Intracellular calcium movements during excitation–contraction coupling in mammalian slow-twitch and fast-twitch muscle fibers

The skeletal muscles of mammals account for ∼40% of body weight and for ∼25% of the basal metabolic rate (Rolfe and Brown, 1997). Approximately half of this muscle mass consists of slow-twitch fibers, and the other half consists of fast-twitch fibers (also called type I and type II fibers, respectively). Small numbers of other fiber types, such as superfast fibers and true-slow fibers, are also found in specialized muscles such as eye and jaw muscles (Hess, 1970; Hoh, 2002; Andrade et al., 2005). The basic unit of activity in the two main fiber types is the “twitch,” in which a single action potential (AP) on the fiber’s surface membrane elicits a brief contractile response. This article concerns the transient increase in the myoplasmic free calcium concentration (Δ[Ca²⁺]), which is the key intermediate signaling event between excitation and contraction. As [Ca²⁺] rises, Ca²⁺ binds to troponin, a regulatory protein on the actin filament, thereby enabling myosin to interact with actin and generate the contractile response. When [Ca²⁺] falls, Ca²⁺ dissociates from troponin and contractile activity declines.

Slow-twitch fibers have many similarities and also some important differences when compared with fast-twitch fibers (Berchtold et al., 2000; Allen et al., 2008; Schiaffino and Reggiani, 2011). Slow-twitch fibers are more resistant to fatigue than fast-twitch fibers, partly because of their larger mitochondrial volume and higher activity of oxidative enzymes (Schwerzmann et al., 1989; Jackman and Willis, 1996). Also, as the naming system implies, the time course of the contractile response of slow-twitch fibers is substantially slower than that of fast-twitch fibers. For example, in rat motor units studied in the anesthetized animal, the time of peak of the twitch response and the time between peak and half-relaxation are three- to fivefold larger in slow-twitch units of the soleus muscle than in fast-twitch units of the extensor digitorum longus (EDL) muscle (Table 1, A). Similar differences in twitch kinetics are found in individual fibers and in small bundles of fibers from mouse soleus and EDL muscles studied after removal of the muscles from the animal (Table 1, B and C).

Part of the difference in contractile speed between slow-twitch and fast-twitch fibers is attributable to a difference in myosin isoforms. For example, in rat muscle, the major myosin isoform found in soleus fibers has a cycling rate at saturating [Ca²⁺] that is about one third of that of the major isoform in EDL fibers (Unsworth et al., 1982; Bottinelli et al., 1994). Some of the fiber-type differences in twitch kinetics likely also arise because of differences in Δ[Ca²⁺] (see below) and in the troponin isoforms (van Eerd and Takahashi, 1976; Potter et al., 1977; Sweeney et al., 1990).

Fig. 1 diagrams the major intracellular movements of Ca²⁺ that take place during a twitch. An AP initiated on the surface membrane propagates into the transverse (T)-tubular system, where specialized voltage-sensing molecules (dihydropyridine receptors [DHPRs]) move to their activating position (Schneider and Chandler, 1973; Hollingworth and Marshall, 1981; Ríos and Brum, 1987; Tanabe et al., 1988). The DHPRs then activate the SR Ca²⁺ release channels, whose large cytoplasmic domain spans the gap between the T-tubular and SR membranes at the triadic junction (Franzini-Armstrong and Nunzi, 1983). As the release channels open, Ca²⁺ moves from the SR into the myoplasm under a large chemical driving force. A large local increase in [Ca²⁺] ensues, which drives the diffusion of Ca²⁺ throughout the sarcomere (Cannell and Allen, 1984; Escobar et al., 1994; Baylor and Hollingworth, 1998; Hollingworth et al., 2000; Gómez et al., 2006). As Ca²⁺ diffuses, it binds to sites on various myoplasmic constituents (termed Ca²⁺ “buffers” in this article), the most important of which are indicated in Fig. 1: (a) troponin, which, as noted above, has regulatory sites (Ca²⁺-specific sites) that mediate contractile activation; (b) ATP, which acts as a mobile buffer for Ca²⁺ and Mg²⁺; (c) more slowly reacting, less mobile buffers for Ca²⁺ and Mg²⁺ (“SlowB”), such as parvalbumin; and (d) the SR Ca²⁺ pump, which resequesters Ca²⁺ within the SR, translocating two Ca²⁺ ions for each ATP consumed (Weber et al., 1966). (e) If a Ca²⁺ indicator dye is introduced into the myoplasm, some Ca²⁺ will also bind to the dye. If the indicator is well chosen and other features of the experiment are favorably arranged, the optical signal from the indicator can be used to monitor the amplitude and time course of Δ[Ca²⁺] (described in next section). From Δ[Ca²⁺] and information from the literature about the concentrations and kinetic reactions of the major myoplasmic Ca²⁺ buffers, quantitative estimates can be made about the complexation of Ca²⁺ with the buffers and thus about the amount and time course of SR Ca²⁺ release and reuptake (compare calculations described below).

