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Department of Physiology, University of Aarhus, DK-8000 Århus C, Denmark
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ABSTRACT |
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In rat skeletal muscle, electrical stimulation increases Ca2+ influx leading to progressive accumulation of calcium. Excitation-induced Ca2+ influx in extensor digitorum longus (EDL; fast-twitch fibers) and soleus muscle (slow-twitch fibers) is compared. In EDL and soleus, stimulation at 40 Hz increased 45Ca uptake 34- and 21-fold and 22Na uptake 17- and 7-fold, respectively. These differences may be related to the measured 70% higher concentration of Na+ channels in EDL. Repeated stimulation at 40 Hz elicited a delayed release of lactic acid dehydrogenase (LDH) from EDL (11-fold increase) and soleus (5-fold increase). Continuous stimulation at 1 Hz increased LDH release only from EDL (18-fold). This was associated with increased Ca2+ content and was augmented at high extracellular Ca2+ concentration ([Ca2+]o) and suppressed at low [Ca2+]o. The data support the hypothesis that excitation-induced Ca2+ influx is mediated in part by Na+ channels and that the ensuing increase in intracellular Ca2+ induces cellular damage. This is most pronounced in EDL, which may account for the repeated observation that prolonged exercise leads to preferential damage to fast-twitch fibers.
lactic acid dehydrogenase release; electrical stimulation; Na+ channels; muscle damage; extensor digitorum longus
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INTRODUCTION |
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ELECTRICAL STIMULATION OF skeletal muscle has been shown to produce a marked increase in the uptake of Ca2+, both in vivo (18, 19, 37) and in vitro (7, 22, 24). We have recently obtained evidence that the major part of this uptake is mediated by Na+ channels (22). It would be expected, therefore, that excitation-induced Ca2+ uptake should increase as a function of the concentration of Na+ channels in skeletal muscle. Accordingly, extensor digitorum longus (EDL) muscles, which contain more Na+ channels than soleus muscles (3), should show a larger excitation-induced influx of Na+ as well as of Ca2+.
An increased resting concentration of free intracellular Ca2+ ([Ca2+]i) has recently been reported following chronic low-frequency stimulation of rat hindlimb muscle (9). Experiments using the Ca2+ ionophore A23187 have shown that that increased [Ca2+]i leads to ultrastructural damage in mouse diaphragm (35). Because cellular damage induced by contractile activity has often been attributed to effects of Ca2+ ions on proteases and lipases (1, 4, 15, 25, 26), it would be of interest to determine whether excitation-induced damage can be detected in soleus and EDL muscles and possibly related to Ca2+ influx. Studies have shown that Ca2+-activated proteases are capable of degrading cellular membranes (39). Loss of cellular integrity can be monitored by measuring the release of large intracellular proteins, e.g., lactic acid dehydrogenase (LDH) (26, 30). The present study was initiated to test two hypotheses: 1) the initial rates of 22Na and 45Ca influx depend on the concentration of Na+ channels in rat soleus and EDL muscles; and 2) the excitation-induced release of LDH from soleus and EDL muscles can be related to the influx and accumulation of Ca2+. Part of the results have been presented in a preliminary form (21).
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MATERIALS AND METHODS |
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Animals. Most experiments were carried out using fed female and male Wistar rats weighing 60-70 g (4 wk old). All handling and use of animals complied with Danish animal welfare regulations and American Physiological Society principles. The animals had free access to fodder (Altromin pellets Nr. 1314, Spezialfutter-werke, Lage, Germany) and water and were kept in a thermostated environment (21°C) with constant day length (12 h). Animals of this size were chosen to obtain muscles of sufficiently small size (20-25 mg) to ensure adequate oxygenation and diffusion of substrate during incubation. A few experiments were performed using adult (22-24 wk old) female Naval Marine Research Institute mice (muscle weight 8-16 mg).
