J. Phy8iol. (1978), 276, pp. 467-479 With 7 text-ftgure8 Printed in Great Britain
467
FILAMENT SLIDING AND ENERGY ABSORBED BY THE CROSS-BRIDGES IN ACTIVE MUSCLE SUBJECTED TO CYCLICAL LENGTH CHANGES
BY F. W. FLITNEY AND D. G. HIRST From the Department of Physiology, University of St Andrews, St Andrews, Fife
(Received 13 October 1976) SUMMARY
1. The effects of single and double cycles of stretch and release on the tension response and relative sliding movement of the actin and myosin filaments in active frog's muscle were investigated. 2. The cross-bridges linking the filaments together are able to accommodate a greater range of filament displacement before becoming detached during a second cycle stretch. providing it commences without delay following the preceding release: sarcomere 'give' then occurs for displacements of around 18 nm, as compared with 12 nm for a first cycle stretch. It is postulated that the difference arises because the myosin heads adopt different 'preferred' positions in the isometric steady-state and at the end of a previous release. 3. Muscle length-tension loops were recorded and used to measure the energy absorbed when a muscle is subjected to cycles of stretch and release. The work absorbed per unit length change increases with increasing displacement of the crossbridges from their initial (isometric) steady-state position, up to the point at which sarcomere 'give' occurs (S2); thereafter it remains constant. 4. More work is absorbed during the first cycle of a double stretch-release combination than during the second. The greater amount absorbed during the first cycle is associated with a correspondingly greater amount of filament sliding in the period following sarcomere 'give'. Sarcomere length-tension loops were constructed and these showed that not less than 80-85 % of the work done on a muscle is absorbed by the sarcomeres themselves. 5. A greater amount of work is done on stretching up to (but not beyond) S2 during second cycle stretch as compared to a first. The difference amounts to about 1 mJ. m-2 per half-sarcomere. 6. The results are compatible with the mechanism for force production proposed by Huxley & Simmons (1973), in which each myosin head generates force in a number of stepping movements, from one attached state to another. It is concluded that (a) during an unloaded, isotonic contraction the working 'stroke' of the head would result in a 10-13 nm relative sliding movement of the filaments, and (b) the potential energy difference separating the two 'preferred' states is 6-9-6 kT per cross-bridge, or 3-4-8 kT per S-i sub-unit, assuming that each one interacts simultaneously with the actin filament.
468
F. W. FLITNEY AND D. C. HIRST INTRODUCTION
It was shown in the preceding paper (Flitney & Hirst, 1978) that a muscle subjected to stretch resists the movement initially by developing a high- force, but when the relative sliding movement of the actin and myosin filaments exceeds 12 nm, the cross-bridges linking the two become forcibly detached, the sarcomeres yield and the slope stiffness of the muscle decreases abruptly. In this paper the effects of single and double cycles of stretch and release on the movements of the filaments and on the tension developed by a muscle are reported. These experiments have shown that at the end of a cycle of stretch and release the tension supported by a muscle is substantially less than the isometric level, even though the sarcomeres themselves have returned to their pre-stretch (isometric) length. This observation is taken to mean that the cross-bridges between the two sets of filaments are somewhat shortened, as a result of which during a subsequent stretch, made without delay, a significantly greater degree of extension (approximately 1P5 x more) is required to induce sarcomere 'give'. The simplest interpretation of these observations is that at the commencement of the second stretch the orientation of the myosin 'heads' with respect to the actin filaments differs from that in the isometric state. The results are compatible with a model proposed by Huxley & Simmons (1971, 1973) in which each cross-bridge generates the force for contraction in a series of stepping movements, from one attached configuration to another. It is impossible from the present results to give an estimate of the actual number of cross-bridge states involved, but the minimum number consistent with the data is either three or four, one detached and two or three attached states, with the force being generated in either one or two stepping movements. METHODS
Recordings of muscle tension, length and sarcomere spacing were made as described in the preceding paper (Flitney & Hirst, 1978). The present experiments involved subjecting muscles to cyclical length changes. Single and multiple cycles of stretch and release were employed. In the majority of experiments, the second cycle of stretch and release followed the first immediately, but in a few it commenced after a predetermined delay. The energy absorbed in taking muscles through cycles of different amplitudes was also measured. The procedure was as follows. Muscles were tetanized and subjected to stretch, followed immediately by a release of the same amplitude and velocity. The displacement signal from the servo-amplifier which was used to control muscle length was fed to the X plates of the oscilloscope and the output of the tension recorder to the Y plates. A Devices 'Digitimer' (type 3290) was used to modulate the beam intensity through the Z input so that only the events occurring during stretch and release were recorded on the screen. The work done on stretching the muscle is mostly returned duringthe subsequent release, but not all of it; the oscilloscope beam describes a clockwise loop and the energy absorbed by the muscle is given by the area enclosed by the loop. All experiments were made at temperatures of 0-3 IC, using stretch-release velocities of not less than 4 mm. sec-.
STRETCH AND RELEASE OF ACTIVE MUSCLE
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RESULTS
Tension changes and filament sliding during single and double cycles It was concluded previously (Flitney & Hirst, 1978, Fig. 7) that during a stretch the actin and myosin filaments must be displaced by 12 nm (mean + S.D. = 12-3 + 0 9 nm; n = 10) before the cross-bridges linking them together are forcibly broken. Fig. 1A compares their relative movement during first and second cycle stretches. The upper record shows the tension response to a double cycle of stretch and release and the lower record shows the form of the external length change. The tension response and the movement of the filaments during the second stretch are markedly different from those during the first. The results obtained for three muscles treated similarly were as follows. First, the point S2 is reached for a displacement of around 18 nm (mean +S.D.: 18-3 + 1.0 nm), approximately 1-5 x greater than is required to induce sarcomere 'give' in the case of a first stretch (Fig. 1 B). Secondly, the tension held by the muscle at S2 is similar in the two cases: 1-38 P0 (1st cycle) and 1-40 P0 (2nd cycle). Thirdly, at the end of the first release (immediately before restretching) muscle tension has fallen to 0 73 P0, although by this time the sarcomere length is back to its initial (pre-stretch) value. This last point is especially significant and will be referred to again later (p. 473). Length-tension relation of the sarcomeres during first and second cycle stretches. The results for the muscles referred to above are presented in the form of two sarcomere length-tension diagrams in Fig. 2. Filament displacement resulting from stretch is plotted against muscle tension (above and below P0). The mean stiffness of the muscles in the period up to rapid 'give' (estimated from the slopes of the lines relating muscle tension to sarcomere extension, AP/tXS) is not substantially different in the two cases; 5-8 x 1012 N. m-2 per m extension of each half-sarcomere (1st cycle) and 5-3 x 1012 N.M-2 per m extension of each half sarcomere (2nd cycle). It was shown in the previous paper (Flitney & Hirst, 1978), that sarcomere stiffness is proportional to filament overlap and we concluded that it represents the collective stiffness of the cross-bridges linking the actin and myosin filaments together; the simplest interpretation for the small change observed here (ca. 9 %) is that the number of attached cross-bridges is not altered appreciably by stretch and release of a muscle under the present conditions. This point is taken up again later. By contrast, during the period of 'give' the stiffness of the sarcomeres falls by 25-30 x . Velocity of filament sliding and extent of movement during sarcomere 'give'. During rapid 'give' the filaments slide at a rate of at least 1 4 nm. msec-1. This is about 8 x faster than the value calculated on the assumption that their rate of sliding is determined only by the speed of the external length change. It should be emphasized that this is the minimum velocity since it is estimated from two consecutive frames of the cine-film. The extent of the sliding movement is approximately the same for both first and second cycles (20-21 nm). Rapid shortening of sarcomeres and tension changes during release. The movement of the sarcomeres and the tension response of the muscle during release from a preceding stretch are also shown in Fig. 1. There are two points of interest. First, during the early part of the release, tension falls steeply while the sarcomeres shorten
F. W. FLITNEY AND D. G. HIRST
470
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Fig. 1. A, tension response (AP) and change of sarcomere length (AS) resulting from a double cycle of stretch and release (AL). The point at which the sarcomeres 'give' and where muscle stiffness decreases (S2) is marked by the vertical arrows. Note (a) that a greater amount of filament sliding is required to induce 'give' in the case of a second cycle stretch, and (b) at the end of the first release muscle tension is substantially less than the isometric level even though the sarcomeres have returned to their pre-stretch length. B, filament displacement during a first (1) and second (2) cycle stretch, plotted against time after the commencement of the stretch.
