Cross-bridge attachment and stiffness during isotonic shorteningof intact single muscle fibers

P. J. Griffiths,* C. C. Ashley,* M. A. Bagni,t Y. Ma6da,§ and G. Cecchit*University Laboratory of Physiology, Oxford, OX1 3PT UK;*Dipartimento di Scienze Fisiologiche, Universitc degli Studi di Firenze, Florence, 1-50134 Italy;§EMBL Outstation, Deutsches Elektronen-Synchrotron, D-2000 Hamburg 52, Germany

ABSTRACT Equatorial x-ray diffraction pattern intensities (11 and 111), fiber stiffness and sarcomere length were measured in single, intactmuscle fibers under isometric conditions and during constant velocity (ramp) shortening. At the velocity of unloaded shortening (Vm,)the 110 change accompanying activation was reduced to 50.8% of its isometric value, I,1 reduced to 60.7%. If the roughly linear relationbetween numbers of attached bridges and equatorial signals in the isometric state also applies during shortening, this would predict51-61% attachment. Stiffness (measured using 4 kHz sinusoidal length oscillations), another putative measure of bridge attachment,was 30% of its isometric value at Vma,. When small step length changes were applied to the preparation (such as used for constructionof Ti curves), no equatorial intensity changes could be detected with our present time resolution (5 ms).

Therefore, unlike the isometric situation, stiffness and equatorial signals obtained during ramp shortening are not in agreement. Thismay be a result of a changed crossbridge spatial orientation during shortening, a different average stiffness per attached crossbridge, ora higher proportion of single headed crossbridges during shortening.

INTRODUCTIONIn striated muscle the proteins actin and myosin arearranged as interdigitating filaments axially along themuscle cells. According to the widely accepted cross-bridge theory of muscle contraction ( 1-3), force followsthe attachment of crossbridges (periodic projectionsfrom the surface of the myosin filaments) to the actinfilaments. Attachment is accompanied by an increase infiber instantaneous stiffness and a change in the equato-rial x-ray diffraction pattern from the quasi-crystallinearrangement ofthe protein filaments (4). In the isomet-ric state, the equatorial intensity changes accompanyingactivation are proportional to axial force (5), and aretherefore thought to indicate the proportion of cyclingbridges. Instantaneous stiffness changes upon activationare thought to arise from an elastic component asso-ciated with each individual attached crossbridge, hencestiffness may also indicate the degree of crossbridge at-tachment. We have recently reported the first successfulapplication of time-resolved x-ray diffraction to intactsingle muscle fibers under isometric conditions (6). Wefound good agreement between the time course ofchanges in equatorial signals and fiber stiffness both dur-ing activation and isometric relaxation. We have nowextended our observations to the isotonic condition.

Previous studies on whole muscle under isotonic con-ditions (i.e., during shortening at constant force) sug-gested that equatorial intensities are either unchanged orincrease slightly (7) or change towards their resting lev-els by more than 50% oftheir plateau values during short-ening at Vmax (8). However, stiffness measurements sug-gest a larger change in the proportion ofattached bridges

during muscle shortening (a decline of70% as indicatedin references 9-1 1 ), suggesting that the proportion ofattached crossbridges indicated by stiffness and equato-rial intensities may not be in agreement under isotonicconditions. Recent motility assays ofisolated contractilesystems suggest that the fraction ofattached bridges mayeven increase during shortening ( 12, 13). Clearly, anymodel of the crossbridge cycle must predict the propor-tion of attached bridges during shortening, and so thedetermination of this proportion is of great importance.But comparison of previous studies of the fraction ofattached bridges during shortening in living fibers iscomplicated by the difference in the preparations (wholemuscle versus single fibers) and species used for x-raydiffraction and stiffness measurements. In addition, pre-cise control and measurement of shortening velocity inwhole muscle experiments is difficult, and must involvea margin oferror. There are also no data showing comple-mentary stiffness and x-ray measurements during thesame experiment. We have therefore studied the behav-ior of stiffness and equatorial intensities during shorten-ing in single intact muscle fibers of the frog, where timeresolved sarcomere length, x-ray diffraction, and me-chanical measurements can be made on the same prepa-ration, and the complications ofa multicellular prepara-tion are avoided. We find that indeed stiffness and equa-torial signals do not agree, stiffness consistentlyreporting a smaller fraction of bridges in an attachedstate.

