-30 A X 30 A (118). Thus, counting both proteins,- 1,500-2,000 A of protein surface are removed from thesolvent-protein interface upon formation of the rigorbond. The free energy change upon formation of an inter-face of this magnitude is expected to be large. Comparisonwith other proteins, which associate without changingtheir conformation, suggests that -40 J l A- l mall1 is lostupon formation of an interface. Thus, if actin and myosinassociate without large structural changes in the proteins,the formation of the actomyosin interface should release-60-80 kJ/mol(62). This is considerably larger than thatobserved experimentally at 25C and at physiological saltconcentration: 30 kJ/mol (reviewed in Ref. 134), whichmay be an indication that formation of the interface isaccompanied by energetically significant conformationalchanges. However, it is diff icult to calculate energeticsdirectly from structures, and the affin ity may be domi-nated by a few key residues, as observed for some protein-protein associations (15). It is interesting to note thatthere are few highly conserved residues in the region ofmyosin identif ied as the actin b inding site, in spite of thefact that actin is a highly conserved protein (20). Thusthe energetics of the formation of the actomyosin inter-face may depend critically on the details of the proteinsurfaces, and not just on the area buried.

The major point here is that both the structure ofthe complex and direct experimental determination agreethat there is a large decrease in free energy upon forma-tion of the actomyosin bond. This decrease is similar tothe work performed in an actomyosin interaction, -40kJ/mol, discussed in section IVC. As argued below, due tothe high mechanical efficiency of muscle, much of thisfree energy must be used to produce mechanical work.


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676 ROGER COOKE Volume 77causes a major decrease in the affinity of myosin for actin,the structures obtained with these ligands resembled thatfound in the absence of nucleotides (37, 129, 131). Eitherthe affinity can be altered by subtle changes in structure,or more dramatic changes occur that have not beentrapped in these crystal forms.

A second class of structures shows significant shiftsin selected secondary elements (relative to the first class)and includes the structures obtained with ADP . AIF andADP V04 at the active site. Both the AlF4 group and theV04 group were observed at a position further from theP-phosphate of ADP, suggesting that these structures mayrepresent transition states of the hydrolysis step (37, 131).Only subtle changes in the conformation of the proteinwere seen in the vicinity of the nucleotide, a result that isconfirmed by the spectra of bound fluorescent nucleotides(41, 112). However, the presence of V04 or AlF4 at theactive site induced significant shifts in the positions ofseveral secondary elements. There was a partial closureof the cleft that bisects the catalytic domain and signifi-cant shifts in the region adjacent to the light chains. Thelatter change can be plausibly linked to interactions atthe phosphate binding site. A bond is formed betweenAlF4 or V04 and the amide of a glycine (457 in Dictyostel-ium, 466 in chicken myosin) that is conserved across allmyosins. Note that in the following discussion all residuenumbers will refer to chicken myosin, shown in Figure 1,although the structure discussed may be from Dictyostel-ium. After Gly-466, the chain makes a loop extendingtoward the actin binding site, and then returns in an espe-cially long helix, 475-506, ending near the fulcrum thatlies near the end of the neck region. This helix is shownin orange in Figure 1. The position of this helix showsonly small changes near the nucleotide, but there is asignificant shift at the end near the fulcrum. An even largerchange is seen in the position of another helix, 697-709,that lies adjacent to the 475-506 helix discussed above.This helix, which contains two highly reactive cysteineresidues, is shown in pink in Figure 1. It rotates by > 10and is displaced by >2.5 A in the structure obtained withAlF4. There is a dramatic shift in the position of theCOOH-terminal region of the catalytic domain, which isadjacent to the beginning of the long neck helix and tothe 697-709 helix. Relative to the structure obtained withBeF,, this region has translated by more that 23 A androtated by -70. If this region were rigidly connectedto the rest of the neck region (which is absent in thesestructures), these structural changes would imply a largeshift in the relative orientations of the neck and the cata-lytic domain. Holmes (58) has proposed that these struc-tural changes are of the correct magnitude and directionto explain the power stroke. However, the lack of thelight chain, which would be adjacent to this region, sug-gests that these conformational changes should be inter-preted with some caution.

Although the details of the effects of nucleotides onthe structure of myosin may have to await better struc-tures that include the neck region, it is clear from the workdescribed above that the presence of phosphate analogsthought to mimic a transition state in the hydrolysis ofthe nucleotide have generated significant shifts in the re-gion of myosin adjacent to the neck, exactly what wouldbe expected if this region acts as a lever arm. These struc-tures support the hypothesis, depicted in Figure 2, that theorientation of the neck region changes upon nucleotidehydrolysis, from one that more closely resembles rigor toone that may be closer to that occurring at the beginningof the power stroke. The spectra of fluorescent probeson light chain-l show that the neck region undergoes aconformational change upon nucleotide hydrolysis (93).The conduit for these changes s formed by several helices,which also form the most highly conserved region in themolecule (20). Mutations in this region of the molecule canhave a drastic effect on myosin function (77, 124, 125).These helices, denoted by orange and pink in Figure 1, alsoform a direct connection between the actin binding siteand the interface with the neck, a connection that mustexist if the formation of the actomyosin interface providesfree energy that helps drive the power stroke, as discussedin section nC. Both helices have counterparts in thekinesin family motors and in the G proteins, and one ofthem, shown in orange in Figure 1, is structurally homolo-gous to a region of the G proteins known as switch II.

D. Homology Between Myosinand the Microtubule Motors

Kinesin and nonclaret disjunctional protein (ncd) aretwo motors that move in opposite directions along micro-tubules. The gross structures of these motor proteins re-semble that of myosin with two globular motor domainsattached to a coiled-coil a-helical rod. Recently, the struc-tures of the motor domains of both proteins complexedwith ADP have been solved to atomic resolution (82, 126).The structures of the two motors are very similar to eachother and are composed of an eight-stranded, mostly par-allel P-sheet flanked on either side by three cu-heliceswitha small subdomain composed of a three-stranded P-sheetto one side. The secondary elements of the microtubularmotors were found to overlap with corresponding second-ary structural elements of myosin in the vicinity of thenucleotide binding sites. In particular, seven of the eightP-strands and all six of the major helixes overlap withcorresponding elements in myosin, with a root-mean-square deviation of 3.5 A. Such structural similarity wasunexpected, since there is no discernible homology be-tween the primary sequences. Even more striking was thefinding that there are residues at certain structural sitesthat are conserved absolutely across both families of mo-


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T 1 ^^_July 1997 . - - - - - - - - - - _ -AGlUlVl Y OSlN MECHANCS 677tor proteins. For instance, the switch II glycine of myosin,466, has a counterpart, Gly-234 in the kinesin structure,that is also conserved across al l the kinesin fami ly ofmotors. The highly conserved helix that follows the switchII glycine of myosin also has a counterpart in the microtu-bule motors. In both families of motors, this helix runsfrom the nucleotide region to the junction with the lever(myosin) or putat ive lever (microtubule motors).

