INTRODUCTION

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MECHANICAL RELAXATION IN skeletal muscle fibers can be divided into four phases. First, there is an initiation phase beginning after the last stimulus during which force remains approximately constant. The second phase consists of a slow, almost linear decay in force during which the sarcomeres remain isometric. This slow phase is followed by a shoulder during which the sarcomeres begin to move and then followed by a fast, exponential phase in which sarcomere movements are amplified (6). The factors that determine the rates of the slow and fast phases have not been well established. This is in large part due to the difficulty in gaining access to the interior of the fiber while maintaining the ability to produce a physiologically rapid decrease in Ca²⁺. Skinned fiber preparations allow access to the contractile apparatus but eliminate the Ca²⁺ sequestration ability of the fiber that is essential for physiological relaxation. Therefore, studies of relaxation have been largely limited to the use of intact fibers. Some factors that have been suggested to affect the rate of relaxation are the rate of Ca²⁺ removal from the sarcoplasm (11, 16), Ca²⁺ dissociation from troponin C (TnC) (13), and sarcomere motion (12).

This paper describes two methods of producing relaxation in skinned fibers that result in rates similar to those seen in intact fibers. First, fibers were mechanically skinned with the sarcoplasmic reticulum (SR) left intact. Ca²⁺ released by photolysis of the caged Ca²⁺ DM-Nitrophen (15) was subsequently sequestered by the SR. This procedure results in a force transient similar to a twitch. Second, photolysis of the caged Ca²⁺ chelator diazo-2 (1) was used to rapidly reduce the Ca²⁺ level in actively contracting skinned fibers, thus mimicking the relaxation seen from a tetanus. This second method was then used to investigate the roles of Ca²⁺ and sarcomere stability on the rates of relaxation.

	MATERIALS AND METHODS

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Skinned and intact fibers. Fibers from the tibialis anterior muscle of the frog Rana temporaria were mechanically skinned on a cooled (~10°C) stage under a dissecting microscope as previously described (21). Fibers that sustained visible damage to the myofibrils during skinning were discarded. Aluminum T-clips were attached to the ends of the skinned fibers, and the fiber ends were fixed in a 25% glutaraldehyde solution to provide a firm, minimally compliant attachment to the experimental apparatus (4). If the protocol required the destruction of the SR, the fibers were soaked for 30 min in relaxing solution containing 1% Triton X-100. Electron micrographs of fibers after Triton X-100 treatment indicated complete destruction of all intracellular membranes (M. Yamaguchi, P. A. Wahr, and J. A. Rall, unpublished observations). Fibers were used within a few hours of being skinned and remained in dissecting solution until transfer to the experimental chamber.

Experimental apparatus. The experimental apparatus has been described in detail previously (21). Briefly, skinned fibers were mounted by the T-clips in one of three 325-µl chambers milled in a spring-mounted aluminum block between a Cambridge force transducer (Cambridge Technologies, series 400, Watertown, MA) and either a small motor (Cambridge Technology, model 372) for rapidly shortening the fiber or a stationary hook. Solutions were changed by manually lowering the block containing the chambers, sliding a new chamber underneath the fiber, and then raising the block. Small aluminum inserts were used with the caged compounds to decrease the volume of the chambers to 50-100 µl. The striation spacing of the fiber was adjusted to 2.4 µm by measuring the first-order diffraction pattern from a 5-mW HeNe laser directed through the fiber.

Solutions. The bathing solutions for the preparation of skinned fibers were prepared according to a computer program developed by R. Godt (Medical College of Georgia), whereas the solutions containing caged compounds were prepared using a program developed by Fabiato (7). The components of these solutions are given in Table 1. Dissecting and relaxing solutions were prepared from stocks and refrigerated. Caged compound solutions were made up in stock solutions containing all ingredients except creatine phosphokinase (CPK) and the caged compound and stored frozen. Diazo-2 (Molecular Probes, Eugene, OR) was dissolved at high concentration in a small amount of the stock and later diluted to the appropriate concentration. DM-Nitrophen (Calbiochem, La Jolla, CA) was weighed out and added to the stock solution as a powder. These solutions were kept frozen in aliquots of ~200 µl until the time of the experiment. These aliquots were prepared frequently in small amounts and used within several days. The dissociation constants for Ca²⁺ and Mg²⁺ from DM-Nitrophen at 10°C utilized in these studies were 21.0 nM and 14.1 µM, respectively, as determined previously (21). Shortly before the experiment, the solution containing the caged compound was thawed and ~1 mg/ml CPK was added just before use. Care was taken to avoid exposing solutions containing caged compounds to excessive light to prevent degradation of the caged compound.

