MS 2799, pp. 689-708
Journal of Physiology (1994), 481.3
689
Storage and release of mechanical energy by contracting
frog muscle fibres
G. A. Cavagna, N. C. Heglund, J. D. Harry and M. Mantovani
Istituto di Fisiologia Umana, Universita di Milano, 20133 Milan, Italy
1.
2.
3.
4.
5.
6.
7.
8.
9.
Stretching a contracting muscle leads to greater mechanical work being done during
subsequent shortening by its contractile component; the mechanism of this enhancement is not
known.
This mechanism has been investigated here by subjecting tetanized frog muscle fibres to
ramp stretches followed by an isotonic release against a load equal to the maximum
isometric tension, To. Shortening against To was taken as direct evidence of an absolute
increase in the ability to do work as a consequence of the previous stretch.
Ramp stretches (0-5-8-6% sarcomere strain, confined to the plateau of the isometric
tension-length relationship) were given at different velocities of lengthening (0f03-1f8
sarcomere lengths s-1). Isotonic release to T. took place immediately after the end of the
ramp, or 5-800 ms after the end of the largest ramp stretches. The length changes
taking place after release were measured both at the fibre end and on a tendon-free
segment of the fibre. The experiments were carried out at 4 and 14 'C.
After the elastic recoil of the undamped elastic elements, taking place during the fall in
tension at the instant of the isotonic release, a well-defined shortening took place
against T. (transient shortening against T.).
The amplitude and time course of transient shortening against To were similar at the
fibre end and in the segment, indicating that it is due to a property of the sarcomeres
and not due to stress relaxation of the tendons.
Transient shortening against To increased with sarcomere stretch amplitude up to about
8 nm per half-sarcomere independent of stretch velocity.
When a short delay (5-20 ms) was introduced between the end of the stretch and the
isotonic release, the transient shortening against To did not change; after longer time
delays, the transient shortening against T. decreased in amplitude.
The velocity of transient shortening against To increased with temperature with a
temperature coefficient, Qlo, of - 2-5.
It is suggested that transient shortening against To results from the release of
mechanical energy stored within the damped element of the cross-bridges. The crossbridges are brought into a state of greater potential energy not only during the ramp
stretch, but also immediately afterwards, during the fast phase of stress relaxation.
It is well known that an active muscle resists stretching
with a force greater than that exerted during an isometric
contraction (Katz, 1939). The greater force developed
during stretching involves a greater storage of mechanical
energy in the undamped elastic elements of muscle, and a
greater elastic work is done when the force falls during a
subsequent shortening. The force enhancement above the
isometric value does not imply per se a storage of mechanical
energy within the contractile component of muscle, and
does not explain the greater amount of work done by a
previously stretched muscle when it shortens against a
constant force (Cavagna & Citterio, 1974; Cavagna, Citterio &
Jacini, 1975; Edman, Elzinga & Noble, 1978; Sugi &
Tsuchiya, 1981; Cavagna, Mazzanti, Heglund & Citterio,
1986). In fact, if the force is held constant during
shortening, the greater amount of work cannot be derived
in a simple way from the release of elastic energy stored in
the stretched undamped elastic elements. Possible origins
690
G. A. Cavagna and others
of this enhanced work capacity are (1) the recoil of a viscoelastic system charged during stretching; (2) a greater
number of attached cross-bridges due, for example, to a
more favourable overlap between filaments induced by the
previous stretching; or (3) a modification of the state of the
individual cross-bridges. Data reported in the literature
are contradictory and do not allow these possibilities to be
distinguished.
A greater energy output after stretching has been
reported for sarcomere lengths greater than 2-3 ,um, i.e. on
the descending limb of the tension-length relationship,
but it was not found on the plateau of the tension-length
relationship (Edman et al. 1978; Edman, Elzinga & Noble,
1981). However, a transient shortening against the maximum
isometric tension (To) resulted from ramp stretches
confined to the plateau of the tension-length relationship
in both the whole muscle and single fibres (Cavagna et al.
1975, 1986). On the other hand, no sign of a transient
character to the increased load-sustaining ability was
found after quick decreases in load applied during isotonic
lengthening (Sugi & Tsuchiya, 1981).
In this paper we investigate the effect of previous
stretching on the ability of tetanically stimulated frog
muscle fibres to do positive work during subsequent
shortening against a tension equal to the maximum
isometric tension, To. Shortening against such a maximum
tension was taken as expression of an absolute energy gain
due to the previous stretching (not a relative energy gain)
as that described on the descending limb of the
tension-length relationship; Edman et al. 1978). In order
to determine if this energy is released directly by the
contractile component, the length changes of the
sarcomeres during shortening were measured in a tendonfree segment of the fibre by means of a striation follower
(Huxley, Lombardi & Peachey, 1981). In addition, shortening
was simultaneously measured at the fibre end in order to
determine the contribution of stress relaxation of tendons
and other end compliance. Fibre and sarcomere shortening
against To were measured after ramp stretches of different
velocity and amplitude; all motion was confined to the
plateau of the tension-length relationship. In some
experiments, measurements were made at two different
temperatures (4 and 14 °C), and a variable duration isometric
pause was left between the end of the stretch and the
release to To. The results suggest that previous stretching
increases the ability of the individual cross-bridges to do
work; they seem to reach, and retain for an appreciable
time interval after stretching, a level of potential energy
unattainable during an isometric contraction.
METHODS
Several components of the apparatus used (fibre chamber,
stimulator, force transducer and motor system) and the
procedure followed to dissect, mount and stimulate the fibre
have been described in detail by Cavagna (1993).
J. Physiol. 481.3
Muscle fibres
Frogs (Irish Rana temporaria) were killed by decapitation
followed by destruction of the spinal cord. Fibres of the caput
laterale of the tibialis anterior muscle were used. (Maximum
isometric force = 4-64 + 1-54 mN, developed at a length of
5.93 + 045 mm, with a contracting sarcomeres length of
2 14 + 0 04 /sm and a cross-section of 22796 + 5530 Zsm2;
means + S.D. of all the fibres studied at 4 °C, n = 37.) Fibres
were used only if the isometric tension measured at the
optimum fibre length was greater than 100 kN m-2; the
decrease in isometric tension during an experiment averaged
5.3%.
Experiments lasted up to 16 h and were stopped when (1) all
of the desired information was obtained (23% of experiments);
(2) the striation follower signal deteriorated due to interfering
optical impurities, blurring of sarcomeres or lateral movement
of the fibre (50%); (3) the fibre no longer responded to
stimulation (23%); or (4) force feedback failed (4%).
All data obtained were used unless (1) fibre inhomogeneity
(see below) was greater than 30%; (2) an aberrant shortening
against To was present after the elastic recoil (see the section
Abnormal tracings, and Fig. 4); (4) large vibrations of the
motor were initiated by the isotonic release; (5) the average
force applied during transient shortening against To was
smaller than 1 000 T. or larger than 1-045 T. (except for Fig.
13); (5) discontinuities (jumps) in the striation follower tracing
led to more than a 10% error in the measured length change;
or (6) the end of transient shortening against To was
undefined. These requirements reduced the number of data
included in Figs 5, 7, 9 and 10 (157 tetani recorded on 44 fibres,
33 at 4 °C, 7 at 14 °C and 4 at both temperatures) to about onethird of the tetani initially recorded.
Fibre and sarcomere force and length change
measurements
The fibre was suspended in Ringer solution between a force
transducer (Huxley & Lombardi, 1980) and a motor capable of
ramp displacements up to + 0-2 mm and step displacements
complete in about 100 i,s. The motor position was used to
monitor length changes at the fibre end.
Simultaneously with measuring the length changes of the
whole fibre, the average length change of sarcomeres in a
tendon-free segment of the fibre was measured using a
striation follower similar to that described by Huxley et al.
(1981). The output of this apparatus (A V) is the difference
between two voltages which are proportional to the number of
sarcomeres moving past two laser spots delimiting a segment
of the fibre. In each laser spot the image of ten contiguous
sarcomeres is optically averaged and the resulting single-cycle
sinusoidal light intensity pattern is exactly imposed upon five
contiguous photodiodes. Because the image of the averaged
sarcomeres looses registration with the five photodiodes as the
sarcomeres change length, the maximum strain which can be
measured is limited to approximately 45 nm per halfsarcomere (Fig. 2).
