Articolo3

Journal of Piysiology (1993), 462, pp. 161-173 With 6 figures Printed in Great Britain

161

EFFECT OF TEMPERATURE AND VELOCITY OF STRETCHING ON STRESS RELAXATION OF CONTRACTING FROG MUSCLE FIBRES

BY G. A. CAVAGNA From the Istituto di Fisiologia Umana, Universita' di Milano, 20133 Milan, Italy

(Received 7 February 1992) SUMMARY

1. Active muscle resists stretch with a tension greater than it can develop at constant length, but at the end of lengthening the extra tension disappears, at first rapidly and then more slowly.

2. This unexplained trend of muscle stress relaxation was studied at two different temperatures (4 and 14 째C) and after ramp stretches of different velocity (0 2-2-2 fibre lengths s-1) on frog muscle fibres near slack length.

3. The velocity of the fast fall in tension increases with temperature much more than that of the slow fall. In addition, the amplitude of the fast fall in tension increases with the velocity of stretching whereas that of the slow fall decreases.

4. It is hypothesized that some of the energy absorbed by the muscle during stretching is used to raise the chemical energy level of the cross-bridges, and this energy transfer occurs during and after stretching.

INTRODUCTION

Active muscles are as commonly stretched in vivo as they shorten. For example, during constant speed, level terrestrial locomotion the mechanical energy absorbed by active muscles when they are stretched during each step is about equal to that delivered when they shorten (Cavagna, Komarek & Mazzoleni, 1971). Muscles make good use of the mechanical energy absorbed during stretching since they are able to perform more work during subsequent shortening (Cavagna, Dusman & Margaria, 1968). This increase in work is due in part to elastic energy stored during stretching, and in part to an enhancement of the contractile machinery. If a short time interval is left between stretching and shortening, as may happen in vivo, some of the stored elastic energy is lost due to the tension decay (stress relaxation), but the extra work done by the contractile component may even increase beyond the level attained without time interval (Cavagna, Mazzanti, Heglund & Citterio, 1986). Muscle stress relaxation has been described by several authors, but its mechanism remains unclear; possibilities include the detachment of differently strained cross-bridges (Cavagna & Citterio, 1974), the action of two populations of cross-bridges, one with fast kinetics and the other with slow (Colomo, Lombardi, Menchetti & Piazzesi, 1989), or the recoil of visco-elastic elements (Edman, Elzinga & Noble, 1981; Morgan, MS 1100

162

G.A.CAVAGNA

1990). The events taking place during stress relaxation are investigated in this study by analysing the time course of tension decay at two different temperatures and after ramp stretches of different velocity.

METHODS

Dissection of the fibre Frogs were killed by decapitation followed by destruction of the spinal cord. The fibre was dissected from the caput laterale of the tibialis anterior muscle of the frog (Rana temporaria) under Ringer solution at room temperature using a stereomicroscope with dark-field illumination. Tshaped clips (Ford, Huxley & Simmons, 1977), cut from aluminium foil by a photographic process, were attached to each tendon of the fibre. The tendon left between the clip and the fibre was about 0-2 mm. The maximum relaxed fibre length, attained at the end of the ramp stretch, was 5 62 + 0 45 mm (mean + S.D., n = 12) in a first series of experiments performed on twelve fibres with a stress relaxation period of 280-300 ms, and 6-10+0-46 mm (mean+s.D., n = 8) in a second series of experiments performed on eight fibres with 800 ms stress relaxation period; at this length the average relaxed sarcomere length was 2-19 ,um (see Experimental Procedure below).

