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© 2014.PublishedbyTheCompanyofBiologistsLtd|JournalExperimentalBiology(2014)217,2825-2833doi:10.1242/jeb.099127 *Author ([email protected]) for correspondence AB T2N1N4,Canada. Kinesiology,Human Performance Lab, Calgary, Faculty of Calgary, University of and energy requirementsofeccentriccontractionspredicted byhis muscle activationandforceproduction), realizedthiswhenforces (the currentparadigmforthemolecularmechanismunderlying Huxley, whofirstformulatedthecross-bridgetheoryofcontraction production (Huxley, 1957),eccentriccontractionsarenot.Andrew described andexplainedbycurrenttheoriesofmuscle force contractions (muscleisactivelyshortening)arereasonably well by gravityaswewalkdownthestairs. produces forcesthataresmallerthantheactingonmuscle are activetocontrolthemovement,butonlyadegree that example, whendescendingasetofstairs,ourkneeextensormuscles anomaly, theyoccurduringmosteverydaymovements.For muscle. Althougheccentriccontractionsmaybethoughtof as an acting onamusclearegreaterthantheforcesproducedby activation, eccentriccontractionsoccurwhentheexternalforces an activemuscleisstretched.Becausemusclestendtoshortenupon Eccentric musclecontractionsaredefinedasinwhich , enhancement, Instability, Poppingsarcomerehypothesis, KEY WORDS:Cross-bridgetheory, Eccentriccontraction,Force eccentric musclefunction. by providingevidenceoftitin’s contributiontoactiveforcein model anddemonstratetheadvantagesofthree-filament function. Here,Iidentifytheproblemsoftwo-filamentsarcomere filament cross-bridgemodelinisometricandconcentricmuscle simultaneously notaffecting thepropertiespredictedbytwo- the unexplainedpropertiesofeccentricmusclecontraction,while , althoughnotfullyproven,wouldaccountformanyof muscle. Thisroleoftitinasathirdforceregulatingmyofilamentin length, thusincreasingitsstiffness andforceuponstretchofactive binding sitesfortitinonactin,therebyreducingtitin’s free-spring stiffness, andcross-bridgeattachmenttoactinisthoughtfreeup activation, titinbindscalciumatspecificsites,therebyincreasingits () andactiveforce-dependentmanner. Uponmuscle sarcomeres byadjustingitsstiffness inanactivation-dependent evidence, thatathirdfilament,titin,isinvolvedinforceregulationof observations ineccentriccontractions.Here,Isuggest,andprovide contracting muscle,ithasfailedmiserablyinexplainingexperimental explaining thepropertiesofisometricallyandconcentrically While thistwo-filamentsarcomeremodelhasworkedwellin the interactionbetweencontractilefilamentsactinandmyosin. been thoughttooccurexclusivelythroughtherelativeslidingofand Muscle contractionandforceregulationinskeletalmusclehave Walter Herzog* The roleoftitinineccentricmusclecontraction COMMENTARY Introduction ABSTRACT While isometric(constantmusclelength)andconcentric of activelylengtheningmuscles. evolved tolimitdamage,andexplainsomeofthesurprisingfeatures with eccentricmusclecontractions,thespecialfeaturesthathave Here, Iwillattempttodiscusssomeofthedifficulties associated difficult fieldforinvestigationthatwillholdanumberofsurprises. describe thateccentricmusclecontractionscompriseawideand processes thattakeplaceduringshortening.’ Hethenwentonto and furtherthat‘thesespecialfeatureshavelittlerelationtothe allow thiselongationtotakeplacewithoutdamagingthemuscle’ and that‘Iimaginespecialfeatureshavebeenevolvedwhich active muscleissomethingthathappensinverymanymovements’ contractions, Huxley(Huxley, 1980)statedthat:‘Elongationsof book ‘ReflectionsonMuscle’,whilediscussingeccentric 1938; AbbottandAubert,1951;JoumaaHerzog,2013).Inhis theory vastlyexceededtheexperimentallyobservedvalues(Hill, bridge actionand musclecontractionaredescribed bymodelsthat 20 stateshavebeendescribed intheliterature,commonlycross- stretches orreleases.Although cross-bridge modelswithmorethan the advantagethatitcouldexplain forcetransientsfollowingquick states (HuxleyandSimmons,1971). Thismultiple-statemodelhad adapted byAndrewHuxleyand extendedtomultipleattachment bridge actionlikelyinvolved rotation (Huxley, 1969),aconcept attached andonedetached.HughHuxleythenproposedthatcross- The theoryproposedin1957hadtwocross-bridgestates, one (ATP), oneATP percross-bridge cycle. partially byBrownianmotionandthehydrolysis of filaments. Theseinteractionsbythecross-bridgesweredriven on thethinfilaments,therebypullingpast thick filaments thatinteractcyclicallywithspecificattachmentpoints uniformly arrangedsideprojections(cross-bridges)onthe thick (Huxley, 1957).Histheorywasbasedontheideathatthereare sets offilamentswassupposedtooccur:thecross-bridgetheory mathematical frameworkofhowthisrelativeslidingthe two years later, AndrewHuxleythenprovided thefirstmolecularand the relativeslidingofthickandthinfilaments(Fig. Rather, theysuggestedthatmusclecontractionoccurredthrough they argued independentlythatthickfilamentsdidnotshorten. (Huxley andNiedergerke, 1954;HuxleyandHanson,1954)where published theirseminalworkontheslidingfilamenttheory activation (Huxley, 1953),andheAndrewHuxleythen hinted attheideathatthickfilamentsdidnotshortenupon thereby producingmuscleactivation.However, HughHuxley thought toundergo calcium-inducedshorteningatspecificpoints, long myosinfilamentsthatwerealignedinstrands causing muscleshorteningandforceproduction.Specifically, the configuration intoacoil-like thick, A-bandfilamentstobetransformedfromahelix-like (calcium release)causedthemyosinfilamentsthatcomprise filaments inthecentreofsarcomeres.Itwasthoughtthatactivation force productionwereassociatedwiththeshorteningofthick Prior tothe1950s,ithadbeenassumedthatmuscleactivationand Mechanisms of contraction Mechanisms of Fg 1 (Fig. ), thereby

