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Single-myosin crossbridge interactions with actinfilaments regulated by troponin-tropomyosinNeil M. Kad*, Scott Kim*, David M. Warshaw*, Peter VanBuren, and Josh E. Baker*

Departments of *Molecular Physiology and Biophysics and Medicine, University of Vermont, Burlington, VT 05405

Edited by James A. Spudich, Stanford University School of Medicine, Stanford, CA, and approved October 1, 2005 (received for review July 28, 2005)

Striated muscle contraction is governed by the thin filament

regulatory proteins troponin and tropomyosin. Here, we investi-gate the molecular mechanisms by which troponintropomyosin

inhibits myosins interactions with the thin filament in the absence

of calcium by using a laser trap. The displacement events for asingle-myosin molecule interacting with a reconstituted thin fila-

ment were shorter (step size 5 nm) and prolonged (69 ms)compared with actin alone (11 nm and 26 ms, respectively).

However, these changes alone do not account for the degree of

inhibition of thin filament movement observed in an ensembleassay. Our investigations of single- and multiple-myosin molecules

with regulated thin filaments suggest the primary basis for this

inhibition derives from a 100-fold decrease in the probability ofmyosin attaching to actin. At higher myosin concentrations, short

bursts of motility are observed in a laser trap consistent with thestrong binding of a single-myosin crossbridge, resulting in coop-

erative binding of other cycling crossbridges. We confirmed this

cooperativity in the in vitro motility assay by observing thinfilament translocation in the absence of calcium but at low [ATP],

consistent with rigor activation. We have developed a simplemechanistic model that reproduces and provides insight into both

the observed single-myosin molecule and ensemble data in theabsence of Ca2. These data support the hypothesis that thin

filament inhibition in the absence of Ca2 is largely achieved bymodulating the rate of attachment andor transition from theweakly to strongly bound state.

muscle regulation single molecule thin filament laser trap

Force generation in striated muscle results from myosin cy-clically interacting with actin, a Ca2-regulated process me-diated by the actin-associated regulatory proteins, troponin (Tn)and tropomyosin (Tm). Early studies suggested that the Ca2-dependent movement of TnTm on actin functioned as anon-off switch, regulating myosin binding to actin (1, 2).However, subsequent studies indicated that myosins interaction

with the thin filament is graded, leading to the proposal that Tmequilibrates among three states (3, 4): blocked, closed, and open(5). These biochemical data were supported by more recentstructural data (6). In theabsenceof Ca2, Tm sterically preventsmyosin from binding to actin by occupying the blocked state (7).Upon Ca2 binding to Tn, Tms equilibrium position shiftstoward the closed state, exposing sites that allow myosin weak

binding while still inhibiting isomerization to the strong bindingstate (6). Once bound, myosins weak-to-strong binding transi-tion shifts Tms equilibrium position further toward the openstate, permitting cooperative binding of additional myosins byexposing neighboring actin binding sites (8, 9). Thus, myosinstrong binding to actin is required to fully activate the thinfilament (10).

Characterization of striated muscle thin filament regulationhas relied extensively on the collective behavior of many myosinmolecules, e.g., skinned muscle fibers and solution studies. Byreconstituting fully regulated thin filaments from isolated pro-teins and using the in vitro motility assay, Ca2dependentmodulation of thin filament motility can be investigated at themolecular level (1114). In this simple system, motility is still the

result of tens to hundreds of myosin molecules interacting withthe thin filament. In contrast, with a laser trap assay (1517) onecan measure the interaction of a single-myosin molecule with aregulated thin filament to specifically assess how TnTm inhibitsmyosin binding in the absence of Ca2 and how myosin strongbinding leads to cooperative activation of the thin filament.

Here, we report that in the absence of Ca2 the apparent rateof myosin strong binding to a reconstituted thin filament isreduced 100-fold with a more modest effect (2-fold) onmyosins step size and strong binding duration. Interestingly,laser trap studies indicate strong binding of a single-myosinmolecule can, even in the absence of Ca2, cooperatively accel-erate the binding of neighboring myosin molecules. With the

in vitro motility assay, we confirmed this cooperative behavior;thin filament motility was fully activated in the absence of Ca2

by reducing the MgATP concentration analogous to previoussolution studies demonstrating rigor activation of actinmyosin

ATPase activity (18). In agreement with several models of thinfilament regulation (3, 5, 1923), our data indicate that thinfilament regulation in the absence of Ca2 is largely achieved bymodulating the rate of attachment andor transition from the

weakly to strongly bound state.