Muscle preparation and incubation. The animals were killed by decapitation, and intact soleus or EDL muscles were dissected out as previously described (10, 27). The standard incubation medium was a Krebs-Ringer bicarbonate buffer (pH 7.4) containing (in mM) 120.2 NaCl, 25.1 NaHCO3, 4.7 KCl, 1.2 KH2PO4, 1.2 MgSO4, 1.3 CaCl2, and 5 or 10 D-glucose. Incubations took place at 30°C under continuous bubbling with a mixture of 95% O2 and 5% CO2 in a volume of 2-5 ml. After preparation, the muscles were equilibrated in the standard medium for 30 min before further incubation. This procedure has been shown to allow the maintenance of constant K+, Na+, and Ca2+ contents for several hours in vitro (14, 16). Control experiments measuring tetanic force every 10 min in EDL and soleus muscles showed that this remains constant for at least 2.5 h in vitro.
Electrical stimulation. An experimental setup allowing the simultaneous direct stimulation of 12 muscles was used. Each muscle was placed between two platinum electrodes surrounding the central part of the muscle. The muscles were mounted at resting length so as to allow isometric contractions. Single pulses with an amplitude of 10 V and a duration of 1.0 ms were used. Frequency, amplitude, and pulse duration were checked with a HAMEG HM 207 oscilloscope.
45Ca uptake. Resting and stimulation-induced uptake of 45Ca was determined essentially as earlier described (12, 16). After 30-min equilibration in unlabeled buffer, the muscles were incubated in buffer containing 45Ca (0.5 µCi/ml) for 15 min so as to allow the isotope to reach all fibers. Stimulation occurred during the last 30-60 s of this incubation. This was followed by washout (4 × 30 min) at 0°C in 3 ml Ca2+-free Krebs-Ringer bicarbonate buffer containing 0.5 mM EGTA to remove extracellular Ca2+. The muscles were then blotted, weighed, and soaked overnight in 3 ml 0.3 M TCA. The following day, the activity of 45Ca in the TCA extract was determined by liquid scintillation counting (Packard, TriCarb 2100 TR). After correction for loss of intracellular Ca2+ during the washout in the cold (for details, see Ref. 22), the 45Ca uptake was calculated from the specific activity of 45Ca in the incubation buffer. The excitation-induced uptake was calculated from the difference in intracellular 45Ca between the resting and stimulated muscles.
22Na uptake.
Resting and stimulation-induced 22Na uptake was measured as
45Ca uptake with the following exceptions: the incubation
time with 22Na was reduced to 5 min to avoid reextrusion of
22Na already taken up by the muscles; and during the last
part of this incubation, soleus muscles were stimulated for 60 s,
whereas EDL muscles were only stimulated for 15 s. After
incubation, the muscles were washed (4 × 15 min) at 0°C in 3 ml
Na+-free Tris-sucrose buffer to remove extracellular
22Na (17). 22Na activity of the
TCA extract was determined by
-counting. As previously described,
the values for 22Na uptake were corrected for loss of
intracellular 22Na during the washout in the cold
(11). This procedure was shown to allow the quantification
of excitation-induced increase in 22Na influx
(23).
Determination of LDH. Muscle cell integrity was monitored by measuring LDH release into the incubation medium. After the muscles were mounted for isometric contractions and incubation in 5 ml buffer, they were prewashed (4 × 30 min) before stimulation. This was done to wash out any LDH released from cells damaged during excision of the muscles. The muscles were either stimulated at 40 or at 1 Hz. The muscles stimulated at 40 Hz were either given one bout of stimulation of 30- or 60-s duration or 30 bouts of stimulation of 30-s duration with 90 s of rest in between. All muscles were then allowed to rest for 120 min. The 1-Hz stimulation was given continuously for 240 min. During the entire incubation period, the muscles were moved to new tubes every 30 min, and 250-µl buffer samples were taken immediately after removal of the muscle.
