Fast-twitch skeletal muscle fibers are often exposed to motor neuron double discharges (≥200 Hz), which markedly increase both the rate of contraction and the magnitude of the resulting force responses. However, the mechanism responsible for these effects is poorly understood, likely because of technical limitations in previous studies. In this study, we measured cytosolic Ca2+ during doublet activation using the low-affinity indicator Mag-Fluo-4 at high temporal resolution and modeled the effects of doublet stimulation on sarcoplasmic reticulum (SR) Ca2+ release, binding of Ca2+ to cytosolic buffers, and force enhancement in fast-twitch fibers. Single isolated fibers respond to doublet pulses with two clear Ca2+ spikes, at doublet frequencies up to 1 KHz. A 200-Hz doublet at the start of a tetanic stimulation train (70 Hz) decreases the drop in free Ca2+ between the first three Ca2+ spikes of the transient, maintaining a higher overall free Ca2+ level during first 20–30 ms of the response. Doublet stimulation also increased the rate of force development in isolated fast-twitch muscles. We also modeled SR Ca2+ release rates during doublet stimulation and showed that Ca2+-dependent inactivation of ryanodine receptor activity is rapid, occurring ≤1ms after initial release. Furthermore, we modeled Ca2+ binding to the main intracellular Ca2+ buffers of troponin C (TnC), parvalbumin, and the SR Ca2+ pump during Ca2+ release and found that the main effect of the second response in the doublet is to more rapidly increase the occupation of the second Ca2+-binding site on TnC (TnC2), resulting in earlier activation of force. We conclude that doublet stimulation maintains high cytosolic Ca2+ levels for longer in the early phase of the Ca2+ response, resulting in faster saturation of TnC2 with Ca2+, faster initiation of cross-bridge cycling, and more rapid force development.

During cyclic muscular activity in vivo, mammalian motor units are characterized by patterns of excitation that commence with two or sometimes three high-frequency action potentials (up to 200 Hz) followed by a series of relatively low-frequency (20–80 Hz) stimuli. These so-called “doublet” excitation patterns have been observed in rodents (Hennig and Lømo, 1985; Gorassini et al., 2000) and humans (Desmedt and Godaux, 1977) and typically involve fast-twitch motor units (Zehr and Sale, 1994). Doublet discharges can increase tetanic force output by 44% and decrease contraction times by 50% compared with controls (Burke et al., 1976; see Binder-Macleod and Kesar [2005] for a review), a phenomenon that has been described by some as the “catch-like” property of skeletal muscle (Burke et al., 1970).

Doublet stimulation is reported to enhance force production by significantly elevating SR Ca2+ release (Duchateau and Hainaut, 1986). More recently, Cheng et al. (2013) used the Ca2+-sensitive dye indo-1 to show that an initial 200-Hz doublet action potential results in a transient increase in peak tetanic free [Ca2+] during the first 15 ms of the response that was ∼100% greater than that elicited at a stimulation rate of 70 Hz alone. Cheng et al. (2013) concluded that the increased peak free Ca2+ observed in response to a doublet stimulus reflected an increased release of Ca2+ in response to the second pulse. Similar reasoning was used to explain the effects of triplet stimulation on SR Ca2+ release (Abbate et al., 2002).

These studies suggest that doublet stimulation significantly increases initial Ca2+ release. However, to obtain an increase in SR Ca2+ release during doublet stimulation, the Ca2+ released in response to the second stimulation must be greater than the first, which is incompatible with previous studies showing a marked decrease in Ca2+ release shortly after an initial release caused by Ca2+-dependent inactivation of the ryanodine receptors (CDI; Baylor and Hollingworth, 2003; Capote et al., 2005; Barclay, 2012). For these reasons, we suspected that limitations in previous tracking of cytosolic Ca2+ over time (cytosolic Ca2+ transient: [Ca2+]C (t)) caused by the use of a high-affinity Ca2+ indicator and insufficient temporal resolution (500 Hz) have resulted in a distorted view of the tetanic Ca2+ response in previous studies (Abbate et al., 2002; Cheng et al., 2013) and led to erroneous conclusions.

Although doublet stimulation may not be increasing SR Ca2+ release, the pattern of Ca2+ signaling activated is likely to be altered in a way that enhances the activity of the force generation system. Therefore, the relationship between [Ca2+]C (t) and the binding of Ca2+ to the contractile regulatory sites of the contractile apparatus needs to be taken into consideration when trying to interpret changes in [Ca2+]C (t) in relation to SR Ca2+ release and to understand the physiological mechanisms responsible for the effects of doublet stimulation on force development. In fast-twitch muscle, any initial, rapid succession of action potentials releasing Ca2+ to the cytoplasm needs to result in binding of Ca2+ to two sites on troponin C (TnC; of different affinities) to induce contraction. The kinetics of Ca2+ binding to the TnC sites during high-frequency stimulation events such as doublets has not been explored, in part because the changes in [Ca2+]C (t) during doublet stimulation have not been clearly defined with appropriate temporal resolution.