The average sarcomeres strain within the segment was
calculated from the striation follower output as follows. The
initial number of sarcomeres between the laser spots is
N1 = tseg/li where 1seg is the segment length and li is the initial
sarcomere length. Since the signal corresponding to the
movement of one sarcomere past a laser spot is 0-03922 volts
(10 V/255 steps, lengthening results in a positive A V), the final
J. Physiol. 481.3
Stretch effect on work output by muscle
number of sarcomeres between the spots, Nf, is given by
Nf = Ni - (A V/0 03922). The percentage sarcomere strain is:
OO(final length initial length)
-
initial length
or
loci {(
segINf) (seg/Ni))
691
preferred so that fibre motion under the laser spots was
minimized. Twitches and short tetani were given to the fibre
during the above operations; the exact stimulus threshold was
measured at the experimental temperature. Sarcomere length
changes during passive fibre strain and isometric tetanic
contraction at If,O were recorded (Cavagna, Heglund, Harry &
Passerini, 1990).
-
Experimental procedure
( lseg/Ni)
or
Ni-)Nf
Nf
1oo(
Hence:
(IOOA
(0-03922 Iseg
-
A V4)
(1)
Sarcomere strain is not proportional to the striation follower
output due to the term A VI, in the denominator of eqn (1); this,
however, has a negligible effect, being at a maximum at about
4% of 0-03922 lseg. The maximum sarcomere count capacity
127 for stretching and 128 for shortening.
A microcomputer controlled the timing (01 ms resolution)
and most other aspects of the experiment, including the
oscilloscope memory and data acquisition, triggering the
stimulator, the striation follower and the channels of the
oscilloscopes, determining and recording the value of the
isometric force plateau, controlling the appropriate length or
force level of the ergometer, reading the data from the
memory of the oscilloscopes and doing the required
measurements and calculations on the data.
was
-
Pre-experimental procedure
Each experiment was preceded by a fixed succession of
operations during which the fibre data required for the
experiment were collected and the striation follower was
calibrated. 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 fibre length corresponding to this position, lf o,
was the same for all stretch amplitudes. (This procedure was
not followed for the first six of the forty-four fibres studied,
with the consequence that for two of them the length reached
at the end of the largest stretches was 0-125 and 0-2 mm
greater than that reached at the end of the smallest stretches.)
The relaxed sarcomere length, 18sr' at the fibre length lf,o
was set at 2'19 ,sm (2'09-2-24 in two of the first six fibres; no
appreciable difference found in the results) by adjusting the
position 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
x32 objective and a x25 micrometre eyepiece. Sarcomeres near
the tendons were usually slightly shorter than 2-19 ,um.
The cross-sectional area of the fibre was measured as
described by Ford, Huxley & Simmons (1977). The relaxed fibre
length (excluding tendons and attachments), If oX was then
measured by means of a micrometer eyepiece fitted to a
stereomicroscope (x 16). A suitable segment of fibre
(800-1280 ,um long) was found by moving the two laser spots
along the fibre and by changing their relative position. In
general, the segment choice was based upon the absence of
connective tissue or other impurities near the laser spots; the
half of the fibre towards the stationary force transducer was
Two 4-channel digital oscilloscopes (Nicolet 4094, Madison,
WI, USA), labelled END and SEG, were used to record the
force and length changes of the fibre and sarcomeres,
respectively. Sample experimental tracings are shown in Figs
2 and 3. The records taken by each oscilloscope were stored on
disk (Nicolet XF-44).
The relaxed fibre was first shortened from 1f,o by the
amount of the planned subsequent stretching (Alstr). At the
end of shortening, the fibre was given a few stimuli to take up
its slack. The slow trace of the END scope was triggered and
the fibre was stimulated to tetanus isometrically. When a
force plateau was detected by the computer, a ramp of a preset
amplitude and duration was sent to the ergometer. If the
entire stretch length was within the range of the striation
follower, the slow trace of the SEG oscilloscope and the
striation follower were triggered 2 ms before the beginning of
the ramp; otherwise, for large stretches, the slow SEG trace
and the striation follower were triggered 3 ms before the end
of the ramp. In either case, the fast traces of both oscilloscopes
were triggered 3 ms before the end of the ramp.
At the end of the ramp, or after a preset time interval
during which the fibre was held active at the stretched length,
a signal proportional to the isometric tension, measured just
before the start of the ramp (To), was sent to the ergometer,
and the ergometer was switched to force feedback mode. After
a preset time interval, stimulation was stopped and the fibre
was brought back to its initial length under position control.
At the beginning of each experiment the fibre was released,
without previous stretching, from a state of isometric
contraction to a force about 0 9 times the isometric value;
release was made from the final length reached by the fibre
during stretching, If,..
Motor vibrations (%-442 kHz lasting about 2 ms), initiated
by the isotonic release, disturbed both the force and length
records (Figs 2 and 3); in addition, the force trace was affected
after release by an upward drift (-2 5% of T.). As shown in
Figs 2 and 3, these artifacts do not prevent determination of
the transition from the end of the elastic recoil (lasting about
100 ,as) to the beginning of transient shortening against To
(lasting on average about 60 ms at 4 °).
Measurements were made directly by the microcomputer
from the oscilloscope tracings; points used in the calculations
were selected by eye using cursor controls. The beginning and
the end of transient shortening against T. were determined
respectively on the fast length tracing (at the end of the elastic
recoil) and on the slow length tracing; any offset between the
two oscilloscope traces (fast and slow) was taken into account.
Measurement of sarcomere strain with the striation
follower
Sarcomere strain during the shorter ramp stretches (normally
less than 30 nm per half-sarcomere, exceptionally 45 nm per
half-sarcomere; Figs 2, 6 and 11) and during the transient
shortening against To was measured from the striation
692
J. Physiol. 481.3
G. A. Cavagna and others
follower output, the segment length and the initial sarcomere
length within the segment (eqn (1)).
The initial length of sarcomeres contracting against T. at
the beginning of the transient shortening against T. has been
taken as:
182 =
sO(f
Ale8f)
(2)
1f,o
where 18O is the length of the contracting sarcomeres
developing the tension To at the maximal fibre length If O; Is2
is the length of the contracting sarcomeres developing tension
To at the fibre length 1f,o - Alef after the fibre elastic recoil,
Ale,f. The initial length of the sarcomeres within the segment
at start of the ramp, 18br, was calculated from 182 using the
striation follower outputs during the elastic recoil and the
ramp stretch, respectively. Since these outputs are
proportional to the fractional number of sarcomeres moving in
and out the segment, the calculation is easily done.
Estimation of sarcomere strain during large ramp
stretches
When the ramp stretch was too large to be entirely recorded
by the striation follower, strain of the sarcomeres within the
segment during the entire ramp stretch had to be calculated
assuming a uniform distribution of fibre length changes among
all sarcomeres.
The length change imposed by the motor on the fibre, Al tr,
may be divided into the length change of the sarcomeres, Al8,
and the tendons, Alt:
A = A/str AlI.
(3)
As a contracting fibre is stretched, the force initially rises
abruptly, but after a length change of approximately 2% of
the initial sarcomere length, the force settles to a roughly
steady value. It follows that Al. is smaller than Alstr during
the tension rise, whereas it approaches A l8tr at the end of large
stretches.
The effect of the tendon length change on the measurement
of sarcomere length during stretching was estimated as
follows. The average length of sarcomeres contracting
isometrically within the segment at the beginning of the
ramp, 18 br, was calculated as:
|s
br = ls, ot
Atr
(4)
assuming (1) the isometric tension To, and therefore A lt, are
the same at the maximum fibre length, 1f,OX and at the
beginning of the ramp, i.e. at the length If 0 - Alstr (this is true
if Alstr occurs within the plateau of the tension length
diagram; see below); and (2) the length of the sarcomeres
within the segment changes in proportion to the length
change of the relaxed fibre when it is shortened by Alstr (after
rearranging the sarcomere lengths with a few stimuli). The
calculated length change of contracting sarcomeres during the
ramp is therefore:
Al80
= 18,
-4,brX
where 1I,1 is the sarcomere length at the end of the ramp, i.e.
at start of the elastic recoil, determined as described in the
preceding section.
In the largest ramp stretches used (0 4 mm imposed to the
fibre end), Isbr was 1X989 + 0-027 /am (mean + S.D., n = 77); the
largest sarcomere length 1,,, was 2-136 + 0 034 sum
(mean + S.D., n = 44); these sarcomere lengths correspond to
isometric tensions of 0-996 T. at 18 br and 0-992 T, at 184,
(interpolated from the values in Table 1 of Bagni, Cecchi,
Colomo & Tesi (1988)).