471 STRETCH AND RELEASE OF ACTIVE MUSCLE relatively slowly. Secondly, after this initial period of slow shortening the velocity of filament sliding increases abruptly, at a speed in excess of 1 0 nm. msec-1. As before, there is some uncertainty in giving a precise figure because the estimate is
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Fig. 2. Sarcomere length-muscle tension curves during stretch for three muscles subjected to double cycles of stretch and release. The stiffness of the sarcomere is high during the early part of the stretch, decreases abruptly during 'give' and then partially recovers during the remainder of the stretch. First stretch, A; second stretch, B.
F. W. FLITNEY AND D. G. HIRST made from two consecutive frames, but the value could not be less than this (it is of interest to compare it with the rate at which the filaments slide in an unloaded isotonic contraction; the data given by Hill (1 970) yield a figure of around 1 7 nm . msec-1 for a frog sartorius at 0 'C). The extent of the sliding movement during rapid shortening is around 10-20 nm (mean 14-5, n = 5) for both first and second cycle releases. It is probable that this phase of the response is caused by cross-bridge re-attachment, resulting from realignment of the myosin heads with active sites on the actin filaments. This is consistent with the observation that the point at which rapid shortening commences is not constant, but depends upon the degree of extension of 472
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Fig. 3. Tension response resulting from a double cycle of stretch and release in which the second cycle follows the first after a delay of about 500 msec. The degree of extension required to induce sarcomere 'give' (indicated by the abrupt decrease of muscle stiffness) is only slightly greater in the case of the second stretch. Note (a) the recovery of isometric tension between the end of the first release and the start of the second stretch, and (b) the more abrupt levelling-off cf tension during the second stretch.
the sarcomeres beyond 'give' during the preceding stretch. The following values from Fig. 1 serve to illustrate the point. During the first cycle stretch the sarcomeres are extended by 37 nm in this period, and the rapid phase of the shortening commences when, in the early part of the release, they have been displaced by 36 nm in the opposite direction. The corresponding values for the second cycle are 24 nm and 20 nm. This explanation is reinforced by the observation that the rate of fall of tension declines markedly during and immediately after rapid shortening; indeed, in many records it reverses during the remainder of the release. Tension response during a delayed second cycle. The response to a delayed second stretch is different. Fig. 3 shows two cycles of stretch-release separated by an interval of 500 ms. During this period the muscle practically regains its full isometric tension. The response to a second cycle is then similar to that for the first (and might
STRETCH AND RELEASE OF ACTIVE MUSCLE 473 have been identical, had a greater delay been allowed); S2 occurs for extensions (whole muscle) of 395 sum (1st cycle) and 430 /tm (2nd cycle). The effects of delaying the second cycle have not been investigated fully, but the indications are that a muscle may recover from the effects of the first cycle of stretch and release if sufficient time is given. It appears that the time course of the 'recovery' process follows that for the redevelopment of tension when the muscle is not re-stretched following a release. Energy absorbed during cycles of stretch and release Work absorbed in cycles of different amplitudes. Except for very small amplitudes, the work absorbed during a stretch exceeds that returned during subsequent release. The amount absorbed is measured from the areas of the muscle length-tension loops. A
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Fig. 4. Oscilloscope recordings of muscle length-tension loops made during first (top row) and second (bottom two rows) cycles of stretch and release. The 'loops' are open for first and closed for second cycles. Amplitude of length change indicated under each record (,sm).
It has been seen that the level of tension existing immediately before and immediately after a single stretch release cycle is not the same; typically, at the end of a previous release (made at a velocity of 4 mm. sec-1) it has fallen to near 0 7 PO. In contrast, tension at the beginning and end of a second cycle is the same, providing the second cycle follows the first without delay. Fig. 4 shows muscle length-tension loops for a series of single cycles of stretch and release, A, and a series of second cycles, B, of different amplitudes. The loops for first cycles are open, and those for second (or subsequent) cycles are closed. The areas enclosed by the loops are plotted against the amplitude of the length oscillation in Fig. 5. (In the case of first cycle 'loops', the area is closed-off by drawing a straight line between the open ends.) The amount of work absorbed for a given
F. W. FLITNEY AND D. G. HIRST cycle amplitude, W, is greater for first (open) than for second (closed) cycles. In both cases, W is negligible for small amplitudes ( < 50 jum, first cycle, and < 100 ,um, second cycle) but increases progressively with increasing amplitudes, up to around 550 ,tm. Thereafter, the amount of energy absorbed by the muscle increases linearly with increasing cycle amplitudes, by 0-66 x 10-5 J. M-2 per half-sarcomere per ,um (mean slope of dashed lines). 474
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Fig. 6. Sarcomere length-muscle tension loops constructed from changes in the spacing of the diffraction spectra produced by a muscle subjected to two consecutive cycles of stretch and release. The work done on each half sarcomere is given by the area of the loop. 1, first cycle; 2, second cycle.
