INTRODUCTION

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UNDER PHYSIOLOGICAL CONDITIONS, striated muscle develops force through the ATP-mediated cyclic interaction of myosin cross bridges with actin filaments. However, solution studies show that the actomyosin interaction is capable of hydrolyzing a number of both naturally occurring and synthetic ATP analogs (15, 23, 24). In addition, in skinned fiber preparations, which retain the three-dimensional geometry of the myofilaments, several of these ATP analogs support force production and shortening (16, 18, 23). The nucleotide triphosphate CTP has been of particular interest, because during maximum Ca²⁺ activation of skinned fibers CTP produces levels of active force and stiffness similar to those seen with ATP (16, 22). Furthermore, in solution, CTP is hydrolyzed by myosin at a significantly higher rate than is ATP (16), and, in skinned fibers, it produces a higher rate of force (i.e., tension) redevelopment following a brief unloaded shortening (k_tr; see Ref. 22). In contrast, the maximum velocity of fiber shortening [extrapolation to zero force from force-velocity relation (V_max)] is reduced when CTP replaces ATP (16, 19). Thus CTP has been a useful tool in probing the chemomechanical coupling in striated muscle fibers.

Striated muscle contractions in vivo frequently involve shortening against a submaximum load. Consequently, to provide a complete description of the effect of a change in substrate on muscle function, it is necessary to assess muscle mechanics under a wide range of loads. However, although the force-velocity relationship has been used to extrapolate maximum rates of shortening with various nucleotides (e.g., Refs. 16, 18), there have been no detailed analyses of the effect of nucleotide substrate on the function of muscle shortening against a load.

This paper examines the effect of substituting CTP for ATP as the nucleotide substrate on muscle function under the physiological condition of shortening against a load. Toward this end, for the first time, the power output in single skinned muscle fibers was examined in detail in the presence of either ATP or CTP. Because CTP decreases the maximum isometric force (P_o) and V_max, compared with results obtained with ATP, we tested the hypothesis that peak power would also be reduced by this change in nucleotide.

In addition, muscle fiber type has been shown to be a significant factor in determining the Ca²⁺-activated force and cross-bridge kinetics following a change in nucleotide (22). In maximally activated fibers, fiber-type differences in power output and shortening velocity in response to a change in nucleotide may be expected to be dominated by differences in the myosin isoform composition. Therefore, force-velocity and force-power curves were constructed under maximally activating conditions both in rat soleus, which expresses the cardiac /slow type I myosin heavy chain isoform (14), and in rabbit psoas fibers, which express the fast myosin IId isoform (1).

We found, surprisingly, that despite a decrease in both P_o and V_max, peak power was unaffected in either fast or slow fibers by the change in nucleotide. We demonstrate that this unexpected result can be explained by nucleotide-dependent changes in the rates of cross-bridge attachment and detachment, as described by Huxley's (10) model of contraction. However, the Huxley model does not reveal the cross-bridge transitions that underlie changes in curvature of the force-velocity curve. We discuss possible cross-bridge state transitions, based on current kinetic models of the cross-bridge cycle (8, 9), that could contribute to the curvature of the force-velocity relationship.

	METHODS

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Skinned fiber preparations. Experiments were performed on skinned fibers obtained from the soleus muscle of adult female Sprague-Dawley rats and the psoas muscle of adult male New Zealand White rabbits. Small bundles of fibers were isolated from muscles under cold relaxing solution and tied to glass capillary tubes. Fiber bundles were then skinned in relaxing solution containing 50% glycerol overnight at 4°C. The bundles were then stored at 20°C until use for up to 4 wk.

Individual fibers were pulled from a bundle and mounted between a force transducer (model 400A, Cambridge Technology, Cambridge, MA) and a galvanometer (Cambridge Technology), as previously described (13). Overall muscle fiber length (ML) was then adjusted to obtain a sarcomere length of 2.50-2.55 µm. The fiber width and depth were measured to determine the cross-sectional area (CSA; assumed to be elliptical). A 10-mW laser was directed through the fiber from below to follow changes in the sarcomere spacing, as previously described (22).