Chamber, Ringer solution and stimulation The fibre was mounted in a quartz chamber (13 x 45 mm bottom surface, 4 mm depth) with a vertical slit (0 5 mm wide) in each of the walls of its smaller dimension to allow entry of glass hooks (about 100 ,um diameter), one attached to a force transducer and the other, on the opposite side, to a motor used to change fibre length. The fibre was suspended between these hooks by means of the two clips attached to the tendons in the chamber partially filled with Ringer solution (in mM: 115-5 NaCl, 2-0 KCl, 1-8 CaCl2, 2-0 sodium phosphate buffer, pH 7 0). The motor, and hence the hook supporting one end of the fibre, could be moved in the three directions to align the fibre relative to the force transducer under microscopic inspection. After alignment, a perspex frame holding two platinum stimulating electrodes on each side of the fibre (0-5 mm thick, 2-5 mm high, 12-5 mm long, and 3 mm apart) and a thin thermocouple for continuous monitoring of the Ringer solution temperature was fixed above the chamber. Filling of the chamber with Ringer solution was then completed. Stimulation consisted of an even number of alternating polarity square pulses (0 5-1 0 ms width) with an amplitude 1-5 times threshold and a frequency necessary to produce a fused tetanus (25 Hz at 4 째C and 40-50 Hz at 14 째C). Voltage, duration, frequency and number of pulses could be pre-set on a stimulator (F. Haer Plusar 6bp, modified) driving a custom-made power stage. Ten to twenty minutes, according to the number of pulses given, were allowed for the fibre to recover between successive tetani.

Temperature and conditioning of the chamber Temperature of the saline could be set to the desired value by circulating fluid from a constant temperature bath (Churchill thermocirculator) through large channels in an aluminium block that jacketed the chamber. A slit (12 x 2-3 mm), milled through the bottom of the block (32 mm thick) allowed the fibre to be illuminated from below without interposition of the circulating fluid. The motor, the chamber, and the force transducer were enclosed in a Perspex box through which dry air was slowly recirculated to prevent condensation of water vapour and stabilize the force transducer base line (Cavagna et al. 1986). The whole system was supported on a modified microscope stage which could be moved along both axes of the horizontal plane (Zeiss ACM microscope stand). The average temperatures used were 4-1 + 0-3 (mean + s.D., n = 18) and 14 3 + 0-3 째C (mean + S.D., n = 8) in the first series of experiments (300 ms stress relaxation period) and 3-97+0-12 (means+s.D._ n = 25) and 14-12+0-19 째C (mean +s.D., n = 27) in the second series of experiments (800 ms stress relaxation period).

Force transducer The force transducer and its driving circuit were similar to those described by Huxley & Lombardi (1980) and by Cambridge & Haines (1959). The resonant frequency of the force transducer was 30 kHz and its sensitivity ranged between 167 and 232 mV mN-1. Calibration was

STRESS RELAVATION OF COlNTRACTILG MUSCLE

163

achieved either by hanging weights on the hook of the force transducer detached from the chamber or, in situ, by pulling and releasing a thin calibrated glass rod, attached to the hook by a silk filament loop, at room and low temperature. Consistent results were obtained.

Motor system The motor consisted of a hand-wound aluminium coil suspended in the annulus of a vibrator magnet (Ling 101) by a cellulose acetate suspension. A tiny carbon tripod was mounted on the coil and supported a glass hook for attaching the fibre; the tripod also carried a black nylon flag shadowing two photodiodes (Siemens BPW34) from an infrared light-emitting diode (General Electric F5E 1) to monitor the position of the end of the fibre. The total weights of the moving part of the motor (coil, suspension, tripod and flag) were 0 75 (1 Q coil) and 0-87 g (0-8 Q coil) in the two motors used for the experiments reported in this paper. Current was fed through the coil by a BurrBrown OPA-512 power amplifier capable of + 15 A surges and powered by a custom-made supply of + 35 V. The maximum calibrated displacement of the coil was + 0-2 mm. With this apparatus step displacements imposed to the fibre were usually complete in less than 100,us. Step length changes are not essential for this study, but a high deceleration at the transition between the end of the ramp and start of the isometric interval is necessary to prevent a fall in the force before the ramp stretch is completed; a fall in the force during the final part of the stretching period would in fact modify the time course of the first, fast phase of stress relaxation which must occur completely after the end of the stretch.