475 STRETCH AND RELEASE OF ACTIVE MUSCLE Work absorbed by the sarcomeres. A question which should be asked is: How much energy is absorbed by the sarcomeres themselves, as distinct from other elements in the muscle? To answer this point, experiments were made in which sarcomere movements were recorded during first and second cycles and length-tension loops for the sarcomeres (rather than for the whole muscle) were constructed. It is assumed in what follows that the tension recorded at the extremities of the muscle is equal to that borne by each sarcomere, which is very nearly true at the short muscle length used, there being little contribution from parallel elastic elements. Fig. 6 shows the result obtained in one such experiment. The muscle was subjected to two consecutive cycles of + 1020 jum. Again, the work absorbed is given by the area of the loops. The values obtained were 4 mJ.M-2. half-sarcomeres-1 (first cycle) and 3 15 mJ.m-2.half-sarcomere-1 (second cycle). The corresponding figures, estimated from length-tension loops for the whole muscle, were 4-6 and 3.75 mJ. M-2. half-sarcomere-1, respectively. This experiment, and others of a similar nature, showed that the major part of the work absorbed in taking a muscle through a cycle of stretch and release (not less than 80-85%) is absorbed by the sarcomeres themselves. They also reaffirm the observation, made above, that the work absorbed during a first cycle is substantially greater than during a second. It is probable that this difference arises because a greater amount of non-returnable work is associated with sliding of the filaments after sarcomere 'give' in the case of a first cycle. DISCUSSION
The results are consistent with the model put forward recently by Huxley & Simmons (1971, 1973) which describes a possible mechanism for force production by muscle. Their hypothesis envisages the cross-bridge as being made up of two components arranged in series: an instantaneous elastic element (their AB linkage) and a damped force-generating element (Fig. 7). The myosin head is thought to have a small number of attachment sites through which it can bind to corresponding sites on an actin active region. It is postulated that the simultaneous attachment of the head at two consecutive sites constitutes a stable state and that force is generated by a stepwise movement along the actin filament, from one such stable position to the next, each having a progressively lower potential energy than the preceding one. Huxley & Simmons consider that the most likely number of attachment sites is four, with three stable states and the full range of movement taking place in two steps. The extent of filament sliding required to induce sarcomere 'give'. The different amounts of filament sliding required to reach S2 in first and second cycle stretches can be explained if it is postulated that the instantaneous elastic components of the cross-bridges are in a somewhat shortened state at the end of a preceding release, due to a shift in the 'preferred' position of the attached myosin heads, say from position II to III in the model shown in Fig. 7 (based on Huxley & Simmons (1971) Fig. 5). It is not difficult to see why position II might be favoured at the peak of a tetanus. When a head attaches initially it is able to move with relative ease to the next position and in so doing generate tension. As a result of this tension, which increases
F. W. FLITNE Y AND D. G. HIRST 476 progressively as the tetanus develops, the probability of the head making the next step is reduced. If it should do so, then the likelihood of it becoming detached by combining with ATP is increased. The combination of these two factors means that at the peak of a tetanus the heads are energetically constrained to spend most of their time in an intermediate position. It is postulated that the stituation is different at the end of a preceding release. If one discounts for the present the possibility that the number of cross-bridges is reduced by the preceding stretch and release (a point discussed later) then the conclusion to be drawn from Fig. 1 A is that their A
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Fig. 7. Schematic representation of the events occurring during first and second cycle stretches. A single myosin head is shown attached to an actin filament (1) at the peak of an isometric tetanus, immediately before a first stretch; and (2) at the end of a preceding release, before a second stretch. Part of the stretch is absorbed by extension of the elastic linkage and part by backward rotation of the attached head. The two right-hand diagrams depict the position of the head at the commencement of sarcomere 'give'. In each case, one of the two attachment sites for the initial attached state is shown as already having been forcibly broken, the other is as yet still attached.
configuration is altered in some way. One explanation for this is that during release the AB linkages are progressively unloaded, thereby facilitating cross-bridge cycling, so that at the end of the release, when the muscle is in a relatively 'low tension' state, there is a net shift in the distribution of the re-attached heads, such that they now preferentially occupy position III in Fig. 7. Now, consider what happens when a muscle is stretched. During the early part of the movement tension is generated by extension of the AB link only, but at some point, the attached head begins to be forced backwards, against its tendency to move to the next position of lower potential energy. Tension continues to rise, the length change now being shared between backward rotation of the head and further extension of the elastic linkage. Taking data from an actual experiment (Fig. 7), sarcomere 'give' occurs when the force has risen to 1-35 P0 and for a relative displacement of the filaments of 11 8 nm. The corresponding displacement for a second cycle stretch is 18-3 nm and tension rises to 1 38 PO.
STRETCH AND RELEASE OF ACTIVE MUSCLE 477 An estimate of the amount of movement taken up by rotation of the attached head, as distinct from extension of the connecting elastic linkage, can be made (below) and this places a lower limit of 5 nm for the axial distance separating the two 'preferred' positions and an upper one of 6-5 nm. Two assumptions are made. First, the instantaneous elastic element displays Hookean characteristics. This can be inferred from Huxley & Simmons (1971, 1973) and Ford, Huxley & Simmons (1976) T1 curves. Secondly, that there is no substantial change in the number of attached cross-bridges at the end of a preceding release. This seems likely since (a) the mean slope stiffness of the sarcomeres during a subsequent stretch is approximately the same as that during a first stretch, (b) the level of tension reached at S2 during a second stretch is not significantly different from that attained during a first stretch, and (c) the work done during stretches sufficient to reach (but not exceed) S2 is greater during a second stretch, even though for much of the movement the force on the muscle is less. There is no doubt that under certain conditions of stretch and release, following rapid changes of load, for example Huxley, 1971) there i8 a change in the number of attached cross-bridges, but the pattern of sarcomere movements and the accompanying tension response observed during a 81ow release (Fig. 1 A) suggests that under the present conditions cross-bridges detach, but have sufficient time to reattach (p. 472), so that at the commencement of the second stretch (made without delay) the number linking the filaments together is virtually unchanged. Finally, it is difficult to see why fewer cross-bridges would permit a greater degree of filament sliding to occur in the period up to S2The question raised now is, how much of the imposed sliding movement is translated into rotation of the attached cross-bridge head? Since the two elements of the cross-bridge are arranged in series, the AB links are sustaining a force of 1-35P1 at S2 and they will therefore be extended to 1-35 x 4-5 nm (the isometric length; Ford et al. 1976) = 6-07 nm, an increase of 1-57 nm. This means that head rotation accounts for 11-8-1-57 = 10-23 nm of the observed filament displacement. The situation will be different for a second stretch, where the heads preferentially occupy position III rather than II in Fig. 7. Similar reasoning then shows that of the total 18-3 nm of movement, 2-92 nm goes into extending the links, leaving 15-38 nm to be accounted for by rotation of the heads. The conclusion to emerge from this is that the two preferred positions are separated by a distance of around 15-38 - 10-23 = 5-15 nm. If the above correction for extension of the links is omitted, an upper estimate of 18-3 - 11-8 = 6-5 nm is obtained.
