Cooperative Mechanisms in the Activation Dependence of the Rate of Force Development in Rabbit Skinned Skeletal Muscle Fibers

In skeletal muscle, Ca²⁺ binding to low affinity sites on troponin C (TnC) initiates a series of molecular events that ultimately allow strong binding of cross-bridges to actin and subsequent force development (for review see Gordon et al. 2000). During relaxation, dissociation of Ca²⁺ from TnC initiates inactivation of the thin filament and subsequent detachment of cross-bridges from actin. While Ca²⁺ binding to TnC is required for contraction, complete activation of tension and the kinetics of tension development appears to arise from interactive effects of Ca²⁺ binding to TnC and cross-bridge binding to actin (Lehrer 1994; Gordon et al. 2000). Previously, McKillop and Geeves 1993 proposed a general model for the regulation of muscle contraction in which the thin filament exists in three distinct states; i.e., blocked, closed, and open. In this model, Ca²⁺ binding to TnC shifts the thin filament from the blocked state to the closed state, which appears to involve Ca²⁺-dependent movement of tropomyosin (Haselgrove 1973; Huxley 1973; Parry and Squire 1973). In the presence of Ca²⁺, strong binding of cross-bridges to actin shifts the thin filament from the closed state to the open state. Thus, complete activation of the thin filament in terms of numbers of strongly bound cross-bridges requires both Ca²⁺ and strong-binding myosin cross-bridges, an idea which has gained considerable experimental support (Gordon et al. 2000).

It is well established that the regulation of Ca²⁺-activated force in striated muscles involves cooperative interactions within the thin filament. This is evident, for example, in the biphasic form of the force-pCa relationship, which is steeper at low levels of Ca²⁺ than at high because of greater intermolecular cooperation at forces less than ∼0.50 P_o (for review see Moss 1992). Furthermore, most investigators have observed that the steepness of the force-pCa relationship is relatively high in skeletal muscle, i.e., Hill coefficients of 4 and greater (Moss 1992). Since skeletal TnC has just two low affinity Ca²⁺ binding sites (for review see Grabarek et al. 1992), the large Hill coefficients observed in skinned fibers are generally thought to manifest cooperative processes in the activation of contraction. For example, activation of one region of the thin filament by Ca²⁺ or strong-binding cross-bridges appears to increase the likelihood of activation of adjacent regions (for review see Lehrer 1994).

A model of activation proposed by Campbell 1997 predicts that cooperative interactions within the thin filament are a dynamic component of force development in striated muscles. Cross-bridge binding to the thin filament was proposed to cooperatively increase the number of cross-bridges bound to the thin filament and the rate of subsequent cross-bridge binding. In fact, there are several reports that the rate of force redevelopment (k_tr) in skeletal muscles varies as much as 10-fold when [Ca²⁺] is varied from threshold to maximal values (Brenner and Eisenberg 1986; Metzger et al. 1989; Swartz and Moss 1992; Palmer and Kentish 1998). Typically, k_tr is thought to be the sum of forward and reverse rate constants describing the transition between non–force- and force-generating states, i.e., f_app and g_app, respectively (Brenner and Eisenberg 1986). A model in which f_app varies with the level of activator Ca²⁺ has been proposed to account for the activation dependence of k_tr (Brenner 1988), but this and other models (Landesberg and Sideman 1994; Hancock et al. 1997; Regnier et al. 1998; Brenner and Chalovich 1999) do not account for the effects of strong-binding cross-bridges on k_tr (Swartz and Moss 1992). According to Campbell's model, the Ca²⁺ dependence of k_tr is not due to direct effects on either f_app or g_app, but instead arises because of effects of strongly bound cross-bridges to cooperatively recruit noncycling cross-bridges. At low [Ca²⁺], the number of noncycling cross-bridges is high, so that progressive cooperative recruitment of cross-bridges from this pool would slow the overall rate of force development. The first cross-bridges that bind recruit additional cross-bridges, which then bind and recruit still more cross-bridges, and so forth, until the force becomes steady. At higher levels of Ca²⁺, cooperative slowing of the rate of force redevelopment would be minimized because Ca²⁺ binding to TnC would immediately recruit most cross-bridges into the cycling pool, leaving few cross-bridges available for cooperative recruitment. If this model is correct, eliminating the effects of molecular cooperation would be expected to eliminate the activation dependence of k_tr, i.e., k_tr should be similar at all levels of activation. Previous studies on skinned fibers used a strong-binding, non–force-generating derivative of myosin subfragment-1 (i.e., N-ethylmaleimide–modified myosin subfragment-1 or NEM-S1) to increase the number of strongly bound cross-bridges and found that NEM-S1 increased k_tr at submaximal levels of activation, i.e., at low [Ca²⁺] or low force (Swartz and Moss 1992). However, activation dependence of k_tr was not completely eliminated by NEM-S1, since k_tr at intermediate levels of activation was still less than at low or high levels of activation.

The present study was done to further investigate the mechanisms underlying the activation dependence of the rate of force development in skinned skeletal muscle fibers, which was done by varying the degree of molecular cooperation during activation. Fibers were treated with NEM-S1 to promote strong binding of endogenous cross-bridges (Swartz and Moss 1992), or subjected to partial extraction of TnC to limit the spread of activation along the thin filament (Brandt et al. 1984, Brandt et al. 1990; Moss et al. 1985), or both. Our findings show that it is necessary to apply both NEM-S1 and the partially extracted TnC to completely eliminate the activation dependence of k_tr.