1). Three 2825

The Journal of Experimental 2826 2). binding site)(Rayment etal., 1993) (Fig. hydrolysis) andthreeattached (ADP·P, ADP andemptynucleotide have approximatelyfivestates: twodetached(pre-andpost-ATP COMMENTARY muscle lengthonthespeedofcontraction. Muscle propertythatdescribesthedependenceofmaximalforceatoptimal on thelengthofmuscle. Muscle propertythatdescribesthedependenceofmaximal,isometricforce An elongated,multinucleatedcell. connective tissue,theperimysium. Segment ofmusclescontainingfibresthatisenclosedbyadistinct activated. An eccentricmusclecontractionisoneinwhichstretchedwhile muscle length. of musclefunctioninwhichisometricforcedecreaseswithincreasing The descendinglimboftheforce–lengthrelationshipdescribesregion contraction. A concentricmusclecontractionisoneinwhichshortensduring relative slidingofactinpastmyosinthatisdrivenbythehydrolysisATP. that cyclicallyattachtospecificbindingsitesonactin,therebyproducinga contraction occursthroughtheinteractionofmyosin-basedcross-bridges The currentparadigmofmusclecontraction.Itstatesthat to actininacyclicmanner. sidepieceemanatingfromthethick()filamentthatattaches state inthecross-bridgecycle. Inhibits cross-bridgesfromgoingtheweaklytostronglybound limb oftheforce–lengthrelationship. muscle andintroducedthenotionofinstabilityondescending Muscle physiologistwhopopularizedtheforce–velocitypropertyofskeletal length. muscle functioninwhichisometricforceincreaseswithincreasing The ascendinglimboftheforce–lengthrelationshipdescribesregion description ofthecross-bridgetheoryin1957. Muscle physiologist(1917–2012)whoformulatedthefirstmathematical andmyosin,poweredbyATP. Force inmuscleproducedthroughtheinteractionofcontractilefilaments filaments. Contractile proteininthesarcomerecomprisingmaincomponentofthin titin. Immunoglobulin domainoftitinoccurring attheproximalanddistalendsof theory in1953. Muscle physiologist(1924–2013)whofirstdescribedtheslidingfilament A. V. Hill Ascending limb A. F. Huxley Active force Actin Glossary Ig domain H. E.Huxley Force–velocity relationship Force–length relationship Fibre Fascicle Eccentric lengthening Descending limb Concentric shortening theory Cross-bridge Cross-bridge Butanedione monoxime active musclestretching. Muscle propertyassociatedwiththeincreaseinpassiveforcefollowing connective tissuestructuresonthefibre,fascicleandmusclelevels. structural proteintitinonthemyofibrillarlevelandalsobycollagen-based Force inmusclenotrequiringenergy(ATP) andprimarilyproducedbythe with actin. A uniquesequencewithintitinthoughttobeapossiblebindingsitefor thick filament. Contractile proteininthesarcomerecomprisingmaincomponentof Long muscleproteinsinsarcomeres,suchasactin,myosinandtitin. A sub-cellularorganellecomprisedofseriallyarrangedsarcomeres. Protein bandinthemiddleoftwohalf-sarcomeres. muscle lengthdoesnotchange. Without changeinlength;anisometricmusclecontractionisonewhich Protein bandattheendofasarcomere. attachment siteonactininthecross-bridgetheory. The distanceofthecross-bridgeequilibriumpositiontonearesteligible Regulatory proteininsarcomeres. Regulatory proteininsarcomeres. line totheM-band. Structural proteininsarcomeresspanningthehalfsarcomerefrom Z- . Sarcomeric contractilefilamentconsistingprimarilyofactin,troponinand Sarcomeric contractilefilamentconsistingprimarilyofmyosin. the relativeslidingoftwocontractileproteinsactinandmyosin. Theory ofcontractionthatsupposesmuscleoccursthrough Smallest structuralunitofcontractioninskeletalmuscle. isometric force. following activemusclestretchingcomparedwiththecorrespondingpurely Muscle propertythatdescribestheincreaseinsteady-stateisometricforce for smallchangesinlength. muscle functioninwhichisometricforceremainsthesame,andismaximal, The plateauregionoftheforce–lengthrelationshipdescribes lysine residues. A uniquesequencewithintitinthatisrichinproline,glutamate,valineand many experimentally observedphenomena extremelywell, the mechanismsofcontraction forthepasthalfcentury. Itpredicts PEVK region PEVK region Passive forceenhancement Passive force N2A region Myosin M-band/line Isometric Z-line/band ‘x’ distance Tropomyosin Titin filament Thin filament Thick Sliding filamenttheory Sarcomere Residual forceenhancement Plateau region The cross-bridgetheoryhasbeen theparadigmforexplaining The JournalofExperimentalBiology(2014)doi:10.1242/jeb.099127

The Journal of Experimental Biology COMMENTARY Walcott andHerzog,2008).Bydefinition,theseratefunctionsare thermodynamically consistentratefunctions(Howard,2001; and/or biochemicalcross-bridgestatesthatareconnectedby 2008). history-dependent propertiesofmuscles(Walcott andHerzog, al., 1985),andtheycannotexplainexperimentallyobserved energy efficiency ofeccentriccontractionsaccurately(Woledge et cross-bridge modelshavedifficulties predictingtheforceand contractions areincreased(AbbottandAubert,1952).Classic requirement isdecreased,andforcesfollowingeccentric with isometricorconcentriccontractions(Hill,1938),energy with avarietyofuniqueproperties.Forceisincreasedcompared Active lengtheningofmuscle(eccentriccontraction)isassociated the nextsection. Woledge etal.,1985).Someofthesefailureswillbediscussedin properties ofeccentricallycontractingmuscles(Pollack,1990; but failstopredictsomeofthebasicandgenerallyaccepted particularly thoseinvolvingisometricandconcentriccontractions, Eccentric muscle contractions Z-band B Actin filament Myosin filament A Actin filament Myosin filament Cross-bridge modelscanbethoughtofasaseriesmechanical Soleus A Equilibrium position of M-site PEVK x Thick filament(myosin) A-band N2A