Materials and Methods

Proteins. Skeletal muscle myosin was prepared from chicken pec-toralis and stored in glycerol at20C as described (24). Before use,myosin was further purified to eliminate denatured myosin bycentrifugation with equimolar actin and 1 mM MgATP in myosin

buffer (see Buffers below) (25). N-ethylmaleimide-modified skele-talmyosin was prepared asdescribed (24) and was used to bind actinor reconstituted thin filaments to the polystyrene beads in a lasertrap assay (17). Actin was isolated from chicken pectoralis muscle(26). Tn and Tm were isolated from bovine cardiac muscle asdescribed (27). Thin filaments (i.e., actin, Tn, and Tm) werereconstituted as reported (11) and diluted into actin buffer (seebelow) with excess (100 nM) Tn and Tm. Under these conditionsthin filaments remained fully regulated for hours as demonstratedby the lack of movement in an in vitro motility assay in the presenceof ATP and absence of Ca2 [log 10 Ca concentration (pCa) 8, data not shown]. Actin and thin filaments were labeled withequimolar tetramethyl-rhodamine-phalloidin before use (11, 12).

Buffers. Myosin buffer contained 0.3 M KCl, 25 mM imidazole, 1mM EGTA, 4 mM MgCl2, and 10 mM DTT, adjusted to pH 7.4.

Actin buffer contained 25 mM KCl, 25 mM imidazole, 1 mMEGTA, 4 mM MgCl2, 10 mM DTT, and oxygen scavengers (0.1mgml1 glucose oxidase, 0.018 mgml1 catalase, and 2.3 mgml1

Conflict of interest statement: No conflicts declared.

This paper was submitted directly (Track II) to the PNAS office.

Abbreviations: Tn, troponin; Tm, tropomyosin; pCa, log 10 Ca concentration.

To whom correspondence should be addressed. E-mail: warshaw@physiology.med.

uvm.edu.

Present address: Department of Biochemistry, University of Nevada, Reno, NV 89557.

2005 by The National Academy of Sciences of the USA

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glucose) adjusted to pH 7.4. Motility solutions containing varyingcalcium andor MgATP were prepared as described (12).

Laser Trap. Detailed protocols for the laser trap assay have beendescribed (17, 25). Contractile proteins were added to theexperimental f low cell chamber with the following series ofsolution incubations: (i) skeletal myosin (0.120 gml) for2 min; (ii) 20 l of 0.5 mgml BSA in myosin buffer for 1 min;(iii) 3 20 l of actin buffer; and (iv) 3 20 l of actin buffer

with 10 M MgATP, tetramethyl-rhodamine-phalloidin-actinor tetramethyl-rhodamine-phalloidin-thin filaments, N-ethylmaleimide-modified skeletal myosin-coated beads, and100 nM excess Tn and Tm to ensure stoichiometric binding

when thin filaments were studied. Experiments were per-formed at 25C.

By manipulating the microscope stage, an N-ethylmaleimide-modified skeletal myosin-coated bead was captured in each ofthe two laser traps, and the ends of a single actin or reconstitutedthin filament were then attached to the beads. The filament waspretensioned to 4 pN, and then brought near a skeletalmyosin-coated,3-m-diameter silica microsphere serving as apedestal. The bright-field image of one bead attached to thefilament was projected onto a quadrant photodiode detector,and signals were acquired for bead displacement parallel to thefilaments long axis. Signals were recorded for at least 120 sbefore moving the bead-filament-bead to another pedestal

within the flow cell. These data records were digitized at 4 kHzafter initial filtering at 2 kHz.

Laser Trap Data Analysis. Myosin strongly binds to an actinfilament, undergoes its powerstroke, and displaces the filament.The binding of myosin attenuates the Brownian motion of thebead-filament-bead (see Fig. 2a) and shifts its mean position (16,17). Using mean-variance analysis (17, 28) we determined thedisplacement or step size, d, generated by the myosin power-stroke, the duration, ton, that the myosin remains strongly boundto actin, and the total number of events within a data record.From the number of events, a frequency of attachment can be

readily calculated by dividing the total record time by thisnumber.