The activity of LDH in the buffer was determined by measuring the decrease in the concentration of the substrate NADH by conversion of pyruvate to lactate (expressed as U/g wet wt; 1 unit being the amount of enzyme that catalyzes the utilization of 1 µmol substrate/min). The 250-µl buffer sample was mixed with 2.65 ml of a phosphate buffer (0.1 M, K2HPO4 titrated with KH2PO4 to pH 7.0) containing NADH (0.4 mM) and pyruvate (0.4 mM), and the absorbance of NADH was measured at 340 nm 30 s after mixing and again 4 min after mixing. The temperature was kept at 30°C. Spontaneous release of LDH was monitored in resting control muscles. The amount of LDH released during the incubations was related to the total tissue content of LDH, which was determined as follows: tissue samples weighing 20-25 mg were homogenized at 0°C in 2 ml phosphate buffer (0.1 M, pH 7.00). This was done by homogenizing for 15 s with an ULTRA-TURRAX (T25) tissue homogenizer and by 15 passes with a Potter-Elverhjelm homogenizer. After centrifugation of the homogenate at 0°C (2,100 g, 10 min), the LDH activity in the supernatant was determined as described above.Ca2+ contents. Muscles weighing 20-25 mg were soaked overnight in 3 ml 0.3 M TCA. Ca2+ content was determined by atomic absorption spectrophotometry (Philips PU 9200, Pye Unicam, Cambridge, UK) using 1.5 ml of the TCA extract after addition of KCl to a final concentration of 2.4 mM (18). The muscle extracts were measured against a blank, and standards (12.5, 25, and 50 µM CaCl2) containing the same amount of TCA and KCl. This procedure was shown to give the same values for Ca2+ content as the previously used procedure in which Ca2+ was measured in the clear supernatant obtained by centrifugation of a homogenate in 0.3 M TCA.
Na+ contents. Muscles weighing 20-25 mg were soaked overnight in 3 ml 0.3 M TCA. The Na+ content of the TCA extract was determined using a Radiometer FLM3 flame photometer (Copenhagen, Denmark) with lithium as internal standard.
[3H]saxitoxin binding.
The concentration of Na+ channels was determined as the
specific displaceable saxitoxin binding essentially performed as
earlier described (3, 23) Intact muscles
weighing 20-25 mg were incubated for 2 h at 4°C in
Krebs-Ringer bicarbonate buffer containing [3H]saxitoxin
(0.05 µCi/ml) and unlabeled saxitoxin to a final concentration of
2.5 × 10
8 M. After incubation, the muscles were
blotted, weighed, and soaked overnight in 2 ml 0.3 M TCA. The activity
of [3H]saxitoxin in the TCA extract was determined by
liquid scintillation counting. The unspecific uptake was determined as
the [3H]saxitoxin taken up by the muscle after 2 h
incubation at 4°C in Krebs-Ringer bicarbonate buffer containing
[3H]saxitoxin (0.05 µCi/ml) and unlabeled saxitoxin to
a final suprasaturating concentration of 2.5 × 10
6
M. With the use of specific activity of [3H]saxitoxin in
the incubation buffer, specific displaceable
[3H]saxitoxin binding was calculated as the difference
between the total [3H]saxitoxin uptake in muscles
incubated in 2.5 × 10
8 M saxitoxin and the
unspecific uptake of [3H]saxitoxin in contralateral
controls incubated in 2.5 × 10
6 M saxitoxin.
Force development. In control experiments, the effects on contractility of long-term low-frequency stimulation was tested using force transducers, as previously described in detail (13).
Chemicals and isotopes. All chemicals used were of analytical grade. TTX and nifedipine were purchased from Sigma Chemical (St. Louis, MO), saxitoxin was from Calbiochem (Bad Soden/TS, Germany), and NADH and pyruvate were from Boehringer Mannheim (Germany). 45Ca (0.59 Ci/mmol) was obtained from the Danish Atomic Energy Commission (Risø, Denmark), and 22Na (4.1 Ci/mmol) and [3H]saxitoxin (39 Ci/mmol) were from Amersham International (Buckinghamshire, UK).
Statistics. Results are given as mean values ± SE. The statistical significance of any difference between groups was ascertained using t-test for unpaired observations.
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RESULTS |
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22Na and 45Ca uptake during electrical
stimulation.
As shown in Fig. 1, electrical
stimulation at 40 Hz induced a significant increase in the uptake of
22Na in both soleus and EDL. Compared with the rate of
uptake in resting soleus, stimulation induced a sevenfold increase,
whereas in EDL, the increase was 17-fold. The stimulation-induced
uptake was more than twice as high (+121%) in EDL than in soleus.
Likewise, 45Ca uptake was increased by electrical
stimulation (21-fold increase in soleus and 34-fold in EDL; Fig.