The aims of this study were first to accurately determine the time course of changes in free Ca2+ concentration in response to constant frequency and doublet stimulation and second to estimate the underlying differences in SR Ca2+ release and binding to TnC in response to the different stimulation protocols. To achieve the first of these aims, changes in free Ca2+ were measured using a fast, low-affinity Ca2+ indicator allied with high temporal resolution laser-scanning microscopy. The second aim was addressed by mathematical modeling of the release and distribution of Ca2+ in fibers in response to the stimulation protocols used in the experimental studies.

We found that the initial high-frequency doublets elicited by motor units are aligned with the Ca2+ binding kinetics of TnC to induce a powerful force response, a mechanism that could be fully accounted for by modeling Ca2+ movements based on the high temporal resolution imaging of cytoplasmic free Ca2+.

All experiments were approved by the Animal Ethics Committee of the University of Queensland (Ca2+ measurements) and the Animal Ethics Committee of the University of Western Australia (force measurements).

Fiber preparation

The isolation, culturing, and dye loading of interosseous fibers have been described in detail previously (Cully et al., 2012). 6-wk-old male C57BL/6J mice were killed by cervical dislocation, and the interosseous muscles were removed and placed in 3 ml of Dulbecco’s modified Eagle’s medium (glucose: 5 mM) containing 1.5 mg/ml collagenase type-1 (Sigma-Aldrich) digestion solution for 30 min at 30°C. Intact interosseous muscles were incubated overnight at 30°C in Dulbecco’s modified Eagle’s medium containing 5 mM glucose, 5% fetal calf serum, and 1 mg/ml penicillin and 1 mg/ml streptomycin. The muscles were then gently triturated to release single fibers.

Ca2+ measurements

Isolated fibers responding to field stimulation were transferred to a custom-made experimental chamber and positioned above the coverslip base. Fibers were loaded with the Mag-Fluo-4AM or Fluo-4AM (5 µM for 15 min) at room temperature in a HEPES-based Ringer solution (mM: 145 NaCl, 2.5 CaCl2, 2 MgCl2, 10 HEPES, 3 KCl, and 5 glucose). After the loading period, the dye containing Ringer solution was replaced with a dye-free Ringer solution containing the myosin II ATPase inhibitor N-benzyl-p-toluene sulphonamide (100 µM), to prevent cross-bridge cycling and associated movement artifacts. The chamber was placed above the inverted lens (63×, oil immersion) of a 5 LIVE (ZEISS). Isolated fibers were stimulated via platinum electrodes using supramaximal square wave pulses (0.3-ms duration) delivered by an SD9 square pulse stimulator (Grass Technologies Inc.). The stimulator was triggered at various time intervals using Chart 8 stimulator software in conjunction with a PowerLab data acquisition/stimulation system (ADInstruments) and a PC. The polarity of the stimulation electrodes was kept constant during experimentation. During stimulation, Ca2+-related fluorescence changes were measured in line scan mode, and data were sampled every 0.111 ms (Edwards et al., 2012), unless otherwise stated. The Ca2+-sensitive dyes trapped in the cytoplasm of the fibers were excited by the 488-nm line of an argon laser, and fluorescence emission was collected in the range >500 nm. Line scan image–derived fluorescence data were exported as a text file and analyzed using Excel (Microsoft).

In control measurements, fibers were activated at 70 Hz (10 stimulation pulses). Stimulation during the doublet measurements was similar to controls with the exception that the first two action potentials of the train were at 200 Hz. Doublet and control tetani were collected in the same recording. The doublet tetanus was delivered first, followed by the control tetanus, 1.2 s later. Control measurements were also made, where two consecutive control tetani were delivered 1.2 s apart. All experiments were performed at room temperature (22–24°C).

In some experiments, the effect of doublet stimulation on Ca2+ release was measured under conditions similar to those reported previously by Cheng et al. (2013) using the same temporal resolution (500 Hz) and Fluo-4, which has similar affinity to Ca2+ as indo-1 (see Results).

To ensure only fast fibers were used in this study, only fibers exhibiting the Ca2+ transient shape characteristic for type IIb/IIx fibers were selected for analysis (Calderón et al., 2009, 2014).

Force measurements

Experiments assessing the impact of doublet stimulation on tetanic force responses were undertaken using isolated extensor digitorum longus (EDL) muscles from 6-wk-old male C57BL/6J mice. EDL muscles from C57BL/6J mice primarily contain fast IIb/x fibers (IIb/x fibers 88%, type IIa fibers 12%; Rinaldi et al., 2012), as used in the Ca2+ experiments in this study. Therefore, the use of intact muscle preparations in this study should provide a relatively accurate estimate of the effects of doublet stimulation on force production in fast IIb/x fibers.

