J. Physiol. (1974), 239, pp. 1-14 With 4 text-ftigure" Printed in Great Britain
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EFFECT OF STRETCHING ON THE ELAS CHARACTERISTICS AND THE CONTRACTILE COMONNT OF FROG STRIATED MUSCLE
By GIOVANNI A. CAVAGNA AND G. CITTERIO From the Istituto di Fisiologia Umana dell'Universitd di Milano e Centro di Studio per la Fisiologia del Lavoro Muscolare del C.N.R., Milano, Italy
(Received 19 June 1972) SUMMARY
1. The force-velocity relationship and the stress-strain curve of the so-called series elastic component (s.e.c.) of frog sartorius, semitendinosus and gastrocnemius have been determined during shortening against a given force (isotonic quick-release) and at high speed (controlled release): (a) from a state of isometric contraction and (b) after stretching of the contracted muscle. In both cases the muscle was released from the same length: this was usually slightly greater than the muscle's resting length. 2. The muscle released immediately after being stretched is able to shorten against a constant force, P, equal to or even greater than the isometric force, P0, at the same length. When the force P applied to the muscle is reduced below P0 the velocity of shortening is greater after stretching, and the force-velocity curve is therefore shifted along the velocity axis: the shift is maximal when P is near to P0 and it decreases rapidly with decreasing P. 3. The extent of shortening of the s.e.c. required to make the force fall from P0 to zero is 50-100 % greater when the muscle is released immediately after stretching than when it is released from a state of isometric contraction. This difference is found by using either the controlled release method or the isotonic quick-release method. 4. If a time interval is left between the end of stretching and the onset of shortening of the contracted muscle (controlled release method), the length change of the s.e.c., for a given fall of the force, is reduced and approaches that taking place when the muscle is released from a state of isometric contraction. 5. Curare does not affect the results described above, indicating that these do not depend on modification of the neuromuscular transmission. 6. It is concluded that stretching a contracted muscle modifies tempo1-2
GIOVANNI A. CAVAGNA AND G. CITTERIO rarity: (a) its elastic characteristics, as shown by the greater amount of mechanical energy released for a given fall of the force at the muscle's extremities, and (b) its contractile machinery, as it is suggested by the change of the force-velocity relationship. 2
INTRODUCTION
When muscles shorten during everyday activity, it is not always from a relaxed state or from a state of isometric contraction as it usually is under laboratory conditions; frequently shortening begins immediately after the contracted muscles have been forcibly stretched by some external force. For instance, this mode of muscular contraction is preponderant in running and in jumping. The effect of stretching an active muscle on the following positive work phase was tested experimentally and it was found that an active muscle shortening immediately after forcible stretching is able to do more work than it would have while shortening at the same speed from a state of isometric contraction (Cavagna, Dusman & Margaria, 1968). In order to determine the origin of the additional amount of work done by the previously stretched muscle, it is necessary to know the elastic energy stored during stretching. This can be determined if the trend of the stress-strain curve of the series elastic elements is known up to the force values, greater than the isometric one, P0, attained during stretching. The stress-strain curve has been determined on frog gastrocnemius by releasing the muscle against different loads after stretching it to raise the force above Po (Cavagna, 1970); in that paper it was assumed that the same stress-strain curve holds, from P0 to zero, both when shortening begins from an isometric contraction and immediately after stretching. This, however, is not true: as shown by the experiments described below, the stress-strain curve of the 'series ' elastic elements and the speed of shortening in isotonic conditions are temporarily changed by previous stretching of the active muscle. METHODS
