proportional to the rise in tension as the muscle was stretched.

Transcription

1 J. Physiol. (1975), 247, pp With 5 text-figures Printed in Great Britain THE RELATIONSHIP OF ADENOSINE TRIPHOSPHATASE ACTIVITY TO TENSION AND POWER OUTPUT OF INSECT FLIGHT MUSCLE BY JUDITH PYBUS AND R. T. TREGEAR From the A.R.C. Unit of Muscle Mechanisms and Insect Physiology, Department of Zoology, University of Oxford, Oxford OX1 3PS (Received 28 May 1974) SUMMARY 1. On a simple model of actomyosin interaction, the tension cost (ATP hydrolysed/unit tension) and the frequency of low amplitude oscillation optimum for work production are both determined by the rate of detachment from the actin filament of the myosin crossbridge. To test this model, the two parameters were measured under different conditions using glycerol-extracted Lethocerus cordofanus dorsal longitudinal flight muscle fibres. 2. The ATPase activity of the static muscle rose by an amount approximately proportional to the rise in tension as the muscle was stretched. 3. When the muscle fibres were sinusoidally oscillated at 5-1 Hz by 2 % of their resting length they produced a large amount of mechanical power and hydrolysed approximately twice as much ATP per unit mean tension as they did when static. The ATPase activity was linearly related to the mean tension during oscillation. 4. The experiments were repeated at temperatures between 12 and 3 C and the tension cost and the optimal frequency of oscillation of the fibres were found to rise with temperature. 5. Removal of phosphate from the incubating medium reduced both the tension cost and the optimal working frequency. Addition of pyrophosphate or sulphate reduced both parameters still further. 6. From these results the tension cost of static muscle was shown to be proportional to its optimal working frequency. 7. ATPase activity rose monotonically with power production at workproducing frequencies and at moderate degrees of stretch. A high absolute efficiency was found under a wide range of conditions. 8. The proportionality between tension cost and optimal frequency is evidence for the proposed model of actomyosin interaction.

2 72 JUDITH PYBUS AND R. T. TREGEAR INTRODUCTION Since its discovery (Jewell & Riiegg, 1966) the glycerol extracted preparation of waterbug flight muscle has been used for a wide variety of observations on the structure and behaviour of the contractile matrix (for a general review of the field, see Tregear, 1975). The particular advantage of the preparation is that it allows measurement of ATP hydrolysis in the matrix either during continuous isometric activation or during sinusoidal oscillations of length in which the muscle performs a large amount of mechanical work. It is therefore peculiarly suitable for the study of the relations between the ATP hydrolysed and the tension or work produced by muscle. Many such studies have been made, notably by Riiegg and his collaborators (Schidler, 1967; Steiger & Riiegg, 1969; Riiegg & Stfimpf, 1969; Breull, 1971); they have obtained correlations between ATP hydrolysed and the two mechanical parameters and have hence been able to estimate the 'chemomechanical efficiency' of the muscle (work/atp hydrolysis) and its 'tension cost' (ATP hydrolysis/tension.time) under various chemical and mechanical conditions. The aim of the present experiments was to test a two-state model of crossbridge action. Theoretical predictions from the two-state model On the simplest model of crossbridge action, such as that proposed by Huxley (1957), the bridge is either attached, in which state it is capable of performing mechanical work, or it is detached. The optimum angular frequency for work production at low amplitude oscillation of length is, on such a model, equal to the sum off and g, the rate constants governing the attachment and detachment steps (Thorson & White, 1969), 27rF = f+g. X-ray diffraction studies show that only 1-2 % of bridges are attached simultaneously during working oscillation of active flight muscle (Armitage, Miller, Rodger & Tregear, 1973) so g must be 5-1 times larger than. Thus the optimum angular frequency for work production at low amplitudes approximates to g. On the two-state theory, and assuming that each cycle of attachment is accompanied by hydrolysis of one molecule of ATP (Lymn & Taylor, 1971), it follows that each ATP hydrolysis is accompanied by the production of tension. The magnitude of the tension impulse P, produced by an attached crossbridge, depends on the mean instantaneous tension, -, and the mean probability of detachment, g, which determines the duration of attachment (P = j5/g). The magnitude of the tension impulse per bridge