Several different Ca²⁺ indicators have been used in skeletal muscle fibers in pursuit of a reliable method to measure the amplitude and time course of Δ[Ca²⁺] (Baylor and Hollingworth, 2011). Furaptra (also called mag-fura-2; Raju et al., 1989), which is a fluorescent Ca²⁺ indicator of the “tricarboxylate” family, has yielded some of the most useful quantitative information to date about Δ[Ca²⁺] (Konishi et al., 1991; Delbono and Stefani, 1993; Claflin et al., 1994; Delbono and Meissner, 1996; Hollingworth et al., 1996, 2008, 2012; Rome et al., 1996; Baylor and Hollingworth, 2003, 2007; Harwood et al., 2011). Furaptra’s chromophore, which is similar to that of fura-2 (Grynkiewicz et al., 1985), undergoes a large change in both absorbance and fluorescence upon binding Ca²⁺. In contrast with fura-2, furaptra has a low affinity for Ca²⁺, with a dissociation constant (K_D,Ca) that is estimated to be 96 µM in the myoplasmic environment (Konishi et al., 1991; Baylor and Hollingworth, 2003). Because furaptra’s low affinity is achieved by virtue of a fast off-rate constant for Ca²⁺, which is probably at least several thousand per second in myoplasm at 20°C (Naraghi, 1997; Baylor and Hollingworth, 1998), furaptra should always respond rapidly to changes in [Ca²⁺]. These features make furaptra a very valuable indicator for measuring the large and brief Δ[Ca²⁺] that occurs in skeletal muscle fibers during AP-evoked activity. Some valuable kinetic information about Δ[Ca²⁺] in mammalian fibers has also been obtained with mag-fluo-4 (Capote et al., 2005; Calderón et al., 2009, 2010; Hollingworth et al., 2012), another low-affinity tricarboxylate fluorescent indicator that reacts rapidly with Ca²⁺ (Hollingworth et al., 2009).

Fig. 2 A shows examples of indicator-related Ca²⁺ signals (top two rows of traces) and tension responses (third row of traces) recorded in mouse soleus fibers that were activated by a single AP (dashed traces) or a brief high-frequency train of APs (five APs at 67 Hz; continuous traces). Fig. 2 B shows similar recordings in EDL fibers. The traces are averaged results from several similar experiments in which one fiber within a bundle of intact fibers was micro-injected with the membrane-impermeant (K⁺ salt) form of either furaptra or mag-fluo-4; thus, only one fiber contributed to the change in fluorescence (ΔF) in each experiment. Based on the markedly different speeds of the contractile responses in Fig. 2 (see legend), the fibers from soleus and EDL muscles have been classified as slow-twitch and fast-twitch, respectively; biochemical properties such as the myosin heavy chain isoform were not determined.

