Dependence of energy output on force generation during muscle contraction JACK A. RALL Department of Physiology,
Ohio State University,
RALL, JACK A. Dependence of energy output on force generation durirtg muscle contraction. Am. J. Physiol. 235(l): CZOC26, 1978 or Am. J. Physiol.: Cell Physiol. 4(l): C20-C26, 1978. -It has been proposed that the energy (heat + work) output of an isometric twitch is determined by the force that is generated under conditions of invariant activation, irrespective of muscle length. To test the effect of length and force on total energy output, muscles were stretched by increments beyond the muscle length at which twitch force is maximum (b) and then stimulated; energy output and force then were measured. These data were compared with isovelocity twitches in which stimulated muscles, initially at different lengths, shortened (near maximum velocity) a constant distance and then redeveloped tension at lengths < I+. If energy liberation was determined by force generation, plots of energy output versus force produced would be parallel with isovelocity twitches liberating extra energy as shortening heat. As predicted, the ratio of the slopes (n = 13) of these relations, 0.98 t 0.02, was not different from 1 and the shortening heat coefficient (&&, measured from the difference in intercepts), 0.15 t 0.01, was near to the expected value. Therefore, energy liberation in twitches appears to be uniquely determined by force generation and not by muscle length. Rana pipiens skeletal muscle; heat production; getics; isometric and isovelocity contractions
muscle ener-
IN AN ATTEMPT to develop a thermodynamic framework for theories of muscle contraction, it has been proposed (3, 6, 8) that the net energy (E) liberated by contracting muscle can be explained by the following relation
E = A + f(P, t) + aFX + W where A is a term representing muscle activation, and the other terms collectively designate the energy liberation associated with crossbridge cycling under different mechanical constraints. Specifically, the activation term represents the energetic effects of Ca2+ cycling starting with Ca2+ release from the sarcoplasmic reticulum (SR) and interaction with the myofibrils to active reaccumulation by the SR. Indirect evidence (4, 8, 9) suggests that this Ca2+ cycling energy liberation is independent of muscle length. The crossbridge cycling energy liberation includes a term associated with the work done by the muscle, W, and one associated with the energetic effects of shortening per se, aFX. Thus, the energy liberated as a consequence of shortening equals the distance shortened, X, multiplied by a shortening heat coefficient, CY~,whose value is dependent on the load during shortening. The general function,
Columbus,
Ohio 43210
f(P,t), represents the energy liberation associated with the development and maintenance of force. Presumably, during a twitch this function is dominated by force (4, 6, 8, 9). An important point in the above formulation is that muscle length per se is not considered a determinant of energy liberation. For example, this relation implies that isometric twitches of equal force generated at lengths less than I+, (L, is the muscle length at which twitch force is maximum) and at lengths greater than L, will liberate the same energy if the other terms in the relation remain constant. But a comparison of the results of Chapman and Gibbs (I), Homsher et al. (4), and Smith (9) clearly shows that isometric twitches of equivalent force liberate more energy at lengths less than L, than at lengths greater than L,. But this result is difficult to interpret because, at lengths less than L+, and specifically less than the muscle slack length, the muscle tends to lengthen toward L, during rest. Therefore, the subsequent twitch would be expected to liberate a larger than normal amount of energy attributed to internal shortening and internal work, i.e., W + +X. Also, the time integral of force development is different at short and long muscle lengths (9). In fact, Gibbs and Gibson (2) have attempted to explain muscle energy liberation in terms of the time integral of tension as an alternative to peak twitch tension. Moreover, it has never explicitly been proven that the energy liberation associated with force development per se in a twitch is dependent on the amplitude of force production and not the time integral of force production or muscle length. The experiments described in this paper have been designed to dissociate the effects of force production from muscle length and the time integral of force production and, thus, they test the proposition that, in a twitch, the term f(P, t) is best represented by the amplitude of force development alone. MATERIALS
AND METHODS
General. Specimens of Rana pipiens of both sexes were obtained from the Steinhilber Co. (Oshkosh, Wis.) and kept in moist tanks at 6OC.The tanks were flushed several times daily with cold water. On the day before an experiment an animal was killed by decapitation and the dorsal heads of a pair of semitendinosus muscles were dissected. The muscle pair, still attached to the pelvic bone, was aerated overnight in 95% 02, 5% CO2 at 4°C in a Ringer solution containing (mM): 95.0, NaCl;
cm 0363-6143/78/0000-0000$01.25 Copyright 0 1978 the American Physiological Society Downloaded from www.physiology.org/journal/ajpcell by ${individualUser.givenNames} ${individualUser.surname} (132.210.236.020) on January 12, 2019.
ENERGY
OUTPUT
DURING
MUSCLE
C21
CONTRACTION
20, NaHCO,; 2.5, KCl; 1.0, MgCl,; 1.0, CaCl,; at a pH of 7.0. All experiments were performed at 0°C. The muscle length at which twitch force was maximum, I+, ranged from 20 to 23 mm, whereas the blotted weight of the muscle pairs (M) ranged from 0.056 to 0.113 g. Peak twitch tension per cross-sectional area (P,, (L, /M)) averaged 248 t 5 mN/mm’ (mean t SE; n = 13) and the accompanying energy liberation averaged 17.8 t 0.5 mJ/g.
