Intersarcomere dynamics during fixed-end tetanic contractions of ...

J. Phy8iol. (1979), 293, pp. 365-378 365With 9 text-ftguresPrinted in Great Britain

INTERSARCOMERE DYNAMICS DURING FIXED-END TETANICCONTRACTIONS OF FROG MUSCLE FIBRES

By F. J. JULIAN AND D. L. MORGANFrom the Department of Muscle Research,

Boston Biomedical Research Institute, 20 Staniford Street,Boston, MA 02114, U.S.A.

(Received 31 October 1978)

SUMMARY

1. The stability of sarcomere lengths along single twitch fibres from frog muscleswas examined during fixed-end tetani, using a spot follower apparatus to monitorthe length of a central segment.

2. Internal movement, with most of the fibre lengthening and small regions atthe ends shortening as the contraction proceeded, was always seen at fibre lengthsbeyond those corresponding to a sarcomere length of 2-3 pim.

3. The rate of lengthening of the central region was fastest during the slow phaseof tension rise (creep) but continued at a slower rate throughout the tetanus. Theseobservations are in accord with the idea that progressive development of sarcomerenon-uniformity is responsible for the creep phase.

4. Observations at various muscle lengths of the rate of decay of tension andthe duration of the slow phase of relaxation suggest that movement during relaxationis due to sarcomere length non-uniformities and variations of decay rate withsarcomere length.

5. The rate of tension fall after stimulation ceases in an isometric sarcomere,and the factors which determine that rate, are discussed in view of evidence fromfixed-end and length-clamped tetani, and recently reported experiments usingaequorin.

INTRODUCTION

During tetanic stimulation, the active tension in a particular sarcomere may beexpected to depend on the sarcomere length and rate of change of length (shorten-ing velocity), and to some extent, on the previous history of movement and stimu-lation. Simple models predict that the history would act only by changing thepopulation distribution of attached cross-bridges (Huxley, 1957), and so effects ofhistory would be expected to decay entirely, with a time constant comparable tothe cross-bridge cycle time. Thus, after velocity has been constant for at leastseveral cycle times, tension should be determined entirely by length and shorteningvelocity. These ideas are supported by the existence of a well-defined force-velocitycurve, at least during shortening. As has been previously discussed (Hill, 1953), alength-tension curve with a region where tension decreases with increasing length,such as the sarcomere length-tension curve (Fig. 4) of Gordon, Huxley & Julian

0022-3751/79/4560-0811 $01.50 © 1979 The Physiological Society

F. J. JULIAN AND D. L. MORGAN

(1966b), predicts instability of sarcomere lengths in that region. It is important,however, to note that the force-velocity relationship always acts to stabilize sarco-mere lengths, as a lengthening sarcomere always develops more tension, and ashortening sarcomere always less, than when isometric at the same length. Themuch greater slope of the force-velocity relationship during slow lengtheningthan during shortening means that the presence of lengthening sarcomeres in afibre will particularly strongly stabilize the existing sarcomere length distribution.Huxley & Peachey (1961) reported non-uniform sarcomere lengths, in particular

short sarcomeres near the ends of fibres tetanized at long lengths, and correlatedthe development of these non-uniformities with the slow phase of tension rise,called 'creep' by Hill (1953), seen in fixed-end tetani at long lengths. Later experi-ments (Gordon, Huxley & Julian, 1966a) using the spot follower apparatus showedthat the creep could be substantially reduced, if not entirely eliminated, by main-taining the length of a central uniform segment of the fibre constant during thecontraction, rather than the over-all fibre length.Huxley & Simmons (1970) showed that the 'shoulder' in the tension record

during relaxation was correlated with the beginning of internal length rearrange-ment. Length clamping a central segment during relaxation (Huxley & Simmons,1972, Fig. 1) has the dual effect of decreasing the rate of decline of tension beforethe shoulder and of delaying the shoulder.From these results, it is clear that intersarcomere dynamics are important in

tetanic contractions, and must be considered as a possible cause of any phenomenonbeing investigated. This paper considers fixed-end contractions in detail, and attemptsto explain various features in terms of the sliding filament theory and intersar-comere dynamics.