The experiments have been performed on the sartorius, semitendinosus and gastrocnemius muscle of Rana eaculenta and on the sartorius of toad (Bufo bufo). The muscles, dissected with care, were immersed in oxygenated Ringer solution kept at 0-2° C in the experiments on the isotonic lever and at 0° C in those on the Levin & Wyman ergometer. Stimulation was carried out at the minimal frequency necessary to have a fused tetanus (5-10 stimuli/sec); stimuli above maximal were given by means of a Grass stimulator (model S4K) when the gastrocnemius was excited through the nerve and in some initial experiments in which the muscle was stimulated at the extremities. Subsequently alternating condenser discharges (time constant up to 10 msec) were used for direct stimulation: these were conveyed to the
MECHANICS OF PREVIOUSLY STRETCHED MUSCLE
3
sartorius and semitendinosus muscles through a platinum multielectrode assembly and to the gastrocnemius through electrodes at its extremities. The interval between successive stimulations was about 15 min. The muscles were stimulated in one case (Fig. 1A) at a length (called in this paper lo) at which the muscle just began to show resting tension. The force, Fpe, sustained at this length by the parallel elastic elements of the relaxed muscle was 10-50 g for gastrocnemius and 3 g at a maximum for sartorius and semitendinosus: the force developed at this length during stimulation by gastrocnemius and sartorius is near to the maximal isometric force; for semitendinosus it can be appreciably less because tension first appears in the parallel elastic elements of this muscle at a length greater than the optimal length. As soon as the force reached a constant value in an isometric tetanic contraction, the muscle was allowed to shorten at high speed on a Levin & Wyman ergometer (as in Fig. 1) or against a constant force on an isotonic lever. In the other case (Fig. 1B) the muscle was stimulated isometrically at a shorter length (2.5 mm below 10 in the experiments on the Levin & Wyman ergometer and 1-2 mm below 10 in those on the isotonic lever); when the force had reached a steady value, the muscle was forcibly stretched to a length, 10, exactly equal to the length of release in A and then allowed to shorten as in A. The force developed during shortening on the Levin & Wyman ergometer and the speed of isotonic contraction, in A and in B, were compared. As mentioned above the length of the muscle before release (equal in A and in B) is referred to throughout the paper as 10 and the net force (total force minus Fpe) developed by the muscle in isometric conditions at this length is referred to as P0. In some experiments the sartorius, the semitendinosus and the gastrocnemius were curarized by immersion in Ringer solution with D-tubocurarine at a concentration of 5-10 x 1O-5 g/cm3. The muscles were left in the saline with curare for at least 2 hr before the beginning of the experiment: complete block of the neuromuscular transmission was checked on the gastrocnemius by stimulation through the nerve. Contraction against a constant force. The force-velocity relationship of the contractile component of the frog gastrocnemius was determined from the tracings obtained by means of the isotonic quick-release apparatus described in a previous paper (Cavagna, 1970). An improved version of this set-up was constructed for the sartorius and the semitendinosus: the isotonic lever used for these muscles had a lever ratio of 20: 1 and an equivalent mass of 0 110 g at the point of attachment of the muscle (3-5 cm from fulcrum). The lever was pivoted on miniature ball bearings and weights were hung from it on a compliant connexion. The procedure followed in the experiment with the isotonic lever was similar to that illustrated in Fig. 1 for the Levin & Wyman ergometer. In one case, A, the muscle was stimulated isometrically at a length, l0, at which Fpe began to be detectable and then it was released against different loads by operating an electromagnetic catch (Wilkie, 1956). In the other case, B, the muscle was stimulated isometrically at a length 1-2 mm shorter than lo: when the isometric force reached a maximum (this was checked on a force-time tracing not illustrated here) it was stretched up to lo and released immediately after as in A. Stretching of the active muscle on the isotonic lever lasted 0 1-0 2 sec and was accomplished by hand by means of the device illustrated in a previous paper (Cavagna, 1970). The shortening of the muscle was recorded by means of a photocell detecting the movement of the lever and the force developed by the muscle by means of a transducer to which the fixed end of the muscle was attached. Experimental tracings so obtained are given in Fig. 4. The velocity of shortening was measured from the slope of the length-time tracing over the first 60-100 msec after the abrupt change of length due to the recoil of the series elastic elements.
