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1 J. Phy8iol. (1966), 184, pp With 11 text-figure8 Printed in Great Britain CONTRACTION KINETICS OF STRIATED MUSCLE FIBRES FOLLOWING QUICK CHANGES IN LOAD BY M. M. CIVAN* AND R. J. PODOLSKY From the National Institute of Arthritis and Metabolic Diseases, Bethesda, Maryland, U.S.A. (Received 1 January 1965) SU3MMARY 1. The contraction kinetics of single striated muscle fibres and small fibre bundles from the frog and the toad were measured when the load was changed from P0 to L < P0. Simultaneous recordings were made of displacement at one end and force at the other end of the preparation. 2. After the load was changed, the contractile force generally reached a steady value before the contraction velocity became steady. The amount of time required for isotonic contraction to become steady depended on the change in fractional load and on the temperature; it did not depend on sarcomere length in the range 2-2-3O0,u or on the number of fibres in the preparation. The characteristics of the non-steady state are described in terms of the displacement deviation (the difference between the actual displacement at a given time and the back extrapolation of the steady phase of the displacement record) and the null times (the times at which the displacement deviation became zero, measured relative to the time at which the contractile force first reached the value of the load). 3. The time average of the transient velocity was approximately equal to the final steady velocity. 4. The product of the null time following a given relative force step and Vmax, the steady velocity of unloaded contraction, was found to be independent of temperature. This is taken as evidence that the isotonic velocity transients originate in the contractile mechanism. 5. The non-steady state following step changes in load is identified with the motion of cyclic contraction mechanisms. The motion of the specific model formulated by A. F. Huxley (1957) was compared with that of frog muscle fibres and, although the transients in the two systems differ in detail, the characteristic dimensions are of the same order. * Present address: Cardiorenal Unit, Masachusetts General Hospital, Boston, Massachusetts, U.S.A. 33 Physiol. 184

2 512 M. M. CI VAN AND R. J. PODOLSKY INTRODIUCTION When striated muscle contracts under constant load, a steady state is generally established in which (a) the contractile force balances the force of the load, and (b) the contraction velocity is constant. The steady state can be characterized by a force-velocity relation (Fenn & Marsh, 1935; Hill, 1938; Aubert, 1956). The way in which this steady state is established following a change in load has concerned a number of authors. In his interpretation of the isometric myogram as the interaction of a contractile element and an elastic element in series, Hill (1938) assumed that the velocity of the contractile element depends only on the instantaneous value of the load, which implies that the steady velocity for a given force is established without delay. Jewell & Wilkie (1958) examined this point by studying the contraction of frog sartorius muscle when the load was suddenly changed from the full isometric force to a lower value. The experimental technique was to record the motion of a lever to which the muscle was coupled when the conditions were changed from isometric to isotonic. Although their records were obscured by transients due to the inertia of the lever, Jewell & Wilkie took their results as evidence that, at 20 C, the 'change of (muscle) velocity follows the change in force very quickly-probably in less than 1 msec and certainly less than 6 msec.' By measuring force at the fixed end of the muscle as well as motion of the lever, Podolsky (1960) was able to distinguish transients due to lever inertia from those generated by the muscle per se. It was concluded that the non-steady phase of the motion following lever release could not be attributed solely to mechanical interaction of the lever inertia with the ' series elastic element' (Hill, 1950); there was an additional component that appeared to originate in the contractile element of the muscle. These additional transients, which lasted as long as 20 msec at 00 C, were called isotonic velocity transients to emphasize the fact that they occurred while the contractile force was essentially constant. The aim of the present experiments was to characterize the isotonic velocity transients in single muscle fibres and small fibre bundles and to see to what extent these effects can be attributed to the contractile mechanism. The motion following quick changes in load was studied in preparations from frog and toad semitendinosus muscles and the influence on this motion of certain variables such as temperature and sarcomere length was examined. Some of the results have already been reported briefly (Civan & Podolsky, 1964).

3 CONTRACTION KINETICS OF MUSCLE FIBRES 513 METHODS Fibre preparation Fibres were isolated from the semitendinosus muscle of the frog Rana pipiens or the tree toad Bufo fowleri. The tendons were generally pared down to about a third of the original diameter and stainless steel connectors (0-1 mm in diameter and about 3 mm in length) were attached by means of two separate square knots of braided surgical silk (Deknatel, type 4-0 non-capillary) (Fig. 1, insert); the muscle was then transferred to an acrylic plastic dissecting chamber filled with Ringer solution, and all but one or a small number of fibres were cut away; the total length of tendinous material that remained between the connectors was mm. In several preparations the connectors were attached closer to the fibre insertions and the length of tendinous material was reduced to about 3 mm. The Ringer solution had the following composition (mm): NaCl, 115-5; KCI, 2-5; CaCl2, 1-8; Na2HPO4+NaH2PO,4 3-0 (ph = 7.0); tubocurarine Cl was added to a concentration of 9 mg/l. After the dissection was completed, the relation between sarcomere length and fibre length was found by stretching the preparation to various lengths and counting striations in two different 40 /e lengths near the middle of the preparation with an ordinary light microscope (standard filar micrometer; Leitz UIMK 50X objective, 6 mm free working distance, used with a narrow illuminating cone); the average striation spacing obtained in this way will be referred to as the central sarcomere length. At a central sarcomere length of 2-5 ja, frog fibres (excluding the tendinous material) were from 11 to 19 mm in length and toad fibres were mm in length; fibre diameters ranged from about 20 to 85 /% in both species. The larger diameter fibres were selected for single fibre preparations; multiple fibre preparations generally contained both large and small diameter fibres. Stimulation chamber This was an acrylic plastic chamber fitted with a multi-electrode assembly (Fig. 1). The eleven L-shaped platinum electrodes were connected as alternate anodes and cathodes. The wire connectors at the ends of the preparation were hooked to force and displacement transducers, which were carried on micro-manipulators. The position of the preparation was adjusted to bring it close to the electrodes, and the fibre length was adjusted to produce a known central sarcomere length. Pre-cooled Ringer solution at temperatures from 1-2 to C was continuously circulated through the chamber. Displacement tran8ducer This was a modification of the light beam-photodiode system described by Norris & Carmeci (1965). The moving element was an anodized aluminium lever (thickness, 0-12 mm) pivoted on jewelled bearings. The long arm of the lever dipped into the Ringer solution and the preparation was attached at a point 20 mm from the pivot. The short arm of the lever could be loaded by means of a stretched spring connected 3 mm from the pivot. Movement of the lever varied the amount of light falling on a photodiode, which had a sensitivity of 1-2 V/mm movement of the lever tip. The output of the photodiode was displayed on the upper beam of a double-beam oscilloscope (Tektronix, Type 502). Force tran8ducer This consisted of an RCA 5734 transducer tube with an extended plate shaft. The extension was a 13 mm length of thin-walled stainless-steel tubing, the distal part of which was flattened in the plane of the force; the compliance at the point of attachment of the preparation was 0-025,u/mg wt. The transducer was connected to a conventional bridge circuit giving a sensitivity of 1-2 mv/mg wt. and the output was displayed on the lower beam of the double-beam oscilloscope. Noise and drift gave rise to an uncertainty of about 1 mg wt. in the force measurement. 33-2

