Effect of fatigue on rate of isometric force development in mouse fast- and slow-twitch muscles C. J. BARCLAY Department

of Physiology,

University

of Auckland, Auckland, New Zealand

Barclay, C. J. Effect of fatigue on rate of isometric force development in mouse fast- and slow-twitch muscles. Am. J. Physiol. 263 (CeU Physiol. 32): C1065C1072, 1992.-Changes in the rate of isometric force development with fatigue were measured in vitro (25°C) using mouse soleus and extensor digitorum longus (EDL) muscles. Muscles were fatigued using 30 tetanic contractions. Rate of force development was determined from the rate constant of an exponential curve fitted to the rising force phase of a tetanus. For both muscles, when the intertetanus interval was 3 s, maximum isometric force and relaxation rate were significantly reduced in the final tetanus relative to the values in the first tetanus. Rate of force development in soleus muscles transiently increased and then decreased a small amount. The final rate was 92.7 2 3.3% (n = 4) of the initial rate. In contrast, the rate of force development in EDL muscles increased to 133.7 k 3.3% (n = 4) of the initial rate. This increased rate was evident from the second tetanus of the series, was fully established after 5 tetani, and the magnitude of the increase in rate was inversely proportional to intertetanus interval and was independent of presumed energy expenditure. The enhanced rate decayed with a time constant of 14.3 t 2.0 s and was independent of presumed energy expenditure. Most of these observations can be explained by the effects of Pi on cross bridge kinetics. Other possible mechanisms, involving more rapid activation, are also suggested. skeletal muscle; rate of rise of force; inorganic valbumin

phosphate;

par-

MANY ASPECTS ofmuscle fatigue have been studied in detail, there have been very few reports, and no systematic investigation, of changes in the rate of force development with fatigue. The rate at which force is developed at the start of an isometric tetanus depends on the processes involved in activation of the myofilaments by Ca2+ and the subsequent generation of force by the actin-myosin cross bridges. Although changes in rate of force development have not been investigated, available evidence indicates that both activation and cross bridge kinetics are likely to be altered in fatigued muscle. Isometric force development is generally thought to be limited by steps in the cross bridge cycle, subsequent to activation (1, 31). If so, the rate of isometric force development would depend on the rates of cross bridge attachment and the subsequent transition of cross bridges to a force-producing state (see Refs. 7 and 11 for details of this cross bridge model). It is known that the net rate of these two processes is greater when the concentration of Pi around the myofibrils is increased (11). Elevated Pi concentration is a characteristic of fatigued muscle (see Ref. 33 for a review). Therefore, if cross bridge kinetics determine the rate of force development, it might be expected that isometric force development would be more rapid in fatigued muscle. However, little is known about how other changes to the intracellular environment of fatigued muscle might affect cross bridge attachment. For example, in fatigued frog muscle fibers, the rate of isometric force development is slowed,

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although the rate at which stiffness increases at the start of the contraction is unaltered (7). Thus the delay between cross bridge attachment, as indicated by stiffness, and transition to a force-producing state appeared to have been increased by fatigue. This indicates that other effects of fatigue, besides Pi accumulation, may also affect force development. It has also been suggested that force development, at least in the early stages of a tetanus, may be limited by the kinetics of activation by Ca2+ rather than cross bridge kinetics (8). In moderately fatigued muscle, the peak intracellular Ca2+ concentration during a tetanus is greater than that in the unfatigued muscle (32), indicating that the Ca2+ concentration gradient between the sarcoplsmic reticulum (SR) and the myofibrils is increased. If so, then activation would be more rapid and, assuming activation kinetics limit the rate of force development, force would develop more rapidly. Thus, regardless of whether the initial rate of force development in a tetanus is limited by activation kinetics or cross bridge kinetics, it is reasonable to predict that isometric force will develop more rapidly in moderately fatigued muscle. This hypothesis was tested in the current investigztion using both fast- and slowtwitch muscles from the mouse. One of the distinguishing features of these two types of muscle is the contrast in their ability to resist fatigue (28). In general, the mechanical performance of slow-twitch muscle is relatively unaffected by repeated contraction. In contrast, the mechanical performance of fast-twitch muscle becomes impaired more rapidly and to a greater extent than that of slow-twitch muscle. Therefore, if fatigue is expected to be associated with an increased rate of force development, and since mechanical properties of fasttwitch muscles are generally more altered by fatigue than those of slow-twitch muscle, then it would be anticipated that the relative increase in the rate of force development will be greater in a fast-twitch muscle than in a slow-twitch muscle. In accordance with the general fatigue resistance of slow-twitch muscle, a series of fatiguing tetani caused only small changes in the rate of force development in the slow-twitch soleus muscle. The rate initially increased and then decreased. In accordance with the above hypothesis, the rate of force development in the fast-twitch extensor digitorum longus (EDL) muscle increased as the muscle fatigued, and the magnitude of this change was much greater than that seen in the soleus muscle. METHODS Preparation Soleus and EDL muscles were dissected from adult female mice (Swiss, CDl) weighing 16-20 g. Animals were killed by