Myothermal measurements. Energy liberation during contractions at 0°C was measured as heat plus work produced, Experiments were designed in such a way that the internal and external work production was insignificant or was returned to the muscle during relaxation as heat. Heat production was measured with a calibrated integrating thermopile (5, 11). This type of thermopile minimizes sampling errors and uncertainties in calibration with some temporal resolution sacrificed in the process (e.g., see Fig. 1). It consists of a thermopile made of a series of 25pm silver plated constantan thermocouples contained in a region 2.25 cm in length, on which slabs of insulated silver 2.45 cm long, 0.4 cm wide, and 125 pm thick have been placed. A 12.5 ,urn diameter insulated Nichrome wire (California Fine Wire Co., Culver City, Calif.) was bonded to the silver surface on both sides of the thermopile to serve as a heating element by which the system could be calibrated. This thermopile has previously been described (5) and designated as W2. Calibration was performed as described previously (11). The calibration was performed twice on each muscle pair and the values, in millijoules per microvolts, were averaged. Thus, the output of the thermopile, in microvolts, was multiplied by the calibration factor for each muscle pair and divided by the blotted muscle mass to obtain the energy liberation in millijoules per gram. Myothermal records were corrected electronically for an exponential heat loss (7 = 15.6-26.5 s). For some of the isovelocity
A 0.3N
experiments the muscles shortened from a length greater than L 03 where resting tension was not zero. Passive shortening from these lengths results in a slight heat absorption because of the thermoelastic properties of the muscle. Therefore, a correction was made for this heat absorption by releasing the passive muscle at the same velocity and for the same distance and by recording the heat absorptio n and add ing it to the subsequent record in which the muscle was stimulated and released. The average maximum correction for heat absorption due to the thermoelastic properties of the muscle for any individual experiment was 4% (range, O-9%) of the net energy liberated during the contraction. Mechanical measurements . Force measurements were made with the use of capacitan .ce transducers having a resonant frequency of 3 kHz and a compliance of 0.02 pm/mN. When a muscle pair was constrained to contract at a constant velocity (isovelocity contraction) an ergometer, constructed from a modified speaker magnet and voice coil, was employed. Performance characteristics of this type of ergometer have been described (5). Briefly, the ergometer could provide displacements with a frequency response that was flat from 0 to 70 Hz. The ergometer was capable of positive and negative displacements, with velocities from 0 to 100 cm/s. Displacements were predetermined within the range of O-2 cm. The beginning of the displacement was timed within the range of 0 to 10 s with respect to the stimulus. Experimentul design. To test the proposition that energy liberation was dependent on force development and not on the time integral of force development or muscle length, the following experimental -approach was employed. Muscles were stimulated at various lengths beyond Lo to produce isometric twitches and energy output and force measured. These data were compared to isovelocity twitches in which stimulated muscles, initially at different lengths, shortened (near maximum velocity starting 30 ms after the stimulus) a constant distance and then redeveloped force at lengths less than Lo. These experiments allowed a comparison of the energy liberation for an equivalent force development at lengths less than and greater than I+ Under these conditions external work production, w, should be nearly zero and the shortening heat, cy~X, should be a constant factor. Thus plots of energy output versus force would be expected to be parallel with the isovelocity twitches liberating extra energy as shortening heat if energy liberation were determined by force generation. Experiments were done by alternating the order of the isometric and isovelocity series of contractions. During- any given experimental series that lasted 20-30 min the muscles were stimulated at 90-s intervals and 20-30 min of rest in Ringer was allowed between each series. Best fitting lines for the energy liberation versus force production data were determined with leastsquares linear regression analysis. 3
B b
6mJ/g
FIG. 1. Isometric twitch force production (A) and energy liberation (B) at 0,86 (b) and 1.2 L+-, (a). Although force generated was equivalent, preshortened contraction liberated 14% more energy. Note difference in time integral of force production and delay in force development. L, = 22 mm, muscle mass (blotted) (M) = 0.078 g. Initial deflection on heat records is stimulus artifact (both heat records start from same base line). Integrating thermopile obscures somewhat temporal resolution of heat signal.
RESULTS
Energy liberation and force production in shortened and stretched isometric twitches. Figure 1 shows a
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c22
J. A.
sample record of force production (Fig. 1A) and energy liberation (Fig. 1B) for two isometric twitches generating an equivalent force at a length greater than L, (Fig. la, 1.2 L,) and at a length less than L, (Fig. lb, 0.86 L,). Despite the peak force equivalency the twitch at 0.86 L, liberated approximately 14% more energy. The twitch at 0.86 L, displays a longer delay in force development with a shorter delay in energy liberation. This observation is probably accounted for by an increase in internal shortening at 0.86 L, with an increased shortening heat production. Also, the time integral of tension is less at 0.86 L, than at 1.2 L,. These data along with other results from this experiment are plotted in Fig. 2. For an equivalent force production, the preshortened muscle liberates more energy than the prestretched muscle. The significance of this result is questionable because of the probable increase in internal shortening heat and work production in the preshortened twitches, The stretch experiment in Fig. 2 is considered to produce the best estimates ofA and f (P, t) (4, 8, 9). The intercept in Fig. 2 from the prestretched isometric twitch data is interpreted as the energy liberation associated with Ca2+ cycling, A, and the slope, the energy liberation per unit force developed, is taken as a measure of the energetic effects of crossbridge cycling off (P, Q. Thus, the energy liberation during isometric twitches can be analyzed in the form
A
13 4 Lo r
RALL
0.9 6 L,
I
I
b
a
1.18 Lo
C
lOmJ/g
E = A + f(P, t> where f(P, t) includes the contribution of internal shortening heat and work to the isometric twitch. The average equation for these experiments (n = 13) is E, mJ/g = 6.01 (50.14) where
P,lP,,
is the ratio
+ 11.95 (~0,4O)P,lp,,
of the stretched
length
force
16
OSHORTEN
FIG. 2. Plot of energy liberation vs. isometric force development for preshortened twitches (0) and prestretched twitches (m). Data for preshortened series were obtained by shortening muscle to 0.82 L, and then stretchin .g bY increments and stimulating at various lengths. Data for prestretched series were obtained in a separate run by starting at I+, and stretching muscle by increments, stimulating to 1.32 I+,, and then returning to I+ by increments and stimulating. Same muscle as Fig. 1. Intercept is 37% of total energy produced at I.+, for stretched series. P,, L+,/M = 242 mN/mmK r (correlation coefficient) = 0.996 for preshortened series and 0.999 for prestretched series.