The composition of relaxing solution was as follows (in mM): 100 KCl, 20 imidazole, 4 MgATP, 2 EGTA, and 1 free Mg²⁺, pH 7.0 at 22°C. Activating solution contained (in mM): 79.2 KCl, 20 imidazole, 14.5 creatine phosphate, 7 EGTA, 5.42 MgCl₂, and 4.68 ATP, with [Ca²⁺]_free ranging from 1 nM (i.e., 9.0 pCa) to 32 μM (i.e., 4.5 pCa), pH 7.0 at 15°C and an ionic strength of 180 mM. A computer program (Fabiato 1988) was used to calculate the final concentrations of each metal, ligand, and metal–ligand complex based on stability constants listed by Godt and Lindley 1982.

Fast-twitch skeletal muscle fibers were obtained from the psoas muscles of adult New Zealand rabbits. Bundles of ∼30 fibers were dissected from psoas muscles while in relaxing solution. Each bundle was tied with 4/0 suture to glass capillary tubes, placed in relaxing solution containing 1% Triton X-100 for 4–5 h at 4°C, and then stored in relaxing solution containing 50% glycerol at −20°C for up to 3 wk. Chemically skinned fibers were ready for experimental use 1–2 d after dissection.

Before each experiment, an individual skinned psoas fiber was carefully pulled from one end of a fiber bundle and mounted between a force transducer (model 400A; Aurora Scientific) and a DC torque motor (model 308B; Aurora Scientific) in an experimental apparatus similar to one described previously (Moss 1979). A fiber segment 1.0–1.5 mm long remained exposed to the solution between the force transducer and the motor. Before mechanical measurements, the experimental apparatus was set on the stage of an inverted microscope (Carl Zeiss, Inc.). The length and force signals of each fiber were digitized at 1 kHz, using a 12-bit A/D converter (model AT-MIO-16F-5; National Instruments Corp.), and displayed and stored on a personal computer using customized software (LabView Full Development System for Windows, version 5.01; National Instruments Corp.). Length changes were driven by computer-generated voltage commands, which were output to the torque motor via a 12-bit D/A converter. All experiments were performed at 15°C and at a sarcomere length of ∼2.35 μm in relaxing solution. During activation and relaxation, sarcomere length and fiber dimensions were recorded on videotape using a video camera (model WV-BL730; Panasonic) and VHS recorder (model SVO-1420; Sony).

Mechanical measurements were first performed on all fibers under control conditions (N = 33). Next, fibers were either subjected to (1) partial extraction of TnC (N = 15), (2) treatment with NEM-S1 (N = 18), or (3) both (N = 15); and mechanical measurements were repeated.

Approximately 50% of endogenous TnC was specifically extracted from thin filaments of psoas fibers using a modification of a method reported previously (Metzger and Moss 1991). After initial measurements of mechanical properties, each psoas fiber was bathed for 1–3 min in a TnC extraction solution containing 10 mM imidazole, 5 mM EGTA and 200 μM trifluoperazine dihydrochloride (TFP; Sigma-Aldrich), pH 7.0 at 15°C. The fiber was subsequently washed three to four times in fresh relaxing solution to remove any residual TFP. Sarcomere length during the extraction protocol was ∼2.35 μm. Maximal Ca²⁺-activated force was significantly reduced after partial extraction of TnC, ranging from 0.15 to 0.65 of the P_o measured in the preextracted fiber. Measurements of k_tr and force were subsequently obtained as functions of pCa in the partially TnC-extracted fibers. Control experiments demonstrated that incubating the partially TnC-extracted fibers for ∼30 s in relaxing solution containing 0.6 mg skeletal TnC/ml resulted in complete recovery of steady-state force and restored Hill coefficients to control values (data not shown).

Myosin subfragment 1 (S1) was purified from rabbit fast-twitch skeletal muscle and modified with N-ethylmaleimide (NEM) as described previously (Swartz and Moss 1992). Although NEM-S1 significantly increases myosin ATPase activity in solutions containing myosin, regulated actin, and Ca²⁺ (Williams et al. 1984; Greene et al. 1987), it exhibits no ATPase activity of its own (Williams et al. 1984). NEM-S1 forms long lasting complexes with actin in the presence or absence of Ca²⁺ and ATP (Swartz and Moss 1992). In the present study, the concentration of NEM-S1 was estimated by absorbance at 280 nm (with light-scattering correction performed at 320 nm) using a mass absorptivity of 0.75 and a molecular mass of 118,000 D for S1. A stock solution of NEM-S1 was prepared by overnight dialysis against a solution containing 20 mM imidazole, pH 7.0, and 1 mM DTT. A working solution of NEM-S1 was prepared immediately before use by mixing equal volumes of NEM-S1 stock and a 2× stock of pCa 9.0 solution. NEM-S1 was adjusted to the desired concentration by adding the appropriate amount of 1× pCa 9.0 solution. Before mechanical measurements, each fiber was incubated for 15 min at 15°C in solution of pCa 9.0 containing either 3, 6, or 10 μM NEM-S1. The skinned fiber was subsequently transferred to activating solutions of varying pCa without NEM-S1 to measure the steady-state force and the rate of force redevelopment. After mechanical measurements, the skinned fiber was returned to the pCa 9.0 solution containing NEM-S1.

