1Division of Sport and Recreation, Auckland University of Technology, Auckland 1020; 2Department of Physiology, School of Medicine, University of Auckland, Auckland 92019, New Zealand; and 3Department of Cellular and Molecular Medicine, Neuromuscular Research Center, University of Ottawa, Ottawa, Ontario, Canada K1H 8M5
Submitted 31 December 2003 ; accepted in final form 11 May 2004
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ABSTRACT |
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potassium; skeletal muscle contraction; membrane potential; myotonia
There are several reasons to consider the involvement of Cl in fatigue processes. Cl channels are present in the surface and transverse (t) tubular membranes of mammalian skeletal muscle (4, 11, 14, 19), and Cl moves into muscle during t-tubular action potentials (20) or with K+-induced depolarization of the sarcolemma (27, 36). Intense electrical stimulation or exhaustive exercise is associated with raised [Cl]i in animal and human muscle (17, 22, 24, 25, 30), and although plasma [Cl] is largely unchanged (24, 30, 31), the [Cl] in the lumen of the t tubules may fall as Cl enters the muscle fiber. However, to date, t-tubular [Cl] has not been measured, and the extent to which the transsarcolemmal Cl gradient changes during fatigue is unknown.
Several authors have suggested that Cl channels may diminish K+ efflux and/or stabilize the membrane potential (EM) during stimulation, i.e., prevent excessive depolarization (1, 11, 14, 15, 31, 32). The detrimental effects of a decreased K+ gradient across the sarcolemma, which occur during some types of fatigue (17, 22, 25, 3032), are thought to be mediated by depolarization of the sarcolemma, leading to inactivation of Na+ channels and hence causing a smaller action potential amplitude and inexcitability (7, 32, 37). Normal extracellular [Cl] ([Cl]o), together with high sarcolemmal Cl conductance, may protect against the detrimental effects of K+ on membrane potential. Indeed, K+-induced depolarization in nonfatigued muscle occurs more rapidly and to a greater extent at low than at normal [Cl]o (13, 14, 21, 26).
The few studies that have looked at the effect of [Cl]o on contractile performance during fatigue have presented conflicting findings (6, 12, 16). Fatigue during a prolonged tetanus was more rapid at low [Cl]o (15 mM) in soleus muscle fibers (6) or when the sarcolemmal Cl conductance was pharmacologically reduced in extensor digitorum longus (EDL) muscles (12). In contrast, De Luca et al. (12) found that fatigue with repeated tetanic stimulation was attenuated. When [Cl]o was lowered by one-half in diaphragm muscle, the moderate fatigue observed with repeated tetanic stimulation was unaffected (16). These discrepancies could be explained if a possible Cl effect on fatigue depended on the fatigue paradigm of the muscle studied.
The findings and arguments presented above led to our main hypothesis: normal [Cl]o protects against excessive fatigue in situations in which run-down of the transsarcolemmal K+ gradient occurs. These situations include 1) higher stimulation frequencies and longer durations, thereby inducing greater K+ movement as a result of more action potentials; 2) continuous rather than intermittent tetanic stimulation due to less time for recovery of K+ gradients; and 3) stimulation of fast-twitch EDL rather than slow-twitch soleus muscles because of greater K+ movement per action potential in fast-twitch muscle (31). Preliminary results were presented previously in abstract form (9).
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MATERIALS AND METHODS |
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Adult female mice (Swiss CD-1) of 2030 g body wt were killed by cervical dislocation or anesthetized with pentobarbital sodium (Somnotol; MTC Pharmaceuticals, Cambridge, ON, Canada) by intraperitoneal injection (0.8 mg/10 g body wt). Intact muscles were dissected in the control solution, which was continuously gassed with carbogen (95% O2-5% CO2) at room temperature (2123°C). Soleus and EDL muscles were used as representatives of slow-twitch and fast-twitch muscles, respectively (5, 7). The study was approved by the Animal Ethics Committee of the University of Auckland and the Animal Care Committee of the University of Ottawa.