FIG, 3, Muscle I.ength (A), twitch force production m, and energy liberation (C) for an isometric contraction at 1.14 L( a) and an isovelocity contraction with shortening starting at 1.18 L, and ending at 0.96 I+ (b). For isovelocity twitch, 30 ms after stimulation, muscle was released at a constant velocity of 20 mm/s for 5 mm, redeveloping force 0.28 s after stimulation. Note: equivalency of force production, zero force developed during shortening, difference in time integral of tension, and difference in energy liberation. Heat record is uncorrected for heat absorption during isovelocity shortening due to thermoelastic properties of muscle. L, = 22 mm; M = 0.088 g.
production to the force developed at L,. The intercept is, on the average, 33% of the energy liberated at L+,. Energy liberation and force production in isovelocity and stretched isometric twitches. The experiment described above does not support the proposal that energy liberation is dependent on force and not muscle length. The experiments in this section are designed to overcome the difficulties of the preshortening experiment. Figure 3 is a sample record of two twitches producing an equivalent force. One twi tch was isometri .c (Fig. 3a) at 1.14 L, and the other was an isovelocity twitch (Fig* 3b) starting at 1.18 L, and redeveloping force at 0.96 I+ During the shortening at 2 cm/s no appreciable force was developed and, therefore, external work was zero. Despite the fact that the developed force was the same, the energy liberation was greater in the isovelocity twitch. This would be expected to be due to, at least in part, the shortening he& contribution to -the twitch. This sample result and other data from the same experiment are shown in Fig. 4. The lower line represents the results from the prestretched isometric
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ENERGY
OUTPUT
DURING
MUSCLE
c23
CONTRACTION
the muscle generates an equivalent force at a length less than L, as compared to a length greater than I+. The constant difference between the lines of Fig. 4 represents the shortening heat per gram of muscle, apX/M in mJ/g. For this example (Fig. 4) the value of the shortening heat coefficient, a&r (results are expressed per P,, to account for variation in intrinsic strength of different muscles), is 0,15. The average value is 0.15 t 0.01 (range, 0.11-0.18) (n = 13). Thus, the energy liberation in these isovelocity twitches can be described in the following way
24
E = A + f(P, t) + q,qX 0 ISOVE
LOCtTY
(2cmk)
and from the results of these experiments
4
E, mJ/g = 6.01(*0.14) + 11.95(*0.40)P,/Pot om 0
I
0.2
1
1
1
1
1
0.6 0.8 1.0 1.2 Force, N FIG. 4. Plot of energy liberation vs. force development for prestretched isometric twitches (a) and isovelocity twitches (0). Prestretched series was performed as described in Fig. 2. For isovelocity series muscle was stretched by increments from 1.05 to 1.2 I+ and released, at a velocity of 20 mm/s for 5 mm, 30 ms after stimulus. Force was redeveloped in range of 0.82-0.98 I&, 0.28 s after stimulus. Records have been corrected for thermoelastic heat measured during passive muscle shortening. Ratio of slopes, isovelocity to isometric, is 0.996. Open circles (0) on prestretched line are isometric twitches at beginning and end of isovelocity series of contractions. Same muscle as Fig. 3, &L,/M = 254 mN/mm? r = 0.996 for stretch data and 0.996 for isovelocity data.
+ 0.15(-+0.0l)x(P,,/M)
0.4
twitches as in Fig. 2. The upper line constitutes the data from isovelocity twitches like the one described in Fig. 3. In each twitch the muscle shortened the same distance at the same velocity. Redeveloped force was varied by varying the starting length, in this example from 1.05 to 1.2 I+,. Unlike the results in Fig. 2 the lines in this figure are parallel. The ratio of the slopes, isovelocity series/isometric series, is 0.996, The average ratio when zero force is developed during shortening is 0.98 t 0.02 (range, 0.91-1.09) (n = 13). Among individual experiments muscle shortening ranged from 2 to 5 mm (0.09-0.23 I+), at velocities from 14 to 20 mm/s, and force was redeveloped 0.17-0.28 s after the stimulus. As an approximate indication of the variability of any set of data about its regression line, the average correlation coefficient for the isometric data was 0.996 t 0.001 (n = 13) and, for the isovelocity data, 0.993 -t 0.002 (n = 13). Thus, when the large internal shortening of the preshortened isometric twitches is prevented, the energy that is liberated, which is attributed to force development, is not determined uniquely by muscle length. Also the energy liberation is not uniquely determined by the time integral of tension. This point is suggested by the difference in the time integral of tension shown in the records of Fig. 3. In fact, if one plots energy 1iberation versus the time integral of twitch tension for the data of Fi .g+ 4, the slopes are no longer parallel. The ratio of slopes becomes 1.55 instead of 0.996. If all the data are plotted in a similar fashion the average ratio of the slopes, isovelocity serieslisometric series, becomes 1.47 + - 0.06 (range, 1.1-1.95) (JZ = 13) instead of 0.98 * 0.02. The increased ratio of slopes results because the time integral of tension is less when
where X is in millimeters, grams.