GIOVANNI A. CAVAGNA AND G. CITTERIO
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Contraction at a given 8peed. Dynamic force-length diagrams were determined according to the procedure described above and illustrated in Fig. 1, by means of a Levin & Wyman ergometer: this was driven by a piston fed with compressed air and operated by an electrovalve (an improved version of that used by Cavagna et al. 1968). On this ergometer the shortening of the muscle can follow immediately stretching and the speed of shortening and/or stretching can be independently varied from 0-2 to about 200 mm/sec. The length change, Al, imposed on the muscle was 2-5 mm in all the experiments. Al was recorded by means of a potentiometer (Helipot, Mod 3351) fixed to the fulcrum of the lever; after amplification (by a 2A60 Tektronix amplifier) the corresponding signal was displayed on the abscissa of a Tektronix oscilloscope (type 564 storage): simultaneously it was also recorded as a function of time. The force was measured by means of a strain-gauge transducer to which the fixed extremity of the muscle was attached. The transducer was protected from the saline surrounding the muscle by an impermeable rubber coat: its characteristic frequency was 1660 Hz in the set-up used for the gastrocnemius and 1040 Hz in that used for the sartorius and the semitendinosus; the transducers were tested up to 2 kg and 200 g, respectively, and found to be linear. The transducer output was displayed on the ordinate of the oscilloscope, after amplification by a 3A9 Tektronix differential amplifier. The simultaneity of the force and displacement recordings on the oscilloscope was tested by determining the force-length diagram of a spring at different speeds with the same apparatus used for the muscle. The tibial end of sartorius and semitendinosus and the plantaris end of gastrocnemius were connected to the lever by means of a rigid bar to which the tendons were clamped; at the other extremity, the femur epiphysis (gastrocnemius) or a piece of the pelvic bone (sartorius and semitendinosus) were attached directly to the transducer. Thanks to these connexions the compliance of the apparatus was very low: 2 x 10-5-4 x 10-5 mm/g, according to whether the force was falling from 1 or 2 kg, respectively, in the set-up for the gastrocnemius, and 3-4 x 10-5 mm/g in that for sartorius and semitendinosus; for these last muscles the force involved were so low that the deformation of the apparatus was negligible (200 g x 3-4 x 10-5 mm/g = 0-007 mm).
MECHANICS OF PREVIOUSLY STRETCHED MUSCLE
5
RESULTS
Modification of the elastic characteristic of contracted muscle induced by stretching In Fig. 2 are illustrated dynamic force-length diagrams as obtained on four different muscles according to the procedure illustrated in Fig. 1. On the left, A, shortening of the muscle begins from a state of isometric contraction; on the right, B, shortening takes place immediately after stretching of the contracted muscle. Fig. 1. Schematic diagrams showing the procedure followed to determine the dynamic force-length tracings illustrated in Fig. 2. The length changes of the muscle, determined by the movement of the arm of the Levin & Wyman ergometer, and the force developed by the muscle, measured by means of a force transducer, are given as a function of time (left hand tracings) and as X-Y plots (right hand tracings: dynamic force-length
diagrams). In A the muscle at rest was first lengthened (a) by the arm of the ergometer to a length (called in the paper lo) at which the parallel elastic elements began to be under tension; the force developed by these elements attains a maximum value (Fpenmx) at the end of stretching, and then it decreases, as the muscle is kept stretched at the greater length, towards an almost stable value: this is the value referred to throughout the paper as Fpe1 The muscle was then stimulated isometrically (b) and when the force reached a constant value, it was allowed to shorten at high speed by operating the ergometer's arm (c). The length change imposed by the ergometer to the muscle was always 2-5 mm. During shortening the force fell to zero to rise again at the end of the movement of the ergometer's arm (d). The same events, expressed as X- Y plots, show: the force-length diagram of the parallel elastic elements (curve a) recorded during stretching the relaxed muscle, the small drop of the force due to stress-relaxation of these elements followed by the rise of the force during the isometric stimulation of the muscle (vertical line b), the dynamic force-shortening curve of muscle recorded during release on the Levin & Wyman ergometer (curve c) and the redevelopment of tension at the end of the movement of the ergometer (vertical line d). In B the muscle was stimulated isometrically (a) at a length 2-5 mm shorter than in A; as the isometric force reached a constant value it was forcibly stretched in the contracted state by the Levin & Wyman ergometer, so that when the length, lo was attained, after 2-5 mm stretching, the force developed was greater, about double, than the isometric force at the same length. Immediately at the end of stretching the movement of the ergometer was reversed (c'): this is accompanied by a drop of the force which then rises again (d) as the ergometer stops. The X-Y plots on the right show: the vertical line a recorded during the isometric stimulation at a length 1-25 mm and the dynamic force-length diagrams recorded during stretching the contracted muscle to 10 (b) and during shortening at high speed (c'): the redevelopment of tension (d) at the end of shortening is superimposed to the vertical line a.