3 TENSION COST IN FLIGHT MUSCLE 73 cycle is related to the energetic cost of tension production of the whole fibre. If and only if remains constant, tension cost is a reftexion of the duration of attachment, and so of g. When the muscle is static, g is equal to g. Thus mechanical and chemical studies of muscle activity can both give rise to measurements of g, the detachment rate constant on a simple two-state model. If the model is correct, the two experimental parameters should be proportional to one another. We have looked for such proportionality in the present experiments by comparing tension cost and optimum oscillation frequency under various different conditions. Riiegg, Schhdler, Steiger & Muller (1971) recorded a decrease in the frequency of isometric oscillations following step changes in length performed in the absence of phosphate. White & Thorson (1972) observed a decrease in the rate of change of tension in the absence of phosphate. Variation in the calcium concentration (Abbott, 1973a, b) and ionic strength (SchAdler, Steiger & Riiegg, 1971) and temperature (Aidley & White, 1969; Pringle & Tregear, 1969) have also been found to accompany variations in the speed or optimum frequency of contraction. Of these possible variables, temperature and the effect of anions, including phosphate, were tested. A brief report of the results has already been published (Pybus & Tregear, 1973). METHODS Material Dorsal longitudinal muscles of Lethoceru8 cordofanus were dissected from freshly killed bugs and immersed in a neutral glycerol solution (5 % glycerol, 1 mm-kcl, 1 mm dithiothreitol, 5 mm-kh2po4:k2hpo4 buffer at ph 7). To assist penetration of glycerol into the fibres the muscles were kept under low pressure and the solutions shaken for 24 hr. They were then stored at - 18 C for 1-16 weeks. Small bundles of fibres were removed as required for experiments; only muscles which would provide and maintain a high power output were used. Incubation 8olution8 The standard incubation medium consisted of 5 mm-mg-atp at ph 6*95 and 1 nm (relaxing) or 1-5 /LM (activating) free Ca2+ concentration; ph was buffered by 1 mm-kh2po4:k2hpo4, except where otherwise stated, and pca by 4 mm- CaEGTA:EGTA (EGTA = ethylene glycol bis(-aminoethyl ether) N,N -tetraacetic acid). 1 mm-nan3 was added to all solutions to inhibit mitochondrial ATPase (Ruegg & Tregear, 1966). Other anions were added, where stated, as K+ or Na+ salts. The ionic strength (m) was made up to -8 M with KCl. Ionic species and concentrations were computed from the known stability constants (Sillen & Martell, 1964; Perrin & Sayce, 1967). Where conditions, e.g. temperature, were changed, the effect of the change on the ionic composition of the medium was computed and allowed for in making up the medium.

4 74 JUDITH PYBUS AND R. T. TREGEAR Incubation technique A bundle consisting of one or two muscle fibres was dissected out and fixed to stainless-steel pins by a sheath of cellulose glue, applied dissolved in acetone. The pins were attached to the driven-oscillation apparatus described by Jewell & Ruegg (1966), in which the muscle may be held at any desired mean length and oscillated by a known amplitude about that length. A digital resolved component indicator (Solartron JM 16) provided the sinusoidal signal to the length vibrator and correlated these length changes with tension changes measured by an RCA 5734 mechanoelectrical transducer. The oscillatory response was thus recorded as tension changes in phase and in quadrature with the length changes; it was also displayed graphically on an oscilloscope as a length-tension hysteresis loop. The mean tension during oscillation was estimated from the centre of gravity of the loop, relative to a base line established by briefly slackening the fibres to zero tension. Transducer drift did not allow continual monitoring of tension but experiments showed that mean tension and power output in one fibre at one frequency and amplitude are closely coupled so that small adjustments of length made to maintain a constant power output as a consequence establish a constant tension. Hence mean tension, work per cycle, and power output of a fibre were continuously monitored, and could be maintained at chosen values, during incubation. The fibres were incubated in -2 ml ATP-salt solution for 1-3 min, at 2 C unless otherwise stated. Fibre performance was kept constant at the selected frequency and amplitude of oscillation during one incubation as described above. One fibre was used for an average of three successive incubations until its performance deteriorated, probably due to strains received when the fibres were moved in or out of the solutions. Mechanical conditions were adjusted to give the optimal power output that could consistently be maintained over the 2 min period necessary for performing chemical estimations on the incubation medium. 2 % amplitude of oscillation was selected; higher amplitudes gave greater work initially, but led to progressive fibre damage, signalled by gradual and irreversible loss of tension and work. The frequency was adjusted to that providing optimal power output at 2% amplitude for the particular fibres used. Estimation of ATP hydroly8ed At the end of incubation -18 ml. of incubating medium was removed and its content of either ADP or inorganic phosphate was measured. Blank measurements were made on medium which had not been used for incubation of fibres, to obtain an estimate of ADP or Pi present as contaminant in the solutions. Phosphate was measured by spectrophotometric estimation of butanol-extracted phosphomolybdate by the method of Marsh (1959). ADP was assayed by enzyme-coupled oxidation of NADH, estimated spectrophotometrically (Bergmeyer, 1965). As this method proved more accurate and easier to operate, it was preferred except where large quantities of added ADP in the solution made it impractical. The most probable source of error in this method is adenylate kinase, which is known to be in high concentration in Lethocerus flight muscle (Abbott & Leech, 1973), and could reduce the amount of ADP present. Theoretically equilibrium should be reached with degradation of an experimentally insignificant concentration of ADP. In control experiments to check this point, a set of experimental solutions was split into two aliquots and one analysed of for ADP (qadp) and phosphate (qp) produced by the fibres; qadp = 7-7 ± -8 (s.e. mean) n-mole, qp = 7-9 ± 1-1 n-mole, q(adpp) ± 1-2 n-mole, fifteen expts. Thus there was no significant difference between the two estimates although it is evident that a small difference would not have been detected.