The rate constant of force redevelopment (k_tr) in skinned psoas fibers was assessed using a modification of an experimental protocol described previously (Brenner and Eisenberg 1986). Measurement of k_tr involves a mechanical slack-restretch maneuver to dissociate bound cross-bridges from actin in a steadily Ca²⁺-activated preparation. Each skinned fiber was transferred from relaxing to activating solutions of varying pCa (i.e., pCa 6.6–4.5) and allowed to generate steady-state force. The preparation was rapidly (<2 ms) slackened by 20% of its original length, resulting in an abrupt reduction of force to zero (i.e., <5% of steady isometric force). This was followed by a brief period of unloaded shortening (e.g., 20–25 ms) after which the fiber was rapidly (<2 ms) restretched to its initial length. Force redevelopment following the slack-restretch maneuver and force recovery to the original steady-state value reflect the rate of cross-bridge cycling between weakly bound and strongly bound, force-generating states (Brenner and Eisenberg 1986). A k_tr-pCa relationship was obtained by first maximally activating the skinned fiber in a solution of pCa 4.5, and then in a series of submaximally activating solutions between pCa 6.6 and 5.6. To assess any decline in maximal k_tr, the fiber was activated in a solution of pCa 4.5 at the end of each protocol. The reference value of maximal k_tr for each submaximal activation was obtained by interpolation between the initial and final measurements of maximal k_tr. The apparent rate constants of force redevelopment (k_tr) were estimated by linear transformation of the half-time of force redevelopment, i.e., k_tr = 0.693/t^1/2, as described previously (Regnier et al. 1998). Most k_tr measurements were done without sarcomere length control, although experiments performed with sarcomere length control yielded quantitatively similar results (see Fig. 8). Force redevelopment traces in a representative skinned psoas fiber at maximal and submaximal levels of Ca²⁺ activation are shown in Fig. 1: the top panel depicts the mechanical release-restretch maneuver imposed to determine the rate of force redevelopment (k_tr); and the bottom panel illustrates changes in submaximal force in solutions of pCa 6.1 (trace b) and pCa 6.0 (trace c) under control conditions. The change in force is expressed relative to maximum force (P_o) generated by the same fiber under control conditions when exposed to solution of pCa 4.5 solution (trace a).

During measurements of k_tr, each skinned psoas fiber was exposed to solutions of varying pCa and allowed to develop steady-state force. The difference between steady-state force and the force baseline after the slack step was measured as the total force at that pCa. Active force was obtained by subtracting Ca²⁺-independent force, measured in solution of pCa 9.0, from the total force. Force-pCa relationships were determined by expressing submaximal force (P) at each pCa as a fraction of maximal force (P_o) determined at pCa 4.5, i.e., P/P_o. The apparent cooperativity in the activation of force development was inferred from the steepness of the force-pCa relationship at forces <0.50 P_o, and was quantified using a Hill plot transformation of the force-pCa data (Strang et al. 1994). We focused on this region of the curve because the force-pCa relationship is biphasic, with most of the cooperative activation evident at forces less than 0.50 P_o (Moss 1992). The force-pCa data were fit using the equation, P/P_o = [Ca²⁺]ⁿ/(kⁿ + [Ca²⁺]ⁿ), where n is the Hill coefficient, and k is the [Ca²⁺] required for half-maximal activation.

The extent of TnC extraction was assessed using SDS-PAGE and ultrasensitive silver staining (Sweitzer and Moss 1993). Upon completion of a given experiment, ∼0.75 mm of fiber segment was placed in a microfuge tube containing SDS sample buffer (10 μl/mm segment length) and stored at −80°C until analyzed for TnC content. The proportion of TnC present in the fiber was determined by densitometric analysis of silver-stained gels using a GS-670 imaging densitometer and Molecular Analyst software (BioRad Laboratories). To quantify the amount of TnC extracted, the ratio of TnC/(MLC1 + MLC3) was determined for each fiber (Moss 1992). The ratio measured in the extracted fiber segment was divided by the ratio obtained from a segment obtained from the same fiber before extraction to yield an estimate of the TnC content of the partially TnC-extracted segment.

All data are expressed as mean ± SEM. Where appropriate, either a two-tailed t test for independent samples or a paired t test was used as a post hoc test of significance, with significance set at P < 0.05.

Our studies of cooperative mechanisms in skinned skeletal muscle fibers involved two perturbations that previously have been shown to alter cooperation in the activation of contraction. NEM-S1 was used to mimic the effects of strong-binding cross-bridges to further activate Ca²⁺-dependent tension and the rate of tension development (Swartz and Moss 1992), and thin filaments were partially TnC-extracted to disrupt near-neighbor cooperativity between adjacent functional groups (one troponin, one tropomyosin, and associated actins) in the thin filament (Brandt et al. 1984; Moss et al. 1985).

NEM-S1 had pronounced effects on maximal Ca²⁺-activated tension (P_o), Ca²⁺-independent tension, Ca²⁺ sensitivity of tension (pCa₅₀), and Hill coefficient (n₂) in single skinned psoas fibers, as reported earlier (Swartz and Moss 1992) and summarized in Table. The application of 3, 6, or 10 μM NEM-S1 increased Ca²⁺-independent tension at pCa 9.0 in a concentration-dependent manner (Fig. 2). At the two highest concentrations used, the increase in Ca²⁺-independent tension was accompanied by small (at 6 μM) or large (at 10 μM) reductions in maximal Ca²⁺-activated tension, indicating that at these concentrations NEM-S1 competed with endogenous cross-bridges for binding sites on actin. For this reason, 6 μM NEM-S1 was preferentially used in most of the experiments described below. The increases in Ca²⁺-independent tension are most likely due to cooperative activation of the thin filament by NEM-S1, thereby allowing strong binding of endogenous cross-bridges (Swartz and Moss 1992).