P,, in newtons, and M in
DISCUSSION
It has been proposed (4, 9) that the energy liberated during an isometric twitch could be fractionated into a component attributed to Ca’+ cycling and another component associated with crossbridge cycling. Operationally this was done by plotting energy liberation as a function of prestretched isometric twitch force production as shown in Figs. 2 and 4. The intercept was interpreted to represent the Ca’+ cycling energy liberation (33% of the total in these experiments) and indirect evidence was provided that this value was length independent. The slope represented the crossbridge cycling energy liberation and this energy production was presumed to be best described as a function of the amplitude of the isometric force generation. This interpretation did not include muscle length as an unique determinant of energy liberation in isometric twitches. Nonetheless, Smith (9) has shown, and Figs. 1 and 2 verify, that the energy liberation is greater for an equivalent force at a length less than I+ than at a length greater than I+. It has been suggested (9) that the short length twitch liberated more energy because of an increase in internal shortening heat and in work production. Still the question remains: is muscle energy liberation uniquely determined by force production or muscle length? If the former is true it should be possible to demonstrate that the energy liberation associated with force production i.s the same, as long as the force is the same, irrespective of muscle length at which the force is generated. This is precisely what is shown in the experiment described in Figs. 3 and 4. Plots of energy liberati’on versus force production for isovelocity and prestretched isometric twitches are parallel (Fig. 4). The strict parallel relationship, ratio of slopes 0.98 t 0.02, strongly supports the contention that force development per se is a determinant of energy liberation and not muscle length. Also, this result appears to be independent of variations in the time integral of force production (Fig. 3). The quantitative difference between these straight line relationships (Fig. 4) represents the shortening heat. From this data a value for the shorten-
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C24 ing heat coefficient , aF /PO,, can be obtained, 0.15 t 0.01, which is similar to other results, 0.16-0.20 (3, 7). Thus, the formulation presented in the introduction can predict quantitatively the energy liberated in isovelocity twitches under these conditions. These results strongly suggest that the difference between the data in Fig. 2 can be attributed to an increase in internal shortening heat and work production as preshortened muscle length decreases. For example, if the difference in the intercepts of Fig. 2 is considered to be due predominantly to shortening heat production, it is possible to estimate the amount of muscle shortening that occurred under these conditions. Because the shortening heat, abTX(P,,/M), is 4.2 mJ/g from the difference in intercepts of Fig. 2 and aF = 0.14, P = 0.88 N and M = 0.078 g for this muscle pair, X bgcomes 2.7 mm or 12% of the muscle test length (L,). This calculation suggests that at extremely short muscle lengths the muscle shortens approximately 12% of L, when stimulated to produce an isometric twitch. Therefore, the twitch liberates more energy than would be predicted on the basis of force development alone. These results also provide indirect evidence that the energy liberation associated with Ca2+ cycling is not altered by muscle length (from L, to 1.33 L,) or by
J.
A. RALL
changes in muscle length (in the range of 0.78-1.22 L). The strict parallel relationship shown in Fig. 4 suggests that the energy liberation attributed to Ca*+ cycling (the intercept of the prestretched isometric twitches) is the same in the isovelocity twitches. Another, though less likely, possibility is that the Ca2+ cycling energy liberation changes with muscle length in such a way &s not to effect the parallel relationship or to make this relationship fortuitous. Recent experiments (10) with the Ca2+ sensitive bioluminescent protein aequorirr have shown that the light flash attributed to Ca2+ release is altered by muscle length. One would then predict that the energy liberation associated with Ca2+ cycling should also be altered. Apart from the fact that the aequorin experiments were done at a different temperature (15°C) than these experiments, the myothermic data reported herein suggest that if the amount of Ca2+ released changes with muscle length these changes must be small at 0°C. More experiments are needed to further clarify this point. Thi s work ation, Central Received
was supported, in part Ohio Heart Chapter.
26 September
1977; accepted
Y‘
by the American in final
form
Heart
Associ-
23 January
1978.
REFERENCES J. B., AND C. L. GIBBS. Energetics of isometric and isotonic twitches in toad sartorius. Biophys. J. 12: 215-226, 1972. 2. GIBBS, C. L., AND W. R. GIBSON. Energy production in cardiac isotonic contractions. J. Gen. Physiol. 56: 732-750, 1970. 3. HOMSHER, E., W. F. H. M. MOMMAERTS, AND N. V. RICCHIUTI. Energetics of shortening muscles in twitches and tetanic contractions. J. Gen. Physiol. 62: 677-692, 1973. 4. HOMSHER, E., W. F. H. M. MOMMAERTS, N. V. RICCHIUTI, AND A. WALLNER. Activation heat, activation metabolism and tension-related heat in frog semitendinosus muscle. J. Physiol. London 220: 601-625, 1972. 5. HOMSHER, E., AND J+ A. RALL. Energetics of shortening muscles in twitches and tetanic contractions. I. A reinvestigation of Hill’s concept of the shortening heat, J. Gen.. Physiol. 62: 663676, 1973. 1. CHAPMAN,
6. MOMMAERTS, W. F. H. M. Energetics of muscular contraction. PhysioZ. Rev. 49: 427-508, 1969. 7. RALL, J. A., E. HOMSHER, AND W. F. H. M. MOMMAERTS. Heat production and phosphocreatine (PC) hydrolysis with unloaded shortening in Rana pipiens semitendinosus muscles. Federation Proc. 32: 346, 1973. 8. RALL, J. A., AND B. A. SCHOTTELIUS. Energetics of contraction in phasic and tonic skeletal muscles of the chicken. J. Gem PhysioZ. 62: 303-323, 1973. 9. SMITH, I. C. H. Energetics of activation in frog and toad muscle. J. PhysioE. London 220: 583-599, 1972. 10. TAYLOR, S. R., R, RUDEL, AND J. R, BLINKS. Calcium transients in amphibian muscle. Federation Proc. 34: 1379-1381,-1975. 11. WILKIE, D. R. Heat, work and phosphylcreatine breakdown in muscle. J. Physiol. London 195: 157-183, 1968.