METHODS

Preparation

Twitch fibres, together with pieces of tendon at either end were dissected from anteriortibial muscles of frogs (Rana temporaria) which had been stored before use in a moist environ-ment at about 4 'C. The dissection was carried out at room temperature, under a stereomicro-scope equipped with a dark field illuminator, in a Ringer solution, using knives made eitherfrom pieces of razor blade or 27 gauge hypodermic needles (o.d. 0-016 in). The Ringer solutioncontained (mM): NaCl, 115; KCl, 2.5; CaCl2, 1.8; Na2HPO4, 2-15; NaH2PO4, 0-85, pH 7 0. Asmall hole was cut in each tendon and transfer to the experimental chamber was carried out in asmall glass spoon.

Experimental chamber

The experimental chamber was machined from a block of aluminum (Fig. 1) which wasthickly coated with PTFE (DuPont Teflon) and fitted with a glass floor for observation of thefibre. Peltier effect thermo-electric modules (Cambion Thermionic Corporation) were mountedbetween the rear top surface of the plate and a water-cooled heat sink and used to control thetemperature of the Ringer, which was measured by a thermistor probe. The motor and trans-ducer were mounted on three-dimensional positioners fixed to a Perspex sheet attached to theblock. A titanium arm (see Fig. 2) with a piece of 0-008 in. diameter stainless-steel wire attachedwas fixed to the motor shaft and dipped into the fluid in the chamber. A similar piece of wirewas attached to, but electrically insulated from, the tension transducer. The electrodes weremade of bright platinum and had active surfaces approximately 3 mm high running parallelto the fibre over its whole length, one on each side and approximately 5 mm away.

366

INTERSARCOMERE DYNAMICS IN FIXED-END TETANI 367

Heat sink Thermoelectric modules

Water inlet : ' Water outlet- - - - - - -.L--

Experimental Fibre Electrode 3-wayno Lt M~~~~~~~~~~~~~icrorneerw ~~~~~~transduce

Motor mount- _~~~~~~~~~__Base plate

Fig. 1. Experimental block. A description is in the text.

Procedure

Still working under the stereomicroscope, the fibres were suspended between the motor andtransducer by slipping the pieces of wire protruding from these devices through the holes inthe tendons and tying a loop of 10-0 nylon suture around wire and tendon as near as possibleto the end of the fibre. The fibre was then stretched to slightly longer than the maximumlength at which it was to be used, usually about 3-0 #Am mean sarcomere length. Two markers,of finished size 0-7 x 0-3 mm, made from titanium foil by cutting and folding the edges similarlyto the method of Gordon et al. (1966a), were gripped in a spring-loaded glass jaw and thinlycoated with tap grease. The jaw was positioned and clamped in the chamber, holding themarkers about 1 mm from the chamber floor and 2 mm apart. Using the manipulators, the fibrewas positioned centrally over the markers so that they bracketed the end-plate region of thefibre, then lowered onto them, and a light 'collar' of grease built over the fibre at each marker,sticking to the grease already on the marker on each side of the fibre. The glass jaw was thenopened, and the fibre with attached markers moved away. After the jaw was removed, thefibre was positioned in the centre of the chamber, and the whole assembly moved to the stageof a light microscope. Using a Zeiss 40/0.75 water immersion objective and a Zeiss 5 x eye-piece, any part of the fibre could be photographed on Polaroid film and mean striation spacingquickly determined by measuring the total length of fifty sequential sarcomeres with verniercalipers. The light sources were an incadescent lamp for observation and a xenon flash lampfor photography, each fitted with a narrow band green filter. A 35 mm camera could be sub-stituted, along with an Olympus 20/0.40 water immersion objective lens, to enable photographyof a larger segment of fibre on Kodak high contrast copy film. Calibration was always carriedout by use of a calibrated microscope slide. Fibre cross-section was estimated, using Polaroidphotographs to measure width and the calibrated focussing knob of the microscope to measuredepth.Experiments were performed at a variety of temperatures, from 4 'C to 20 'C and no qualita-

tive differences seen. When temperatures below dew-point were used, the entire apparatus wasenclosed in a box and an air-conditioner used to prevent condensation.