In the recordings in Fig. 2, the indicator’s fluorescence was collected from a length of fiber of ∼300 µm; thus, the fluorescence signals represent a spatial average from many sarcomeres. To ensure that the fluorescence signals were minimally influenced by movement artifacts, the fibers were stretched to a long sarcomere length (average value of 3.7 µm), which greatly reduces the fiber’s contractile response. The raw indicator measurements (topmost traces in Fig. 2) are shown in units of furaptra’s ΔF/F_R, the change in the indicator’s fluorescence divided by its resting fluorescence. The second row of traces shows the ΔF/F_R waveforms transformed to units of Δ[Ca²⁺] based on a two-step procedure (Baylor and Hollingworth, 2003). In the first step, the ΔF/F_R traces were scaled by the factor −1.07 (a calibration constant specific to furaptra fluorescence measured with excitation wavelengths of 410 ± 20 nm and emission wavelengths of 530 ± 60 nm), which converts the fluorescence change to the underlying change in the fraction of furaptra bound with Ca²⁺, Δf_CaD. The Δf_CaD traces are shown in Fig. 2 (C and D; traces with noise, which are described further below). In the second step, the Δf_CaD traces were converted to Δ[Ca²⁺] with the equation for 1:1 binding between Ca²⁺ and a low-affinity indicator: Δ[Ca²⁺] = K_D,Ca · Δf_CaD/(1 − Δf_CaD). As described in the next section, a more accurate estimate of spatially averaged Δ[Ca²⁺] can be obtained from the Δf_CaD traces with a different analytical approach.

In Fig. 2 A, Δ[Ca²⁺] during a single twitch in slow-twitch fibers has a peak of ∼10 µM and a full duration at half-maximum (FDHM) of ∼8 ms; the corresponding values in fast-twitch fibers are ∼18 µM and ∼5 ms, respectively (Fig. 2 B). These differences between fiber types are highly reproducible and are diagnostic of the fiber type (Hollingworth et al., 2012). During the high-frequency stimulation (five APs at 67 Hz), peak Δ[Ca²⁺] in slow-twitch fibers rises ∼20% above that elicited by the first AP; in contrast, in fast-twitch fibers, the peaks of Δ[Ca²⁺] elicited by subsequent APs have about the same amplitude as that elicited by the first AP. In both fiber types, the rate of decay of Δ[Ca²⁺] from its fifth peak is much smaller than that from its first peak. As described below, the reason for the progressive decrease in this decay rate with later APs in the train is that there is a progressive increase in the occupancy of the myoplasmic Ca²⁺ buffers with Ca²⁺ and, consequently, a decrease in the rate at which the buffers bind Ca²⁺ (Melzer et al., 1987; Hollingworth et al., 1996, 2012; Carroll et al., 1997; Baylor and Hollingworth, 2007).

Given the spatially averaged estimate of Δ[Ca²⁺] obtained from the furaptra Δf_CaD signal (Fig. 2), a spatially averaged estimate of the change in concentration of Ca²⁺ bound to the sites on any particular myoplasmic Ca²⁺ buffer can be calculated if the buffer concentration is known and a reaction scheme and reaction rate constants are available for the site (e.g., Robertson et al., 1981; Baylor et al., 1983; Cannell and Allen, 1984; Hollingworth et al., 2006; see also Fig. 5, described below). Table 2 lists the concentrations of the buffer sites considered in the calculations described here and in the next section; the reaction schemes and rate constants are given in Baylor and Hollingworth (2007) and Hollingworth et al. (2012). If the calculated changes in concentration of Ca²⁺ bound to these various buffers are summed and added to that of Δ[Ca²⁺] plus Δ[CaDye], one obtains a spatially averaged estimate of the total concentration of Ca²⁺ released by the SR. A more accurate estimate of Δ[Ca²⁺] and the other Ca²⁺ changes, however, can be obtained if the Δf_CaD signal from the indicator is simulated with a multi-compartment model of the myoplasmic Ca²⁺ movements based on a reaction–diffusion model (Cannell and Allen, 1984; Baylor and Hollingworth, 1998, 2007; Jiang et al., 1999; Novo et al., 2003; Hollingworth et al., 2012). Models of this type, in addition to using information about the reactions of Ca²⁺ with its buffers, incorporate information about (a) the dimensions of the sarcomere; (b) the locations of the Ca²⁺ release sites, the Ca²⁺ buffers, and Ca²⁺ pumping; and (c) the myoplasmic diffusion coefficients of the mobile myoplasmic constituents (free Ca²⁺, mobile buffers such as ATP, etc.). Calculations with these models reveal steep gradients in Δ[Ca²⁺] within the sarcomere. One consequence of these gradients is that the degree of saturation of the buffers with Ca²⁺ varies markedly at different times and sarcomeric locations. In the case of furaptra, this variation introduces error into the estimation of Δ[Ca²⁺] from the measured Δf_CaD signal and the 1:1 binding equation (Hirota et al., 1989; Baylor and Hollingworth, 1998, 2007). By taking into account the Δ[Ca²⁺] gradients, reaction–diffusion models are thought to yield more accurate estimates of spatially averaged Δ[Ca²⁺], of the amplitude and time course with which Ca²⁺ binds to the myoplasmic Ca²⁺ buffers, and of the amount of SR Ca²⁺ release.