GIOVANNI A. CAVAGNA AND G. CITTERIO In A the muscle at rest was first lengthened by the Levin & Wyman ergometer to a length, 10, at which it just began to show resting tension; the velocity of lengthening was usually low (3-4 mm/sec), but it was very high (about 200 mm/see) in the bottom left tracing obtained on the frog gastrocnemius: this is shown by a relevant increase of the force (curve a) in the parallel elastic elements, which then settles to a low value at the end 6
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Fig. 2. Experimental tracings of dynamic force-length diagrams of muscle determined as shown in Fig. 1. A, during rapid shortening from a state of isometric contraction (average final speed: 190 mm/sec) and B, during shortening (at 170 mn/sec) immediately after stretching the contracting muscle. The muscles, immersed in saline at 0° C, are from top to bottom: frog sartorius (M = 0-13 g, 10 = 3-9 cm), frog semitendinosus (caput ventralis: M = 0-051 g, 10 = 1P8 cm), toad sartorius (M = 0-175 g, 10 = 3-7 cm) and frog gastrocnemius (M = 0-447 g, 10 = 2-45 cm). The dotted lines in B show the force-length diagram obtained during shortening from P0 (left) for comparison with that obtained during a shortening of the stretched muscle. The letters along the tracings correspond to those given in Fig. 1. In the case of gastrocnemius the force-length diagram of the parallel elastic elements obtained during lengthening of the relaxed muscle at the speeds used with the contracted muscle is also given for comparison (curve a in the bottom-right picture), it can be seen that at these speeds the force exerted by the muscle at rest is a negligible fraction of that developed during activity (the tracings obtained on toad sartorius are disturbed by artifacts due to stimulation; part of the tracings of the frog sartorius have been intensified).
7 MECHANICS OF PREVIOUSLY STRETCHED MUSCLE of the movement. About 5 see after lengthening the relaxed muscle was stimulated isometrically (vertical line b) and when the isometric force reached a constant value the ergometer was operated so that the active muscle was allowed to shorten (curve c). The velocity of shortening imposed by the ergometer was always much greater than the maximal speed of shortening of the contractile component under zero load (the final speed reached was on the average 190 mm/sec, corresponding to about v/l0 = 5 se-' for sartorius, 8 sec-' for gastrocnemius, and 10 see-1 for semitendinosus): as a consequence the contractile component was unable to maintain the muscle under tension during shortening and the force fell rapidly to zero. Under these conditions the force-length diagram recorded from P0 to zero is mainly due to the quick recoil of the undamped series elastic elements and approaches their force-shortening curve. As expected from the force-velocity relationship, tension was redeveloped by the contractile component at the end of movement (v = 0) after 2-5 mm shortening (vertical line, d, superimposed on the line, a). In Fig. 1 B the muscle was first stimulated isometrically at the shorter length (vertical line a), it was then forcibly stretched (curve b) to the same length, to, as in A and finally allowed to shorten actively at high speed (on the average 170 mm/sec; curve c'). Also in this case the force fell to zero during quick shortening to rise again at the end of the movement (line d). The speed of stretching was kept low (3-4 mm/see) in order to prevent an appreciable 'give' of the muscle: this however did occur in the case of semitendinosus as shown by the fall of the force taking place during stretching of this muscle. It is apparent from the four tracings in Fig. 2B that during stretching the contracted muscle the force attains values 1-5-2 times greater than the isometric force at the same length (given by the height of the vertical lines b in Fig. 2A). Correspondingly the force-length diagram obtained during shortening (curve c') starts from a higher value of force and a greater amount of shortening of the muscle is required before the force falls to zero. This is what one would expect from the behaviour of a spring: the higher is the force at the extremities of a spring, the greater will be its shortening after release. In the case of muscle however things are not so simple as shown by the dotted lines in Fig. 2 B: these represent the curves c, obtained during shortening from a state of isometric contraction (Fig. 2A), shifted to the right until P0 matches an equal value of the force developed during shortening immediately after stretching. It can be seen that the two curves diverge: when the force falls from P0 to zero the shortening of the muscle is 50-100 % greater in the after stretch condition and correspondingly more mechanical energy is released. This difference never failed to appear in our
experiments.