MeasurementThe tension transducer was a metal capacitance type with a compliance of 0-76 mm/N and

resonant frequency of approximately 2 kHz. The capacitance was series-resonated at 5 MHzwith an inductor, and coupled unto a phase detector circuit similar to that described byCambridge & Haines (1959). The output noise in a 10 kHz bandwidth was equivalent to lessthan 5 AN.

F. J. JULIAN AND D. L. MORGANB

Collector lens

gMirror Cathode ray tube

Fig. 2. Physical arrangement of apparatus. A, for photography;B, for use of the spot follower apparatus.

Photomultipliers

Position

Fibre 'S9 Objective

sio

Collector lens

\ /Ca~thode\ /ray tube _

Fig. 3. Block diagram of spot follower system. PMA is photomultiplier amplifier; PDA,position deflexion amplifier; LDA, length deflexion amplifier. The position and length

deflexion adjustment controls are used to position the spots with the feed-backloops open. The PMA offsets are adjusted so that a fully covered and a fully uncoveredspot give outputs of equal magnitude but opposite sign, i.e. zero output for half-

covered spots. The feed-back loops are then closed using the switches.

368A

Motor;

lass floor

INTERSARCOMERE DYNAMICS IN FIXED-END TETANI 369The length of the fibre was initially measured with a dial gauge by translating the experi-

mental stage and observing the fibre microscopically. The micromanipulators for moving boththe motor and tension transducer incorporated micrometer heads. Movement of the motorarm was signalled by a capacitance bridge circuit, using the rotor of the motor as movingvane. The circuitry for this was supplied with the motor (General Scanning) and the calibra-tion and linearity checked by photomicroscopy of the motor arm, using multiple exposurephotographs.The spacing of the markers, i.e. the length of the central segment, was measured using a

spot follower system similar to that of Gordon et al. (1966a), and shown in Figs. 2 and 3. Thereare several differences between this and the earlier system. Photomultipliers (EMI type 9524B)were used rather than photocells enabling the use of lower intensity spots, prolonging cathoderay tube life. This system was designed to be used with shorter fibres (typically 6 mm whenjust taut), and hence smaller marker spacings. This meant that the light from the two spotscould not be conveniently separated while focused on the markers as before, and so a microscopeobjective lens (Leitz 6/0-18) was used to refocus the spots onto two prisms acting as mirrors(see Fig. 3) mounted in place of the eye-piece tube. The dual lens system below the stage enabledthe over-all length of the light path to be adjusted without changing the 'gain' of the system,i.e. the magnification of spot separation from tube face to the plane of the markers. Operationof the system was essentially the same as Gordon et al. (1966a), feed-back being used to keep thespots on the tube face in such positions that their images in the plane of the fibre followed theedges of the markers, so that only half as much light reached the photomultipliers as whenthe markers were absent. In all records shown, lengthening is upwards, and calibration barsare in nm per half-sarcomere.

Motor and control loops

The motor used was a G100PD from General Scanning Inc. Either the motor arm positionor marker spacing signal could be compared with a reference signal and the difference used todrive the motor. Stabilization of the control loop was achieved by velocity feed-back (deriva-tive of motor position), a variable lag network in the feed-back loop, and variable proportions ofvoltage and current feed-back around the power amplifier. These were all adjusted to give anoptimum step response. The compliance at the end of the motor arm with the feed-back operatingwas measured as 2 mm/N.