Another sequence, Ser-243, Ser-244, Arg-245 in myo-sin, is conserved across both families of motor proteinsand interacts with the nucleotide. In the structure of myo-sin, these three residues are part of a section of the poly-peptide that covers the phosphates, effectively shieldingthem from the solvent, shown in yellow in Figure 1. Inthe kinesin superfamily of motors, the correspondingpolypeptide is located further from the phosphates, pro-viding a much more open nucleotide pocket in which thephosphates are exposed to the solvent. This region is ho-mologous to switch I of the G proteins, where it has beenshown to undergo nucleotide-mediated conformationalshifts (the G proteins are discussed in sect. n5). The ob-servation of such a highly conserved sequence adjacent tothe nucleotide suggests that it is involved in an importantinteraction with the nucleotide and the bound magnesium.The observation that it is found in two different locationsrelative to the nucleotides in the structures of the twodifferent motors suggests that this region may undergonucleotide-induced conformational changes. Differentconformers may have been crystallized in the two differ-ent families.

ity of the microtubule motors is thought to involve highlycooperative interactions between the heads and may con-sist of a hand-over-hand action in which one of the kinesinmotor heads is always attached to the microtubule (144).AIthough the two heads of myosin def inite ly do not coop-erate to remain attached to the actin filament during thecycle as proposed for kinesin (143), the two heads mightalso operate in a sequential mechanism under some cir-cumstances, discussed in section ~~23.The neck region ofmyosin appears to act as a lever arm. The structure ofthe corresponding region in the microtubule motors isnot known, but its primary sequence does not have thecharacteristics expected for a lever arm.

E. Structural Similarity Between Myosinand G Proteins

Although the regions of the kinesin motors that corre-spond to the neck region of myosin are not present in thecrystal structures, their locations, as inferred from thelocations of the COOH-terminal of kinesin or the NH2-terminal of ncd, are both in a region homologous to thelong a-helix which forms the neck of myosin. Thus thechains connecting the catalytic regions to the rest of themolecule have the same geometric relationship to the nu-cleotide pocket in myosin, kinesin, and ncd.

The general secondary structural homology betweenkinesin, ncd, and myosin, and particularly the homologyof certain residues located at funct ionally significant sites,suggests that the two families of motors operate by asimilar mechanism. What does this homology tel l us aboutthe mechanism of myosin? Kinesin motors are known totake 8-nm steps corresponding to the repeat distance be-tween microtubule dimers (3, 63). These steps were mea-sured for two-headed kinesin motors, and the step sizefor a single interaction is not known. There is evidencethat the 8-nm step can be resolved into two smaller steps,suggesting that i t is not the result of a single power stroke(21). The step size for myosin remains controversial, butif it were to be equal to the monomer repeat of the actinpolymer, it would correspond to 5.5 nm, a distance thathas some experimental support. The mechanism of motil-

There is considerable structural similarity betweenthe nucleotide-binding regions of the G proteins and thoseof myosin, ncd, and kinesin (68, 117, 119, 126). The Gproteins act as molecular switches that transduce a signalfrom cell surface receptors to downstream effecterssuch as cyclases (for review, see Ref. 5). The bindingof an activated receptor displaces a tight ly bound GDP.Subsequent bind ing of GTP displaces the receptor. Thisseries of interactions is similar to that which occurs be-tween actin and myosin, with actin promoting the releaseof bound ADP and the binding of ATP releasing the actinfrom myosin. In the GTP state, the G proteins also interactwith downstream effecters. Thus the nucleotide-bindingdomain of the G proteins provides a structure that sensesthe phosphorylation state of the bound nucleotide, di-phosphate or triphosphate, and transmits this informationto a distant interface to affect the interaction with recep-tors and effecters. Conversely, the binding of these pro-teins can affect the interact ion between the G proteinand nucleotide, altering nucleotide affinity and hydrolysisrates. The structural similarity between myosin and theG proteins suggests that the core of the nucleotide-bindingregion of myosin acts in a similar fashion, with two inter-actions being affected, one with actin and one with theneck region.The G proteins have been crystallized in a numberof different nucleotide complexes, leading to a detailedpicture of the conformational changes that are producedby different nucleotide states (reviewed in Refs. 5, 102).These studies have identif ied two regions of the G proteinsthat undergo extensive conforrnational changes uponchanges in the bound nucleotide. These regions have beennamed switch I and switch II. Switch I contains highlyconserved residues that interact with the terminal phos-phates and bound divalent action. Switch II originates ina highly conserved glycine residue followed by an a-helixrunning at a sharp angle to the core B-sheet. When the


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678 ROGER COOKE Volume 77bound guanine nucleotide changes from triphosphate todiphosphate, there is a significant shift and rotation of theloop and a-helix constituting switch II, with more modestchanges occurring in the region of switch I.The structures of the motor proteins in the vicinityof the bound nucleotide are similar to the nucleotide-binding domains of the G proteins (68,82, 119). The nucle-otide pockets of all three families of proteins are com-posed of a P-sheet with cu-helices at specific positionson either side. Both motors contain a conserved glycinefollowed by a loop and a helix, which correspond toswitch II regions of the G proteins. The myosin helix cor-responding to the switch II helix of the G proteins is thelong and very highly conserved helix, shown in orange inFigure 1. A highly conserved region corresponding toswitch I of the G proteins is found in the upper region ofthe catalytic domain of myosin, shown in yellow in Figure1. Four important structural elements common to all threefamilies of proteins form a contiguous region originatingin the four ,&strands that lie under the nucleotide. OneP-strand precedes the P loop. The strand adjacent to thisstrand (above it in Fig. 1) continues into the switch IIregion. The next strand in the sheet is connected to theswitch I region. The strand on the other side of theP-loop strand (below it in Fig. 1) continues into the helixthat lies adjacent to the switch II helix, containing thereactive cysteines in myosin and colored pink in Figure1. Together, these four structural elements probably formthe core of the route of communication between the nu-cleotide and the rest of the molecules.

The very direct structural homology between myosinand the G proteins suggests that conformational changesdriven by the state of the nucleotide in myosin may besimilar to those in the G proteins. Changes between di-phosphate and triphosphate nucleotides drive modestchanges in the conformation of switch I and switch II,which in turn affect the affinities of the G proteins forboth upstream and downstream effecters (5). This wouldsuggest a model in which binding of actin to myosin drivesspatially limited conformational changes promoting therelease of first phosphate and then ADP from myosin andthat the binding of ATP to the binding site causes changesin turn to the switch II region, which promotes release ofactin. In fact, the structural changes seen n the G proteinsresemble those seen in myosin. One region of myosin isobserved to move significantly in the myosin l ADP l AlF4and myosin ADP V04 structures (relative to the myo-sin ADP l BeF, structure). This region includes Gly-466,the highly conserved helix that follows it, and the helixthat lies directly adjacent to this highly conserved helix(37, 131). The direct connection formed between the nu-cleotide site, the actin site, and the interface betweenthe catalytic region and the neck suggests that either thenucleotide or actin could affect this interface, altering theorientation of the neck region. It is also dramatic that the

two switch regions, which are known to move relative toone another in the G proteins, lie on opposite sides of theactin site cleft in myosin. Thus any movement of theseregions in myosin would be transmitted to a region closeto the actin binding site. These homologies suggest thatmyosin could act like a G protein transducing a signalfrom an upstream receptor, actin, to the nucleotide site,and from the nucleotide site back to the receptor. AI-though it is tempting to consider the neck region as adownstream effector, whose orientation is altered, theanalogy here is less clear. As argued in section rvC, thesource of free energy that directly produces the powerstroke comes mainly from the formation of the bond be-tween myosin and actin. The highly conserved helix thatlies at the core of the switch II region forms a clear con-nection between the actin interface and the interface be-tween the catalytic domain and the neck region. Thus theneck region is affected directly by actin, in addition toinfluence from the nucleotide. No equivalent effect hasbeen shown to occur for receptor binding to G proteins.