How many cross-bridge states? These considerations lend some support to the hypothesis that force generation occurs as the result of discrete changes in the position of the attached heads, from one stable state to another. It is impossible to conclude with certainty how many cross-bridge states exist, although on the basis of our results and those of Huxley & Simmons, we favour a minimum of three or four: two or three attached states and one detached state. The argument is as follows. Consider first the model in Fig. 7, in which there are three attached states, designated I (not shown, but inferred from the diagram), II and III. The initial part of the cross-bridge cycle involves the transition from the detached state to state I, and the force generating steps which follow are the transitions I -÷II and II -- III. The results show that the axial distance separating states II and III is around 5 nm (corrected estimate). The amount of sliding movement required to reach S2 during a single stretch is approximately twice this distance (10-23 nm) which suggests that all three attached states are equally spaced. On this scheme, the relative sliding movements of the filaments associated with each cross-bridge 'stroke' in an unloaded isotonic contraction would be between 10 nm (based on corrected estimates) and 13 nm (uncorrected estimates). The figure of 5-2 nm obtained above for the best estimate of the spacing of the
F. W. FLITNEY AND D. G. HIRST attachment sites is of interest, since it corresponds closely with the centre-to-centre spacing of the actin monomers in the F actin strands (Hanson, 1968). It is tempting to speculate on the basis of this that the myosin heads bear sites which interact sequentially with three consecutive pairs of actin monomers, the first defining state I, and the other two, the tension bearing states II and III. There are steric difficulties with a model of this kind, and the spacing between the postulated attached positions and its close correspondence with the spacing of the actin monomers may only be coincidental. Furthermore, the locations of the force generating element and the instantaneous elasticity within the cross-bridge are not known with certainty. A. F. Huxley & Simmons (1973) have emphasized that while their 1971 model adequately explains their experimental findings, it is by no means unique. A number of equally plausible alternatives is given by Huxley (1974). There is another point to consider too. The results obtained with double stretches might be explained, if in the isometric state the time-average position of the cross-bridge heads was midway between only two stable states, an initial attachment state A and a tension bearing state B, so that on stretch and release they would end up in positions A and B respectively. Force production during attachment would then be a single step process, from A to B, and the figures derived above for the spacing between the preferred states (5 nm) and for the amount of sliding required to reach S2 during a first stretch (10 nm) would then refer to rotation of the head about its mean isometric position. Potential energy difference between the two 'preferred' states. The amount of work done on stretching to the point at which the cross-bridges are forcibly detached is readily estimated from the areas under the curves relating muscle force to filament sliding. It was seen that during a first cycle stretch head rotation accounts for approximately 10 nm of movement, and during a second stretch, approximately 15 nm. When these distances are related to muscle force, the work absorbed turns out to be 318 mJ.m-2.half-sarcomere-I (first stretch) and 4-29 mJ.m-2.halfsarcomere'1 (second stretch). The difference between the two, approximately 1 mJ . M-2. half-sarcomere-1, represents the potential energy difference between the two preferred positions. The number of cross-projections on the myosin filaments is estimated to be 5 x 1016 M-2. half-sarcomere-I (Huxley, 1963) which gives a figure of 2 x 10-20 J for the potential energy difference per cross-bridge. This figure assumes that all the cross-projections are attached, but it is known from X-ray diffraction studies that this is not the case. Recent studies (Haselgrove & Huxley, 1973; Matsubara, Yagi & Hashizume, 1975) suggest that 50-80% are so engaged, which gives figures of 2 5-4 x 10-20 J, or 5-97-9-56 kT, for the energy difference between the two states. These values compare closely with the figure of 7-3 kT for the work done per crossbridge, calculated by Huxley & Simmons (1971) from measurements of muscle efficiency (Hill, 1939) and phosphorylereatine break-down (Wilkie, 1968). At face value, this would seem to rule out a two-step mechanism, since the work done per cross-bridge would then have to be in the range 12-18 kT to be consistent with our results. However, the discrepancy disappears if the estimate for the potential energy difference between the two states is partitioned equally between each of the two cross-bridge S, sub-units, giving values of 34.5 kT per step. This may be on appro478
479 STRETCH AND RELEASE OF ACTIVE MUSCLE priate correction to make, since the two heads are connected through a common linkage to the myosin filament. We thank Action Research for the Crippled Child for financial support. We are grateful to Drs R. M. Simmons, D. A. Jones and W. G. S. Stephens for valuable discussion, and to Mr Robert Adam for technical assistance. REFERENCES FLITNEY, F. W. & HIRST, D. G. (1978). Cross-bridge detachment and sarcomere 'give' during stretch of active frog's muscle. J. Phy8iol. 276, 449-465. FLITNEY, F. W., HIRST, D. G. & JONES, D. (1976). Effects of temperature and velocity of stretch on maximum tension borne by the sarcomeres in contracting muscle. J. Phy8iol. 256, 127-128P. FORD, L., HuxLEY, A. F. & SIMMONS, R. (1976). The instantaneous elasticity of frog skeletal muscle fibres. J. Physiol. 260, 28-29P. HANSON, J. (1968). Recent X-ray diffraction studies of muscle. Q. Rev. Biophys. 1, 177-216. HASELGROVE, J. & HUXLEY, H. E. (1973). X-ray evidence for radial cross-bridge movement and for the sliding filament model in actively contracting skeletal muscle. J. molec. Biol. 77, 549568. HILL, A. V. (1939). The mechanical efficiency of frog's muscle. Proc. R. Soc. B 127, 434-451. HILL, A. V. (1970). First and Last Experiments in Muscle Mechanic. London: Cambridge University Press. HUXLEY, A. F. (1971). The Croonian Lecture, 1967. The activation of striated muscle and its mechanical response. Proc. R. Soc. B 178, 1-27. HUXLEY, A. F. (1974). Review lecture: Muscular contraction. J. Phy8iol. 243, 1-44. HUXLEY, A. F. & SIMMONS, R. M. (1971). Mechanical properties of the cross-bridges of frog striated muscle. J. Physiol. 218, 59-60P. HUXLEY, A. F. & SIMMONS, R. M. (1973). Mechanical transients and origin of muscular force. Cold Spring Harb. Symp. quant. Biol. 37, 669-680. HUXLEY, H. E. (1963). Electron microscope studies of natural and synthetic protein filaments from striated muscle. J. molec. Biol. 7, 281-308. MATSUBARA, I., YAGI, N. & HASEIzuME, H. (1975). Use of an X-ray television for diffraction of the frog striated muscle. Nature, Lond. 255, 728-729. WILKIE, D. R. (1968). Heat, work and phosphorylcreatine breakdown in muscle. J. Physiol. 195, 157-183.