METHODS

Address correspondence to Dr. P. J. Griffiths, University Laboratoryof Physiology, University of Oxford, Parks Road, Oxford, EnglandOX 1 3PT, United Kingdom.

a) Experimental protocolSingle muscle fibers isolated from the tibialis anterior muscle of frogs(Rana temporaria) were mounted in a chamber and positioned in the

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FIGURE I Measurement of tension and stiffness during fiber shorten-ing. (A) ramp shortening (upper trace) with superimposed sinusoidallength oscillations at 3 kHz. applied at the plateau of a tetanic tension(lower panel); (B) expansion ofa central portion ofthe records in (A)to show length (upper trace) and force (lower trace) oscillations. Notethe absence of phase shift between records. Over the period duringwhich the fiber was shortening, the sampling rate of the oscilloscopewas increased to 0.1 ,us-', elsewhere the sampling rate was 1 ms' . Thischange of sampling rate enabled us to record the whole force responsewhile having adequate time resolution during the period ofshortening.Vertical calibration: (A) 178 kN m-2 or 3.2% b0, (B) 27 kN m-2 or0.23% lo. Horizontal calibration: (A) 2 ms between the two small verti-cal bars, 20 ms outside, (B) 570 ,us.

x-ray beam from the source DORIS (beam dimensions 4 x 0.3 mm,A = 0.15 nm). Chamber temperature was maintained at 4°C. Alumin-ium clips on the tendons to reduce series compliance were used tomount the fiber horizontally between a moving coil motor and a capaci-tance transducer. The position of the fiber in the x-ray windows wasadjusted until central and horizontal, then the whole chamber wasraised or lowered in small steps until the height corresponding to thestrongest diffraction pattern was found. Throughout this alignmentprocedure, the x-ray beam was greatly attenuated to avoid fiber dam-age. The design of the chamber and the details of the beamline havebeen published elsewhere (6). The fiber was then electrically stimu-lated (stimulation frequency 20 Hz) to induce a tetanus of 400 msduration. At the plateau of the tetanus a period of constant velocity(i.e., ramp) shortening was initiated. This was achieved using the mo-tor under servo control to impose changes of length on the fiber at apredetermined velocity. The period of constant velocity shortening waspreceded by a quick step release sufficient to discharge tension to theappropriate level for the chosen velocity of ramp shortening. Totalshortening was not greater than 9% of initial fiber length (la), and theinitial sarcomere length was chosen so that throughout the period ofshortening fibers remained within the plateau region ofthe length-ten-sion relationship. Shortening velocity was controlled by a moving coilmotor capable ofcompletinga step within 100 ss. Our isotonic shorten-ing protocol was repeated at 3 minute intervals, collecting equatorialintensity levels every 5 ms for subsequent averaging. Typically, 10 to 20tetani were required to collect sufficient counts for analysis ofthe equa-torial intensity changes. In some fibers, after about half the requirednumber oftetani had been recorded, a series oftetani with length oscil-lations was obtained to determine fiber stiffness during shortening.Stiffness was calculated from the force response to 4 kHz sinusoidallength oscillations of 0.05% lo peak to peak in amplitude. Force wasrecorded using a capacitance force transducer (50 kHz resonant fre-quency). Care was taken to ensure that no phase shift could be detectedbetween force and length signals during stiffness measurements, whichwould indicate fiber resonance ( 14). If a phase shift was detected, thefrequency ofthe length oscillations was slightly reduced. An example ofthe protocol for stiffness measurement in shown in Fig. 1. Throughoutthe experiment, sarcomere length in the center ofthe region ofthe fiberexposed to the x-ray beam was monitored using a laser diffractometer

system (6), and time resolved sarcomere length changes were recordedsimultaneously with the force and intensity data.

Equatorial patterns were collected on a one-dimensional crossedwire detector ( 15). Counts from 128 output channels were stored (to-gether with sarcomere length, fiber length, beam intensity and force) ina local VAX 11/750 computer.

b) Data analysisThe intensity ofreflections is proportional to the square ofthe quantityof mass in the beam. Because shortening of the fiber introduces moremass into the beam, necessarily introducing a movement artifact intothe intensity ofthe reflections, some correction strategy was required toremove this effect. For example, fiber shortening by 5% of its lengthwould introduce 5% more mass into the beam, with consequent10.25% elevation of intensities. Previous studies ofequatorial intensitydependence on sarcomere length (4) have avoided this difficulty byplotting the ratio of Ilo to II,, but this results in loss of informationabout the behavior of individual reflections which we wished to retain.A correction strategy could be to estimate the extent of individual