5 TENSION COST IN FLIGHT MUSCLE The amount of ADP or phosphate produced by a fibre bundle was found to be proportional to incubation time, as had been observed before (Ruegg & Tregear, 1966). Results were therefore cited as hydrolysis rates and termed 'ATPase activity', expressed in pmoles ATP hydrolysed per centimetre fibre per minute (p-mole. cm-'. min-'). E8timation of the optimum working frequency The frequency of oscillation at which most work was produced (F) was used as an index of mechanical performance of the fibres. This was measured at 2 % amplitude, i.e. that standard for the chemical studies (F2.); and at -2% (FO.2). At this low amplitude the mechanical performance of flight muscle closely matches the theoretical performance predicted from Thorson & White's (1969) interpretation of the twostate model and hence F *2 can be taken as an estimate of g. Low amplitude studies were most easily performed using the computer-controlled procedure designed by Abbott (197), which is rapid and accurate relative to the ATPase measurements. Alternatively, measurements were made using the Solartron JM16. Root mean square values of the mid-length tension difference were plotted against the logarithm of frequency, and optimum frequency for work at -2 and 2 % amplitude estimated from the graph. Numerical treatment For each defined set of conditions, ATPase activity was plotted against mean tension, experiments in similar conditions but on different fibre bundles being plotted on the same axes. On the assumption that the overwhelming error lay in the ATPase activity estimations, a regression of ATPase activity upon tension was calculated, and the resulting regression coefficient termed tension cost; it is cited in moless ATP hydrolysed per centimetre fibre per minute per Newton of mean tension exerted molee. cm-'. min-'. N-1). Tension cost is'the inverse of the more often used term, holding economy (e.g. Goldspink, Larson & Davies, 197). As measurements were made under static and dynamic mechanical conditions, a static (C.) and dynamic (CD) tension cost was obtained for each condition. 75 RESULTS Relaxing solution When the free calcium ion concentration was very low (approx. 1 nm), the muscle fibre ATPase activity was also initially very low, p-mole. cm-1. min- (S.E. of mean, five expts.) and the fibres did no oscillatory work. On prolonged incubation in Ca2+-free solution the ATPase rose; after 2-3 hr it was p-mole. cm-'. min- in the same experiments, and in the two cases tested the fibres did a small amount of oscillatory work; see Pybus (1972) for further details. Such prolonged immersions in Ca2+-free solution were avoided in all subsequent experiments. Activating solution General observations In the presence of high concentrations of free Ca2+ (1-5 fm), the muscle ATPase activity was raised even when the fibres were slack ( p-mole. cm'. minm-, ten expts.). When the fibres were stretched by

6 76 76 ~JUDITH PYBUS AND B. T. TREGEAB Mean tension (pun-fibre-') CI E 15I B 7.5 CI E I E U d a- I- 1 [- 5 I I U ȯ 5 1 Mean tension (pn.fibre-') I I I II o Extension (%Q~ ' Fig. 1. For legend see facing page. t I I 1-3 % of their resting length, 1, their tension and ATPase both rose (Fig. 1 A, open circles). Once stretched by this amount the fibres would produce work when oscillated. Measurement of chemical activity during working oscillation at 2 % and optimum frequency showed that under these conditions ATPase and mean fibre tension were still related approximately linearly, but the over-all ATPase rate was higher than in the

7 TENSION COST IN FLIGHT MUSCLE 77 isometric case so that the slope was steeper (Fig. I A, filled symbols). Most fibres produced optimal work at an initial stretch of 2-3 % lo. If they were stretched beyond 3 % 1 the mean tension in the oscillating muscle rose further but the work production fell (Fig. 1 B, dashed lines). Under these 15 E E* / LI co so 1 ISO Mean tension (,un. fibre-') Fig. 2. The relation of ATPase activity to mean tension of muscle fibres oscillated at 2 % amplitude and at a frequency above that at which positive work was produced by the fibres. Filled circles represent points obtained from a number of different fibre bundles (1 or 2 observations obtained from each bundle) incubated in the same medium and at the same temperature. Frequency of oscillation varies from 1 to 25 Hz but in no case was positive work produced at the frequency selected. Open circles represent points obtained from slack, static fibres (see text). Fig. 1. The relation of ATPase activity and power output to mean tension in individual experiments. A: ATPase activity at different mean fibre tensions of fibre bundles stretched statically (open circles), or stretched during oscillatory length changes of 2- % 1 and optimal frequency for work production, 5 to 8 Hz (filled symbols). Each line joins points obtained from successive incubations on one fibre bundle. B: ATPase activity and power output of fibres at different degrees of extension, and thus at different mean tensions. Two experiments, each on one fibre bundle only. Oscillation amplitude 2 %, frequency 8 Hz (circles) and 7 Hz (squares). Interrupted lines and open symbols (- - -) represent power output, continuous lines and filled symbols (-*-) represent ATPase activity of oscillating muscle. The degree of extension of the fibres in one experiment (designated by the squares) is shown.