C M-line Actin 12 PEVK 5 Thin filament(actin) release ADP +ATP observed observations,buthasyettobeprovencorrect. mechanisms, andproposeasolutionthatexplainsallhitherto surrounding residualforceenhancement,identifycompeting explanation. Below, Iwillattempttosummarizetheobservations bridge thinking,anditsmolecularoriginshaveeludedsatisfactory muscle physiologists,asitdefiesexplanationwithcurrentcross- residual forceenhancement(Edmanetal.,1982)hasintrigued corresponding forcesnotprecededbystretching.Thisso-called active musclelengtheningareincreasedcomparedwiththe and uniformlyobserved,thatthesteady-stateforcesfollowing of thecontractilehistory. However, itisgenerallyacknowledged, all history-dependencedisappearsandmuscleforceisindependent a shorttransientphasefollowingmuscleshorteningorstretching, in thedirectiontowardsZ-line(Fig. attachment siteclosesttothecross-bridge’s equilibriumposition compressed), whileitsnearestattachmentsiteisdefinedasthe elastic elementhaszeroforce(itisneitherstretchednor position isdefinedasthelocationatwhichcross-bridge’s attachment siteonactin(Fig. of across-bridge’s equilibriumpositiontoitsnearesteligible exclusively basedonHuxley’s so-called‘x’ distance,thedistance intermediate Transient cleft closure Pi release Hydrolysis Titin Initiate stroke power I-band The JournalofExperimentalBiology(2014)doi:10.1242/jeb.099127 4 3 Z-band to ADP. phosphate releasedfromATP whenATP ishydrolysed permission). Pi,inorganicphosphate,i.e.thefree and theactinattachmentsite.(Adaptedprintedwith based ontheatomicstructureofcross-bridgehead proposed byRaymentetal.(Raymental.,1993) (Huxley andSimmons,1971).(C)Cross-bridgemodel cross-bridge headandmultipleattachmentstates state. (B)1971cross-bridgemodelwitharotating 1957) withtwostates,anattachedandadetached cross-bridge modeldescribedbyA.Huxley(Huxley, Fig.

.Threeclassiccross-bridgemodels. 2. manner. (cross-bridge attachment)-dependent in anactivation(calcium)-andforce and ,changesitsstiffness passive forceinisolatedsarcomeres the sarcomere,providesmostof which stabilizesmyosininthecentreof and theadaptablemolecularspringtitin, filament) andmyosin(thickfilament), with thecontractileproteinsactin(thin Fig.

2A). Thecross-bridge’s equilibrium

.Schematicfigureofasarcomere 1.

2A).Therefore, following (A) First 2827

The Journal of Experimental Biology 2828 in musclefibres eitheratcoldtemperaturesortreated withthecross- bridges. However, findingsofincreasedresidualforceenhancement with asubstantialincreasein theproportionofattachedcross- 2005), suggestingthatforceenhancement islikelynotassociated marginally increased(SugiandTsuchiya, 1988;RassierandHerzog, either unchangedfromisometric referencecontractionsorjust evaluated musclestiffness intheforce-enhancedstate,stiffness was et al.,1981).However, inthefewstudies thatsystematically associated withacorrespondingincreaseinmusclestiffness (Ford of attachedcross-bridges,thenresidualforceenhancementwould be the two). increasing theaverageforcepercross-bridge(oracombination of by increasingtheproportionofattachedcross-bridges,or(2) by theory, therearetwowaystoincreasecross-bridgebasedforces:(1) between actinandmyosinfilaments.Accordingtothecross-bridge caused byanincreasedforcetransmissionthecross-bridges Force enhancementfollowingeccentricmuscleactioncould be engagement ofpassivestructuralelements. limb oftheforce–lengthrelationship,andthirdwith uniformities) whenmusclesareactivelystretchedonthedescending development ofstructuralnon-uniformities(sarcomerelengthnon- the activeforceproducingcross-bridges,secondwith three basicideashaveemerged. Thefirsthasbeenassociatedwith mechanism forforceenhancementhasnotbeenidentified.However, with forceenhancement,aconvincingandgenerallyaccepted on forceenhancement,andagreementthepropertiesassociated and Aubert,1952).Despiteanabundanceofconsistentobservations eliminated instantaneouslywhenamuscleisdeactivated(Abbott increase inpassiveforce(HerzogandLeonard,2002),canbe (Morgan etal.,2000;Herzog2012a),isaccompaniedbyan descending thantheascendinglimbofforce–lengthrelationship of thespeedstretch(Edmanetal.,1982),isgreateron of stretch(Edmanetal.,1982;Herzog2006),isindependent of muscles(Herzogetal.,2012c),itincreaseswiththemagnitude residual forceenhancementhasbeenobservedatallstructurallevels 3).This corresponding forceforapurelyisometriccontraction(Fig. the steady-stateforcefollowinglengtheningwillbegreaterthan When amuscle,fibre,myofibrilorsarcomereisactivelylengthened, trace representstheforce-enhancedstatefollowingactivestretchingofasinglesarcomere. passive stretchwhiletheblacktraceisanactiveofamyofibril.Finally, forceandlength,whiletheblack inC,thegreytraceisisometricreference ThegreytraceinBisa the isometricreferenceforceandlength,whileblacktracesrepresentenhancedstatesfollowingthreestretchmagnitudes. greytraceinAisolated myofibriland(C)inasingle,mechanicallysarcomere.Notealsothepassiveforceenhancement(PFE)(A,B).The represents Fig. COMMENTARY Cross-bridge mechanismforforceenhancement Residual forceenhancement If forceenhancementwascausedbyanincreaseintheproportion

.Forceenhancementonthreestructurallevelsofskeletalmuscle. 3.