III . STRUCTURE AND MECHANICS OFDIFFERENT STATES IN THEACTOMYOSIN INTERACTION

The general framework of the kinetic scheme shownin Figure 2 was first proposed by Lymn and Taylor (92),who demonstrated that the binding of ATP to actomyosinrapidly dissociated the proteins, followed by hydrolysis ofthe ATP and subsequent rebinding of a myosin-productscomplex to actin. The energetics of the states and thekinetics of the transitions between them have now beenmeasured in detail in solution and, to a lesser extent, infibers. The mechanical properties of many of these stateshave been probed by measurement of the mechanics offibers and, in particular, of fibers in the presence of nucle-otide and phosphate analogs that populate specific states.A number of reviews have covered the kinetics andenergetics of the actomyosin interaction thoroughlyand should be consulted for a more detailed account(6, 17, 43-45, 53, 132). In particular, Geeves and co-work-ers (43, 44, 133) have presented a model in which thebinding of myosin to actin is a multistep process, involvingfirst a collision complex, followed by two isomerizations.The kinetics and the energetics of the isomerizations arestrongly influenced by the nature of the nucleotide at theactive site. Data obtained from the high-resolution atomicstructures of myosin, from models of the actomyosin com-plex, and from a variety of lower resolution techniquessuch as spectroscopic probes, X-ray diffraction, and elec-tron microscopy have together led to a structural modelof the actomyosin interaction, outlined schematically atthe top of Figure 2. A major goal is to now identify thekineticallv defined states with the structural states. One


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July 1997 ACTOMYOSIN MECHANICS 679such identification is shown in Figure 2 and discussed indetail in sections III and IV.

A. Detached StatesThe binding of ATP to the rigor actomyosin complexleads to a ternary complex followed by rapid dissociationof myosin from actin (92). In the model shown in Figure2, M* ATP represents the complex of myosin and ATP,which occurs directly following the release of myosinfrom actin. The nucleotide is subsequently hydrolyzedwhile the myosin is either detached from actin or isweakly bound to it. There is good evidence that the con-formation of myosin is altered by nucleotide hydrolysis.Low-angle scattering of neutrons and X-rays as well aselectric birefringence have all shown that the structure ofthe myosin head can be altered by bound nucleotides,

with the structure becoming more compact in the pres-ence of bound ADP and phosphate (54, 98, 146). As dis-cussed in section IIC, the structure of the catalytic regionwith ADP l BeF, at the active site, thought to resemble theATP state, is different from that obtained with ADP l VO,at the active site, thought to resemble a transition statein hydrolysis. Low-angle scattering shows little structuralchange between myosin with bound ADP l VO, and myosinundergoing steady-state hydrolysis, in which ADP l Pi isthe predominant state. This shows that the state foundwith bound ADP l VO, is structurally similar to the posthy-drolysis state. Together, these structural studies suggestthat hydrolysis alters the relative orientations of the neckregion and the catalytic domain. Thus the conformationof myosin is depicted in Figure 2 as changing during thehydrolysis of ATP. Before hydrolysis, the orientation ofthe neck relative to the catalytic domain is shown as simi-lar to that found at the end of the power stroke. However,the exact nature of these changes is not known, and thechange proposed in Figure 2, a reversal of the powerstroke, remains hypothetical.The energetics involved in nucleotide hydrolysis havebeen studied in detail. Although the free energy changeoccurring during hydrolysis is not great, calorimetryshows that significant changes occur in the enthalpy andentropy, with an unfavorable change in enthalpy, 83kJ/mol, being compensated for by a favorable change inentropy (79). The magnitude of the energies involvedshows that a significant change in conformation has oc-curred. It is attractive to assume that the conformationalchanges occurring during nucleotide hydrolysis representthe recocking of some springlike elements within the myo-sin head. The power stroke could then be generated by therelease of this spring. Electric fields applied transiently tomyosin have shown that myosin can be distorted and thatthe stiffness associated with this distortion is large, suffi-cient to help drive a power stroke (54). However, as ar-

gued in section IN?, much of the conformational energydriving the power stroke originates from the formation ofthe actomyosin interface, and it is not known how the totalenergy required is partitioned between this process andthe release of a springlike element within the myosin head.

B. Nature of the Pre-Power-Stroke StatesThe catalytic region of myosin binds to actin at thebeginning of the power stroke, states A* M l ATP andA* Me ADP l Pi. The bond between actin and myosin atthis point is weak, and the structures and mechanicalproperties of the cross bridges in these states are onlypartially defined (6, 45, 137). The states A* M l ATP andA l M l ADP l Pi are populated only transiently in active fi-bers. It is important to understand the mechanical proper-ties of these states, because many of them are putative

pre-power-stroke states. Because of their transient nature,these states can best be studied when t,heir populationsare increased. A series of nucleotide analogs or phosphateanalogs, discussed in detail in section IIIC, all appear toalter the cycle in such a way that the two above states,or states that resemble them, are populated at the expenseof force-producing states. Although a considerable bodyof data now characterizes the properties of many of thesestates, a clear picture has not emerged. The data suggestthat in the presence of these analogs, myosin crossbridges are bound weakly to actin in states that resembleA l M l ATP or A l M l ADP l Pi, but that multiple substatesexist for different conditions. In a low-ionic-strength re-laxing solution, cross bridges can bind weakly to actin ina bond characterized by rapid rates for attachment anddetachment (8). It is notable that none of the above states,induced by analogs in the presence of Ca, has beenshown so far to resemble this state. The details of theseexperiments and their interpretation are discussed below.Several analogs produce a triphosphate state. BothGTP and adenosine 5-0-(3-thiotriphosphate) (ATPyS)have low rates for the hydrolysis step; thus the predomi-nant nucleotide state is a triphosphate or thiotriphosphate(25, 148). Fibers activated in ATPyS generate little or notension but have a stiffness that resembles that of activefibers in magnitude and frequency dependence (25). Stud-ies of electron paramagnetic resonance (EPR) probesshow that at least a small fraction (6- 15%)of the catalyticdomains is oriented as in rigor in the presence of ATPyS(30, 122), and our own results show that -20% are ori-ented in GTP (E. Pate and R. Cooke, unpublished data).Additional myosin heads are probably attached to actinbut disordered (2, 122). There is a very rapid disorderingof fluorescently labeled light chain regions upon releaseof caged ATP, at a point before much of the ATP has beenhydrolyzed (1). Thus these ATP-like states suggest thatATP binds to myosin at the end of the power stroke,


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680 ROGER COOKE Volume 77producing a mixture of states, a small fraction of whichhave myosin catalytic domains that are oriented as inrigor and most of which are disordered. The frequencydependence of the stiffness shows that this actin-myosinbond is transitory, with rapid detachment and attach-ments occurring (25). Together, these results show thatthe binding of ATP has greatly weakened the bond be-tween actin and myosin, producing a more disordered andtransitory complex.

The crystal structure of myosin complexed with BeF,is similar to that obtained in the absence of nucleotides,and the position of the BeF, relative to ADP suggestedthat it was likely to resemble the state with bound ATP(37). Fibers activated in the presence of BeF, show com-plete inhibition of force at saturating ligand concentra-t.ions (12). Thus i t would appear that the binding of theseATP analogs produces a dramatic reduction in the affinityof myosin for actin, without greatly altering the structureof the catalytic domain. The results for another analog,PPi, is similar, with lit tle change in the structure of themyosin head (129) and with lit tle change seen in the orien-tation of the catalyt ic domain in fibers, but with a consid-erable change in the affinity of myosin for actin (31, 108,122) It thus appears that the strength of the actomyosinjbond can be changed by many orders of magnitude bymodest changes in the structure of the myosin head andin particular with little change in the conformation of thea&in site cleft. However, some structural changes mustoccur before hydrolysis to account for the lower actinaffinity, and in fact, changes in protein structure are re-ported by the fluorescence of tryptophan or boundetheno-nucleotides (1, 72, 123).