NEM-S1 also potentiated submaximal Ca²⁺-activated force in a concentration-dependent manner (Fig. 3). Mean pCa₅₀ was significantly increased after treatment with either 6 μM NEM-S1 (ΔpCa₅₀ = 0.07 ± 0.01, P < 0.05) or 10 μM NEM-S1 (ΔpCa50 = 0.12 ± 0.03, P < 0.05), so that Ca²⁺ sensitivity of force was increased. Such increases are consistent with the idea that, at low levels of Ca²⁺, NEM-S1 promotes the formation of strongly bound, force-generating cross-bridges (Swartz and Moss 1992). At higher Ca²⁺ concentrations, i.e., pCa < 5.9, NEM-S1 had small or negligible effects on Ca²⁺-activated forces relative to the control. Commensurate with the increase in force at low levels of Ca²⁺, NEM-S1 significantly reduced the slope of the force-pCa relationship for Ca²⁺-activated tensions <0.50 P_o (n₂), an effect that increased with increasing concentrations of NEM-S1 (Fig. 3 B and Table).

To further examine the mechanisms of cooperative activation of thin filaments, single fibers were first incubated with 200 μM TFP to partially extract TnC and were subsequently treated with NEM-S1. Such an approach allows dissection of the relative roles of cross-bridge binding and near-neighbor interactions in the thin filament in activation of contraction. In these experiments, segments of each fiber were analyzed by SDS-PAGE (Fig. 4) before TnC extraction (lane 1), after partial TnC extraction (lane 2), after TnC extraction plus NEM-S1 (lane 3), and after readdition of skeletal TnC to a previously extracted fiber (lane 4). Densitometric scans of the gels indicated that ∼50% of the endogenous TnC was extracted from psoas fibers under the conditions used. Furthermore, the extraction procedure was specific for TnC since the relative amounts of other myofibrillar proteins (e.g., myosin light chains, TnI, and TnT) were unchanged.

Partial extraction of TnC had reversible effects on maximal Ca²⁺-activated tension (P_o), Ca²⁺-independent tension, Ca²⁺ sensitivity of tension, and the Hill coefficient (n₂), which are summarized in Table. As reported previously (Brandt et al. 1984, Brandt et al. 1990; Moss et al. 1985; Brandt and Schachat 1997), partial extraction of TnC resulted in a significant decrease in maximum Ca²⁺-activated tension, presumably because of the inactivation of thin filament functional groups. Subsequent treatment of partially TnC-extracted fibers with NEM-S1 resulted in a further reduction in maximal Ca²⁺-activated tension similar to that observed after NEM-S1 treatment alone. Although resting tension was unaffected by partial TnC extraction alone, TnC extraction elicited significant increases in NEM-S1–induced Ca²⁺-independent tension (Fig. 2). The increase in Ca²⁺-independent tension, as the percent maximum force in untreated fibers, was less than that observed because of NEM-S1 treatment alone, suggesting that TnC extraction reduced the number of NEM-S1 or endogenous cross-bridges bound to actin, perhaps by disrupting near-neighbor interactions between adjacent functional groups. However, when scaled to the maximum force after TnC extraction, the combined effects of TnC extraction and NEM-S1 were greater than with NEM-S1 alone.

Partial extraction of TnC also affected the Ca²⁺ sensitivity of tension and reduced the responsiveness of fibers to NEM-S1 (Fig. 5). Mean pCa₅₀ in control fibers was 5.97 ± 0.01, which decreased to 5.75 ± 0.02 after extraction of TnC (ΔpCa₅₀ = 0.22 ± 0.03, P < 0.05). Subsequent treatment with 3 μM NEM-S1 did not alter the Ca²⁺ sensitivity of force (ΔpCa₅₀ = 0.01 ± 0.01); however, 6 μM NEM-S1 increased the Ca²⁺ sensitivity of force, i.e., pCa₅₀ increased to 5.89 ± 0.02 (ΔpCa₅₀ = 0.15 ± 0.01; P < 0.05), a mean value near that observed in TnC-replete fibers when treated with NEM-S1 (Table). Partial extraction of TnC and successive treatment with increasing concentrations of NEM-S1 resulted in progressive reductions in the steepness of the force-pCa relationship (Table), suggesting that the effects of these two treatments on cooperativity are additive and most likely involve different molecular mechanisms.

According to Campbell 1997 model of regulation, cooperative interactions within the thin filament, such as cross-bridge–induced cross-bridge binding, are thought to speed the rate of force redevelopment (k_tr), and may provide the basis for the steep activation dependence of k_tr in the skeletal muscle fibers observed by Brenner 1988 and others. Previous work in which NEM-S1 was found to accelerate k_tr at all submaximal levels of Ca²⁺ activation (Swartz and Moss 1992) provided strong support for this idea. However, the picture that emerged from that study was incomplete since in the presence of NEM-S1, k_tr was maximal at low and high levels of activation but less than maximal at intermediate levels of activation. Therefore, we have done additional experiments in an attempt to determine the basis for activation dependence of k_tr in the presence of NEM-S1 (data are summarized in Table). This was done by examining the activation dependence of k_tr in the presence of varying amounts of NEM-S1 and also by partial extraction of TnC to perturb cooperative interactions within the thin filament.