artifacts separately. For example, as changes in sarcomere length dur-ing shortening are known from our sarcomere length records, a correc-tion for increasing mass in the beam during shortening could be ap-plied. Since beam intensity is also continuously monitored during theexperiment, a further correction for fluctuations in beam intensity isalso possible. However, multiple corrections of this nature may intro-duce more errors than they remove, since the effects of incorrect esti-mation of each artifact become cumulative. This approach also as-sumes knowledge of the source of all artifacts and the availability of asuitable correction procedure for each (which is not available, forexam-ple, in the case of vertical displacement ofthe fiber). Instead we chose adifferent strategy. For each time frame in an experiment we calculatedthe "spectrum intensity," the integrated intensity over the whole por-tion ofthe equatorial pattern recorded by the detector. Each frame wasthen normalized for its spectrum intensity to give a constant spectrumintensity throughout the experiment. In this strategy we assumed thatthe spectrum intensity, after correction for all shortening artifacts,would have remained constant. This assumption is not based on anytheoretical grounds, but on experimental observations. Our previousexperience with isometric contractions (6) indicated that spectrum in-tensity changed little upon activation of fibers in which little move-ment occurred (as indicated by the sarcomere pattern). This procedureshould correct for fluctuations in beam intensity, fiber shortening, andvertical displacement, and permit comparisons of spectra to be madewhen experimental parameters are being varied in successive experi-ments on the same fiber (e.g., changes of sarcomere length or shorten-ing velocity).The time course of intensity changes were measured either by inte-

gration ofwhole areas (including background) below the peaks (6), orby a curve fitting procedure ( 16) which excluded the contribution ofbackground intensity. Ignoring differences in noise levels and absoluteintensities, the two methods gave essentially identical time courses andrelative magnitudes of intensity changes. The curve fitting method firstobtains estimates of intensity levels from an exponential backgroundsubtraction (fitted by eye) from the original spectrum, then uses theseestimates as starting points to fit 6 Gaussians ( 10, 1 1, 20, 21, 30, and Z)to each half of the original pattern, with suitable expressions for thebackground. The form of the model used for fitting was therefore:

y(x) = a, + a2x + a3x2 + a4 exp(a5x)

n76 bi exp((x--j)14aj)2i= vi(2 1/2i-i i(r

where x is the distance from the origin of the pattern to the centre ofreflection i, y(x) the intensity of the spectrum at x, ais the constantsdefining the background, and bi, ,ui and a, the area, mean, and stan-

Gnfih et l. X-a ifato ySotnn ies15Gnffiths et al. X-Ray Diffraction by Shortening Fibers 1151

dard deviation of each ofthe 6 Gaussians. The positions of 10, 20, and30 are fitted as integer multiples ofthe 10 spacing, while 11, 21, and Zspacings are treated as independent variables. All figures showingchanges in intensity have decreases in 10 intensity plotted upwards toaid comparison with the 11 and tension signals.

Unless otherwise stated, mean values ofquantities are quoted plus orminus the standard deviation.

Stiffness was calculated as the ratio ofthe peak to peak amplitudes offorce and length changes during the 4 kHz sinusoidal oscillations.Force and length signals were recorded on a Nicolet 2082 digital oscil-loscope because of the much higher time resolution required in theanalysis of stiffness data (Fig. 1).

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Upon stimulation of the fiber to produce an isometrictetanus, the 10 equatorial intensity (I1o) fell by 46.5 +2.5% and 11 intensity (1l ) increasedby 139.7 ± 26.9% ata sarcomere length of2.2 ,um (110 and I1 I calculated as thearea of the respective reflections). Only the fitted spec-trum procedure was used to obtain these values, sincebackground intensity is not included in reflection inten-sities when using this method. These means include onlydata from fibers used for the present analysis of the ef-fects of shortening, but are consistent with the 110/111intensity ratios reported in our previous work on fibersin the isometric state (6). We shall refer to these inten-sity changes as the "equatorial signals."We then tested the validity of our assumption that

corrected total spectrum intensity would not change dur-ing a contraction, the basis of our corrections for move-ment artifacts. Under isometric conditions, the spec-trum* intensity remains virtually constant during thetransition from activation to relaxation, as we had ob-served previously (6). As will be shown, the recoveryfrom isotonic shortening to a new tetanus plateau alsooccurs under isometric conditions, and we found thatthis recovery also occurs without appreciable change intotal spectrum intensity. However, since shortening in-troduces extra mass into the beam, one cannot expectuncorrected total spectrum intensity to remain constantwhen sarcomere length is being changed. We thereforeexamined the static spectra from relaxed fibers over arange of sarcomere lengths, and corrected the total spec-trum intensity for incident beam intensity and totalmass exposed to the beam (inversely proportional to thesarcomere length change). Since these measurementswere static, fiber alignment in the beam could be opti-mized before each measurement, and hence the effects ofvertical displacement of the fiber are removed (which isnot possible during time resolved measurements). Ourfindings are shown in Fig. 2. Over the range ofsarcomerelengths examined, a small increase in total spectrum in-tensity could be detected (0.32 per micron sarcomerelength). Since our range ofshortening did not exceed 9%10 only a 6% reduction of total spectrum intensity can beexpected as a result of shortening in our time resolvedisotonic data. Furthermore, since an increase in fiber