General caged compound protocol. Fibers were mounted in a chamber filled with relaxing solution. The sarcomere length was set at 2.4 µm, and the fiber was transferred to a chamber containing the caged compound solution. The fiber was soaked until a plateau in the force trace was reached or, if no force was developed, for a minimum of 2 min. The fiber was removed from the chamber and then flashed in air. The temperature was noted, and the fiber returned to relaxing solution. Thus the fibers were allowed to be in air for <3 s. Fibers were allowed a 5-min rest in relaxing solution before the next flash.

Data analysis. Twitches and twitchlike contractions were fit to the equation where k_R and A_R are the rate and amplitude of the relaxing phase and k_C and A_C are the rate and amplitude of the force-producing phase, F is force, and t is time. The fast, exponential phase of relaxation from tetani and tetanus-like contractions was fit to the equation where k_r1 and k_r2 are the rate constant of the fast phase of relaxation, to evenly spaced points along the curve from the first 500 ms following the shoulder. Because the shoulder is fairly broad, t_o was used as an estimate of its position (t_shoulder) for analytical purposes.

	RESULTS

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Twitchlike and twitch contractions. Twitchlike contractions were induced in skinned fibers and compared with twitch contractions in intact fibers. Figure 1A shows the time course of a twitch and tetanus in an intact fiber. Mechanical skinning of the fibers leaves the SR able to take up Ca²⁺ released on photolysis of DM-Nitrophen. In the tetanus-like experiments described below, the amount of Ca²⁺ released on photolysis exceeded the Ca²⁺-sequestering capacity of the SR. Therefore, to produce a transient force similar to a twitch, it was required that the Ca²⁺ released on photolysis be reduced. This reduction in Ca²⁺ release was accomplished by reducing the fraction of DM-Nitrophen bound with Ca²⁺ by decreasing the Ca²⁺ concentration in the DM-Nitrophen solution (with an increase in the Mg²⁺ concentration to prevent the MgATP concentration from decreasing, see twitchlike SR solution in Table 1). Flash photolysis of DM-Nitrophen under these conditions produced a twitchlike contraction, as shown in Fig. 1B (trace marked Triton). Destruction of the SR by soaking in Triton X-100 abolished these twitchlike contractions and produced a forceful, tetanus-like contraction with little relaxation (Fig. 1B, trace marked +Triton). This result indicates that Ca²⁺ sequestration by the SR was indeed responsible for the relaxation.

View larger version (18K): [in this window] [in a new window]   Fig. 1.   Twitch and twitchlike contractions in intact and skinned fibers. Twitch or twitchlike responses are compared with tetanus or tetanus-like responses from the same fiber. A: intact single fiber. B: sarcoplasmic reticulum (SR)-induced relaxation, which is abolished by destruction of SR with 1% Triton X-100 for 30 min (fiber activated in twitchlike solution SR, free Mg2+ concentration = 0.19 mM, see Table 1). C: relaxation induced by Ca2+ rebinding to Mg · DM-Nitrophen. Fiber was activated in twitchlike solution DM (high Mg2+-DM, free [Mg2+] = 0.19 mM) or in tetanus-like solution (low Mg2+-DM, free [Mg2+] = 36 µM, see Table 1). D: twitchlike and twitch responses from A-C normalized to peak force to show similarity in kinetics.

Characterization of diazo-2 relaxation. Diazo-2-induced relaxation was produced in fibers where the SR was destroyed to ensure a uniform Ca²⁺ activation throughout the fiber. An example is shown in Fig. 2A, in which the parameters of the fit of the contraction and relaxation are described. The magnitude of relaxation produced by photolysis of diazo-2 was limited to ~70% of the maximum force produced by photolysis of 2 mM DM-Nitrophen. This limitation probably is due to the fact that the dissociation constant for Ca²⁺ binding on photolysis decreases ~10⁵ for DM-Nitrophen (15) but only increases ~30-fold for diazo-2 (1). Photolysis of diazo-2 produced nearly complete relaxation in fibers activated at pCa 5.8 to produce 75.5 ± 4.3% (n = 5) of F_max. The diazo-2-induced relaxation displayed the same phases as seen during relaxation from a tetanus in intact fibers as shown by the example in Fig. 2B in which relaxations from skinned and intact fibers are compared.