Consistent with earlier results, k_tr was found to vary ∼10-fold as Ca²⁺ activation was varied from near threshold to maximal levels. As shown in Fig. 6 A for a single submaximal pCa (pCa 6.1), the rate of force redevelopment at submaximal concentrations of Ca²⁺ was accelerated by NEM-S1, with the degree of acceleration increasing with the concentration of NEM-S1 (Fig. 6 A, traces b–d), compared with control (trace a). Under identical experimental conditions, another fiber was subjected to partial TnC extraction and subsequent treatment with 6 μM NEM-S1 (Fig. 6 B). As summarized previously, k_tr under control conditions varied with the level of Ca²⁺ activation, increasing when Ca²⁺ concentration was increased from pCa 5.9 (Fig. 6 B, trace b) to pCa 4.5 (Fig. 6 B, trace a). After partial extraction of TnC, the steady force decreased at each pCa, but the rate of force redevelopment (Fig. 6 B, trace c) at pCa 5.9 was nearly equivalent to that of the preextracted fiber at the same pCa. Subsequent treatment with 6 μM NEM-S1 significantly increased steady force at pCa 5.9 and markedly accelerated the rate of force redevelopment (Fig. 6 B, trace d).

The relationship between k_tr and steady-state isometric force (as a measure of the level of activation due to Ca²⁺ binding and cooperative mechanisms) was variably affected by interventions to increase numbers of strongly bound cross-bridges (i.e., NEM-S1) and to disrupt near-neighbor cooperativity in the thin filament (partial extraction of TnC). As shown in Fig. 7 A, k_tr during maximal activation was unaffected by NEM-S1, but k_tr values at low levels of activation were increased to levels either identical to (at 3 μM NEM-S1) or greater than (at 6 or 10 μM NEM-S1) the values obtained in maximally activated fibers. At intermediate levels of activation, NEM-S1 increased k_tr to greater than the control values, but k_tr was still less than maximal. Similar effects of NEM-S1 were observed in fibers that were subjected to sarcomere length control during measurements of k_tr (Fig. 8). Progressive increases in the concentration of NEM-S1 further increased the value of k_tr at intermediate levels of activation, but even the highest concentration used (10 μM) did not accelerate k_tr to maximal values. In the absence of Ca²⁺ (pCa 9.0), application of NEM-S1 induced active tension development (Fig. 9 and Table); under these conditions, k_tr was supramaximal when compared with the maximal values measured at pCa 4.5 under control conditions.

Partial extraction of TnC also increased k_tr at intermediate levels of activation as compared with the control (Fig. 7 B). In fact, the increase in k_tr varied with the extent of TnC extraction, i.e., fibers containing smaller amounts of residual TnC exhibited faster rates of force redevelopment during submaximal activation (Fig. 10). Subsequent treatment of partially TnC extracted fibers with 3 μM NEM-S1 resulted in a k_tr–relative force relationship similar to that observed with NEM-S1 treatment alone, although k_tr at each level of activation was somewhat greater than the value obtained with NEM-S1 alone. However, the combination of partial TnC extraction and 6 μM NEM-S1 increased k_tr at each level of activation to values greater than the maximum measured in control fibers and completely eliminated the activation dependence of k_tr (Fig. 7 B).

The results of the present study show that strong binding of cross-bridges to actin increases the rate of force development in skeletal muscle and suggest that cooperativity in cross-bridge binding is an important determinant of activation kinetics. NEM-S1 increased the k_tr measured during submaximal activations, with greatest effects at low levels of activation where NEM-S1 increased k_tr to values greater than the maximum observed in control fibers at saturating [Ca²⁺]. From this result, it is evident that the rate of force development measured in control fibers at pCa 4.5 is not a true maximum. Although NEM-S1 dramatically accelerated k_tr, strong binding of cross-bridges does not entirely account for the activation of cross-bridge kinetics, since NEM-S1 alone was insufficient at intermediate levels of activation to increase k_tr to maximal or to completely eliminate the activation dependence of k_tr. Instead, elimination of activation dependence required both NEM-S1 and partial extraction of TnC from the thin filament. Since partial extraction of TnC should disrupt near-neighbor communication between functional groups in the thin filament (Brandt et al. 1984, Brandt et al. 1990; Moss et al. 1985), we conclude that activation dependence of k_tr results from effects of strongly bound cross-bridges to cooperatively recruit additional cross-bridges within the same and neighboring regions of the thin filament.

Ca²⁺ binding to TnC initiates muscle contraction, but complete activation of tension and the kinetics of tension development appears to involve cooperative effects due to cross-bridge binding to actin (for reviews see Lehrer 1994; Gordon et al. 2000). Biochemical data suggest that activation is a positive cooperative process (Williams et al. 1984, Williams et al. 1988), such that activation of a thin filament functional group (estimated to be ± 10–14 actin monomers; Geeves and Lehrer 1994; Swartz et al. 1996) by Ca²⁺ and/or strong binding cross-bridges influences the activation of neighboring functional groups (Lehrer 1994). Cooperation is apparent in contracting muscle in the greater than expected (on the basis of the numbers of Ca²⁺ binding sites on TnC) steepness of the tension-pCa relationship, especially at low levels of Ca²⁺ (for review see Moss 1992), and previously observed effects of strong-binding cross-bridges to speed the rate of submaximal force development in skinned skeletal muscle fibers (Swartz and Moss 1992).