Evaluation of fibre inhomogeneity during lengthening
As expected, the calculated sarcomere stretch was a fraction of
the length change imposed by the motor, and this fraction
increased with stretch amplitude as follows: 0-76 + 0413
(mean + S.D., n = 5) when A1str = 0 05 mm; 0-88 + 0414 (n = 17)
when Alasr=O01 mm; 0 95+0-06 (n= 22) when Alstr =
0-2-0-3 mm and 0 99 + 0-02 (n = 77) when Alstr = 0 4 mm. In
the experiments where sarcomere strain during stretching was
not measured with the striation follower, a calculated
sarcomere strain had to be used as the abscissa in Fig. 5.
In the fibres where the sarcomere strain was both calculated
as described above and measured by the striation follower, an
index of inhomogeneity was determined from the ratio
between measured and calculated sarcomere strain during the
ramp. Only data showing a ratio included between 0 7 and 1-3,
i.e. an inhomogeneity <30%, were accepted. Furthermore,
the relationship between measured and calculated sarcomere
strain (Fig. 1) was used to calculate the sarcomere strain
appropriate for that particular fibre when stretch amplitude
was too large to be measured by the striation follower.
Abnormal tracings
The end of transient shortening against To was usually clearly
defined by an inflection on the curve, where the velocity
became zero or negative (Figs 2, 3 and 6); occasionally the
inflection was not present and the end of transient shortening
against To was taken as the point of divergence of the tracing
6_
E0
X
2
-
,
Calculated sarcomere strain (%)
(5)
Figure 1. Evaluation of sarcomere inhomogeneity during
lengthening
Sarcomere strain during the ramp, measured with the
striation follower, is plotted as a function of sarcomere strain
calculated assuming complete fibre homogeneity during the
stretch (see Methods). The difference between the continuous
line and the dashed unity slope line indicates that the
sarcomeres within the segment lengthened about 14% less
than the average sarcomeres along the whole fibre. The same
fibre is used in Figs 2, 3 and 6.
J. Physiol. 481.3
Stretch effect on wowrk output by muscle
from a backward extrapolation of the subsequent slow
shortening phase (Fig. 8). The rare records (< 2%) where the
end of transient shortening against T. could not be determined
due to a blunt curvature were discarded.
In 87% of the trials, the time course and amplitude of
transient shortening against T. was about the same in the
segment and in the whole fibre. One of the experiments where
this was not the case is illustrated in Fig. 4B (38 °C) and C
(14 C), which can be compared to a normal trace from the
same fibre in Fig. 4A (37 °C). A fast shortening takes place
after the elastic recoil and before the beginning of transient
shortening against T. in the striation follower record (Fig. 4B
and C), but not on the fibre end record (insets); this fast
shortening was usually followed by damped oscillations, more
or less pronounced, on the segment record. Due to this
shortening, the sarcomere length change taking place from the
end of the elastic recoil to the end of transient shortening
against To was on average 51% larger than the same reading
693
made at the fibre end. Contrary to transient shortening
against T., the velocity of this aberrant shortening and the
period of its associated oscillations did not change appreciably
with temperature in two fibres where the phenomenon was
observed at 4 and 14 °C (e.g. Fig. 4). In the fibre shown in Fig.
4, this aberrant shortening occurred after some normal tetani
(as in Fig. 4A) and remained in all the successive tetani made.
These records were excluded.
RESULTS
General description of the experimental
tracings
Figure 2 shows an example of the records made when the
entire ramp could be followed by the striation follower.
The two left panels indicate the force developed by the
A
B
6-
- 600
a),
_ a
4-
- 400 z
tI
C
.)
*ii
0 o
z O
.o
a)
2-
/~ ~ ~ ~ ~ ~ ~ X ~ ~
I
-
Lengthe
E
z
-.d
(a
C
.cL.0
Y
C
(c
0
.U)
C
e.
-200 a)
D
D "
200a)
oE0
a)
.0
IL
0
I
0
400
800
1200
0
100
Time (ms)
200
300
Time (ms)
C
D
-600
- 600
5-
a
N
,,,<
-
-
4-
E
Length
.0
E
- 400 z
C
cco
C
C
2) C
200
,
Force
3
._
5
10
Time (ms)
15
0
coi
L-
U)
Length
E&
-
0
.)
-200
Force
-i
0
a) '40-
0
-
3-
=E
D0o
z400
0)
)-50-
co a)
20
C/)
30
0
5
10
Time (ms)
15
Figure 2. Experiment where sarcomere length changes could be recorded from the beginning
of the ramp
The oscilloscope records show fibre tension (same signal on all panels), fibre length changes measured
at the fibre end (A and C), and sarcomere length changes measured by means of the striation
follower (B and D). In B, the sarcomere length during the entire ramp stretch is recorded; the inset
above the length trace shows, for comparison, the fibre length changes during the transient
shortening against To. Horizontal and vertical arrowheads indicate respectively the beginning and
the end of transient shortening against To. Temperature, 3-5 °C; contracting sarcomere length lSso,
2X11 #sm at the maximal fibre length; o, 6415 mm; fibre cross-section, 26627 4um2.
1f
20
a)
.0
694
J. Physiol. 481.3
G. A. Cavagna and others
fibre and the length changes imposed by the motor; the
two right panels indicate the same signal of force plus the
length changes of sarcomeres as measured by the striation
follower. Figure 2A shows the whole experiment on a slow
time scale (500 ,us point-'); the tetanized fibre was
subjected to a ramp stretch (0 3 mm in this case) resulting
in the rise in the tension above the maximum isometric
value, To. Immediately after the end of the ramp, a force
equal to or slightly greater than the isometric force was
applied to the fibre. This resulted in a sudden fall of the
force with a simultaneous elastic recoil of the fibre,
followed by a transient shortening against To. In Fig. 2B,
the oscilloscope was triggered 2 ms before the beginning of
the ramp stretch so that the entire lengthening of
sarcomeres could be recorded (100 #ss point-'). The inset
above the length trace shows for comparison the fibre
length changes at the end of the ramp, during the elastic
recoil and the transient shortening against T.. The inset
was obtained by plotting on the same time scale the length
changes of the fibre (Fig. 2A) multiplied by 10 (1%
strain t 10 nm per half-sarcomere) and added to an offset.
The similarity of the transient shortening against T.
tracings obtained at the fibre end and on the segment is
apparent despite the different measurement methods.
The force and length changes taking place 3 ms before
release, during release (lasting about 100 #ss) and for about
17 ms after release are recorded on a faster time scale
(5 ,us point-') in Fig. 2C and D. These tracings were used to
measure the beginning of transient shortening against T.
(arrowhead) with an accuracy greater than that possible in
the slow tracings.
Figure 3 shows oscilloscope records obtained when the
ramp stretch imposed by the motor to the fibre was too
large to be followed entirely by the striation follower. In
this case, the striation follower and the segment
oscilloscope traces (Fig. 3B) were triggered 3 ms before the
A
B
8-
-600
-600
e|
6C
LU)
Length
I
I-R
I
4-
.e
/
, !
Ii/
Force
-400 zE
-400 E
E
Y
cO
0
a,- 50-
-
:it
2-
60-
Ca'
-
A
E
X
40-0
2E
C')
40-
e
-200
_
--~~~~~~~~~~~
-200
Force
800
0
1200
50
Time (ms)
C
n
-
~~~~~~~~~~~~~~~~i
400
.o
0
g
C
Length
100
Time (ms)
150
20v
1 50
200
D
- 600
- 600
7-
60cm
a) ZD
_40E
- 4005
._0C
-
6-
A ,L<
'
co
Q
E
0
Length
.2
-20
Lnth
._
-200
Force
-
e
.0
5-
-
a)
c 'oc
li
Ta)
-400 E
xY
a00 40-
LL
C
-200 e
a
e.co
-D
c, c
Force
.
coc 40 _n
0
5
10
15
20
Time (ms)
Figure 3. Experiment where
the ramp
0
5
10
15
Time (ms)
sarcomere
length changes began to be recorded
near
the top of
Oscilloscope records obtained when the ramp stretch was too large to be entirely followed by the
striation follower. In this case, the striation follower and the oscilloscope traces in the upper right
panel were triggered 3 ms before the end of the stretch. Other details are as in Fig. 2.
20
J. Physiol. 481.3
A
Stretch effect on work output by muscle
25 20-
D
0
(D
-.
-=E
8
00
=
0)coC
2&
E
15 -
,
2?
a)
co00
-r E
0 o
.4
cm
11
E
W
CDO
&
CD,L.E
-300
C
C
c
.2
5-
F
Force -150
0
200
.D_I
LL
20
10
- 600
20 -
20
cm D
00,
..;
CE
SW
0
10-
ens~~~~~~~~Lnt
CeE
z
1L-
E
25-
0 D
-450
5-
100
B
15-
&
i8
E
C
-600
0C
10 -
&-0
9
20-
co
CC0-.-
k -4
695
- 450
vE
z
-300
.o
.L
0
tC=E
/1 .4__
15
15 -
0)0
co co
=0-.
c
<-
0
D--i
9E
10*
10
-
E oC2.