View larger version (14K): [in this window] [in a new window]   Fig. 2.   Comparison of relaxation in skinned and intact fibers. A: an example of a maximum DM-Nitrophen-induced contraction and a diazo-2-induced relaxation from the same fiber with method of analysis illustrated. tshoulder and kshoulder, Time and rate of slow (shoulder) phase of relaxation; kr1 and kr2, fast-phase rate constants; Fpre, force developed by preceding maximal contraction; Finit, initial force; Ffinal, final force. B: an example of diazo-2-induced relaxation from high initial force superimposed on relaxation from an electrically stimulated intact fiber (1.3-s tetanus).

Effect of sarcomere stabilization on relaxation. The sarcomere pattern in skinned fibers deteriorates with activation. To minimize this effect, fibers were repeatedly released and restretched during contraction. This procedure has been shown to stabilize the sarcomeres during contraction (3). When this procedure to stabilize sarcomere uniformity was not used, the kinetic parameters of the subsequent relaxation were significantly increased (Table 3). The parameters of the slow phase, k_shoulder and t_shoulder, are ~1.7- to 2-fold faster than in fibers subjected to the stabilization protocol, which in turn are 1.8-fold faster than in the intact fibers. The fast phase parameters, k_r1 and k_r2, which with stabilization are not significantly different from intact fibers, are also increased when sarcomere stabilization is not employed. Thus it is inferred that the relaxation rates are influenced by sarcomere uniformity, i.e., more uniform sarcomeres lead to slower relaxation rates.

Effect of altered Ca²⁺ level on relaxation. The amount of force produced before photolysis of diazo-2 varied with the level of Ca²⁺ in the diazo-2 solution, and this force level was taken as a measure of the level of Ca²⁺ activation of the thin filament. Figure 3 compares the diazo-2-induced relaxation from high (1.0 F_init/F_max) and low (0.2 F_init/F_max) force. Plots of the kinetic parameters of relaxation vs. relative force are shown in Figs. 4 and 5. It is apparent from Figs. 4 and 5 that the overall rate of relaxation is faster from low force. Both the k_shoulder (Fig. 4A) and the t_shoulder (Fig. 4B) are slowed with increased Ca²⁺-activated force. Also, k_shoulder is 6- to 15-fold more sensitive to the relative Ca²⁺-activated force level [150.2 ± 31.7 s¹/F_rel (where F_rel = F_init/F_max), Fig. 4A] than the fast-phase rate constants (k_r1 = 28.6 ± 11.3 s¹/F_rel, Fig. 5A; k_r2 = 9.4 ± 3.3 s¹/F_rel, Fig. 5B). It is important to note that the absolute values of these parameters (k_shoulder, t_shoulder, k_r1, and k_r2) were not dependent on the diazo-2 concentration in the range of 1-4 mM. This result suggests that the Ca²⁺ sequestration rate is not limiting the overall rate of relaxation. These results are in agreement with the hypothesis that the slow phase is dominated by the rate of Ca²⁺ removal from TnC, whereas the rate of the fast phase is dominated by the rate of cross-bridge detachment and is therefore relatively insensitive to Ca²⁺. It must be remembered, however, that fibers soaked in a high-pCa solution require a much longer activation time to reach a steady-state force than fibers exposed to a lower pCa. It is possible that these differences in activation times might lead to an increased level of sarcomere disorder under low-force conditions, which would cause an increase in the overall rate of relaxation (Table 3). However, this prediction would be contrary to the reported result that lower activation levels lead to decreased sarcomere disorder (8, 9, 14).

View larger version (10K): [in this window] [in a new window]   Fig. 3.   Comparison of diazo-2 relaxation from high and low Ca2+-activated force. In the trace marked high force, fiber was activated in a pCa 5.0 solution and induced to relax by photolysis of diazo-2 from Finit/Fmax of 1.0 to Finit/Fmax of 0.67 (where Finit is force developed in diazo-2 solution immediately preceding flash photolysis and Fmax is average force from DM-Nitrophen contractions given before and after each diazo-2 contraction). In the low-force trace, a different fiber was activated in a pCa 6.0 solution and induced to relax from Finit/Fmax of 0.2 to 0 force. Force traces have been normalized.