Solutions and Chemicals
The control physiological saline solution was composed of (in mM) 122.2 NaCl, 25.0 NaHCO3, 2.8 KCl, 1.2 KH2PO4, 1.2 MgSO4, 1.3 CaCl2, and 5 D-glucose and was equilibrated with carbogen. This solution contained 128 mM Cl, which is slightly higher than the values of 95120 mM Cl normally seen in the extracellular fluid of humans and other mammals (4, 24, 25, 31). Solutions with low [Cl] (10 mM) were created by replacing NaCl with equimolar sodium methylsulfate (Sigma). A very low [Cl] was chosen rather than a Cl-free solution, in which resting EM are unstable (2, 13, 16, 29). In a few experiments, gluconate was tested as the Cl substitute, but the resting force was unstable and there was a large transient depression of peak tetanic force, which may be related to Ca2+ binding (4). These effects differed from those of methylsulfate, so gluconate was not used further. Solutions with raised [K+] (9 mM) were created by replacing 5 mM NaCl with 5 mM KCl in the control or low [Cl] solution, referred to as 9K or 10Cl + 9K solutions, respectively. In a few experiments, 9-anthracene carboxylic acid (9-AC) (Sigma-Aldrich), a drug that blocks the sarcolemmal Cl channel (2, 4, 11), was used. 9-AC was dissolved in ethanol and then diluted in the control solution to produce a final concentration of 100 µM; this concentration was used previously to abolish Cl effects completely (2, 4, 11). The temperature of solutions in all experiments was 25°C.
Force Recording and Stimulation
Two experimental setups were used as described in detail previously (5). In the first setup, isometric contractions were evoked by electrical stimulation using two massive parallel platinum plates that engulfed the muscle. These plate electrodes provide a uniform electric field over the entire muscle and presumably trigger an action potential simultaneously at all sites along the length of the surface membrane, and the action potential then propagates down the t-tubular membranes. Muscles were mounted vertically by their tendons to a force transducer (semiconductor strain gauge KSP-2-E3; Kyowa Electronic Instruments, Tokyo, Japan) in 100 ml of solution in a muscle chamber and then immersed in a temperature-controlled water bath. The standard bipolar stimulation pulses (28 V/cm, 0.1 ms) were supramaximal for the twitch. They were computer generated and delivered to the plate electrodes via a purpose-built MOSFET (metal-oxide semiconductor field-effect transistor) power amplifier. Twitches and tetanic contractions of varying duration were initiated from a computer using a custom-written LabVIEW program. Contractions were displayed simultaneously on a chart recorder (Gould model 2400), with selected contractions recorded digitally (at 400 Hz) on the computer.
In the second setup, both force and EM were measured in the same muscle. Isometric contractions were evoked using two platinum wires, which traversed the muscle in a plane above and below the muscle and were located toward the ends of the muscle. These wire electrodes presumably triggered an action potential over a smaller area of sarcolemma, which is first propagated along the surface membrane before descending the t-tubular membranes. Muscles were mounted horizontally by their tendons to a force transducer (Cambridge model 300) in a 2-ml chamber. A flow-through system (15 ml/min) permitted oxygenated saline solution to enter the muscle chamber and subsequently to be recirculated. Stimulation pulses generated with a Grass S88 stimulator and a Grass SIU5 isolation unit (10 V, 0.3 ms) were supramaximal for the twitch. Contractions were continuously monitored on a chart recorder, while selected contractions were recorded using a Keithley Metrabyte analog-to-digital board (model DAS-50). Sampling rates were 20 kHz for the twitch and 5 kHz for the tetanus. Waveforms were later analyzed for peak force (difference between maximum force during a contraction and the baseline force), fade (force measured when the last stimulus was applied, i.e., at 500 ms for EDL or at 2 s for soleus, normalized as a fraction of the peak force for a contraction) and one-half relaxation time (time required for force to decrease from 100 to 50% of its peak value during the relaxation phase of a contraction).
The standard experimental protocol involved first stretching the muscle to the length that produced peak tetanic force. Tetanic contractions (125 Hz, 2 s) were then evoked every 5 min in the control solution until a steady force was achieved. Muscles with a rapid (>0.2% min1) run-down of peak tetanic force were rejected. Muscles were then exposed to the low [Cl] solution until a steady-state force was achieved (usually 60 min) and subsequently to the control solution again. When force or EM experiments were done with raised [K+]o, each muscle was exposed to 1) the 10 mM Cl solution and then 10 mM Cl + 9 mM K+ solution and 2) the 9 mM K+ solution.