Δ Muscle Force (N) length (mm) 10 20 40 60 0 5 0 0 A Time (s) 5 FE PFE 10

Sarcomere Stress length (μm) (nN μm–2) 100 150 200 250 2.4 3.4 50 0 0 BC 20 (A) Forceenhancement(FE)inanentiremuscle(catsoleusat37°C),(B) Time (s) with theoreticalconsiderations(Walcott andHerzog,2008). cannot beexplainedeasilywithcross-bridgeaction,inaccordance unlikely. Therefore,itappearsthatresidualforceenhancement this scenariohasnotbeenscientificallyeliminatedbutishighly their originallengthtoaccountforsuchanincreaseinforce.Again, cross-bridges wouldneedtobeextendedalmostthreetimesof shown toaverage285%insinglesarcomeres(Leonardetal.,2010), rather unlikely. Furthermore,becauseforceenhancementhasbeen proposal thatcannotbefullyrejectedatthistime,butseems remain attachedforminutesfollowingactivemusclelengthening,a this ideaisratherunlikely, exceptifoneproposedthatcross-bridges without theconfoundingeffects offatigue(Leonardetal.,2010)], is longlasting[minutesinmyofibrils,wherethiscanbetested cross-bridges remainsconstant.Becauseresidualforceenhancement average forcepercross-bridgewhiletheproportionofattached without acorrespondingincreaseinstiffness. be expectedtoresultinanincreasecross-bridge-basedforce (Rassier andHerzog,2005;Lee2008a),whichwould part byaconversionofweaklytostronglyboundcross-bridges experimental circumstances,forceenhancementmightbecausedin bridge inhibitorbutanedionemonoximesuggestthatinthose and theireffects onforceenhancementwere insofarappealingas al., 1996). on thedescendinglimbofforce–length relationship(Allingeret static, ratherthanthedynamic, evaluation ofthestiffness of muscles the apparentsofteningbehavior ofmusclewasanartifactthe relationship (Rassieretal.,2003a; Rassieretal.,2003b),andthat perfectly stableonthedescendinglimbofforce–length range. Inthemeantime,ithasbeenshownthatsarcomeres are presumed softeningbehaviorofmuscleonthatpartitsworking relationship (Hill,1953;Gordonetal.,1966)becauseof the thought tobeunstableonthedescendinglimbofforce–length from theproposalthatmusclesegmentsandsarcomeres were 4).Thisideaoriginated limb oftheforce–lengthrelationship(Fig. uniformities duringactivemusclelengtheningonthedescending uniformities, specificallythedevelopmentofsarcomerelength non- enhancement wasassociatedwiththedevelopmentofstructural non- For morethanthreedecades,theprimarymechanismfor force Structural non-uniformitymechanismforforceenhancement 40 Force enhancementcouldalsobecausedbyanincreaseinthe The ideaofdevelopmentsarcomere lengthnon-uniformities 60 PFE The JournalofExperimentalBiology(2014)doi:10.1242/jeb.099127

Sarcomere Stress length (μm) (nN μm–2) 100 200 300 2.4 3.4 0 0 Time (%) 50 FE 100

The Journal of Experimental Biology COMMENTARY might produce the observedresidualforceenhancement observed that thedevelopmentofhalf-sarcomere lengthnon-uniformities sarcomere lengthsthatmatter but thehalf-sarcomerelengths,and 2010). isometric referenceforcesbyalmost afactorofthree(Leonardetal., in singlesarcomeresandproduced forcesthatexceededthe sarcomeres (Leonardetal.,2010);and(4)forceenhancementoccurs Herzog, 2008b),myofibrils(Joumaaetal.,2008a)andsingle (Abbott andAubert,1952;Schacharetal.,2002),fibres(Lee and forces attheplateauofforce–lengthrelationshipinmuscles forces intheenhancedstatecaneasilyexceedmaximalisometric Morgan etal.,2000)andsingle fibres(Petersonetal.,2004);(3) force–length relationshipsinmuscles(AbbottandAubert,1952; enhancement hasbeenobservedontheascendinglimbof the force-enhanced butalsointheisometricreferencestates;(2) force that sarcomerelengthnon-uniformitiesarepresentnotonlyin the isometric referencecontractions(Joumaaetal.,2008a),suggesting similar orsmallernon-uniformitiesthanthecorrespondingpurely more stable(Edmanetal.,1982)sarcomerepropertiesandwith forces intheenhancedstatehavebeenfoundtobeassociatedwith predictions above,thefollowingobservationshavebeenmade:(1) residual forceenhancement.Specifically, regardingthefour limb oftheforce–lengthrelationshipisnotamajorcontributorto uniformities duringactivemusclelengtheningonthedescending studies, suggestingthatthedevelopmentofsarcomerelengthnon- uniformity theoryhavebeenrejectedbyfindingsinexperimental non-uniformities todevelop. definition, multiplesarcomeresarerequiredforsarcomerelength (4) forceenhancementcannotoccurinasinglesarcomere,asby isometric forcesattheplateauofforce–lengthrelationship;and 1953)]; (3)forcesintheenhancedstatecannotexceedmaximal sarcomeres arestableinthatregion(Gordonetal.,1966;Hill, on theascendinglimbofforce–lengthrelationship[as reference contractionsarenot;(2)forceenhancementcannotoccur development ofsarcomerelengthnon-uniformitieswhileisometric predictions arethat:(1)forceenhancementisassociatedwiththe following activelengthening.Themostimportantofthese could beusedtomaketestablepredictionsaboutmusclebehavior sarcomere lengthnon-uniformitytheoryforforceenhancement the frameworkofcross-bridgetheory. Furthermore,the this mechanismcouldexplainforceenhancementperfectlywithin et al.(Gordonal.,1966)withpermission. descending limbandtheplateauregionindicated. Fig. In recentyears,ithasbeen argued thatmaybeitisnot the All fourofthesebasicpredictionsthesarcomerelengthnon-

.Sarcomereforce–lengthrelationship,withtheascendingand 4.