1B). Again, the stimulation-induced uptake was twofold
higher (+100%) in EDL than in soleus. When the extracellular
concentration of Ca2+ was increased from 1.27 to 5.00 mM,
the stimulation-induced 45Ca uptake increased twofold in
soleus (from 0.069 µmol · g wet wt
1 · min
1 at 1.27 mM Ca2+ to 0.135 µmol · g wet wt
1 · min
1 at 5.00 mM
Ca2+) and threefold in EDL (from 0.141 µmol · g
wet wt
1 · min
1 at 1.27 mM
Ca2+ to 0.469 µmol · g wet wt
1
· min
1 at 5.00 mM Ca2+), the increase in
45Ca uptake now being 250% higher in EDL than in soleus.
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1 · min
1 for soleus and 0.183 ± 0.029 µmol · g wet wt
1 · min
1 for EDL, corresponding to a 6- and 28-fold increase,
respectively.
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6 M), the
stimulation-induced uptake of 45Ca in EDL muscle was
reduced by 79% (Fig. 3). A similar
reduction was observed in soleus muscle (
71%). Stimulation in the
presence of both TTX and the L-type Ca2+-channel blocker
nifedipine (10
5 M) reduced the uptake of 45Ca
to the level of the resting controls. In the resting muscles, TTX and
nifedipine produced no significant change in 45Ca uptake.
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Na+ channels.
As shown in Table 1, the concentration of
Na+ channels measured using a [3H]saxitoxin
binding assay was 70% higher in EDL than in soleus. This difference
could, for a large part, explain the higher stimulation-induced uptake
of 22Na in EDL compared with soleus. In soleus, the
stimulation-induced uptake of Na+ equaled 2.69 nmol
· g wet wt
1 · action potential
1,
which accords very well with earlier observations (33).
This corresponded to an average of 261 Na ions · channel
1 · action potential
1. In
EDL, the stimulation-induced Na+ uptake corresponded to an
average of 339 Na ions · channel
1 · action
potential
1.
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6 M), indicating that it largely
depends on the opening of Na+ channels. 45Ca
uptake was twofold higher in EDL than in soleus.
LDH release To evaluate whether electrical stimulation and possibly the Ca2+ taken up during stimulation resulted in muscle fiber damage, release of the enzyme LDH from the muscle cells was measured as a marker of loss of cellular integrity.
Applying the protocols from the previous experiments (stimulating EDL at 40 Hz for 30 s or soleus at 40 Hz for 60 s) did not give rise to an efflux of LDH neither during stimulation nor during the following 120-min rest period. When stimulation at 40 Hz was repeated 30 times, no increase in LDH release was observed during the final 30 min of stimulation. However, a marked delayed release of LDH was observed following 90 min of rest. To determine the fraction of LDH released, total LDH activity was measured in EDL and soleus muscle homogenates. In EDL, the activity was 585 ± 13 U/g wet wt, and in soleus, it was 185 ± 8 U/g wet wt measured using the LDH assay and recorded at 30°C (n = 6 muscles). In the experiments with repeated stimulation at 40 Hz, the fraction of LDH released from EDL during a 30-min sampling period reached 0.56% 90-120 min after cessation of stimulation, which is an 11-fold increase from the resting rate of release (P < 0.001). In soleus, the stimulation at 40 Hz led to a significant (P < 0.01), although smaller (5-fold), increase in LDH release (Table 2).
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1 · 240 min
1, corresponding to
2.0% of the total LDH content. In buffer containing 5.00 mM
Ca2+, the accumulated loss was 22.5 U · g wet
wt
1 · 240 min
1, corresponding to
3.8% of the total LDH content. At 0.30 mM Ca2+, the
accumulated loss was 5.2 U · g wet wt
1 · 240 min
1, which is 0.9% of the total. In comparison, at
1.27 mM Ca2+, the resting muscles released 2.75 U · g wet wt
1 · 240 min
1, which is 0.5%
of the total.