4 514 M. M. CIVAN AND R. J. PODOLSKY General procedure As shown in Fig. 1, the lever was fixed in position by stops A and K, the loading spring was adjusted with micro-manipulator G, and the resting tension of the preparation was recorded as a base line for the force trace. The fibre (or fibre bundle) was then stimulated (1 msec monophasic pulses, 15-30/sec) with about 3 times threshold voltage for up to 1 sec in frog preparations and 2 sec in toad preparations. The fibre was either kept isometric, or, D F Fi..tiulbr-and Mechanical ground T s I K_ -ER-- Ringer solution m c cm Fig. 1. Stimulation chamber and recording system. The preparation Pis hooked to the plate shaft extension R of the force transducer tube H and to the lever L by means of wire connectors N, Q. The insert (scale enlarged 5 times) illustrates the knot arrangement used in tying the connectors to either pared dow-n tendon (shown) or tendinous material close to the fibre insertions. The lever is pivoted at B and is loaded by means of a spring F, the length of which is adjusted with a micro-manipulator G. The long arm of the lever is restrained by a fixed stop A and an electromagnetically controlled stop K; the short arm forms a vane D which blocks part of a light beam C directed towards a photodiode (not shown); E is a point to which a driving spring can be attached. A partition (not shown) which extends from the left side of the chamber to the right end of the electrode array supports the electrodes 0 and separates the Ringer solution entrance I from the exit J; pre-cooled Ringer solution flows past the preparation and then behind the partition to exit J; temperature is measured with a thermistor probe S. The mechanical ground (interrupted line) links elements with a common base. after full isometric force was developed, the load on the fibre was quickly changed by withdrawing stop K electromagnetically. With frog fibres, the time of release ranged from 0-4 to 0-8 sec after the start of stimulation; with toad fibres, the corresponding time ranged from 0-6 to 1-8 sec. The interval between runs was usually 100 sec or longer. Recording was generally started just before the lever was released; displacement and force were shown either as functions of time on the upper and lower beams of the double-beam oscilloscope or as x-y plots on a single beam. The traces were photographed on Polaroid film and enlargements were used for analysis. Characteristics of the recording and attachment systems The recording system was tested with a steel spring having a compliance ( ge/mg wt. in range mg wt.) close to that of a single fibre preparation and a mass of 2-2 mg. The spring was hooked between the force transducer (unloaded natural period, 0-77 msec) and the displacement transducer and then subjected to quick changes in load. From Appendix

5 CONTRACTION KINETICS OF MUSCLE FIBRES 515 eqn. (1-10), the total equivalent mass of the moving system was estimated to be 3-7 mg, of which 0-7 mg came from the steel spring, 0-5 mg from the loading spring, and the remaining 2-5 mg from the lever. Figure 2a shows the response with the spring in air: the change in displacement (upper trace) was proportional to the change in force (lower trace) and oscillation in the displacement record was reflected exactly in the force record. The chord compliance during the force step (1V8,u/mg wt.) was about the same as the dynamic compliance during the oscillation (see Appendix 2). The observed natural period (5-2 msec) was in good agreement with the value calculated from the observed chord compliance and the estimated total equivalent mass (see Appendix eqn. (1-13)). When the spring and the transducers were immersed in water to the extent shown in Fig. 1, the motion was more strongly damped and the natural period increased to 7 msec (Fig. 2b); the latter effect was probably due to the contribution of the fluid displaced during the motion to the total equivalent mass. To test the linkage between the contractile part of the fibre and the recording system, similar experiments were made with lengths of tendinous material (from the semitendinosus f100/l D 055~~~~~~~~~~ Tmg wt." 1 msec a -L1 0 ju J lp1 b o/s mg wt. 10 msec 075 c d e Fig. 2. Response of passive elements to load changes. Upper trace, displacement; lower trace, force. Displacement and force transducer coupled by passive elastic element. (a) Steel spring tied to 10 mm of 4-0 braided, non-capillary, surgical silk. (b) Same as a, except that steel spring and transducers immersed in water to the extent shown in Fig. 1. (c-e) Pelvic tendon from frog semitendinosus muscle; 8-1 mm length immersed in Ringer solution. In each run the electromagnetically controlled lever stop (K, Fig. 1) was first positioned to generate a force of about 200 mg wt. and then the load was changed to the effective force of the loading spring (F, Fig. 1) by withdrawing the stop; recording was started just before the lever was released; the magnitude of the force step is given as a fraction of the initial force.

6 516 M. M. CIVAN AND R. J. PODOLSKY muscle) to which a pair of steel connectors were attached: one end of the tendon was pared down to about a third of the initial diameter and a connector attached as shown in the insert of Fig. 1; a second connector was tied to connective tissue at the other end of the tendon, close to the normal insertion of the fibre; the equivalent mass of the preparation was estimated to be about 0-9 mg. Records of force steps applied to a connector-tendon-connector assembly prepared in this way are shown in Fig. 2c-e; the chord compliance ( /mg wt.) was much less than that of the steel spring and the natural period ( msec) was accordingly reduced (Appendix eqns. (1-13), (2.4), and (2.7)). The connector-tendon-connector assembly continued to shorten after the force reached the steady value; the shortening velocity increased with the size of the force step. However, even for a large force step (Fig. 2 e), the magnitude of this effect was relatively small, amounting to an additional shortening of about 0 5,u/mm tendon length in the first 10 msec following the force step and considerably less than this in subsequent 10 msec intervals- Other experiments in which the distance between connectors was varied showed that both the apparent compliance during the load change, and the time-dependent compliance following the load change, were proportional to the length of tendinous material between the connectors. RESULTS Preparations from frog muscles Response to changes in load. A typical experiment with a frog fibre bundle (seven fibres) is shown in Fig. 3. Figure 3 a is the isometric force; Figure 3b is the response to a quick decrease in load and Fig. 3c-l show similar responses on an expanded time base. When the lever was released the force exerted by the preparation (lower trace) quickly fell from the isometric value P0 and settled at a steady value, PL, equal to the force exerted by the load (see Appendix 3); runs with different loads will be characterized by the force step, AP = PO PL, or the relative force step, AP/Po. It is convenient to separate the motion during which the contractile force fell from P0 to PL from the subsequent motion; this is done on the records with a vertical interrupted line drawn through the initial intersection of the force trace with the final steady value of this trace; the intersection of this line with the abscissa defines to and with the displacement (upper) trace defines xo. The response before to is the well known loss of tension during 'quick release'; if the transducer compliances are negligible, the force-displacement relation in this phase characterizes the series elastic element of the fibre preparation (Hill, 1950; Jewell & Wilkie, 1958). Although the contractile force reached a steady value shortly after to, the contraction velocity usually passed through a relatively long transient phase before converging to a steady value (Fig. 3d-ik). A useful parameter for characterizing the non-steady motion is the difference between the actual displacement and the back extrapolation of the steady phase of the displacement trace; this parameter will be referred to as the displacement