The rate constant of force redevelopment (k_tr) in steadily activated skeletal muscle preparations exhibits an ∼10-fold activation as [Ca²⁺] is increased from threshold to saturating levels, which was originally shown by Brenner and Eisenberg 1986 and, subsequently, has been reported by other groups. Brenner (Brenner 1988; Brenner and Chalovich 1999) has explained the activation dependence of k_tr using a model in which Ca²⁺ influences the rate constant of cross-bridge attachment to actin, f_app, i.e., f_app decreases when [Ca²⁺] is lowered, presumably by an allosteric mechanism. Such a model does not straightforwardly account for our observation that strong-binding cross-bridges (NEM-S1) markedly accelerate k_tr, an effect which is greatest at low levels of Ca²⁺ activation: but, our results don't exclude the possibility that this type of mechanism modulates kinetics in control fibers. A simple explanation is that increased [Ca²⁺] effectively increases f_app as a consequence of the cooperative effects of increased numbers of cross-bridges bound to the thin filament.

At least two models of activation might be used to explain the activation dependence of k_tr. Landesberg and Sideman 1994 developed a model in which the activation dependence of the rate of force development in cardiac muscle was due to a cross-bridge binding–dependent increase in Ca²⁺ binding affinity of TnC. Alternatively, the steep activation dependence of k_tr can be explained by the cooperation-mediated slowing of force development at low levels of activation (Campbell 1997), which is the framework we will use to discuss our results. In Campbell's model, cross-bridges are distributed between cycling and noncycling populations: cycling cross-bridges undergo repeated transitions between non–force-bearing and force-bearing states (under the influence of the rate constants f_app and g_app), whereas noncycling cross-bridges are recruited to the cycling population as a result of Ca²⁺ binding to troponin or cooperative effects of strong binding cross-bridges to enhance activation of the thin filament. At lower levels of Ca²⁺, a smaller fraction of cross-bridges is initially recruited into the cycling population as a direct result of Ca²⁺ binding to the thin filament, so that most cross-bridges are in the noncycling pool and, thus, are available for cooperative recruitment to the cycling pool. Progressive recruitment of cross-bridges from the noncycling pool would then slow the rate of force development. In contrast, at high levels of Ca²⁺, the rate constant of force development is much greater because most cross-bridges are recruited to the cycling pool when Ca²⁺ binds to troponin, which leaves few cross-bridges available in the noncycling pool for subsequent cooperative recruitment. At a saturating [Ca²⁺] of pCa 4.5, the rate constant of force development will thus be equal to f_app + g_app.

The results of our study provide support for models of regulation in which cross-bridge interaction kinetics are activated by cross-bridge binding to the thin filament. Experiments here show that force at submaximal [Ca²⁺] is increased due to activating effects of strongly bound cross-bridges, which confirms results from earlier studies from this and other laboratories (Swartz et al. 1996 and references therein). The Ca²⁺ dependence of k_tr appears to involve two factors: activating effects due to cross-bridge binding to the thin filament, and near-neighbor interactions between adjacent functional groups, such that activation of a given functional group facilitates cross-bridge binding in neighboring functional groups. Thus, Ca²⁺ does not seem to regulate kinetics (e.g., by binding to a regulatory site) but, instead, has indirect effects on kinetics by influencing the number of cross-bridges bound to actin. Our results also show that cooperative effects due to cross-bridge binding to thin filaments are large but insufficient to completely account for activation dependence of k_tr, since it was necessary to add NEM-S1 and disrupt near-neighbor cooperativity in the thin filament to achieve maximal k_tr at all levels of activation.

In this study, partial extraction of TnC was used to disrupt the spread of activation between adjacent functional groups in the thin filament, presumably because of constitutive inactivation of functional groups from which TnC was removed (Brandt et al. 1984; Moss et al. 1985; for review see Moss 1992). Our findings that the maximum force and the steepness of the force-pCa relationship were reduced by TnC extraction (Table and Fig. 5) confirm earlier results (Brandt et al. 1984, Brandt et al. 1990; Moss et al. 1985; Metzger and Moss 1991) and support the idea that near-neighbor interactions between functional groups contribute to force development in skeletal muscle.

Whereas steady-state Ca²⁺-activated force was reduced after TnC extraction, the rate constant of force redevelopment (k_tr) increased at each submaximal force, when compared with nonextracted fibers (Fig. 7 B). Although not anticipated in Campbell 1997 model of activation, this result is consistent with the idea that cooperative interactions between thin filament functional groups contribute to a slowing of force development at low activation. By extracting TnC, these interactions were presumably disrupted and cooperative recruitment of cross-bridges from neighboring functional groups was reduced or eliminated, thereby speeding the rate of force development. By varying the amount of TnC extracted, it should be possible to vary the rate of force development independent of [Ca²⁺], which is what we observed. Fibers containing less TnC and, therefore, having fewer functional groups that could be activated by Ca²⁺ exhibited a faster rate of force redevelopment at each submaximal force (Fig. 10). Although it might be possible to explain these results by an alternate mechanism (e.g., direct effects on f_app due to extraction of TnC), a modification of Campbell 1997 model to include near-neighbor interactions that cooperatively recruit cross-bridges to strongly bound states also accounts for our results (Razumova et al. 2000).

As reported earlier (Swartz and Moss 1992), treatment of fibers with NEM-S1 reduced the steepness of the force-pCa relationship (Table). This decrease in the apparent cooperativity of activation can be explained by near saturation of the myosin cross-bridge binding component of thin filament activation due to binding of NEM-S1. NEM-S1 also induced concentration-dependent increases in the resting (Ca²⁺-independent) tension, submaximal Ca²⁺-activated force, and the Ca²⁺ sensitivity of force, i.e., a left shift of the tension-pCa relationship (Table and Fig. 3). Together, these results support the idea that binding of NEM-S1 to actin increased the level of thin filament activation and increased the number of endogenous cross-bridges in strongly bound force-generating states.