2.10 2.20 2.30 2.40 2.5 2.5 2.70

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FIGURE 2 Total spectrum intensity (total detector counts) versus sar-comere length. Data obtained from 8 fibers. Total spectrum intensityexpressed as a fraction of that at a sarcomere length of 2.06 im sarco-mere length. The spectrum intensity was corrected for main beam in-tensity and for the mass of fiber exposed to the beam, taking the beamintensity and mass exposed to be unity at the normalizing sarcomerelength (2.06 ,um). A linear regression fit of the data yielded the lineshown on the figure, whose slope is 0.320 ± 0.237 gm-' (95% confi-dence interval).

length is accompanied by a decrease in fiber radius, caus-ing an increase in fiber mass in the most intense region ofthe beam, this 6% reduction of total spectrum intensityduring shortening may be a slight overestimate of theeffect, and so we believe our correction procedure basedon the assumption of constant total spectrum intensityduring shortening to be justified.

Since under isotonic conditions, equatorial signalswere to be recorded under conditions ofchanging sarco-mere length, we first studied the effect of sarcomerelength on '10 and II, in both the activated and relaxedstate under isometric conditions (Fig. 3). For consis-tency with our time-resolved data during shortening, allspectra from any given fiber have been normalized fortotal spectrum intensity. In the relaxed state, 110 changedlittle over the range of sarcomere lengths we examined,but Ill fell abruptly beyond a sarcomere length of 2.2,um. Below 2.2 ,um, II I intensity variation with sarcomerelength is similar to that of '10. In the activated state Iloincreased linearly with sarcomere length and II, fell, ap-parently less steeply than in the relaxed state, althoughthe range of sarcomere lengths we examined was rathershorter, and the decline is therefore less well defined.When a fiber was allowed to shorten at a constant

velocity after having reached the isometric tensionplateau, equatorial signals were either unaffected or felltowards their levels in the resting fiber, depending on theshortening velocity. When the tetanized fiber shortenedat velocities of less than 0.4 Vm., the 10 and 11 equato-rial signals showed no detectable change from their levelsat the tetanus plateau. As the velocity of shortening wasincreased from 0.4 Vmax to Vmax, 10 and 11 signalschanged towards their levels in the relaxed fiber. Fig. 4shows the spectra obtained in the relaxed, plateau, and

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FIGURE 3 Equatorial intensities (Ilo V; I,I, A) versus sarcomerelength in the relaxed (upper panel) and activated (lower panel) statesunder isometric conditions. All intensities determined by fitting Eq. 1to the equatorial spectrum. Lines through the data points are linearregression fits over the whole range ( I,o) or over the range above 2.2 rm(II,) of sarcomere length values. Both 10 and 11 intensities have beennormalized to their respective values at a sarcomere length of 2.2 ,umfor ease of data representation and to permit data from several fibers tobe pooled. For this reason, the large absolute intensity differences be-tween 10 and 11 reflections are not apparent in either the relaxed or theactivated state. The fitted lines have slopes of -0.09 im-' (relaxed)and 0.76 Am` (activated) for I,1 points, and -2.38 Am' (relaxed) and-0.66 A,m (activated) for I,, points beyond 2.2 MLm. The dashed partof the fitted line for I,, points is an extension of the fitted line obtainedin the range of sarcomere lengths greater than 2.2 ,Mm.

shortening states from the same fiber, with the best fit ofthe 6 Gaussian model superimposed. Shortening waspermitted until the equatorial signals had reached asteady state level. The time required to attain a steadystate level in equatorial intensities increased when theshortening velocity decreased, whereas force reached itssteady state level almost immediately after the initial