8 8 ~GIOVANNI A. CA VAGNA AND G. CITTERIO
When the muscle is forcibly stretched during contraction and then it is kept active at the stretched length, the force attained during stretching falls gradually with time to settle at a value appreciably greater than the isometric one (Abbott & Aubert, 1952). This fall of the force suggests an internal rearrangement of the muscle towards, but not to, the state attained when the muscle contracts at the same length in isometric conditions. This was tested by releasing the muscle, from lo: (1) from a state of isometric contraction, (2) immediately after stretching and (3) after an interval (0.3-1-6 sec) following the end of stretching. It was found that the dynamic force-shortening curve recorded when release takes place after an appreciable lag of time following the end of stretching, differs from that recorded immediately after stretching and approaches that determined from a state of isometric contraction. It is concluded that -the modification of the elastic characteristics of the contracted muscle induced by stretching has a transient character and it tends to disappear with the time after
stretching. Force-velocity relationship of muscle shortening in isotonic conditions from a state of isometric contraction and immediately afterdsretching In a first series of experiments the force-velocity relationship of frog gastrocnemius was determined on twelve muscles (average weight, M = 0-392 +0-027 g; 10 = 2-4 + 0-1cm; Po= 840±+42 g:mean and s.E. of mean, n = 12); of these eight were released (from l0) both from a state of isometric contraction and immediately after having been stretched and four from a state of isometric contraction only. The results, given in Fig. 3, indicate that over most of the force-velocity diagram the previous stretching does not modify appreciably the speed of shortening; only three data (indicated by the arrows) suggested that the muscle is capable of a greater speed of contraction when released, immediately after stretching, against high values of force. The effect of previous stretching on the speed of shortening against high force values, near to or greater than Po0, was tested further in a second series of experiments on gastrocnemius, sartorius and semitendinosus. Some indicative experimental tracings and force-velocity curves are given in Fig. 4. It can be seen that the speed of shortening is usually greater for the previously stretched muscle, as shown by the corresponding force-velocity curve being shifted to the right (interrupted line). For instance, in record 4 (obtained on frog semitendinosus) the muscle was stimulated isometrically (at a length, l0, at which Fpe, was about 1 g) and then it was released against a constant force (36 g) very near to the isometric force before release which was 36-5 g; it appears that the muscle is barely able to shorten against
MECHANICS OF PREVIOUSLY STRETCHED MUSCLE 9 such a high force so that its velocity of shortening is very low, as indicated by the full point, 4, on the left-hand tracing. In record 5 the same muscle was stimulated isometrically at a length about 1 mm shorter, it was then forcibly stretched to 10, and then released against the same load of 36 g as in record 4: however in this case the muscle shortens against this load with a velocity appreciably greater, as shown by the slope of the length-time tracing and by the cross, 5, in the corresponding force-velocity diagram.