States resembling those that follow ATP hydrolysiscan be selectively populated by addition of the Pi analogs,A1F4, or vanadate (Vi) or by addition of 2,3-butanedionemonoxime (BDM), a small molecule that binds to andst#abilizes the A l M l ADP l Pi state (12, 13, 23, 51, 116, 157).They can also be populated, but to a lesser degree, byadded Pi. Here, the fiber properties depend on both themethod used and the conditions. At lOC, all of theseinhibi t force more than stiffness, suggesting an A* M lADP. Pi-like state that is stiff, and most inhib it velocity,suggesting that they present a drag that slows filamentmotion (12, 13,23). However, at high temperatures Vi doesnot inhib it velocity, and added Pi does not inhibit velocityat any temperature (109, 111). There is no apparent corre-lat ion between stiffness and whether a state exerts a dragthat inhibits filament motion.The orientation of the catalytic domain in theA l M l ADP l Pi-like state remains unresolved. There is evi-dence that myosin heads can bind to actin with eitherordered or disordered catalytic domains, depending onthe conditions. The spectra of spin probes attached toCys-707 show that the states that are stabilized by additionof BDM or AlF4 display complete disorder, while mechani-

cal stiffness remains high (116, 155). In contrast, addedPi causes no loss of order of this domain, which remainsoriented as in rigor (156). The populat ion of pre-power-stroke states can also be enhanced, transiently, after pho-tolytic release of ATP from caged ATP, and the resultsobta ined are compatible with the conclusion that somepre-power-stroke states are ordered. During the rise oftension that followed release of ATP in rigor muscle fi-bers, the orientations of fluorescent probes attached toCys-707 did not change (136). After bind ing of the liber-ated ATP to the myosin head, high concentrations of pre-power-stroke states will be achieved very rapidly. Thusthe rise in force occurs upon the transition from non-force-generating, pre-power-stroke states to force-gener-ating power-stroke states. The lack of a change in theprobe spectra during this transition can be expla ined ifthe probe orientations in some of the pre-power-strokestates and the power-stroke states are the same.

No clear picture has emerged from these data. Thereare probably several weakly bound A l M l ADP l Pi-likestates with different properties. Some of these have or-dered catalytic domains, whereas others have disorderedcatalytic domains. Some provide a drag to filament mo-tion, whereas others do not. The generation of force ap-pears to involve a transition from attached and disorderedmyosin heads to ones in which the catalytic domains arewell ordered on actin (discussed in more detai l in sectionIvA). The observation that the orientation of the catalyticdomain in at least some of these states is the same as thatin rigor at the end of the power stroke suggests that theorientation of this domain does not change during thesubsequent portion of the power stroke. The propertiesof these states are supposedly determined by a shift inthe switch II region, changing the relative positions ofthe upper and lower regions of the catalytic domain, andaltering the actomyosin interface.

C. Release of PhosphateThe transition to a force-generating state, A l M* l ADP,

is produced by the release of phosphate (52, 53). Directmeasurement of free phosphate using a mutant phosphatebinding protein has shown that this step is also the rate-limit ing step in the myofibrillar ATPase cycle (85). Thus thepredominant states in an active fiber are M ADP l Pi andA l M l ADP l Pi, and the states that follow phosphate releaseand precede hydrolysis are together only a small fraction ofthe total. Because these states include the A l M* l ADP andA* M ADP states that are thought to generate tension, itwould appear that this result suggests again that the fractionof force-generating cross bridges is small.Addition of Pi inhibits tension, due to a reversal ofthe Pi release step. Tension inhib ition is linear with log[Pi] as expected from cross-bridge models assuming that


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July 1997 ACTOMYOSIN MECHANICS 681Pi release is involved in the transition into force-generat-ing states (109). Tension can be inhibited by 50%or more,showing that the force-generating states that follow Pirelease account for >50% of the tension generated (76,95,106,109). Measurements of the tension decrease followingrelease of caged Pi show that Pi binding is fast and thatthe transition is complex with the step from low-force tohigh-force states being an isomerization of the proteinstructures that accompanies phosphate release (24, 147).The observation that addition of physiological concentra-tions of Pi can inhibit tension shows that this step is notdriven by a large drop in free energy in an active fiber.In the state that follows Pi release, A l M* l ADP, themyosin head exerts a force on actin at the beginning of thepower stroke. The properties of this state are relativelyuncharacterized due to its transient nature and the lackof analogs that selectively populate it. By extrapolationfrom states that precede and follow it in the cycle, onecan surmise that the catalytic domain is ordered on actin,that the bond between myosin and actin is not as strongas that in rigor, and that the actomyosin complex is in astrained conformation. The free energy of this complexdecreases as one proceeds through the power stroke, andat least some of the free energy liberated is used to pro-duce work. Thus the release of phosphate, which is itselfnot a strongly driven step, acts as a switch that allowsthe myosin head to proceed to force-generating states.D. Nature of the Post-Power-Stroke States

The end of the power stroke in striated muscle isthought to occur at the rigor A* M state. The structureof this state has been studied extensively. The catalyticdomain is attached strongly to actin in a rigid orientationthat cannot be altered by external forces (10,16, 121, 138).The light-chain region is also ordered, although probablyto a lesser degree than the catalytic domain (48, 84). Incontrast to the catalytic region, the orientation of the light-chain region can be altered by an external force (69).Addition of ADP does not change the orientation of eitherregion in skeletal muscle, although it does alter the orien-tation of some probes attached to Cys-707 (10, 32, 136).Addition of ADP does alter the orientation of the neckregion of some other myosins, as discussed in detail insection rv,4.IV. THE POWER STROKEA. Structural Changes

The structural changes occurring in the force-gener-ating states shown in Figure 2 have been studied usinga number of techniques. Both electron microscopy and

X-ray diffraction have shown that there is considerabledisorder in the cross bridges of active fibers, relative toeither rigor or relaxed fibers (57, 66). A variety of probesattached to Cys-707, to nucleotides, or to the light chainshave been studied in active fibers. All of these studiesare complicated by uncertainties in the exact fraction ofmyosin heads that are generating force at any one time.It is clear that a fraction of heads attaches to actin withtheir catalytic domains oriented as at the end of the powerstroke (10, 18, 121, 152). The magnitude of the fraction isvariable, l&30%, at 20C and a crucial question iswhether all of the force-generating heads are containedin it. The fraction of force-generating heads is also contro-versial, but several different approaches (discussed be-low) suggest that it is also in the range of 15-t30%,strengthening the hypothesis that all force-generatingheads have ordered catalytic domains. There is anotherfraction attached to actin with disordered heads, wit,h thesteps leading from non-force- to force-producing statesaccompanied by a disorder-to-order transition in the cata-lytic domain (2, 67, 139). It is not clear whether somedisordered heads can generate tension; however, the cata-lytic domain is rigidly attached to actin during at leastmuch of the power stroke. If the catalytic region does notrotate, another portion of the molecule probably does,and the neck region is the most likely candidate. Probesattached to the neck region report almost total disorderin active fibers so that states must exist with orderedcatalytic domains and disordered neck regions (49, 84).Although this result is compatible with a rotation of theneck region, it does not prove that a rotation occurs. Re-cent studies provide more definitive evidence.The rotation of the neck region during the powerstroke has been supported more directly by the observa-tion that fluorescent probes change their angle duringforce transients of both rigor and actJive muscle fibers(69). The direction of the angular change was different forrigor and active fibers, indicating that t)he average angle ofthe neck region was different in these two states. Theobserved magnitude of the change was small, but thiscould be indicative of a larger change if only a few headsare attached.