Fig. 3 diagrams the multi-compartment model that we have used in the analysis of the furaptra Ca²⁺ measurements in mouse fibers. The myoplasmic water volume of a half-sarcomere of one myofibril is considered to be the basic unit of interest, and this volume is divided into 18 compartments of equal size. The buffer concentrations, as well as the locations of SR Ca²⁺ release and pumping, are assigned appropriately to the various compartments (see legend of Fig. 3 and Table 2). To relate the calculations with the model to the furaptra measurements, the model is driven by an assumed waveform for the SR Ca²⁺ release flux. The time course of this flux is estimated from the single-compartment (spatially averaged) version of the model (Baylor et al., 1983; Hollingworth et al., 1996), for which the release flux is fully determined by Δ[Ca²⁺] and the specified properties of the Ca²⁺ buffers. The amplitude of the flux waveform in the multi-compartment model is then adjusted iteratively until the amplitude of the simulated, spatially averaged Δf_CaD waveform matches that of the measured Δf_CaD waveform. The overall success of this approach is evaluated by a comparison of the time courses of the simulated and measured Δf_CaD waveforms. If these time courses are in agreement, it is reasonable to believe that the simulations give an approximate description of the underlying Ca²⁺ movements. In Fig. 2 (C and D), the top superimposed traces show examples of such comparisons, and the bottom traces show the SR Ca²⁺ release fluxes used to drive the simulations. The good agreement between the simulated Δf_CaD waveforms (noise-free traces) and the measured Δf_CaD waveforms (traces with noise) indicates that this strategy is successful in both fiber types.

Fig. 4 summarizes some results from these multi-compartment simulations. Responses in slow-twitch and fast-twitch fibers are shown as continuous and dashed traces, respectively. Fig. 4 A compares responses to a single AP, and B compares them to five APs at 67 Hz. For simplicity in the presentation, all waveforms in Fig. 4 have been spatially averaged; i.e., each trace was calculated as the average of the corresponding changes in the 18 compartments of the model. (Examples of waveforms calculated for the individual compartments are given in Baylor and Hollingworth, 2007). The traces in Fig. 4 are (from bottom to top): (a) Δ[Ca²⁺]; (b) the change in concentration of Ca²⁺ bound to the regulatory sites on troponin (Δ[CaTrop]); (c) the fractional occupancy of the troponin regulatory sites with Ca²⁺ (f_CaTrop, which, for this variable, includes the resting occupancy); (d) the change in concentration of Ca²⁺ bound to the sites on the slowly reacting buffers (Δ[CaSlowB], which includes Ca²⁺ binding to parvalbumin in fast-twitch fibers and to the troponin-nonspecific sites in slow-twitch fibers; see Table 2); (e) the change in concentration of Ca²⁺ bound to the SR Ca²⁺ pumps (Δ[CaPump]); (f) the change in concentration of Ca²⁺ returned to the SR as a result of Ca²⁺ pumping (Δ[CaPumped]); and (g) the total concentration of released Ca²⁺ (Δ[Ca_T]). Not shown, but included in the calculation of Δ[Ca_T], are Δ[CaATP] and Δ[CaDye] (see legend of Fig. 4). Except for f_CaTrop, these traces are shown in concentration units referred to the myoplasmic water volume.