Timing, stimulation

The experiment was controlled by a digital timer which controlled stimulation, motorreference signal generation, photographic flash and recording equipment.

Stimulation was by square wave, amplified by a power amplifier and coupled via a 10 OLFpaper capacitor to the electrodes. Thus, current pulses of alternating polarity and 100 ,tsecduration passed through the solution and fibre. Stimulation frequencies given in Figure legendsare pulses per sec, i.e. twice the frequency of the square wave, and were chosen as sufficient toproduce e smooth tetanus. Stimulus amplitudes of 1-3 times threshold and rest periods of100 sec per sec of stimulation were routinely used.

Recording and analysisIn the early experiments, signals were recorded on a storage oscilloscope (Tektronix D13),

and photographed on Polaroid type 107 film. In most of the experiments a digital oscilloscope(Nicolet Explorer III) was used. This sampled (typically 1024 samples/trace) and digitized(12 bits) the incoming signals and stored the samples in internal memory from which they weredisplayed on the screen. Traces could be shifted, magnified up to 64 times in each direction,measured by cursors and numeric display, and plotted at constant pen speed rather thanconstant sweep speed on an X-Y plotter (Hewlett-Packard). A minidiskette unit built into theoscilloscope was used for long-term storage and retrieval of data.

370 F. J. JULIAN AND D. L. MORGAN

RESULTS

In the interest of brevity and clarity, the diagrammatic sarcomere length-tensiondiagram of Gordon et al. (1966b) is reproduced here as Fig. 4, annotated with theterms and expressions which will be used in the following text.

Typical families of active tension traces recorded during fixed-end contractionsat various lengths are shown in Fig. 5 for muscle lengths less than, and in Fig. 6

Short Moderately long Very longAscending limbPlateau Descending limbSteep Shallow

PoC

C

1 5 2 2:5 3 3.5Sarcomere length (mm)

Fig. 4. The sarcomere length-tension curve of Gordon et al. (1966b). This diagrammaticform of the observed curve is used here to define terms used in the text. Tension isnormalized and sarcomere lengths are in /tm.

Fig. 5. Isometric tetani at short lengths. The numbers on the curves are the passivesarcomere lengths near the centre of the fibre in 1um, the unlabelled traces being 1 9 and2-0 ,m. 16 0C, stimulation frequency 50 sec-'.

for muscle lengths beyond the plateau of the length-tension diagram. In Fig. 7tension and marker spacing records are shown from another fibre during isometriccontractions beyond the plateau.The initial rate of rise of tension appeared remarkably constant over a range of

sarcomere lengths from 1-7 ,um to beyond 3 0 ,tm. Below the slack length of thefibre, corresponding to approximately 2 Itm sarcomere length, there is a delaybefore the tension begins to rise, presumably the time required to take up the slack

INTERSARCOMERE DYNAMICS IN FIXED-END TETANI 371in the fibre. For sarcomere lengths below 1P6 /m, the delay increases much morequickly with decreasing sarcomere length, and the initial rate of rise of tensionbecomes much less. This correlates with the dramatic decrease in unloaded shorten-ing velocity seen by Gordon et al. (1966b) at these lengths.

2 2

2 mN

500 msec

Fig. 6. Isometric tetani at long lengths. The numbers on the curves are the passivesarcomere lengths near the centre of the fibre in jam, the unlabelled trace being 2-4 jIm.ItIC, stimulation frequency 30 sec-1.

2-2

2-8 _

24

3-0

3.4

2-6

3-2

4 mN

65 nm

1 sec

Fig. 7. Isometric tetani with marker spacing records at long lengths. The upper traceof each pair represents the distance between the markers, i.e. the length of a centralsegment of the fibre with lengthening up. The calibration is nm/half sarcomere. Thenumbers are the passive sarcomere lengths near the centre of the fibre in /sm. 20 TC,stimulation frequency 80 sec-'.