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CO, narcosis.All proceduresconformed with local ethical standards. A total of 32 soleusand 38 EDL muscleswas used.The cross-sectionalarea of muscleswas estimated by dividing muscle massby length, assuminga cylindrical geometry and a density of 1.06 mg/mm3 (29). The mean cross-sectionalarea of soleusand EDL muscleswas0.35 & 0.02 and 0.46 t 0.03 mm2, respectively. Theseareascorrespondto averageradii of 0.33mm for soleusmusclesand 0.38 mm for EDL muscles. During dissectionand experiments, muscleswere bathed in oxygenated (95% O,-5% CO,) Krebs-Henseleit solution of the following composition (in mM): 118 NaCl, 4.75 KCl, 1.18 MgS04, 24.8 NaHCO,, 1.18 KH2P04, 2.54 CaCl,, 10.0 glucose,and 0.025d-tubocurarine, aswell as 20 U/l insulin. Force recordings were madewith musclesheld vertically in a stainlesssteelchamber containing -100 ml of solution. The chamber was immersedin a water bath to maintain the temperature at 25°C.

IN FATIGUE

force signalswere well describedby a single exponential (r* > 0.98, SE estimate < 0.08 mN for maximum forces typically 100 mN). After each experiment, musclelength and mass(blotted and with tendons removed) were measured.Force wasnormalized for musclecross-sectionalarea. Experimental

Protocols

At the start of each experiment, muscle length was set to slightly above slack length, and the stimulus strength for maximal twitch force was determined. For the remainder of the experiment a supramaximal stimulus, 20% above that producing maximum twitch force, was used. This stimulus strength wastypically 35 V/cm. A seriesof brief tetani were then usedto set musclelength to that at which maximum tetanic force was produced (l,,). A contraction protocol, consistingof 30 tetanic contractions, wasdevisedto fatigue muscles.Stimulus pulsefrequencieswere Stimulation and Force Recording set to those that had been found to produce maximum tetanic Stimulation, data acquisition, and data analysis were con- force for each muscle.For EDL musclesthe frequency was200 trolled by a laboratory microcomputer (Tandon PCA) running Hz and for soleusmuscles120 Hz. The duration of tetani was custom-written programs.Force data were acquired usinga 12- 0.9 s for EDL and 1.5 s for soleusmuscle.These combinations bit A/D converter (LabMaster, Scientific Solutions). Muscles of pulsefrequency and tetanus duration resultedin both muscles were stimulated via a pair of platinum plate electrodes,0.8 cm receiving the samenumber of stimulus pulsesin eachtetanus. apart, using 100~ps rectangular pulses.Pulse duration and fre- The severity of the contraction protocol was varied by altering quency were set by a stimulator (Digitimer DlOO), and the the interval betweencontractions (the time betweenthe cessaduration of tetanic contractions was controlled by the micro- tion of stimulation in onetetanus and the start of stimulation in the next) while keeping tetanus duration constant. Intervals computer. Muscles were mounted with one tendon clamped to a rigid ranging from 3 to 120 s were used. frame and the other end attached to a force transducer via a short length of hypodermic wire (26-gauge,British Standard Statistical Analysis Wire Gauge). A silk thread (6-O) was used to tie the muscle One-way analysis of variance wasusedto assessthe statistitendon to the wire connecting rod. The force transducer con- cal significance of alterations in measuredvariables during a sisted of a magnesium alloy bar with semiconductor strain contraction protocol and with intertetanus interval. Where necgauges(KS-2-E3, Kyowa) bonded to its upper and lower sur- essary,post hoc analysiswasperformed using a modification of faces.The resonant frequency of the transducer, with hypoder- the Scheffe test describedby Rodger (26). A paired Student’s t mic wire attached, was800 Hz. Power spectral analysisof force test was used to assessthe influence of muscle length during records revealed that the maximum frequency componentsof fatigue on the changesin measuredvariables. All statistical thesesignalswere~100 Hz at 25°C. Force signalswere sampled decisionsweremadewith respectto the 95% level of confidence. at between 300 and 500 Hz. The total complianceof the trans- Resultsare presentedas meanst SE. ducer and silk thread was 2 pm/mN. This correspondedto a decreasein musclelength of -2% when maximum tetanic force RESULTS was produced. On-line analysis of isometric force signalsinvolved calcula- Change in Rate of Force Development tion of maximum force and rates of force development and Force signals recorded from EDL and soleus muscles in relaxation. Rates of force development and relaxation are ex- the first and last contractions of the most severe contracpressedas the rate constant of a single exponential function tion protocol used (3-s intervals between contractions) fitted to the time courseof the rising and falling phases,respec- are shown in Fig. 1. In both muscles maximum force is tively, of the force record (31). Rate of force development was reduced, although the extent of this reduction is much determinedfrom a curve fitted between5 and 90% of the maximum force. Relaxation rate was determined from the force greater in the EDL muscle. In addition, the slowing of signal recorded after stimulation had ceasedby fitting a curve relaxation that occurs in fatigued muscle is apparent. It is over the region between 80 and 15% of the force immediately very difficult to assess from these signals whether the rate before cessationof stimulation. Both these sections of tetanic of force development has altered. To visualize changes in B