(D ).-
E
-
cr)
5'
_
PM
5-
2?
%
1-
Force -150
._
iL
0
100
20
C
0
0
C
:-._
15
OC
c
Ev
- 450
15 44
E
--a
10
E
10
Length
-
-
300
-
150
F--_
OC
Co.--
-
0
Force
5-
.0
5
0
0
0
100
Time (ms)
200
.C
co
0
c _
R
i
z
0
00
fIIv
c
O.-
-
00
CE
c 0
- 600
20 -
25
00,
20
10
200
10
Time (ms)
Figure 4. Evidence for the recoil of a passive visco-elastic structure
The three left panels show the length changes of sarcomeres (lower trace in each panel) and of the
fibre (inset). The three right panels show, on a much shorter time scale, force and sarcomere length
changes occurring near the isotonic release. The arrowheads indicate the end of the elastic recoil of
the undamped elastic elements. A, 37 00, shows normal traces such as those illustrated in Figs 2 and
3. B, 3-80C and C, 14-00C, subsequently recorded on the same fibre, show an additional fast
shortening against To, followed by damped oscillations (T = 3X3 ms) taking place after the elastic
recoil; this is not observed at the fibre end (insets). Note tha/ this additional fast shortening against
To and the period of the subsequent damped oscillations are not increased appreciably by the 10 0C
increase in temperature from panels B to C. (The oscillations in the left panel of C have the same
period of the stimulation, T = 25 ms). Contracting sarcomere length; 18'OX 2-10 #sm at the maximal
fibre length; If O, 5-2 mm; fibre cross-section, 17161 /sm2.
20
IL
J. Phy8ioL. 481.3
G. A. Cavagna and others
amplitude for the left panels and large for the right). The
amplitude of transient shortening against To is plotted in
Fig. 7 as a function of the velocity of lengthening (same
data as Fig. 5, grouped in four classes of sarcomere strain).
Figures 6 and 7 show that when the ramp stretch is
large (greater than 2%), transient shortening against To
attains about the same value independent of the velocity
of lengthening. When the stretch is small and the velocity
of lengthening is high, an oscillatory response of the
sarcomere length changes may take place after release
(Pringle, 1949; Armstrong, Huxley & Julian, 1966;
Cavagna et al. 1986).
end of the stretch and the lengthening of sarcomeres
during the whole ramp stretch was calculated as described
in the Methods. Again, the inset shows the similar trend of
the length changes of the whole fibre and the sarcomeres
during transient shortening against To.
Experiments similar to those described in Figs 2 and 3
were made with different sarcomere stretch amplitudes
(0-5-8&6%) and lengthening velocities (0-03-1-8 sarcomere
lengths s-1). In some experiments, as shown in the
examples of Figs 8, 11 and 12, a time interval (5-800 ms)
was left between the end of lengthening and release to T..
-
Effect of stretch amplitude
Effect of a time interval between stretch
and release
The amount of transient shortening against To, measured
at the fibre end and on the segment when the contracting
fibre is released to To immediately after the end of the
ramp, is plotted in Fig. 5, irrespective of the lengthening
velocity, as a function of the sarcomere length change
imposed during the ramp stretch. The amplitudes of
transient shortening against To measured by the striation
follower (@) and by the motor displacement at the fibre
end (0) are, on average, equal. In both cases, transient
shortening against T. increases with sarcomere stretch
amplitude up to about 8 nm per half-sarcomere.
The effect of a time interval between the end of the stretch
and the release was studied at two temperatures (4f1 + 0-6 °C,
n = 56 and 14-4 + 0-2 °C, n = 21, means + S.D.) after large
ramp stretches (0 4 mm at the fibre end, 7*3% sarcomere
strain on average) of different velocity (0f16-1f82 sarcomere
lengths s-1). An example of the tracings recorded in the same
fibre without a time interval and with a 5 ms time interval
is given in Fig. 8. Results obtained on twenty-six fibres are
grouped in Fig. 9 into two classes of lengthening velocity.
When the fibre is kept tetanically stimulated and in
isometric conditions at the end of a ramp stretch, the force
falls progressively towards the isometric value, at first
rapidly and then more slowly (stress relaxation). This is
shown in Fig. 9A by the drop in tension to Ti, taking place
at the instant of the isotonic release, after the time
intervals given on the abscissa. The ability to shorten
against To during the stress relaxation period changes as
indicated in Fig. 9B.
During the first 20 ms of stress relaxation, the
amplitude of transient shortening against To does not
change appreciably (insets in Fig. 9B). Subsequently,
transient shortening against To decreases with a time
course similar to that of the slow decay in tension. This is
The point at which sarcomere strain is equal to zero is
plotted for comparison and shows the average transient
shortening against To taking place after release from a state of
isometric contraction to about 0 9 T. (see Methods); its value,
-3-5 nm per half-sarcomere, is in good agreement with that
measured as the horizontal distance between the T, and T2
curves at 0 9 To in Fig. 13 of Ford et al. (1977) (about 3-4 nm per
half-sarcomere).
Effect of the velocity of lengthening
Figure 6 shows experimental tracings of sarcomere length
changes taking place during transient shortening against
To after ramp stretches of different velocity (increasing
from top to bottom) and of two amplitudes (small
10 -
0
8-
Figure 5. Effect of stretch amplitude on the
transient shortening against To,
Transient shortening against To as measured at the
fibre end (0) and on the segment (0) when the fibre
17
8E
is released to To immediately after the end of the
ramp. Data are plotted irrespective of the velocity
of lengthening (0-03-1-44 sarcomere lengths s-).
The points represent the mean values (± S.D., n is
given by the numbers near the symbols) of data
obtained on thirty fibres tetanized at an average
temperature of 3-6 + 0'9 °C (mean + S.D., n = 90),
and grouped into the following intervals along the
abscissa: 0, > 0-1, > 1-2, > 2-4, > 4-6, > 6-8'5.
The point at a sarcomere strain of zero shows the
transient shortening taking place after release from
an isometric contraction to 0-91 To.
co
6-
t13
-_..
:. 15
E
c
4- 27 :.
7
._
0)
i -,
2-
Cen
0
2
4
Strain (%)
6
8
697
Stretch effect on work output by muscle
J. Physiol. 481.3
65 -
60O
55 -
i~~
50 -
100
20
a)
200
300
65
0
1
15
60 -
10
55 4
5
50-1
00
100
200
200
300
100
200
30C
l
100
200
30(
onn
Tuu
qnVIn
juu
E0
co
'a
A*
Ec
0
A
0
20
65 0
15
60
10
55 -.
AC
0)
c
E1-C0c
m
-
it
(D
E0
0
Cl)
5-
50-
A
100
20 -
200
300
A
450
65-
15 -
60
10 -
55 -.
I.
5-
50-
_
I
i
~
~
~
~
~
~
~
~
~
~
~
~
~
~
~
~
~
~
45
0
200
100
Time (ms)
300
-
u
A
1 Un
IlUU
Time (ms)
Figure 6. Sarcomere shortening against T. after ramp stretches of different amplitude and
velocity
Left panels, 01 mm imposed by the motor to the fibre end; right panels, 0 4 mm. The entire ramp is
recorded in the left panels whereas only the end of it is shown in the right panels. Stretch velocity
increases from top to bottom (left panels: 0-13, 0-21, 0-44 and 0-84 sarcomere lengths s-'; right
panels: 0-15, 0-27, 0 53 and 1P06 sarcomere lengths s-1). The amplitude of the transient shortening
against T. is from top to bottom: 6-0, 6-1, 4-6, 4-8 nm per half-sarcomere (left panels) and 8-4, 8-7, 8-6
and 8-9 nm per half-sarcomere (right panels). Note that when the stretch amplitude is large (right
panels) the amplitude of the transient shortening against T. remains about constant irrespective of
stretch velocity. Same fibre as shown in Figs 2 and 3; temperature, 3-4 ± 0-05°C (mean + S.D.,
n = 8).
698
J. Physiol. 481.3
G. A. Cavagna and others
time scale, the force and the length changes imposed to the
fibre end before, during and after the ramp stretch.
The rate constant of transient shortening against Ti,
calculated as shown in Fig. 12, is plotted in Fig. 13 as a
function of the drop in tension, relative to T, at the
moment of the isotonic release. It appears that (1) the rate
constant increases linearly with the amplitude of the fall
in tension, and (2) the average rate constant is larger at
1400 (0-588 + 0'166 ms 1, mean + S.D., n = 18) than at 40C
(0 244 + 0116 ms-1, mean + S.D., n = 23), for a temperature
coefficient, Qlo, of 2 4.
better shown in Fig. 10, where transient shortening
against T. is plotted as a function of the tension drop at
the moment of the isotonic release (i.e. after different stress
relaxation periods). It appears that during the initial fast
phase of stress relaxation, the ability of shortening against
To remains on average unaltered in spite of the large
reduction of tension.