The motor was controlled by an operational amplifier that summed a command signal, a feedback signal and its time derivative. The command signal was fed by digital-to-analog converters (D/A) from a microcomputer and it was proportional to the desired position of the motor. The feedback was the signal of the two photodiodes monitoring the position of the motor coil. The position command signal was, in turn, the sum of the signals provided by two D/A converters. The first D/A converter (which could be operated also from the computer keyboard) made it possible to shorten or lengthen the fibre in steps of about 2 ,um; this was used to give a resting length offset to the fibre prior to each experiment. The second D/A converter was used to maintain the fibre in isometric conditions for any pre-set time and/or to output the appropriate ramp stretching the fibre; in addition, this converter was used to trigger the digital oscilloscope (resolution 0-1 ms).

Experimental procedure The motor coil was first moved 0-2 mm from its neutral position to the position reached at the end of the ramp stretch. The relaxed sarcomere length at this position was set at 219 ,um using the fine motion control of the whole motor. Sarcomere length was determined by averaging counts of twenty or more contiguous sarcomeres at different points along the fibre using a microscope with a x 32 objective and a x 25 micrometer eyepiece. Sarcomeres near the tendons were usually slightly shorter than 2 19 /tm. The length of the relaxed fibre was then measured by means of a micrometer eyepiece fitted to a stereomicroscope above the trough. Twitches and short tetani were given to the fibre during the above operations; the exact stimulus threshold was measured after the desired temperature was reached. Prior to each experiment, the relaxed fibre was first shortened by the amount of subsequent stretching, i.e. 04 mm in these experiments. At the end of shortening, the fibre was stimulated a few times to take up its slack, a digital oscilloscope (Nicolet 4094, 500 Its point-') was triggered and the fibre was then stimulated to tetanus in isometric conditions.

In the experiments with a 280-300 ms stress relaxation period the duration of stimulation increased with ramp duration (39-3-314-3 ms) from 1120 (28 pulses; time interval between stimuli, T = 40 ms) to 1360 ms (34 pulses, T = 40 ms) at 4 'C, and from 950 (38 pulses, T = 25 ms) to 1200 ms (48 pulses, T = 25 ins) at 14 0C. With 800 ms stress relaxation period, the duration of stimulation was 1600-1840 ms (40 46 pulses, T = 40 ms) at 4 째C and 1550--1800 ms (62-72 pulses, T = 25 ms; in one experiment 78 90 pulses, r = 20 ms) at 14 0(1. The fibre force was continuously measured by a microcomputer through an A/i) converter. When a force plateau was detected, a 0-4 mm ramp of a pre-set duration was senit to the ergometer via a D/A converter, resulting in the linear lengthening of the fibre and the rising of the force above the isometric value (Fig. 1). At the end of the ramp, the stimulated fibre was maintained in isometric conditions for the stress relaxation period lasting in different experiments 280-300 ms or 800 ms. The digital oscilloscope data were first stored on disk (Nicolet XF-44) and subsequently read by a Macintosh II microcomputer. Data during the stress relaxation period were then normalized with a procedure similar to that used by

164

G.A. CA VAGNA

Ford et al. (1977) to describe the fast tension recovery after sudden length changes. The normalized data were plotted and fitted by the Levenberg-Marquardt algorithm (KaleidaGraph 2.0.2: General Curve Fit) to calculate the constants of the two exponential terms describing the stress relaxation curve (eqn (1)).

Discussion of the experimental procedure The time course of stress relaxation was first analysed on twelve fibres in experiments where the longest time interval left at the end of the stretch was 280-300 ms. All of the tension decay curves recorded during these intervals (eighteen at 4 °C and eight at 14 °C) were utilized in the present study and the results are reported in Fig. 2 and in Figs 5 and 6 (squares). In all these experiments the fit of eqn (1) to the data was as good as that shown in Fig. 2 and the variability of the results is shown by the scatter of the squares in Figs 5 and 6. A duration of stress relaxation of 280-300 ms was considered to be short enough to prevent fatigue (which particularly at 14 °C may modify the time course of tension decay), and long enough to calculate correctly the relative size of the fast and slow fall in tension (Af and As in eqn (1)) and the rate constant, r,, of the fast phase of stress relaxation (complete in about 30 ms at 4 °C and 15 ms at 14 °C: see insets in Fig. 2). Truncation of the stress relaxation period was expected, however, to increase the calculated rate constant of the slow phase. In fact, a lower value for the rate constant of the slow phase (0-0025 ms-1 instead of 0 009 ms-1, see Fig. 5) has been reported when longer time intervals were allowed at 4 °C (Colomo et al. 1989).