8 78 JUDITH PYBUS AND R. T. TREGEAR conditions ATPase activity continued to rise in parallel with mean tension (Fig. 1 B, continuous lines). When oscillated at frequencies above 1 Hz and at 2 % amplitude, the fibres produced no oscillatory work but the ATPase activity remained much greater than that of a slack muscle ( p-mole. cm-'. min-', twelve expts.) and again it rose monotonically with tension (Fig. 2). In the majority of experiments each fibre bundle yielded only one or 1 C E A EU a' E IL 5._J 1 Mean tension (#N.fibre-') 5 >- NE X -. I _-1 U> E C U 2 V %I C.. I.E VI,'._ Temperature-' (K-1 x 13) Fig. 3. For legend see facing page. 3-6

9 TENSION COST IN FLIGHT MUSCLE 797 two measurements ofatpase activity under similar mechanical conditions. Those cases where more than two measurements were obtained are presented in Fig. 1. Data from other experiments were amalgamated and plotted on one pair of axes, as in Fig. 3 A. Zero tension measurements obtained on static fibres were included in calculation Of CD as control experiments showed that oscillation did not change the ATPase activity of a slack fibre. In Table 1, measurements of CD including and excluding the zero tension points obtained on static muscle are shown (CD, estimates I and II). Examination of the two estimates shows that inclusion of these points does not significantly affect the value of CD but reduces considerably the s.e. of the measurement. Estimate I Of CD was therefore used for further analysis. Analysis of the regression lines and tension costs obtained from the amalgamated data shows that the collected results lead to the same conclusion as the data from individual experiments shown in Fig. 1: ATPase activity increases linearly with tension and more ATP is hydrolysed per unit tension when the fibres are oscillated than when they are statically stretched. The intercepts on the graphs show that, especially in the isometric contractions, the ATPase activity of the slack muscle represents a large fraction of the total ATP hydrolysis. The results of all experiments in which power production was measured were plotted as ATPase activity against power production, as in Fig. 4. Only points from the portion of the graph in which power production rose monotonically with ATPase activity were included. Points in which the power output of the fibres was reduced because they were stretched beyond the optimum length for power production were omitted (see Fig. 1 B). Fig. 3. The effect of ambient temperature on the relation of ATPase activity to mean fibre tension. A: variation of ATPase activity with mean tension at 2' C. Points obtained from a number of different fibre bundles (1 or 2 observations obtained from each bundle). Open circles (--) represent experiments on -static muscle, filled circles (-@-) represent experiments on fibres oscillated at 2-% amplitude and optimal or near optimal working frequency. Dashed line ) shows regression of ATPase activity upon mean tension of static muscle. Continuous line ( ~) shows regression of ATPase upon mean tension of oscillatory muscle. Regression coefficients and standard errors for different temperatures are given in Table 1. B: Arrhenius plot to show effect of temperature. Ordinate, static (CQ) and oscillatory (C,)) tension costs and optimal working frequency at - 2 % amplitude (F.-2) and 2- % amplitude (F2.-), plotted on a logarithmic scale. Abscissa, reciprocal of absolute temperature, OK-L. Measurements of Cs, CD, are regression coefficients taken from Table 1. Measurements of F.2 and F2 * also taken from Table 1.

10 8 JUDITH PYBUS AND R. T. TREGEAR (v.e4.' P*,4 N, ;.I 2 E- r 6E o i "E Ca a) o- 1 CO CO Co C: X s 1 +l eq ldco oob - --I CO t- I a)cq CD CO CO +l N CO N eq cq '- - CO 3O S o C w C.4 Q 4 Pj2 Ca 1-4 a) H H4' 23 o I- _ C-) o -I bo E-.4. F - { * H U,._a M * U C.,- co 24- CO so COX ~ N O C N * * * * O - C-~1 *.- +l C_ t C CO _ - CO N, O- CO1 - - U, ~"~CCC " C.) +l O 1 CI CO 9 C1 O OI eq m C:1 = t-. d. N V--- V, 1 Nt-1 CB Xo +1 W fri V 114 m rlt) -Pa C +l CO CO W 4 Q +1 m1 o - o -- -.Oo_ 'a)h CQ.n IC ~~Ca. C C 5, V-ụ q co o )- * t w H-