7 CONTRACTION KINETICS OF MUSCLE FIBRES mg I100Y t- - ioomg lomsec I 10 msec a /I1OOWt10 msec ~0#. 0 se d e If c 1-44~ ~ ~ ~ - 0*47 0*62 g h 1oo 1 IiooP, 20# ) I i k I Fig. 3. Response of frog muscle fibres to changes in load. Upper trace, displacement; lower trace, force. Bundle of seven fibres (26. ii. 65), diameters not recorded; fibre length excluding tendon, 15 mm; tendon length, 3 mm; sarcomere length, 2-4,; temperature range, C; stimulus, 15 pulses/sec. (a) Isometric force, (b)-(l) load changed at about 500 msec after stimulation began. In a and b, recording started just before stimulation began and continued for about 900 msec; time scale given in a. In c through 1, time base expanded 10-fold and recording started after full isometric force had developed but shortly before the lever stop was withdrawn; time scale given in c. P0, mg wt.; force step magnitude as fraction of P0 is given alongside force trace. In c through I the force record is steady 2-6 msec after the force first reaches the value of the load. Arrows mark the null points

8 518 M. M. CI VAN AND R. J. PODOLSKY deviation, Ay; the value of Ay is zero in the steady state, while in the nonsteady state Ay is positive or negative depending on whether the actual displacement is above or below the extrapolated displacement. It is also useful to note the points at which the displacement deviation became zero (arrows in Fig. 3); the corresponding time co-ordinates, measured from to, will be referred to as null times, T1, T2... The steady phase of the motion was found by positioning a straight hairline over the terminal part of displacement trace and picking out the best linear segment by eye; the extension of this line was the base line from which Ay was measured. There was, of course, some uncertainty in positioning the hairline, which gave rise to a corresponding uncertainty in evaluation of the null time. The upper and lower limits to the value of a null time for a given trace could be estimated by swinging the hairline through the maximum reasonable range and measuring the times corresponding to Ay = 0 at the two extremes (see Fig. 5 a). The natural oscillation of the lever system appeared in the force trace as an oscillation about the steady value and in the displacement trace as a proportional perturbation (an analysis of this inertial effect is given in the Appendix). The amplitude and duration of this effect increased as the force step was increased; for the runs in Fig. 3, the duration ranged from 2 to 6 msec. The natural period for force steps less than 0-5P0 was about 2 msec (Fig. 3c-h); this is also the value calculated with Appendix eqn. (1-13) from the average chord compliance (0.30,/mg wt.) and the equivalent mass of the moving system (3 0 mg). For greater force steps the natural period was longer; this change was associated with an increase in the value of the chord compliance (Fig. 3i-k). Influence of force step magnitude on the velocity transient. With small force steps, a steady contraction velocity was generally established almost as soon as the step was completed (Fig. 3c); certain exceptional responses will be discussed below. When the force step was increased, the contraction velocity after to was first greater than, and then less than, the steady value (Fig. 3d and e); in these cases Ay was negative. With still larger force steps there were several null times, as though the motion approached a steady velocity by means of a damped oscillation (Fig. 3f-j); in these cases, Ay was negative for times between to and T1, and positive between r1 and r2. The back extrapolation of the steady phase of contraction intersected the displacement trace at a time close to to, indicating that the time average of the transient velocity was approximately equal to the final steady value. The null times depended on the magnitude of the force step. The first null time decreased from about 43 to 6 msec when AP was increased from 0 16 to 0 62 Po (Fig. 3d-i; also see Fig. 6a); although for greater force steps the first null point was obscured by the natural oscillation (Fig. 3j and k), the decrease in r1 with force step magnitude appeared to continue over the entire range of steps. The second null time decreased from about 32 to 10 msec when AP was increased from 0-36 to 0-87 P0 (Fig. 3f-k). Since the decrease in both the first and second null time was accompanied by an increase in steady contraction velocity, there was a tendency

9 CONTRACTION KINETICS OF MUSCLE FIBRES 519 for the displacement from xo to each null point to remain constant. In Fig. 3, for example, the distance from xo to the first null point (marked by arrows below displacement trace) ranged from about 35 to 60,, while the corresponding distance to the second null point (arrows above trace) was ,1. The response for a given force step was independent of the sequence in which runs were made except for small steps (AP < 0-2 P0), in which case the number of times the preparation had previously been stimulated seemed to be a factor. This effect can be seen by comparing Fig. 3c and 1; in the former run, which was the eleventh tetanus in the series, contraction was steady soon after to, while in the latter, which was a similar force step during the twenty-ninth tetanus, the velocity decreased continuously for about 50 msec after to. This change in the response was almost certainly due to fatigue, as the steady contraction velocity for loads close to P0 is roughly proportional to (P0- L) and the value of P0 before release in run 31 was noticeably decreasing. In several other preparations where the motion after small force steps was not steady, the value of P0 during the 25 msec before the load was changed appeared to be steady; however, since these records were from runs made late in a series, or from runs in which the interval between successive tetani was intentionally made much shorter than usual, contraction in these cases was probably influenced by an effect of fatigue that became evident during the response. Single fibre preparation. The response of a single frog fibre to a series of load change is given in Fig. 4. Although the natural oscillation of the lever system in this case was slower than with a fibre bundle (Fig. 3) and the resolution of the non-steady motion was therefore more limited, the isotonic velocity transients for a given relative force step, AP/Po, were essentially the same as those in the fibre bundie. For AP < 0 5P0, the period of the natural oscillation of the lever system was 5-6 msec; the value calculated from the average chord compliance (2-3 /i/mg wt.) and the equivalent mass of the moving system (3.0 mg) is 5-2 msec (Appendix eqn. (1-13)). As in the case of the fibre bundle, the natural period increased when the force step exceeded 0-5P0, and this was correlated with an increase in the chord compliance (Fig. 4e-f ). It should be noted that the quick displacement required to reduce the force to a given fraction of P0 for the records in Fig. 4 (single fibre) was generally within 10 % of those in Fig. 3 (bundle of seven fibres) even though the magnitude of the change in force was about 8 times greater in the case of the fibre bundle. Each force trace also contained a burst of extra noise in the 20 msec after to (also see Figs. 7 and 9). This effect was not correlated with any property of the non-steady contraction or with the magnitude of the force step; it can almost certainly be attributed to the excitation of natural vibrations in the force transducing system. The effect of the velocity transient was most conspicuous when the load change was about 0*4 P0 (Fig. 4c): in this case, at the time when the force trace returned to the steady value so that the inertial contribution to the