The effect of truncation of the records to 280-300 ms on the measured values of the constants of eqn (1) was investigated on eight more fibres using a stress relaxation period of 800 ms. At the end of this period, tension was on average 7-2 + 2-6 % greater (mean + S.D., n = 52) than the initial isometric value (before stretch). All of the data obtained (twenty-five tetani at 4 °C and twentyseven at 14 °C) gave results similar to those described in Figs 1, 3 and 4 and are represented by the circles in Figs 5 and 6. All the curves were normalized (as (T- T,)/((T - T,) where Ti and T2 are the tensions at the beginning and end of the stress relaxation period) over the whole 800 ms time interval. The sampling interval of the force signal by the digital oscilloscope was 0-5 ms in all cases except in twelve records at the slowest stretching velocity (about 0-2 fibre lengths s-1) where it was 1 0 ms; in the last experiment, however, a sampling interval of 0 5 ms was also used for the slowest stretching velocity.

The interpolating curve failed to fit adequately the fast phase of stress relaxation at 14 °C when all the data of the 800 ms time interval were used (O in Fig. 4). This was possibly due to the relatively small number of data describing the fast phase of stress relaxation (about 30/1600) and to fatigue progressively modifying the trend of the curve. The size, Af, and the rate constant, rf, of the fast phase of stress relaxation were therefore calculated, both at 14 and at 4 °C, using the data of the first 100 ms of the 800 ms normalized curve (the first 50 ms in five experiments at the slowest stretch velocity) ( x in Fig. 4). The 100 ms time interval was arbitrarily taken as a compromise which could be used for both temperatures. Better fits of the fast phase could be obtained with different time intervals: for example, the highest value of r, in the top graph of Fig. 5, 0 4048 mns-' for the 100 ms fit (correlation coefficient, R = 0 9978), changes to 0-3456 ms-1 in a 25 ms fit (R = 0-9987) and to 0-3678 ms-1 in a 12-5 ms fit (R = 0 9987). All the data of the 800 ms normalized curve were used to calculate the size, As, and the rate constant, rs, of the slow phase of stress relaxation.

It must be emphasized that eqn (1) is used in this study to describe the modification of stress relaxation with temperature and stretch velocity, without implying that the two exponential terms actually govern the elementary mechanisms responsible for it.

Contracting sarcomnere length at the end of the ramp, when the force stretching the tendons is high, must have been less than the relaxed sarcomere length at the same motor position (2-19 ,tm).

It follows that this study is not concerned with the long-lasting 'residual force enhancement' occurring after stretching to sarcomere lengths greater than 2-25 ,um (Woledge, Curtin & Homsher, 1985).

Relatively large stretches (on average 7-4% of the initial fibre length) were used in order to approach a steady state during lengthening at high velocity (see Fig. 3 of Cavagna et al. 1986). In addition, the motor velocity normalized by fibre length (abscissa of Figs 5 and 6), which includes lengthening of tendons during the force rise at the beginning of the ramp, approaches the average velocity of lengthening of sarcomeres when the stretch amplitude is large.

STRESS RELAXATION OF CONTRACTING MUSCLE mm

mN

84-

0-

Force

4-

1-2

T,

,ri-I

0-

0-6

8-

1-2

mm

8-

- 0-8

04

4-

- 04

0-

-o

-O

0-6

8-

mN

- 0-8

-

Length

165

1' *8

0-6

1-2

1-8

- 0-8

8-

-

04

4-

- 04

-

0

0-

-0

- 0-8

(

18

0-6

1-2

1-8

-0-8

8-

4-

-04

4-

-

0-

-0

0-

-0

!V

0-6

8-

1-2

0-6

1-8

k

0-8

8-

04

4-

- 0-8

/

1-2

I

0-4

1-8

-

0-8

-

0-4

:I

4-

-

00

1-2

---%

0-

-0

0-6

1-

1-8

0

-0 0-6

12

18

Time (s)

Fig. 1. Oscilloscope records of fibre force (upper trace in each panel) and length (lower trace) are shown as a function of time (s) for one fibre undergoing an isometric contraction, 0-4 mm stretch and 800 ms stress relaxation. To indicates the maximum isometric tension before the stretch, T1 and T2 the tensions at the beginning and at the end of the stress relaxation period. Temperature was lower for the left panels (3-9 째C) and higher for the right panels (14-0-141 째C). Stretch velocity was, from top to bottom: 0-227, 0-795, 1-589 and 1-818 initial fibre lengths s-. Final fibre length after stretch 6-0 mm.