View larger version (18K): [in this window] [in a new window]   Fig. 4.   Kinetics (kshoulder, A) and duration (tshoulder, B) of the slow phase of relaxation induced by photolysis of diazo-2 vs. relative force. Solid lines are least squares linear regression fits to data; 95% confidence intervals are indicated by dashed lines. A: kshoulder, with slope = 150.2 ± 31.7 s1/Frel, y-intercept = 158.2 ± 22.5 s1, r = 0.807, n = 14. B: tshoulder, with slope = 111.8 ± 12.5 ms/Frel (where Frel = Finit/Fmax), y-intercept = 1.0 ± 8.9 ms, r = 0.933, n = 14.

View larger version (17K): [in this window] [in a new window]   Fig. 5.   Kinetics [kr1 (A) and kr2 (B)] of the fast phase of relaxation vs. relative force. Solid lines are least squares linear regression fits to data; 95% confidence intervals are indicated by dashed lines. A: kr1, with slope = 28.6 ± 11.3 s1/Frel, y-intercept = 40.5 ± 8.0 s1, r = 0.347, n = 14. B: kr2, with slope = 9.4 ± 3.3 s1/Frel, y-intercept = 11.0 ± 2.3 s1, r = 0.408.

	DISCUSSION

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The transition from the slow to the fast phase of relaxation occurs when the sarcomeres cease to be isometric (6). This transition indicates that the kinetics of cross-bridge detachment is dependent on the amount of mechanical strain on the individual cross bridges. This factor is not present in solution studies of the actomyosin ATPase. For this reason, a major goal of this study was to develop a method of producing relaxation in skinned fibers with kinetics similar to those seen in intact fibers. This goal was accomplished through the use of diazo-2 to rapidly (within a few milliseconds) decrease the Ca²⁺ level in skinned fibers (17, 18). Because excessive sarcomere movement is expected to accelerate the kinetics of the slow phase of relaxation and shorten its duration, it was necessary to minimize end compliance in the fiber through the use of glutaraldehyde fixation of the ends to characterize slow-phase relaxation (4).

Because Ca²⁺ sequestration by diazo-2 is considerably faster than by intact SR and because the rate of Ca²⁺ removal may be a determinant of the relaxation rate (11, 16), a potential concern is that the relaxation induced by photolysis of diazo-2 is qualitatively different from that in the intact fiber. It must be remembered, however, that in intact fibers the fall in Ca²⁺ concentration precedes and is considerably faster than that of force relaxation following both twitches and tetani (2, 5). Therefore, the rate of Ca²⁺ sequestration cannot be the sole determinant of the rate of relaxation but may influence the overall relaxation rate. Consequently, the increased rate of Ca²⁺ sequestration by diazo-2 over the SR may serve to increase the overall rate of relaxation but should not alter the fundamental kinetic pathways. Indeed, relaxation in response to diazo-2 is qualitatively similar, in both slow and fast phases, to relaxation in intact fibers (see Fig. 2), indicating that the mechanism of relaxation is likely to be qualitatively similar for both the intact and skinned fibers. Thus the kinetics of relaxation can be studied in skinned fibers. This preparation has the advantage of having a fiber interior that is accessible to manipulation of factors thought to play a role in determining the rate of muscle relaxation. However, the rates of relaxation observed in skinned and intact fibers have quantitative differences. The relaxation in response to diazo-2 photolysis in skinned fibers is initially faster but later slower and not as complete as that seen in intact fibers. Differences in the kinetics of relaxation in skinned fibers compared with intact fibers may be due to changes in the end compliance, contractile filament lattice spacing, and/or sarcomere homogeneity of the fibers produced by skinning.