quick release (the amplitude ofthe release was chosen toreduce force to the appropriate isotonic level for the sub-sequent ramp). For example, when shortening at Vmax,90% of the steady state equatorial signals was reachedwithin 25 ms (Fig. 5), while at 0.6 Vmax 60 ms was re-quired (Fig. 6). It can be seen that while the equatorialchange in Fig. 5, obtained at close to Vma. is quite pro-nounced, in Fig. 6 it is much less evident, despite a sub-stantial reduction in tension. Because steady state inten-sities were reached after a delay during shortening, wecompared the isometric and isotonic intensities obtainedjust before the end of the ramp and after the redevelop-ment of isometric tension. This method avoids any ef-fects due to the change in sarcomere length which resultsfrom the shortening, since the recovery of tension afterthe ramp was found to occur under isometric conditions(as indicated by the output of our laser diffractometersystem). However, it should be noted that changes inlattice spacing are associated with the redevelopment oftension under these conditions ( 17), and the influenceofthis on equatorial intensities during tension redevelop-ment is not fully understood. The distance shortenedwas such that the sarcomere length on termination ofshortening was still within the range of full overlap,where intensity changes as a function of sarcomerelength are small in the isometric state. On restoration ofisometric conditions at the end of the ramp shortening,both 10 and 11 reflections recovered to their isometriclevels with a shorter half-time of recovery than that ob-served for the redevelopment of isometric tension, as isalso observed during the rise of tetanic tension. It hasbeen shown that during redevelopment oftension follow-ing a period of shortening, the rise of stiffness also leadsthat oftension ( 18 ), and has a similar time course to thatofthe recovery ofthe equatorial signals shown here. The11 reflection tended to reach or slightly overshoot itssteady state isometric level somewhat faster than 10 dur-ing this recovery phase.When stiffness was measured during identical condi-

tions of shortening to those used for the intensity data, amuch more pronounced effect of shortening velocity onstiffness was apparent. At 0.4 Vmax stiffness was reducedto 55% of its plateau value, while at Vm,,, the stiffness wasreduced to 30% of plateau stiffness in agreement withearlier findings (9-11). In some fibers the effect of aquick step release (amplitude < 1% 40, completed in 0.5ms), rather than a ramp, was studied. Within the timeresolution (5 ms) of our experiments no change in equa-torial signals could be detected as a result of the step.The variation of stiffness and equatorial signals with

tension during shortening from 8 fibers is shown in Fig.7. The upper panel shows the force-velocity relationshipobtained for our data points and the associated fittedcurve using a simple two state model (1). The lowerpanel shows intensity signals from 10 and 11 reflectionsand stiffness as a function ofthe force during shortening,

Griffiths et al. X-Ray Diffraction by Shortening Fibers 1153

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FIGURE 4 Equatorial patterns from the relaxed (A) and activated isometric fiber (B), during shortening (C), and after redevelopment ofisometrictension on termination of shortening (D). The central region of each spectrum is the shadow of the backstop. Each spectrum was normalized fortotal spectrum intensity. Total exposure time 600 ms, average of 30 tetani. In the isotonic state, shortening velocity was 2.69 nm per halfsarcomereper second. Individual points are counts in each channel, the continuous line is the fitted spectrum using the 6 Gaussian model.

normalized to a value of one in the activated isometricstate, and zero in the resting state. The line in the lowerpanel close to the stiffness points is the predicted fractionofattached bridges based on the constants obtained fromthe upper panel. Because the quality ofsarcomere lengthrecords was unsatisfactory in some fibers, velocity isplotted as fiber lengths per second so as to include alldata available. It can be seen that the equatorial signalshave similar values at a given force, while stiffness valuesare considerably smaller. The fitted intercept ofthe nor-malized 110 points on the ordinate axis has a value of0.508, that of the normalised II, points at 0.607 (thiscorresponds to shortening at Vm.). If the relation be-tween equatorial intensities and crossbridge attachmentobserved under isometric conditions can be applied dur-ing steady shortening, this result suggests that the num-

ber of attached crossbridges was reduced to 5 1-61% ofthe isometric situation when shortening at Vmax. Thestiffness points fall offbelow 0.1 P0 because ofthe effectsof tendon compliance, but points obtained above 0.1 P0can be extrapolated to their intercept on the ordinate at avalue of about 0.3, in agreement with previous findings(9-11). This suggests that during shortening at Vma,only 30% of crossbridges are attached, compared to theisometric condition.

DISCUSSIONThe fraction of crossbridges attached during shorteningis one ofthe parameters by which the values of rate con-stants used in models of muscle contraction are con-strained. Whole muscle studies of equatorial intensity

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FIGURE 5 Sarcomere length (top panel), equatorial signals (Ilo, ; I,, 0) and force (A) (lower panel) during isotonic shortening at close Vm.x.Electrical stimulation begins at the arrow. Shortening velocity 2.01 ,m per half sarcomere per second. Intensities measured without backgroundsubtraction. Spectra normalized for integrated intensity. Camera length 4.8 m, average of 20 tetani. Sampling rate 5 ms. Sarcomere lengthmonitored throughout tetanus by laser diffractometer system. Time in milliseconds.

changes during isotonic shortening have produced con-flicting data, indicating either very little change (7) or achange of the order of 50% (8). Stiffness measurementsduring shortening have shown similar dependence ofstiffness on shortening velocity to that reported here (9-11). That stiffness falls more gradually than tension canbe accounted for by the presence of negatively strainedbridges, which contribute to fiber stiffness but reduce

tension. Hence at Vmax, where tension is zero, cross-bridge attachment (and therefore stiffness) may be quitehigh. Motility assays suggest that during shortening, thefraction of attached bridges remains large, based on re-duced force noise during shortening compared to theisometric state ( 12) and evidence of a relatively longworking stroke time ( 13).