10 520 M. M. CIVAN AND R. J. PODOLSKY displacement deviation could be neglected, the displacement deviation reached a magnitude of almost 18,u. A similar measurement was made for the other frog preparations to get a rough idea of the variability of the transient effect. In twelve of thirteen preparations, five of which were single fibres, the magnitude of Ay at the time the force trace returned to the steady value averaged 17, and ranged from 6 to 31,u (temperature, a. ]7o sz J1 ISOM '015 ~ ~ ' - -~ ~~~~ 0271j mg wt. 10 msec a b c 00,* I0i f200# i 'i- Am -, d e f Fig. 4. Response of a single muscle fibre from the frog to changes in load. Upper trace, displacement; lower trace, force. Fibre dissected from the semitendinosus muscle (21. ii. 64); diameter, 60,u; fibre length excluding tendon, 15 mm; tendon length, 12 mm; sarcomere length, 2-9 #t; temperature range, ' C. Fibre stimulated at 15 pulses/sec; recording started after full isometric force had developed and shortly before the lever stop was withdrawn. P0, mg. wt; force step magnitude as fraction of P0 is given alongside the force trace. In a through e the force record is steady 3-5 msec after the force first reaches the value of the load; in f the force record has a periodic component (period = 15 msec) which also appears in the displacement record. 1-3 C; force step, P0; time, 3-6 msec after to; sarcomeres/ fibre, ); in the thirteenth preparation, the noise in the force and displacement traces resulted in a background uncertainty of 8,u and an effect greater than this was not evident. The value of r1 in these runs ranged from 9 to 20 msec, but there was no correlation between r1 and P0. Influence of temperature on the velocity transient. When the temperature was increased above the usual value of about 2 0, the steady state following a given force step was approached in the same general way, but the value of the first null time decreased (Fig. 5). The influence of temperature on the null time for a range of force steps is shown in Fig. 6a. The temperature effect was completely reversible, and it appeared to be unrelated

11 CONTRACTION KINETICS OF MUSCLE FIBRES 521 to the increase in the stimulus frequency needed to produce a fused tetanus at the higher temperature, as a similar increase at 2 C was without effect on the null time. When the same relative force step was applied at different temperatures (T' and T') the ratio of the observed first null times (r', and r"1) appeared to be inversely related to the ratio ofthe corresponding steady concentration velocities (V' and V"). In order to make a quantitative study of this relation, the influence of temperature on the steady motion was measured by the mean value of the ratio V/ V' for relative forces 0 1, 0 3, and 0 5; according to the force-velocity relation of Hill (1938), this parameter, I S Jsos t I5o8 X I5,o#z 1/- \ WZ LE Sva _ X f0 mg wt. lomsec a b c Fig. 5. Influence of temperature on the frog isotonic velocity transient. Upper trace, displacement; in b and c, upper horizontal trace is the base line. Lower trace force. The same (approx.) relative force step was applied to a bundle of three fibres at three different temperatures. Fibres dissected from the semitendinosus muscle (1. iv. 64); diameters, 33, 55, and 72 pt; fibre length excluding tendon, 13 mm; tendon length, 14 mm; sarcomere length 2 3,/; (a) temperature, 1-9 C; stimulus frequency, 15/sec; P0, 205 mg wt.; force step, 0 43 P0; steady velocity, 2-3 mm/sec; (b) temperature, 6.70 C; stimulus frequency, 25/sec; P0 = 230 mg wt; force step, 0-41 P0; steady velocity, 3-4 mm/sec; (c) temperature, C; stimulus frequency, 25/sec; P0 = 265 mg wt.; force step, 0 44 P0 (traces not discernible during most of the quick release); steady velocity, 4 9rmm/sec. T, is a graphical estimate of the first null point. The method of estimating the uncertainty in T is shown in a where the two sloping interrupted lines mark the range within which straight lines can be fitted to the steady phase of the motion; in b and c the sloping broken line is the best estimate of the steady phase of the motion. which will be referred to as pv) is a good estimate of V,axIV/ ax, the ratio of the maximum steady contraction velocities at two temperatures. When Tr Pv was plotted as a function of the relative force step for T' = 1.90 C and T" = 4 8, 6-7, and C, the data defined a line which was praotically the same as that given by r (Fig. 6b). This implies that (7-'/7) Pv is close to unity and that the product r1vm. is independent of temperature. Further evidence for this conclusion is provided by Table 1 a, in which results obtained from several frog preparations are summarized. For each