G. A. CA VA GNA

166

X

xX

0 0 CY)

0 t

CY)

o~~~~~~~~~

o~~~~~~~~~

0

CY)

fi

X X

0

CN

CN

0 0 CN

E X X X6oo

I

o~~~~~~~~ oo

X

0

-E

0 0 CN

E 0

0

Xx

X

cn

X'

X X

0 0

0

x

oo

0 0

XX 0

0 0

O

0

0

o0

-I (0

00

cl

db

60

66

0

r-0 o

co6

6o

6o

0

E 0

X

XI

xX

'

X

0

q

XX

X

X

0

x

x

xX

0

0 0

0

U,

0 0

E

iX_X x

X

T

W C-' 6 6 6 6

04

-O

X

00 (o

!-

0 C4

fl

X

(

V)

5000-

8

O

0 0

c

C

0 =

0 wO

0

o

-I

I

00

6

CD

t

66

N

r-

6

-1

0~~6 o06 oC o

(ZL - l) / (Zl-1 )

STRESS RELAXATIOAN OF CONTRACTING MUlSCLE

167

RESULTS

Figure 1 shows typical experimental tracings: temperature was lower for the left panels and higher for the right panels; stretch velocity increased from top to bottom.

In each panel the fibre was first stimulated to tetanus in isometric conditions. Once tension reached a constant level, To, a ramp stretch was applied to the fibre. The tension reached at the end of the stretch, T1, fell subsequently to T, as the fibre was kept active under isometric conditions for 800 ms. In another set of experiments the procedure was identical but the stress relaxation period was limited to 280-300 ms.

The tension, expressed as a fraction of the total fall in tension during stress relaxation, is plotted in Fig. 2 as a function of the time from the end of lengthening for experiments where stress relaxation was truncated at 280-300 ms, and in Figs 3 and 4 for the experiment of Fig. 1, in which stress relaxation time was 800 ms. The tension decay was assumed to be the sum of two exponential terms describing the fast and the slow phases of stress relaxation:

(T- T2)1(T - T2)

=

Af exp [-rf(t-to)] +A exp [-rs(t-to)].(1

Af and rf, in the first term of eqn (1), are respectively the size and the rate constant of the fast phase of stress relaxation and As and rs, in the second term, are the size and the rate constant of the slow phase; to is the time at the beginning of the stress relaxation period.

In the experiments with 280-300 ms stress relaxation, an accurate fit of the experimental points was always obtained both at 4 and at 14 째C (O in Fig. 2). Each term of eqn (1) is plotted separately in the insets of Fig. 2: it can be seen that the fast phase of stress relaxation is complete in about 30 ms at 4 째C and 15 ms at 14 'C. When the stress relaxation period was prolonged to 800 ms, the fast phase of stress relaxation was not adequately fitted at 14 'C when using all the data of the curve (O in Fig. 4), whereas an accurate fit was obtained by using the data in a shorter time interval of the same curve ( x in Fig. 4). The constants Af and rf were therefore determined by fitting the first 50-100 ms of the 800 ms normalized curve (see Methods). In each experiment the same interval was used at 14 and at 4 'C to avoid interference with the study on the effect of temperature. The constants As and rs were determined by fitting all the data of the 800 ms normalized curve (continuous lines in Fig. 3).

The values of the constants rf, rs and A, are given in Fig. 5 as a function of the velocity of stretching (As ~ 1 -Af, depending on the quality of the fit (see Fig. 6C and D) was omitted for clarity). It can be seen that increasing the normalization period from 300 to 800 ms has little effect on the rate constant of the fast phase of stress relaxation both at 4 and at 14 'C (see average values below), whereas it decreases markedly the rate constant of the slow phase.