Fatigue was induced using two types of stimulation protocol: 1) continuous tetanic stimulation (at 50 or 125 Hz) for 40 s or 2) intermittent tetanic stimulation in which contractions were evoked (at 125 or 50 Hz for 500 ms) every second for 100 s. In soleus, contractions recovered fully after fatigue with either protocol, and fatigue runs repeated after 60 min had a similar profile. Hence fatigue was assessed with a precontrol, low-[Cl]o run followed by a postcontrol fatigue run in the same muscle. In EDL muscle, fatigue was assessed using only repeated tetanic stimulation with wire electrodes, and the peak force recovered to only 87 ± 3% (n = 9) of the initial value after this fatigue. In consequence, fresh EDL muscles from contralateral legs of the same animal were used to quantify fatigue at control and low [Cl]o. To make a direct comparison with EDL, this was also done in soleus muscle (with the use of wire electrodes). We found that there was no quantitative difference in the effect of low [Cl]o on fatigue in soleus muscle when fatigue runs were repeated on the same muscle or were performed on contralateral muscles.
Membrane Potentials
Conventional glass microelectrodes filled with 3 M KCl (tip potentials <5 mV, tip resistances 715 M) were used to measure EM in surface fibers of soleus muscles as described in detail previously (5). Resting EM were determined from chart or computer recordings with single action potentials. Action potentials were elicited with a single 10-V, 0.3-ms pulse delivered via the same wire electrodes that evoked contraction. They were recorded using a WPI electrometer (model M-707) and digitized at a sampling rate of 400 kHz. Action potentials were obtained when force was at a steady-state level at control and low [Cl]o in the same muscles. The criteria for accepting resting and action potentials, along with a description of waveform analysis, are presented elsewhere (5).
Statistics
Data are presented as means ± SE for the number (n) of muscles (force) or fibers/muscles (resting and action potential) unless stated otherwise. Statistical analyses involved analysis of variance (ANOVA). Force and EM measurements at different frequencies and K+, Cl conditions were from different muscles (whole-plot design), while the different times (fatigue) were from the same muscles (split-plot design). ANOVA was performed using the general linear model procedures of SAS statistical software (SAS Institute, Cary, NC). The least-squares difference (LSD) was used to locate significant differences (34). The level of significance was taken as P < 0.05, and only these effects are reported.
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RESULTS |
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Changing [Cl]o from the control value of 128 mM to 10 mM induced a transient depression of the tetanus in nonfatigued slow-twitch soleus muscles (plate electrodes). At 5 min, the peak tetanic force (125 Hz) was 90 ± 1% (n = 18) of control. However, this effect then reversed over 2060 min so that the steady-state force level was unchanged (Fig. 1A). A striking feature at low [Cl]o was the appearance of a hump during the late phase of tetanic relaxation. The hump had a mean amplitude of 22 ± 5% (n = 14) of peak tetanic force. Figure 1B shows that the Cl channel blocker 9-AC (100 µM) also induced a hump during tetanic relaxation in soleus muscle; the amplitude of the hump increased with stimulation frequency and averaged 26% of peak tetanic force (125 Hz). The peak tetanic force with 9-AC was 98 ± 1% (n = 4) of control. Twitches were unaffected at low [Cl]o, but tetanic contractions evoked at submaximal frequencies were slightly potentiated at low [Cl]o or with 9-AC. For example, the peak force at 50 Hz increased from 88 ± 1 to 94 ± 1% (n = 10) of that at 125 Hz at low [Cl]o.
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The peak force during prolonged tetanic contractions at 50 Hz in soleus muscles was the same in control and low [Cl]o conditions until 10 s, when fatigue became exacerbated at low [Cl]o. By 40 s, the relative force at low [Cl]o was 19% less than in the control (Fig. 3A). Fatigue was also assessed at 125 Hz, a frequency thought to induce greater ionic changes than 50 Hz, and it indeed increased the rate of fatigue compared with 50 Hz in the control solution (Fig. 3, A and B). At low [Cl]o, fatigue was exacerbated early at 125 Hz so that at 10 s, the relative force was 72% compared with 84% for the control (Fig. 3B). However, this effect reversed by 40 s of stimulation, and there was slightly less fatigue at low than at control [Cl]o.
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Soleus muscles (plate electrodes).