467
FILAMENT SLIDING AND ENERGY ABSORBED BY THE CROSS-BRIDGES IN ACTIVE MUSCLE SUBJECTED TO CYCLICAL LENGTH CHANGES
BY F. W. FLITNEY AND D. G. HIRST From the Department of Physiology, University of St Andrews, St Andrews, Fife
(Received 13 October 1976) SUMMARY
1. The effects of single and double cycles of stretch and release on the tension response and relative sliding movement of the actin and myosin filaments in active frog's muscle were investigated. 2. The cross-bridges linking the filaments together are able to accommodate a greater range of filament displacement before becoming detached during a second cycle stretch. providing it commences without delay following the preceding release: sarcomere 'give' then occurs for displacements of around 18 nm, as compared with 12 nm for a first cycle stretch. It is postulated that the difference arises because the myosin heads adopt different 'preferred' positions in the isometric steady-state and at the end of a previous release. 3. Muscle length-tension loops were recorded and used to measure the energy absorbed when a muscle is subjected to cycles of stretch and release. The work absorbed per unit length change increases with increasing displacement of the crossbridges from their initial (isometric) steady-state position, up to the point at which sarcomere 'give' occurs (S2); thereafter it remains constant. 4. More work is absorbed during the first cycle of a double stretch-release combination than during the second. The greater amount absorbed during the first cycle is associated with a correspondingly greater amount of filament sliding in the period following sarcomere 'give'. Sarcomere length-tension loops were constructed and these showed that not less than 80-85 % of the work done on a muscle is absorbed by the sarcomeres themselves. 5. A greater amount of work is done on stretching up to (but not beyond) S2 during second cycle stretch as compared to a first. The difference amounts to about 1 mJ. m-2 per half-sarcomere. 6. The results are compatible with the mechanism for force production proposed by Huxley & Simmons (1973), in which each myosin head generates force in a number of stepping movements, from one attached state to another. It is concluded that (a) during an unloaded, isotonic contraction the working 'stroke' of the head would result in a 10-13 nm relative sliding movement of the filaments, and (b) the potential energy difference separating the two 'preferred' states is 6-9-6 kT per cross-bridge, or 3-4-8 kT per S-i sub-unit, assuming that each one interacts simultaneously with the actin filament.
468
F. W. FLITNEY AND D. C. HIRST INTRODUCTION
It was shown in the preceding paper (Flitney & Hirst, 1978) that a muscle subjected to stretch resists the movement initially by developing a high- force, but when the relative sliding movement of the actin and myosin filaments exceeds 12 nm, the cross-bridges linking the two become forcibly detached, the sarcomeres yield and the slope stiffness of the muscle decreases abruptly. In this paper the effects of single and double cycles of stretch and release on the movements of the filaments and on the tension developed by a muscle are reported. These experiments have shown that at the end of a cycle of stretch and release the tension supported by a muscle is substantially less than the isometric level, even though the sarcomeres themselves have returned to their pre-stretch (isometric) length. This observation is taken to mean that the cross-bridges between the two sets of filaments are somewhat shortened, as a result of which during a subsequent stretch, made without delay, a significantly greater degree of extension (approximately 1P5 x more) is required to induce sarcomere 'give'. The simplest interpretation of these observations is that at the commencement of the second stretch the orientation of the myosin 'heads' with respect to the actin filaments differs from that in the isometric state. The results are compatible with a model proposed by Huxley & Simmons (1971, 1973) in which each cross-bridge generates the force for contraction in a series of stepping movements, from one attached configuration to another. It is impossible from the present results to give an estimate of the actual number of cross-bridge states involved, but the minimum number consistent with the data is either three or four, one detached and two or three attached states, with the force being generated in either one or two stepping movements. METHODS
Recordings of muscle tension, length and sarcomere spacing were made as described in the preceding paper (Flitney & Hirst, 1978). The present experiments involved subjecting muscles to cyclical length changes. Single and multiple cycles of stretch and release were employed. In the majority of experiments, the second cycle of stretch and release followed the first immediately, but in a few it commenced after a predetermined delay. The energy absorbed in taking muscles through cycles of different amplitudes was also measured. The procedure was as follows. Muscles were tetanized and subjected to stretch, followed immediately by a release of the same amplitude and velocity. The displacement signal from the servo-amplifier which was used to control muscle length was fed to the X plates of the oscilloscope and the output of the tension recorder to the Y plates. A Devices 'Digitimer' (type 3290) was used to modulate the beam intensity through the Z input so that only the events occurring during stretch and release were recorded on the screen. The work done on stretching the muscle is mostly returned duringthe subsequent release, but not all of it; the oscilloscope beam describes a clockwise loop and the energy absorbed by the muscle is given by the area enclosed by the loop. All experiments were made at temperatures of 0-3 IC, using stretch-release velocities of not less than 4 mm. sec-.