In Vitro Motility. The movement of actin and regulated thinfilaments over a myosin-coated surface (100 gml myosin) wasdetermined as described (12, 29). Specifically, thin filamentmotility can be characterized in terms of: (i) the mean velocityof movement; (ii) the percent of filaments moving in a smoothand continuous fashion (defined as filaments having a standarddeviation of velocity less than half the mean velocity); and (iii)the percent motile filaments (defined as filaments moving 0.33ms).

Results

Regulated Thin Filament Motility. Reconstituted thin filamentswere fully regulated as demonstrated by the effect of calcium onmyosin-based thin filament sliding (Fig. 1). As reported (11, 12),the velocity, Vactin, of regulated thin filaments increased sigmoi-dally with increasing Ca2 concentrations in the presence of 2mM MgATP (Fig. 1a). Fitting the velocity data to the Hillequation yieldsa pCa50 of 6.40 0.04, a Hill coefficient of 1.940.32, and a maximal velocity of 6.0 0.2 ms. These data werealso analyzed in terms of the percent that were motile andpercent of filaments moving smoothly (Fig. 1b). At high Ca2

concentrations all filaments are motile and most move smoothly(76%). At subsaturating Ca2, theproportion of motile filamentsdecreases with a smaller percent of these filaments movingsmoothly.

Laser Trap Studies Using Unregulated Actin Filaments. Vactin in themotility assay is the result of many myosin molecules interactingsimultaneously with a given thin filament. How regulation isachieved in terms of myosins ability to interact with the thinfilament was investigated by limiting the number of myosins ina laser trap assay.

Fig. 2a is a sample displacement record obtained when anunregulated actin filament was lowered onto a pedestal surfacethat had been incubated with 0.1 gml myosin. At this con-centration only a single-myosin molecule on average interacts

with the actin filament (30). At 10 M MgATP, we observedisolated mechanical events occurring at a frequency, f, of 1.75 0.3 s1. Events were analyzed by using mean-variance (seeMaterials and Methods) to give an average step size, d, of 10.9 1.2nm anda step duration, ton, of2 6 4 m s (n 11 experiments)(31). When the myosin density was increased by a factor of 100(i.e., incubated with 10 gml), relatively continuous actinfilament movement was observed with an average velocity of0.14 0.08 ms (Fig. 2b). This velocity is slower than that seenpreviously in the motility assay (Vactin 0.47 0.06 ms) withsimilar myosin density and [MgAT P] (31). The slower velocity in

the laser trap is likely the result of the resistive load imposed bythe laser trap.

Laser Trap Studies Using Regulated Thin Filaments. Fig. 2c shows atypical laser trap displacement trace obtained from a regulatedthin filament interacting with a myosin surface incubated with

Fig.1. Thinfilamentmotility versus pCa.(a) Regulated thinfilamentvelocity

versuspCain an in vitromotilityassay.(b) Thinfilament motilitydata analyzed

as the percentage of motile filaments (F) and percentage moving smoothly

() as a function of pCa. The pCa50 for motile filaments is 6.81 0.04, which

was significantly greater thanthe pCa for smoothly moving filaments (6.43

0.06; P 0.001).

Fig. 2. Sample data traces obtained in a laser trap, showing displacement

events of unregulated actin filaments (a and b) and regulated thin filaments (c

andd).(a andb) Displacement eventsobtained whenunregulated actinfilaments

interact withsurface sparsely coated withmyosin (0.1gml myosin incubation)(a) and surface densely coated with myosin (10 gml myosin incubation) (b). (cand d) Displacement events obtained when regulated thin filaments interact

with surface sparsely coated with myosin (0.1 gml myosin incubation) (c) andsurface densely coated with myosin (10 gml myosin incubation) (d).

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0.1 gml myosin. Unlike data obtained at this surface densitywith unregulated actin (Fig. 2a), the frequency of events wasextremely low (0.01 s1), preventing determination of the stepsize and duration. As expected for a completely reconstitutedthin filament, the low event frequency was uniformly observedalong the entire sampled length of the thin filament at both 25and 100 mM KCl (data not shown). However, at 100-fold highermyosin density with 10 gml incubation (Fig. 2d), the eventfrequency (0.5 0.3 s1) resembled that of unregulated actin at0.1 gml incubation. Under these conditions, we determinedthe average step size, d 5.0 0.9 nm (n 11 experiments),and step duration, ton 69 33 ms (n 11 experiments). Thisd was 50% shorter (P 0.001; unpaired t test), whereas the ton was twice as long (P 0.001; unpaired t test) compared with