Temperature markedly increases the rate constant of the fast fall in tension (average Q1o = 2 1 for both normalization periods) whereas it has little effect on the rate constant of the slow fall in tension (average Q1o = 1-14 and 1 22 for the 300 ms respectively the 800 ms normalization periods). At both temperatures the rate constant of the fast fall in tension increases with stretch velocity (Abbott & Aubert, 1952; Colomo et al. 1989), whereas the rate constant of the slow fall in tension is

G. A. CA VA GNA

168

1-

1-

0-8

-

0-8 -

0-6 0-4

-

0-6 0-4

0-2

-

0-2

0-2 -

0

2

0

200

400

600

0-6

1 0-8 06

0-4

0-4

1

0-8

,I

0-2

800

0

200

400

600

800

0

200

400

600

800

0

200

400

600

800

0

200

400

600

800

0-2

~-

0-2

0 0

200

400

600

800

I-

I-V I..

1

0-8

0-8

0-6

0-6

0-4

0-4

0-2

0-2

0

0

200

400

600

0

800

1

1

0-8

0-8

0-6

0-6

0-4-

0-4

0-2

02

0

0

200

400

600

-

0

800

t-to (ms) Fig. 3. Normalized tension is plotted as a function of time from the end of the stretch (t - to) for the experiment shown in Fig. 1. The continuous lines were calculated from eqn (1) using all the data of the 800 ms stress relaxation period. Note that, unlike Fig. 2 (O), the fit at 4 째C is better than at 14 'C. Other indications as in Fig. 1.

independent of stretch velocity (Colomo et al. 1989). The size of the fast phase of stress relaxation, Af, changes similarly with speed at 4 and 14 0C, but it is shifted to the right at higher temperature (Fig. 5, bottom).

The values of the rate constants, averaged without regard of stretch velocity, are at 4 'C:

STRESS RELAXATION OF CONTRACTING MUSCLE 10-8

1-

* U

-

0-8 a

06 -

0-4 0-2

06

-

0-4

-

-

02

-

0

20

40

60

80

100

0-L

1-

1

0-8 -

0-8

0-6 0-4 0-2

a a

20

0

0

40

60

80

100

0-2 0-

20

40

60

80

100

20

40

60

80

100

0

0-6 0-4

a

-

0-

I--

S0

-

0-L

169

Q

0

1-

I

1

1

aB

0-8

-

0-8

0-6

-

0-6

0-4 -

888-@*@

0-4

a

0-2 -

0-2

0-L

0-O 0

20

40

60

80

100

a

1

6

1-

0-8

-

0-8

0-6

-

0-6

02

Fi 0

20

*6S.g.<

0-2I

40

60

80

0

20

40

80

100

60

80

100

6

020-2I

100

60

8 0

20

40

t-to (ms)

Fig. 4. First 100 ms of the curves in Fig. 3. Data are plotted every 5 ms to retain clarity. *, experimental points; 0, interpolation using all data of the 800 ms stress relaxation period as in Fig. 3; x interpolation using the data of the first 100 ms only. It can be seen that at 14 째C (right panels) the crosses, unlike the open circles, describe adequately the fast phase of stress relaxation. Note that the velocity of the fall of the force, indicated by the vertical distance between the symbols, increases with the velocity of stretching (from top to bottom) and with temperature (from left to right). ,

G.A.CAI'A GNVA

170

rf = 0 123+00319 ms-1 and rs = 0-0091 +00006 ms-1 (mean +S.D., n = 18 observations on 8 fibres with 300 ms stress relaxation period) rf = 0-121 + 00445 ms-' and rs = 0-0039 + 0-0003 ms(mean+ S.D., n = 25 observations on 8 fibres with 800 ms stress relaxation period). At 14 C: rf = 0 255 +0-0285 ms-' and rs = 0-0104+0-0004 ms-1 (mean + S.D., n = 8 observations on 5 fibres with 300 ms stress relaxation period); rf = 0-251 + 00651 ms-1 and r, = 00048 + 00003 ms(mean +S.D., n = 27 observations on 8 fibres with 800 ms stress relaxation period).