11 TENSION COST IN FLIGHT MUSCLE 81 There is a large positive intercept on the ATPase activity axis ( p-mole. cm-'. min-, ninety-five expts.) representing a considerable rate of ATP hydrolysis in the absence of power production. The regression of ATPase activity upon power output was calculated and the reciprocal of the regression coefficient taken as an estimate of the ability of the muscle to convert chemical energy into external work. This function was termed the chemomechanical coupling factor of the muscle, Ec. It is cited in kj external work produced/mole ATP hydrolysed. E 1 'E/ E5_ (U co a- I-- < 5 1 Power output (uj.cm-,.min-,) Fig. 4. The relation between ATPase activity and power output of fibres at 25 C. Points from overstretched fibres (see Fig. 1 B) omitted. Amplitude of oscillation 2-%, frequency close to that optimal for work production. Regression line of ATPase activity upon power output shown. For regression coefficient + S.E. see Table 1. Variation of conditions (i) Temperature. At 8 C little work could be obtained from the fibres and their ATPase activity was very low, no more than 2 p-mole. cm-'. min- even when the fibres were stretched and oscillated. At and above 12 C work could be obtained from the fibres and the maximum work-percycle at the optimum frequency did not vary greatly (range, nj. cm-1. cycle-1). The optimum frequency for work production was consistently less at high amplitude of oscillation (2- %) than at low amplitude (.2 %) under the same conditions and at both amplitudes the optimum frequency rose steadily as the temperature was raised (Table 1). The static and dynamic tension costs both rose with increased temperature (Table 1). An Arrhenius plot of the parameters indicated that all have a similar activation energy of about 45 kj/mole (Fig. 3B). The ATPase activity observed at zero tension output, i.e. the intercept ATP hydrolysis

12 82 JUDITH PYBUS AND R. T. TREGEAR rate, also increased with temperature (I, Table 1). On the other hand the chemomechanical coupling factor did not vary significantly with temperature (Table 1). (ii) Omission of phosphate. Removal of phosphate is known to alter greatly the mechanical performance of glycerol-extracted flight muscle (Rfiegg et al. 1971; White & Thorson, 1972). Replacement of phosphate by 1 mm histidine reduced the optimum working frequency by approximately a factor of two but raised the work-per-cycle by a similar factor, so that the power production at the optimum frequency was relatively little affected; the calculated chemomechanical coupling factor was also unchanged. Both estimated tension costs were lower than in phosphate buffer (Table 2). TABLE 2. The effect of alterations of anion composition on muscle parameters Optimum Chemoworking mechanical frequencies Tension costs coupling (Hz) molee. cm-'. min-'. N-1) factor ram ~ r A- I (kj. mole-') Solution Foe2 F2. Ca8D Ec 1 mm phosphate buffer 9 9 6f (52) 4f3 ± -4 (13) 15 ± 2 (95) + 1 mm sulphate (6) 3.6 ± 1 (8) (7) mm pyrophosphate (16) 6-5 ± -8 (26) 19 ± 5 (26) 2 mm histidine buffer (17) 2-9± -5 (56) 15 ± 4 (29) + 1 mm sulphate (21) 5 ±+1- (1) mm pyrophosphate (14) 199± -2 (33) 16 ± 3 (18) Estimate I of CD used. Temperature 2 C;,u = -8 M. (iii) Addition of anions to solutionas. The effect of adding 1 mm-k2so4 to histidine buffered solutions was tested; as a control 1 mm-k2so4 was also added to phosphate solutions. Addition of sulphate to histidine buffered solutions did not abolish the non-linearities characteristic of the absence of phosphate, and it reversibly reduced the optimum working frequency of the fibres. Maximum work-per-cycle was also halved so that the power production was very low, and the chemomechanical coupling factor could not be estimated. Tension cost was also extremely low, and could not be estimated accurately (Table 2). In the presence of phosphate buffer, 1 mm-k2so4 had no obvious effect on either the mechanical performance or any of the other parameters (Table 2). In the presence of phosphate, pyrophosphate increased the dynamic tension cost (Table 2) but had no qualitative effect on the mechanical behaviour. In the absence of phosphate it had inconsistent effects. In the experiments in which both ATPase and mechanical performance were measured, it lowered both optimal