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Fig. 1. Examples of force recordings from extensor digitorum longus (EDL; A) and soleus (B) muscles in 1st and last tetani of a series of 30 contractions. Intertetanus interval was 3 s for both muscles. In both muscles, final contraction is that in which peak force is lowest and relaxation slowest. In final tetanus of series, rate of force development in EDL muscle had increased to 139% of value in 1st tetanus. In 1st tetanus rate was 24.1/s and in final tetanus was 33.51s. For soleus muscle, rate of force development in final tetanus was reduced to 92.6% of rate in 1st. Absolute rates in 1st and last tetani were 12.2 and 11.3/s, respectively.

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FORCE DEVELOPMENT Tetanus

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Fig. 2. Force development and relaxation phases from same force recordings as shown in Fig. 1. Force has been normalized to emphasise changes in rates of force development and relaxation. Markedly shorter time required for force to develop to a maximum (i.e., faster rate of force development) in fatigued EDL muscle is clearly visible (A). In contrast to rate of force development, force relaxation in EDL is considerably slowed. Development of force in fatigued soleus muscle followed a very similar time course to that in 1st tetanus of series (B). As in EDL muscle, relaxation rate was clearly slowed.

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force dynamics more clearly, the force development and relaxation phases, with maximum forces normalized, are shown in Fig. 2. The striking observation is that, in the final (30th) contraction of the series, force developed by EDL muscles reaches its maximum level more rapidly than in the first unfatigued contraction (Fig. 2A). Thus the fatigued EDL muscle develops force more rapidly, although to a lower absolute level (Fig. lA), than a fresh muscle and also relaxes more slowly. In soleus muscle, this enhanced rate of force development after 30 tetani is entirely absent (Fig. 2B). Relaxation is slowed, but less dramatically than in the EDL muscle. The average changes in maximum force and in the rates of force development and relaxation for soleus and EDL muscles are summarized in Table 1. Time Course

Figure 3 shows the rate of force development in successive tetani during a series of 30 contractions. The rate of force development in EDL muscles in the second tetanus of the series is already significantly greater than that in the first tetanus. After just five tetani, the rate of force development is the same as in the final tetanus of the series. The average rate constant of force development in the first contraction was 33.1 t 1.2/s (time constant of 30.2 ms). In the 30th contraction the rate of force development had increased to 133.7 t 3.3% of that in the first contraction. To determine whether the increase in rate of force development in EDL muscles depended on tetanus duration, the initial part of the contraction series, in which the rate increased, was performed using much shorter tetani. Using 0.15-s tetani (but still with an intertetanus interval of 3 s), the rate in the fifth tetanus had increased to 117.1 t 3.7% (n = 4) of the initial value (Fig. 3). When Table 1. Comparison of effect of a series of 30 tetani on maximum force, rate of force development, and rate of relaxation in EDL and soleus muscles EDL

Soleus

Maximum force 38.4t2.5 88.6k1.5 Rate of force development 133.7t33 92.7t3.3 Rate of force relaxation 56.6k3.7 76.3k2.2 Values are means & SE of each variable in last tetanus of series expressed as percentage of value in 1st tetanus; n = 4. All these final values differ significantly from those measured in 1st tetanus of series. EDL, extensor digitorum longus.