The shape of the later stages of the tension trace is very characteristic of themuscle length. In the range 1*7-2-2 ,um the tension typically rose quickly andremained nearly steady as long as the tetanus was continued. At shorter sarcomerelengths, the tension rose in a slow continuous curve to a final steady value. Forlengths beyond the plateau the fast upstroke of tension was followed by a slow creepphase, which generally became more distinct at longer sarcomere lengths, and whichvaried in duration and slope to some extent from fibre to fibre and from time to

F. J. JULIAN AND D. L. MORGAN

time, depending on the previous history of the fibre. However, the amount of creeptension was never so large that tensions equal to the plateau tension were achievedbeyond 2 3 j#m, as shown by Iwazumi, Pollack & ter Keurs (1977). An example ofvariation with history is shown in Fig. 8 which shows two successive tension recordstaken from a fibre which had been tetanized at 2 1 ,um sarcomere length, left slackfor some minutes, manually stretched to 3 0,um sarcomere length, tetanized (tracea), rested at 30 #sm, and then tetanized again (trace b). The second record showeda shorter, steeper creep phase. Shortening, stimulating while short, and relengthening

gf_~~~~~~~~~1mN

500 msec

Fig. 8. Successive tetani on a 'fresh' fibre. Trace a is the first tetanus at long length,and trace b the next tetanus, without any length changes between. Note that the base-lines have been offset for clarity, but that trace a does develop more tension. 14 'C,stimulation frequence 40 sec-', mean sarcomere length 3 0 jtm.

produced a third tetanus very similar to the first. When the stimulation was con-tinued long enough, the creep phase always ended, and was followed by a slowdecline.The marker spacing records during this part of the contraction are very significant

(Fig. 7). At the plateau (2.2 4am) there is very little internal movement. (The initialshortening was probably due to slack in the fibre or to tendons stretching.) Atlonger lengths, stretching of the central segment is observed, and a biphasic nature,synchronous with the phases of the tension record becomes apparent. This move-ment always continued for the whole duration of the contraction, even after thetension had peaked and begun to decline. Thus, no part of a fixed-end tetanus atsarcomere lengths beyond the plateau was fully isometric, in the sense that therewas absolutely no movement. Internal movement was always seen. At very longlengths (beyond 3-0 ,tm sarcomere length), the total amount of movement beganto decrease again, although the total tension rise during the creep phase did not.Careful examination shows that at least the major part of this decrease occurredin the second phase, i.e. after the peak in the tension record.The tension records during relaxation also had several consistently observable

features. The slow phase of relaxation and the subsequent shoulder were mostclearly seen at sarcomere lengths beyond 2-0 /tm, i.e. on the plateau and descendinglimb of the length-tension curve. The slope and duration of this phase were alsosomewhat variable from fibre to fibre, and with previous history of stimulation.

372

INTERSARCOMERE DYNAMICS IN FIXED-END TETANI 373

However, the duration always decreased monotonically with increasing fibre length.Straight lines drawn through this phase to the time axis did not intersect it inany consistent sequence, and it appeared that the intersection point was essentiallyindependent of fibre length, the scatter being greater for a 'new' fibre than for onewhich had been repeatedly tetanized at various lengths. Segment length-clampedfibres, e.g. Julian, Sollins & Moss (1978), Fig. 1 a, show very little scatter. An intercept

/ 1 ~~~~110nm| t ~~~~~~1 mNl1~~~~~~~~~~~~~~~~~ s

Fig. 9. Different segments of the same fibre. Traces a and b represent the length changes(lengthening up) of two adjacent segments of a fibre recorded during two successivetetani. The calibrations are in nm/half sarcomere, and are slightly different due toslightly different initial segment lengths (115 nm for a, 110 nm for b). The two accom-panying tension records are superimposed as trace c. 11 0C, stimulation frequency25 se,', mean sarcomere length 3-0 /tm.