EDL muscles (n = 8) were removed surgically under anesthesia (40 mg/kg pentobarbitone) and mounted onto an in vitro muscle test system (model 1205A; Aurora Scientific Inc.; Pinniger et al., 2012). Muscles were maintained in an organ bath containing mammalian Ringer solution (mM: 121 NaCl, 25 NaHCO3, 11.5 glucose, 5.4 KCl, 2.5 CaCl2, 5 HEPES, and 1 MgSO4, pH 7.3) bubbled with carbogen (5% CO2 in O2; BOC). The Ringer was maintained at 25°C, which is reported to be optimal for the maintenance of in vitro muscle force (Segal and Faulkner, 1985). After muscles were removed, the mice were euthanized by an overdose of pentobarbitone.

Muscles were stimulated with platinum electrodes using supramaximal square wave pulses (0.3-ms duration) provided by a high-power bi-phase current stimulator (Aurora Scientific Inc.). The stimulator was triggered at various time intervals using Chart 7 stimulator software and a PowerLab data acquisition/stimulation system (ADInstruments). Before experiments commenced, muscles were set to a length producing maximum isometric twitch force (optimal muscle length). In control measurements, muscles were stimulated with 10 pulses at 70 Hz. Doublet measurements were similar except the first two action potentials were delivered at 200 Hz. 70 Hz is close to the mean motor neuron discharge rate in rodents (Hennig and Lømo, 1985; Gorassini et al., 2000). 2-min intervals were maintained between tetanic stimulations to prevent onset of muscle fatigue (Sitparan et al., 2014). Force output was recorded using a PowerLab data acquisition system and LabChart 7 software (ADInstruments).

Statistics

The data are presented as means ± SEM. Statistical analysis was undertaken using the graphical software package Prism (Graph Pad Software). The absolute amplitudes of initial Ca2+ spikes transients measured in the Ca2+ transients were compared using a paired t test. The relative change in the minimum fluorescence between Ca2+ spikes that occurred during the Ca2+ transients in control and doublet traces was compared using a repeated measures two-way ANOVA followed by a Šídák’s multiple comparisons test.

Mathematical modeling

To provide insight into the mechanisms underpinning force enhancement by doublet stimulation, a mathematical model was used to describe the kinetics of Ca2+ distribution within muscle fibers and the generation of force. The model was based on those described earlier (Robertson et al., 1981; Baylor et al., 1983) and is summarized in Fig. 1 A. It is described by six differential equations of the form described in detail previously (Baylor and Hollingworth, 1998) and which were solved using a program developed using Maple software (version 2016.1; Maplesoft).

The concentrations of Ca2+ binding and other relevant compounds (Table 1) and parameter values (Table 2) used for the model were taken from Baylor and Hollingworth’s (Baylor and Hollingworth, 2003, 2007, 2012) models applicable to mouse muscle fibers. The rate constants were adjusted from 16°C, as used by Baylor and Hollingworth, to 22°C assuming a Q10 (i.e., the increase in rate for a 10°C increase in temperature) of 2. The interaction between Ca2+ and the fluorescent indicator was not included in the model. Instead, it was assumed that the measured Ca2+ signal provided a faithful representation of the time course of the free Ca2+ transient; this is true for Mag-Fluo-4 (Baylor and Hollingworth, 2011). On this basis, the free Ca2+ transient predicted by the model was compared directly with the measured signal (Fig. 1 B).

Removal of Ca2+ from the myoplasm into the SR was modeled as described previously (Ríos and Brum, 2002). The rate of removal was assumed to have a sigmoidal dependence on [Ca2+]C, a maximum rate of 4,670 µM/s (determined empirically to achieve a good match between measured and simulated Ca2+ transients) and to pump at 50% of the maximum rate when [Ca2+]C was 2.5 µM (Baylor et al., 2002). A small, constant rate Ca2+ leak from the SR of 2 nM/s was included in the model. This leak rate and the pump characteristics established a realistic resting [Ca2+]C of 0.05 µM (Bakker et al., 1993). The resting [Ca2+]C determines the fractions of the Ca2+ buffers occupied by Ca2+ in the muscle before stimulation.

A novel aspect of the model was incorporation of force generation. It was assumed that the formation of force-generating actomyosin cross-bridges (labeled “AM” in Fig. 1 A) was enabled by binding of the Ca2+ to the second binding site on TnC (Tn-Ca2, Fig. 1; Ashley and Moisescu, 1972). Note that the second site could only be filled once the first binding site was occupied by Ca2+. The rate constants for formation and dissociation of force generating cross-bridges were set so that the predicted time course of twitch force at 16°C matched that described for mouse EDL muscle by Baylor and Hollingworth (2003). The rates were adjusted to 22°C using a Q10 of 2. Examples of simulated force responses are shown in Fig. 1 C.

Simulations started with all the Ca2+ in the SR and the leak being the only source of Ca2+ entry into the myoplasm. Once the occupancy of the Ca2+-binding sites on ATP, TnC, and parvalbumin settled to steady values, the response to stimulation was simulated by invoking a transient release, or releases if multiple stimuli were being modeled, of Ca2+ from the SR with an asymmetric time course described by two exponentials, one rising and the other falling (Baylor and Hollingworth, 2012). The design of the model was validated by ensuring that it accurately reproduced Baylor and Hollingworth’s simulations when using their parameter values for 16°C. Thereafter, parameters appropriate for 22°C were used.