X-ray evidence from whole muscle experiments on

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Griffiths et al. X-Ray Diffraction by Shortening Fibers 1155

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FIGURE 6 Sarcomere length, equatorial signals, and force during shortening at a velocity sufficient to reduce force to 0.2 P0. Panels and symbols asin Fig. 1. Shortening velocity 1.39 ,m per half sarcomere per second. Time in milliseconds.

shortening has certain limitations, since sarcomerelength changes may not be uniform and the condition ofthe preparation is difficult to evaluate. Motility assayslack the mechanical constraints of position and separa-tion on the actin-myosin interaction that exist within amyofilament lattice. It has been shown that lattice spac-ing changes occur as a result of force development andredevelopment in living fibers ( 17), which suggests a ra-dial component of crossbridge force exists, whose mag-nitude varies with lattice spacing. The constraints im-

posed on the crossbridge cycle by lattice spacing and ra-dial forces generated during activation are unknown, butare either absent or greatly modified in motility assays.The single intact fiber preparation avoids the problemsofwhole muscle, allowing precise measurement ofsarco-mere length, shortening, and tension development,while maintaining the highly structured arrangement ofthe contractile proteins which is lost in motility assays. Italso permits the measurement of fiber stiffness withgreater precision than is possible in whole muscle.

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FIGURE 7 Top panel: force-velocity curve obtained from intact singlefibers used in x-ray diffraction and stiffness measurements. Ordinate:Velocity in muscle lengths per second; abscissa: relative tension. Thefitted line yields a Vmax of 2.59 muscle lengths per second. Lower panel:normalized equatorial signals (110, A; 111, 0) and stiffness (u) duringisotonic shortening as a function of relative force (PI/P0). Data plottedfrom 8 fibers. The lines drawn through the intensity points are linearregression fits to the intensity in each case (A, 10; B, 11). The best fitgave values for the equatorial signals at zero relative force (i.e., Vmax ) of60.65 ± 6.12% ofthe isometric signal forI10, 50.76 ± 4.45% for I,1 (95%confidence interval). The line close to the stiffness points (C) showsthe expected fraction of attached crossbridges based on the best fitobtained of the force and velocity of shortening shown in the upperpanel to the A. F. Huxley 1957 model ( 1) for the points plotted (f1 +g1 = 1 15 s-', g2 = 337 s-, h = 15 nm) using a Marquardt-Levenbergfitting routine. At velocities close to Vmax, stiffness falls away because ofthe increased contribution of tendon compliance to total stiffness. Thestiffness at Vmax is therefore obtained by extrapolation.

In the intact single fiber preparation under isometricconditions, the time courses of changes in both stiffnessand equatorial signals during the rise of tetanic tensionand relaxation are similar (6). Here we report a cleardisagreement between these two putative measures ofcrossbridge attachment during shortening. As shorten-ing velocity increases, stiffness falls off steadily to reach30% of its isometric value at Vmax, while the equatorial

signals remain virtually unchanged at velocities less than0.5 Vmax, then fall to reach 51-61% of their isometricvalue at Vmax. We will now consider some possible expla-nations for the disparity between the estimates of cross-bridge attachment from these two techniques.

First, one should consider any intrinsic limitations inthe estimation of attachment by x-ray diffraction. Thedependence of equatorial intensities on the fraction ofattached bridges has been shown only in the isometriccase (5), and during shortening a population of bridgesmay exist whose structure gives rise to an equatorial pat-tern which causes us to overestimate the fraction of at-tached bridges. However, equatorial signals from both10 and 11 reflections behave similarly, which is consis-tent with a change in the number of attached bridges(though not exclusively so). Since intensities are sensi-tive to lattice disorder and lattice spacing, these factorsmight cause us to underestimate the intensity changedue to shortening, leading to the disparity between stiff-ness and intensity data. Our studies indicate that latticespacing can affect intensities quite strongly, but the equa-torial intensities which we have examined are all affectedby about the same amount and in the same direction,increased during lattice expansion, reduced by latticecompression. It is known that the redevelopment of ten-sion from the isotonic to the isometric state is associatedwith a lattice compression ( 17) at the plateau of thelength tension relationship. However, since the intensitychanges associated with shortening per se are in oppositedirections for the 10 and 11 reflections, the effect of lat-tice expansion during shortening would be to cause the10 signal to be overestimated, and the 11 signal to beunderestimated. In Fig. 7, for example, correction forlattice spacing would tend to bring line A (for 10) andline B (for 11 ) closer together, but would not cause thecorrected lines to approach the stiffness points and socannot account for the disparity between stiffness andequatorial signals. As regards disorder, an indication oflattice disorder is a broadening of reflections propor-tional to the square of their distance from the origin ofthe pattern. An increase in this type of disorder can bedetected in the transition from the relaxed to the isomet-ric activated state in Fig. 4, where the 11 reflectionbroadens noticeably. Upon activation, the increased dis-order may cause the 10 signal to be overestimated and 11underestimated. We find that during shortening this dis-order decreases only slightly, compared to the isometrictetanus plateau, even when isotonic force is close to zero,and so any effect of disorder on the absolute intensitychange associated with the transition from isotonic toisometric contraction will be very small. Therefore, incomparison to the equatorial signal changes associatedwith activation, the change in the 11 signal associatedwith shortening would be overestimated, while that asso-ciated with 10 underestimated. In addition, since the ef-fects ofdisorder are more pronounced on reflections fur-