Electron micrographs of acto-Sl show that the re-lease of ADP generates a substantial movement of theneck region, with little motion of the catalytic domain(73, 149). This effect was seen with Sl of smooth musclemyosin and a nonmuscle myosin. The orientations ofprobes on the neck region of skeletal muscle or skeletalacto-Sl do not rotate upon ADP release (48). Probes onthe neck region of a smooth muscle Sl do rotate (-20)and the orientation of smooth muscle myosin before ADPrelease resembles hat of skeletal myosin t ADP (47). Thusthe movement seen in the smooth and nonmuscle myosinsprobably represents an additional power stroke, which fol-lows the main power stroke that occurs between the two


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682 ROGER COOKE Volume 77states A l M* l ADP and A l M l ADP, shown in Figure 2. Rota-tion of the neck region upon release of ADP in smooth andnonmuscle myosins provides strong evidence that the neckcan rotate while the catalytic domain remains stationary,a key hypothesis for models of the power stroke in skeletalmuscle. Although the power stroke in skeletal muscle oc-curs in different steps, these observations nonetheless sug-gest that it also involves a rotation of the neck region.

Studies of in vitro motili ty by truncated myosin mole-cules have also lent support to the conclusion that theneck region operates as a lever arm during the powerstroke (89, 90, 142). Extraction of one of the ligh t chainssignificantly reduces the velocity observed in vitro, andextraction of both reduces the velocity to -10% of con-trol. Extraction of the regulatory ligh t chain from skeletalmuscle also reduced velocity, with no effect on tension(105j. If the number of light chains is altered by deletingor adding light chain binding regions to the heavy chain,the velocity generated in vitro is linearly proportional tothe length of the lever arm, with velocity actually increas-ing upon addition of an extra light chain (142 j. Extrapola-tion of the velocity to zero suggested that the fulcrum ofthe lever arm is close to the end of the long helix thatforms the backbone of the neck region, -10 A into thecatalytic domain (142 j. However, this extrapolation alsodepends on the attachment time, which has not been mea-sured in these experiments. A similar fulcrum was alsosuggested by the rotation of the neck seen upon ADPrelease described above. These studies, together withthose described in the preceding paragraphs, show thatthe neck region acts as a lever arm, amplify ing more mod-est conformational changes in the catalytic domain. Therole of the regulatory light chain is more complex, ex-erting a modulatory affect on the activation of skeletalmuscle, and it is interesting to note that substitution of amutant light chain that does not bind calcium greatly in-hibits tension (26 j.

Any structural model of force production, such as theone discussed above, must be compatible with and shouldultimately explain the mechanics of muscle fibers. If thestructural model involving the rotation of the neck regionis correct, then the length of the power stroke is probablysmall. As argued in section vG, the power stroke in musclefibers is followed by a drag stroke, in which actomyosindissociation is occurring. In addition, when fibers arestretched, myosin heads are probably pul led into positionsthat precede the power stroke. The fact that the lever armmust be capable of traversing al l of these regions suggeststhat the power stroke is likely to be short, closer to 5 nmthan to 12 nm. We also argue that a short power stroke iscompatible with current mechanical data.B. Role of the Two-Headed Structure of Myosin

Can the two heads of myosin generate force simulta-neously? The two heads are attached to each other at a

point that is close to the junction of the neck and the rod.It would appear that the connection between the myosinheads would prevent both of them from participating insuch a specific interaction simultaneously. A recent studyhas suggested that the S2 region adjacent to the head maybe capable of unraveling, which would alleviate stericcontraints between the two myosin heads (78). However,even if unraveling occurs in active fibers, it would still begeometrically diff icult for both heads to exert force onthe same filament. One head would be displaced from theother by the 5.5-nm repeat of the actin filament, as wellas by the twist between adjacent monomers in the long-pitch helix, producing a considerable distance betweenthe head-rod junctions of two myosin heads. Although itis sti ll possible that two heads could interact with twodifferent filaments, the simultaneous generat ion of forcewith one filament is unlikely. Direct support for this con-clusion has recently been obtained from measurementsof the force generated by heavy meromyosin (HMM) andby Sl, which are found to be the same, discussed below(104). It is possible, however, that a second head couldbe weakly attached to actin by a flex ible interaction, suchas that postulated to occur between a disordered myosinpolypeptide and the NH,-terminal of actin, whereas thefirst head is involved in a power stroke. Such an interac-tion would promote a very rapid attachment of the secondhead, upon the detachment of the first. Whether this infact happens is highly speculative at this point; however,it is a testable hypothesis. Unfortunately, the best tool forinvestigating this hypothesis, direct measurements of steplengths in vitro, is complicated by thermal fluctuations.C. Energetics

What is the direct source of free energy driving thepower stroke? Ultimately, of course, the energy comesfrom the hydrolysis of ATP; however, hydrolysis does notoccur during the power stroke, and free energy appearsto be shuttled among different forms during the cycle.The two processes that appear to involve large changesin free energy are the formation of tight bonds betweenactin and myosin and between myosin and ATP (see Refs.43, 44 for review). The hydrolysis step involves lit tlechange in free energy. At the beginning of the powerstroke, myosin is bound weakly to actin, and at the endof the power stroke, it is bound tightly to actin, with thisbond being broken by the subsequent tight bond withATP. Hydrolysis of the ATP then breaks the tight bondbetween the nucleotide and the protein and allows thetwo products to be released separately. Neither the re-lease of Pi nor the release of ADP is a strongly drivenprocess in active fibers. Thus myosin goes through a cyclein which it is alternately bound tightly to either actin orto nucleotides. In this regard, the force-generating cycle


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July 1997 ACTOMYOSIN MECHANICS 683of myosin resembles the cycle of the G proteins in whichbinding of an activated receptor releases bound diphos-phates, with binding of triphosphates releasing the re-ceptor.One energetically significant process that accompan-ies the power stroke is the formation of a tight actomyosininterface. The strength of the actomyosin bond increasesduring the passage from A l M l ADP l Pi to A l M. The areaburied by the formation of the actomyosin interface iscompatible with a large change in free energy (62), andthe efficiency of muscle contraction would require thatmuch of this free energy be used to perform mechanicalwork. The exact loss in free energy that occurs in thistransition from A* M l ADP l Pi to A* M depends on boththe relative actomyosin affinities of these two states andon their relative populations. More free energy can beobtained in a transition from a highly populated state toa state with a lower population. Although the relativepopulations can only be estimated approximately, it islikely that the end of the power stroke, which is depopu-lated by the rapid binding of ATP, has a smaller populationthan found at the beginning, providing an even greaterfree energy loss.It thus appears that the direct source of much ofthe free energy driving the power stroke comes from theformation of the actomyosin bond and probably also fromthe relative populations of the states involved, which areproduced in part by the tight binding of ATP. Alternatively,free energy could be released from some strained confor-mation of the myosin head. This strained conformationcould have been generated by the structural changes seenin myosin during ATP hydrolysis, discussed above; how-ever, the energetic changes associated with these transi-tions are not known.If the major source of the free energy driving thepower stroke comes from the formation of the actomyosininterface, how does the transduction process occur? Theformation of this interface involves the burial of a largehydrophobic area. The removal of hydrophobic residuesfrom the solvent is driven entropically, not enthalpically.Measurements of the heat evolved using calorimetry showthat the change in enthalpy upon formation of the actomy-osin bond is in fact positive, +25 kJ/mol (134). Thus thisprocess is driven forward not by changes in the internalenergy of the system, which are unfavorable, but by thefact that it is going from a less probable to a more proba-ble state. If such a process does mechanical work, thefirst law of thermodynamics requires that the work bepaid for by a corresponding change in the internal energyof the system. In entropically driven processes, the workis produced by capturing a thermal fluctuation. In thecontext of the actomyosin interaction, one can imaginethe following possible sequence. Myosin binds loosely toactin, possibly via flexible bonds. The transition to astronger bond involves extension of an elastic element.