tetanus duration was 0.9 s, the corresponding value was 132.0 t 5.7% (n = 4). Tetanus duration also affected the change in relaxation rate over a series of five contractions. In the first tetanus of the series, there was no significant effect of tetanus duration on relaxation rate. After five 0.9-s tetani, relaxation rate was reduced to 85.4 -+ 1.4% of the initial rate. However, when using 0.15-s tetani, relaxation rate in the fifth tetanus had actually increased slightly to 107.6 t 3.4% of the initial rate. The rate of force development in soleus muscles also changed significantly during the series of tetani. The rate was significantly greater than that in the first tetanus between the 8th and 13th contractions and significantly lower in the final tetanus. However, the magnitudes of these changes were very small. In the first contraction, the rate of force development in soleus muscles was 14.8 t 1.0/s (time constant of 67.6 ms). In the final tetanus, the average rate was 13.7 t 0.5/s or 92.7 t 3.3% of the rate in the first tetanus. The inconsequential functional effect of such a small change in the rate of force development is evident from the force signals (Fig. 2B). Influence of Intertetanus

Interval

A set of experiments was performed to assess the influence of the interval between contractions on the changes in rate of force development. The effect of the time interval between tetani on the magnitude of changes in both force and rate of force development over a series of 30 contractions is shown in Fig. 4. When the intertetanus interval was 30 s or less, the force produced by EDL muscles decreased significantly (Fig. 4A). The more closely spaced the contractions, the greater the decrease in force. When the intertetanus interval was 3 s, force fell from an initial value of 307.4 t 32.4 mN/mm2 (n = 4) to a final value equivalent to 38.4 t 2.5% of this initial force. For force development, the converse was true; the rate increased significantly for all intervals of 12 s and less, and the magnitude of the increase was greatest at the shortest intertetanus interval. Thus the greatest increase in rate of force development (to 133.7 t 3.3% of the initial value) coincided with the greatest decrease in force (to 38.4 t 2.5%). F or soleus muscles, the only significant changes in both force and rate of force development occurred in the two most severe contraction protocols, in which the intertetanus intervals were 3 and 5 s (Fig. 4B). When the interval was 3 s, force decreased to 88.6 t 1.5% of the initial value (320.7 t 29.1 mN/mm2, n = 4), and the

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FORCE DEVELOPMENT

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Fig. 3. Rate of force development, relative to rate in 1st tetanus of series (horizontal line), in successive tetani in a series. Time interval between tetani, for both EDL and soleus muscles, was 3 s. Open symbols, data from EDL muscles. Circles, values recorded during series of 0.9-s tetani; squares, rate of force development recorded from five 0.15-s tetani, also with interval of 3 s.

rate of force development initial value.

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decreased to 92.7 t 3.3% of the

Influence of Magnitude of Energy Expenditure

The changes in muscle function with fatigue probably result from alterations in myoplasmic composition (5,9). The majority of metabolites that accumulate in fatigued muscle (e.g., Pi, H+, ADP, see Ref. 33) are products of the breakdown of ATP and phosphocreatine. Because force generation is the major energy-consuming process in contracting skeletal muscle (12), the accumulation of metabolites should be reduced if force generation is reduced. This can be achieved by reducing the overlap between the actin and myosin filaments. To assess whether metabolite accumulation may underlie the alterations in rate of force development, eight EDL and six soleus muscles underwen t both the stan .dard fatigue protocol and also performed anoth .er series of 30 tetani in which only the first and last tetani were performed with muscle length at 1,; the intervening tetani were all performed with muscle length at 120% 1,,. At this length, tetanic force was reduced to -40% of that produced at 1,. The order of presentation of the two protocols was varied so that equal numbers of muscles performed each of the two protocols first. When muscle length was 120% l,, changes in the rate of force development were assessed between the first and last tetani, both of which were performed at 1,. To quantify the total decrease in force generation in the series of tetani, the total force-time integral (the sum of the force-time integrals for each tetanus) was determined. The total force-time integral was significantly lower when muscle length was 120% 1, during the fatigue protocol ,. For soleus and EDL muscles, the force-time integral was reduced to 65 -t 13 and 61t 11%, respectively, of that at 1,. When soleus muscles were fatigued at 120% l,, the slight slowing in the rate of force development was eliminated and, in fact, reversed. The final rate of force development was 107.6 t 2.4% of the rate at the start of the series. In contrast to soleus, the change in rate of force development in the EDL muscle was unaffected by in-