Solutions. ATP-containing solutions were prepared by using the program of Fabiato (7) to calculate final concentrations of metals, ligands, and metal-ligand complexes. These solutions contained 7 mM EGTA, 14.5 mM creatine phosphate, 20 mM imidazole, pMg 3.0, and 4 mM or 200 µM MgATP at 15°C. The pCa was set at 4.5 (activating) or 9.0 (relaxing), and KCl was added to bring the ionic strength to 180 mM. The pH was adjusted to 7.0 at 15°C. Solutions were made with 4 and 10 mM MgCTP replacing the ATP by assuming that the H⁺ and metal-binding constants of CTP were identical to those of ATP (16). In some experiments, additional creatine phosphokinase (CPK; 500 U/ml), which is capable of regenerating both ATP and CTP, was added to solutions to increase the nucleotide triphosphate buffering capacity of the fiber. This level of CPK is several times larger than that typically added to skinned fibers (5, 17). Results with and without added CPK were identical, indicating that the endogenous buffering capacity of the fibers was adequate for these experiments (see RESULTS).

Separate wells in the experimental chamber were used for ATP- and CTP-containing solutions to minimize residual contamination when changing nucleotides. In addition, fibers were washed twice with relaxing solution containing the new nucleotide before activating solutions were applied. Fibers were maximally activated with 4 mM ATP before and after each series of experiments to monitor any deterioration in force production. The ratio of final force to initial force was 0.996 ± 0.028 (n = 9) for psoas fibers and 0.989 ± 0.011 (n = 19) for soleus fibers.

Slack tests. The rate of unloaded shortening was assessed by using the slack-test protocol (6). Fibers maximally activated at pCa 4.5 were subjected to a shortening step, and the time between the length change and the beginning of force redevelopment was measured. The fiber was then relaxed and restretched to its original length. The time for force redevelopment from 7-11 shortening steps, measured as the time between the shortening step and the appearance of force just above baseline, was then plotted vs. the length of the shortening step. The unloaded shortening velocity (V₀) was then calculated as the slope of the time for force redevelopment vs. step length (Fig. 1).

View larger version (16K): [in this window] [in a new window]   Fig. 1.   Example of slack-test protocol for rabbit psoas (A) and rat soleus (B) fibers. ATP (4 mM; ) and CTP (4 mM; ) data collected from the same fiber. Insets: length (top) and force (bottom) traces vs. time (ms) used to construct ATP plot. A: initial fiber length (L0) = 1.89 mm; initial sarcomere length (SL0) = 2.53 µm, unloaded shortening velocity [slope of slack test plots (V0)] for ATP [V0(ATP)] = 2.79 muscle length (ML)/s; V0(CTP)= 1.11 ML/s. B: L0 = 1.55 mm, SL0 = 2.57 µm, V0(ATP) = 1.44 ML/s, V0(CTP) = 0.84 ML/s. L, change in length; t, duration of unloaded shortening.

Force-velocity and power curves. Force-velocity curves were constructed by maximally activating the fiber at pCa 4.5 and then allowing the fiber to shorten at a constant submaximal force for 1 s (Fig. 2). The preselected level of submaximal force was feedback controlled at 2,000 Hz via a custom-designed software program, as previously described (22). The fiber was then allowed to relax at pCa 9.0. Shortening velocity was subsequently calculated from the isotonic contraction as the slope of fiber length vs. time during the flat portion of the isotonic force vs. time trace (Fig. 2). The shortening velocity was determined from 4-10 isotonic contractions, with loads ranging from 2 to 80% of P_o under each nucleotide condition. The nucleotide was then changed by washing the fiber twice in relaxing solution containing the new nucleotide, and the process was repeated. In this way, each fiber served as its own control. P_o was determined by shortening the fully activated fiber beyond slack length. P_o was measured at the beginning of the experiment and after every fourth isotonic contraction to monitor any deterioration in fiber performance. The velocity at 0 force, i.e., V_max, was extrapolated by fitting Hill's hyperbolic equation to the force-velocity plots in the form of Eq. 1, where P and P_o are force and maximum force, respectively, and a and b are parameters with units of force and velocity, respectively

(1)

Fibers for which isotonic releases to <10% of P_o were not obtained were excluded from this analysis. Curvature of the force-velocity curves was quantified as a/P_o, a dimensionless parameter that is inversely related to the curvature.

View larger version (27K): [in this window] [in a new window]   Fig. 2.   Protocol for determining shortening velocity from force-velocity curves. A: force vs. time traces of isotonic shortening in a single rabbit psoas fiber for isotonic forces of 0.8, 0.65, 0.50, 0.3, and 0.10 maximum isometric force (Po; a-e, respectively). Forces are normalized to the maximum isometric force (Po = 245.9 kN/m2). B: length vs. time traces corresponding to isotonic traces in A. L normalized to L0 = 2.13 mm. Shortening in traces d and e ends at maximum allowed L (500 µm). SL0 = 2.53 µm.