To test whether mechanical force could be causing the release of LDH,
contractile force of the EDL muscle during long-term stimulation at the
different Ca2+ concentrations was tested in separate
experiments using force transducers. After 120 and 240 min of
stimulation at 1 Hz in normal Krebs-Ringer, EDL muscle maintained
42 ± 1% and 37 ± 3% of the original force (5.5 ± 1.0 g, n = 7), respectively. EDL muscles stimulated at 5.00 mM Ca2+ maintained 44 ± 3% and
40 ± 4% of the initial force after 120 and 240 min,
respectively. When placed in buffer with only 0.30 mM Ca2+,
the muscle maintained 31 ± 2% and 29 ± 1% of the initial
force after 120 and 240 min of stimulation, respectively
(n = 3-4). Earlier reports have shown that soleus
maintains 72% of the initial force (7.8 ± 0.8 g,
n = 4) after 240 min of stimulation at 1 Hz at 1.27 mM
Ca2+ under similar conditions (22). These
results show that despite the fact that soleus muscle continues to
develop force after 240 min of stimulation at 1 Hz, no release of LDH
was observed. Furthermore, the large increase in LDH release observed
in EDL muscle incubated at 5.00 mM Ca2+ was not associated
with an increased force development compared with the muscles
stimulated at 1.27 mM Ca2+. These observations indicate
that the loss of LDH cannot be the outcome of mechanical damage as
such. Conversely, the 80% reduction in LDH release observed in muscles
stimulated in 0.30 mM Ca2+ compared with muscles stimulated
in 1.27 mM Ca2+ cannot be explained by a large loss of excitability.
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DISCUSSION |
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Na+ and Ca2+ fluxes in EDL and soleus. In skeletal muscle, excitation is elicited by the opening of voltage-dependent Na+ channels and ensuing influx of Na+. In keeping with this, electrical stimulation elicits a marked rise in the uptake of 22Na (17, 23), which increases with the frequency of stimulation. We have previously shown that this excitation-induced 22Na uptake is closely correlated to a concomitant uptake of 45Ca and that the uptake of both ions is suppressed by TTX. The excitation-induced 45Ca uptake could not be attributed to Na+/Ca2+ exchange (22). More importantly, veratridine, which increases the open time of Na+ channels, also stimulates the uptake of 45Ca, and this effect is suppressed by TTX (22). These observations suggested that Na+ channels could mediate Ca2+ influx, and a recent publication demonstrated that also in cardiac myocytes, Na+ channels may mediate Ca2+ influx (36). The present study was initiated as a further testing of the hypothesis that in skeletal muscle, Na+ channels may transport Ca ions.
We have compared EDL, a muscle mainly composed of fast-twitch fibers, with soleus, which contains mainly slow-twitch fibers. We find that EDL contains 70% more Na+ channels than soleus. The increase in 22Na uptake induced by electrical stimulation is 121% larger in EDL than in soleus. In EDL, intracellular Na+ is lower (11.2 ± 0.8 µmol/g wet wt, n = 12) than in soleus (15.3 ± 0.5 µmol/g wet wt, n = 5) (33), and the membrane potential in EDL is more negative than in soleus (32). Thus the electrochemical gradient for Na+ is steeper, and this could contribute to the somewhat larger excitation-induced Na+ influx per channel. The excitation-induced 45Ca uptake was 100% larger in EDL than in soleus. In EDL, 79% of the excitation-induced increase was suppressed by TTX, and when nifedipine was added on top of that, the excitation-induced 45Ca uptake was reduced to zero. Previous studies have shown that nifedipine alone only reduces the excitation-induced 45Ca uptake by 17% and that uptake of 45Ca in the presence of veratridine was not significantly reduced by addition of nifedepine (22). This indicates that only a minor part of the excitation-induced Ca2+ influx is mediated by Ca2+ channels. TTX prevents excitation and obviously may prevent excitation-induced Ca2+ influx. It is difficult, therefore, in experiments with electrical stimulation to prove that the TTX-suppressible fraction of 45Ca uptake is mediated by Na+ channels. In favor of this idea, however, is our observation that in EDL, the stimulation-induced increase in 22Na and 45Ca uptake is 121% and 100% larger than in soleus, respectively. Thus the larger population of Na+ channels in EDL is associated with almost the same relative elevation of excitation-induced influx of Na+ and Ca2+. Moreover, as can be calculated from the values given in Table 1, the ratio between the excitation-induced uptake of 22Na and 45Ca per action potential in the two muscles is closely comparable (140:1 in soleus and 138:1 in EDL). Measurements of Na+-channel permeability in frog and rat skeletal muscle showed that no inward currents could be detected with only Ca2+ in the extracellular medium (8, 34). However, in these studies, the Ca2+ concentration used was 90 mM or higher, and as pointed out by Campbell and Hille (8), due to the "hyperpolarizing" effect of such high Ca2+ levels, the potentials used in the experiments might have been insufficient to open Na+ channels. This would prevent the detection of any Ca2+-mediated current. At variance with this, our studies were performed using a Ca2+ concentration of 1.27 mM, and the Ca2+-uptake data were based on the measurement of isotopic Ca2+. Stimulation experiments using soleus and EDL muscle from adult mice showed that the difference in excitation-induced 45Ca uptake is not restricted to rat muscle. The standard 40-Hz stimulation procedure resulted in an excitation-induced uptake in mouse soleus and EDL that was very close to that observed in rat muscle. There was, however, a larger difference between the excitation-induced uptake in soleus and EDL with EDL taking up four times as much Ca2+ as soleus. This could be related to the fact that the muscles from adult mice are completely differentiated with a higher fraction of fast-twitch fibers in EDL and a lower fraction of slow-twitch fibers in soleus. This differs from 4-wk-old rats in which the differentiation of fibers is not yet complete (5).Excitation-induced LDH release. During prolonged stimulation with single twitches, LDH release increased markedly in EDL but not in soleus. In EDL muscle, this was associated with a significant increase in Ca2+ content, whereas in soleus, the same stimulation regime was earlier shown to produce no significant increase in Ca2+ content (22). In EDL, the stimulation-induced increase in LDH release was markedly augmented when extracellular Ca2+ was increased to 5.00 mM and abolished when Ca2+ was lowered to 0.30 mM. Moreover, increasing Ca2+ from 1.27 to 5.00 mM clearly increased the excitation-induced uptake of 45Ca. In view of the fact that these experiments were all performed using muscles of the same size, the difference in LDH release is unlikely to reflect variations in diffusional delay.
The experiments performed with EDL stimulated in the presence of 0.30 mM Ca2+ or soleus in the presence of 1.27 mM Ca2+ indicate that the LDH release is not the simple outcome of mechanical damage resulting from the contractions. Using repeated tetanic contractions (40 Hz, 30 s on, 90 s off) caused no increase in the release of LDH during stimulation. It did, however, give rise to a delayed release of LDH measured after 90 min of rest. The events leading to damage of the cellular membrane seem to be initiated during stimulation. The damage may take a while to develop, thereby resulting in a delay in LDH release. Furthermore, the diffusion of the large LDH molecule out of the muscle may add to the delay. In EDL, an 11-fold increase in the fractional release of LDH was observed, whereas in soleus, the increase was only fivefold, once again in line with the twofold higher excitation-induced 45Ca uptake in EDL compared with soleus. Taken together, these observations provide strong evidence that the excitation-induced LDH release and plasma membrane leakage depend on the entry of Ca2+ and are likely to be due to an ensuing rise in intracellular Ca2+. The present observations indicate that in muscles with predominantly fast-twitch fibers (EDL), excitation-induced Ca2+ uptake is larger and cell leakage is more pronounced than in muscles with predominantly slow-twitch fibers (soleus). This may explain the repeated observation that during exercise, fast-twitch fibers are more prone to undergo damage than slow-twitch fibers (20, 29, 31, 38).Perspectives
Accumulating evidence indicates that in skeletal muscle, Ca2+ stimulates protein breakdown (2, 28, 40). In skeletal muscle of exercised rats, the Ca2+-sensitive protease calpain was found to be activated (4). Activation of intracellular proteases may degrade membrane proteins (39) leading to the loss of cellular integrity observed in the present stimulation experiments.Also, in sepsis, Ca2+-influx and -content are increased in skeletal muscle, and this is associated with increased protein degradation (6). Taken together, these observations suggest that prolonged elevation of cytoplasmic Ca2+ in skeletal muscle is a general cause of muscle cell damage.
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ACKNOWLEDGEMENTS |
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We thank Ann Charlotte Andersen, Tove Lindahl Andersen, Ebba de Neergaard, Marianne Stürup-Johansen, and Vibeke Uhre for skilled technical assistance.
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FOOTNOTES |
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This study was supported by grants from the Danish Medical Research Council (J.No. 9802488) and the Danish Biomembrane Center.
Address for reprint requests and other correspondence: H. Gissel, Dept. of Physiology, Univ. of Aarhus, DK-8000 Århus C, Denmark (E-mail: HGN{at}fi.au.dk).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Received 17 December 1999; accepted in final form 17 April 2000.
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