The extension of the element is driven by a thermal fluc-tuation, which is captured by the formation of the strongerbond. The solution must cool off by an amount equal tothe work done in extending the elastic element. Relax-ation of the elastic element provides mechanical workwhen the filaments slide past one another. The tight bondis subsequently released by the binding of ATP. Heat isgenerated in this and in other steps so that net heat isreleased during the cycle, satisfying the second law ofthermodynamics, and allowing the cycle to be driven inthe forward direction.It is likely, as argued below, that the events outlinedabove occur several times during a power stroke. Thefrequency of thermal fluctuations decreases exponentiallywith their magnitude so that distributing the energy of thepower stroke into several steps will greatly increase therate with which the steps can occur. The effect of subdi-viding a power stroke, driven by thermal fluctuations, intoseveral steps was discussed by Huxley and Simmons (65).More recently, the rate at which a particle, constrainedby a damped spring, can diffuse to a potential energy ofmagnitude E has been considered by Howard (63), follow-ing an equation formulated by Kramers (81). A particle ofradius 5 nm, constrained by a medium with the viscosityof water and by a spring with a force constant 1 pN/nm,will stretch the spring reaching a potential energy of 10kT in a time of 1.2 ms (k is Boltzmann constant and T istemperature; 1 kT = 2.5 kJ/mol at 300K). This is a reason-able approximation for the diffusion of either the catalyticdomain or the neck region of myosin. The time is suffi-ciently rapid that it could easily be accommodated in theprocesses associated with development of tension, whichoccur in a few milliseconds following a step change inlength, discussed below. However, the time required in-creases steeply with the energy, as exp (EM")IJE/kT).The time required to diffuse to an energy E of 15 Wwouldincrease to -200 ms, far too long to play a role in forcegeneration. The free energy available from ATP is 22 kT,and the high efficiency of muscle would require that alarge fraction of this, -15 kT, is converted to work. Thiscannot be accomplished in a singe step if it is driven bya thermal fluctuation but could be easily carried out intwo steps.D. Summary

The structural and energetic data discussed abovesuggest a model in which a short power stroke is executedby a single myosin head, involving a large rotation of theneck region driven by more subtle conformationalchanges in the catalytic domain. The immediate sourceof energy driving this rotation comes largely from theformation of a stronger bond between actin and myosin.Because this process is driven entropically not enthalpi-


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684 ROGER COOKEtally, much of the mechanical work is paid for by thermalfluctuations, captured by the formation of the actomyo-sin bond or by the subsequent myosin-ATP bond. Therelationship of this model to the mechanics of active mus-cle and single motors is discussed in section v.

coated surfaces, the step size was estimated to be 5 nm.The duty ratio, defined as the fraction of the mechanicalcycle devoted to force generation, was estimated to besmall, - 5%.

B. Force Generation Measured In VitroV. STEADY-STATE MECHANICS OFACTOMYOSIN INTERACTION

Skeletal muscle provides an excellent system formeasuring the mechanics and energetics of the actomyo-sin interact ion. One can measure the force, the work per-formed, as well as the energy consumed al l as a functionof velocity. The transient responses to either force orlength define important aspects of the kinetics of cross-bridge mechanical function. However, the macroscopicnature of this preparation has disadvantages as well asadvantages, and extrapolation of the data to conclusionson the interactions of individual proteins has been diffi-cult. Data obtained from in vitro assays complement thoseobtained from skeletal muscle fibers. Here the force anddisplacement produced by single motors acting on singleactin filaments eliminate many of the ambiguities of thefiber system where one can measure only the propertiesof a large ensemble. However, problems with these assaysalso exist. Brownian motion plays a significant role, par-ticularly in the measurement of displacement. Compli-ance, within both the filaments and the attachment to theapparatus, presents a fundamental problem in both fibersand the in vitro measurements (91). Nonetheless, a combi-nation of results obtained from fiber mechanics and singlemotors has provided a reasonable def inition of the me-chanics of the actomyosin interaction, discussed in moredetail in sections VA-vH.

A. In Vitro Assays of Filament VelocitiesMyosin or myosin fragments, attached to a glass sur-

face, can interact with fluorescently labeled actin fila-ments, translating them at velocities approaching that ob-served in vivo. The observation of filament motion gener-ated by Sl demonstrated that the contractile machineryis contained within the myosin head and an actin filament,ruling out theories that had involved other structures,such as the myosin rod (140). Although not essential forfunction, the myosin rod could s till play some role inthe generation of motion, since the velocity of filamenttranslation by Sl is slower than that of myosin or HMM(140). This assay was further refined to measure the veloc-ity of actin filaments translated by single HMM fragments(143). The velocity, which was -5% of that obtained withmany HMMs, could be used to estimate the step size. Withthe assumption that the ATPase act ivity of the single HMMis similar to that measured from the high-density HMM-

More recently, two methods have been developed formeasuring both the force and step length of single motors.The first of these was a powerful synthesis of physicsand biology, which used optical traps to measure andmanipulate single molecules (35). The second has in-volved the use of micro-needles, which have sufficientflex ibil ity to act as force and displacement transducers(71). Optical traps manipulate micron-sized objects usingthe force generated by changes in the momentum of pho-tons that have been diffracted by the objects. This tech-nique was the first to be used to measure the force anddisplacement generated by single actomyosin interac-tions. A single actin filament was attached at either endto latex beads, whose position could be manipulated bya pair of traps. The actin was next positioned close to athird, immobilized bead that was sparsely coated withmyosin. This apparatus could be employed in two modes.1) If the stiffness of the traps was low, the displacementof the beads due to an actomyosin interaction could bemeasured. These results are discussed in section vD. 2) Ifthe stiffness of the traps was high, using feedback controlof the tweezers positions to immobilize the filament (iso-metric conditions), the magnitude of the force could bemeasured. Finer et al. (35) measured distinct force tran-sients generated by a single myosin molecule interactingwith a single actin filament (see Fig. 3; Ref. 35). A rangeof forces from 2 to 6 pN was found, with an average of-3-4 pN. Similar measurements were made using flexiblemicro-needles, whose displacements, and thus the forceexerted, could be measured accurately. Yanagida and co-workers (71) attached an actin filament to a micro-needleand measured the force generated upon interaction with amyosin filament that was aligned in the correct orientation.They found a range of forces from 4 to 10 pN with anaverage of 6 pN. Because the force generated is expectedto depend on the relative orientations of the myosin mole-cule and the actin filament, it is likely that suboptimalforces due to misaligned proteins are measured in the ex-periments, in which the proteins were not correctly aligned.Thus the force measured for correctly aligned proteinsshould equal the maximum force obtained using unalignedproteins. This is approximately what is observed, sug-gesting that the maximum force generated by a single acto-myosin interact ion is of the order of 5-10 pN.In most models of the actomyosin interact ion, theforce is thought to be high near the beginning of the powerstroke and to be low at the end of the power stroke. Two

Volume 77


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July 1997 ACTOMYOSIN

Az

6a4

0 0.5 1.0 1.5 TiK (s) 2.5 3.0 3.5 4.0B I6.