12 522 M. M. CIVAN AND B. J. PODOLSKY preparation, rl was evaluated at two temperatures (T' = C, T" = C) for force steps of about 0 4 P0; the magnitude of r1 for these steps is much greater than the uncertainty in reading the records, and the influence of temperature can be measured with reasonable accuracy. Pv was calculated from steady contractions at the two temperatures. The value of (r'1/lr) Pv is given in the final column; its mean value is (s.e. of mean), which is not significantly different from unity. This means that the temperature coefficients of r1 and Vmax are equal in magnitude but opposite in sign, and it strongly suggests that both characteristics of the motion are controlled by the same fundamental process c) 24 0 f I I I I I I I I I I I I I I a ~~~~~- 2, I 1O40 -#~~~~~~~~~~-1 21!0 2 6 > Relative force step Fig. 6. Influence of temperature on the frog isotonic velocity transient. Same preparation as in Fig. 5. (a) Abscissa is the force step, AP, expressed as a fraction of the full isometric force; ordinate is the first null time in msec. Data taken at four temperatures (0 C): 19(A); 4-8 (*); 6*7 (U); 10-4 (@); and then again at 1-9 (V). Vertical line through symbol joins extreme estimates of the first null time; uncertainty in the abscissa was less than 3 % of indicated value. Lines fitted to points at each temperature range by method of least squares. (b) Same abscissa as a; ordinate is the product of (i) pv, the average steady velocity ratio for a given relative force (0-1, 0 3, and 05) at temperature T' (4.8 (*), 6*7 (-), and 10'4 (0)) and T' ( 9), and (ii) T"1, the first null time at temperature T'. Interrupted line fitted to points by method of least squares; continuous lines are the same as those in a. Influence of sarcomere length on the velocity transient. As shown in Fig. 7, the approach to the steady state was not affected when the central sarcomere length was changed from 2-2 to 3 0 #s. Since the present experiments were made with fibres in which the central sarcomere length was 3 0 /t or less, it seems unlikely that the small amount of sarcomere length dispersion that exists in such fibres (Huxley & Peachey, 1961) could have affected the results. Quick displacement to zero force. The force-displacement relation of the series elastic element was usually measured at the end of the experiment by b 3' 2 Y-

13 CONTRACTION KINETICS OF MUSCLE FIBRES 523 stimulating the preparation and, after full isometric force was developed, releasing the lever without a load. Force following one release was recorded as a function of time and then, in another release, as a function of displacement. The force generally fell to zero in about 3 msec; the force-displacement relation was not affected by moderate changes in lever speed (M. M. Civan & R. J. Podolsky, unpublished experiments). In a group of five preparations where the fibre length was close to 16 mm (range, mm; 1-5 fibres at sarcomere length 2-5 It; mm of tendinous material between the connectors) the displacement corresponding to the point at TABLE 1. Influence of temperature on the velocity transient in frog and toad muscle fibres. Preparations of N fibres were dissected from the semitendinosus muscle of the frog or toad and force steps AP of about 0-4 P0 were applied at temperatures T' and TN. The first null time T1 (in frog preparations) or the second null time 72 (in toad preparations) was estimated graphically at each temperature; the uncertainty in these null times, taken as half the difference of the extreme estimates, was 1-2 msec. The ratio of the steady velocities at the two temperatures, V"/V',was calculated for relative forces close to 0-1, 0-3 and 0-5; the mean value of these ratios is listed as Pv T' AP l' TN AP TTN Date N (0 C) P0 (msec) (0 C) Po (msec) Pv 7 PV (a) Frog preparations 21. ii X iii iii iii iii iii iv iv * iii Mean 0-96 S.E. of mean (b) Toad preparations 20. iii iii iii iii Mean 1-09 S.E. of mean which the force reached zero appeared to be independent of the number of fibres in the preparation and averaged 260, (range, ,u). The relatively low compliance of the tendinous material (Fig. 2 c-) indicates that more than half of the measured quick displacement took place in the muscle fibre, which corresponds to an average displacement of more than 100 A for each half sarcomere. This estimate of the compliance distributed along the fibre is in reasonable agreement with that of Jewell & Wilkie (1958) who concluded from experiments with intact sartorius muscles that fibres shorten about 1% when the force is reduced from P0 to zero.

14 524 M. M. CI VAN AND R. J. PODOLSKY X ~~~Iso# : I0 S=22/S=3S0 ; \ ~~~~~~~50 mg wt.\ 150 mg wt. 10 msec 1 0 msec o Fig. 7. Influence of sarcomere length in the frog isotonic velocity transient. Upper trace, displacement; lower trace, force. The same (approx.) relative force step was applied to a bundle of five fibres at two different sarcomere lengths. Fibres dissected from the semitendinosus muscle (16. iv. 64); diameters not recorded. Stimulus frequency, 15 pulses/sec; temperature, 2.00 C. (a) Sarcomere length, 2-2 pt; resting tension close to zero; Po, 165 mg wt.; force step, 0-42 P0; fibre length excluding tendon, 14 mm; tendon length, 10 mm; (b) sarcomere length, 3*0,; resting tension, 16 mg wt.; P0, 86 mg wt. above resting tension; force step, 0 47 P0; fibre length excluding tendon, 20 mm. T1 is a graphical estimate of the first null point. Preparations from toad muscles Isotonic velocity transient. The motion of toad fibres following a quick decrease in load (Fig. 8) had the same general properties as that of frog fibres (Fig. 3). For corresponding force steps and temperatures, the values of r1 and T2 were about the same in the two species (compare Figs. 8d and 3g). As in the experiments with frog fibres, the number of fibres in the preparation (five experiments with preparations of 1-4 fibres) did not appear to affect the non-steady state. The most obvious difference in the motion of toad fibres compared with that of frog fibres was in the relative prominence of the displacement deviation between r1 and r2 for force steps close to 0 5 PO; for these steps in frog fibres, the average magnitude of Ay between T1 and -r2 was generally much smaller than that between to and rl (e.g. Figs. 3g, 4c) while in toad fibres the displacement deviation between r1 and r2 was a more conspicuous feature of the non-steady state (e.g. Figs. 8d and 9a). In the toad preparations, the maximum displacement deviation between rl and r2 averaged 8,t and ranged from 4 to 11 /t (temperature, 1-3 C; force step, P0; sarcomeres/fibre, ); the magnitude of Ay measured b

15 CONTRACTION KINETICS OF MUSCLE FIBRES 525 when the force trace just reached a steady value ranged from less than 2 to 15,c. Influence of temperature. The characteristics of the toad fibre motion made it more practical to measure the effect of temperature on the velocity transient by means oft2 rather than T1. As shown in Fig. 9, the value of r2 decreased reversibly when the temperature was increased. The fractional decrease in r2 was close to the corresponding fractional increase in the maximum steady velocity (Table lb), which again suggests a connexion between the rate at which a steady state is established and the rate at which the fibre shortens. Jiop I25# L I50# 125p 0.~~~~~~~~~4 o12x,~~~024 \0-4 0,46. I50 mg 10 msec wt. '-\ a b c d I50# I50,s I50# I100,t e f g h Fig. 8. Response of toad muscle fibres to a change in load. Upper trace, displacement; lower trace, force. Bundle of four fibres dissected from the semitendinosus muscle (11. iii. 64); diameters, 21, 32, 42 and 74 /.&; fibre length excluding tendon, 12 mm; tendon length, 10 mm, sarcomere length, 2-4,; temperature range, C. Fibre stimulated at 15 pulses/sec; recording started after full isometric force had developed and shortly before the lever stop was withdrawn. P0, mg wt.; force step magnitude as fractionof P0 is given alongside force trace. The force record is steady 2-7 msec after the force first reaches the value of the load. DISCUSSION Origin of the velocity tran8ients In the series of elements across which mechanical measurements were made (displacement transducer-tendon-contractile element-tendon-force transducer), there are at least three possible sources of non-steady motion following a change in load: (1) oscillation resulting from the interaction of the equivalent mass with the effective compliance of the moving system, (2) time-dependent compliance of the tendon and/or the attachment system, and (3) non-steady shortening of the contractile element. Accor-