independent of length implies an initial decay rate proportional to the tension, aswould be expected of populations of various numbers of identical cross-bridgesdetaching with the same rate constant. The net result of this feature and the decreas-ing duration of the slow phase with increasing length is that the shoulder or pointof give occurred at a progressively higher proportion of the final tension as themuscle length increased. The marker spacing records show that this slow relaxationperiod was the most nearly isometric time during the whole contraction (e.g. recordfor 2'6,tm, Fig. 7).At sarcomere lengths below 2-1 num, the linear phase and its terminal shoulder

become progressively less distinct. However, where they are distinguishable (Fig. 5,sarcomere length > 1.7 sum), the slope appears to be constant, rather than propor-tional to tension.The later or 'give' phase of relaxation was similarly indistinct at short lengths.

Beyond the plateau region, however, a consistent pattern emerged. After theshoulder, a rapid decrease in tension occurred, accompanied by rapid shorteningof the fibre segment between the markers. At moderately long lengths, this decreasetook the tension to near zero (insignificant passive tension), and the marker spacingrecord showed an overshoot, shortening beyond the initial passive value, and thenreturned to the original point fairly rapidly. As the passive tension increased atlonger lengths, a 'catch' point developed in the tension record, accompanied by a

F. J. JULIAN AND D. L. MORGANdecreased rate of shortening, and the marker separation overshoot decreased anddisappeared. Eventually, for sarcomere lengths beyond 3 2/,tm, both the tensionand marker separation records developed a final phase of very slow monotonicreturn to initial values.

In several experiments, more than two markers were attached to a fibre to enablecomparison of marker spacing records from different parts of a fibre. Significantdifferences were never seen. A typical result is seen in Fig. 9, showing two successivecontractions (tension records superimposed) and the corresponding marker separa-tion records, trace (a) from two markers about the end-plate, and trace (b) usingone of these markers and another one further from the centre of the fibre. Apartfrom a scaling factor (the initial separations are different) the two records are verysimilar.

DISCUSSION

CreepIt is clear that damped instability of sarcomere lengths does occur at lengths

corresponding to the descending limb of the sarcomere length-isometric tensionrelationship, but not at full overlap. The observations made here are consistentwith the explanation of creep offered by others (Hill, 1953; Huxley & Peachey, 1961;Julian et al. 1978). That is basically that the tension increases during the creepphase because a small proportion of the sarcomeres shorten, increasing their tensiongenerating capacity, and stretching the rest, which bear the extra tension in accordwith the stretch part of the force-velocity relationship. After the creep of tensionends, the extra tension above isometric is borne by continued lengthening of mostof the fibre, and beyond mean sarcomere length 3'O Im partly by the passivestiffness. This passive stiffness would account for the reduction of stretch rate seenafter the tension peak at lengths beyond 3-0,tm.

Position and cause of shortening sarcomeres

The nature of the descending limb of the length-tension curve, i.e. decreasingtension with increasing length, predicts that any non-uniformities of sarcomeretension generating capacity will lead to dispersion of sarcomere lengths on activation.Such non-uniformities of strength may result from variations in initial sarcomerelength, fibre area, or degree of activation. We have never found the regions whichcontract during a tetanus at long lengths, nor those that 'give' first during relaxation*to be within the segment of fibre between markers. Photographs taken to studythe shortened sarcomeres have always found them to be within, or immediatelyadjacent to, the tapering portion at the end of the fibre. Consequently, our conclusionis that- the major regions in which sarcomeres shorten and 'give' are normally atthe ends of the fibre. Some fibres may well depart from this norm, as reported byEdman &-Flitney (1978), possibly due to a particularly non-uniform cross-section,or strands of attached connective tissue. If the stronger sarcomeres are normallynear the end, furthest from the point of innervation, and in or near the taper atthe end of the fibre, then shorter passive sarcomere length seems the only viablereason for these sarcomeres having greater strength than the others. This in turn

374

INTERSARCOMERE DYNAMICS IN FIXED-END TETANI 375

is most simply explained by the end regions having greater passive stiffness, perhapsassociated with the insertion of the fibre into the tendon.