0 0.5 1.0 1.5 Ti rAtif 2.5 3.0 3.5 4.0

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Force (pN)FIG. 3. Single force transients near isometric cond itions with 2 mM

ATP (A), 10 ,xM ATP (B), and 1 PM ATP concen trations (0. Top tracein each record shows force in directions along actin filament, whereasbottom trace shows force on bead in perpendicular direction. D: distribu-tion of single force amplitudes obtained from data at various ATP con-centrations are shown at bottom. [From Finer et al. (35). Reprinted withpermission from Nature. Copyright 1994 Macm illan Magazine Lim ited.]

groups have attempted to measure the force generated bysingle motors as a function of the displacement. Onefound that the force varied linearly, as if the attachedmyosin head acted like a simple Hookean spring (34). Thesecond found that the force remained high over much ofthe range of displacements, falling to zero only near theend of the power stroke (153). Thus the dependence offorce on displacement remains undefined.

More recently, Molloy et al. (104) measured the forcegenerated by a single myosin head, Sl. This force wasequal to that generated by a two-headed fragment of myo-sin, HMM; however, the average value of the forces gener-ated by either species, 1-2 pN, was lower than measuredby other workers. They found peak forces up to 3-4 pNfor both the one-headed and two-headed snecies. These

MECHANICS 685results show that the previous results, al l obtained withtwo-headed myosin species, were not measuring a forcethat was the sum of both heads, supporting the conceptthat the two heads do not generate force at the same time.

AI1 of these measurements may be influenced by com-pliance in the system (note: compliance is the inverse ofstiffness). Compliance will allow a myosin head that hasattached to a filament at the beginning of the power stroketo then traverse a portion of the power stroke beforemechanical equilibrium is reached. The compliance of thein vitro systems discussed above is large compared withthat of cross bridges in active muscle, showing that com-pliance exists within the system, probably in the attach-ments of the proteins to the beads or needles. In somemodels of cross-bridge action, an attached myosin headacts like a spring, exerting a force that is maximum at thebeginning of the power stroke and decreases linearly tozero at the end of the power stroke. Compliance wouldmake it diff icul t to measure the maximum force exertedat the beginning of a power stroke, because very fewmyosin heads that attach to the filament would remainat the beginning of their power strokes. Thus the forcesmeasured in the in vitro systems may underestimate thosein active fibers.

C. Force Generated in Isometric MuscleThe force generated by a myosin head measured in

the in vitro assays can be compared with that of musclefibers under similar conditions. The data of Finer et al.(35) were obtained using rabbit myosin at 21C whereasIshijima et al. (71) worked at a slightly higher temperatureof 27C. At 21C glycerinated rabbit muscle fibers producea force close to 0.2 N/mm2, with a greater force found atthe higher temperature, 0.3 N/mm2 (52, 111). The concen-tration of myosin in glycerinated rabbit fibers has beendetermined to be 220 PM (94). Thus a single half-sarco-mere with an area of 1 mm would contain 1.6 X 1011myosin heads, leading to an estimate of the average forceof 1.2 pN/head at 21C. This value is considerably smallerthan the value measured in the in vitro assays, suggestingthat only a small fraction of the myosin heads are generat-ing force at any given t ime in an isometric fiber. However,the comparison of this number with the one obtained invitro for single myosins depends on several assumptions.These involve how the force varies with the position inthe power stroke and what port ion of the power strokeis being sampled in different experiments. If the maximumforce observed in the in vitro assay corresponds to theforce generated by correctly aligned myosin heads and ifthis force exists over much of the power stroke, then theobserved maximum force at 21C of -5-6 pN/head wouldsuggest that a rather smaller number of myosin heads isproducing force at any one time in the isometric fiber, on


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ROGER COOKE Volume 778630

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20z?5 15ss!LL IO

however, their interpretation was different. They sug-gested that thermal fluctuations could account for muchof the observed range. In their analysis, thermal fluctua-4 HMM tions within the system provide relatively large excursionsN s

between the myosin head and the actin filament withwhich it is interacting. Attachment of the myosin head tothe filament during these excursions allows the myosin

5

0-15 -10 -5 0 5 10 15 20 25 30

DisplacementFIG. 4. Frequency distribution of amplitude of discrete single dis-

placem ents generated by Sl and by heavy meromyosin (HMM). Valuesobtained for sma ll displace ments were estimated by increase in systemstiffness when a myosin head attached to actin. [Data replotted fromMolloy et al. (10351

the order of 20--Z%. If, however, the force per interactionis even larger, -10-12 pN, as argued below to accountfor both the length of the power stroke and the efficiencyof muscle contraction, the fraction of force-generatingheads would be smaller, -10%. There could of coursebe attached heads that were not generating force so thatthe total fraction of attached heads would be larger,-2O-25%.D. Length of Power Stroke Measured In Vitro

In the absence of feedback, the laser trap system canbe used to measure the distance traversed in a singleinteraction (35). Discrete displacements could be ob-served when a single actin filament was positioned closeto a myosin-covered bead. The magnitude of the stepsspanned a range from 5 to 15 nm, with an average stepdistance of 11 nm. Displacements could also be observedin the position of a micro-needle, providing a somewhatlonger step distance ranging from 10 to 20 nm (71). Thesemeasurements were all made on two-headed myosin spe-cies.The measurements of displacement encounter moretechnical difficulties than do measurements of tension.The trap stiffness must be low, to permit the motor toproduce a translation. In this mode, the actin filamentis held only loosely by the trap and its thermal motionincreases. The presence of thermal motion will influencethe measurements. Molloy et al. (104) measured the dis-placements generated by both single-headed and double-headed myosin fragments. Like the previous investigators,they found a large range of displacements (see Fig. 4);

to trap a thermal fluctuation in position. This would pro-vide a wide distribution of apparent stroke lengths cen-tered at the actual stroke length. To measure more of thedistribution, it is necessary to measure displacements thatare within the noise of the signal. These displacementscould be detected by using the variance of the signal asa measure of whether a myosin head was attached tothe actin filament. When a head attached, the variancedecreased, i.e., the fluctuations in position were dampedout. By observing the variance, Molloy et al. (104) mea-sured displacements that were too small to produce asignal that was above the noise. When the displacementsproduced by all these events were plotted, they produceda broad distribution that was centered on 3-4 nm for asingle-headed myosin fragment (data replotted in Fig. 4).It might be noted that this shorter displacement is morecompatible with the structural studies discussed aboveand with results of several other approaches as discussedin section vE. A similar plot was constructed for singleHMM molecules interacting with an actin filament. Herethe distribution is even broader than that for Sl (see Fig.4). With all of the data considered, the distribution iscentered on -5-8 nm. This value is a little greater thanthat found for Sl, and the range of displacements extendsto higher values than found for Sl.This technology has now been pushed one step fur-ther by Mehta et al. (97). When a small tension is appliedto the two beads that are attached to either end of theactin filament, the fluctuations of the beads become corre-lated, i.e., they tend to move together. When a myosinhead attaches to the intervening actin, this correlation isinterrupted, providing a clear signal that the myosin hasattached. With the use of this signal, the entire range ofdisplacements produced by HMM was measured, provid-ing a step length of 4-5 nm.In summary, the length of the power stroke has beendifficult to define. The initial studies showed that a myo-sin head can execute a single displacement with a lengthof 5-15 nm, and multiple strokes or strokes of muchgreater length, inferred from other experiments, werenot seen. Fluctuations in the position of the actin fila-ment influence the results, and more recent measure-ments, along with an analysis of the data, suggest thatthe length of the power stroke is close to 5 nm, a distancecompatible with the structural models proposed above.This value may underestimate the true step size due tomisalignment of the myosin heads relative to the actinfilament.