Determinants of the time to shoulder during relaxation. The previously published force records of diazo-2-induced relaxation in skinned frog fibers lack the rate-limiting slow phase of relaxation characteristic of intact muscle (17, 18). In contrast to the previous study, care was taken in the present work to ensure a firm, minimally compliant attachment to the apparatus by glutaraldehyde fixation of the fiber ends. This technique has allowed the observation of the slow phase of relaxation in all force traces examined here. Thus it appears that the fiber must be held at least partially isometric during relaxation for the slow phase to occur. The requirement of sarcomere isometry for the occurrence of the slow phase is in agreement with the observed loss in sarcomere isometry at the time of the transition from the slow to the fast phase (6). This observation leads to the prediction that an increase in sarcomere homogeneity should result in a delayed appearance of the shoulder that has been observed in intact frog fibers (12). This prediction also is confirmed here in skinned fibers by the observation that fibers that were subjected to a rapid release and restretch during force development, which has been shown to improve sarcomere homogeneity (3, 8), exhibited decreased kinetics and longer slow phase durations than fibers that were not subjected to this protocol (see Table 3). Although the lower relative force (F_init/F_max) observed without the shortening protocol (0.73 vs. 0.91, Table 3) is expected to have an effect on the t_shoulder (see Fig. 4B), this cannot be the sole cause of the shorter duration seen without the shortening protocol. The predicted t_shoulder for sarcomere stabilized fibers at a F_init/F_max of 0.73 (Fig. 4B) is 81 ms, which is longer than the value of 49.3 ms (Table 3) observed without the sarcomere stabilization technique. Likewise, the t_shoulder observed in intact fibers (176.8 ms, Table 3) also is considerably longer than predicted from Fig. 4B (111 ms at 1.0 F/F_pre). These results provide convincing evidence that 1) the duration of the slow phase of relaxation is dependent on the ability of the sarcomeres to remain isometric and 2) sarcomeres are less homogeneous in skinned than in intact fibers. Furthermore, the inverse correlation of the rate (Fig. 4A) and duration (Fig. 4B) of the slow phase indicates that the loss of isometric sarcomeres can play a major role in accelerating the overall rate of relaxation.

Modulation of the slow phase of relaxation by Ca²⁺ concentration. The slow phase of relaxation in skinned fibers is 6-15 times more sensitive to Ca²⁺ than the fast phase. Also, the k_shoulder is inversely correlated with the duration of this phase, t_shoulder. Because it is conceivable to have a slow k_shoulder of short duration, the correlation of these two parameters is not necessarily expected. As the level of Ca²⁺ activation is reduced, k_shoulder increases (Fig. 4A) and t_shoulder decreases (Fig. 4B). Thus the slow phase of relaxation is at least in part determined by the level of Ca²⁺ activation. Because none of the components of relaxation is affected by variation of the Ca²⁺ buffering capacity (in the range of diazo-2 from 1 to 4 mM), these results suggest that the fibers relax more slowly when relative force development is high because Ca²⁺ dissociates more slowly from TnC. This conclusion is consistent with the suggestion that the affinity of TnC for Ca²⁺ increases as the number of bound cross bridges increases (10, 20). This increased affinity of Ca²⁺ for TnC would lead to a decreased dissociation rate of Ca²⁺ from TnC and thus a longer slow phase and slower relaxation. Consistent with this suggestion, Johnson et al. (13) recently have shown that as the rate of Ca²⁺ sequestration is increased in intact frog skeletal muscle fibers, the overall rate of relaxation increases until it approaches a rate similar to the rate of Ca²⁺ removal from purified whole troponin. Thus Ca²⁺ removal from troponin appears to be an important rate-limiting step in muscle relaxation.

Fast phase of relaxation. The fast phase of relaxation in response to photolysis of diazo-2 in skinned fibers is well fit by a double exponential equation, whereas in the intact fiber it is more monoexponential. The rates without sarcomere stabilization observed here at 10°C (Table 3) are in reasonable agreement with published results of relaxation induced by photolysis of diazo-2 in frog skinned fibers at 12°C, where rates of 42 s¹ (k_r1) and 12 s¹ (k_r2) have been reported (18). With repeated releases and restretches of the fiber to stabilize the sarcomeres, the diazo-2-induced fast phase rate constants from high force (0.91 F_init/F_pre) correspond closely with those observed in intact fibers (Table 3).

Twitchlike contractions. The twitchlike contractions induced by photolysis of DM-Nitrophen in skinned fibers with intact SR provide a potentially useful model for the study of SR function and relaxation in situ. The kinetics of contraction and relaxation are similar but somewhat slower than those observed in the intact fiber (Table 2). These differences may be due to differences in end compliance in skinned and intact fibers. Another possibility is that the slower kinetics of relaxation may relate to the fact that parvalbumin diffuses out of skinned fibers. Parvalbumin is known to accelerate the rate of relaxation in frog skeletal muscle by about twofold (11). Its absence may explain the slower relaxation rate in skinned fibers. Nonetheless, the overall relaxation rate from a twitch in skinned fibers with functional SR of 10.3 s¹ (Table 2) is similar to the fast phase rate of 13.0 s¹ observed in skinned fibers induced to relax by diazo-2 photolysis (Table 3, with stabilization). This similarity suggests that the same mechanisms underlie relaxation in twitches and tetani.