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Fig. 4. Effect of intertetanus interval on changes in maximum force and rate of force development between 1st and last (i.e., 30th) tetani of series of 30 for EDL (A) and soleus (B) muscles. Both variables are expressed as value in final tetanus relative to that in 1st tetanus of series. For both EDL and soleus muscles, 4 muscles were used at each intertetanus interval, except 2 longest intervals, for which 3 of each type of muscle were used. Note nonlinear time scale where numbers label actual intervals used.

creasing muscle length during the protocol. In the final tetanus (performed at 1,) after a series at 120% l,, the rate of force development was 131.4 t 3.9% of the initial rate, not significantly different from the value of 123.9 t 6.1% I measured at the end of 30 tetani performed at 1,. The increase in muscle length did have some influence on EDL function, however. The slowing of relaxation with fatigue was significantly less when muscles were fatigued at 120% 1, (final value 81.5 t 2.5% of initial value vs. 69.2 t 1.5% at 1,). Disappearance of Enhanced Rate of Force Development in EDL Muscles

The time course of decay of the enhanced rate of force development observed in EDL muscles was estimated by comparing the rate of force development in pairs of tetani separated by various intervals. Figure 5 shows how the magnitude of the increase in rate of force development in the second .tetanus varied with intertetanus interval. This relations hlP presumably reflects the tim .e course of the reversal of the process underly ,ing the enhanced rate.

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Fig. 5. Rate of force development in EDL muscles in 2nd of 2 tetani separated by varying intervals. Rate is expressed as percentage of that recorded in 1st tetanus of pair. Each symbol represents mean value for 4 muscles, except those with intervals of 60 and 120 s, for which 3 muscles were used. An exponential curve has been fitted through mean values using a nonlinear least-squares method. Equation of this curve is y = 28.4 X e(t/o-07)+ 99.7.

Nonlinear regression indicated that the data are adequately fitted by a single exponential with a time constant of 14.3 t 2.0 s. Inclusion of a second exponential term did not significantly improve the fit. DISCUSSION

The results reported above represent the first systematic investigation of force development in fatigued muscle and provide a test of the hypothesis that rate of force development would be increased with fatigue. The data obtained from soleus, at least in the early stages of fatigue, and EDL muscles supported this hypothesis. The striking increase in the rate of isometric force development in fatigued EDL muscles (Figs. 3 and 4) is a novel finding; the few reports in t !he li terature concerning changes in the rate of isometric force development during fatigue, and which include amphibian (7) and fast- and slow-twitch mammalian muscle (2, 18), reveal either a decrease or no change in rate with fatigue. Such results are consistent with those obtained from soleus muscle in the later stages of the fatigue protocol in the current study but are at odds with the result for EDL muscles. However, no previous study has used EDL muscle. For example, Brust (2) also observed a decrease in rate of tetanic force development in mouse soleus muscle. However, as an example of a fast-twitch muscle he used the gastrocnemius muscle, which has a distinctly different fiber type composition to EDL (see Ref. 10). Force development slowed with fatigue in this muscle too (2). The data obtained in the current investigation, showing the contrast between the fast- and slow-twitch muscles (Fig. 2), the time course of the onset (Fig. 3) and decay (Fig. 5) of the enhanced rate of force development in EDL muscle, and the influences of both the total amount of force-generating activity and also the intertetanus interval (Fig. 4) on the magnitude of the change, together provide a sound basis for identifying the underlying mechanism. The major events in the initial development of force in skeletal muscle can be divided into two categories as follows: 1) activation events, including the release of Ca2+

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from the SR, its diffusion to the myofibrils and binding to troponin C, and 2) cross bridge events, i.e., the attachment of actin-myosin cross bridges and their subsequent generation of force. It is generally thought that cross bridge events limit the rate of isometric force development (for review, see Ref. 1). However, this idea is derived almost exclusively from work on amphibian muscle, and there is some evidence that it may not be applicable to mammalian muscle at temperatures ~20°C (25). It has been suggested that, at least in the initial stages of force development, activation kinetics limit force development (4, 8). Contrasts between EDL and soleus muscles in some of the current experiments also raise the possibility that the rate of force development may be limited by different factors in the two muscles. For example, during a series of tetani, the rate of force development in soleus muscles showed only a small transient increase and then decreased, whereas force development in EDL was greatly elevated throughout the contraction protocol. Furthermore, the decrease in rate of force development in soleus muscle was reversed when the total force-time integral was reduced, whereas this procedure had no effect on the change in rate of force development in EDL muscles. Therefore, the following discussion of possible mechanisms underlying the changes in force development considers both activation and cross bridge processes. In addition, alterations to the series compliance of muscle, which produce prominent changes in the rate of isometric force development, are also considered. Series Compliance