unregulated actin (see above).When the myosin density was increased 2-fold (from 10 to 20

gml incubation), both single binding and staircase steppingevents were observed with an average distance moved during astaircase event of 43 2 nm (n 67) (Fig. 3a). Staircases arecaused by multiple myosins simultaneously interacting with thethin filament until all myosins spontaneously detach. Interest-ingly, the frequency of steps within a staircase event (f 11 1 s1, determined as the inverse of the time between steps) ismuch higher than the frequency observed when only single stepspredominate (see above), suggesting that the attachment of onemyosin head to actin cooperatively accelerates the attachmentrate of subsequent heads during a staircase. In addition, bindingof the first myosin to actin affects the step size of subsequent

myosin heads that bind (Fig. 3b). Using mean-variance analysis(Fig. 3c), the displacement of the first step in a staircase was6.6 1.0 nm, whereas the second step was significantly larger(P 0.01, unpaired t test), 13.7 0.8 nm (n 40). Thedisplacement of the first step is comparable to the step sizeobserved when only a single myosin interacted with a regulatedthin filament (see above). The second and subsequent steps in astaircase event were twice that of the first step, resembling themyosin step size with unregulated actin.

Regulated Thin Filament Motility at Low Ca2 with Low [MgATP].

Reconstituted thin filament motion could be restored underinhibitory conditions (i.e., pCa 8) if the [MgATP] was loweredto subsaturating concentrations 75 M. This phenomenon is

analogous to the rigor activation of the actomyosin ATPaseobserved by Bremel and Weber (18).

To fully characterize the apparent activation of the thinfilament by the binding of rigor myosin heads to the thinfilament, Vactin was measured over a range of [MgAT P] between2 and 125 M (Fig. 4). In the presence of Ca2 (pCa 4), Vactin

increased with [MgATP], yielding a Km of 25 M consistent with values determined previously (31). Surprisingly, at low Ca2

(pCa 8) and [MgATP] below the Km, thin filament motility wasobserved at speeds equivalent to those observed at pCa 4. Incontrast, complete inhibition of motility was observed at satu-rating MgATP and pCa 7 (Figs. 1 and 4).

Discussion

To characterize the molecular mechanisms of thin filamentinhibition (see Fig. 1), we have determined the motion of thinfilaments with high spatial and temporal resolution by using thelaser trap under nominal Ca2 conditions (pCa 8). At myosinsurface densities where only a single skeletal muscle myosinmolecule can interact with an unregulated actin filament (i.e.,fully on) (Fig. 2a), binding events are detected at a frequency

(1.75 s1

), limited by both theinherent kinetics of theactomyosinATPase cycle and the spatial constraints placed on the actomy-osin interaction within the laser trap assay. With a regulatedfilament in the absence of Ca2 (i.e., fully off), the eventfrequency is significantly reduced (Fig. 2c). However, a 100-foldincrease in the myosin concentration can restore the eventfrequency to that for unregulated actin (Fig. 2d). Consistent withprior solution biochemical studies (9, 32, 33), we demonstrate atthe single-molecule level that TnTm dramatically reduces thefrequency of actomyosin strong binding events at low Ca2 andthus is the primary cause for complete inhibition of continuousthin filament movement. The extent of inhibition within fibersmay in fact be greater than observed here given the 1,000-folddifference in the heat liberated between resting and activemuscle (34). Although reconstituted thin filaments fully inhibit

in vitro motility, they may be less effective than thin filaments inmuscle at regulating attachment kinetics because of spatialrelationships and other factors.

In addition to modulating the myosin attachment frequency,the presence of TnTm affects the inherent mechanics (i.e., stepsize, d) and kinetics (i.e., step duration, ton) of the actomyosininteraction. In the absence of Ca2, a single-myosin moleculegenerates only half the displacement and remains strongly boundfor twice as long compared with myosin binding to an unregu-lated actin filament. We have previously shown at 10 M ATPthat ton is determined equally by the rate of ADP release frommyosin and the rate of ATP binding to myosin (31). Therefore,TnTm in the absence of Ca2 could modulate one or both ofthese kinetic steps (35).