We initially measured the effect of a 200-Hz doublet pulse on force output in isolated intact EDL muscle exposed to tetanic stimulation (10 pulses, 70 Hz). Doublet stimulation indeed resulted in force responses that increased more rapidly and to higher levels than controls (Fig. 2 A). Doublet stimulation significantly decreased the rise time of the force response (Fig. 2 B) and significantly increased the level of force output from the muscle for at least the first 57 ms (Fig. 2 C). The presence of a doublet also shifted the relationship between normalized force and time to the left (Fig. 2 D; P < 0.05), indicating that the rate constant of force development is significantly increased in the doublet responses. Note that the final level of force in the doublet and control responses was similar. We note that previous studies have used shorter overall periods of stimulation (the arrow on Fig. 2 A indicates the end of stimulation in Cheng et al. (2013), which emphasize the effects of doublet stimulation on peak force during the early phase of the force response (Cheng et al., 2013).

We then examined the effects of 200-Hz doublet stimulation on tetanic (70 Hz) Ca2+ release under similar conditions to Cheng et al. (2013) (i.e., using a high-affinity Ca2+ indicator and sampling at 500 Hz). However, we used laser-scanning microscopy instead of photometry and the Ca2+ indicator Fluo-4 instead of indo-1. Fluo-4 (Kd for Ca2+: ∼345 nM; Paredes et al., 2008) has a similar reported affinity for Ca2+ to indo-1 (Kd for Ca2+: ∼250 nM; Grynkiewicz et al., 1985). At 500-Hz sampling frequency, we found a qualitatively similar apparent increase in the initial peak Ca2+-related fluorescence after doublet stimulation to that reported previously by Cheng et al. (2013) (Fig. 3, representative of three experiments). However, with the enhanced signal-to-noise of laser-scanning microscopy compared with photometry (Edwards et al., 2012), it was possible to resolve individual Ca2+ spikes within the tetanus. In the control tetanus, each of the 10 stimulation events resulted in individual Ca2+ spikes (Fig. 3 A), whereas in the doublet transient, the 10 stimulation pulses resulted in only nine peaks (Fig. 3 B). The apparent fusion of the initial two Ca2+ transient peaks activated by the doublet (Fig. 3 B) is a likely result of sampling below the Nyquist frequency.

To verify that our imaging system (5 LIVE; ZEISS) was capable of accurately tracking [Ca2+]C (t) during high-frequency stimulation in fast-twitch muscle fibers, we line-scanned isolated fibers at 111 µs/line using the low-affinity Ca2+ indicator Mag-Fluo-4, while applying twin field pulses in the range 200–1,000 Hz. The use of a low-affinity dye at high temporal resolution allowed the [Ca2+]C (t) to be resolved, as clearly shown by the twin Ca2+ spikes at each stimulation frequency (Fig. 4 A). Furthermore, importantly, in each case the secondary stimulus did not produce a Ca2+ peak higher than that triggered by the first. This indicates that the amount of Ca2+ released by the first action potential must be significantly greater than the second, suggesting that CDI was occurring under these conditions.

The amount of Ca2+ released in response to the second of a pair of stimuli was quantified using the model of Ca2+ kinetics (described in Materials and methods). This was undertaken by iteratively scaling the amount of Ca2+ released in response to the second pulse until a match was achieved between the amplitudes of the measured and simulated Ca2+ transient peaks arising from the second stimulus. A comparison of the experimental and simulated Ca2+ transients is provided in Fig. 5 (A and B) and the relative Ca2+ release in response to the second of the two stimuli is shown in Fig. 5 C. The analysis indicates that the amount of Ca2+ released by the second stimulus pulse, expressed relative to that released by the first stimulus, was between 15 and 25%, for pulse intervals between 1 and 4 ms. A small addition of Ca2+ to the myoplasm by the second stimulus produced a relatively large Ca2+ transient because the fiber’s rapid Ca2+-buffering capacity is reduced by the binding of Ca2+ released by the first stimulus to TnC, ATP, and parvalbumin. The simulated force responses (Fig. 5 D) showed that a second stimulus could increase peak force by ∼30% compared with the response to a single stimulus. The basis of this effect, in terms of the model used, is a doublet-induced increase in the fraction of TnC molecules with two Ca2+ bound to the regulatory binding sites (Fig. 5, E and, in more detail, F). After a single stimulus, the proportion of TnC with 2 Ca2+ bound reached a peak of 60%; this was increased to 70% by the addition of a second stimulus pulse 2 ms after the first (Fig. 5 F).