Griffiths et al. X Ray Diffraction by Shortening FibersGriffiths et al. X-Ray Diffraction by Shortening Fibers 1157

ther from the origin ofthe diffraction pattern, the overes-timation of the 11 signal change is probably larger thanthe underestimation of that of 10. The effect of this onFig. 7 would be to cause the lines associated with theequatorial signals to diverge from one another, 10 pointsbeing displaced towards the stiffness points, 11 pointsbeing displaced by a somewhat greater amount awayfrom the stiffness points. In view ofthe fact that both setsof equatorial signal points in Fig. 7 are rather close to-gether, we think that disorder effects on the equatorialsignals are not large, and would in any case not be able toexplain the disparity in the estimate of crossbridge at-tachment obtained from the stiffness data.

It is also unlikely that the dependence of equatorialintensities on sarcomere length significantly influencesour findings, since over the range of shortening in ourexperiments the relaxed state intensities are almost in-sensitive to sarcomere length, and in the activated stateonly a 2% change in intensity could be expected (Fig. 3).As can be seen in Figs. 5 and 6, a slight difference inisometric 10 intensity before and after shortening can beobserved, which may result from the sarcomere lengthsensitivity of Ilo in this range. The gradual increase in Iloand decrease in 1,, with increasing sarcomere length inthe activated state (Fig. 3 b) may be consistent with thereduction in the number of cycling bridges as the regionofoverlap becomes smaller. The very sharp decline in I1 Iin the relaxed state with increasing sarcomere length(Fig. 3 a), however, is much steeper than the change infilament overlap, and may be influenced by other fac-tors. For example, changes in sarcomere length are ac-companied by changes in lattice spacing, and thereforesampling of the form factor at different positions. Thiseffect would also influence the sarcomere length depen-dence of '10 and Ill. In addition, increasing lattice dis-order at longer sarcomere lengths could also contributeto a decline in II.We will now consider possible physiological explana-

tions for this disparity. Detached heads might remain inthe vicinity of the actin filament during shortening, af-fecting the equatorial signals, either as a result of diffu-sional delays or activation-induced changes in cross-bridge structure. It is known that in the relaxed state, theS 1 head is freely mobile, and we calculate that the rota-tional and translational diffusion coefficients of S1 arefast enough to ensure a restoration of the relaxed statehead distribution within a few microseconds of head de-tachment, so it is unlikely that diffusional delays follow-ing detachment cause an artificially high attached bridgeestimate from the x-ray data. It is also known ( 19) thatactivation per se does not cause a change in equatorialintensities, and therefore cannot account for the dispar-ity between stiffness and equatorial signals.A further intriguing possible explanation ofthe dispar-

ity between stiffness and equatorial signals during short-ening concerns the number of cycling heads. If it were

assumed that in the isometric activated state, most cross-bridges had both heads attached to the actin filament(either through cooperativity in binding, or because inthe isometric state a large fraction of the crossbridge cy-cle time is spent in attached states), but during shorten-ing a large population had only one head attached (thefraction of cycle time spent in attached states becomingmuch smaller than under isometric conditions), the freehead might be displaced close to a neighboring actin fila-ment, and so contribute to the diffraction pattern as ifattached. If the stiffness of a two-headed attached bridgewere the same as that of a bridge with only one headattached (i.e., stiffness proportional to the number ofattached bridges), the proportion of attached bridges es-timated from stiffness would be the same or greater thanthat estimated from the equatorial signals. If the two-headed bridge were twice as stiffas the bridge with only asingle head attached (i.e., stiffness proportional to thenumber of heads attached), then the equatorial signalswould suggest a greater degree of attachment than thestiffness measurements because ofthe propinquity ofthedetached head to an actin filament. The observationsreported here would therefore be consistent with stiffnessbeing dependent on the number ofattached heads, sinceour equatorial signals do indicate higher levels of attach-ment than does stiffness. The use of stiffness as a mea-sure of crossbridge attachment assumes that all forms ofattached bridge have the same stiffness, so if isotonicbridges were less stiff than isometric, the degree of at-tachment would be underestimated by stiffness measure-ments.Although inadequate for the description of isometric