STRETCH AND RELEASE OF ACTIVE MUSCLE
469
RESULTS
Tension changes and filament sliding during single and double cycles It was concluded previously (Flitney & Hirst, 1978, Fig. 7) that during a stretch the actin and myosin filaments must be displaced by 12 nm (mean + S.D. = 12-3 + 0 9 nm; n = 10) before the cross-bridges linking them together are forcibly broken. Fig. 1A compares their relative movement during first and second cycle stretches. The upper record shows the tension response to a double cycle of stretch and release and the lower record shows the form of the external length change. The tension response and the movement of the filaments during the second stretch are markedly different from those during the first. The results obtained for three muscles treated similarly were as follows. First, the point S2 is reached for a displacement of around 18 nm (mean +S.D.: 18-3 + 1.0 nm), approximately 1-5 x greater than is required to induce sarcomere 'give' in the case of a first stretch (Fig. 1 B). Secondly, the tension held by the muscle at S2 is similar in the two cases: 1-38 P0 (1st cycle) and 1-40 P0 (2nd cycle). Thirdly, at the end of the first release (immediately before restretching) muscle tension has fallen to 0 73 P0, although by this time the sarcomere length is back to its initial (pre-stretch) value. This last point is especially significant and will be referred to again later (p. 473). Length-tension relation of the sarcomeres during first and second cycle stretches. The results for the muscles referred to above are presented in the form of two sarcomere length-tension diagrams in Fig. 2. Filament displacement resulting from stretch is plotted against muscle tension (above and below P0). The mean stiffness of the muscles in the period up to rapid 'give' (estimated from the slopes of the lines relating muscle tension to sarcomere extension, AP/tXS) is not substantially different in the two cases; 5-8 x 1012 N. m-2 per m extension of each half-sarcomere (1st cycle) and 5-3 x 1012 N.M-2 per m extension of each half sarcomere (2nd cycle). It was shown in the previous paper (Flitney & Hirst, 1978), that sarcomere stiffness is proportional to filament overlap and we concluded that it represents the collective stiffness of the cross-bridges linking the actin and myosin filaments together; the simplest interpretation for the small change observed here (ca. 9 %) is that the number of attached cross-bridges is not altered appreciably by stretch and release of a muscle under the present conditions. This point is taken up again later. By contrast, during the period of 'give' the stiffness of the sarcomeres falls by 25-30 x . Velocity of filament sliding and extent of movement during sarcomere 'give'. During rapid 'give' the filaments slide at a rate of at least 1 4 nm. msec-1. This is about 8 x faster than the value calculated on the assumption that their rate of sliding is determined only by the speed of the external length change. It should be emphasized that this is the minimum velocity since it is estimated from two consecutive frames of the cine-film. The extent of the sliding movement is approximately the same for both first and second cycles (20-21 nm). Rapid shortening of sarcomeres and tension changes during release. The movement of the sarcomeres and the tension response of the muscle during release from a preceding stretch are also shown in Fig. 1. There are two points of interest. First, during the early part of the release, tension falls steeply while the sarcomeres shorten
F. W. FLITNEY AND D. G. HIRST
470
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Fig. 1. A, tension response (AP) and change of sarcomere length (AS) resulting from a double cycle of stretch and release (AL). The point at which the sarcomeres 'give' and where muscle stiffness decreases (S2) is marked by the vertical arrows. Note (a) that a greater amount of filament sliding is required to induce 'give' in the case of a second cycle stretch, and (b) at the end of the first release muscle tension is substantially less than the isometric level even though the sarcomeres have returned to their pre-stretch length. B, filament displacement during a first (1) and second (2) cycle stretch, plotted against time after the commencement of the stretch.
471 STRETCH AND RELEASE OF ACTIVE MUSCLE relatively slowly. Secondly, after this initial period of slow shortening the velocity of filament sliding increases abruptly, at a speed in excess of 1 0 nm. msec-1. As before, there is some uncertainty in giving a precise figure because the estimate is
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Fig. 2. Sarcomere length-muscle tension curves during stretch for three muscles subjected to double cycles of stretch and release. The stiffness of the sarcomere is high during the early part of the stretch, decreases abruptly during 'give' and then partially recovers during the remainder of the stretch. First stretch, A; second stretch, B.
F. W. FLITNEY AND D. G. HIRST made from two consecutive frames, but the value could not be less than this (it is of interest to compare it with the rate at which the filaments slide in an unloaded isotonic contraction; the data given by Hill (1 970) yield a figure of around 1 7 nm . msec-1 for a frog sartorius at 0 'C). The extent of the sliding movement during rapid shortening is around 10-20 nm (mean 14-5, n = 5) for both first and second cycle releases. It is probable that this phase of the response is caused by cross-bridge re-attachment, resulting from realignment of the myosin heads with active sites on the actin filaments. This is consistent with the observation that the point at which rapid shortening commences is not constant, but depends upon the degree of extension of 472
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Fig. 3. Tension response resulting from a double cycle of stretch and release in which the second cycle follows the first after a delay of about 500 msec. The degree of extension required to induce sarcomere 'give' (indicated by the abrupt decrease of muscle stiffness) is only slightly greater in the case of the second stretch. Note (a) the recovery of isometric tension between the end of the first release and the start of the second stretch, and (b) the more abrupt levelling-off cf tension during the second stretch.
the sarcomeres beyond 'give' during the preceding stretch. The following values from Fig. 1 serve to illustrate the point. During the first cycle stretch the sarcomeres are extended by 37 nm in this period, and the rapid phase of the shortening commences when, in the early part of the release, they have been displaced by 36 nm in the opposite direction. The corresponding values for the second cycle are 24 nm and 20 nm. This explanation is reinforced by the observation that the rate of fall of tension declines markedly during and immediately after rapid shortening; indeed, in many records it reverses during the remainder of the release. Tension response during a delayed second cycle. The response to a delayed second stretch is different. Fig. 3 shows two cycles of stretch-release separated by an interval of 500 ms. During this period the muscle practically regains its full isometric tension. The response to a second cycle is then similar to that for the first (and might
STRETCH AND RELEASE OF ACTIVE MUSCLE 473 have been identical, had a greater delay been allowed); S2 occurs for extensions (whole muscle) of 395 sum (1st cycle) and 430 /tm (2nd cycle). The effects of delaying the second cycle have not been investigated fully, but the indications are that a muscle may recover from the effects of the first cycle of stretch and release if sufficient time is given. It appears that the time course of the 'recovery' process follows that for the redevelopment of tension when the muscle is not re-stretched following a release. Energy absorbed during cycles of stretch and release Work absorbed in cycles of different amplitudes. Except for very small amplitudes, the work absorbed during a stretch exceeds that returned during subsequent release. The amount absorbed is measured from the areas of the muscle length-tension loops. A
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It has been seen that the level of tension existing immediately before and immediately after a single stretch release cycle is not the same; typically, at the end of a previous release (made at a velocity of 4 mm. sec-1) it has fallen to near 0 7 PO. In contrast, tension at the beginning and end of a second cycle is the same, providing the second cycle follows the first without delay. Fig. 4 shows muscle length-tension loops for a series of single cycles of stretch and release, A, and a series of second cycles, B, of different amplitudes. The loops for first cycles are open, and those for second (or subsequent) cycles are closed. The areas enclosed by the loops are plotted against the amplitude of the length oscillation in Fig. 5. (In the case of first cycle 'loops', the area is closed-off by drawing a straight line between the open ends.) The amount of work absorbed for a given
F. W. FLITNEY AND D. G. HIRST cycle amplitude, W, is greater for first (open) than for second (closed) cycles. In both cases, W is negligible for small amplitudes ( < 50 jum, first cycle, and < 100 ,um, second cycle) but increases progressively with increasing amplitudes, up to around 550 ,tm. Thereafter, the amount of energy absorbed by the muscle increases linearly with increasing cycle amplitudes, by 0-66 x 10-5 J. M-2 per half-sarcomere per ,um (mean slope of dashed lines). 474
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Fig. 6. Sarcomere length-muscle tension loops constructed from changes in the spacing of the diffraction spectra produced by a muscle subjected to two consecutive cycles of stretch and release. The work done on each half sarcomere is given by the area of the loop. 1, first cycle; 2, second cycle.