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July 1997 ACTOMYWJINE. Duty Cycle for Active Myosin Heads

A comparison of the force generated in situ in fiberswith that measured in vitro provides one method for esti-mating the fraction of time that myosin spends generatingforce, known as the duty cycle. The duty cycle is relatedto another parameter of the actomyosin interaction: thefraction of myosin heads attached to actin. The fractionof myosin heads attached to actin has been measured bya variety of techniques, in both isometric and shorteningfibers and in the in vitro filament translation assays. Thefraction of myosin heads that are attached to actin pro-vides an upper limit on the duty cycle, because the frac-tion generating force must be smaller than the fractionattached. Interpretation of a variety of experiments de-pends crucially on the size of the force-generating frac-tion, including the results obtained from the spectra ofspectroscopic probes and from fiber mechanics. For in-stance, the rapid regeneration of the power stroke follow-ing a step decrease in length could be more easily ex-plained if the force-generating fraction is small (87).Estimates of the fraction of myosin heads attachedto actin in isometric fibers vary widely. Fiber stiffness hasoften been used as a measurement of attachment, and thestiffness of active fibers is 75% of that of rigor fibers (46).A high fraction of attached heads is also inferred fromthe spectra of some fluorescent probes (10). In contrast,the fraction of ordered probes seen in EPR spectra is only15-20%, suggesting that only a small fraction of myosinheads are oriented on actin (18, 33, 121). Several aspectsof the X-ray diffraction patterns, notably the lack of alarge increase in the intensities of the actin-based layerlines, are also more easily explained if the attached frac-tion is low (67). Binding to actin protects a certain regionof myosin from proteolysis, and in active fibers, 25% ofthe heads are protected (28).There are uncertainties associated with the interpre-tation of each of the measurements discussed above. Twofactors act to make fiber stiffness overestimate the frac-tion of attached heads. A combination of EPR spectros-copy, to measure the fraction of heads attached, and fibermechanics has suggested that myosin attached by onehead is as stiff as a myosin that has both heads attached(31,108). If, as argued above, both heads of myosin cannotgenerate tension at the same time, all attached crossbridges consist of a single attached myosin head. Withthese two factors taken into account, the observation thatthe stiffness of active fibers is 75% that of rigor fibers(46) would imply that only 37% of the myosin heads areattached. Compliance of the thin filaments could alsocause stiffness to further overestimate the fractionattached, discussed in more detail in section WL On theother hand, stiffness would miss attached heads that hadslack attachments to the thick filament. The fraction oforiented spectroscopic probes probably underestimates

MlWHANlW

the fraction of attached myosin heads, because someattached heads have disordered probes. Proteolysis is per-haps one of the least ambiguous measures of attachment,and the value obtained from it, 25%, ies within the rangedetermined by the other techniques (15-20%, EPR probes) (28). It is also close to the esti-mate obtained by extrapolation from shortening fibers.The fraction of time that a myosin head is attachedto actin during active shortening can be estimated know-ing the velocity, the ATPase activity, and the length of thepower stroke. Here we discuss results obtained at lowervelocities where it is likely that a great majority of myosinheads split ATP (22, 61, 83). In fibers shortening veryrapidly, it is possible that some heads undergo powerstrokes that are detached mechanically without splittingATP, and these results are considered in section vF. Curtinet al. (22) measured the ATPase activity of living frogmuscle shortening at 0.3 muscle lengths/s, finding a valueof 1.12 mmol ATP split l g-l l s-l. Not all of this ATP ishydrolyzed by myosin, and measurements of energy con-sumption as a function of sarcomere length show that40% of the isometric energy consumption at rest length isdue to other processes, such as calcium pumping (29). Inshortening muscle, the hydrolysis rate of the actomyosininteraction increases so that 85% of the observed hydroly-sis can be attributed to actomyosin. Using the adjustedrate of ATP hydrolysis and the myosin head concentrationin living frog fibers of 280 mM, one can calculate that eachhead on average turns over one ATP in -300 rns. Thetime that the head is attached to actin during this 300 mscan be calculated assuming that it is equal to the lengthof the power stroke divided by the velocity. Assuming apower stroke length of 10 nm, one finds that the myosinhead remains attached to actin in a single power strokefor a duration of 28 ms, providing an estimate of the dutycycle close to 10%. If the length of the power stroke isonly 5 nm, the duty cycle will be cut in half, to 5%. Ineither case, the duty cycle calculated for muscles drivenat a rather moderate velocity is found to be small. Datafrom the sliding filament assayssuggest that the duty cycleof the myosin head interacting with an actin filament atmaximum contraction velocity is also small, on the orderof 5% (143).

To extrapolate the data obtained under active short-ening to isometric conditions, the relative number ofattached heads in the two conditions must be estimated.These relative populations can be estimated by assumingthat the stiffness of active cross bridges in isotonicallyshortening fibers is equal to that in isometric fibers. Thestiffness of the muscle shortening at 0.3 lengths/s is -60%of that under isometric conditions (40, 74). If 10% of themyosin heads are attached in active fibers at this velocity(assuming a power stroke length of 10 nm), the compari-son of stiffness would suggest that -17% of the crossbridges are attached in isometric fibers. About one-half


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688 ROGER COOKE Volume 77this number would be attached assuming a shorter powerstroke length of 5 nm. As discussed above, there is goodexperimental support for a power stroke length of -5 nm,suggesting that -10% of the myosin heads are generatingtension in an isometric fiber at any given time.

The above estimates of the fraction attached aremodel dependent. They require an assumption about thelength of the power stroke, and an extrapolation to iso-metric fibers relies on stiffness as a measure of the num-ber of the attached myosin heads. The extrapolation fromisotonic to isometric fibers also rests on an assump-tion on the coupling between the mechanical cycle andATP hydrolysis. If one assumes that at a velocity of 0.3lengths/s some myosin heads attach to actin but do notsplit ATP, then the extrapolation of isotonic to isometricrequires revision, with a proportionately greater duty cy-cle for the isometric fibers. This correction is unlikely toexceed a 50% increase, as discussed in section vF. In spiteof these uncertainties, within the range of reasonable as-sumptions, al l of these estimates of the duty cycle forisotonic contractions and for isometric fibers are low,with a range of values of 5-- 10% for fibers shortening at0.3 lengths/s and lo-25% for isometric fibers. Thus, forthe fiber preparations considered here, amphibian musclefibers at 0C it would appear that the duty cycle in bothisotonic and isometric contractions is small.

F. Coupl ing Between Force Generationand ATP Hydrolysis

Is the myosin cycle tightly coupled to the hydrolysisof ATP, e.g., is one ATP split for each force-generatinginteract ion? The structural studies discussed above sug-gested that myosin and actin went through a cycle ofevents driven by the hydrolysis of one ATP. Although thismost probably does occur at low and moderate velocities,there is good evidence that as the velocity increases, myo-sin heads can undergo multiple cycles per ATP hy-drolyzed. The question of coupling has been studied bothin the in vitro assays and in muscle fibers. In these experi-ments, three parameters are measured: the filament veloc-ity, the rate of ATP turnover per myosin head, and thetime each head spends attached on average to actin duringone ATP turnover. Knowing these three parameters, onecan calculate the distance traversed by a myosin headwhile attached to actin during the splitting of one ATP.This distance could be termed an interaction distance, todifferentiate it from the power stroke distance, which isthe distance traversed during one force-generating inter-action.

These three parameters were estimated in assays offilament velocity in which myosin, attached to a substrate,translated actin filaments (see Ref. 11 for review). Thefraction of myosin heads attached to an actin filament at

any given time could not be measured dire

RCooke-1997-500 Myosin Molecules Per Filament

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