Fig. 3. Short bursts of motility with regulated actin. (a) A sample data trace

showing both individual displacements and long staircase stepping events

generated by multiple-myosin molecules. After each staircase event, the

restoring forceexerted bythe lasertrapreturnsthe thinfilament to itsoriginal

position. (b) Expanded view of the first two steps in a staircase event. To

accentuate thesteps inthe rawdatatrace, a line is drawnthroughthe data to

guide theeye. Region 0 represents thebaselinewhere myosin is detachedand

displacementvarianceis high.Step 1 reflects attachment of thefirst myosin as

evidenced by the decrease in variance. Step 2 is the displacement associated

with the second myosin. (c) The mean-variance histogram of the data in b

showingthe baseline(marked asb) andtwo distinctdisplacement populations

corresponding to a 3-nm step from baseline and a subsequent 16-nm step (or

19 nm relative to baseline).

Fig. 4. Rigor activation in the motility assay. Thin filament velocity at

activating (Ca; pCa 4) and subactivating Ca2 (Ca; pCa 8) concentrations

versus [MgATP].

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In the absence of Ca2, TnTm prevents myosins optimalinteraction with actin (4, 36) and could account for the step sizebeing half that of whole skeletal myosin (see Results). Myosinstwo heads are required to generate a 10-nm displacementbecause single-headed myosin generates only half the displace-ment and remains attached to actin for a longer period after thestep (37, 38). Thus, TnTm at low Ca2 may allow only one ofmyosins two heads to interact with actin, disrupting intrahead

communication that is required to generate a 10-nm step.However, binding of the first myosin molecule appears toovercome the effect of TnTm because subsequent myosins arecapable of generating their normal displacement as evidenced bycomparing the step size of the first and second steps in a staircasestepping event (see Results and Fig. 3b). This scenario is not thecase for unregulated actin where the first and subsequent stepsare 10 nm (37). Therefore, binding of the first head is critical tothe cooperative activation of the thin filament (see below).

A Simple Model: TnTm Inhibits Myosin Strong Binding. Experimentsin the laser trap are able to detect only two actomyosin states: (i)the attached state when myosin is strongly bound, and (ii) thedetached or weakly bound state. With this simple view, we havedeveloped a Monte Carlo model of thin filament regulation in

which TnTm modulates the attachment frequency (f) for agiven number of myosin molecules (nM) by either inhibiting (reg)or accelerating (acc) the rate that myosin transitions from the

weak to the strongly bound state (kws) (see Fig. 5 and Appendix,which is published as supporting information on the PNAS website, for details):

Attachment ratef nM kws accreg.

In the absence of Ca2, the presence of TnTm reduced thefrequency of actomyosin interactions (f) 100-fold (Fig. 6 a vs. c),such that kws was reduced by an inhibition constant (reg 100,see Fig. 5 and Eq. 2 in Appendix). This finding implies that in theabsence of Ca2 99% of the actin binding sites are inaccessible

to myosin strong binding. Geeves and coworkers (39) suggestthat in the absence of Ca2 the regulatory state of the thinfilament is 70% blocked, 25% closed, and 5% open. Because wecannot distinguish between detached or weakly bound myosin inthe laser trap, our prediction of 99% actin site inaccessibility isconsistent with the combined percentage of blocked and closedstates (95%) estimated by Geeves and coworkers (5, 39). Be-cause strong binding events still occur in the laser trap assayunder conditions where myosin should be sterically preventedfrom binding, thermal f luctuations of the Tm on actin (Fig. 5)must temporarily expose actin binding sites (40), which couldalso account for the 5% open-state probability predicted byGeeves and coworkers (5).

Cooperative Regulation Experimentally and in Silico. In a laser trap,20 gml of skeletal muscle myosin is sufficient to supportcontinuous movement of unregulated actin (see Fig. 2b). How-ever, with regulated filaments, at the same myosin concentration,continuous motion was not seen; instead, short bursts of motility(i.e., staircase events) and long pauses were observed (Fig. 3a).To model these short bursts (Fig. 7a), we introduced a coop-erativity constant (acc 10, see Eq. 3 in Appendix) thataccelerated the strong binding rate 10-fold for myosin bindingsubsequent to the first head (Fig. 5). Such cooperativity ofbinding has been observed in earlier solution biochemistrystudies (9, 32). From a structural viewpoint, binding of the firsthead may perturb Tms equilibrium position on actin so thatother heads can bind to nearby myosin binding sitesmore readily.However, these additional heads still do not bind at a rate

equivalent to that with unregulated actin; instead their bindingis still inhibited 10-fold (in our model, accreg 0.1). Thus, wepredict that the myosin binding site accessibility for a regulatedthin filament in the absence of Ca2 is reduced 99%, but with theattachment of a single head the thin filament is activated 10-foldso that 90% of the sites remain inaccessible to strong binding.