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Ohio State University,
RALL, JACK A. Dependence of energy output on force generation durirtg muscle contraction. Am. J. Physiol. 235(l): CZOC26, 1978 or Am. J. Physiol.: Cell Physiol. 4(l): C20-C26, 1978. -It has been proposed that the energy (heat + work) output of an isometric twitch is determined by the force that is generated under conditions of invariant activation, irrespective of muscle length. To test the effect of length and force on total energy output, muscles were stretched by increments beyond the muscle length at which twitch force is maximum (b) and then stimulated; energy output and force then were measured. These data were compared with isovelocity twitches in which stimulated muscles, initially at different lengths, shortened (near maximum velocity) a constant distance and then redeveloped tension at lengths < I+. If energy liberation was determined by force generation, plots of energy output versus force produced would be parallel with isovelocity twitches liberating extra energy as shortening heat. As predicted, the ratio of the slopes (n = 13) of these relations, 0.98 t 0.02, was not different from 1 and the shortening heat coefficient (&&, measured from the difference in intercepts), 0.15 t 0.01, was near to the expected value. Therefore, energy liberation in twitches appears to be uniquely determined by force generation and not by muscle length. Rana pipiens skeletal muscle; heat production; getics; isometric and isovelocity contractions
muscle ener-
IN AN ATTEMPT to develop a thermodynamic framework for theories of muscle contraction, it has been proposed (3, 6, 8) that the net energy (E) liberated by contracting muscle can be explained by the following relation
E = A + f(P, t) + aFX + W where A is a term representing muscle activation, and the other terms collectively designate the energy liberation associated with crossbridge cycling under different mechanical constraints. Specifically, the activation term represents the energetic effects of Ca2+ cycling starting with Ca2+ release from the sarcoplasmic reticulum (SR) and interaction with the myofibrils to active reaccumulation by the SR. Indirect evidence (4, 8, 9) suggests that this Ca2+ cycling energy liberation is independent of muscle length. The crossbridge cycling energy liberation includes a term associated with the work done by the muscle, W, and one associated with the energetic effects of shortening per se, aFX. Thus, the energy liberated as a consequence of shortening equals the distance shortened, X, multiplied by a shortening heat coefficient, CY~,whose value is dependent on the load during shortening. The general function,
Columbus,
Ohio 43210
f(P,t), represents the energy liberation associated with the development and maintenance of force. Presumably, during a twitch this function is dominated by force (4, 6, 8, 9). An important point in the above formulation is that muscle length per se is not considered a determinant of energy liberation. For example, this relation implies that isometric twitches of equal force generated at lengths less than I+, (L, is the muscle length at which twitch force is maximum) and at lengths greater than L, will liberate the same energy if the other terms in the relation remain constant. But a comparison of the results of Chapman and Gibbs (I), Homsher et al. (4), and Smith (9) clearly shows that isometric twitches of equivalent force liberate more energy at lengths less than L, than at lengths greater than L,. But this result is difficult to interpret because, at lengths less than L+, and specifically less than the muscle slack length, the muscle tends to lengthen toward L, during rest. Therefore, the subsequent twitch would be expected to liberate a larger than normal amount of energy attributed to internal shortening and internal work, i.e., W + +X. Also, the time integral of force development is different at short and long muscle lengths (9). In fact, Gibbs and Gibson (2) have attempted to explain muscle energy liberation in terms of the time integral of tension as an alternative to peak twitch tension. Moreover, it has never explicitly been proven that the energy liberation associated with force development per se in a twitch is dependent on the amplitude of force production and not the time integral of force production or muscle length. The experiments described in this paper have been designed to dissociate the effects of force production from muscle length and the time integral of force production and, thus, they test the proposition that, in a twitch, the term f(P, t) is best represented by the amplitude of force development alone. MATERIALS
AND METHODS
General. Specimens of Rana pipiens of both sexes were obtained from the Steinhilber Co. (Oshkosh, Wis.) and kept in moist tanks at 6OC.The tanks were flushed several times daily with cold water. On the day before an experiment an animal was killed by decapitation and the dorsal heads of a pair of semitendinosus muscles were dissected. The muscle pair, still attached to the pelvic bone, was aerated overnight in 95% 02, 5% CO2 at 4°C in a Ringer solution containing (mM): 95.0, NaCl;
cm 0363-6143/78/0000-0000$01.25 Copyright 0 1978 the American Physiological Society Downloaded from www.physiology.org/journal/ajpcell by ${individualUser.givenNames} ${individualUser.surname} (132.210.236.020) on January 12, 2019.
ENERGY
OUTPUT
DURING
MUSCLE
C21
CONTRACTION
20, NaHCO,; 2.5, KCl; 1.0, MgCl,; 1.0, CaCl,; at a pH of 7.0. All experiments were performed at 0°C. The muscle length at which twitch force was maximum, I+, ranged from 20 to 23 mm, whereas the blotted weight of the muscle pairs (M) ranged from 0.056 to 0.113 g. Peak twitch tension per cross-sectional area (P,, (L, /M)) averaged 248 t 5 mN/mm’ (mean t SE; n = 13) and the accompanying energy liberation averaged 17.8 t 0.5 mJ/g.