13 TENSION COST IN FLIGHT MUSCLE 83 working frequency and tension cost, leaving the chemomechanical coupling factor unchanged. However, in later mechanical experiments, it caused an increase in optimal working frequency. Further analysis Inspection of Tables 1 and 2 shows a parallel variation in tension cost and optimum frequency of oscillation. This is exemplified in Fig. 5A where Cs and CD are plotted against FO.2. However, the scatter of the results was too large to provide a good test of proportionality between Fo.2 and either value of C. The data were therefore combined into one relationship in the following manner. The average ratios of Fo.2 to F2. (a) and of Cs to CD (f) were determined from the entire set of results shown in Tables 1 and 2; the individual measurements of F2. and CD were multiplied by a and, respectively to give second estimates of FO.2 and Cs, and averaged with the direct estimates of these parameters. This process was employed rather than a regression technique in order to avoid biasing the data in favour of the higher values observed. The resulting values, FR.2 and C', were closely proportional to one another; there was no indication of curvature in their relationship (Fig. 5B; correlation coefficient 96, eleven expts.). DISCUSSION Efficiency The results show that at moderate fibre extensions and frequencies of oscillation, ATPase activity and power output were monotonically related (Fig. 4). However, under two mechanical conditions tested, overextension (Fig. 1B) and high frequency, this relation did not hold good. Steiger & Ruegg (1969) observed a close coupling between the power output and extra ATPase activity (the increase in the rate of ATP hydrolysis above that observed at static 2 % stretch) in insect flight muscle, such that, at frequencies too high for power production, the ATPase -activity actually declined below that of the static fibres. However, they record that this 'ATP inhibition' was associated with a drop in mean tension and was reversible, showing that their results are consistent with those presented here. Thus the apparent coupling between ATPase activity and power production, interpreted by Steiger & Riiegg as a biochemical manifestation of the 'Fenn effect' (Fenn, 1923), is only observed under certain mechanical conditions. Steiger & Riiegg used the slope of the power versus ATPase activity relationship as an estimate of the efficiency and we have continued their usage with the term 'chemomechanical coupling factor (Ec)'. This is

14 84 JUDITH PYBUS AND R. T. TREGEAR plainly related to the abolute efficiency of work production by the muscle but is not a direct measure of it, because some ATP is hydrolysed when the muscle is not producing external work; this is the intercept of Fig. 4. Such hydrolysis almost certainly arises from cross-bridges exerting tension so the coupling factor is probably an overestimate of the efficiency. However, the greater the power output by the muscle the less is the effect of the intercept subtraction. In the present experiments the muscle at best 1 z C.._ r- E.2CE 5 1 FO.2 (Hz) 5r B 4 z C E. 3 U Ut 2 1 IC, F'.2 (Hz) Fig. 5. For legend see facing page. to

15 TENSION COST IN FLIGHT MUSCLE 85 produced 8 5 1tJ. cm-'. min' of mechanical work for a total ATPase activity of 7 n-mole. cm-'. min-, i.e. the true coupling factor was 12 kj. mole-' (Fig. 4, extreme right-hand points), which is 75 % of the calculated coupling factor at 25 C. This discrepancy could be greatly reduced if either the high powers which a glycerol-extracted muscle can produce briefly (Steiger & Rfiegg, 1969) could be retained indefinitely as they can in life (Machin & Pringle, 1959) or ATPase activity estimations could be made in the short time for which high power outputs were sustained in the present experiments. Even with the present results, two conclusions may be made. First, the efficiency of the preparation is comparable to that obtained from live vertebrate skeletal muscles (Cain, Infante & Davies, 1962; Carlson, Hardy & Wilkie, 1963). On the basis of Kushmerick & Davies' (1969) treatment, the absolute efficiency is at least 28 % (AG = 43 kj. mole-') and probably higher, since at 12 C the observed coupling factor was greater than that at 25 C. Secondly, provided changes in the absolute efficiency are reflected in the coupling factor, the relatively small variation of Ec with conditions (Tables 1 and 2) shows that the actomyosin interactions can operate over a wide range of contraction velocities without loss of efficiency. Tension cost The results show that ATPase activity was linearly related to the mean fibre tension under all conditions tested, and that the tension cost, as estimated by the slope of the regression of ATPase activity on tension, was proportional to the optimum frequency of oscillation (Figs. 5A and B). Fig. 5. Relationship between tension cost and optimal frequency for oscillation. A: static tension cost (Cs, -O-), and dynamic tension cost (CD, *) plotted against optimal frequency of oscillation at -2 % amplitude (F.2). Data from Tables. Lines are average of regression coefficients of tension cost upon F.2 and F.2 upon tension cost. C. and F.2; mean of regression coefficients + s.e. = #mole. cm1. min-. N-1. Hz-'. CD and F.2; mean of regression coefficients + s.e. = /tmole. cm-. min-l. N-'. Hz-'. B: adjusted tension cost (C,') and optimal frequency (Fo.2) plotted against each other. Adjustment as described in text; az = 15 ± 41,,f = * Regression lines of Fo.2 upon C,,, and C' upon FO 2' shown. Regression coefficients; FP.2 on C, = , C, on F'.2 = (*26±.3)-'. Mean regression coefficient ± s.e. =.25 ± 3 gmole. cm-'. min-. N-1. Hz-'.