475 STRETCH AND RELEASE OF ACTIVE MUSCLE Work absorbed by the sarcomeres. A question which should be asked is: How much energy is absorbed by the sarcomeres themselves, as distinct from other elements in the muscle? To answer this point, experiments were made in which sarcomere movements were recorded during first and second cycles and length-tension loops for the sarcomeres (rather than for the whole muscle) were constructed. It is assumed in what follows that the tension recorded at the extremities of the muscle is equal to that borne by each sarcomere, which is very nearly true at the short muscle length used, there being little contribution from parallel elastic elements. Fig. 6 shows the result obtained in one such experiment. The muscle was subjected to two consecutive cycles of + 1020 jum. Again, the work absorbed is given by the area of the loops. The values obtained were 4 mJ.M-2. half-sarcomeres-1 (first cycle) and 3 15 mJ.m-2.half-sarcomere-1 (second cycle). The corresponding figures, estimated from length-tension loops for the whole muscle, were 4-6 and 3.75 mJ. M-2. half-sarcomere-1, respectively. This experiment, and others of a similar nature, showed that the major part of the work absorbed in taking a muscle through a cycle of stretch and release (not less than 80-85%) is absorbed by the sarcomeres themselves. They also reaffirm the observation, made above, that the work absorbed during a first cycle is substantially greater than during a second. It is probable that this difference arises because a greater amount of non-returnable work is associated with sliding of the filaments after sarcomere 'give' in the case of a first cycle. DISCUSSION
The results are consistent with the model put forward recently by Huxley & Simmons (1971, 1973) which describes a possible mechanism for force production by muscle. Their hypothesis envisages the cross-bridge as being made up of two components arranged in series: an instantaneous elastic element (their AB linkage) and a damped force-generating element (Fig. 7). The myosin head is thought to have a small number of attachment sites through which it can bind to corresponding sites on an actin active region. It is postulated that the simultaneous attachment of the head at two consecutive sites constitutes a stable state and that force is generated by a stepwise movement along the actin filament, from one such stable position to the next, each having a progressively lower potential energy than the preceding one. Huxley & Simmons consider that the most likely number of attachment sites is four, with three stable states and the full range of movement taking place in two steps. The extent of filament sliding required to induce sarcomere 'give'. The different amounts of filament sliding required to reach S2 in first and second cycle stretches can be explained if it is postulated that the instantaneous elastic components of the cross-bridges are in a somewhat shortened state at the end of a preceding release, due to a shift in the 'preferred' position of the attached myosin heads, say from position II to III in the model shown in Fig. 7 (based on Huxley & Simmons (1971) Fig. 5). It is not difficult to see why position II might be favoured at the peak of a tetanus. When a head attaches initially it is able to move with relative ease to the next position and in so doing generate tension. As a result of this tension, which increases
F. W. FLITNE Y AND D. G. HIRST 476 progressively as the tetanus develops, the probability of the head making the next step is reduced. If it should do so, then the likelihood of it becoming detached by combining with ATP is increased. The combination of these two factors means that at the peak of a tetanus the heads are energetically constrained to spend most of their time in an intermediate position. It is postulated that the stituation is different at the end of a preceding release. If one discounts for the present the possibility that the number of cross-bridges is reduced by the preceding stretch and release (a point discussed later) then the conclusion to be drawn from Fig. 1 A is that their A
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Fig. 7. Schematic representation of the events occurring during first and second cycle stretches. A single myosin head is shown attached to an actin filament (1) at the peak of an isometric tetanus, immediately before a first stretch; and (2) at the end of a preceding release, before a second stretch. Part of the stretch is absorbed by extension of the elastic linkage and part by backward rotation of the attached head. The two right-hand diagrams depict the position of the head at the commencement of sarcomere 'give'. In each case, one of the two attachment sites for the initial attached state is shown as already having been forcibly broken, the other is as yet still attached.
configuration is altered in some way. One explanation for this is that during release the AB linkages are progressively unloaded, thereby facilitating cross-bridge cycling, so that at the end of the release, when the muscle is in a relatively 'low tension' state, there is a net shift in the distribution of the re-attached heads, such that they now preferentially occupy position III in Fig. 7. Now, consider what happens when a muscle is stretched. During the early part of the movement tension is generated by extension of the AB link only, but at some point, the attached head begins to be forced backwards, against its tendency to move to the next position of lower potential energy. Tension continues to rise, the length change now being shared between backward rotation of the head and further extension of the elastic linkage. Taking data from an actual experiment (Fig. 7), sarcomere 'give' occurs when the force has risen to 1-35 P0 and for a relative displacement of the filaments of 11 8 nm. The corresponding displacement for a second cycle stretch is 18-3 nm and tension rises to 1 38 PO.
STRETCH AND RELEASE OF ACTIVE MUSCLE 477 An estimate of the amount of movement taken up by rotation of the attached head, as distinct from extension of the connecting elastic linkage, can be made (below) and this places a lower limit of 5 nm for the axial distance separating the two 'preferred' positions and an upper one of 6-5 nm. Two assumptions are made. First, the instantaneous elastic element displays Hookean characteristics. This can be inferred from Huxley & Simmons (1971, 1973) and Ford, Huxley & Simmons (1976) T1 curves. Secondly, that there is no substantial change in the number of attached cross-bridges at the end of a preceding release. This seems likely since (a) the mean slope stiffness of the sarcomeres during a subsequent stretch is approximately the same as that during a first stretch, (b) the level of tension reached at S2 during a second stretch is not significantly different from that attained during a first stretch, and (c) the work done during stretches sufficient to reach (but not exceed) S2 is greater during a second stretch, even though for much of the movement the force on the muscle is less. There is no doubt that under certain conditions of stretch and release, following rapid changes of load, for example Huxley, 1971) there i8 a change in the number of attached cross-bridges, but the pattern of sarcomere movements and the accompanying tension response observed during a 81ow release (Fig. 1 A) suggests that under the present conditions cross-bridges detach, but have sufficient time to reattach (p. 472), so that at the commencement of the second stretch (made without delay) the number linking the filaments together is virtually unchanged. Finally, it is difficult to see why fewer cross-bridges would permit a greater degree of filament sliding to occur in the period up to S2The question raised now is, how much of the imposed sliding movement is translated into rotation of the attached cross-bridge head? Since the two elements of the cross-bridge are arranged in series, the AB links are sustaining a force of 1-35P1 at S2 and they will therefore be extended to 1-35 x 4-5 nm (the isometric length; Ford et al. 1976) = 6-07 nm, an increase of 1-57 nm. This means that head rotation accounts for 11-8-1-57 = 10-23 nm of the observed filament displacement. The situation will be different for a second stretch, where the heads preferentially occupy position III rather than II in Fig. 7. Similar reasoning then shows that of the total 18-3 nm of movement, 2-92 nm goes into extending the links, leaving 15-38 nm to be accounted for by rotation of the heads. The conclusion to emerge from this is that the two preferred positions are separated by a distance of around 15-38 - 10-23 = 5-15 nm. If the above correction for extension of the links is omitted, an upper estimate of 18-3 - 11-8 = 6-5 nm is obtained.