Temperature effect on the kinetics of
transient shortening against To
Figure 11 shows sarcomere length changes recorded
immediately after stretching and 5 ms after stretching at
140C for comparison with those recorded with a similar
stretch amplitude, velocity and time delay at about 40C
(Figs 6 and 8). The similar trend of the higher temperature
tracings and of the time scaled lower temperature tracings
show that the velocity of transient shortening against T. is
increased about 2-5 times by an increase in temperature of
10 'C.
No simple curve could be fitted through the tracings in
Fig. 11 to measure more precisely the temperature effect.
However, after a period of stress relaxation, usually
longer than 100 ms, the time course of transient
shortening against T,o is roughly fitted by a single
exponential. Figure 12 shows examples of this curve fit, at
about 4 and 1400, on transient shortening against To
curves recorded after different stress relaxation periods
and velocities of lengthening. The insets show, on a slower
In the experiments illustrated in Fig. 13, the average
tension during transient shortening against T. was
0962 T. -1P055 T. (average, 1P015 T.) at 4 0C, and
0 959 To - 1018 T. (average, 0 995 To) at 14 'C. Restricting the
tolerance to 1000 T. - 1.045 To (as in Figs 5, 7, 9 and 10) leads
to a Qlo of 2-7: this value seems less reliable due to the small
number of items in the mean (n = 8 at 14 'C and n = 16 at 4 0).
DISCUSSION
Figures 2, 3 and 5 show that transient shortening against
To on the plateau of the tension-length relationship is not
due to any tendon-related effect, but solely due to
properties of the sarcomeres. Muscle enhancement due to
previous stretching is therefore not confined to the
descending limb of the tension-length relationship
(Edman et al. 1978) and shortening against To cannot be
10-
2a
0
E0
0
8-
C-
C
CU
6-
2-7%
co
4CO
R
E
----- A
11-_%
4-
J2
0
0
.-C
-
.3
2
2
NH -~~~
2-
co,
0-0
0-5
-
Strain
=
0-7%
1-0
1-5
Stretch velocity (sarcomere lengths s-1)
Figure 7. Effect of stretch velocity on the transient shortening against T.
The data shown by 0 in Fig. 5 have been grouped into four classes of stretch amplitude
(0-532-0-966, 1062-1381, 1P591-3-824 and 4 211-8 47%). The average strain value for each class is
given near the curves. Mean values (± S.D., n is given by the numbers near the symbols) have been
made for the following intervals of the abscissa: 0 029-0 035, 0-109-0-157 and 0 614-0 76 for the
average strain of 0 7%; 0-040-0-041, 0-123-0-241 and 0-828-0-839 for a strain of 1P3%; 0-046-0-267,
0'46-0-514 and 0-849-1-268 for a strain of 2'7%; 0-143-0-265, 0-308-0-619, 0 736-1-203 and
1P279-1 439 for a strain of 6 2%. Note that for the strain of 1P3%, considered to be the maximum for
the cross-bridges to remain attached to actin, transient shortening against T. is about half the
maximum attained with the largest strain, whatever the velocity of lengthening.
explained by a more favourable overlap between filaments
induced by the previous stretching. According to Edman et
al. (1981), load clamp to T. during ramp stretches leads to
zero velocity of shortening; this is contrary to the
observations of Cavagna & Citterio (1974) and Cavagna et
al. (1975) on whole muscle, of Cavagna et al. (1986) on whole
fibres, and to the present study on sarcomeres. These
contradictory findings may be explained by the low
resolution of the apparatus used by the Edman group (see
Fig. 5 in Edman et al. 1981, where a transient shortening
against To cannot be excluded). Shortening 'for some distance
against a load of l1 Po', found by Sugi & Tsuchiya (1981)
after isotonic lengthening, may be related to the transient
shortening against T. described in the present study.
Possible role of passive components
Sarcomere shortening against T. may be due to the
discharge of passive visco-elastic components recruited
during stretching (Morgan, 1990), or to a property of the
A
8-
cross-bridges. According to Morgan's hypothesis, length
changes during stretches of sufficiently high velocity occur
mostly in sarcomeres characterized by low yield tension.
These sarcomeres are quickly stretched to a length where
there is no overlap between thick and thin filaments
('popped sarcomeres'), and their tension is borne by
passive elements only. Confining the ramp stretch to the
plateau of the tension-length relationship reduces the
possibility of gross sarcomere length inhomogeneity, but
may not eliminate it completely. In the present study, the
maximum detectable inhomogeneity accepted was less
than 30% (see Methods and Fig. 1), but popped sarcomeres
uniformly distributed along a fibre may not be detected.
Therefore, the recoil of popped sarcomeres, taking place
after the isotonic release, must be considered as a possible
source of the transient shortening against To.
Three sets of observations are not consistent with this
interpretation of the experimental results: (1) the effect of
stretch velocity; (2) the effect of temperature on the fast
B
-600
-600
ForA
-400
A
E
.
Cl)~
._
in
Force
4-
Length
8-
Length
0-
a)
699
Stretch effect on workc output by muscle
J. Physiol. 481.3
-200
-400 zE
C
co;
CD
C
a)
4-
.0
a
0
._4
~~~~~~Force
X
-200
.0
iL
I
1C
v100
1 000
1200
1100
D
C
1100
1200
70 -V
75-
cD
0
-
0)a)
at)C E
Cc
°E
00
70 -
00
.C 0
c
.C 0
6)0
Ca)
(c
=
-
60
-
E
65 -
0
65
Cc.E
co 0
_
'i_
E_
cuc$
cn
-
-
V
50
100
Time (ms)
150
200
0
50
100
Time (ms)
150
Figure 8. An example of the effect of a short delay between stretch and release on the
transient shortening against To
The two upper panels show the motor position and the tension developed by the fibre before, during
and after the ramp stretch. In B a 5 ms time interval is introduced between the end of the ramp and
release to To; note the fast fall of the force during this time. The panels below show the sarcomere
transient shortening against To; this is greater after the 5 ms time interval (8 9 vs. 7-5 nm per halfsarcomere; arrowheads as in Fig. 2). The experiment was carried out at 4-3°C; lSo, 2-16 /Lm;
If 5-1 mm; cross-section, 15607 /tm2.
o'
X
200
J. Physiol. 481.3
G. A. Cavagna and others
700
phase of stress relaxation (Cavagna, 1993) and (3) the effect
of temperature on the transient shortening against To.
The number of popped sarcomeres should increase as
stretch velocity is increased from below to above the yield
point of the stretch velocity-tension relationship. Likewise,
if the transient shortening against To were related to
popped sarcomeres, it too would be expected to increase;
however, this is contrary to what was found (Fig. 7). At
6-2% sarcomere strain, for example, the same transient
shortening against To was found at 0419 sarcomere lengths
s-A (which is below the yield point; see Figs 7 and 11 of
Lombardi & Piazzesi, 1990) as was found at 1P35 sarcomere
lengths s-' (which is above the yield point). Furthermore,
while a stretch velocity of 0419 lengths s-' is lower than the
threshold required to detect any segment inhomogeneity
(see Fig. 6 of Lombardi & Piazzesi, 1990), it resulted in the
largest transient shortening against T. (Fig. 7).
In the experiment of Figs 2, 3 and 6, the minimum velocity
of lengthening during the two largest ramp stretches was 0-16
lengths s-', i.e. 0-06 VO (the velocity of unloaded shortening of
tibialis anterior fibre at 4 C, V. of approximately 2-6 lengths s-',
was deduced from Woledge, Curtin & Homsher (1985, pp. 53
and 56) and equals the value reported by Lombardi & Piazzesi
(1990) for a tibialis anterior fibre at 5 °C). This relative velocity
is well within the ascending limb of the tensionvelocity of lengthening relationship determined on different
experimental conditions (Fig. 2.21 of Woledge et al. (1985) and
Fig. 12 of Lombardi & Piazzesi (1990)). Accordingly, in the
experiment of Figs 2, 3 and 6, the relative fall in tension
A
1*0-
10o
12
0-8
7
0-8
5
08
3
04
2 2--
2
0*8-
-
12\
0-4
2 2
06
I-
v
r
0
04
10
20
30
02
0o
04
02 -
.
10
.