With limiting numbers of myosin molecules interacting withthe thin filament in the laser trap, it is possible to estimate thedistance over which cooperative activation occurs. For a nitro-cellulose surface incubated w ith 20 gml myosin, where burstsof activity were observed, we previously determined based onNH4-ATPase measurements that 18 heads or nine myosinmolecules are available per m of actin filament length (30), i.e.,111 nm between myosin molecules. Given this intermolecular

Fig. 5. Simple model of thin filament regulation. (Top) For unregulated

actin, the myosin attachment rate is limited by the weak-to-strong binding

transition rate(kws). (Middle) For a regulatedthin filamentreconstitutedwith

Tn and Tm in the absence of Ca2, the myosin attachment rate is reduced by

an inhibition constant (kwsreg). The ability of myosin to bind even in theabsence of Ca2 suggests that thermal fluctuations of Tm on actin (indicatedby a bent Tm and dashed arrow) expose potential binding sites. (Bottom)

However, once a myosin binds strongly to actin, neighboring TnTm regula-

tory units,spanningthreeunits, areactivated, allowing myosins to bind at an

accelerated rate [kws (accreg)].

Fig. 6. Monte Carlo simulation of the interaction of myosin with unregu-

lated(a and b) andregulated(c and d) actin. These datarepresent simulations

ofexperimental data similar tothatin Fig. 2,whichis includedas Insets. (a and

b) Simulated laser trap displacement data at low surface density (0.1 gmlmyosin) (a) and high surface density (10 gml myosin) (b) where continuousvelocity is observed. (c and d) Simulateddatawith regulatedthinfilamentsat

low surface density (0.1 gml myosin the event shown was the only event ina 20-s record) (c) and high myosin surface density (10 gml myosin) (d). SeeAppendixfor simulation conditions.

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spacing, the accelerated binding of heads subsequent to the firston average occurs within three regulatory units distal to theinitial binding event, a distance equal to the next accessible actintarget zone along the TnTm strand. This simple calculationassumes a homogeneous surface density, and there are nosignificant differences in the attached lifetime between the firstand subsequent heads. Therefore, thin filament activation is acooperative process in which the strong binding of a myosin headsets up an activation wave over long distances that is propagatedthrough adjacent TnTm units (6, 4144).

Cooperative Rigor Activation. To enhance the detection of myosinbinding events in the laser trap, experiments were performed atlimiting [MgATP] (i.e., 10 M), which results in a myosin headattached to actin waiting for ATP to bind (31). Therefore,consistent with rigor activation of actomyosin ATPase activity,the model predicted that the short bursts of activity at low[MgATP] (Fig. 3) resulted from rigor activation of the thinfilament (10, 12, 18). To confirm this prediction, we measuredVactin of regulated thin filaments in the motility assay at varying[MgATP]. At saturating MgATP with minimal Ca2 ( pCa7),Vactin is completely inhibited (see Figs. 1 and 4); however, at low[MgATP] (75 M), when the rigor state is significantly pop-ulated, thin filament motility occurs with a Vactin comparable tothat for a fully Ca2-activated thin filament (Fig. 4). The

observed rigor activation of event frequency in a laser trap (Fig.3), rigor activation of velocity in the motility assay (Fig. 4), andrigor activation of ATPase activity in solution studies (18) all areconsistent with a simple model in which Ca2 and rigor headsboth activate actinmyosin binding (Fig. 4 and see Appendix andFig. 9, which is published as supporting information on thePNAS

web site, for details). If so, the proposed model described abovecan provide a mechanistic insight to the dependence ofVactin on[MgATP] for thin filaments in the presence and absence of Ca2.