Power was defined as the product of force and velocity and was normalized by the fiber volume, as determined by the product of fiber length and CSA. The plot of power per volume vs. force was fit to Eq. 2, and peak power was defined as the maximum value of this fit

(2)

In addition, for modeling purposes (see DISCUSSION), force-velocity curves were fit by the Huxley model (10) in the form of Eq. 3. In Eq. 3, f₁, g₁, and g₂ are rates of cross-bridge attachment and detachment, respectively, and h is a constant related to the distance over which a cross bridge may attach

(3)

Curve fitting and statistics. Curve fitting was performed by using the computer program Igor (WaveMetrics, Lake Oswego, OR). Data are presented as means ± SE, unless otherwise noted. ANOVA and Student's t-test were used as tests of significance. The confidence level was set at P < 0.05.

	RESULTS

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P_o. Single fibers from rabbit psoas and rat soleus produced similar amounts of maximum Ca²⁺-activated force when 4 mM ATP was used as a substrate, i.e., 246.4 ± 14 kN/m² (n = 4) and 234.5 ± 12.3 kN/m² (n = 13), respectively. These values are in general agreement with published values (12). The use of CTP to replace ATP resulted in a decrease in the normalized force, as summarized in Table 1. In rabbit psoas fibers, 4 mM CTP resulted in 95 ± 2% of the force/CSA seen with 4 mM ATP. An increase in the CTP concentration to 10 mM produced a further reduction to 75 ± 1% of the ATP-generated force. Rat soleus fibers, in contrast to the psoas fibers, produced only 75 ± 1% of the ATP-generated force with 4 mM CTP. An increase in the CTP concentration to 10 mM produced only a modest further decrease in force to 69 ± 1% of the force produced by 4 mM ATP. These results are in general agreement with previously reported values (16, 22).

View larger version (16K): [in this window] [in a new window]   Fig. 3.   Typical force-velocity curves for rabbit psoas (A) and rat soleus (B) fibers under various nucleotide conditions. , 4 mM ATP; , 0.2 mM ATP; , 4 mM CTP; , 10 mM CTP. Curves are fits to the Hill equation (see Eq. 1). A: Po = 240.1 kN/m2, L0 = 2.10 mm, SL0 = 2.55 µm. B: Po = 297.9 kN/m2, L0 = 2.31 mm, SL0 = 2.52 µm. CSA, cross-sectional area.

View larger version (20K): [in this window] [in a new window]   Fig. 4.   Power vs. force for rabbit psoas (A) and rat soleus (B) fibers. , 4 mM ATP; , 0.2 mM ATP; , 4 mM CTP; , 10 mM CTP. Error bars represent SE for each point. Curves are Eq. 2 drawn by using mean values of a, b, and Po determined by fitting each fiber individually.

View larger version (25K): [in this window] [in a new window]   Fig. 5.   Force-velocity curves from rabbit psoas (A, C) and rat soleus (B, D) fibers. Curves represent the Hill equation (Eq. 1) drawn by using mean values of a, b, and Po obtained from fits to individual fibers. Curves in C and D are normalized to maximum shortening velocity and maximum force under each nucleotide condition to emphasize changes in curvature.

	DISCUSSION

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Studies of skeletal muscle function in vitro typically focus on either isometric force or maximum shortening velocity. However, in the intact animal, muscles contract against widely varying loads. Therefore, in vivo skeletal muscle performance is more dependent on the power output than either isometric force or maximum shortening velocity. In this study, the effect of a change in substrate from ATP to CTP on the force-velocity relationship and power output was examined in fast psoas and slow soleus fibers. Soleus fibers exhibited a lower shortening velocity and higher degree of curvature in the force-velocity curve than did psoas fibers. Consequently, the peak power is less in soleus than in psoas. The change in substrate from ATP to CTP produced substantial decreases in maximum shortening velocity and-significantly reduced maximum force production in both fiber types. Therefore, substantial changes in the product of force and velocity, i.e., power output, would be predicted to result from the nucleotide exchange. It is both surprising and interesting, therefore, that the peak power reported here is unaffected by the nucleotide exchange in either fiber type. This unexpected finding is the result of a significant decrease in the curvature of the force-velocity relationship such that the peak power is maintained. This indicates that at the peak of the power curve the chemomechanical coupling process is equally effective with either nucleotide. Furthermore, the change in nucleotide would be expected to have relatively modest effects in the range of typical in vivo muscle performance, with more severe effects at the extremes of force production and shortening velocity.