The characteristics of elastic elements in series with the contractile element of a muscle are a major determinant of the time course of isometric force development. An increase in series compliance slows the rate of force development (Fig. 8 of Ref. 34). This raises the possibility that the increased rate of force development by EDL muscles reflected a sustained decrease in series compliance (i.e., increased stiffness) that persists for up to 30 s after a tetanus. The notion that the series compliance decreases as the series elastic element comes under tension during a tetanus, and then, following the tetanus, returns back to its precontraction state so slowly seems improbable. In fact, the compliance of the series elastic element of frog muscle, even at O’C, increases rapidly after a contraction (15). Prolonged changes in the series compliance of EDL muscles cannot therefore account for the increased rate of force development. Alterations in Cross Bridge Kinetics

Many experiments, using amphibian muscle, have demonstrated that the rate of isometric force development is limited by cross bridge events occurring after activation of the myofibrils by Ca2+ (1). In this case the * rate of isometric force development depends on the rate of cross bridge attachment and/or the subsequent rate of transition of attached cross bridges to a force-producing state. The only investigation of this aspect of fatigued muscle, using frog muscle fibers, indicated that the rate of cross bridge attachment was unaltered by fatigue but that there was a greater delay before attached cross bridges

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began to generate force, resulting in a slower rate of force development (7). To account for an increased rate of force development, as observed in EDL muscles, requires more rapid cross bridge attachment and/or a more rapid transition to the force-producing state in fatigued muscle than in unfatigued muscle. In some situations, such changes in cross bridge kinetics do occur. Myosin light chain phosphorylation. The rate of force redevelopment during steady-state activation of skinned fast-twitch, but not slow-twitch, muscle fibers from the rat and rabbit is proportional to the extent of myosin light chain phosphorylation (20). However, the temporal pattern of changes in light chain phosphorylation, the mechanism thought to underlie posttetanic potentiation of twitch force, is not consistent with this phenomenon underlying the enhanced rate of force development by EDL muscles observed in the present study. In mouse EDL muscles at 25”C, the phosphate content of myosin light chains does increase during a series of contractions but then continues to increase for a further 20 s after the contractions have ceased (24). In addition, the subsequent decrease in light chain phosphate content is very slow, with a time constant of -5 min (24). In contrast, the increase in rate of force development in mouse EDL muscles was greatest immediately after a tetanus and then decayed with a time constant of -14 s. In light of these temporal inconsistencies, it is improbable that the increased rate of force development by EDL muscles observed in the current study reflected any change in myosin light chain phosphorylation. The effects of Pi on cross bridge kinetics. One of the distinctive characteristics of fatigued muscle, particularly fast-twitch muscle, is an elevation in myoplasmic Pi concentration (see Ref. 33 for a review). Pi affects cross bridge kinetics in a manner that is consistent with the observed changes in maximum force and rate of force development in fatigued EDL muscles. Increased Pi concentration reduces maximum force (5, 9, 11) and also increases the rate at which cross bridges attach and begin to generate force (11). Furthermore, the time course of the onset (Fig. 3) and persistence (Fig. 5) of the enhanced rate of force development, and its dependence on tetanus duration (Fig. 3), are also in accordance with the expected temporal pattern of changes in Pi concentration. For example, in rat muscle undergoing a series of contractions, Pi concentration increased rapidly during the first few contractions before settling to a steady elevated level (17). Once the contractions ceased, Pi concentration returned to precontraction values with a time constant of 29 s at 33°C (17).

One piece of evidence is not consistent with the notion that metabolite accumulation was involved in the enhanced rate of force development; reducing the total force-time integral, and hence, presumably, the steadystate level of Pi, did not reduce the magnitude of the increase in force development. However, it is not certain that metabolite accumulation would have been reduced sufficiently to affect the change in force development, assuming this to be the basis of the enhanced rate in fatigued EDL muscles. Countering this objection, however. was the finding that the procedure was effective in