Myothermal measurements. Energy liberation during contractions at 0°C was measured as heat plus work produced, Experiments were designed in such a way that the internal and external work production was insignificant or was returned to the muscle during relaxation as heat. Heat production was measured with a calibrated integrating thermopile (5, 11). This type of thermopile minimizes sampling errors and uncertainties in calibration with some temporal resolution sacrificed in the process (e.g., see Fig. 1). It consists of a thermopile made of a series of 25pm silver plated constantan thermocouples contained in a region 2.25 cm in length, on which slabs of insulated silver 2.45 cm long, 0.4 cm wide, and 125 pm thick have been placed. A 12.5 ,urn diameter insulated Nichrome wire (California Fine Wire Co., Culver City, Calif.) was bonded to the silver surface on both sides of the thermopile to serve as a heating element by which the system could be calibrated. This thermopile has previously been described (5) and designated as W2. Calibration was performed as described previously (11). The calibration was performed twice on each muscle pair and the values, in millijoules per microvolts, were averaged. Thus, the output of the thermopile, in microvolts, was multiplied by the calibration factor for each muscle pair and divided by the blotted muscle mass to obtain the energy liberation in millijoules per gram. Myothermal records were corrected electronically for an exponential heat loss (7 = 15.6-26.5 s). For some of the isovelocity
A 0.3N
experiments the muscles shortened from a length greater than L 03 where resting tension was not zero. Passive shortening from these lengths results in a slight heat absorption because of the thermoelastic properties of the muscle. Therefore, a correction was made for this heat absorption by releasing the passive muscle at the same velocity and for the same distance and by recording the heat absorptio n and add ing it to the subsequent record in which the muscle was stimulated and released. The average maximum correction for heat absorption due to the thermoelastic properties of the muscle for any individual experiment was 4% (range, O-9%) of the net energy liberated during the contraction. Mechanical measurements . Force measurements were made with the use of capacitan .ce transducers having a resonant frequency of 3 kHz and a compliance of 0.02 pm/mN. When a muscle pair was constrained to contract at a constant velocity (isovelocity contraction) an ergometer, constructed from a modified speaker magnet and voice coil, was employed. Performance characteristics of this type of ergometer have been described (5). Briefly, the ergometer could provide displacements with a frequency response that was flat from 0 to 70 Hz. The ergometer was capable of positive and negative displacements, with velocities from 0 to 100 cm/s. Displacements were predetermined within the range of O-2 cm. The beginning of the displacement was timed within the range of 0 to 10 s with respect to the stimulus. Experimentul design. To test the proposition that energy liberation was dependent on force development and not on the time integral of force development or muscle length, the following experimental -approach was employed. Muscles were stimulated at various lengths beyond Lo to produce isometric twitches and energy output and force measured. These data were compared to isovelocity twitches in which stimulated muscles, initially at different lengths, shortened (near maximum velocity starting 30 ms after the stimulus) a constant distance and then redeveloped force at lengths less than Lo. These experiments allowed a comparison of the energy liberation for an equivalent force development at lengths less than and greater than I+ Under these conditions external work production, w, should be nearly zero and the shortening heat, cy~X, should be a constant factor. Thus plots of energy output versus force would be expected to be parallel with the isovelocity twitches liberating extra energy as shortening heat if energy liberation were determined by force generation. Experiments were done by alternating the order of the isometric and isovelocity series of contractions. During- any given experimental series that lasted 20-30 min the muscles were stimulated at 90-s intervals and 20-30 min of rest in Ringer was allowed between each series. Best fitting lines for the energy liberation versus force production data were determined with leastsquares linear regression analysis. 3
B b
6mJ/g
FIG. 1. Isometric twitch force production (A) and energy liberation (B) at 0,86 (b) and 1.2 L+-, (a). Although force generated was equivalent, preshortened contraction liberated 14% more energy. Note difference in time integral of force production and delay in force development. L, = 22 mm, muscle mass (blotted) (M) = 0.078 g. Initial deflection on heat records is stimulus artifact (both heat records start from same base line). Integrating thermopile obscures somewhat temporal resolution of heat signal.
RESULTS
Energy liberation and force production in shortened and stretched isometric twitches. Figure 1 shows a
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c22
J. A.
sample record of force production (Fig. 1A) and energy liberation (Fig. 1B) for two isometric twitches generating an equivalent force at a length greater than L, (Fig. la, 1.2 L,) and at a length less than L, (Fig. lb, 0.86 L,). Despite the peak force equivalency the twitch at 0.86 L, liberated approximately 14% more energy. The twitch at 0.86 L, displays a longer delay in force development with a shorter delay in energy liberation. This observation is probably accounted for by an increase in internal shortening at 0.86 L, with an increased shortening heat production. Also, the time integral of tension is less at 0.86 L, than at 1.2 L,. These data along with other results from this experiment are plotted in Fig. 2. For an equivalent force production, the preshortened muscle liberates more energy than the prestretched muscle. The significance of this result is questionable because of the probable increase in internal shortening heat and work production in the preshortened twitches, The stretch experiment in Fig. 2 is considered to produce the best estimates ofA and f (P, t) (4, 8, 9). The intercept in Fig. 2 from the prestretched isometric twitch data is interpreted as the energy liberation associated with Ca2+ cycling, A, and the slope, the energy liberation per unit force developed, is taken as a measure of the energetic effects of crossbridge cycling off (P, Q. Thus, the energy liberation during isometric twitches can be analyzed in the form
A
13 4 Lo r
RALL
0.9 6 L,
I
I
b
a
1.18 Lo
C
lOmJ/g
E = A + f(P, t> where f(P, t) includes the contribution of internal shortening heat and work to the isometric twitch. The average equation for these experiments (n = 13) is E, mJ/g = 6.01 (50.14) where
P,lP,,
is the ratio
+ 11.95 (~0,4O)P,lp,,
of the stretched
length
force
16
OSHORTEN
FIG. 2. Plot of energy liberation vs. isometric force development for preshortened twitches (0) and prestretched twitches (m). Data for preshortened series were obtained by shortening muscle to 0.82 L, and then stretchin .g bY increments and stimulating at various lengths. Data for prestretched series were obtained in a separate run by starting at I+, and stretching muscle by increments, stimulating to 1.32 I+,, and then returning to I+ by increments and stimulating. Same muscle as Fig. 1. Intercept is 37% of total energy produced at I.+, for stretched series. P,, L+,/M = 242 mN/mmK r (correlation coefficient) = 0.996 for preshortened series and 0.999 for prestretched series.