16 526 M. M. CIVAN AND R. J. PODOLSKY dingly, the displacement deviation, Ay, can be considered to have two components, Ay = AY1+ AY' where AY1 is the contribution due to (1) and Ay' is the combined contribution of (2) and (3). The -magnitude of Ay1 can be calculated from the deviation of the force trace from the steady value and the dynamic com- I 50g 2.80 I50# 6.50 f50 10 msec I. I mg wt. a a Iiooiy 9.00 r50 mg wt. N fs0# c d Fig. 9. Influence of temperature on the toad isotonic velocity transient. Upper trace, displacement; lower trace, force. The same (approx.) relative force step was applied to a two-fibre preparation at three different temperatures. Fibres dissected from the semitendinosus muscle (12. iii. 64); diameters, 40 and 52 p; fibre length excluding tendon, 8-5 mm; tendon length, 6-5 mm; sarcomere length, 2*0 /%; (a) temperature, 258 C; stimulus frequency, 15/sec; P0, 81 mg wt.; force step, 0-51 P0; steady velocity, 2-7 mm/sec; (b) temperature, 6-5 C; stimulus frequency, 25/sec; P0 = 105 mg wt.; force step, 0-53 P0; steady velocity, 5-5 mrnm/sec; (c) temperature, 9.00 C; stimulus frequency, 25/sec; P0, 109 mg wt.; force step, 0-54 PO; steady velocity, 7-5 mm/sec; (d) temperature, 2.80 C; stimulus frequency, 20/sec; P0, 81 mg wt.; force step, 0-53 P0; steady velocity, 3-2 mm/sec. Sequence of experiments: a, b, c, d. T2 is a graphical estimate of the second null time. 2.80

17 CONTRACTION KINETICS OF MUSCLE FIBRES 527 pliance of the moving system (Appendix eqns. (2.1) and (2 3)). Application of this dissection technique to the runs of Fig. 4, for example, indicates that the displacement deviation in run 4b is generated almost entirely by non-steady shortening of the preparation while that in run 4f is largely the result of a damped oscillation; runs 4c, 4d, and 4e are clearly intermediate cases in which the two components of the non-steady motion can easily be recognized. The possibility that non-steady shortening of the preparation stems from a time-dependent compliance situated in the tendinous material and/or the attachment system is almost certainly excluded by the relatively small magnitude of the additional shortening seen after force steps were applied to isolated tendon preparations (Fig. 2c-e). Furthermore, while the magnitude of the time-dependent compliance in the tendinous material was proportional to its length, the characteristics of the isotonic transients in different preparations appeared to be independent of this length (e.g. compare the motion in Fig. 3, where the preparation contained a 3 mm length of tendinous material, with Fig. 4, where the corresponding length was 12 mm). It seems reasonable, therefore, to attribute the velocity transients that persist in fibre preparations after the inertial oscillation has died out to non-steady shortening of the contractile part of the fibre. This conclusion is also supported by the following additional observations: (1) there was no correlation between P0 and null time for a given change in fractional load; in fact, the isotonic velocity transients recorded from a single fibre from the frog semitendinosus muscle were practically the same as those found in the intact sartorius muscle (compare Fig. 4 in the present study with Fig. 1 in Podolsky (1960)); and (2) there were quantitative differences in the transients recorded from frog and toad single fibres which would not be expected if these effects originated in the recording system. Although localization of the source of the isotonic velocity transients to the contractile part of the fibre does not prove that these transients originate in the contractile mechanism-there could, for example, be a time-dependent compliance within the sarcomere-the fact that the null time has a relatively high temperature coefficient (Table 1, Figs. 5, 6, 9) suggests that it is associated with a chemical rather than a physical process. The additional finding that the temperature coefficients of the null time and Vmax are equal in magnitude but opposite in sign is evidence that both parameters are linked through a common rate process and strongly suggests that the velocity transients are generated by the same myofilament reactions that drive the contraction (some implications of this idea will be considered in the next section). In any event, it is clear that, following force steps exceeding about 0x2 P0, there is a period during 34 Physiol. 184

18 528 M. M. CIVAN AND R. J. PODOLSKY which single-valued force-velocity relations (Hill, 1938; Aubert, 1956) do not describe the motion of the contractile part of the fibre. An obvious but not unimportant conclusion that can be drawn from the observation that the time course of the displacement deviation recorded from single semitendinosus fibres and intact sartorius muscles of the same species is practically the same is that fibre-fibre interaction in the sartorius muscle does not contribute significantly to the non-steady state. In this connexion, it is of interest that some of the effects seen in the present study are also discernible in displacement traces recorded from the sartorius muscle of the English frog; e.g. in Fig. 3a of the study by Jewell & Wilkie (1958) the displacement deviation appears to be negative before the steady state is established in the traces for both 21 and 16 g wt. Although the absence of simultaneous force records makes it difficult to know when the contractile force actually became steady, if to is taken as the intersection of the back extrapolation of the steady contraction with the initial quick displacement the null time for 21 g wt. (L/Po = 0.65) is about 16 msec and that for 16 g wt. (L/Po = 0.50) is about 7 msec, which is reasonably close to corresponding data from the present study (Figs. 3 and 4). Possible interpretation of the velocity transients An interpretation of the present results is suggested by the behaviour of contraction models in which (a), when P < Po, the contractile mechanism and (b) contraction is generates additional force at a rate &P/&t = Pt(P, t) accompanied by loss of force, - 4P/Ix = Px(P, t); the contraction hypothesis formulated by A. F. Huxley (1957) was the first mathematically defined model with these properties. When presented with a constant load, L, such systems generate motion according to the following cycle, P =L At >P+PtAt > L Ax = (PtAt)/Px and the velocity Ax/At is equal to the ratio Pt/Px(Podolsky, 1962). The velocity is initially a function of time and, as time passes and cycling continues, it generally reaches a steady value; the amount of time required for the steady state to become established, as well as the time course of the displacement deviation in the non-steady state, depends on both the initial conditions and specific model parameters. Since many of the physiological and structural observations that have been made with living frog muscle can be accommodated by the A.F Huxley (1957) model, it seemed worth while to compute the model motion