Force (%) 100 50 0 3.65 0 Ascending 1.27 limb Sarcomere length(μm) 1.70 2.00 Plateau region 2.20 Descending Adapted fromGordon limb explain thisevasiveproperty. force–length relationship,thusalternativetheoriesmustbefoundto muscles areactivelystretchedonthedescendinglimbof contraction, ratherthanaspecialeventthatonlyoccurswhen uniformities appeartobeanormalproductofanymuscular half-sarcomeres. Sarcomereandhalf-sarcomerelengthnon- residual forceenhancementisatruepropertyofsarcomeresand and seriallyarrangedhalf-sarcomerepreparations,suggestingthat enhancements ofseveral100%havebeenobservedinsarcomere can berejectedbasedonexperimentalevidence.Furthermore,force enhancement basedonthesarcomerelengthnon-uniformitytheory stretching. contractions andforisometricfollowingactivemuscle expect thiscontributiontobethesameforpurelyisometric uniformities weretocontributeforceproduction,onewould feature ofeccentriccontraction.Therefore,ifsarcomerelengthnon- are aregularoccurrenceofmusclecontractionandnotspecial 2008a), indicatingthatthehalf-sarcomerelengthnon-uniformities enhanced states,asshownpreviouslybyothers(Joumaaetal., more pronouncedinthereferencecomparedwithforce- contractions, therawdataplotssuggestthattheywereequally, ifnot were notsystematicallyevaluatedintheisometricreference importantly, however, althoughhalf-sarcomerenon-uniformities accounted forbythehalf-sarcomerelengthnon-uniformities.More percentage oftheforceenhancementcouldtheoreticallybe and 50%[seefig. associated forceenhancementswereshowntobeapproximately20 sarcomeres andforce-enhancedmyofibrils,respectively, butthe thus expectedincreaseinforce)of~1.3and8.8%forsingle associated withanincreaseinactin–myosinfilamentoverlap(and enhanced state.Thesehalf-sarcomerelengthnon-uniformitiesare 12 Rassier showedmaximalhalf-sarcomerelengthnon-uniformitiesof major contributortoresidualforceenhancement(Rassier, 2012). myofibrils, itwasargued thathalf-sarcomerenon-uniformitywasa experimental workonhalf-sarcomeredynamicsinisolated 2008a), thuseliminatingthatpossibility. However, inrecent compared withthepurelyisometricreferencestate(Joumaaetal., sarcomere non-uniformitiesaresmallerintheforce-enhanced isolated myofibrilpreparationssuggeststhatifanythingatall,half- However, measurementofhalf-sarcomerenon-uniformitiesin consistently infibreandmusclepreparations(Campbell,2009). contractile actinandmyosin. includes titinasa‘contractile’ proteinworking intandemwiththe enhancement, andthenpropose anewmodelofforceregulationthat observations oftitinasthe origin ofpassiveandtotalforce structural role.Inthenextfew paragraphs,Iwilldiscussthe a roleinmusclecontractionthat goesbeyonditspurelypassive (Herzog etal.,2012b;Herzog al.,2012c),andthattitinmightplay contribute substantiallytothetotalresidualforceenhancement might originateinthestructuralproteintitin(Fig. enhancement wasasarcomericproperty. We suggested thatthisPFE et al.,2007),indicatingthatthispassivecomponentof force single-fibre andmyofibrilpreparations(Joumaaetal.,2008b; Lee enhancement’ (PFE;Fig. and Leonard,2002).Thisobservationwastermed‘passive force component thatpersistedwhenthemusclewasdeactivated(Herzog enhancement inthecatsoleuswasassociatedwithapassive In 2002,HerzogandLeonardmadetheobservationthat force Passive mechanismforforceenhancement In summary, thefourmajorpredictionsregardingforce nm insinglesarcomeresand70 The JournalofExperimentalBiology(2014)doi:10.1242/jeb.099127 9 inRassier(Rassier, 2012)],thusonlyatiny

3A,B) andwassubsequentlyobservedin

nm inmyofibrilstheforce-

1), thatitmight 2829

The Journal of Experimental Biology 2830 COMMENTARY passive forcesthree tofourtimesgreaterthan passivelystretched eliminated, andwefoundthat activelystretchedmyofibrilshad active, actin–myosin-basedcross-bridge forceswerecompletely actin–myosin filamentoverlap (~3.8 concentration) tolengths(6–7 actively (highcalciumconcentration) andpassively(lowcalcium stretched, weelongatedsinglemyofibrils fromrabbitposasmuscles muscle isactivelystretchedcomparedwithwhenitpassively enhancement wasneeded. mechanism explainingtheentiremagnitudeofresidual force muscle lengthening(Herzogetal.,2006).Therefore,anadditional merely afractionoftheenhancedforcesmeasuredfollowingactive increases intitinstiffness and forceobservedinthesestudieswere in skeletalmusclecontraction(Herzogetal.,2012c).However, the This isamechanismthatcouldexplainresidualforceenhancement thereby increasingitsstiffness, andthusitsforcewhenstretched. suggest thatuponactivation,titinbindscalciumatspecificlocations, relevant amountsofcalcium(DuVall etal.,2012).Allthesestudies in titinrequires~20%moreforcethepresenceofphysiologically (Joumaa etal.,2008b).Finally, weshowedthatIgdomainunfolding eliminated throughdepletionoftroponinCfromtheactinfilaments passive forcesinmyofibrilswhichcross-bridgebasedwere was confirmedwhencalciumactivationshowntoincrease et al.,2003).Thisinitialresult,performedinskinnedmusclefibres, titin’s stiffness, andthusitsforcewhenmusclesarestretched(Labeit titin bindscalciumuponmuscleactivationandthatthisincreases beyond itspassiveforcecontributioncamewhenitwasshownthat spring length.Thefirstconvincingevidenceforaroleoftitin changing itsinherentstiffness, or(2)byshorteningitsfunctional molecule, canalteritsstiffness inessentiallytwoways:(1)by 2012a; Kellermayeretal.,1997).Titin, like anyotherspring in titiniseffectively prevented(Granzieretal.,1997;Herzog at longsarcomerelengthsifimmunoglobulin(Ig)domainunfolding properties atshortsarcomerelengths(Kellermayeretal.,1997)and upon stretch. that isengageduponmuscleactivationandproducesincreasedforce Herzog, 2004),allpropertiesthathintatapassivestructuralelement muscle immediatelyprecedingstretch(Leeetal.,2001;Rassierand (Edman etal.,1982),anditispartlyoffset byactiveshorteningof (Edman etal.,1982),itisindependentofthespeedlengthening increases withincreasingamountsofactivemusclelengthening enhancement (Noble,1992),asthemagnitudeofforce had alreadybeensuggestedasacandidateforresidualforce muscle forceregulation.EvenpriortoourdiscoveryofPFE,titin 1987). Therefore,titinseemsuniquelyplacedtoplayarolein filaments inthecentreofsarcomeres(HorowitsandPodolsky, becomes weak,andprovidesstabilitytosarcomeresmyosin based forces,becomesstrongwhencross-bridgeforce (Herzog etal.,2012a),isarrangedinparallelwiththecross-bridge passive forcedependsdirectlyonsarcomereandmusclelength in skeletalandcardiacmuscle(Horowits,1992).Finally, titin’s myofibrils (Linke,2000),andasubstantialamountofpassiveforce provide approximately90–95%ofallpassiveforceinsingle band region(Kellermayeretal.,1997).Titin isalsoknownto the otherend(Fig. sarcomeres insertingintotheZ-bandatoneendandM-line initially purelyintuitive.Titin isalongfilamentthatspanshalf- a likelycandidateforthisproperty. Thereasonsforthischoicewere Leonard, 2002),wesoonfocusedonthefilamentousspringtitinas In ordertoidentifythetrueincreaseinpassiveforcewhen a Titin isanentropicspringmoleculewith virtuallyelastic Following thediscoveryofPFEinskeletalmuscles(Herzogand