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Fig. 3. Force-velocity relationship of frog gastrocnemius as obtained on twelve muscles (different symbols) by measuring the speed of shortening in isotonic conditions: (a) from a state of isometric contraction and (b) immediately after stretching (circled symbols). For generality the force is expressed as a fraction of P0 and the velocity as 10/sec. The curve was drawn from Hill's equation using the constants: a/P0 = 0289 and b/i0 = 0-194 sec', determined as described in the text. The data indicated by the arrows suggested that at high force values the speed is greater when shortening begins immediately after stretching (see Fig. 4). For purposes of comparison with the gastrocnemius data (continuous line), the interrupted line refers to the frog semitendinosus of Fig. 4 and it was plotted according to the constants a/PO = 0197 and b/i0 = 0233 sec-' calculated from forcevelocity data obtained on this muscle. The dotted line is an average curve for frog sartorius (a/PO = 0-25 and b/lo = 0325 sec-).
GIOVANNI A. CAVAGNA AND G. CITTERIO
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Fig. 4. On the right are reproduced experimental tracings showing the early length changes, L, of muscle occurring when its force, F, falls abruptly to an isotonic load from a value attained at the length of release, t0, during an isometric contraction (upper tracing three and tracing four) and at the end of forcible stretching of the contracted muscle (all the other tracings). On the left are given the corresponding force-velocity relationships (full points and continuous line: release from a state of isometric contraction; crosses and interrupted line: release at the end of stretching). The numbers near the points refer to the tracings on the right and indicate the order of successive stimulations. The muscles are from top to bottom: frog gastrocnemius (lo = 2-5 cm, 0.1-0.20 C), frog semitendinosus (caput ventralis, M = 0-038g, lo = 2-5 cm, 02-0.60 C) and frog sartorius (M = 0-058 g, 10 = 3-25 cm, 0.2-0.70 C). When the muscle is released immediately after stretching its speed of shortening is greater than when release takes place from a state of isometric contraction. In addition after stretching the muscle is able to lift a weight greater than the isometric force at the length of release, 10 (vertical crosses) and at the length from which stretching begins (open circles). The force developed by the parallel elastic elements before release was about 25 g for gastrocnemius, and 1 g for semitendinosus and sartorius.
111 -MECHANICS OF PREVIOUSLY STRETCHED MUSCLE Since the length of the muscle at the instant of release was exactly. equal in both cases, it is possible to conclude from records 4 and 5 that the muscle is able to shorten immediately after stretching against the same load and at the same length, with a speed appreciably greater than that of shortening from a state of isometric contraction. In addition record 8 shows that the semitendinosus shortens against a force even greater than that developed by the muscle in isometric conditions both at the length of release (cross on the ordinate) and at a length 1 mm shorter, just before being stretched (open point on the ordinate). Similar results were obtained in many other experiments on frog gastrocnemius (upper tracing in Fig. 4), on frog sartorius (bottom tracing in Fig. 4) and on a frog gastrocnemius fully curarized. DISCUSSION
The length change of the muscle shortening on the Levin & Wyman ergometer (Fig. 2) is not only due to the recoil of its elastic structures, but also to the active shortening of the contractile component (the recoil of the apparatus was negligible in the case of sartorius and semitendinosus). Hill (1950) developed a method for correcting the controlled release record for active shortening; according to this method active shortening is determined from the force-velocity relation (Hill's equation); since this relation does not hold immediately after release (see, for example, Civan & Podolsky, 1966) the validity of this method is dubious. However, in order to estimate at least the order of magnitude of this correction we used Hill's equation to calculate active shortening when the force fell from Po to zero in dynamic tension-length records (such as those in Fig. 2) obtained, after stretching and from a state of isometric contraction, on several gastrocnemii and sartorii of frog and toad. In the case of gastrocnemius the constants a/P0 and b/i0 of Hill's equation were determined from the force-velocity data obtained experimentally on twelve muscles (Fig. 3): from these data the constants were calculated from each muscle by the least-squares method; the continuous line in Fig. 3 was drawn according to their average value: a/P0 = 0-289 + 0.016 and b/i0 = 0 1 94 + 0-014 sec'I (mean and 5.E. of mean, n = 12). The three data indicated by the arrows in Fig. 3 were not included in the computation since the velocity of shortening was affected by previous stretching. In the case of sartorius it was assumed a/P0 = 0-25 and b/i0 = 0-325 sec-1 for the frog (Hill, 1970, p. 28) and b/i0 = 0-222 sec'1 for the toad (Hill, 1950).