-I
20
3X10
3~~~~~~~~~
"I
3
___
400
400
800
B
10
10
8
D
0
E
84
8
C
4-
co
Q
6
E
4
a
_- l=-I
I'mU
46
v
C
8
0
10
20
30
0
4
10
20
CD
2
2
0
(I
0
0
400
Time (ms)
0
400
Time (ms)
Figure 9. The effect of a delay between stretch and release on the tension and the transient
shortening against To
A, the fall in tension, relative to To, that occurs during the elastic recoil after different delays
following the stretch (abscissa). B, the amplitude of transient shortening against To as a function of
the same time intervals. Lengthening velocity was 0-16-0-86 sarcomere lengths s' for the left
panels, and 1-1-1-82 for the right panels. 0 and continuous lines, 4-13 + 0-600C (mean+ s.D.,
n = 56); * and interrupted lines, 14-4 + 0-22 °C (mean + S.D., n = 21). Changes during the fast phase
of stress relaxation are expanded in the insets. Mean values + S.D. when larger than symbol size;
n is given by the numbers near the symbols of the upper panels.
30
J. Physiol. 481.3
Stretch effect on work output by muscle
during the elastic recoil, AT/T., at the end of two ramp
stretches at the average velocity of lengthening of
0-79 lengths s-' was about 19% greater than after the two
ramp stretches at 0-16 lengths s-'.
The fast fall in tension taking place when a short delay
is introduced between stretch and release to To may be
thought to be due to stress relaxation of hypothetical
passive visco-elastic elements. This process could be
associated with a gain of mechanical energy by passive
damped elements, with an increase of their subsequent
transient shortening against To (as in Fig. 8). In this case,
however, it would be difficult to explain how stress relaxation
of a passive visco-elastic system may be accelerated by
temperature as is the fast phase of stress relaxation
A
(Q1o = 241,
which is similar to that found by Ford et al.
1977, for the fast recovery of tension) (Cavagna, 1993).
Similarly, Figs 1lA-C, 12 and 13 show that the velocity
of transient shortening against To is increased about 2-5
times when the temperature is increased from 4 to 14 °C.
This is true both when release to T. takes place
immediately after stretching (Fig. 11), after a short time
interval (Fig. lID) or after a long time interval (Figs 12 and
13).
In conclusion: (1) the effect of the velocity of
lengthening (Fig. 7) is not consistent with the generation
of sarcomere inhomogeneity, which is the basis for the
recruitment of passive visco-elastic elements during
stretching, and both (2) the fast phase of stress relaxation
B
12a)
E
0
0
Cuo
io
8-
sa
2
2
I.'
Ea
*
4-
ECcm
C
2
0
co0n
3
1
0
04
0-8
C
04
0-8
D
-
12 -
8-
8-
12
Cu
E08
cn
*~~~~+
--C
2
Ec
Co
CD
4
4-
3
0
CD,
n_I
0
0-8
04
A T/To
0
0-8
0-4
A T/To
Figure 10. Hypothetical processes taking place during stress relaxation
The amplitude of transient shortening against T. (ordinate of Fig. 9B) is given as a function of the
normalized fall in tension during the isotonic release (ordinate of Fig. 9A). A and B, lower velocity
of lengthening (0-16-0'86 sarcomere lengths s-1); C and D, higher velocity of lengthening (1 1-1-82
sarcomere lengths s-). A and C, 4 °C; B and D, 14 'C. Same data as shown in Fig. 9. The continuous
lines through the experimental points are drawn by eye. Their horizontal portion indicates that
during the fast phase of stress relaxation a fall in tension (abscissa) is not accompanied by a fall in
the ability to shorten against To (ordinate); this is due to the two opposite processes indicated by the
interrupted lines (constructed as explained in the text).
J. Phy8iol 481.3
G. A. Cavagna and others
702
associated oscillations (Fig. 4) suggests the aberrant shortening
may be due to the recoil of visco-elastic structures within the
tendon-free segment of the fibre. The average period X of these
oscillations is 2-97 + 051 ms (mean +s.D._ n = 44) at about
4 °C, and 2X67 + 0-72 ms (mean + S.D., n = 12) at about 14 °C,
for a Q1o of H11. Assuming that this is the fundamental period
of a longitudinal stationary oscillation, the velocity will be
(21fO/r) = (E/p)05; taking an average fibre length of 5-9 mm
and p = 1000 kg m-3, Young's modulus E would be
16-20 kN m-2, which is about 2000 times smaller than Young's
modulus of a contracting fibre, and may be due to a slack
and (3) the transient shortening against T. are accelerated
by an increase in temperature with a Qlo 241-2-5, which
is not appropriate for stress relaxation and the viscoelastic recoil of passive structures. These experimental
results suggest that the transient shortening against To
derives from a cross-bridge property and not from the
discharge of a passive visco-elastic system.
-
The relative temperature independence of both the
aberrant shortening velocity and the frequency of the
B
A
220 -
-c E?
0
cc E
O
0
=
c
n
_
60
115-
II/'
go- I/
0-
2&
0
%8ca Ec
ii
C,,.-.
i
E
1400C
\
1
A
14-6 0C
50
0
100
C
100
50
0
D
2
70-
el^
00
aD e
c E
S
I/
o
cct)
0
/
115 -
_
13-90C
60 -
1
!A
)_
E(cog?
°% E
<
4.2 0C (time/2-5)
A
5
-
3.500C (time/2-5)
<SO _
0-II
.','
145 0C
A
A
50
Time (ms)
0
100
100
50
0
Time (ms)
Figure 11. Effect of temperature on the rate of the transient shortening against To taking
place before or during the fast phase of stress relaxation
Sarcomere length changes taking place immediately after stretching (A-C) or 5 ms after stretching
(D). In each panel a comparison is made between tracings obtained at 14 0C and at 4 0C with a
similar amplitude and velocity of the ramp stretch. The original abscissa of the lower temperature
tracings has been divided by 2-5 in order to allow direct comparison with the higher temperature
tracings. A, 14°C: I 8, 2-11 ,um; If ', 6-0 mm; cross-section, 13151 /um2; lengthening velocity, 0-56
sarcomere lengths s
transient shortening against To, 5-4 nm per half-sarcomere. A, 3-5 °C: third
trace from top of left column in Fig. 6. C, 14 °C: 18O, 2412 ,am; If 5-2 mm, cross-section = 13960 mm2;
lengthening velocity, 1-25 sarcomere lengths s-; transient shortening against To, 4-6 nm per halfsarcomere. C, 3'5 °C: lower left trace in Fig. 6. B, 14 6 °C: 1 0, 2412 sm; If
6-2 mm; cross-section,
17197 'am2; lengthening velocity, 1'17 sarcomere lengths s-'; transient shortening against To, 6X8 nm
per half-sarcomere. B, 3X4 °C: lower right trace in Fig. 6 (shifted 2-5 nm downwards). D, 14*5 °C:
18o,c 2 16 Atsm; If o, 6-75 mm; cross-section, 26908 4am2; lengthening velocity, 1l1 sarcomere lengths s-1;
-
,
Os
o'
transient shortening against To 6-9 nm per half-sarcomere. D, 4-2 °C: lower right trace in Fig. 8.
The low frequency oscillations in the higher temperature tracings have the same period as the
stimulation (7 = 18-25 ms). Arrowheads indicate the end of the transient shortening against To.
J. Physiol. 481.3
703
Stretch effect on work output by muscle
A
n
1
B
P3
1
U-I
-
._
5
CY
-.
/
0
I--
4
,-k
a
-
i
0*5
U._
-j
I
0
0
800
05-
-J
O-j
I
-j
D
2
8-
8
,1
0-
0-
-1
0
._
uo
0
1
4-
.co
1
lk
o- 4
I.-
ik_
05
-
0
I
0
800
800
400
0
0
.-.7
0
F
1-
8-
A
~-e
05-
__
_
_
2
_
-
-1
0._
1-
kz
4I.-
a)
D11
-i
0
onn
4 P^n
BOu
1t6U0
5
Time (ms)
10
Time (ms)
Figure 12. Effect of temperature on the rate of the transient shortening against To taking
place during the slow phase of stress relaxation
Sarcomere transient shortening against To recorded at 4 °C (left panels) and 14 0C (right panels: note
the different time scale on the abscissa) after 100-800 ms of stress relaxation and different velocities
of lengthening (given below). Transient shortening against To is expressed as (L L2)/(L, -L),
where L1 and L4 are the sarcomere lengths at the beginning and at the end of the transient. Curves
through the normalized data are single exponential terms. Insets show the force and the length
changes imposed on the fibre before, during and after the ramp, to illustrate the stress relaxation
period and the fall in tension to To during the isotonic release. The rate constants of the exponential
curves are greater at 14 0C than at 4 0C and, at both temperatures, decrease from top to bottom:
0-472, 0 346, 04144 ms-' at 4 0C (left panels); and 0 999, 0 616, 0 508 ms-t at 14 0C (right panels).