0-5

E

0-4 0002 -

cz 0 1 m

<i

0

^

0

0-5

0 01 -

oz

r 1

1.5

2

25

2

2-5

0 015

c

C?<

0

n

t

0-005-

0

0-5

1

1-5

_10-4

o c

0-8-

cc 0

0

Ca

0

05 1.5 1 25 2 Stretch velocity (fibre lengths s '1)

Fig. 5. The coinstants of eqn (1) are plotted as a funetion of stretch velocity calculated by divriding the veloeity of the motor by the initial length of the fibre. Open symbols, 4 째C ; filled svmbols 14 'C. Squares and interrupted lines, data normalized over the first 300 ms of stress relaxation (Fig. 2). Circles and continuous lines, normalization over the first 800 ms of stre.ss relaxation (continuous lines in Fig. 3 for r,', crosses in Fig. 4 for r, and A,). The rate constant for the fast phase of stress relaxation, rf, is on average 2-1 times greater (squares and circles) at 14 'C than at 4 째C, while the rate constant for the slow phase, rs, is on avTerage only 1-14 times greater (squares), or 1 22 times greater (circles) at 14 째(C than at 4 'C. The size of the fast fall in force, A f , changes similarly with speed at both temperatures and with both normalizations, but its trend is shifted to higher stretch velocities at higher temperature.

The total fall in tension during stress relaxation increases with stretch velocity (Fig. 6A); however, a plateau is quickly reached at 4 째C, whereas the same value is attained only at the highest velocity at 14 'C. The total fall in tension times Af and

171

STRESS RELAXYATION OF CONTRACTING MUTSCLE

As yields the fall in tension due to the fast and slow phases of stress relaxation. The fall in tension due to the fast component (Fig. 6B) increases with speed similarly to the total (Fig. 6A), whereas that due to the slow component decreases with speed (Fig. 6C and D).

1B

1- A

o

B

0o

0.8

C:

0

1- C I 0 24-0 024

c t-

1D E1

째

0

024

05

0-6-0

1-

C

0-8-

1

15

2

06 -0

25

1

c

05

1

1-5

2

2-5

D

c

0-8 -o ~-F 0-8 O-

-

0-6

0-6

C

k.~~~~~~~~~~~

040 Fig 6Thtoafalitesoduigsrsrelxto(A)icessoabu o

0-5

1

1-5

2 25

0

Stretch velocity (fibre lengths

0-5

1

1

80%f 2-5

s-1)

Fig. 6. The total fall in tension during stress relaxation (A) increases to about 70-80 % of To with the velocity of lengthening. The increase is entirely due to the fast phase of stress

relaxation (B), which must also compensate for the decrease due to the slow phase (C and D). The ordinate of Fig. 6C was calculated using the As constant obtained by fitting all the data of the stress relaxation period (open circles in Fig. 2 and continuous lines in Fig. 3); the ordinate of Fig. 6D was calculated using the Af constants plotted in Fig. 5; the difference between C and D shows the deviation from a perfect fit where As= 1-Af. Symbols as in Fig. 5.

The ordinate of Fig. 6C was calculated using the As constant obtained by fitting all the data of the stress relaxation curve (open circles in Fig. 2 and continuous lines in Fig. 3); the ordinate of Fig. 6D was calculated using the Af constants plotted in Fig. 5; the difference between C and D of Fig. 6 shows the deviation from a perfect fit where As = 1-A,.

DISCUSSION

Stress relaxation of tendons or other visco-elastic elements would hardly be accelerated by temperature as is the fast phase of stress relaxation and may be considered among the factors possibly affecting the slow phase. These may include detachment of strained cross-bridges, a process which may be less temperature dependent than cross-bridge detachment during shortening or relaxation. On the other hand, detachment of two populations of cross-bridges with different kinetics should be affected by temperature in the same way, unlike the fast and slow phases

172

G. A. CA VA GNA

of stress relaxation. The more likely explanation for the fast fall of force after a ramp stretch seems that given by Huxley & Simmons (1971) to explain the fast tension recovery after step stretches: the transfer of energy from the undamped to the damped structure within the cross-bridges. The average value of the rate constant found in the present study at 4 째C (012 ms-') is similar to that reported in Fig. 4 of Huxley & Simmons to describe the fast recovery of tension after the largest step stretch used at the same temperature (about 0-13 ms-1). In addition, the effect of temperature on the rate of the fast fall of force (average Qlo = 2 1) is similar to that reported by Ford, Huxley & Simmons (Qlo = 2 0-2 5).