How many cross-bridge states? These considerations lend some support to the hypothesis that force generation occurs as the result of discrete changes in the position of the attached heads, from one stable state to another. It is impossible to conclude with certainty how many cross-bridge states exist, although on the basis of our results and those of Huxley & Simmons, we favour a minimum of three or four: two or three attached states and one detached state. The argument is as follows. Consider first the model in Fig. 7, in which there are three attached states, designated I (not shown, but inferred from the diagram), II and III. The initial part of the cross-bridge cycle involves the transition from the detached state to state I, and the force generating steps which follow are the transitions I -÷II and II -- III. The results show that the axial distance separating states II and III is around 5 nm (corrected estimate). The amount of sliding movement required to reach S2 during a single stretch is approximately twice this distance (10-23 nm) which suggests that all three attached states are equally spaced. On this scheme, the relative sliding movements of the filaments associated with each cross-bridge 'stroke' in an unloaded isotonic contraction would be between 10 nm (based on corrected estimates) and 13 nm (uncorrected estimates). The figure of 5-2 nm obtained above for the best estimate of the spacing of the
F. W. FLITNEY AND D. G. HIRST attachment sites is of interest, since it corresponds closely with the centre-to-centre spacing of the actin monomers in the F actin strands (Hanson, 1968). It is tempting to speculate on the basis of this that the myosin heads bear sites which interact sequentially with three consecutive pairs of actin monomers, the first defining state I, and the other two, the tension bearing states II and III. There are steric difficulties with a model of this kind, and the spacing between the postulated attached positions and its close correspondence with the spacing of the actin monomers may only be coincidental. Furthermore, the locations of the force generating element and the instantaneous elasticity within the cross-bridge are not known with certainty. A. F. Huxley & Simmons (1973) have emphasized that while their 1971 model adequately explains their experimental findings, it is by no means unique. A number of equally plausible alternatives is given by Huxley (1974). There is another point to consider too. The results obtained with double stretches might be explained, if in the isometric state the time-average position of the cross-bridge heads was midway between only two stable states, an initial attachment state A and a tension bearing state B, so that on stretch and release they would end up in positions A and B respectively. Force production during attachment would then be a single step process, from A to B, and the figures derived above for the spacing between the preferred states (5 nm) and for the amount of sliding required to reach S2 during a first stretch (10 nm) would then refer to rotation of the head about its mean isometric position. Potential energy difference between the two 'preferred' states. The amount of work done on stretching to the point at which the cross-bridges are forcibly detached is readily estimated from the areas under the curves relating muscle force to filament sliding. It was seen that during a first cycle stretch head rotation accounts for approximately 10 nm of movement, and during a second stretch, approximately 15 nm. When these distances are related to muscle force, the work absorbed turns out to be 318 mJ.m-2.half-sarcomere-I (first stretch) and 4-29 mJ.m-2.halfsarcomere'1 (second stretch). The difference between the two, approximately 1 mJ . M-2. half-sarcomere-1, represents the potential energy difference between the two preferred positions. The number of cross-projections on the myosin filaments is estimated to be 5 x 1016 M-2. half-sarcomere-I (Huxley, 1963) which gives a figure of 2 x 10-20 J for the potential energy difference per cross-bridge. This figure assumes that all the cross-projections are attached, but it is known from X-ray diffraction studies that this is not the case. Recent studies (Haselgrove & Huxley, 1973; Matsubara, Yagi & Hashizume, 1975) suggest that 50-80% are so engaged, which gives figures of 2 5-4 x 10-20 J, or 5-97-9-56 kT, for the energy difference between the two states. These values compare closely with the figure of 7-3 kT for the work done per crossbridge, calculated by Huxley & Simmons (1971) from measurements of muscle efficiency (Hill, 1939) and phosphorylereatine break-down (Wilkie, 1968). At face value, this would seem to rule out a two-step mechanism, since the work done per cross-bridge would then have to be in the range 12-18 kT to be consistent with our results. However, the discrepancy disappears if the estimate for the potential energy difference between the two states is partitioned equally between each of the two cross-bridge S, sub-units, giving values of 34.5 kT per step. This may be on appro478
479 STRETCH AND RELEASE OF ACTIVE MUSCLE priate correction to make, since the two heads are connected through a common linkage to the myosin filament. We thank Action Research for the Crippled Child for financial support. We are grateful to Drs R. M. Simmons, D. A. Jones and W. G. S. Stephens for valuable discussion, and to Mr Robert Adam for technical assistance. REFERENCES FLITNEY, F. W. & HIRST, D. G. (1978). Cross-bridge detachment and sarcomere 'give' during stretch of active frog's muscle. J. Phy8iol. 276, 449-465. FLITNEY, F. W., HIRST, D. G. & JONES, D. (1976). Effects of temperature and velocity of stretch on maximum tension borne by the sarcomeres in contracting muscle. J. Phy8iol. 256, 127-128P. FORD, L., HuxLEY, A. F. & SIMMONS, R. (1976). The instantaneous elasticity of frog skeletal muscle fibres. J. Physiol. 260, 28-29P. HANSON, J. (1968). Recent X-ray diffraction studies of muscle. Q. Rev. Biophys. 1, 177-216. HASELGROVE, J. & HUXLEY, H. E. (1973). X-ray evidence for radial cross-bridge movement and for the sliding filament model in actively contracting skeletal muscle. J. molec. Biol. 77, 549568. HILL, A. V. (1939). The mechanical efficiency of frog's muscle. Proc. R. Soc. B 127, 434-451. HILL, A. V. (1970). First and Last Experiments in Muscle Mechanic. London: Cambridge University Press. HUXLEY, A. F. (1971). The Croonian Lecture, 1967. The activation of striated muscle and its mechanical response. Proc. R. Soc. B 178, 1-27. HUXLEY, A. F. (1974). Review lecture: Muscular contraction. J. Phy8iol. 243, 1-44. HUXLEY, A. F. & SIMMONS, R. M. (1971). Mechanical properties of the cross-bridges of frog striated muscle. J. Physiol. 218, 59-60P. HUXLEY, A. F. & SIMMONS, R. M. (1973). Mechanical transients and origin of muscular force. Cold Spring Harb. Symp. quant. Biol. 37, 669-680. HUXLEY, H. E. (1963). Electron microscope studies of natural and synthetic protein filaments from striated muscle. J. molec. Biol. 7, 281-308. MATSUBARA, I., YAGI, N. & HASEIzuME, H. (1975). Use of an X-ray television for diffraction of the frog striated muscle. Nature, Lond. 255, 728-729. WILKIE, D. R. (1968). Heat, work and phosphorylcreatine breakdown in muscle. J. Physiol. 195, 157-183.