19 CONTRACTION KINETICS OF MUSCLE FIBRES 529 following step changes in load from P0 to L < Po. This was done by simulating the cyclic operation of the model on a digital computer using the parameters selected by Huxley to fit the force-velocity and forceenergy relations of Hill (1938); the results are given in Fig. 10. d Fig. 10. Response of A. F. Huxley (1957) contraction model to step changes in load from P0 to L < P0. Upper curve, displacement; lower curve, force; abscissa, time; insert in c shows contraction during first 20 msec with expanded displacement scale. Displacement curves calculated by simulation of contraction process on a digital computer; the steady phase of isotonic contraction is extrapolated toward to with an interrupted line; force step magnitude as fraction of total force given alongside force record. Model parameters (see Huxley, 1957); fi = sec-1, g1 = 10 Sec-1, g2 = 209 sec-1, h = 156 A. The computed contractions contain velocity transients that are especially conspicuous for the larger force steps. The displacement deviation is either close to or slightly greater than zero for force steps less than 0 37P0 (Fig. loa-c) and negative for force steps exceeding 0-65Po (Fig. lod-f); presumably there is an intermediate force step where the displacement deviation remains close to zero. The motion resembles that of a frog muscle fibre in the following respects: (1) the displacement deviation is close to zero for small force steps; (2) the duration of the non-steady state for some force steps is nearly the same (e.g. r1 is about msec for AP close to 0-5P0 in both theory and experiment); and (3) the magnitude of the displacement deviation (as well as its time course) for certain 34-2

20 530 M. M. CIVAN AND R. J. PODOLSKY about steps is similar (e.g. for AP = 0 5PO, the maximum value of Ay is -10 A/half sarcomere in the inodel (Fig. lod) and about -20 A/half sarcomere in the frog fibre (Fig. 4e). The most obvious differences between the model motion and that of the fibre are: (1) the velocity in the model changes monotonically with time, while in the fibre the difference between the actual velocity and the steady value changed sign at least once; (2) there is never more than a single null time for each force step in the model, while for force steps exceeding about 0-3PO at least two null times were evident in the motion of the fibre; (3) the null time increases when the force step is increased in the model, while in the fibre the opposite was the case; and (4) the maximum displacement deviation occurs in the model after a force step of PO while in the fibre it occurred after a force step of about 0.4PO. Additional computations are required to find out whether these discrepancies can be eliminated by changing the model parameters. These considerations may be relevant to what H. E. Huxley (1964) has called the large-small movement ambiguity, that is, the question ofwhether relative motion of the myofilaments is generated by (a) weak forces exerted over relatively long distances, say A; or (b) strong forces exerted over a relatively short distance, say 5-10 A. Since in the A. F. Huxley (1957) model contraction is generated by cross-links between the primary and secondary myofilaments that act iteratively and exert force over distances as great as 156 A (A. F. Huxley, 1957), to the extent that the characteristic times and distances in the computed motion (Fig. 10) agree with the actual response of frog fibres to force steps (Figs. 3 and 4) the present results can be taken as evidence that contraction in this species occurs by means of relatively large scale movements; this would also imply that a major part of the 'series elasticity' of the fibre (more than 100A/half sarcomere) stems from relaxation of cross-links during 'quick release'. Although it remains to be seen whether a small-movement theory can be formulated to fit the present kinetic data, the fact that the characteristic dimensions of the non-steady motion can be reasonably well accounted for by a theory based on a large-movements probably constitutes the first experimental support for a mechanism of that type. We are grateful to Eleanore Lindemann Weisman for assistingusin this study, particularly for preparing many single muscle fibres. Preliminary work for this study was carried out at the Naval Medical Research Institute and was aided by Contract NR between the Office of Naval Research, Department of the Navy and the Naval Medical Research Institute.

21 CONTRACTION KINETICS OF MUSCLE FIBRES 531 REFERENCES AIJBERT, X. (1956). Le couplage energetique de la contraction musculaire. These d'agregation Universite Catholique de Louvain. Brussels: Editions Arscia. CIVAN, M. M. & PODOLSKY, R. J. (1964). Transient response of isolated fibers following quick release: evidence for a cyclic contraction mechanism. Abstr. Biophys. Soc. FE 5. FENN, W. 0. & MARSH, B. S. (1935). Muscular force at different speeds of shortening. J. Physiol. 85, HILL, A. V. (1938). The heat of shortening and the dynamic constants of muscle. Proc. R. Soc. B, 126, Hiuz, A. V. (1950). The series elastic component of muscle. Proc. R. Soc. B, 137, HUXLEY, A. F. (1957). Muscle structure and theories of contraction. Prog. Biophys. biophys. Chem. 7, HUXLEY, A. F. & PEACHEY, L. D. (1961). The maximum length for contraction in vertebrate striated muscle. J. Physiol. 156, HUXLEY, H. E. (1964). Structural arrangements and the contraction mechanism in striated muscle. Proc. R. Soc. B, 160, JEWELL, B. R. & WILKIE, D. R. (1958). An analysis of the mechanical components in frog's striated muscle. J. Physiol. 143, NORRIS, G. F. & CARMECI, P. (1965). Isotonic muscle transducer. J. appl. Physiol. 20, PODOLSKY, R. J. (1960). The kinetics of muscular contraction: the approach to the steady state. Nature, Lond., 188, PODOLSKY, R. J. (1962). Mechanochemical basis of muscular contraction. Fedn Proc. 21, APPENDIX 1. Natural oscillation of the recording system When one end of a preparation (muscle fibre or spring) is attached to a force transducer and the other end to a loaded lever which functions as a displacement transducer, the mechanical system can be diagrammed as in Fig. 11. For the recording elements, let a = length of long arm of lever (20 mm) b = length of short arm of lever (3 mm) C2= compliance of loading spring (23 gu/mg wt.) C3 = compliance of lever (0 04,u/mg wt.) C4 = compliance of force transducer (0-025,u/mg wt.) M2 = mass of loading spring (22 mg) I = moment of inertia of lever (1000 mg mm2) 2= Im2, equivalent mass of loading spring (7-3 mg) U3= I/a2, equivalent mass of lever (2-5 mg) p = a/b, the lever ratio (6.7) To describe the motion, let cl = compliance of preparation c = ( cjdp)/(po- L), average compliance of preparation during force step from P0 to L t= time X, = length of preparation x2 = length of loading spring X3= displacement of lever tip relative to unstrained position X4= displacement of force transducer relative to unstrained position Ay = displacement deviation during contraction (see text p. 516) C = total effective compliance, eqn. (1.11) I'= I + a2/t_ + b2g2, the moment of inertia of the entire moving system