Our earlier studies of isometric contractions found important fiber-type differences with ATP vs. CTP (22). The main fiber-type differences observed involved the force- and stiffness-pCa curves, which in soleus fibers became much steeper, approaching those of psoas fibers, when CTP replaced ATP. In contrast, psoas fiber force- and stiffness-pCa curves were only slightly affected. However, the relative changes in power output and the force-velocity curves reported here in response to the change in nucleotide were essentially the same in both fiber types examined. Thus, in terms of power output, muscle-type differences are preserved on change in nucleotide. Because the force-velocity and power experiments were performed at maximum Ca²⁺ activation, any interaction between myosin and the thin-filament activation mechanism was likely to be minimized. Therefore, it can be proposed that the nucleotide substrate can exert an effect through two mechanisms. First, there is a direct effect on the cross-bridge cycle that produces the change in curvature of the force-velocity relationship reported here. This effect is relatively independent of the myosin isoform and does not involve any myosin interaction with the thin-filament regulatory system. In addition, as we showed earlier (22), there is a Ca²⁺-sensitive interaction, likely mediated by the thin filament, which is muscle lineage dependent.

There are two main results of replacing ATP by CTP presented here; namely, a decrease in maximum shortening velocity and a decrease in curvature of the force-velocity relationship. Huxley's 1957 model of muscle contraction (10) provides the simplest model for discussing the effects of different nucleotides on the mechanics of contraction. In this two-state model, described by Eq. 3 (see METHODS), force-producing cross bridges bind with a rate determined by the rate constant f₁ and detach with rate constant g₁. Negative force-bearing cross bridges detach with rate constant g₂, and the curvature of the force-velocity relationship is primarily determined by the ratio g₂/(f₁ + g₁) (21). The results from psoas fibers reported here in the presence of 4 mM ATP can be adequately fit with values of 23 s¹ for the sum f₁ + g₁, and 169 s¹ for g₂ (Fig. 6, Table 4). In these fibers, V_max with 10 mM CTP is observed to decrease to ~60% of the 4-mM ATP level. Because the Huxley model predicts that maximum shortening velocity be linearly related to g₂, CTP must decrease g₂ by an amount similar to the decrease in shortening velocity. This is in excellent agreement with the value for g₂ of 97 s¹ obtained by fits to the 10-mM CTP data (Fig. 6, Table 4). Similar results are seen with soleus fibers. The decrease in g₂ also decreases the ratio of g₂/(f₁ + g₁) to a similar extent and, therefore, also results in a twofold decrease in the curvature of the force-velocity relationship. To reproduce the experimentally observed decrease in curvature of between three- and fourfold, the sum (f₁ + g₁) must also increase. This requires, at a minimum, an increase in either f₁ or g₁.

View larger version (16K): [in this window] [in a new window]   Fig. 6.   Comparison of Huxley model (Eq. 3) fit to experimental data from rabbit psoas (A) and rat soleus (B) fibers. , 4 mM ATP; , 10 mM CTP. Curves drawn by using parameters listed in Table 4.

In the Huxley model, an increase in (f₁ + g₁) produces an increase in k_tr. In agreement, we showed earlier that k_tr increases by ~40% in psoas and ~70% in soleus when CTP replaces ATP (22). Because f₁ is usually about fourfold greater than g₁ (e.g., Ref. 10), modeling changes in k_tr are most readily accomplished by changes in f₁. Modeling the increase in k_tr by a similar increase in f₁, as indicated above, results in an additional decrease in curvature of the force-velocity relationship. However, an increase in f₁ also leads to an increase in P_o. No such increase in P_o is observed, but, rather, P_o decreases significantly in both fiber types. To counteract the increased P_o caused by an increased f₁ requires that the force per cross-bridge interaction decrease substantially and/or that g₁ increase. Comparison of the published force-stiffness relationships from fibers constructed with both ATP and CTP indicates that decreases in the force per cross-bridge interaction are relatively small (<10% in psoas; Ref. 22) and would not overcome the increased P_o produced from a substantially increased f₁. Therefore, to mimic the force depression observed with 10 mM CTP, it is also necessary to increase the rate of detachment of positive force-bearing cross bridges, g₁.