A: 4 0 °C; stress relaxation period, At, 300 ms; Vstr, 1P25 sarcomere lengths s-'; AT/To, 0 273;
Iso, 214 /um; 1f,O 5 3 mm; cross-section, 17866 /tm2. C: 3 9 °0; At, 280 is; Vstr, 0'55 s'; AT/T, 0499;
Is OX 241um; If O, 6 0 mm; cross-section, 23600 /sm2; E: 3 9 °C; At, 800 ms; V,t,, 1P64 s'; AT/ITo, 0 062;
lSo) 207 jum; If O, 68 mm; cross-section, 29480 #Mm2. B: 146°C; At, 1OOms; Vstr, 026s-'; AT/To,
0195; '80, 212 ,um; Ifc, 6f2 mm; cross-section, 17197 #Mm2; D: 146 °C; At, 300 ms; Vstr, 105 s-';
AT/To, 0 073; same fibre as above; F: 142 0C; At, 800 ms; Vstr, 1*67 s-5; ATITo, 0 064; 18'O, 2410 /sm;
Ifo, 5 8 mm; cross-section, 23646 /sm2.
-
704
7. A. Cavagna and others
portion of the fibre segment with popped sarcomeres (Morgan,
1990). The average resting 'static' stiffness of a relaxed fibre at
2-06-2-6 /sm sarcomere length is similar (E = 14-5 kN m-2), but
the 'dynamic' stiffness, during the initial steeper tension
change in ramp stretches and releases at 2 2 /tm, is much
greater (E = 228 kN m-2) (Lannergren, 1971).
J. Physiol. 481.3
rate constants for the two phases of stress relaxation that
are much higher than those observed experimentally (see
Appendix). This discordance between the theoretical
model and the present experimental results may be due in
part to differences in the tissue preparation (e.g. the fibre
size); furthermore, the present experimental results
cannot be easily compared with those of Lombardi &
Piazzesi (1990) and Piazzesi, Francini, Linari & Lombardi
(1992) due to the different experimental protocols used
(velocity transients versus tension transients). In addition,
the model by Lombardi & Piazzesi (1990) was not intended
to account for the dynamics of stress relaxation after the
ramp stretch. Nevertheless, comparison of the model
predictions with the empirical data obtained in this study
indicates a need to reconsider the succession of events as
portrayed by Lombardi & Piazzesi (1990), which would lead to
an apparent steady state after a stretch amplitude of
20 nm per half-sarcomere.
The continuous increase of transient shortening against
To up to at least 5% sarcomere strain (- 50 nm per halfsarcomere) suggests that charging of the cross-bridges
occurs over a filament sliding distance greater than that
usually accepted for the cross-bridges to remain attached
to actin (- 12 nm per half-sarcomere). The large amount of
energy released during the transient shortening against To
(up to 1.5 mJ m-2 per half-sarcomere) suggests that some
cross-bridge states are reached during stretching that
possess a level of potential energy unattainable during an
isometric contraction.
The present results confirm the hypothesis that during
the fast phase of stress relaxation, after a ramp stretch,
mechanical energy is conserved through a transfer from
the undamped to the damped element of the cross-bridges
(Cavagna, 1993). In fact, during the fast phase of stress
relaxation, the capability to shorten against T. is retained
(insets in Fig. 9B). In Fig. 10 it is suggested that two
processes occur simultaneously during the stress
It must be pointed out that the effects of temperature
and of the velocity of lengthening described above are only
indirect evidence against stress relaxation of a visco-elastic
system, and do not directly rule out the possibility that
recoil of popped sarcomeres or other passive structures
may contribute to the described transient shortening
against To. Since the effects of temperature and of velocity
of lengthening on dynamic inhomogeneity are not well
understood, some role for passive elastic components
cannot be eliminated entirely.
Possible role of cross-bridges
Transfer of cross-bridges towards states of greater
potential energy during stretching has been hypothesized by
Cavagna et at. (1986) to explain the transient shortening
against To of previously stretched fibres, and by Lombardi
& Piazzesi (1990) to explain the trend of the tension and
stiffness-velocity of lengthening relationships.
Lombardi & Piazzesi (1990) have proposed a cross-bridge
model (see Appendix) which is not consistent with the
isotonic release experiments of the present study. The
model predicts: (1) an abrupt decrease in the transient
shortening against To (particularly at high stretch
velocity) when there is a delay between stretch and release
(Fig. 15), which is not observed in the experiments (Figs 8,
9 and 10); (2) an amplitude of transient shortening against
To which is much smaller than is observed experimentally;
(3) the amplitude of transient shortening against To would
be independent of stretch amplitude and increase with
stretch velocity (Fig. 16), both of which are the opposite of
w"hat is observed experimentally (Figs 5 and 7); and (4)
0
Figure 13. The rate constant of transient
shortening against T. decreases during the slow
phase of stress relaxation
The rate constant of transient shortening against
T,, calculated from exponential curves such as
those illustrated in Fig. 12, is plotted as a function
of the relative fall in tension, A T/To, taking place
at the instant of the isotonic release (abscissa).
0, 4 °C; 0, 14 OC. Note that the rate constant
0-8 -
coI
E
-
Cu
8
04-
a)
01*.'e- 0
*I, ~ 0* ~ *
0
0
ir
increases with the relative fall in tension, and that
at 14 °C it is on average 2-4 times greater than at
4 °C.
0
0.1
Il
AT/To
0-2
0*3
J. Physiol. 481.3
705
Stretch effect on work output by muscle
relaxation period (as indicated by the interrupted lines).
The first process lasts for the duration of the fast phase of
stress relaxation (AT/To = 0 9-0A4 on the abscissa of
Fig. 10) and corresponds to the completion of the charging
of the damped element (upper interrupted line). The
second process lasts for the duration of the slow phase of
stress relaxation (AT/TO = 0 9-0-1 on the abscissa of Fig.
10) and corresponds to detachment of strained crossbridges (lower interrupted line).
During stress relaxation, the fibre is held isometric
(fixed end mode); if no cross-bridge attachment and
detachment occurs, a fall of the force would imply a
shortening of the undamped elements and an equal
lengthening of the damped element of the cross-bridges.
The length change of the undamped elements measured at
the fibre end for a tension drop equal to T. was, on
average, 9-6 nm per half-sarcomere in the experiments of
Fig. 10 at 4 'C. During the fast fall of force (the horizontal
portion of the continuous line in the left panels of Fig. 10),
the tension falls from about 1 9 to 1P4 T. at 4 C, i.e. by
about 0.5 To (inset of Fig. 9A). The damped element would
therefore lengthen during the same interval by 4-8 nm per
half-sarcomere. This corresponds to the vertical distance
between the upper interrupted line and the horizontal
portion of the continuous line in Fig. 10. The upper
interrupted line therefore indicates the transient
shortening against T. that would have been attained by
complete charging of the damped element, during the fast
phase of stress relaxation, in the absence of simultaneous
attachment and detachment of cross-bridges.
The amplitude of transient shortening against To would
therefore increase if only the charging process took place
during the fast phase of stress relaxation (upper
interrupted line). Subtracting the increment of the; upper
interrupted line from the continuous total experimental
curve yields the lower interrupted line, showing the
simultaneous loss of the ability to shorten against To,
possibly due to cross-bridge detachment. The horizontal
portion of the continuous line in Fig. 10, indicating an
unchanged ability to shorten against To, would therefore
result from two opposite processes: a charging process,
taking place during the fast phase of stress relaxation, and
A
60
cUU-
s= 00E
0
s 0
40
a)CU
CC,
4) oE
E
CBE
B
Figure 14. Simulation by the model of Lombardi &
Piazzesi of experimental records
A and B, an isotonic release experiment as calculated
by the model. Prior stretch is given at 0 55 ,um s-' per
co a)
E0)
=OCU"
E
a)-
half-sarcomere for 90 ms. The entire experiment is
shown in A. Detail of stretch and release is shown
in B. Compare with Fig. 2C, an isotonic release
following a long, fast stretch (1 5 ,um s' per halfsarcomere for 55 ms) and a 5 ms isometric delay.