We then imaged Ca2+ transients during control and doublet tetani using the stimulation protocol of Cheng et al. (2013) under the conditions established in Fig. 4 A. Control tetani at 70 Hz resulted in Ca2+ transients that were similar in shape to those reported previously for fast type IIb/IIx fibers under similar conditions (Fig. 6 A; Calderón et al., 2011). When a 200-Hz doublet stimulus was inserted at the start of the tetanus, a second Ca2+ spike was clearly delineable from the first spike (Fig. 6 B). In all fibers, the initial single large Ca2+ spike was followed by Ca2+ spikes that did not reach a peak higher than the initial one (Fig. 6, A and B). The main effect of doublet stimulation was to minimize the drop in [Ca2+]cyto (t) between the first three Ca2+ spikes in the doublet response (Fig. 6 C). There was no significant difference in the amplitude of the initial Ca2+ spike elicited after doublet or control stimulation (initial doublet Ca2+ spike: 111.6 ± 4.2% of initial control 70-Hz response; n = 6).

The basis of the effects of the doublet stimulation on Ca2+ transients and force development were analyzed using the model. As discussed in the Introduction, the interval between stimulus pulses affects the amount of Ca2+ released in response to the second, and subsequent, pulses. With constant 70-Hz stimulation, 45% as much Ca2+ was released by the second stimulus as by the first. In contrast, using the doublet stimulation pattern with the first and second pulses 5 ms apart, the second pulse liberated only 33% as much Ca2+ as the first pulse. The effects of this on the binding of Ca2+ to TnC, which underlies force development, are shown in Fig. 7 B. After the initial high-frequency doublet, the concentration of TnC molecules with both Ca2+-binding sites occupied is greater between 5 and 15 ms after the first stimulus than with constant frequency stimulation (Fig. 7 B, compare dashed and solid lines). This translated into more rapid force development; the modeling indicated that the time taken for force to develop to 50% of maximum is reduced with doublet stimulation from 31 to 23 ms (Fig. 7 D). The simulation further shows that the more rapid increase in force is sustained so that force output was higher throughout the 150 ms of stimulation (Fig. 7 D, inset). As expected, Ca2+ release measurements showed a greater CDI-related decrease in SR Ca2+ release in response to the second stimulus pulse of the doublet tetani compared with the control; however, Ca2+ release in the doublet response returned to control levels shortly after and remained similar to controls for the rest of the response (Fig. 7 E).

The results of this study show that 200-Hz doublet stimulation results in significant increases in the rate of force development and the initial amplitude of resulting force responses, leading to the powerful “ballistic” contractions reported previously under these conditions (Desmedt and Godaux, 1977; Van Cutsem et al., 1998). However, our findings indicate that high-frequency doublet stimulation does not result in an increase in peak free Ca2+ in fast-twitch skeletal muscle fibers, in contrast to previous studies (Duchateau and Hainaut, 1986; Abbate et al., 2002; Cheng et al., 2013), but maintains a higher [Ca2+]C (t) for the first 20 ms of the tetanic Ca2+ transient (Figs. 4, 5, 6, and 7).

Simulation of the changes in Ca2+ binding to the main intracellular Ca2+ buffers during tetanic Ca2+ release shows that the main effect of the second response in the doublet is to more rapidly increase occupation of the second Ca2+-binding site on TnC (TnC2), beyond that which was achieved by the first Ca2+ release response. The increase in the rate of force development shown in this study (Fig. 2 D) ultimately reflects the higher occupancy of TnC2 rather than a change in the rate constant for cross-bridge attachment per se, in terms of the model used in this study. The increased rate of force development reflects the increased modulation of the rate constant for cross-bridge attachment and force generation induced by the earlier increase in the concentration of TnC2. Although the second pulse of the doublet increases saturation of TnC2 with Ca2+, considerably less Ca2+ is actually released in response to the second pulse in the doublet compared with that released by the second pulse in a pair of constant, lower-frequency pulses (Fig. 5 C). However, because of the extent of saturation of the rapid Ca2+ buffers (TnC and ATP) by the first pulse in the doublet, even a relatively small addition of Ca2+ to the myoplasm in response to the second pulse is sufficient to prevent a significant decrease in [Ca2+]C and to increase the fraction of TnC molecules with two Ca2+ bound. Earlier occupation of Ca2+-binding sites on the other cytosolic Ca2+ buffers, after doublet stimulation (Fig. 7 C), would also slow the rate of post-release Ca2+ decay (Baylor and Hollingworth, 2003) and consequently prolong Ca2+ occupancy of TnC, further contributing to the faster rate of force development after doublet stimulation.

Increased saturation of TnC2 underpins the more rapid development of force in response to doublet stimulation, as shown in the modeled force responses in Fig. 5 D, which are in close agreement with the effects of doublet stimulation on force enhancement in intact fast-twitch muscles in vitro (Fig. 2 A). It should be noted that although our results indicate that doublet stimulation has no effect on peak tetanic plateau force production (10 stimulation pulses; Fig. 2 A), stimulation bursts with a smaller number of pulses, such as those typically found in fast-fatigable motor units (Hennig and Lømo, 1985), will increase peak tetanic force output, as shown in Cheng et al. (2013).