As an alternative, an increase in g₁ could be hypothesized to be the primary cause of the increase in (f₁ + g₁) required to produce the experimentally observed increase in curvature of the force-velocity relationship. In this case, the increase in g₁ required to model the increase in k_tr would produce a decrease in P_o that is substantially greater than observed experimentally. To overcome this decrease requires either an increase in the force per cross-bridge interaction, which is not indicated by published force-stiffness records (22), or an increase in f₁. Thus an increase in (f₁ + g₁) to the extent necessary to fit the decreased force-velocity curvature observed when CTP replaces ATP requires increases in both f₁ and g₁.

Taken together, CTP has the apparent effect of increasing both f₁ and g₁ while decreasing g₂. This is sufficient to adequately account for the observed changes in P_o, a/P_o, and V_max reported here and the changes in k_tr reported previously (22). Woledge (25) has argued that an increase in either g₁ or g₂ would be sufficient to lead to a decrease in the efficiency of contraction. It can be predicted, therefore, that CTP is considerably less efficient as a fuel for muscle contraction than ATP. To our knowledge, this point has yet to be investigated experimentally.

Although the two-state Huxley model explains the observed mechanical responses well, kinetic data indicate that the cross-bridge interaction is a multi-step process (see Refs. 8 and 9 for review) and CTP is likely to affect several steps. It would be desirable to explain the observed changes in the force-velocity curve as manifestations of specific changes in a kinetic model. Assignment of kinetic transitions is, of course, model dependent. However, some general features can be gleaned from the above results. The main observation that needs to be explained is the substantial change in the curvature of the force-velocity relationship. It is this change in curvature that allows the peak power to be maintained in the presence of saturating concentrations of either nucleotide. A decrease in the concentration of nucleotide, such that peak power is dramatically reduced, would be expected to produce a significant redistribution of cross-bridge states. Specifically, there would be the formation of a large number of rigor bridges. During muscle shortening, these rigor bridges would oppose movement of the filaments, becoming significantly negatively strained, and lead to a decrease in the apparent g₂, which, in turn, leads to a decrease in curvature (10, 21, 25). However, at low ATP, we found no significant changes in the curvature of the force-velocity relationship in either fiber type. Therefore, changes in curvature, whether due to the difference in the myosin isoform between the two fiber types or due to the change in nucleotide substrate within a single fiber type, must not be the result of noncycling rigorlike states but due to differences in the cycling cross bridges.

The specific cross-bridge state transitions that could underlie the curvature of the force-velocity relationship have not been identified. The product release steps appear to be unlikely candidates for affecting the shape of the force-velocity curve. The rate-limiting step of maximum shortening is thought to be closely coupled to the ADP-release step (8, 9, 20). Therefore, an increase in the ADP concentration is expected to lead to a substantial slowing of the rate of shortening and, consequently, in the power output. Such a slowing of V_max with increasing ADP has been confirmed (4). However, the slowed V_max has not been accompanied by a decrease in curvature of the force-velocity relationship (4), eliminating the ADP release step as the determinate of the curvature. In addition, the release of P_i is widely thought to be associated with the force-producing transition (5, 8, 9), and elevated P_i has been shown to reduce force production but without a change in curvature of the force-velocity relationship (3). Also, we previously observed that the effect of an increase in P_i on the rate of force development was largely independent of the nucleotide (22). Therefore, it appears that the P_i-release step is not greatly affected by the change in nucleotide.

If the product-release steps, which are associated with transitions between weak- and strong-binding states, do not act as mediators of the decreased curvature observed when CTP replaces ATP, then the determination of curvature must involve transitions between other cross-bridge states. The force-velocity curve describes force-bearing states. Therefore, because weak-binding states do not bear significant force, it is probable that transitions involving strong-binding cross-bridge states are implicated in altering the curvature of the force-velocity relationship. The model we used previously to explain the effects of a change in nucleotide substrate contained only one state transition that involved a strong-binding cross-bridge state but not the release of product (22), namely, a weak-to-strong transition before P_i release. This step was determined to be the rate-limiting step of force production in psoas fibers, but not in soleus. Because of this, it seems unlikely that a change in this step would produce a similar effect on the force-velocity curve in both psoas and soleus muscles. Therefore, we propose that the state transition underlying the curvature of the force-velocity relationship is an isomerization between strong-binding cross-bridge states, which occurs after the release of P_i but before the nucleotide diphosphate release. Testing of this proposal will require future studies and the development of cross-bridge models that incorporate such an isomerization.