Compare with Fig. 8.
kz
° E
CD-C
E_
C
0
c0.o
c
CE
ca)
( C,-E
Time (s)
J. Physiol. 481.3
C. A. Cavagna and others
706
3-
i
91
a)
Figure 15. Simulation by the model of Lombardi
& Piazzesi: effect of a time delay after the ramp
stretch
Effect of a stress relaxation period (abscissa) on the
transient shortening against To calculated as
described in the Appendix. Different symbols
correspond to different lengthening velocities:
*, 01 ,um s' per half-sarcomere; *, 0 5; A, 1P0;
x, 1P5. Sarcomere strain was 5% in all cases.
Compare with Fig. 9B.
E
0
4
2-
c
I
'a
0
En
1-
cn
-
0
0
300
200
100
Time (ms)
shortening against T. on the duration of the stress relaxation
period and, as a consequence, on AT/IT (Fig. 13), may be
qualitatively explained as follows. In the elastic recoil, which
immediately follows the isometric delay, the change in length
of each cross-bridge is equal to the change in length of the
entire half-sarcomere. This may be assumed to be true for each
cross-bridge regardless of its initial state of stretch. The elastic
recoil of each cross-bridge is AT/K, and the stiffness K can be
assumed to be equal for all cross-bridges. It follows that the
drop in tension AT is equal for each cross-bridge independent
of its initial strain. The arithmetic mean (T.ob) of the tensions
developed by the cross-bridges after the elastic recoil is given
by:
discharging process, taking place simultaneously during
the slow phase of stress relaxation.
It should be emphasized that the interrupted lines in Fig. 10
are meant only to indicate that two opposite processes may
take place during stress relaxation, without implying that
they represent the actual trend of these processes. In fact, net
cross-bridge detachment during the fast phase of stress
relaxation (invoked as an explanation of the lower interrupted
line) would. decrease the increment of the upper interrupted
line (calculated assuming no detachment) and, as a consequence, the
specular decrement of the lower interrupted line. On the other
hand, the sharp increase in slope of the lower interrupted line
below 0A4AT/Ti is to be expected and is consistent with the
described interpretation of the experimental results. In fact,
during the fast phase of stress relaxation, the fall in tension
(abscissa) is not only due to cross-bridge detachment, but also
(and mainly) due to length readjustment between undamped
and damped elements (Cavagna, 1993). It follows that the
number of cross-bridges detaching for a given fall in tension
(proportional to the slope of the lower interrupted line) must
be less during the fast phase of stress relaxation (lasting
20 ms) than during the remaining portion of the slow phase
a
Tob
(lasting
780
ms,
see
-
AT) +
(TI,2- AT) +
---
+
(Ti, n- AT)]/n,
nTi,b= Toi
AT= [(T,1 + T,2 + -+ Tl,n )/n]-
Tob =Tl -To,b,
where T1 is the mean of the tensions developed before recoil.
T1,b decreases as the duration of the period of stress relaxation
increases: this is shown by the reduction of the fall in tension
b
Fig. 9A).
The dependence of the rate constant of the transient
3-
[(T,
where TI j is the tension developed by each cross-bridge before
the elastic recoil, n is the number of the cross-bridges and
-
of stress relaxation
=
A
x
0
a)
E
0
'o
0
0
0
0
0
2-
CU-
Figure 16. Simulation by the model of
Lombardi & Piazzesi: effect of stretch amplitude
Effect of stretch amplitude (abscissa) on transient
shortening against To as calculated using the same
model as Fig. 15. Symbols as in Fig. 15. Compare
with Fig. 5.
E
c
C)
._S
1-
C
0
s'
2
0
2
I
4
Strain (%)
6
8
J. Physiol. 481.3
707
Stretch effect on work output by muscle
AT during the elastic recoil (insets in Fig. 12). In addition, the
tension developed after recoil will be larger than To b in the
cross-bridges which were more tense before release and smaller
than Tob in the cross-bridges which were less tense before
release. The greater the difference in the T, tensions before
release, the greater the tension supported by the more
strained cross-bridges after release and the smaller their
transfer velocity towards states of lower potential energy
(according to the theory of Huxley & Simmons (1971)). It is
likely that the most strained bridges detach during the stress
relaxation period and are replaced by freshly attached cross-
bridges developing a force similar to that in an isometric
contraction. Some of the highly strained cross-bridges
however must remain attached after 800 ms of stress
relaxation in order to account for the residual shortening
against T., but the small average tension before release, T15,b
indicates that most of the cross-bridges are unstrained. As
mentioned above, this large difference in tension between the
few strained and the many unstrained cross-bridges may
account for the slow rate constant observed after long stress
relaxation periods.
APPENDIX
The symbols used in this Appendix are precisely those used by Piazzesi et al. (1992).
We investigated the degree to which the cross-bridge cycling model presented by Lombardi
& Piazzesi (1990), and refined by Piazzesi et al. (1992), could account for the experimental
results described above.
We have implemented a numerical solution to the governing differential equations as put
forward in Lombardi & Piazzesi (1990, p. 167) using the constants and expressions for k1 through
k6 as specified in Piazzesi et al. (1992, pp. 707-708). The following changes to this model (as
originally published) were incorporated.
(1) Our expression for k_5 and k6 is
1995
-105(x + 1)
0
exp(0 8(x - 4 5)) + 34 78x - 157 51
7017
x<-20
-20 < x < -1
-1 < x 4-5
4-5 < x < 15-5
x>15-5.
-
The change is in the expression for the range 4 5 < x ( 15-5. As shown in Piazzesi et al.
(1992), namely
k_5 and k6 = exp(0 8(x - 4 5)) + 34 78x - 174-9,
the rate functions become negative in the range 4 5 < x < 4-985. As defined in the model, all
rate functions must be positive for all x.
(2) A computational methodology for holding the model in an isotonic condition was
developed (see below).
(3) Time steps during the calculation were 20 ,ss step-' during the initial activation and
steady stretch, 5 #ts step-' for the 10 ms immediately following the release to isotonic and
20 us step-' thereafter. The fine time steps early in the isotonic release were required to
maintain a steady force in the face of rapidly changing cross-bridge distributions. Spatial
discretization was 0 05 nm as suggested in Piazzesi et al. (1992).
To test our computational technique, we duplicated certain conditions used by Piazzesi et
al. (1992). Both cross-bridge distributions and force records computed by our program compare
almost exactly with those shown in Piazzesi et al (1992).
The equations defining the model presume that sarcomere length is an independent
variable. To permit the model to simulate a force clamp experiment, in which sarcomere
length is now a dependent variable, the following computational steps were taken. At the
beginning of an isotonic time step, the force being generated by the cross-bridge distributions
(T'urrent) is calculated and compared with the desired isotonic force (T2Sc) If RCurrent > Ti0 the
cross-bridge distributions are moved together to the left (toward smaller x) to reduce the force;
similarly, if Tcurrent < Tiso the distributions are moved to the right (larger x) to increase the
force. This process of comparing forces and moving distributions proceeds iteratively until
Tcurrent is acceptably near Tiso (the range of acceptability is defined as Tiso ± Ttoieranc; for these
simulations Ttolerance = 00O01T.). These adjustments to cross-bridge distribution positions,
which maintain the desired isotonic force, are made at the beginning of the isotonic time step.
708
0. A. Cavagna and others
J. Physiol. 481.3
This motion is then added to (or subtracted from) the previous half-sarcomere length and the
calculations for the time step then proceed as usual. That is, migrations of cross-bridges
between states are computed using the rate function values appropriate to the new locations of
the distributions.
Figure 14A and B shows a simulation that replicates the experimental conditions of Fig. 2.
Figure 14C replicates the experimental conditions in Fig. 8.
Isotonic simulations included appropriate ranges of stretch velocity, stretch amplitude and
isometric pause after stretch. For each run, the magnitude and duration of transient
shortening against T. were measured in the same manner used to analyse experimental traces.
These data are summarized in Figs 15 and 16.
We also explored the model's ability to account for the time course of stress relaxation
(Cavagna, 1993). In the simulations, ramp stretches of different velocity (0-11, 0 55, 0 99, 1-54
and 2-00 ,sm s-' per half-sarcomere) and sufficient amplitude to reach a steady state in the
tension record were followed by an isometric period of 800 ms. The time course of the resulting
drop in tension was analysed in the same manner as described in Cavagna (1993). We found
that the model results were well fitted by a double exponential curve indicating a fast and a
slow phase of stress relaxation; the corresponding rate constants are on average 0-250 ms-1 for
the fast phase and 0-026 ms-' for the slow phase. These values are much higher than the
average values observed experimentally: 0-121 ms-' for the fast phase and 0 0039 ms-' for the
slow phase (Cavagna, 1993; stress relaxation period = 800 ms).
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Acknowledgements
This study was supported by a grant from the Italian
Ministero dell' Universit'a e della Ricerca Scientifica
Tecnologia.
Received 18 October 1993; accepted 16 June 1994.