FIG, 3, Muscle I.ength (A), twitch force production m, and energy liberation (C) for an isometric contraction at 1.14 L( a) and an isovelocity contraction with shortening starting at 1.18 L, and ending at 0.96 I+ (b). For isovelocity twitch, 30 ms after stimulation, muscle was released at a constant velocity of 20 mm/s for 5 mm, redeveloping force 0.28 s after stimulation. Note: equivalency of force production, zero force developed during shortening, difference in time integral of tension, and difference in energy liberation. Heat record is uncorrected for heat absorption during isovelocity shortening due to thermoelastic properties of muscle. L, = 22 mm; M = 0.088 g.
production to the force developed at L,. The intercept is, on the average, 33% of the energy liberated at L+,. Energy liberation and force production in isovelocity and stretched isometric twitches. The experiment described above does not support the proposal that energy liberation is dependent on force and not muscle length. The experiments in this section are designed to overcome the difficulties of the preshortening experiment. Figure 3 is a sample record of two twitches producing an equivalent force. One twi tch was isometri .c (Fig. 3a) at 1.14 L, and the other was an isovelocity twitch (Fig* 3b) starting at 1.18 L, and redeveloping force at 0.96 I+ During the shortening at 2 cm/s no appreciable force was developed and, therefore, external work was zero. Despite the fact that the developed force was the same, the energy liberation was greater in the isovelocity twitch. This would be expected to be due to, at least in part, the shortening he& contribution to -the twitch. This sample result and other data from the same experiment are shown in Fig. 4. The lower line represents the results from the prestretched isometric
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ENERGY
OUTPUT
DURING
MUSCLE
c23
CONTRACTION
the muscle generates an equivalent force at a length less than L, as compared to a length greater than I+. The constant difference between the lines of Fig. 4 represents the shortening heat per gram of muscle, apX/M in mJ/g. For this example (Fig. 4) the value of the shortening heat coefficient, a&r (results are expressed per P,, to account for variation in intrinsic strength of different muscles), is 0,15. The average value is 0.15 t 0.01 (range, 0.11-0.18) (n = 13). Thus, the energy liberation in these isovelocity twitches can be described in the following way
24
E = A + f(P, t) + q,qX 0 ISOVE
LOCtTY
(2cmk)
and from the results of these experiments
4
E, mJ/g = 6.01(*0.14) + 11.95(*0.40)P,/Pot om 0
I
0.2
1
1
1
1
1
0.6 0.8 1.0 1.2 Force, N FIG. 4. Plot of energy liberation vs. force development for prestretched isometric twitches (a) and isovelocity twitches (0). Prestretched series was performed as described in Fig. 2. For isovelocity series muscle was stretched by increments from 1.05 to 1.2 I+ and released, at a velocity of 20 mm/s for 5 mm, 30 ms after stimulus. Force was redeveloped in range of 0.82-0.98 I&, 0.28 s after stimulus. Records have been corrected for thermoelastic heat measured during passive muscle shortening. Ratio of slopes, isovelocity to isometric, is 0.996. Open circles (0) on prestretched line are isometric twitches at beginning and end of isovelocity series of contractions. Same muscle as Fig. 3, &L,/M = 254 mN/mm? r = 0.996 for stretch data and 0.996 for isovelocity data.
+ 0.15(-+0.0l)x(P,,/M)
0.4
twitches as in Fig. 2. The upper line constitutes the data from isovelocity twitches like the one described in Fig. 3. In each twitch the muscle shortened the same distance at the same velocity. Redeveloped force was varied by varying the starting length, in this example from 1.05 to 1.2 I+,. Unlike the results in Fig. 2 the lines in this figure are parallel. The ratio of the slopes, isovelocity series/isometric series, is 0.996, The average ratio when zero force is developed during shortening is 0.98 t 0.02 (range, 0.91-1.09) (n = 13). Among individual experiments muscle shortening ranged from 2 to 5 mm (0.09-0.23 I+), at velocities from 14 to 20 mm/s, and force was redeveloped 0.17-0.28 s after the stimulus. As an approximate indication of the variability of any set of data about its regression line, the average correlation coefficient for the isometric data was 0.996 t 0.001 (n = 13) and, for the isovelocity data, 0.993 -t 0.002 (n = 13). Thus, when the large internal shortening of the preshortened isometric twitches is prevented, the energy that is liberated, which is attributed to force development, is not determined uniquely by muscle length. Also the energy liberation is not uniquely determined by the time integral of tension. This point is suggested by the difference in the time integral of tension shown in the records of Fig. 3. In fact, if one plots energy 1iberation versus the time integral of twitch tension for the data of Fi .g+ 4, the slopes are no longer parallel. The ratio of slopes becomes 1.55 instead of 0.996. If all the data are plotted in a similar fashion the average ratio of the slopes, isovelocity serieslisometric series, becomes 1.47 + - 0.06 (range, 1.1-1.95) (JZ = 13) instead of 0.98 * 0.02. The increased ratio of slopes results because the time integral of tension is less when
where X is in millimeters, grams.