The total correction for the shortening of the contractile component and of the apparatus (required for the gastrocnemius only) turned out to be, on the average, 7 % of the total recorded shortening for the gastrocnemius, 13 % for the frog sartorius and I11 % for the toad sartorius. The difference between the force-shortening curves recorded after stretching
12 GIOVANNI A. CA VAGNA AND G. CITTERIO and from a state of isometric contraction was not affected appreciably. The correction was probably even smaller for the semitendinosus, since the speed imposed to the muscle during release was relatively higher (v/50 = 10 sec-'). The tracings given in Fig. 2 seem therefore to be fairly representative of the recoil of the elastic elements without a significant error due to the shortening of the contractile component. In the literature are reported tension-length diagrams of the series elastic elements determined from the abrupt length changes of muscle taking place (as in Fig. 4) when the force is suddenly reduced from the isometric value to different isotonic loads (isotonic quick-release method: Wilkie, 1956; Jewell & Wilkie, 1958). As it has been shown that the forcevelocity relation is not instantaneously obeyed after release, the procedure of extrapolating back the length-time tracing to the time of release in order to estimate the length change of the elastic structures is questionable. However, it is worth noting that studies by the isotonic quick-release method have also shown that the length change of the elastic structures, for the same fall of the force, was greater after stretching than from a state of isometric contraction: actually the force-shortening curves determined by the isotonic quick-release method were not appreciably different from those determined by the controlled release method (Fig. 2). Little doubt therefore exists, as a result of the present experimental findings, that previous stretching modifies the elastic characteristics of contracted muscle in the sense that more elastic energy can be released for the same fall of the force. In order to estimate the elastic energy stored by stretching a muscle during contraction, when the force attains values greater than P0, it was hitherto thought (Hill, 1950; Cavagna et al. 1968; Cavagna, 1970; and Hill, 1970, page 80) that it was possible to extrapolate the force-shortening curve of the series elastic elements determined as usually up to Po. By doing such an extrapolation however Cavagna et al. (1968) were unable to account completely for the additional amount of work done by the toad sartorius when shortening after stretching. This is explained, at least in part, by the present results, which indicate that this extrapolation is meaningless since the curve determined by releasing the muscle from P0 does not hold after stretching.
Why are the force-velocity and the force-shortening relationships modified by previous stretching of the contracted muscle? The fact that when a muscle is released after being stretched while active, it is capable of doing work on loads that it could not have lifted at all if released during an isometric contraction (Fig. 4) can be due to: (1) a greater (or more efficient) mobilization of chemical energy by the
MECHANICS OF PREVIOUSLY STRETCHED MUSCLE 13 contractile component (brought about for example by a greater number of active sites of interaction between actin and myosin), or (2) the recoil of a stretched visco-elastic element taking place when the tension in the muscle is suddenly reduced from the high values attained during stretching to a smaller load. We have no evidence to reject either of these possibilities with certainty. On the other hand we do not see how the previous stretching of the contracted muscle may induce a time-dependent modification of a passive elastic element (tendons and other structures merely transmitting tension) similar to that described by the force-shortening curves given in Fig. 2. A different interaction between actin and myosin seems to be responsible for the change of the force-shortening curve. Huxley & Simmons (1971) determined the force-shortening curve of the s.e.c. of a single fibre when shortening took place, during a state of isometric contraction: (a) from the optimum fibre length (maximum overlap between actin and myosin) and (b) from a greater length (reduced overlap). The shortening of the s.e.c. necessary to reduce the force to