In the presence of Ca2 Vactin is proportional to dton (31, 45),so that Vactin is limited by the rate of myosin detachment (g 1ton), which is determined by both the rates of ADP release andthe MgATP binding to myosin (31). Thus, as the [MgATP] islowered, Vactin slows as myosin spends an increasing amount of

time, ton, attached to actin waiting for ATP to bind (Fig. 7b). Incontrast, in the absence of Ca2 and at high [MgATP], we haveshown that the rate of myosin attachment limits Vactin (see Fig.4). However, at low [MgATP], the prolonged attached lifetimeof the rigor state cooperatively activates the thin filament (Fig.5), resulting in an increased actinmyosin binding frequency anddetachment limited thin filament movement even in the absenceof Ca2 (see Figs. 3 and 7a). This mechanistic view of rigoractivation is predicted by our model, as demonstrated by thestriking similarity between the simulated and actual Vactin data(Fig. 7b vs. Fig. 4). In addition, the model predicts that thesimilarity in Vactin observed at 10 and 60 M MgATP in theabsence of Ca2 (Fig. 4) results from different underlying motilemechanisms (Fig. 8). At 10 M MgATP the attached myosinlifetime is sufficiently long to result in multiple myosins bindingto and steady motion of the actin filament (Fig. 8a), with myosindetachment limiting Vactin. At 60 M MgATP, myosins shorterattached lifetime reduces the probability of rigor activation,

resulting in discontinuous thin filament motility comprised ofbursts of motility and pauses (Fig. 8b). During the bursts, the

velocity is limited by myosins detachment rate; however, thepause duration is limited by myosins attachment rate. Whenthe average velocity over time is determined at 60 M MgATP,including pauses, its value is nearly identical to that at 10 MMgATP even though the dynamics of filament motion aresubstantially different. In fact, the model predicts that thepercent of filaments moving smoothly is far greater at 10 M

versus 60 M MgATP, which agrees with the experimental data(Fig. 8c).

Conclusion. The laser trap data presented here suggests thatalthough the inherent mechanics and kinetics of a single-myosin

Fig.7. Cooperative activationunderlies the short bursts of motility,which in

turn leads to rigor activation at low [ATP]. (a) With a 10-fold activation of

strong binding for heads at 20 gml myosin (acc 10, see Appendix) shortburstsof motilityequivalentto Fig.3 arepredicted.(b) Simulatedthinfilament

velocities at activating (Ca; pCa 4) and subactivating Ca2 (Ca; pCa 8)

concentrations versus [MgATP] weresimulated at 100gml myosin using thesame parameters as in Fig. 6 but with varying [MgATP] (see Appendix fordetails).

Fig. 8. Predicting the mode of filament motion. (a and b) Velocities were

simulated from individual model filament runs at 10 M ATP (a) and 60 M

ATP(b). (c)A t1 0M ATPthinfilamentmotionis continuous,leadingto a high

percentage of filaments moving smoothly, which compares well with the

experimental data. At 60M ATPthe model predicts fewer filaments moving

smoothly because of pauses between detachment limited runs, which is also

consistent with the experimentally observed data.

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molecule are altered 2-fold by the presence of TnTm, thesealterations are not large enough to completely inhibit thinfilament velocity at low Ca2. Therefore, TnTm regulates actinin the absence of Ca2 by reducing the probability of myosinsfirst encounter w ith actin 100-fold. However, upon myosinbinding, the thin filament is activated 10-fold from its inhibitedstate because of activation of neighboring regulatory units.Because strong binding of the first head can only partiallyactivate the thin filament, we infer that regulation must be at

least a three-state process where further activation is associatedwith the binding of Ca2, akin to the blocked, closed, and openstates (5).

At higher [Ca2], regulation may have additional modulatoryeffects on actomyosin kinetics as evidenced in motility studies

where regulated thin filament velocity and force are enhanced

over actin alone (12, 46) and by the Ca2-dependent changes inthe rate of tension redevelopment, ktr, in fiber studies (47).Future studies will likely provide greater molecular insight to thestructural dynamics of TnTm movement on actin because thedevelopment of single-molecule f luorescence detection tech-niques may allow simultaneous assessment of TnTm motioncoupled with mechanical measurements of the regulated acto-myosin interaction.

We thank Amy Armstrong, Kelly Begin, and Joe Gorga for assistance with experiments; Guy Kennedy for technical support; and JeffreyMoore and Edward Debold for helpful discussions. This study wasfunded by National Institutes of Health Grant HL59408 (to D.M.W.),National Institutes of Health Grant HL077637 (to P.V.), and NationalInstitutes of Health Grant P20RR018751-01 (to J.E.B.).

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