1), withknownspring-likepropertiesintheI- μm persarcomere)muchbeyond μm persarcomere)where 3.8 μm myofibrils beyondactin–myosinfilamentoverlap(lengthsgreaterthan obtained withslowstretches(0.1 μm Fig. et al.,2012)have beenproposed(butbyno meansproven)as titin ontoarotatingthinfilament (Monroyetal.,2012;Nishikawa (Fig. Binding oftitintoactinattheN2A regionornearthePEVK length, thusincreasingitsstiffness andforcewhenstretched. actin uponforceproduction,thereby reducingtitin’s freespring that titin’s proximalregions(thoseclosetotheZ-band)attach this latterforceincreaseisachieved,butthesimplestexplanation is production increasestitin’s stiffness dramatically. Itisnotclearhow binding uponactivation,andthatcross-bridge force whose stiffness, andthusforce uponstretch,isincreasedbycalcium when maximumcross-bridgeforceswereallowed(Fig. stretching werealsoreducedtoapproximatelyhalfofthoseobtained approximately halfofmaximum,thepassiveforcesuponmyofibril is activelystretched.Finally, whenreducingtheactiveforcesto required toincreasethetitin-basedpassiveforceswhenamyofibril stretched muscle,andthatsomehow, cross-bridgebasedforcesare is justasmallpartoftheenhancedforceobservedinactively (result notshown),supportingtheideathatcalciumbindingtotitin ‘actively’ and ‘passively’ stretchedmyofibrilstoafewpercent butanedione monoximereducedtheforcedifferences between stretching) butinhibitingcross-bridgeattachmentsthrough myofibrils inahighcalciumconcentrationsolution(active differences (LeonardandHerzog,2010).Stretchingthesame myofibrils, indicatingthattitinwasindeedresponsibleforthese any forcedifferences betweenactivelyandpassivelystretched reduced passiveforcestoafewpercentoforiginalandeliminated 5).Eliminationoftitinfromthesepreparations myofibrils (Fig. Leonard etal.(Leonardal.,2010),withpermission]. filament overlapislostandonlypassiveforcesarepossible[adaptedfrom shaded areaindicatestheregionofsarcomerelengthswhereactin–myosin indicates theregionwhereactinandmyosinfilamentsoverlap;non- production ispossibleinthesemyofibrilpreparations.Theshadedarea further thatoncetitin’s functioniseliminated,neitherpassivenoractiveforce increase inforcetheabsenceofactin-myosinbasedcross-bridges.Note overlap) thanthepassivelystretchedmyofibrils,indicatingasubstantial myofibrils havemuchgreaterpassiveforces(beyondactin–myosinfilament was eliminatedbyshortexposuretotrypsin.Notethattheactivelystretched depleted referstopassiveandactivemyofibrilstretchingwhentitin’s function overlap. Passivereferstomyofibrilsthatwerestretchedpassively. Titin are smallbecauseofsubstantial(~70%)lossactin–myosinfilament myofibrils werefullyactivatedat~3.4 stretched whilefullyactivated.Halfforcereferstoexperimentsinwhich Combined, theseresultssuggestthattitinisamolecularspring

.Myofibrilforce(stress)asafunctionofsarcomerelength 5. Force (nN μm–2) 1) (Herzogetal.,2012b;Herzog etal.,2012c)orwindingof 100 200 300 400 500 600 700

sarcomere 0 2 The JournalofExperimentalBiology(2014)doi:10.1242/jeb.099127 − Titin depleted Passive Half force Active 1 2.5 ; non-shadedarea). Sarcomere length(μm) 3 μm

s

− sarcomere 3.5 1 Active referstomyofibrilsthatwere sarcomere − 4 1 where activeforces − 1 ) ofsingle 4.5

5). 5

The Journal of Experimental Biology COMMENTARY paradigm isregulatedbythreesarcomericproteins,actin,myosin regulation, stiffness andenergetics foreccentricmusclecontractions. isometric andconcentriccontractions,butalsoexplainsforce to thecross-bridgetheory, notonlyexplainsforceregulationin an inherentlynewparadigmofmusclecontractionthat,incontrast predictions oftheoldparadigm(Kuhn,1962).Here,Iamproposing far unexplainedphenomenawhilemaintainingthesuccessful paradigm. Thenewparadigmneedstoexplainawholeseriesofthus existing scientificparadigmwithanewandmorepowerful A revolutioninscienceisdescribedasthereplacementofan that haveescapedaconsistentmolecularexplanation. and incorporatesallfindingsintheareaofresidualforceenhancement concentric, isometricandmostimportantlyineccentriccontractions, contrast toallcross-bridgemodels,itcanpredictmusclepropertiesin production thatneedsrigoroustesting,ithastheadvantagethat,in a proposalfornewmechanismofmusclecontractionandforce force-regulating propertiestothesarcomere.Althoughthisismerely traditional cross-bridgetheory, butaddstitinasathirdfilamentwith passive forceregulationinskeletalmusclethatincorporatesthe actively contractingmuscles. possible mechanismsforforceandstiffness modulationoftitinin production muscle andforce contraction of forProposal anewtheory A B I-band Instead oftwocontractileproteins,actinandmyosin,forceinthis In thislastsection,Iwillproposeapossiblemodelforactiveand Z-line hc iaet Thinfilaments Thick filaments stretch Active Calcium Z Initial position A-band M-line Actin Titin Myosin Passive stretch 0 1 C . . . 4.5 3.5 2.5 1.5 Normalized force Sarcomere length(μm) Initial position Calcium A ctc t iiv v a t iio FE Fg 6). (Fig. specific bindingsitesandbind(atahithertounknownsite)toactin to attachactinfilaments,butalsowillcausetitinbindcalciumat In thethree-filamentmodel,activationnotonlycausescross-bridges requirement ofeccentriccontractions. the residualforceenhancementanddecreasedenergy many phenomenaobservedineccentricmusclecontraction,suchas concentric musclecontractions,andaddsasimpleexplanationto regulation canexplainallexperimentalobservationsinisometricand Specifically, thefollowingthree-filament theoryofmuscleforce active forceconditions(LeonardandHerzog,2010b)(Fig. beyond actin–myosinfilamentoverlapunderpassiveandvarious (Leonard andHerzog,2010b)observedinmyofibrilsstretched support fromcross-bridge-dependentincreasesintitinforce attachment hasnotbeendemonstrateddirectly, buthasstrong Herzog, 2010b).Selectivebindingoftitinuponcross-bridge stiffness andthusitsforcewhenstretchedactively(Leonard and selectedIgdomainsoftitin(DuVall etal.,2012),increasetitin’s such astheE-richregioninPEVKdomain(Labeitetal.,2003) upon cross-bridgeattachment.Calciumbindingtoidentifiedregions, as aspringthatbindscalciumuponactivationandtoactin on actinandaredrivenbyATP hydrolysis(Huxley, 1957),titinacts via myosin-basedcross-bridgesthatcyclicallyattachtospecificsites and titin.Whileactinmyosinplaytheirusualroleinteract The three-filamentmodelofmusclecontraction o n Passive Calcium bindingtoactinhasbeenidentifiedforatleasttwo force stretch Active The JournalofExperimentalBiology(2014)doi:10.1242/jeb.099127 FE, forceenhancement. occurs thatwilldeterminewheretitinbindstoactin. on theinitialsarcomerelength,whereactivation passive forcecurveuponactivationdependscrucially reduction oftitin’s free-spring length.Theshiftofthe because ofthecalciumbindingtotitinand passive (titin-based)forceincreasesuponactivation force–length relationships.Notethatinthismodel,the stretched passively. (C)Activeandpassivesarcomere stretched activelycomparedwithwhentheyare even moretitin-basedforcewhensarcomeresare stiffness totheremnantfree spring,therebyadding upon activation,providinganadditionalincreasein Simultaneously, calciumbindstospecificsitesontitin sarcomere lengthisshortthanwhenlong. stretch fortheremnantfreespringwheninitial distal site(longinitiallength),thusexperiencingmore at amoreproximal(shortinitiallength)or lengths, respectively(toppanel),titinwillbindtoactin sarcomeres areactivatedfirstattheshortandlong (middle panel;passivestretch).If,however, the sarcomere lengthandpassiveforceisthesame from thesetwoinitialconfigurations,the and along(right)initiallength.Ifpassivelystretched panel wehavetwo(half)sarcomereswithashort(left) including titinasaforce-regulatingprotein.Inthetop panel). (B)Schematicproposalofmusclecontraction illustration ofthethree-filamentsarcomere(bottom sarcomere isolated(middlepanel)andaschematic micrograph ofasinglemyofibril(toppanel)with filament besidesactinandmyosin.(A)Electron incorporating titinasthethirdforce-regulating Fig.