The decline in force with repeated tetanic stimulation at 125 Hz was faster at low than control [Cl]o during the first 50 s (Figs. 4 and 5A). This fatigue was exacerbated even by the second tetanic contraction (Fig. 4), and at 10 s of stimulation the peak force at low [Cl]o was 68% of the initial force compared with 88% at control [Cl]o (Fig. 5A). However, with continued stimulation, this difference disappeared so that the final extent of fatigue at 100 s was 34% of the initial force in each case. When fatigue was induced at 50 Hz in the control solution, peak force fell slightly in the first 1015 s and then was maintained at 90% of initial force until 50 s, when it again fell (Fig. 5B). At low [Cl]o, the fatigue profile was the same initially and then became exacerbated after 30 s of stimulation. At 50 s, the relative force was 73% at low [Cl]o compared with 87% for control [Cl]o.
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Soleus muscles (wire electrodes). A comparison of fatigue induced with repeated tetani (125 Hz) with wire or plate electrodes in the control solution (Figs. 5A and 6A) shows that fatigue profiles were similar for the first 30 s but then fell more rapidly with wire stimulation. At low [Cl]o, fatigue also occurred more rapidly so that at 10 s of stimulation, the peak force was 44% of initial force compared with 90% of initial force at control [Cl]o. This Cl effect was about twice as great with wire as with plate electrodes over the first 30 s of stimulation. The final forces at 100 s were the same at control and low [Cl]o, i.e., 22% of initial force. Moreover, there was no fade during fatiguing stimulation in the control solution (500-ms tetanus), whereas fade appeared during fatigue at low [Cl]o, i.e., to 0.57 ± 0.06 at 100 s.
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Influence of Low [Cl]o with Raised [K+]o on Force and Membrane Potential in Nonfatigued Muscle
A possible mechanism for the increased rate of fatigue at low [Cl]o is that a stimulation-induced decline of the transsarcolemmal K+ gradient could cause greater force depression as a result of greater depolarization at low [Cl]o. We tested this hypothesis by looking for interactive effects between raised [K+]o (9 mM) and low [Cl]o on force and resting EM in nonfatigued soleus muscles. The tetanus depression with raised [K+]o occurred more rapidly and to a greater extent at low [Cl]o. After just 1 min, the peak force (125 Hz) fell to 55% of initial force with exposure to 10 mM Cl + 9 mM K+, whereas it was still 99% of initial force with 9K (Fig. 7). The subsequent reduction of force over 656 min followed a similar trend between 10Cl + 9K and 9K, with the result being that the final steady-state force at 10Cl + 9K was about one-half that at 9K. Reducing the frequency to 50 Hz partially restored peak force, but the value was still lower at low [Cl]o (Table 2). In addition, the effects of 9 mM K+ and low [Cl]o were synergistic on fade (50 and 125 Hz). In contrast, peak twitch force was augmented under these steady-state conditions. Finally, a slowing of twitch relaxation occurred at low [Cl]o and persisted when [K+]o was raised (Table 2), yet the hump seen during relaxation of the tetanus had disappeared (data not shown).
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DISCUSSION |
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Role of [Cl]o in Contraction of Nonfatigued Muscle
The peak tetanic force of slow-twitch soleus (Fig. 1A) and fast-twitch EDL muscles was unchanged after equilibration at low [Cl]o, as was seen with diaphragm muscle (16, 29), and was consistent with an unchanged resting EM (Table 1). However, several changes of contractile properties occurred under steady-state conditions at low [Cl]o.
Fade was exacerbated at low [Cl]o to a greater extent with wire electrode stimulation than with plate electrode stimulation (Fig. 2). On the basis of the idea that plate electrodes trigger action potentials simultaneously all along the muscle fiber whereas wire electrodes elicit action potentials in a smaller area of sarcolemma, which are then propagated (5), we suggest that low [Cl]o impairs propagation of action potential trains along the surface membrane. This failure appears to be minimal in the early phase of a train, because peak tetanic force is not affected in the same manner as the force seen at 2 s. The depolarization that normally occurs during a 2-s train of action potentials (5), because of a reduced K+ gradient, may be greater at low [Cl]o. Greater depolarization may then lead to greater Na+ channel inactivation, which in turn may lower the overshoot and Ca2+ release, thereby inducing fade.