Modeling of the effects of high-frequency doublets on Ca2+ release shows that CDI is extremely rapid in fast twitch fibers, markedly decreasing Ca2+ release during the second response of the doublet to 15–20% of initial SR Ca2+ in <1 ms (Fig. 5 C). The degree of CDI found in this study under tetanic conditions, where Ca2+ release during the second pulse of burst was ∼33% of the first for the doublet (5-ms pulse interval) or 45% of the first for controls (15-ms pulse interval), was very similar to the values reported recently by using a different experimental approach (Barclay, 2012). Barclay (2012) estimated SR Ca2+ release during tetanic stimulation from ATP turnover–derived SR Ca2+ reuptake measurements made in the absence of cross-bridge cycling and found that Ca2+ release during the second pulse of a tetanus was ∼30% of that occurring in response to the first pulse for a 5-ms pulse interval and ∼40% of the first for a 15-ms pulse interval. The values found here are also in the same range as those reported by Baylor and Hollingworth (2007), who developed the modeling methodology used in this study, where 25% as much Ca2+ was released in response to the second stimulus compared with the first for a 15-ms interpulse period (based on Ca2+ transients measured at 16°C). The results of this study also indicate that the magnitude of CDI elicited by the doublet (5-ms pulse interval) returns to control levels by the third pulse of the 10-pulse protocol and remains relatively constant during the rest of the response, in keeping with previous findings using different methodology (Barclay, 2012). Overall, these results suggest that CDI provides a finely tuned negative feedback mechanism that matches SR Ca2+ release to inter-pulse stimulus duration, in order to provide the minimum Ca2+ release required to maintain significant occupation of TnC2 with Ca2+.

In this study, we showed that fibers responded to stimulation frequencies of up to 1 KHz with two clear Ca2+ release events (Fig. 4 A), which to the best of our knowledge is the first time this ability has been reported in skeletal muscle. However, our simulation data suggest that doublet stimulation rates in the range 200–1,000 Hz will all result in similar increases in TnC2 binding (see Figs. 5 E and 7 B), suggesting that doublet frequencies >300 Hz would not further increase force enhancement (Fig. 5 D) and would be of little functional value. In keeping with this, doublet frequencies in vivo are usually around 200 Hz. For example, in humans, mean doublet frequencies have been shown to be around 180 Hz (Christie and Kamen, 2006), whereas in fast muscle of rats, mean doublet frequencies between 160 and 290 Hz have been reported (Gorassini et al., 2000). In fact, high doublet frequencies (>250 Hz) may be detrimental. Burke et al. (1976) measured muscle force output and electromyography (EMG) in response to motor-neuron doublet stimulation and reported a decrease in force enhancement and a reduction in the EMG response to the second stimulation pulse at pulse intervals of 4 ms or less. Given that our findings indicate the loss of EMG is unlikely to be caused by an inability of the fiber to react to the second stimulus, higher frequency doublets may be ineffective because of a failure of neurotransmission at these high stimulation frequencies, at least in sedentary animals.

In summary, the results of this study show that doublet stimulation results in maintained higher values of [Ca2+]C (t) during the early portion of tetanic Ca2+ release (Fig. 6 C). Our results and others (Baylor and Hollingworth, 2007, 2012) indicate that the enhancement of skeletal muscle force production can be fully explained by the increased Ca2+ availability in the cytoplasm resulting from doublet stimulation and its main effect to rapidly increase the saturation of TnC2. Finally, these findings do not support the existence of any doublet-induced “catch-like” process of force enhancement in fast-twitch skeletal muscle. Rather, doublet activation works through the normal force-summation mechanism, where it acts to significantly increase the rate of force development during the early phase of contraction and, presumably, more powerful force responses under isotonic conditions. Therefore, a more appropriate description than catch-like for the effects of doublet stimulation on force production would be doublet-induced rapid summation.

This work was supported by the Sabbatical Leave Program of the University of Western Australia to A.J. Bakker and an Australian Research Council (ARC) Discovery Project to B.S. Launikonis. B.S. Launikonis was a Future Fellow of the ARC.

The authors declare no competing financial interests.

Author contributions: A.J. Bakker: conceptualization, investigation, methodology, formal analysis, writing–original draft, and writing–review and editing. T.R. Cully: investigation, methodology, and writing–review and editing. C.D. Wingate: investigation, formal analysis, and writing–review and editing. C.J. Barclay: conceptualization, investigation, methodology, formal analysis, and writing–review and editing. B.S. Launikonis: conceptualization, investigation, methodology, formal analysis, and writing–review and editing.

Eduardo Ríos served as editor.