16 86 JUDITH PYBUS AND R. T. TREGEAR As with the efficiency measurements, the slope of the regression line is only an obviously valid estimate of the tension cost if the intercept is zero. This is not so, there being a positive intercept ATPase activity of around 15 p-mole. cm-'. min- in every case. The phenomenon has been observed by SchAdler (1967) who recorded a higher Ca2+ threshold for tension than for ATPase activity. Part of the ATP hydrolysis at zero tension is probably caused by actomyosin interaction, since ATPase activity is much lower in the absence of calcium, provided that incubation is not unduly prolonged. The zero-tension interactions have a mechanical effect; if the length of the fibre is set so that tension is just not produced, after about 2 min a few milligrams of tension are often observed. If, under conditions of zero tension, the individual actomyosin interactions are the same as during positive tension production, but the tension produced is being used to overcome internal forces inside the muscle structure, the true zero tension will be represented in Figs. 2 and 3A by the intercept of the regression line on the tension axis. This intercept should be the same under similar mechanical conditions. Consequently an increase in the slope of the regression of ATPase activity on tension should be accompanied by an increase in the intercept of the regression line on the tension axis. This effect is observed when the ambient temperature is raised (Table 1, last column). On this basis we have assumed that the regression coefficients are valid estimates of tension cost. The tension cost of static muscle, so estimated, was proportional to the optimal working frequency of the muscle (Fig. 5). This relationship was maintained even when changes in the free anions within the contractile matrix induced large changes in both parameters. It is therefore probable that both parameters depend upon the same biochemical event which, on the two state hypothesis, is the rate constant of detachment g (see Introduction). The proportionality further shows that under these conditions p, the mean tension during attachment, is invariant. When the muscle was oscillated the tension cost rose. Vertebrate skeletal muscle allowed to shorten and do mechanical work also shows an increased 'tension cost' in that the tension is lower and the rate of ATP hydrolysis higher than under isometric activation (Carlson et al. 1963; Marechal, 1964). On the two state hypothesis the increase in tension cost is supposed to arise from two factors, a decrease in the mean tension (-) and an increase in the mean detachment rate constant (g) as a consequence of interfilament movement (Huxley, 1957). The movement employed in the present experiments is large in molecular terms, 24 nm/half-sarcomere (lo = 1 2 jtm; 2% amplitude). This is considerably greater than the range of action of an actomyosin linkage as deduced from quick-release experiments (Podolsky, Nolan & Zaveler, 1969; Huxley & Simmons, 1971) so

17 TENSION COST IN FLIGHT MUSCLE that many of the linkages formed probably move through a major part of their range whilst attached. This conclusion is also indicated by the relatively high efficiency observed. On this basis large movements of the actomyosin linkages result, on average, in a comparatively small change in the ratio 5/g; either one of these parameters changes in the direction opposite to that anticipated on the theory or both change by less than a factor of 2. The preceding discussion has been based on the two state hypothesis. White (1973) has shown that a three state model more accurately predicts the mechanical response of insect flight muscle oscillated at high amplitude. However in the more complex model the rate constant of the step in which the actomyosin complex ceases to generate tension most probably has the same significance as that of g in the simpler model, so that the conclusions drawn above remain valid. These results are consistent with the current general concept, that muscle produces force by forming actomyosin linkages which exert tension for a certain time before detaching again. In insect flight muscle the crossbridge detachment rate constant appears to determine both contraction speed and tension cost as if it were the primary functional variable. It is interesting to speculate whether this is a general principle; do myosins of different muscles differ functionally in their value of g? 87 REFERENCES ABBOTT, R. H. (197). Computer control of mechanical experiments on muscle. Biochem. J. 121, 3-4P. ABBOTT, R. H. (1973a). An interpretation of the effects of fibre length and calcium on the mechanical properties of insect flight muscle. Cold Spring Harb. Symp. quant. Biol. 37, ABBOTT, R. H. (1973b). Stretch and calcium activation of glycerol-extracted insect fibrillar muscle. J. Physiol. 231, ABBOTT, R. H. & LEECH, A. R. (1973). Persistence of adenylate kinase and other enzymes in glycerol-extracted muscle. Pfliiyers Arch. ges. Physiol. 344, AIDLEY, D. J. & WHITE, D. C. S. (1969). Properties of glycerinated fibres from the tymbal muscles of a Brazilian cicada. J. Physiol. 25, ARMITAGE, P. M., MILLER, A., RODGER, C. D. & TREGEAR, R. T. (1973). The structure and function of insect muscle. Cold Spring Harb. Symp. quant. Biol. 37, BERGMEYER, H.-U. (1965). Methods of Enzymatic Analysis. New York: Academic Press. BREULL, W. (1971). Myofibrillar ATP-splitting in the elementary contractile cycle of an insect flight muscle. Experientia 27, CAIN, D. F., INFANTE, A. A. & DAVIES, R. E. (1962). ATP and PC as energy supplies for single contractions of working muscle. Nature, Lond. 196, CARLSON, F. D., HARDY, D. J. & WILKIE, D. R. (1963). Total energy production and phosphocreatine hydrolysis in the isotonic twitch. J. gen. Physiol. 46,