In Fig. 4 A, peak Δ[Ca_T] in response to one AP in a slow-twitch fiber is 107 µM, which is achieved with a peak SR Ca²⁺ flux of 57 µM/ms and a flux FDHM of 1.7 ms (see also Fig. 2 C); the corresponding values for a fast-twitch fiber are 349 µM, 205 µM/ms, and 1.6 ms (see also Fig. 2 D). The modeled spatially averaged Δ[Ca²⁺] in slow-twitch fibers has a peak amplitude of 7.6 µM and an FDHM of 4.9 ms. As expected from Fig. 2, the corresponding values in fast-twitch fibers are larger and briefer, 16.1 µM and 3.7 ms. These properties of spatially averaged Δ[Ca²⁺] obtained with the multi-compartment models are thought to be more accurate than those obtained above with the single-compartment analysis (Fig. 2, A and B). The multi-compartment estimates of the FDHM of Δ[Ca²⁺] are substantially briefer: 4.9 versus 8 ms for slow-twitch fibers and 3.7 versus 5 ms for fast-twitch fibers. In both fiber types, peak Δ[Ca²⁺] is a small fraction of peak Δ[Ca_T] (<0.1); i.e., the great majority of the released Ca²⁺ is rapidly bound by the Ca²⁺ buffers, with only a small fraction remaining free.

In Fig. 4 A, peak Δ[CaTrop] shows a large difference between the two fiber types: 86 µM for slow-twitch fibers and 227 µM for fast-twitch fibers. This difference arises primarily because fast-twitch troponin has two Ca²⁺ regulatory sites per molecule, whereas slow-twitch troponin has only one (van Eerd and Takahashi, 1976; Potter et al., 1977; Robertson et al., 1981; Sweeney et al., 1990). If, however, the concentration of Ca²⁺ bound to the troponin regulatory sites is normalized by the total concentration of these sites (120 µM in slow-twitch fibers and 240 µM in fast-twitch fibers; Table 2), peak f_CaTrop is similar in slow-twitch and fast-twitch fibers: 0.79 and 0.95, respectively. Δ[CaSlowB] is also very different in the two fiber types, with values of 9 and 146 µM, respectively, at t = 50 ms. This difference reflects the large concentration of parvalbumin that is found in mouse fast-twitch glycolytic fibers compared with slow-twitch fibers, which have little or no parvalbumin (compare Table 2). Δ[CaPump] is also quite different in the two fiber types, with 10 µM in slow-twitch fibers and 28 µM in fast-twitch fibers at t = 50 ms. The primary reason is that the concentration of Ca²⁺ pump molecules is larger in fast-twitch fibers: 120 versus 48 µM (Table 2). A second reason is that, because Δ[Ca²⁺] is larger in fast-twitch fibers, the fractional occupancy of the pump sites with Ca²⁺ is larger. (Note: fast-twitch and slow-twitch fibers have different proportions of the two main isoforms of the Ca²⁺ pump molecules found in skeletal muscle, denoted SERCA1 and SERCA2a, but the functional properties of the two isoforms are similar; Lytton et al., 1992; Wu and Lytton, 1993.) Because of the larger amplitude of Δ[CaPump] in fast-twitch fibers, Δ[CaPumped] is also larger, with values at t = 50 ms of 3.7 µM for fast-twitch fibers and 1.1 µM for slow-twitch fibers. Ca²⁺ pumping is a relatively slow process, with an estimated turnover rate at saturating [Ca²⁺] of 3–4 s⁻¹ (16°C; Inesi et al., 1982; Young et al., 2003); thus, the resequestration of the released Ca²⁺ into the SR is not expected to be completed until several seconds after stimulation.

Fig. 4 B, which compares responses for the case of five APs at 67 Hz, reveals several new features. First, in both fiber types, the increments in Δ[Ca_T] caused by the second through fifth APs are much smaller than that caused by the first. Considered as a fraction of the first release, the values vary from 0.30 to 0.13 in slow-twitch fibers and from 0.26 to 0.15 in fast-twitch fibers (see also bottommost traces in Fig. 2). These marked reductions in release are thought to be caused primarily by the process of Ca²⁺ inactivation of Ca²⁺ release, in which a rise in [Ca²⁺] is sensed by the release system to inhibit release (Baylor et al., 1983; Schneider and Simon, 1988; Baylor and Hollingworth, 1988, 2007; Jong et al., 1995). The molecule(s) that mediates this negative feedback remains to be fully identified, although an interaction between calmodulin and an identified site on the SR release channel may be involved (Yamaguchi et al., 2011). This feedback has an obvious physiological function, as it prevents [Ca²⁺] from rising to higher levels than is required to activate the myofilaments, thereby avoiding: (a) an unnecessary delay in fiber relaxation after cessation of APs, (b) extra expenditure of ATP by the Ca²⁺ pumps to resequester Ca²⁺, and (c) potential damage to the mitochondria caused by excessive uptake of Ca²⁺.