.Proposednewmodelofmusclecontraction 6. 2831

5).

The Journal of Experimental Biology sarcomeres with usefulforcecontributions. decrease, therebyallowing for agreaterworkingrangeof increases inforcewhentheactin–myosin-based cross-bridgeforces limb oftheforce–lengthrelationship. Third,itwouldprovide it wouldprotectmusclesagainst muscleinjuriesonthedescending force state(Butleretal.,2001)at essentiallynoenergy cost. Second, which connectsmyosinwithactin andestablishesalong-lasting mechanism ofmolluscanmusclebythetitin-likeproteintwitchin, role, therefore,mightbesimilartothatobservedinthe catch at virtuallynoenergy costin eccentriccontractions.Titin’s active little resistance,whileprovidinggreatpassive(titin-based)resistance threefold. First,itwouldallowforpassivemuscleelongationagainst muscles andassociatedproperties.Theprimaryexamples are implications foractiveandpassiveforceregulationinskeletal of titintoactiveforceproductionwouldalsohavesomeintriguing stability ofmyosininthecentresarcomere. the descendinglimbofforce–lengthrelationship;and(4) the contraction; (3)thestabilityofsarcomeresandmusclesegments on stretching; (2)theenergetic efficiency ofeccentric muscle residual forceenhancementobservedfollowingactivemuscle the followingobservationswouldhaveareadyexplanation:(1) unaccounted propertiesofskeletalmusclecontraction.Forexample, dependent mannerisconfirmed,itwouldexplainseveral in thelaboratoryofDrNishikawaatNorthernArizonaUniversity. through ongoingtitinsegmentlabelingworkinourlaboratoryand needs carefulstudy, butwilllikelybeknownwithinthenext3 (Nishikawa etal.,2012;Herzog2012b;2012c), multiple locationsoroccursinanaltogetherdifferent way where thisbindingoccurs,andwhethercanoccurat However, iftitinindeedbindstoactininaforce-dependentmanner, long half-sarcomere,andthuswillproduceagreatertitinforce. spring titinsegmentsisgreaterfortheinitiallyshortthan stretched activelytothesamelength,stretchofremnantfree- initially longhalf-sarcomere.Therefore,ifbothhalf-sarcomeresare to actinfortheinitiallyshorthalf-sarcomerecomparedwith will haveattachedatamoreproximal(closertotheZ-line)location the twohalf-sarcomeresarestretchedactively(bottomrow),titin and theforcetransmittedbytitinissameaswell.However, if the elongationoftitinforbothinitialsarcomerelengthsissame, stretched (notitinbindingtoactin)acertainlength(middlerow), passive (left)andalong(right)half-sarcomere.Ifpassively with anactin,myosinandtitinfilamentareshownforashort 2832 spring length,andthegreatertitin’s stiffness andforceuponstretch. to actin.Themoredistalthistitinbindingsite,theshorterfree- transmitted bytitinwilldependprimarilyonthebindingsiteof comes atvirtuallynoadditionalenergy cost.Theactualforce stiffness intitinwillresultanincreasedforceuponstretch,which activation (calcium)alone.Foreccentriccontractions,theincreasein the presenceofcross-bridgeforcesbutnotin bridge binding,thusallowingtitin’s free-springlengthtoshortenin tropomyosin freeuptitinbindingsitesonactinuponstrongcross- a mechanismwherebytheregulatoryproteinstroponinand (Leonard andHerzog,2010b)],apossibleexplanationmightinclude actin–myosin-based force[ratherthanjustcalciumactivation titin’s contributiontoactiveforcerequirescross-bridgebindingand been experimentallyverified 2013), whilebindingoftitintoactinuponforceproductionhasnot al., 2003),andspecificimmunoglobulindomains(DuVall etal., parts oftheprotein,E-richportionPEVKregion(Labeitet COMMENTARY However, asidefromtheseproperties,the proposedcontribution If theproposaloftitin’s forceregulation inacalcium-andforce- Fig. 6 illustratesthisscenario.Inthetoprow, twohalf-sarcomeres in situ.However, becauseweknowthat