Abbate
,
F.
,
J.D.
Bruton
,
A.
De Haan
, and
H.
Westerblad
.
2002
.
Prolonged force increase following a high-frequency burst is not due to a sustained elevation of [Ca2+]i
.
Am. J. Physiol. Cell Physiol.
283
:
C42
C47
.
Ashley
,
C.C.
, and
D.G.
Moisescu
.
1972
.
Model for the action of calcium in muscle
.
Nat. New Biol.
237
:
208
211
.
Bakker
,
A.J.
,
S.I.
Head
,
D.A.
Williams
, and
D.G.
Stephenson
.
1993
.
Ca2+ levels in myotubes grown from the skeletal muscle of dystrophic (mdx) and normal mice
.
J. Physiol.
460
:
1
13
.
Barclay
,
C.J.
2012
.
Quantifying Ca2+ release and inactivation of Ca2+ release in fast- and slow-twitch muscles
.
J. Physiol.
590
:
6199
6212
.
Barclay
,
C.J.
2015
.
Energetics of contraction
.
Compr. Physiol.
5
:
961
995
.
Baylor
,
S.M.
, and
S.
Hollingworth
.
1998
.
Model of sarcomeric Ca2+ movements, including ATP Ca2+ binding and diffusion, during activation of frog skeletal muscle
.
J. Gen. Physiol.
112
:
297
316
.
Baylor
,
S.M.
, and
S.
Hollingworth
.
2003
.
Sarcoplasmic reticulum calcium release compared in slow-twitch and fast-twitch fibres of mouse muscle
.
J. Physiol.
551
:
125
138
.
Baylor
,
S.M.
, and
S.
Hollingworth
.
2007
.
Simulation of Ca2+ movements within the sarcomere of fast-twitch mouse fibers stimulated by action potentials
.
J. Gen. Physiol.
130
:
283
302
.
Baylor
,
S.M.
, and
S.
Hollingworth
.
2011
.
Calcium indicators and calcium signalling in skeletal muscle fibres during excitation-contraction coupling
.
Prog. Biophys. Mol. Biol.
105
:
162
179
.
Baylor
,
S.M.
, and
S.
Hollingworth
.
2012
.
Intracellular calcium movements during excitation-contraction coupling in mammalian slow-twitch and fast-twitch muscle fibers
.
J. Gen. Physiol.
139
:
261
272
.
Baylor
,
S.M.
,
W.K.
Chandler
, and
M.W.
Marshall
.
1983
.
Sarcoplasmic reticulum calcium release in frog skeletal muscle fibres estimated from Arsenazo III calcium transients
.
J. Physiol.
344
:
625
666
.
Baylor
,
S.M.
,
S.
Hollingworth
, and
W.K.
Chandler
.
2002
.
Comparison of simulated and measured calcium sparks in intact skeletal muscle fibers of the frog
.
J. Gen. Physiol.
120
:
349
368
.
Binder-Macleod
,
S.
, and
T.
Kesar
.
2005
.
Catchlike property of skeletal muscle: recent findings and clinical implications
.
Muscle Nerve.
31
:
681
693
.
Burke
,
R.E.
,
P.
Rudomin
, and
F.E.
Zajac
III
.
1970
.
Catch property in single mammalian motor units
.
Science.
168
:
122
124
.
Burke
,
R.E.
,
P.
Rudomin
, and
F.E.
Zajac
III
.
1976
.
The effect of activation history on tension production by individual muscle units
.
Brain Res.
109
:
515
529
.
Calderón
,
J.C.
,
P.
Bolaños
,
S.H.
Torres
,
G.
Rodríguez-Arroyo
, and
C.
Caputo
.
2009
.
Different fibre populations distinguished by their calcium transient characteristics in enzymatically dissociated murine flexor digitorum brevis and soleus muscles
.
J. Muscle Res. Cell Motil.
30
:
125
137
.
Calderón
,
J.C.
,
P.
Bolaños
, and
C.
Caputo
.
2011
.
Kinetic changes in tetanic Ca2+ transients in enzymatically dissociated muscle fibres under repetitive stimulation
.
J. Physiol.
589
:
5269
5283
.
Calderón
,
J.C.
,
P.
Bolaños
, and
C.
Caputo
.
2014
.
Tetanic Ca2+ transient differences between slow- and fast-twitch mouse skeletal muscle fibres: a comprehensive experimental approach
.
J. Muscle Res. Cell Motil.
35
:
279
293
.
Capote
,
J.
,
P.
Bolaños
,
R.P.
Schuhmeier
,
W.
Melzer
, and
C.
Caputo
.
2005
.
Calcium transients in developing mouse skeletal muscle fibres
.
J. Physiol.
564
:
451
464
.
Cheng
,
A.J.
,
N.
Place
,
J.D.
Bruton
,
H.C.
Holmberg
, and
H.
Westerblad
.
2013
.
Doublet discharge stimulation increases sarcoplasmic reticulum Ca2+ release and improves performance during fatiguing contractions in mouse muscle fibres
.
J. Physiol.
591
:
3739
3748
.
Christie
,
A.
, and
G.
Kamen
.
2006
.
Doublet discharges in motoneurons of young and older adults
.
J. Neurophysiol.
95
:
2787
2795
.
Cully
,
T.R.
,
J.N.
Edwards
,
O.
Friedrich
,
D.G.
Stephenson
,