A second noteworthy feature in Fig. 4 B is that peak f_CaTrop is close to 1 in both fiber types: 0.93 in slow-twitch fibers and 0.96 in fast-twitch fibers. Thus, in both fiber types, the models predict that Δ[Ca²⁺] during repetitive stimulation rises to a level at which activation of the myofilaments is not limited by [Ca²⁺]. The conclusion that the troponin regulatory sites are rapidly and nearly completely occupied with Ca²⁺ in both fiber types while the rate of tension development is much slower in slow-twitch than in fast-twitch fibers (see tension traces in Fig. 2, A and B) is consistent with observations in chemically skinned rodent fibers that the rate at which myosin produces force at saturating [Ca²⁺] is inherently slower with slow-twitch than with fast-twitch myosin (Metzger and Moss, 1990). Because the troponin regulatory sites and the sites on the other buffers (e.g., “SlowB”) become increasingly occupied with Ca²⁺ during the high-frequency stimulus, the ability of these sites to bind newly released Ca²⁺ decreases; as a result, there is a progressive decrease in the rate of decay of Δ[Ca²⁺] from its individual peaks during the train. Consistent with the longer lasting Δ[Ca²⁺] waveform, Δ[CaSlowB], Δ[CaPump], and Δ[CaPumped] all rise to substantially higher levels than those that occur with a single AP.

As noted above, the calculations indicate that the troponin regulatory sites rapidly bind a large fraction of the released Ca²⁺ in both slow-twitch and fast-twitch fibers. The fraction is smaller in fast-twitch fibers, however, because fast-twitch fibers have relatively larger concentrations of sites on the other buffers (Table 2), which compete with troponin for Ca²⁺. Thus, to achieve full occupancy of their regulatory sites, fast-twitch fibers must release substantially more Ca²⁺ than is expected from their twofold larger concentration of regulatory sites. The ability of fast-twitch fibers to release three- to fourfold larger amounts of Ca²⁺ than slow-twitch fibers (topmost traces in Fig. 4) at three- to fourfold larger rates (bottommost traces in Fig. 2) is achieved by means of comparable increases in the fractional volume of their SR (Eisenberg, 1983) and, concomitantly, in the number of the SR Ca²⁺ release channels and their controlling DHPR molecules (Hollingworth and Marshall, 1981; Lamb and Walsh, 1987; Franzini-Armstrong et al., 1988; Delbono and Meissner, 1996). The functional advantage of the large concentration of the slow-buffer sites in fast-twitch fibers is that a substantial fraction of the Ca²⁺ that is initially bound by troponin is subsequently bound by these sites (Gillis et al., 1982; Baylor et al., 1983; see also Fig. 4). By serving as a temporary myoplasmic storage site for released Ca²⁺, the slow buffers contribute importantly to the more rapid decline of Δ[Ca²⁺] that occurs in fast-twitch fibers, which helps to speed their contractile relaxation. An example of this slow-buffer function taken to an extreme occurs in the superfast swimbladder fibers of the toadfish (Opsanau tau), where the concentration of parvalbumin is nearly fourfold larger than that in mouse fast-twitch fibers (2.7 vs. 0.75 mM; Hamoir et al., 1980; Appelt et al., 1991; Tikunov and Rome, 2009), and the unusually brief Δ[Ca²⁺] elicited by an AP in swimbladder fibers can be maintained for extended periods at stimulation frequencies as high as 100 Hz (16°C; Rome et al., 1996; Harwood et al., 2011).