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reducing the slowing of relaxation with fatigue. The rate of force development by soleus muscles increased a small amount both in middle of the series of tetani (Fig. 3) and also when the total force-time integral was reduced. If accumulation of Pi caused the increased rate of force development in both muscles, then it would be predicted that the rate of force development would increase less in soleus muscle, because Pi concentration would be lower than in EDL muscle (6). However, force development eventually became slower in the soleus muscle and hence may also be affected by some other factor(s). As mentioned previously, the different effects on force development in the two muscles of reducing the total force-time integral suggests that force development is sensitive to different factors in soleus and EDL. The rate of force development may even be limited by different processes in the two muscles. Ca2+ Kinetics and Rate of Force Development If the rate of force development is n.ot limited

bY cross bridge kinetics, then is it possible that fo rce deve lOPment in these muscles is limited by the kinetics of activation by Ca2+3 There is evidence that the process limiting the rate of force development in rat soleus and EDL muscle is different at temperatures ~20°C than at lower temperatures. As temperature is increased beyond 2O”C, the factor by which reaction velocity changes per 10°C (QlO) of the rate-limiting process is reduced from 2.5 to 1.6 (25). The high Q10 at low temperatures suggests th .at chemical kinetics, such as cross bridge interaction, are in volved in the rate-limiting process. The low &lo at higher temperatures is more suggestive of a mechanism involving dfifusion, for example activation. The relative SR contents of frog and mouse muscle provides further indirect evidence that is qualitatively con sistent with the notion that, in mouse EDL muscle, in con trast to frog muscle, activation may be slow relative to cross bridge events. The SR content of mouse EDL muscle cells is only 60% of that of frog sartorius muscle; only 5.5% of EDL -muscle cell volume -is occupied by SR (19) compared with 9.1% of frog sartorius (22). However, for a quantitative assessment of activation kinetics in the two muscles, more detailed information regarding, for example, the relative surface areas of the terminal cisternae and the density and opening probabilities of Ca2+ release channels in the two muscle types would be required. This information is not available for both types of muscle. However, the differences described are sue h tha .t it is not unreasonable to assume that activation is slow in mouse EDL muscles compared with that in frog muscle. If the rate of activation does limit force development, then the rate of force development would depend on the net flux of Ca2+ from the SR to troponin C binding sites on the myofibrils and on the sensitivity of the contractile elements to Ca 2+. The latter, determined from the slope of the relation between force and Ca2+ concentration, decreases in conditions designed to mimic fatigue (9) and hence could not account for an increased rate of force development. The rate at which Ca2+ diffuses from the SR to the myofibrils depends on the rate of release of Ca2+ from the SR. the Ca2+ concentration gradient between the SR and l

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myofilaments, and on the rates of Ca2+ uptake by the SR and other Ca2+ buffers, such as parvalbumin. In moderately fatigued mouse muscle, the concentration gradient may actually be greater than that in unfatigued muscle. Peak intracellular free Ca2+ concentration is greater in moderately fatigued mouse muscle fibers, although, as fatigue becomes more severe, peak Ca2+ levels decrease (32). In addition, alterations to myoplasmic composition are likely to slow the removal of Ca2+ from the myoplasm into the SR (32), which would also tend to accelerate the transfer of Ca2+ from the SR to the myofibrils. Although the release of Ca 2+ from the SR and its diffusion to the myofibrils involves many interacting factors (for review see Ref. 33), it is possible that the flux of Ca2+ to the myofibrils is increased in moderate fatigue. As pointed out previously, the time course of removal of some metabolites is also similar to the time course of diminution of the enhanced rate of force development in EDL muscles. Hence changes in net rate of diffusion of Ca2+ could have contributed to the increased rate of force development seen in EDL muscles and, transiently, in soleus muscles. Parvalbumin and rate of force development. Another possible mechanism is founded on the premise that the intracellular Ca2+ buffer parvalbumin affects the rate of transfer of Ca 2+ from the SR to the myofibrils. Parvalbumin is present in high concentrations in mouse EDL muscles (-0.4 mM; see Ref. 10). The kinetics of parvalbumin-Ca2+ reactions have been determined for purified parvalbumin from frog muscle and can be used to assess whether parvalbumin could affect Ca2+ transfer to the myofibrils in the early stages of a tetanus. In the following calculations it has been assumed that the Ca2+ binding kinetics of frog muscle parvalbumin, determined in vitro (14), are applicable to parvalbumin in living mouse muscle. Parvalbumin binds Ca2+ sufficiently rapidly (this rate is limited by dissociation of Mg2+ from parvalbumin) that a significant proportion of the Ca2+ released during the force development phase of a tetanus could be bound as follows: 0.4 mM parvalbumin binds 0.8 mM Ca2+ (23) with a rate constant of 0.93/s at 0°C (14) or, using a &lo of 1.9 (13), a rate of 4.6/s at 25OC. Assuming 40% of the parvalbumin binding sites are already occupied by Ca2+ at rest (14), then during the force development phase of contraction of an EDL muscle (0.1 s), -0.1 mM Ca2+ could be bound. This is likely to be a significant fraction of the total (free plus bound) intracellular Ca2+ during the force development phase of a tetanus. For example, in frog sartorius muscle, which has 40% more SR (22) than mouse EDL muscle (19), the total intracellular Ca2+ concentration during a prolonged tetanus reaches 0.9 mM (30). Not only does parvalbumin have the potential to bind a large fraction of Ca2+ released during force development, but also the rate of dissociation of Ca2+ from parvalbumin is sufficiently slow [time constant -0.6 s at 25°C (14), assuming a Q 1o of 2.3 (13)] that a second contraction could commence before all the bound Ca2+ had dissociated from parvalbumin. In this case, less Ca2+ would be bound during the rising phase of the second contraction, enhancing the net flux of Ca2+ from the SR