18 88 88 ~JUDITH PYBUS AND R. T. TREGEAR FENN~, W.. (1923). A quantitative comparison between the energy liberated and the work performed by the isolated sartorius muscle of the frog. J. Phy8iol. 58, GOLDspiNK, G., LARSON, R. E. & DAvIEs, R. E. (197). Energy supply and use in different hamster muscles. Z. vergi. Phy8iol. 66, HUXLEY, A. F. (1957). Muscle structure and theories of contraction. Prog. Biophy8. biophy8. Chem. 7, HUXLEY, A. F. & Sm~moNs, R. M. (1971). Proposed mechanism of force generation in striated muscle. Nature, Lond. 233, JEWELL, B. R. & RUEGG, J. C. (1966). Oscillatory contraction of insect flight muscle after glycerol extraction. Proc. R. Soc. B 164, KUSHMERIcK, M. J. & DAVIES, R. E. (1969). The chemical energetics of muscle contraction. II. The chemistry, efficiency and power of maximally working sartorius, muscle. Proc. R. Soc. B 174, LYmN, R. W. & TAYLOR, E. W. (1971). The mechanism of adenosine triphosphate hydrolysis by actomyosin. Biochemistry, N.Y. 1, MAcHIN, K. E. & PRINGLE, J. W. S. (1959). The physiology of insect fibrillar muscle. II. Mechanical properties of a beetle flight muscle. Proc. R. Soc. B 151, MAR19CHAL,. (1964). Thesis, Brussels. Editions Arsica. MARSH, B. B. (1959). Estimation of inorganic phosphate in the presence of adenosine triphosphate. Biochim. biophy8. acta 32, PERRIN, D. D. & SAYCE, I. G. (1967). Computer calculation of equilibrium concentrations in mixtures of metal ions and complexing species. Talanta 14, PODOLSKY, R. J., NOLAN, A. C. & ZAVELER, S. A. (1969). Crossbridge properties derived from muscle isotonic velocity transients. Proc. natn. Acad. Sci. U.S.A. 64, PRINGLE, J. W. S. & TREGEAR, R. T. (1969). Mechanical properties of insect fibrillar muscle at large amplitudes of oscillation. Proc. R. Soc. B 174, PYBUS, J. H. (1972). Hydrolysis of ATP by muscle. D.Phil. Thesis, Oxford University. PYBUS, J. H. & TREGEAR, R. T. (1973). Actomyosin linkage and contraction. Cold Spring Harb. Symp. quant. Biol. 37, RUEGG, J. C., SCHADLER, M., STEIGER, G. J. & MULLER, G. (1971). Effects of inorganic phosphate on the contractile mechanism. PflieaArh1e.hao. 325, Rt-;EG, J. C. & STUMPF, H. (1969). The coupling of power output and myofibrillar ATPase activity. Pfliugera Arch. ge8. Phyaiol. 35, RUEGG, J. C. & TREGEAB, R. T. (1966). Mechanical factors affecting the ATPase activity of glycerol-extracted insect fibrillar flight, muscle. Proc. R. Soc. B 165, SCHADLER, M. (1967). Proportionale Aktivierung von ATPase-Activitiit und Kontraktionsspannung dursch Calciumionen im isolierten contractionilen Structuren vershiedenes Muskelarten. Pfliiger8 Arch. ge8. Phyaiol. 296, 7-9. SCHADLER, M., STEIGER, G. & RUEGG, J. C. (1971). Mechanical activation and isometric oscillation of insect fibrillar muscle. Pflilger8 Arch. ge8. Physiol. 33, SILLEN, L. G. & MARTELL, A. E. (1964). Stability Cons8tant8 of Metal-Ion Complexes. Chem. Soc. Spec. Publ. 17. STEIGER, G. J. & RUEGG, J. C. (1969). Energetics and 'efficiency' in the isolated contractile machinery of insect flight muscle at various frequencies of oscillation. Pfliugers Arch. ge8. Physiol. 37, THORSON, J. & WHITE, D. C. 5. (1969). Distributed representations for actin-myosin interaction in the oscillatory contraction of muscle. Biophy8. J. 9,

19 TENSION COST IN FLIGHT MUSCLE 89 TREGEAR, R. T. (1975). The biophysics of fibrillar insect flight muscle. In Insect Muscle, ed. USHERWOOD, P. New York: Academic Press. WHITE, D. C. S. (1973). Links between mechanical and biochemical kinetics of muscle. Cold Spring Harb. Symp. quant. Biol. 37, WHITE, D. C. S. & THORSON, J. (1972). Phosphate starvation and the non-linear dynamics of insect fibrillar flight muscle. J. gen. Physiol. 6,