The feature most characteristic of tetanic contractions at low [Cl]o was the appearance of a hump (or aftercontraction) during relaxation (Fig. 1A); the hump was also induced with the Cl channel blocker 9-AC (Fig. 1B). An aftercontraction is a well-known symptom of myotonic muscle (4, 28, 29, 33) in which sarcolemmal Cl channels are absent (19, 28). The mechanism for the aftercontraction is likely to be repetitive firing of action potentials once stimulation ceases, as was shown to occur at low [Cl]o (1, 29), with Cl channel blockade (4, 35), and in myotonic muscle (1, 28, 29, 33). Moreover, repetitive firing increases with stimulation frequency (1), as does the amplitude of the aftercontraction (Fig. 1B). Moreover, a prolonged twitch relaxation at low [Cl]o is distinct from the hump, because it persisted at 9 mM K+ (Table 2) when the hump had disappeared. The mechanism for this slowed relaxation remains to be established.
Resting EM was unchanged in muscles equilibrated at low [Cl]o (Table 1), as some have observed (21, 23, 27) but in contrast to the hyperpolarization that others have reported (2, 13). The immediate effect of lowering [Cl]o is depolarization (2, 13, 14, 21, 27), which may explain the transient depression of the tetanus (Fig. 7). The small decrease in overshoot of single action potentials at low [Cl]o (Table 1) contrasted to no effect seen with Cl channel blockade (35) but would have negligible effect on peak twitch force (5). Slower repolarization of the action potential, which was seen in the t tubules in frog fibers (20), was not detected in the surface membrane in the present study.
Effects of Low [Cl]o and Raised [K+]o on Force and Resting EM in Nonfatigued Muscle
Raised [K+]o and low [Cl]o act synergistically to cause greater and more rapid depression of both peak tetanic force (Fig. 7) and fade at low [Cl]o (Table 2). The faster force decline can be explained by more rapid depolarization (13, 14, 21, 26), with greater peak force depression and fade being explained by greater sarcolemmal depolarization (Refs. 13, 14, 21, and 26, as well as the present study). Although the difference in resting EM that we observed between 10 mM Cl + 9 mM K+ and 9 mM K+ was only 5 mV, this greater depolarization occurs on the steep part of the curve relating peak tetanic force and resting EM (7, 8). Indeed, a 5-mV difference in resting EM, between 60 and 55 mV, is associated with an 50% reduction of peak tetanic force (125 Hz) (7).
Slower K+-induced depolarization in the presence of normal rather than low [Cl]o can be explained using the Goldman-Hodgkin-Katz (GHK) equation when the sarcolemmal Cl conductance is high (i.e., high Cl-K+ conductance ratio) (15, 23, 26, 31). Because Cl contributes to resting EM when the fiber becomes depolarized with raised [K+]o relative to the Cl equilibrium potential (ECl) (21, 27), this will prevent the full effects of raised [K+]o from being seen until Cl enters the fiber to make ECl similar to resting EM (27, 36). In contrast, when [Cl]o is low, the full effects of raised [K+]o on resting EM are seen (7) and depolarization occurs more rapidly (13, 14, 21, 26).
Role of [Cl]o in Skeletal Muscle Fatigue
Our fatigue data (Figs. 36) strongly support the hypothesis that normal [Cl]o allows better maintenance of peak tetanic force in situations in which run-down of the transsarcolemmal K+ gradient is likely to occur. Impairment of action potentials in the sarcolemma is commonly thought to explain fatigue during prolonged tetani (6, 22, 31). This explanation may be germane to our model of fatigue with repeated tetanic stimulation because M-wave amplitude is reduced (18) and force recovers with longer stimulation pulses (8) or at lower stimulation frequencies (Fig. 4). At low [Cl]o, fatigue was accelerated regardless of the stimulation frequency, the stimulation electrodes used, or the muscle type studied (Figs. 36). First, fatigue at low [Cl]o was exacerbated early with either continuous or intermittent tetanic stimulation at 125 Hz (Figs. 3B, 4, 5A), whereas at the lower frequency of 50 Hz, fatigue was exacerbated only after a delay (Figs. 3A, 5B). This is consistent with the requirement of a sufficient number of action potentials to allow marked run-down of the K+ gradient for low [Cl]o to have detrimental effects on force. Second, the early rate of intermittent tetanic fatigue at low [Cl]o was about doubled when wire rather than plate electrode stimulation was used in soleus muscle. This could be explained with an earlier failure to propagate action potentials along the surface membrane with wire stimulation at low [Cl]o. Third, although fast-twitch muscle may have higher sarcolemmal Cl conductance than slow-twitch muscle (4), it was difficult to determine whether low [Cl]o had a more rapid effect on fatigue in EDL than in soleus muscle (Fig. 6), because the fatigue was already very rapid in EDL muscle at normal [Cl]o.