22 532 M. M. CI VAN AND R. J. PODOLKSY L = P2/p, effective force of loading spring on the preparation M = total equivalent mass, eqn. (1410) P1 = force exerted by preparation P2 = force exerted by loading spring PL = steady value of force exerted by preparation for a given load T = natural period of the mechanical system y = chord compliance, eqn. (2.4) e = cl - -l, the difference between the compliance of the preparation at a given force, and the average compliance during a force step from P0 to that force = dynamic compliance, eqn. (2.1) C = rotation of short arm of lever (recorded as displacement by the light beam-photodiode system) = equivalent mass of preparation T = half-period of sine wave approximation for the displacement deviation qs = rotation of lever relative to angle of mechanical balance The equation of motion for the lever is d20 If p-= (ap - bp2)coos (11 (1-1) S II ~~~~~~~~~~~~~~~~~~~~I ~~~~~~~~~~~~~~~~~~~~I I a II II v I Fig. 11. Co-ordinates for analysing motion of recording system. T represents the mechanical ground and B is the pivot point of the lever. xl, X2: lengths of preparation and loading spring, respectively; x3, x4: displacement of lever tip and force transducer, respectively, relative to unstrained position; 0, rotation of short arm of lever (recorded as displacement). See Appendix for further details.

23 CONTRACTION KINETICS OF MUSCLE FIBRES 533 which, for small values of 0, can be approximated by F d2o= ap1-bp2 (1-2) The angle of mechanical balance is the value of 6 for which P1 = L. Consider a virtual rotation, qs, away frork the angle of mechanical balance. Then -aq = Ax1 + AX3 + AX4, (1-3) bs = Ax2. (1.4) When CM > C3/a3, the natural period for motion of the long arm of the lever will be much shorter than that of the entire moving system; in this case, P1-L = Axl/cl = zax3!c3 = AX4/c4, (1.5) P2-pL = Ax2/c2. (1.6) Combining eqn. (1-3) with eqn. (1.5), and eqn. (1-4) with eqn. (1-6), P1 = L-aa/(c1+c3+c4), (1.7) P2 = pl+bqs/c2 (1.8) and eqn. (1.2) becomes Idt2 = a p2c2 (1.9) Defining the total equivalent mnw9 M = I'/a2 =,ul + (A2/p2) + 3 (1-10) and the total effective compliance eqn. (1-9) becomes C-- [C +Ca+C4+p2C.] (1-11) M d2s _ (1.12) which is the equation of motion for the equivalent mechanical system. The natural period is T = 27rJCM (1.13) 2. Dynamic and chord compliance8 A measure of the total effective compliance in force step experiments is the dynamic compliance, the ratio of (i) the recorded displacement oscillation, and (ii) the corresponding force oscillation. Denoting this ratio by C, aqs P1-L (2.1) which, according to eqns. (1-3) and (1-5), becomes C = C1+C3+C4 (2-2) so that eqn. (1-11) can be written C C p2c2 (2-3) In the present study, C < p2 C2 and C is essentially equal to C; however, the accuracy with which C can be evaluated is limited, as the amplitude of the natural oscillation is relatively small, particularly when the damping is near to critical. A more practical measure of C is the chord compliance, the ratio of (i) the quick displacement required to reduce the force from P0 to L, and (ii) the magnitude of the force step. Denoting this ratio by y, = a(opo-ol) (2.4) PO-L Since the torque on the lever before and after a force step is the same, y does not depend on the lever compliance. Therefore, according to eqns. (1-3) and (1.5) Y = C1+C4, (2-5)

24 534 M. M. CI VAN AND R. J. PODOLSKY where cl is the average value of cl during the force step. The curvature of the forcedisplacement relation during quick release indicates that cl = cl-c, (2.6) where e is a positive parameter that depends on the force. Using eqns. (2*5) and (2-6), eqn (1 11) can be written C y+e6+ C3 p2c2 (2.7) When L > lpo, 6 + C3 < y < p2c2 and y is essentially equal to C; when L < IPO, e may be of the same order as y, in which case y underestimates C. In the present study, the chord compliance for single fibre preparations was about 2 iu/mg wt. Since this is much larger than C3 and C4, and much less than p2c2, the effective compliance under these conditions was essentially that of the preparation per se. Although the chord compliance was smaller for fibre bundles than for single fibres, with preparations of up to seven fibres it remained larger than C3 and C4 and the effective compliance was still largely that of the preparation. 3. The inertial effect during non-steady motion A lever system with a constant load is essentially a mechanical device for imposing force clamp on the muscle fibre. However, because of the inertia of the moving system, the force generated by the fibre is not actually constant during non-steady motion. The extent to which the contractile force deviates from a steady value can be estimated as follows. If jax11 > IX31 + IAx4l, eqns. (1-2), (1-3), and (1.10) show that Mdxl = dt2- Pl-L. (3.1) Suppose L is constant. Then when contraction is steady, the contractile force has the steady value PL and P= L. (3.2) When contraction is not steady, the fibre generates additional force to accelerate the moving system and the contractile force deviates from the steady value by the amount (P1-PL) From eqns. (3-1) and (3.2), this force deviation is Pl-PL=Md-tl dt2x.(3*3) If the trajectory of the displacement deviation, Ay, is approximated by a half sine wave of period 2r, P1-PL = r2 Ay (3.4) and the displacement and force traces appear to be coupled by the compliance T2/1T2M. For either the natural oscillation of the system or non-steady contraction with T = IT, this compliance is equal to C, eqn. (1-13). For non-steady contraction with r > IT, this compliance is greater than C and the force deviation for.a given displacement deviation is therefore less than that which occurs during the natural oscillation. For our apparatus, M = 3 mg and eqn. (3.4) becomes (P.-PL) = 3Ay/T2 mg wt. (Ay in,u; r in msec). As the noise on the force trace was about 1 mg wt., this relation shows that inertial effects will not be detectable when Ay/T2 < 0-33 /t msec-2. Since the maximum value of Ay in the present study was about 30,t, apparently isotonic conditions will certainly be maintained when T > 10 msec; for T < 10 msec, the appearance of the inertial effect will depend on the corresponding value of Ay.