Fig. 5 illustrates several relevant differences between the modeled troponin reactions in slow-twitch and fast-twitch fibers. Ca²⁺ binds to the single regulatory site on each slow-twitch troponin molecule with a simple 1:1 reaction (Fig. 5 A), whereas Ca²⁺ binds to the two sites on each fast-twitch troponin molecule in a two-step reaction (Fig. 5 B). The rate constants for the slow-twitch reaction, which were estimated from information in Davis et al. (2007) in combination with comparisons of the type shown in Fig. 2 C (Hollingworth et al., 2012), are 0.4 × 10⁸ M⁻¹ s⁻¹ for the on-rate (k₊₁) and 26 s⁻¹ for the off-rate (k₋₁) (16°C); the corresponding value of K_D (= k₋₁/k₊₁) is 0.65 µM. In contrast, with fast-twitch troponin, Ca²⁺ is thought to react with the two regulatory sites with positive cooperativity (Fuchs and Bayuk, 1976; Grabarek et al., 1983; see also Baylor et al., 2002). To achieve cooperativity in the modeled troponin reaction, the first Ca²⁺ ion binds with low affinity and the second with high affinity. The reaction rate constants are k₊₁ = 1.77 × 10⁸ M⁻¹ s⁻¹ and k₋₁ = 1,542 s⁻¹ (K_D,1 = 8.72 µM), and k₊₂ = 0.885 × 10⁸ M⁻¹ s⁻¹ and k_-2 = 17.1 s⁻¹ (K_D,2 = 0.193 µM), respectively (Baylor et al., 2002; Davis, J.P., S.B. Tikunova, D.R. Swartz, and J.A. Rall. 2004. Biophysical Society 48th Annual Meeting. Abstr. 1135; Hollingworth et al., 2006). The steady-state level of free [Ca²⁺] that gives half-occupancy of these sites (Ca²⁺₅₀) is 1.3 µM (= sqrt (K_D,1 × K_D,2)), which is twice Ca²⁺₅₀ for the slow-twitch troponin reaction. These features are consistent with observations on mammalian skinned fibers that the tension–pCa curve in fast-twitch fibers is right-shifted with respect to that in slow-twitch fibers and has a steeper dependence on [Ca²⁺] (Kerrick et al., 1976; Stephenson and Williams, 1981; Ruff, 1989; Danieli-Betto et al., 1990). For example, in rat fibers, the [Ca²⁺] levels for half-activation of tension are ∼1.2 and ∼0.6 µM, respectively, for fast-twitch and slow-twitch fibers (22°C; sarcomere length of 2.7–2.8 µm; Stephenson and Williams, 1981).

Fig. 5 (C and D) presents a theoretical single-compartment analysis of some of the kinetic consequences of the modeled troponin reactions in the two fiber types. As revealed by this analysis, the more rapid rate of dissociation of Ca²⁺ from the regulatory sites that is observed in Fig. 4 B in fast-twitch fibers compared with slow-twitch fibers is explained by the more rapid decline of Δ[Ca²⁺] in fast twitch fibers, not by an inherently faster rate of Ca²⁺ dissociation from the fast-twitch regulatory sites. In Fig. 5 C, the bottom trace shows a pulse of [Ca²⁺], which starts at 50 nM (= [Ca²⁺]_R), rises in a square-wave fashion to 5 µM, where it remains for 50 ms, and then returns to the resting level, again in a square-wave fashion. The top trace shows the calculated Δ[CaTrop] response for slow-twitch troponin (compare Fig. 5 A), which rises exponentially from the resting level of 8.6 µM with a rate of 226 s⁻¹ to 106 µM (= 88.5% of saturation), and then decays back to the resting level with a rate of 28 s⁻¹. Fig. 5 D shows a similar calculation for the doubly occupied Ca²⁺ state of fast-twitch troponin (Ca₂Trop in Fig. 5 B), which is the troponin state that likely controls activation of the myofilaments. Here, the concentration of Ca²⁺ that is bound to the active state (= 2 × [Ca₂Trop]) is 0.4 µM at rest and rises to 217 µM at peak (= 90.5% of saturation). Because the fast-twitch troponin reaction involves two-steps, neither the “on” nor “off” response exactly follows a single-exponential time course. Nevertheless, both responses are very well fitted by single-exponential time courses (not depicted), with effective on- and off-rates of 153 and 17.2 s⁻¹, respectively. The effective off-rate in Fig. 5 D is smaller than that in Fig. 5 C, although Ca²⁺₅₀ is larger in fast-twitch than in slow-twitch fibers (1.3 vs. 0.65 µM). A significant advantage of the two-step cooperative troponin reaction (Fig. 5 B) is that it allows a more switchlike (all-or-nothing) control of the actomyosin system during activity. For example, the fraction of the troponin molecules in the activated state (the Ca₂Trop state) is negligible at rest in fast-twitch fibers (0.001), whereas, in slow-twitch fibers, the resting fraction in the CaTrop state (0.071) is not entirely negligible. The latter value would be expected to lead to a slight activation of the actomyosin system in slow-twitch fibers at rest and could contribute to the higher rate of resting energy consumption that has been reported in mouse soleus muscle compared with EDL muscle (Decrouy et al., 1993; Norris et al., 2010).