R.M.
Murphy
, and
B.S.
Launikonis
.
2012
.
Changes in plasma membrane Ca-ATPase and stromal interacting molecule 1 expression levels for Ca2+ signaling in dystrophic mdx mouse muscle
.
Am. J. Physiol. Cell Physiol.
303
:
C567
C576
.
Desmedt
,
J.E.
, and
E.
Godaux
.
1977
.
Ballistic contractions in man: characteristic recruitment pattern of single motor units of the tibialis anterior muscle
.
J. Physiol.
264
:
673
693
.
Duchateau
,
J.
, and
K.
Hainaut
.
1986
.
Nonlinear summation of contractions in striated muscle. II. Potentiation of intracellular Ca2+ movements in single barnacle muscle fibres
.
J. Muscle Res. Cell Motil.
7
:
18
24
.
Edwards
,
J.N.
,
T.R.
Cully
,
T.R.
Shannon
,
D.G.
Stephenson
, and
B.S.
Launikonis
.
2012
.
Longitudinal and transversal propagation of excitation along the tubular system of rat fast-twitch muscle fibres studied by high speed confocal microscopy
.
J. Physiol.
590
:
475
492
.
Gorassini
,
M.
,
T.
Eken
,
D.J.
Bennett
,
O.
Kiehn
, and
H.
Hultborn
.
2000
.
Activity of hindlimb motor units during locomotion in the conscious rat
.
J. Neurophysiol.
83
:
2002
2011
.
Grynkiewicz
,
G.
,
M.
Poenie
, and
R.Y.
Tsien
.
1985
.
A new generation of Ca2+ indicators with greatly improved fluorescence properties
.
J. Biol. Chem.
260
:
3440
3450
.
Hennig
,
R.
, and
T.
Lømo
.
1985
.
Firing patterns of motor units in normal rats
.
Nature.
314
:
164
166
.
Lamboley
,
C.R.
,
S.A.
Kake Guena
,
F.
Touré
,
C.
Hébert
,
L.
Yaddaden
,
S.
Nadeau
,
P.
Bouchard
,
L.
Wei-LaPierre
,
J.
Lainé
,
E.C.
Rousseau
, et al
2015
.
New method for determining total calcium content in tissue applied to skeletal muscle with and without calsequestrin
.
J. Gen. Physiol.
145
:
127
153
.
Paredes
,
R.M.
,
J.C.
Etzler
,
L.T.
Watts
,
W.
Zheng
, and
J.D.
Lechleiter
.
2008
.
Chemical calcium indicators
.
Methods.
46
:
143
151
.
Pinniger
,
G.J.
,
T.
Lavin
, and
A.J.
Bakker
.
2012
.
Skeletal muscle weakness caused by carrageenan-induced inflammation
.
Muscle Nerve.
46
:
413
420
.
Raymackers
,
J.M.
,
P.
Gailly
,
M.C.
Schoor
,
D.
Pette
,
B.
Schwaller
,
W.
Hunziker
,
M.R.
Celio
, and
J.M.
Gillis
.
2000
.
Tetanus relaxation of fast skeletal muscles of the mouse made parvalbumin deficient by gene inactivation
.
J. Physiol.
527
:
355
364
.
Rinaldi
,
M.
,
K.
Maes
,
S.
De Vleeschauwer
,
D.
Thomas
,
E.K.
Verbeken
,
M.
Decramer
,
W.
Janssens
, and
G.N.
Gayan-Ramirez
.
2012
.
Long-term nose-only cigarette smoke exposure induces emphysema and mild skeletal muscle dysfunction in mice
.
Dis. Model. Mech.
5
:
333
341
.
Ríos
,
E.
, and
G.
Brum
.
2002
.
Ca2+ release flux underlying Ca2+ transients and Ca2+ sparks in skeletal muscle
.
Front. Biosci.
7
:
d1195
d1211
.
Robertson
,
S.P.
,
J.D.
Johnson
, and
J.D.
Potter
.
1981
.
The time-course of Ca2+ exchange with calmodulin, troponin, parvalbumin, and myosin in response to transient increases in Ca2+
.
Biophys. J.
34
:
559
569
.
Segal
,
S.S.
, and
J.A.
Faulkner
.
1985
.
Temperature-dependent physiological stability of rat skeletal muscle in vitro
.
Am. J. Physiol.
248
:
C265
C270
.
Sitparan
,
P.K.
,
C.N.
Pagel
,
G.J.
Pinniger
,
H.J.
Yoo
,
E.J.
Mackie
, and
A.J.
Bakker
.
2014
.
Contractile properties of slow and fast skeletal muscles from protease activated receptor-1 null mice
.
Muscle Nerve.
50
:
991
998
.
Van Cutsem
,
M.
,
J.
Duchateau
, and
K.
Hainaut
.
1998
.
Changes in single motor unit behaviour contribute to the increase in contraction speed after dynamic training in humans
.
J. Physiol.
513
:
295
305
.
Zehr
,
E.P.
, and
D.G.
Sale
.
1994
.
Ballistic movement: muscle activation and neuromuscular adaptation
.
Can. J. Appl. Physiol.
19
:
363
378
.

Abbreviations used:
[Ca2+]C (t)

cytosolic Ca2+ transient

CDI

Ca2+-dependent inactivation of the ryanodine receptors

EDL

extensor digitorum longus

EMG

electromyography

TnC

troponin C

Author notes

*

A.J. Bakker and T.R. Cully contributed equally to this paper.

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