Linear phase of relaxationIf the sarcomeres which contract and those which 'give' are, indeed, the same

ones, a connexion between the two forms of behaviour might be expected. Onepossibility is suggested by the observations. of 'slope and duration of the linearphase of relaxation. If the tetanus is continued long enough, the shortening sarco-meres will shorten over the plateau and down the ascending limb, tending slowlytowards the point where the tension generating capacities of lengthening andshortening sarcomeres are equal. As contractions are carried out at longer fibrelengths, the shortening sarcomeres can be expected to shorten further down theascending limb, since the tension is lower. The records of relaxation suggest thatthese shorter sarcomeres relax more quickly, whereas all the sarcomeres withlengths corresponding to the descending limb relax at about the same rate (in percent per see). This would both cause the ends to give, and cause this to occur earlierin contractions at longer length, where the difference in sarcomere lengths, and hencerelaxation times is greater. Thus, the observation that 'the duration of mechanicalactivity varies along the length of the fibre' (Edman & Flitney, 1978) may beexplained simply by the different sarcomere lengths at the end of the tetanus. Itmay be noted that Figs. 6 and 7 and all our other records showing the time from endof stimulation to 'give' decreasing with increasing sarcomere length, contradictEdman & Flitney's (1978) statement that this time increases. The only explanationwhich we can suggest is that termination of the tetanus before the end of the creepphase would be expected to give different results if our suggested explanation iscorrect. These authors did not specify the duration of their tetani, and we have notexperimented with this variable.The shallow part of the descending limb of the sarcomere length-tension curve

(Fig. 4) is perhaps the least understood part of that curve (Gordon et al. 1966b;Julian et al. 1978). The most basic question is whether the tension decreases relativeto the plateau because (a) there are fewer active cross-bridges, (b) some other forceopposes shortening, or (c) each cross-bridge exerts a smaller force. The observationhere that decay rate is constant rather than proportional to tension is most simplyaccommodated by (b) above. In this explanation, the same number of bridgesinitially decay at the same rate as on the plateau, but a constant compressive forcereduces the net tension. Some other evidence is available (Bressler & Clinch, 1975;Sandberg & Carlson, 1966; Aubert, 1956), suggesting that metabolic activity andmuscle stiffness do not decrease with tension in this range, also supporting scheme(b) above (or possibly (c)).

The 'very uniform fibre'The result shown in Fig. 8, that the fibre, when presumably more uniform, and

with a slower creep rate, in fact developed more creep tension than it did whenless uniform, provides the basis for some speculation as to the performance of a'very uniform fibre'. By extrapolation from these results, a fibre with very littlepassive sarcomere length dispersion would be expected to give a tetanus with a

F. J. JULIAN AND D. L. MORGAN

long, slow creep phase, but generating a very large creep tension. This somewhatparadoxical result may be explained as follows. Greater uniformity of sarcomerelengths will not produce stability. A sarcomere length-tension relationship witha descending limb means that sarcomere lengths in a fibre are inherently unstable.The degree of initial non-uniformity will only affect the rate of development andthe pattern of non-uniformities, not whether or not non-uniformities will develop.