The effect of temperature and velocity of stretching on the size of the fast fall in tension (Fig. 6B) is also qualitatively consistent with this interpretation. The fast fall in tension would be due to an incomplete energy transfer, existing at the end of the stretch, from undamped to damped elements of cross-bridges. This imbalance would increase with velocity of lengthening due to the shorter time available during the stretch; since the transfer is faster at a higher temperature (Ford et al. 1977), a greater velocity would be required to have the same fall in tension.

According to this interpretation, the fast phase of stress relaxation would represent a conservation, not a loss, of energy by the contractile machinery. From this point of view, the undamped elastic elements of bridges would have the physiological function of temporarily storing mechanical energy during negative work, when the speed of stretching is too high to allow a simultaneous transfer of energy into the damped elements. This mechanism would allow energy to be reused during a subsequent shortening, even if a short interval of time is left between the end of stretching and the beginning of shortening.

I wish to thank Miss R. Garofolo for her skilful assistance and Dr N. C. Heglund for his invaluable work on the manuscript. Drs N. C. Heglund and J. D. Harry created most of the software used in this study. This study was supported by the Ministry of Education of Italy.

REFERENCES

ABBOTT, B.C. & AUBERT, X. M. (1952). The force exerted by active striated muscle during and after change of length. Journal of Physiology 117, 77-86.

CAMBRIDGE, G. W. & HAINES, J. (1959). A new versatile transducer system. Journal of Physiology 149, 2-3P. CAVAGNA, G. A. & CITTERIO, G. (1974). Effect of stretching on the elastic characteristics and the contractile component of frog striated muscle. Journal of Physiology 239, 1-14.

CAVAGNA, G. A., DUSMAN, B. & MARGARIA, R. (1968). Positive work done by a previously stretched muscle. Journal of Applied Physiology 24, 21-32.

CAVAGNA, G. A., KOMAREK, L. & MAZZOLENI, S. (1971). The mechanics of sprint running. Journal of Physiology 217, 709-721.

CAVAGNA, G. A., MAZZANTI, M., HEGLUND, N. C. & CITTERIO, G. (1986). Mechanical transients initiated by ramp stretch and release to Po in frog muscle fibers. American Journal of Physiology

251, C571-579.

COLOMO, F., LOMBARDI. V., MENCHETTI, G. & PIAZZESI, G. (1989). The recovery of isometric tension after steady lengthening in tetanized fibres isolated from frog muscle. Journal of Physiology 415, 130P. EDMAN, K. A. P., ELZINGA, G. & NOBLE, M. I. M. (1981). Critical sarcomere extension required to recruit a decaying component of extra force during stretch in tetanic contractions of frog skeletal muscle fibres. Journal of General Physiology 78, 365-382.

STRESS RELAXATION OF CONTRACTING MUSCLE

173

FORD, L. E., HUXLEY, A. F. & SIMMONS, R. M. (1977). Tension responses to sudden length change in stimulated frog muscle fibres near slack length. Journal of Phy8iology 269, 441-515.

HIUXLEY, A. F. & LOMBARDI, V. (1980). A sensitive force-transducer with resonant frequency 50 kHz. Journal of Phy8iology 305, 15-16P. HUXLEY, A. F. & SIMMONS, R. M. (1971). Proposed mechanism of force generation in striated muscle. Nature 233, 533-538.

MORGAN, D. L. (1990). New insights into the behaviour of muscle during active lengthening.

Biophy8ical Journal 57, 209-221.

WOLEDGIE, R. C., CURTIN, N. A. & HOMSHER, E. (1985). Energetic A8pects of Muscle Contraction.

Academic Press, London.