At submaximal levels of activation, NEM-S1 increased the rate of force redevelopment at each level of activation, but the increase was much greater at very low than at intermediate levels of activation. As the concentration of NEM-S1 was increased, k_tr at low levels of activation was increased to maximal and supramaximal values. One possible way to explain this phenomenon is that at low levels of Ca²⁺, the increased force and maximal values of k_tr are manifestations of preferential Ca²⁺ binding to functional groups in which NEM-S1 is also bound. The combined activating effects of Ca²⁺ and strongly bound cross-bridges within these functional groups would facilitate binding of endogenous cross-bridges and would accelerate the rate of binding. Although this is a plausible mechanism, it does not account for all of our results, since fibers activated with NEM-S1 in the absence of Ca²⁺ developed small forces but yielded k_tr values that were maximal or supramaximal. This finding indicates that k_tr measured in control fibers at pCa 4.5 is not the maximum value for this variable. Furthermore, it is possible to achieve maximal and even higher values of k_tr in the absence of Ca²⁺ binding to TnC (i.e., at pCa 9.0) simply by increasing the numbers of strong-binding cross-bridges in the form of NEM-S1. We don't know the mechanism of this effect, but it is possible that such high values of k_tr are due to a combination of NEM-S1 binding to a few discrete regions of the filament, and isolation of these regions from adjacent, inactive regions by intervening troponin complexes having no Ca²⁺ bound. The first condition would arise if the binding of NEM-S1 was not uniform along the thin filament, and would limit the number of endogenous cross-bridges that could bind to the thin filament, and thereby account for the small forces developed in the absence of Ca²⁺. The second condition would reduce or eliminate communication between adjacent functional groups, eliminate near-neighbor cooperative recruitment of cross-bridges from the noncycling pool, and thereby speed k_tr. The fact that NEM-S1 does not further accelerate k_tr in maximally Ca²⁺-activated fibers is consistent with both ideas, i.e., if NEM-S1 is nonuniformly distributed along the thin filament, then the maximum value of k_tr would be limited by cooperative recruitment of cross-bridges from adjacent functional groups with less or no NEM-S1 bound.

At intermediate levels of activation (indexed by force or [Ca²⁺]), k_tr measured in the presence of NEM-S1 was less than that observed at low and maximal activations, but was much faster than control values measured at similar levels of force or Ca²⁺ (Fig. 7 A). The finding that k_tr in the presence of NEM-S1 is not maximal at all levels of activation suggests that the thin filament is not saturated by Ca²⁺, cross-bridge binding, or by both. Again, it seems likely that NEM-S1 binding to the thin filament is not uniform, resulting in some regions with NEM-S1 bound and other regions with less or no NEM-S1. As discussed above, functional groups with NEM-S1 bound should be activated at lower levels of Ca²⁺, because of a greater Ca²⁺ binding affinity, and the rate of force development would be maximal because of the combined effects of Ca²⁺ and bound cross-bridges. By similar reasoning, those with less or no NEM-S1 would be recruited at higher (intermediate) levels of Ca²⁺ and will have fewer bound cross-bridges, i.e., cross-bridge activation of these functional groups is less, and force development is therefore slower. The fact that the records of force redevelopment at intermediate activation are well fit by a single rate constant suggests that the mix of variably activated functional groups confers a single level of activation to the entire thin filament. Thus, the effective size of a functional group appears to increase as [Ca²⁺] is increased to intermediate levels; the central region of the functional group has the greatest amounts of Ca²⁺ and NEM-S1 bound. Because of this, the rate of force development at intermediate levels of activation will be slowed because of cooperative recruitment of cross-bridges into the end regions of the functional group or adjacent functional groups. Ultimately, at high [Ca²⁺], fewer inactivated functional groups remain and the impact of cooperative interactions is reduced, but not totally eliminated since, in control fibers, k_tr never achieves the maximum possible value. Correspondingly, the time course of force redevelopment becomes progressively faster, and k_tr converges to the value obtained during maximal activation.

The effects of NEM-S1 to accelerate k_tr appear to be significantly greater than the effects due to partial extraction of TnC (Fig. 7 B). This result suggests that effects on kinetics due to cross-bridge binding within functional groups are greater than effects due to near-neighbor interactions between functional groups. Nevertheless, both mechanisms contribute to activation kinetics, since it was necessary to add NEM-S1 and partially extract TnC to eliminate the activation dependence of k_tr.

Partial extraction of TnC or application of NEM-S1 has been shown to independently alter the Ca²⁺ activation of force in skeletal muscle, effects that are additive or synergistic. When fibers were treated in either way, the steepness of the force-pCa relationship was reduced (Table), indicating a decrease in the apparent cooperativity of activation. Importantly, effects on steepness were much greater in fibers subjected to both interventions, i.e., extraction of 50% TnC and application of 6 μM NEM-S1, than with either alone. At present, we do not have a unique explanation for this result, but a simple model is one in which initial cross-bridge binding facilitates additional binding in the same and adjacent functional groups. In such a model, partial extraction of TnC would reduce steepness by disrupting near-neighbor interactions within the thin filament, and NEM-S1 would reduce steepness by cooperatively increasing the number of endogenous cross-bridges that bind within a functional group or in neighboring functional groups at each submaximal pCa.