years ezg .A,Load .R,Jna .adHro,W. Herzog, and A. Jinha, T. R., Leonard, J.A., Herzog, il A.V. Hill, A. Panchangam, and M. DuVall, V., Joumaa, T., Leonard, W., Herzog, T. R. Leonard, and M. DuVall, W., Herzog, D.E. Rassier, and E.J. Lee, W., Herzog, and TheCanadaResearchChairProgramme. Sciences andEngineeringResearchCouncilofCanada,TheKillamFoundation W.H. isfundedbytheCanadianInstitutesofHealthResearch,Natural The authordeclaresnocompetingfinancialinterests. rnir . elrae,M,Hle,M n rmiá,K. Trombitás, and M. Helmes, M., Kellermayer, H., Granzier, ezg .adLoad T. R. Leonard, and W. Herzog, X.M. Aubert, and B.C. Abbott, X.M. Aubert, and B.C. Abbott, convincing explanationfordecades. sliding filamenttheories(AbbottandAubert,1952),buthaseluded been identifiedpriortotheformulationofcross-bridgeand explanation fortheresidualforceenhancement,apropertythathas (passive) resistancethatcomesatnoextra(energetic) cost,andan against littleresistanceandelongationofactivemusclegreat decreases atlongmusclelengths,elongationofpassive system (titin)whenforceintheother(actin-myosin) muscle withsomeelegantproperties:anincreaseinforceforone adds athirdmyofilament,titin,tothecontractilemechanism. is thatitincorporatesandassertsthecross-bridgetheory, andmerely than afullyestablishedtheory. However, thebeautyofthisproposal skeletal muscles(Fig. proposed hereforcontractionmechanismsandforceregulationin regulation willneedfurtherelucidation,andthusthemodel (calcium)-dependent manner. Themoleculardetailsofthisforce now acceptedthattitincanchangeitsstiffness inanactivation and althoughtitin’s roleisbynomeansunderstoodindetail,it enhancement, westumbledacrosstheforce-regulatingroleoftitin, studying oneoftheseunexplainedproperties,residualforce properties ofmusclesobservedduringeccentriccontractions.By proteins actinandmyosin.However, itdoesnotaccountformany (Huxley, 1957).Itreliesonforce regulationthroughthecontractile choice formusclecontractionmechanismsthepasthalfcentury References Funding Competing interests odn .M,Hxe,A .adJla,F. J. Julian, and A.F. Huxley, A.M., Gordon, R.M. Simmons, and A.F. Huxley, L.E., Ford, K.S. Campbell, M.J. Siegman, and D.J. Hartshorne, S.U., Mooers, S.R., Narayan, T. M., Butler, W. Herzog, and M. Epstein, T. L., Allinger, da,K .P,Ezna .adNbe M.I. Noble, and G. Elzinga, K.A.P., Edman, W. Herzog, and M. Amrein, J.L., Gifford, M.M., DuVall, force regulation:arolefortitin? .Sc B R. Soc. Biomech. three filamentmodelofskeletalmuscle stabilityandforceproduction. reflected insinglemyofibrils? . skeletal muscle:anewmechanism. thin-filament extraction. and mechanismofpassiveforcedevelopmentinratcardiacmyocytesprobed by tension withsarcomerelengthinvertebratemusclefibres. during andafterchangeoflength. slow stretches. and filamentoverlapinstimulatedfrogmusclefibres. after stretchofcontractingfrogsinglemusclefibers. Biol. emergent mechanicalbehaviorinamathematicalmodelofmuscle. catch muscle. (2001). Themyosincross-bridgecycleanditscontrolbytwitchinphosphorylationin 29, 627-633. descending limboftheforce-lengthrelation.A theoreticalconsideration. Biophys. J. properties oftitinimmunoglobulindomain27inthepresencecalcium. A greatadvantageofthisthree-filamentmodelisthatitendows In summary, thecross-bridge theoryhasbeentheparadigmof 5 , e1000560. (1938). Theheatof shortening andthedynamicconstants of muscle. 9 126 , 175-191. 42, 301-307. The JournalofExperimentalBiology(2014)doi:10.1242/jeb.099127 , 136-195. Biophys. J. Proc. R.Soc.B (2009). Interactionsbetweenconnectedhalf-sarcomeresproduce J. Physiol. Biophys. J. 6) needstobeseenassuch–aproposalrather 80, 415-426. 574 J. Biomech. , 635-642. 139 Exerc. SportSci.Rev. (1951). Changesofenergyinamuscleduringvery (2002). Forceenhancementfollowingstretchingof (1952). Theforceexertedbyactivestriatedmuscle J. Physiol. , 104-117. 73, 2043-2053. J. Exp.Biol. 45, 1893-1899. (2012b). Molecularmechanismsofmuscle (2006). Residualforceenhancementin (1996). Stabilityofmusclefibersonthe 117 (1981). Therelationbetweenstiffness (1982). Residualforceenhancement 205 , 77-86. (1966). Thevariationinisometric J. Gen.Physiol. , 1275-1283. J. Physiol. 40, 50-57. (2012a). Aretitinproperties (2013). Alteredmechanical J. Physiol. (1997). Titin elasticity 311, 219-249. 80, 769-784. 184 PLOS Comput. (2012c). The J. Biomech. , 170-192. Mol. Cell. Proc. Eur.

The Journal of Experimental Biology elrae,M .Z,Sih .B,Gaze,H .adBsaat,C. Bustamante, and H.L. Granzier, S.B., Smith, M.S.Z., Kellermayer, enr,T .adHro,W. Herzog, and T. R. W. Leonard, Herzog, and V. Joumaa, E.J., Lee, Lee, un T. S. Kuhn, W. Herzog, and T. R. Leonard, D.E., Rassier, V., Joumaa, W. Herzog, and T. R. Leonard, V., Joumaa, aet . aaae . it . uia . u . amr,S,Fnk . Labeit, T., Funck, S., Lahmers, Y., Wu, H., Fujita, C., Witt, K., Watanabe, D., Labeit, W. Herzog, and V. Joumaa, R.M. Simmons, and A.F. Huxley, R. Niedergerke, and A.F. Huxley, J. Hanson, and H. Huxley, Huxley, A.F. uly H.E. Huxley, uly A.F. Huxley, H.E. Huxley, J. Howard, COMMENTARY e,H . ezg .adLoad T. Leonard, and W. Herzog, H.D., Lee, e,E .adHro,W. Herzog, and E.J. Lee, oois .adPdlk,R.J. Podolsky, and R. Horowits, oois R. Horowits, A.V. Hill, actin-myosin-based cross-bridgeinteraction. tweezers. 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The Journal of Experimental Biology