zero was about the same in (a) and in (b) in spite of the initial force being much greater in (a) than in (b). This showed that the series compliance was located in the cross-bridges: when the number of these was increased as in (a) the total force was proportionally greater but the shortening of each cross-bridge, and then of the fibre, was the same. By superimposing the force-shortening curves obtained by Huxley & Simmons, one observes that the curve originating from the higher value of the isometric force runs below that starting from the lower one: this is the contrary to that observed in the present experiments (dotted lines in Fig. 2). These may be interpreted on the basis of the following assumptions. (1) The elastic recoil of the 'tendons', t, taking place when the force falls from P0 to zero, is equal when the muscle shortens immediately after stretching and when it shortens from a state of isometric contraction. (2) The cross-bridges which at the end of stretching are subjected to a force greater than that corresponding to an isometric contraction are in an unstable condition and have a probability to break which is higher the greater is their strain. The interpretation of the results reported in this paper would then be as follows: for a given fall of the force, the elastic recoil of the most strained cross-bridges taking place when the muscle is released immediately after stretching, y, is greater than the recoil of the cross-bridges taking place when the muscle is released from a state of isometric contraction, x. In fact the present findings indicate that (t + y)/(t + x) is 1-5-2 (i.e. the amount of shortening required to make the force fall from Po to zero is 1*5-2 times greater after stretching); if, for example, t = x (as suggested by Jewell &
14 GIOVANNI A. CA VAGNA AND G. CITTERIO Wilkie for frog sartorius, 1958) then it follows that y = 2x or y = 3x. When at the end of stretching the muscle is kept active at the stretched length, the more strained bridges, which are also the fewer, being the less stable, will be the first to break (assumption 2): this would explain both the rapid fall of the force taking place in this condition (Abbott & Aubert, 1952) and the reduction of the compliance of the force-shortening curve recorded by releasing the muscle at the end of an interval of time. If n unstable bridges were subjected all to the same force, they would disappear at the end of stretching with a rate: -dn/dt = kn and the relationship between log n and t would be linear: i.e. the logarithm of the excess of force F above the isometric value (or above the steady value attained after the end of stretching) would decrease linearly with time. We tested this in some preliminary experiments, and found that usually logF does not fall linearly with t but more rapidly immediately after stretching. In addition if all the unstable bridges were subjected to the same tension, the disappearance of a fraction of them during the interval following stretching would lead to an increase and not to a decrease of the compliance as observed. Both these considerations are consistent with the idea that at the end of stretching the bridges are under different degree of tension and that the most strained ones are the first to break (assumption (2)). REFERENCES
ABBOTT, B. C. & Au-BERT, X. M. (1952). The force exerted by active striated muscle during and after change of length. J. Phy8iol. 117, 77-86. CAVAGNA, G. A., DUSMAN, B. & MARGARIA, R. (1968). Positive work done by a previously stretched muscle. J. apple. Physiol. 24, 21-32. CAVAGNA, G. A. (1970). The series elastic component of frog gastrocnemius. J. Physiol. 206, 257-262. CIVAN, M. M. & PODOLSKY, R. J. (1966). Contraction kinetics of striated muscle fibres following quick changes in load. J. Physiol. 184, 511-534. JEWELL, B. R. & WILKiE, D. R. (1958). An analysis of the mechanical components in frog's striated muscle. J. Physiol. 143, 515-540. HILL, A. V. (1950). The series elastic component of muscle. Proc. R. Soc. B 137, 273-280. HILL, A. V. (1970). First and Last Experiments in Muscle Mechanics, 1st edn., pp. 28, 80. Cambridge: Cambridge University Press. HuxT. Y, A. F. & SIMMONS, R. M. (1971). Mechanical properties of the cross-bridges of frog striated muscle. J. Physiol. 218, 59-60P. WILKIE, D. R. (1956). Measurement of the series elastic component at various times during a single muscle twitch. J. Physiol. 134, 527-530.