In a more uniform fibre, sarcomere lengths will still be unstable, but those sarco-meres which begin to contract are only able to do so at a slower velocity due to smallerdifferences in tension generating capacity. Thus, instead of a few sarcomeres con-tracting rapidly, and quickly raising the tension above the isometric capacity ofall the others, and thus stretching them, the tension rises more slowly and moresarcomeres are able to begin to contract, so that the proportions of shortening andlengthening sarcomeres are more nearly equal. This means that the (fewer) stretchingsarcomeres can be stretched more quickly and hence generate more tension, whilethe (more) shortening sarcomeres are contracting less quickly, generating moretension and taking longer to pass over the plateau of the length-tension relationship.This prolongs the creep as it is this passing off the descending limb which decreasestheir strength and causes the tension to start falling. Hence, a more uniform fibre,like a length-clamped fibre, will have a slower creep phase, enabling more accurateestimation of the isometric tension by extrapolation as in Gordon et al. (1966a,Fig. 13), but the peak or final tension reached may well be greater, and more inerror as an estimate of the isometric tension, than for a less uniform fibre. What isclear from the literature is that measuring the peak tension does not give consistentresults (compare Ramsey & Street, 1940; Iwazumi et al. 1977, Fig. 1B; and ourFig. 6) while measurement of the fast phase only is very consistent (Gordon et al.1966b; Julian et al. 1978; Iwazumi et al. 1977, Fig. lA).under a wide range ofexperimental conditions.

Isometric turnover ratesWhen it was first realized that the slow linear phase of relaxation was isometric,

and the later exponential phase was accompanied by extensive movement and socould not be taken to represent anything fundamental, Huxley & Simmons (1972)noted that this did not necessarily mean that this slow decay of tension was a trueindication of the detachment rate of cross-bridges. They noted the other possibilitythat the 'active state' fell at this rate when the muscle was isometric. Since then,two pieces of evidence have come forward which suggest that this slow declinedoes reflect the rate of detachment of cross-bridges. The photoprotein aequorinhas been used as an indicator of intracellular free Ca2+ concentration. The publishedrecords of Blinks, Rudd & Taylor (1978) show the luminescence returning to base-line levels well before the shoulder of relaxation (see their Fig. 14). Although thereare some uncertainties in the use of aequorin, it seems clear that free Ca2+ concentra-tion falls much more quickly than tension. The second piece of evidence to be takenwith this is the measurements of the dynamics of the binding of Ca2+ to isolatedtroponin C by Johnson, Charlton & Potter (1978), which showed a half-time ofapproximately 3 msec for removal of Ca2+ from the Ca-specific sites. Together these

376

INTERSARCOMERE DYNAMICS IN FIXED-END TETANI 377

results suggest that ions bound to troponin during contraction are removed muchmore quickly than the fall in tension. The conclusion that isometric detachment isindeed as slow as suggested by the slope of the linear phase of relaxation is thussupported. In fact, the records of Huxley & Simmons (1972, Fig. 1) of fixed endand segment length-clamped relaxations on the same fibre show, in accord with ourown observations, that segment clamping both prolongs and decreases the slope ofthe linear phase, suggesting that the truly isometric detachment rate is very slow.The presence of rigor complexes has been shown to increase the calcium affinity

of troponin in thin filaments (Bremel & Weber, 1972). It has been suggested thatforce-generating complexes may have a similar effect (Weber & Murray, 1973), andthat in this way, Ca2+ removal could control the rate of relaxation. However, thenumber of attached cross-bridges in a length-clamped fibre would be only slightlygreater than in the slowly stretching region of a fixed-end fibre, the tension actuallybeing smaller, whereas the difference in time to 'give' can be substantial. Hence, itseems unlikely that this type of co-operativity can explain the effects of lengthclamping.

This work was supported by the following grants: an N.I.H. research grant, HL-16606,from the National Heart, Lung and Blood Institute, and grants from the American HeartAssociation, No. 77-616, and the Muscular Dystrophy Association.

REFERENCES

AUBERT, X. (1956). Le Couplage Energetique de la Contraction Musculaire. Bruxelles: EditionsArscia.

BLINKS, J. R., RUDEL, R. & TAYLOR, S. R. (1978). Calcium transients in isolated amphibianskeletal fibres: detection with aequorin. J. Physiol. 277, 29-323.

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