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to the myofibrils. The degree of saturation of parvalbumin binding sites would increase in successive contractions until a steady state was reached. Furthermore, brief tetani would result in a lower degree of saturation of parvalbumin than longer tetani. Brief tetani were observed to result in a smaller increase in rate of force development (Fig. 3), again consistent with the idea that the enhanced rate of force development was a consequence of the saturation of parvalbumin with Ca2+. Thus the observed changes in rate of force development in EDL muscle are qualitatively consistent with the idea that force development in these muscles was limited by the flux of Ca2+ to the myofibrils and that this was influenced by parvalbumin. In quantitative terms, the most obvious discrepancy is that the elevated rate of force development persisted much longer (time constant of decay - 14 s) than would be predicted from the measured rate of dissociation of Ca2+ from parvalbumin purified from frog muscle (time constant -0.6 s). Assuming this rate of dissociation is indeed applicable to mouse muscle, there is some evidence that, in the myoplasm, dissociation proceeds much more slowly than in vitro determinations indicate. For example, measurement of the decline of myafter stimulation (again in oplasmic Ca2+ concentration frog muscle fibers) has revealed a very slowly declining component (16, 21). This slow component, thought to reflect Ca2+ dissociating from parvalbumin, has a time constant of between 8 and 13 s at 25OC (16, 21, 27), assuming a Qlo of 1.4 (21). It is not clear why the dissociation rate would be so much slower in vivo than in vitro. It could arise from a protracted elevation of myoplasmic Ca2+ concentration following a contraction, resulting in further binding of Ca2+ to parvalbumin during this time (3). It is interesting, however, that the estimated time constant for the decay of the elevated rate of force development in mouse EDL muscles is very similar to that of the slow phase of decline in myoplasmic Ca2+ concentration in frog muscle. Two other observations made in this investigation are also consistent with the parvalbumin hypothesis. Assuming that force development in mouse soleus muscles is also limited by Ca 2+ kinetics, then the absence of any large increase in rate of force development in these muscles is in accordance with their lack of parvalbumin (10). The lack of effect of reducing the total force time integral of the increase in rate of force development in EDL muscles can also be explained in terms of the parvalbumin hypothesis. Parvalbumin-Ca2+ interactions would be expected to be independent of actin-myosin overlap and largely unaffected by moderate variation in metabolite levels. Conclusion

Several mechanisms have been proposed to account for the observed changes in force development, particularly the striking increase in force development rate in fatigued EDL muscle. Most of the observations on EDL, and to some extent soleus, muscle can be explained in terms of the effect of Pi accumulation on cross bridge kinetics. Two alternative mechanisms, based on the premise that force development is limited by activation kinetics rather than cross bridge kinetics, were also proposed. Both these

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mechanisms involve an enhanced rate of transfer of Ca2+ from the SR to the myofilaments. In one proposal, changes in SR Ca 2+ handling result in a steeper Ca2+ concentration gradient between the SR and myofilament. The alternative activation-based mechanism raised the possibility that the binding of Ca2+ by parvalbumin may affect the rate of force development in EDL muscles. It is, however, beyond the scope of the current experiments to distinguish among these mechanisms proposed to underlie, in particular, the striking increase in rate of force development in EDL muscles. Invaluable technical assistance was provided by S. Glasson. Drs. D. Loiselle (Auckland) and D. A. Smith (Monash) provided helpful comments on ideas contained in this manuscript. This work was funded by the Auckland Medical Research Foundation’s Isaacs Medical Research Fellowship. Address for reprint requests: C. J. Barclay, Dept. of Physiology, Monash Univ., Clayton, Victoria 3168, Australia. Received 19 November 1991; accepted in final form 9 June 1992.

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