force transients, a simple two state crossbridge modelcan describe the isotonic condition quite well. The de-pendence of force and stiffness on shortening velocity iswell fitted at steady state to the fraction of attachedbridges predicted by the model of A. F. Huxley (1), asshown in Fig. 7. However, the transient solution of thismodel (20) describes neither the time course ofthe forcetransient nor the magnitude and time course of the ap-proach of the equatorial signals to steady state valuesduring shortening adequately, using the constants deter-mined from the steady state fit. Application of the two-state model to motility assays leads to the predicted pro-portion of attached bridges rising during shortening atmoderate to high velocities ( 13), since a reduction ofcrossbridge noise from a single actin filament duringsliding is observed compared to the isometric case, whichmay result from a larger fraction of the ATPase cycletime being spent in force-generating states during short-ening. This expectation is contrary to the behavior ofboth the stiffness and the equatorial signals in our find-ings, although these authors also report that shortening isassociated with a large fall in stiffness. Clearly the twostate model of A. F. Huxley (1) is inadequate to explainour findings, and when applied to motility assays leads to

1158 Biophysical Journal Volume 64 April 19931158 Biophysical Journal Volume 64 April 1993

estimates of crossbridge attachment during shorteningwhich are at variance with both our stiffness and ourx-ray signals.The analysis of the behavior of fluorescently labeled

actin filaments in free motion on a field ofmyosin headsindicates at least 75% ofthe ATPase cycle time is spent inforce-producing states ( 12). This value is comparable tothat predicted under isometric conditions (21), andwould require a large working stroke for the attachedcrossbridge. A means of avoiding such a long workingstroke time might be found if force were exerted by"weakly bound" crossbridge states (12), which couldachieve several attachment/detachment cycles duringone ATPase cycle time. We consider this unlikely to oc-cur in living cells, since it is known that these "weaklybound' states" are present only in very small amounts atphysiological ionic strength in frog muscle, and that theirequilibrium kinetics are very fast (22). It can be shownthat the frequency response of the stiffness of weaklybound bridges as measured by sinusoidal length oscilla-tions can be described by the equation (22, 23):

M(f) = 2irf/(kb + 4ir2f2)1/2

where kb is the detachment rate constant, fthe frequencyof sinusoidal length oscillations used to measure stiff-ness. If kb is 104 s-1 (22), at 4 kHz we would expect todetect 93% of weak bridge stiffness, hence stiffness andequatorial signals should be almost equal. Nevertheless,a multiple state model containing a strongly bound at-tached state with sufficiently fast equilibrium kinetics tobe largely invisible to stiffness measurements at 4 kHzwould account for the disparity between x-ray and stiff-ness data.Whatever the cause of the difference between stiffness

and equatorial signals, the absence of a pronounced ef-fect of shortening on intensity data reported previously(7) from whole sartorius muscles ofRana temporaria islargely consistent with our findings. The load duringshortening in their experiments was never smaller than0.14 P0, which, from Fig. 7, would cause a change inequatorial signals of at most 25%, and less than 10% at0.25 Po or above. Furthermore, they were unable to ex-clude the period required to reach steady state intensityfrom their data collection during shortening, whichwould cause an underestimation of the intensity changeat any given shortening velocity. The dependence ofequatorial signals on force during shortening reportedhere is smaller than that previously reported (8) in wholesartorius muscles ofRanapipiens, where a fall in equato-rial signals to 50% oftheir isometric level during shorten-ing at 0.1 P0 was found, whereas we obtain a fall to only51-61% of isometric signals even when shortening atclose to Vma. Although quantitatively different fromour results, these previous studies support our findingthat changes in equatorial intensities during shortening

are smaller than the accompanying changes in fiber stiff-ness, and that therefore in the isotonic state one of thesetwo techniques is an unsuitable measure of crossbridgeattachment.

The authors are indebted to the members of the European MolecularBiology Laboratory Outstation in Hamburg for their expert assistancein this project, and to Mr Paolo Garzella for helpful suggestions anddiscussions.

Supported by the Medical Research Council, European Molecular Biol-ogy Laboratory, Consiglio Nazionale di Recherche, and the NationalInstitutes of Health.

Receivedfor publication 1 7 August 1992 and in finalform 21December 1992.

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