P,, in newtons, and M in
DISCUSSION
It has been proposed (4, 9) that the energy liberated during an isometric twitch could be fractionated into a component attributed to Ca’+ cycling and another component associated with crossbridge cycling. Operationally this was done by plotting energy liberation as a function of prestretched isometric twitch force production as shown in Figs. 2 and 4. The intercept was interpreted to represent the Ca’+ cycling energy liberation (33% of the total in these experiments) and indirect evidence was provided that this value was length independent. The slope represented the crossbridge cycling energy liberation and this energy production was presumed to be best described as a function of the amplitude of the isometric force generation. This interpretation did not include muscle length as an unique determinant of energy liberation in isometric twitches. Nonetheless, Smith (9) has shown, and Figs. 1 and 2 verify, that the energy liberation is greater for an equivalent force at a length less than I+ than at a length greater than I+. It has been suggested (9) that the short length twitch liberated more energy because of an increase in internal shortening heat and in work production. Still the question remains: is muscle energy liberation uniquely determined by force production or muscle length? If the former is true it should be possible to demonstrate that the energy liberation associated with force production i.s the same, as long as the force is the same, irrespective of muscle length at which the force is generated. This is precisely what is shown in the experiment described in Figs. 3 and 4. Plots of energy liberati’on versus force production for isovelocity and prestretched isometric twitches are parallel (Fig. 4). The strict parallel relationship, ratio of slopes 0.98 t 0.02, strongly supports the contention that force development per se is a determinant of energy liberation and not muscle length. Also, this result appears to be independent of variations in the time integral of force production (Fig. 3). The quantitative difference between these straight line relationships (Fig. 4) represents the shortening heat. From this data a value for the shorten-
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C24 ing heat coefficient , aF /PO,, can be obtained, 0.15 t 0.01, which is similar to other results, 0.16-0.20 (3, 7). Thus, the formulation presented in the introduction can predict quantitatively the energy liberated in isovelocity twitches under these conditions. These results strongly suggest that the difference between the data in Fig. 2 can be attributed to an increase in internal shortening heat and work production as preshortened muscle length decreases. For example, if the difference in the intercepts of Fig. 2 is considered to be due predominantly to shortening heat production, it is possible to estimate the amount of muscle shortening that occurred under these conditions. Because the shortening heat, abTX(P,,/M), is 4.2 mJ/g from the difference in intercepts of Fig. 2 and aF = 0.14, P = 0.88 N and M = 0.078 g for this muscle pair, X bgcomes 2.7 mm or 12% of the muscle test length (L,). This calculation suggests that at extremely short muscle lengths the muscle shortens approximately 12% of L, when stimulated to produce an isometric twitch. Therefore, the twitch liberates more energy than would be predicted on the basis of force development alone. These results also provide indirect evidence that the energy liberation associated with Ca2+ cycling is not altered by muscle length (from L, to 1.33 L,) or by
J.
A. RALL
changes in muscle length (in the range of 0.78-1.22 L). The strict parallel relationship shown in Fig. 4 suggests that the energy liberation attributed to Ca*+ cycling (the intercept of the prestretched isometric twitches) is the same in the isovelocity twitches. Another, though less likely, possibility is that the Ca2+ cycling energy liberation changes with muscle length in such a way &s not to effect the parallel relationship or to make this relationship fortuitous. Recent experiments (10) with the Ca2+ sensitive bioluminescent protein aequorirr have shown that the light flash attributed to Ca2+ release is altered by muscle length. One would then predict that the energy liberation associated with Ca2+ cycling should also be altered. Apart from the fact that the aequorin experiments were done at a different temperature (15°C) than these experiments, the myothermic data reported herein suggest that if the amount of Ca2+ released changes with muscle length these changes must be small at 0°C. More experiments are needed to further clarify this point. Thi s work ation, Central Received
was supported, in part Ohio Heart Chapter.
26 September
1977; accepted
Y‘
by the American in final
form
Heart
Associ-
23 January
1978.
REFERENCES J. B., AND C. L. GIBBS. Energetics of isometric and isotonic twitches in toad sartorius. Biophys. J. 12: 215-226, 1972. 2. GIBBS, C. L., AND W. R. GIBSON. Energy production in cardiac isotonic contractions. J. Gen. Physiol. 56: 732-750, 1970. 3. HOMSHER, E., W. F. H. M. MOMMAERTS, AND N. V. RICCHIUTI. Energetics of shortening muscles in twitches and tetanic contractions. J. Gen. Physiol. 62: 677-692, 1973. 4. HOMSHER, E., W. F. H. M. MOMMAERTS, N. V. RICCHIUTI, AND A. WALLNER. Activation heat, activation metabolism and tension-related heat in frog semitendinosus muscle. J. Physiol. London 220: 601-625, 1972. 5. HOMSHER, E., AND J+ A. RALL. Energetics of shortening muscles in twitches and tetanic contractions. I. A reinvestigation of Hill’s concept of the shortening heat, J. Gen.. Physiol. 62: 663676, 1973. 1. CHAPMAN,
6. MOMMAERTS, W. F. H. M. Energetics of muscular contraction. PhysioZ. Rev. 49: 427-508, 1969. 7. RALL, J. A., E. HOMSHER, AND W. F. H. M. MOMMAERTS. Heat production and phosphocreatine (PC) hydrolysis with unloaded shortening in Rana pipiens semitendinosus muscles. Federation Proc. 32: 346, 1973. 8. RALL, J. A., AND B. A. SCHOTTELIUS. Energetics of contraction in phasic and tonic skeletal muscles of the chicken. J. Gem PhysioZ. 62: 303-323, 1973. 9. SMITH, I. C. H. Energetics of activation in frog and toad muscle. J. PhysioE. London 220: 583-599, 1972. 10. TAYLOR, S. R., R, RUDEL, AND J. R, BLINKS. Calcium transients in amphibian muscle. Federation Proc. 34: 1379-1381,-1975. 11. WILKIE, D. R. Heat, work and phosphylcreatine breakdown in muscle. J. Physiol. London 195: 157-183, 1968.
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