The combination of TnC extraction and application of NEM-S1 also had greater effects on the activation dependence of k_tr than either treatment alone. In fact, addition of 6 μM NEM-S1 to partially TnC-extracted fibers increased k_tr to greater than maximal values at all levels of activation and completely eliminated the activation dependence of k_tr (Fig. 7 B). These results strongly suggest that the slowing of k_tr observed in untreated fibers at low and intermediate levels of activation is due to cooperative binding of cross-bridges within the same and neighboring functional groups, and the acceleration of k_tr at high levels of activation reflects a decrease in the importance of such cooperation. This conclusion is consistent with Campbell 1997 model of activation in which slowing of k_tr at low levels of activation involves progressive cooperative recruitment of cross-bridges from noncycling to cycling states. However, to account for the effects of TnC extraction to accelerate k_tr, this model must be expanded to include near-neighbor effects, i.e., cross-bridge binding in one functional group seems to cooperatively activate adjacent functional groups and thereby induce further cross-bridge binding (Razumova et al. 2000). In support of this idea, partial extraction of TnC was needed to completely eliminate the activation dependence of k_tr.

Most measurements of k_tr in the present study were done without sarcomere length control, which has been shown previously to result in underestimation of the rate constant by as much as 50% because of mechanical effects of end compliance at the points of attachment to the fiber (Brenner 1988). Such slowing, if undetected or variably present, could distort the results and affect our conclusions. Several lines of evidence suggest that this was not the case here. First, the mean maximum k_tr obtained in control fibers (∼14 s⁻¹ was ∼80% of the value [∼18 s⁻¹] obtained in an earlier study using sarcomere length control; Metzger et al. 1989). The 10-fold variation in k_tr is similar to that observed under sarcomere length control. Second, under conditions that eliminated the activation dependence of k_tr, i.e., NEM-S1 plus partial extraction of TnC, k_tr was identical at all levels of activation regardless of force (Fig. 7 B), again indicating that variations in end compliance with developed force were not the basis for activation dependence of k_tr. Finally, in several fibers in which sarcomere length control was used, the effects of NEM-S1 on the activation dependence of k_tr were similar with (Fig. 8) and without (Fig. 7 A) sarcomere length control.

Another possibility is that NEM-S1 actually stiffens the fiber, thereby increasing k_tr at each level of activation. We regard this as highly unlikely for a couple of reasons. First, in our previous measurement of k_tr (Metzger et al. 1989), sarcomere length clamping at very low levels of activation (P/P_o = 0.14, pCa 6.2) resulted in k_tr values of ∼1 s⁻¹. This is much lower than the values of k_tr measured in the present study in the presence of NEM-S1 (∼16 s⁻¹) and with both NEM-S1 treatment and partial extraction of TnC (∼19 s⁻¹). Second, treatment with NEM-S1 alone had no effect on k_tr in maximally activated fibers (k_tr = ∼14 s⁻¹), but NEM-S1 plus partial extraction of TnC increased k_tr to ∼19 s⁻¹.

Our results support the idea that Ca²⁺ activation of isometric force involves significant contributions due to cooperativity in cross-bridge binding (for most recent review see Gordon et al. 2000), i.e., NEM-S1 increased the Ca²⁺ sensitivity of force. The fact that partial extraction of TnC reduced the Ca²⁺ sensitivity of force suggests that cooperation in cross-bridge binding occurs both within and between neighboring functional groups.

Our results also indicate that the Ca²⁺ dependence of the kinetics of force development can be completely eliminated by a combination of strong-binding cross-bridges (treatment with NEM-S1) and disruption of near-neighbor cooperativity in the thin filament (partial extraction of TnC). Although it is tempting to conclude from these results that cross-bridge binding is the primary activator of cross-bridge kinetics, our results do not exclude the possibility that other mechanisms are operative under physiological conditions, where the number of strongly bound cross-bridges is certainly less than in our experiments with NEM-S1. In support of the this idea, k_tr in control fibers did not increase substantially until Ca²⁺-activated isometric forces were greater than half-maximal (Fig. 7 A). Thus, it is possible in our experiments that strong binding cross-bridges in the form of NEM-S1 are such potent activators of the thin filament that other activating processes involving the effects of Ca²⁺ binding to potential regulatory sites, such as regulatory light chain (Diffee et al. 1995), are masked. Another possibility is that cross-bridge binding to the thin filament increases Ca²⁺ binding affinity of TnC, and the resulting increase in Ca²⁺ binding increases f_app (for review see Gordon et al. 2000).

We also observed that the effects on k_tr because of NEM-S1 alone were greater than the effects of TnC extraction alone. At first glance, this suggests that cooperativity in the activation of contraction is predominantly due to cross-bridge binding within functional groups, with much lesser contributions due to near-neighbor cooperation between adjacent functional groups. However, it must again be recognized that the addition of NEM-S1 in our experiments substantially increases the number of strong-binding cross-bridges above that normally found in skeletal muscle fibers under physiological conditions. Thus, it is likely that strong-binding cross-bridges are not as dominant in activating contraction in living muscles, and that near-neighbor mechanisms play a proportionately greater role than implied by our present results with NEM-S1. Our finding that partial extraction of TnC was required to completely eliminate the activation dependence of k_tr is consistent with this conclusion.

The authors thank Chad Warren for the preparation of NEM-S1 and Dr. James Graham for SDS-PAGE analysis of the muscle fibers.

This study was supported by grant HL-54581 from the National Institutes of Health to R.L. Moss.