The results described in connection with Figs. 2, 4, and 5 were obtained at 16°C, an experimental temperature that facilitates survival of the fibers outside the animal. To assess the functioning of the fibers at more physiological temperatures, some measurements like those in Fig. 2 have also been performed at higher temperatures (22, 28, and 35°C; Hollingworth et al., 1996, 2012; Baylor and Hollingworth, 2003). For example, in fibers at 28°C stimulated by a single AP, the following parameter values were reported for slow-twitch (soleus) fibers versus fast-twitch (EDL) fibers: (a) time of peak and FDHM of twitch tension: 97 and 480 ms versus 23 and 97 ms, respectively; (b) peak amplitude and FDHM of Δ[Ca²⁺]: 9 µM and 4.4 ms versus 21 µM and 2.0 ms; and (c) the amount and peak rate of SR Ca²⁺ release: 120 µM and 105 µM/ms versus 358 µM and 473 µM/ms (Baylor and Hollingworth, 2003). These relative differences between fiber types are quite similar to those reported above at 16°C, and it is reasonable to believe that similar relative differences apply under fully physiological conditions.

The waveforms in Fig. 4 provide detailed estimates of the major myoplasmic Ca²⁺ movements that take place in mouse slow-twitch and fast-twitch fibers during twitches and brief tetani. Although it is too much to expect that all aspects of these comparisons are error free, we believe that the basic features shown in Fig. 4 provide a reasonable working model of Ca²⁺ signaling in the two fiber types. Hopefully, future measurements will permit corrections and refinements of the estimated Ca²⁺ movements. The analysis reveals that, for comparable stimuli, slow-twitch fibers release ∼0.3 times the amount of SR Ca²⁺ as fast-twitch fibers. A corollary prediction is that, to resequester the released Ca²⁺, the SR Ca²⁺ pumps in slow-twitch fibers consume ∼0.3 times the ATP as that in fast-twitch fibers. This factor is similar to that which characterizes the total ATP consumption during brief contractions of slow-twitch versus fast-twitch fibers (20°C; Crow and Kushmerick, 1982); in this case, however, the ATP consumption is mainly caused by myosin, with a minor fraction caused by the SR Ca²⁺ pumps (Barclay et al., 2007).

One interesting avenue for future investigation concerns the time course with which Δ[Ca²⁺] declines to zero after stimuli like those in Fig. 2. In both slow-twitch and fast-twitch fibers, our measurements with high-affinity fluorescent Ca²⁺ indicators reveal that this decline—and hence the time of pumping Ca²⁺ back into the SR—continues for some seconds (16°C). It remains to be determined how well the model predictions of Δ[Ca²⁺] on this slow time scale agree with these measurements. Another avenue concerns the properties of Δ[Ca²⁺] and the associated myoplasmic Ca²⁺ movements in fibers of the fast-twitch oxidative subtype (fatigue-resistant fast-twitch fibers; Berchtold et al., 2000; Schiaffino and Reggiani, 2011), which are not considered here. In mice, these fibers make up a significant fraction of the fibers in both soleus and EDL muscles (e.g., Crow and Kushmerick, 1982; Haida et al., 1989; Maréchal et al., 1995; Allen et al., 2001; Asmussen et al., 2003), and they remain to be studied with the methods described in this article.

We thank Drs. E. Michael Ostap and Lawrence C. Rome for comments on an early version of the manuscript.

This work was supported by grants from the U.S. National Institutes of Health (GM 086167) and the Muscular Dystrophy Association.

Richard L. Moss served as editor.