Our fatigue data with prolonged tetani at 50 Hz and low [Cl]o (Fig. 3A) are consistent with those in other studies in which continuous stimulation was used (6, 12). At 125 Hz, the fatigue at low [Cl]o at the end of a 40-s tetanus was unexpectedly attenuated (Fig. 3B). We speculate that this latter effect may be due to a large depolarization during stimulation so that the voltage sensor proteins in the t tubules are directly activated by the depolarization. The lack of effect of low [Cl]o on fatigue with repeated tetanic stimulation seen by Esau and Sperelakis (16) is likely to be due to the fatigue not being severe (80% initial force) and the transsarcolemmal K+ gradient not changing much. Moreover, De Luca et al. (12) showed that fatigue was slower with repeated tetanic stimulation when Cl conductance was chronically reduced with 9-AC in EDL muscles. We have shown that this drug caused a large increase in baseline force with repeated tetanic stimulation, which may explain the slower fatigue that De Luca et al. observed, and we cannot eliminate the possibility of nonspecific effects of 9-AC.
Because low [Cl]o had little effect on peak force in nonfatigued muscle, we suggest that the hastening of fatigue must be due to an interaction between low [Cl]o and some other stimulation-induced change. A likely mechanism is hastened fatigue at low [Cl]o that occurs when the K+ gradient starts to run down during stimulation. The interactive depressive effect of raised [K+]o and low [Cl]o on peak tetanic force (Fig. 7), which we attribute to more rapid and greater K+-induced depolarization, may well reflect, in part, the scenario during fatigue. This may mean that any buildup of [K+] in the t-tubular lumen causes greater depolarization with low [Cl]o of the t-tubular membranes, leading to more Na+ channel inactivation and action potential impairment at this site (11, 36). In addition, any t-tubular membrane depolarization may spread passively to the surface membrane (because of a longer membrane space constant at low [Cl]o; Refs. 15, 23), which could interfere with surface membrane action potentials and further contribute to the decline in force. We cannot exclude a contribution of greater K+ efflux during action potentials at low [Cl]o (14), but a Cl effect directed via the sarcoplasmic reticulum seems unlikely (10).
The reason that the final extent of fatigue was similar at normal and low [Cl]o (Figs. 46) is unknown but may indicate that any contribution from [Cl]o to resting EM is markedly diminished at the end of fatigue. According to the GHK equation (13, 27), the ratio of Cl to K+ conductance determines the effect of [Cl]o on resting EM. Any fatigue-induced acidosis may reduce Cl conductance (4, 31), and/or any increase in K+ conductance (32) may act to reduce the Cl-to-K+ conductance ratio. Under these conditions, [Cl]o would contribute little to resting EM and the full effects of K+ would then be seen at both normal and low [Cl]o, so the extent of fatigue would be similar.
The small (10%) and transient tetanus depression at low [Cl]o in nonfatigued muscle suggests that a similar large reduction of the transsarcolemmal Cl gradient would not by itself cause much fatigue. This finding does not exclude the possibility that a smaller rapid fall in t-tubular [Cl] may exacerbate the fatigue caused by an increase in [K+]o, lower [Na+]o, or lower [Ca2+]o (3, 8). Moreover, the possibility that a stimulation-induced increase in [Cl]i per se, rather than reduced transsarcolemmal Cl gradient, may impair Ca2+ release from the sarcoplasmic reticulum seems unlikely (10).
In summary, we demonstrate that normal [Cl]o protects against severe fatigue induced with either prolonged or repeated tetani in slow-twitch soleus and fast-twitch EDL muscles of the mouse. The simplest explanation for the effect of Cl on fatigue is that normal [Cl]o protects against excessive depolarization after a large stimulation- or exercise-induced decline in the transsarcolemmal K+ gradient.
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GRANTS |
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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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. Section 1734 solely to indicate this fact.
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