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(Circulation Research. 1995;76:154-160.)
© 1995 American Heart Association, Inc.

Articles

Rate of Tension Development in Cardiac Muscle Varies With Level of Activator Calcium

Matthew R. Wolff, Kerry S. McDonald, Richard L. Moss

From the Departments of Medicine (M.R.W.) and Physiology (K.S.M., R.L.M.), University of Wisconsin School of Medicine, Madison.

	Abstract

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Abstract In skeletal muscle, the rate of transition from weakly bound to force-generating crossbridge states increases as calcium concentration is increased. To examine possible calcium sensitivity of this transition in cardiac muscle, we determined the kinetics of isometric tension development during steady activation in detergent-permeabilized rat ventricular trabeculae (n=7) over a range of calcium concentrations. Force-generating crossbridges in activated trabeculae were disrupted by a brief, rapid release and restretch equivalent to 20% muscle length (15°C), which resulted in a subsequent phase of tension redevelopment that was well fit by a monoexponential function (rate constant, k_tr). Sarcomere length was monitored by laser diffraction and held constant during tension redevelopment by an iterative adaptive feedback control system. The k_tr increased from 3.6±0.8 s^-1 at the lowest calcium concentration studied (pCa 5.9) to 9.5±1.3 s^-1 during maximal activation (pCa 4.5). The relationship between relative k_tr and relative tension was approximately linear over a wide range of [Ca²⁺] (r²=.94). This result differs quantitatively from results in skeletal muscle, in which k_tr is sensitive to [Ca²⁺] primarily at higher activation levels. This observation is also inconsistent with a recent suggestion that the rate of force development in living myocardium is independent of the activation level. Our results in skinned myocardium can be explained by a model in which calcium is a graded regulator of both the extent and rate of binding of force-generating crossbridges to the thin filament.

Key Words: Ca²⁺ • crossbridges • cardiac muscle • skeletal muscle • crossbridge kinetics • contraction

	Introduction

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As originally proposed by Huxley in 1957,¹ generation of force in striated muscle results from cyclic interactions between myosin heads on the thick filament and actin subunits within the thin filament, a process energetically driven by the hydrolysis of ATP and regulated by calcium. Calcium regulates contraction by binding to troponin C, thereby shifting the position of tropomyosin within the thin filament and allowing force-generating interactions of myosin with actin. The mechanism by which the number of force-generating crossbridges is controlled remains unresolved, although two nonexclusive mechanisms have been proposed. In the steric hindrance model of regulation,^{2 3 4 5} calcium functions as a switch, in that increased calcium concentration recruits additional actively cycling crossbridges in an all-or-nothing manner; ie, once activated, each crossbridge exhibits maximal cycling kinetics.

Alternatively, calcium may regulate force by altering the kinetics of crossbridge cycling.⁶ In this model, calcium modulates the distribution of crossbridges between force-generating (strongly bound) and non–force-generating (weakly bound) states because of its effects on the rate constants governing the transitions between these two states, whereas the total number of cycling crossbridges remains constant (Fig 1). In a simple two-state model such as proposed by Huxley,¹ the rate of isometric tension development equals the sum of the forward (f) and backward (g) rate constants. Subsequent kinetic analyses of actomyosin in solution have indicated that there are multiple biochemical intermediates in the process of ATP hydrolysis and have led to more complex crossbridge models (for a review, see Geeves⁷ or Taylor⁸ ).

View larger version (10K): [in this window] [in a new window]   Figure 1. Diagram shows a two-state crossbridge model similar to the one proposed by Huxley.1 The transition from detached, non–force-generating crossbridges to attached, force-generating crossbridges is governed by a rate constant f. Likewise, crossbridge detachment is governed by a rate constant g. If the reverse rate constants (f- and g-) are very small, which Huxley considered likely given the energetic efficiency of contraction, the overall cycle would have first-order kinetics, and the rate of isometric tension development is the sum of f+ and g+. Isometric tension (P) can be determined by the equation P=F · n · f+/(f++g+), where F is the mean force per attached crossbridge, n is the number of cycling crossbridges, and the ratio f+/(f++g+) represents the proportion of cycling crossbridges in the attached, force-generating state. In this model, calcium could theoretically regulate force by either controlling n or modulating crossbridge kinetics (ie, by altering f and/or g).

Evidence supporting a kinetic mechanism of force regulation was provided by Brenner,^{9 10} who measured the kinetics of tension redevelopment in permeabilized, steadily activated rabbit psoas fibers after a rapid length release/restretch maneuver that mechanically disrupted most force-generating crossbridges. The subsequent redevelopment of tension was well fit by a single exponential function, suggesting that the multiple transitions between non–force-generating and force-generating crossbridge states could be approximated by a first-order reaction with apparent forward (f_app) and reverse (g_app) rate constants, corresponding to the simple forward and backward rate constants shown in Fig 1. The rate constant of tension redevelopment (k_tr) was found to be sensitive to calcium concentration,¹⁰ suggesting a role of calcium in modulating crossbridge interaction kinetics. Based on a linear relation between isometric tension and fiber ATPase, Brenner concluded that the apparent rate constant of crossbridge dissociation (g_app) was insensitive to calcium. Together, these data suggested that the regulation of force above 30% of maximal activation could be explained entirely on the basis of the calcium sensitivity of f_app and did not appear to be due to recruitment of actively cycling crossbridges (firm conclusions could not be reached for activations less that 30% maximal because of scatter in the data).

Subsequent studies using similar mechanical perturbations have shown that the rate of formation of strongly bound, force-generating crossbridges is calcium sensitive in slow as well as in fast skeletal muscle.^{11 12} In contrast, a recent study by Hancock et al¹³ reported no calcium sensitivity of the rate of force development in cardiac muscle, suggesting a fundamental difference in the mechanism of calcium regulation of tension. However, the method they used to determine the rate of tension redevelopment differed from the earlier work in skeletal muscle. The goal of the present study was to further investigate whether the mechanism by which calcium regulates force in cardiac muscle differs qualitatively from that in skeletal muscle using techniques similar to those used in previous studies on skeletal muscle. We found that the rate of isometric tension development varied with calcium concentration, although this relationship differs quantitatively from that seen in fast skeletal fibers. Although our results do not exclude an effect of calcium in governing the total number of cycling crossbridges, they do suggest that force generation in cardiac muscle is regulated at least in part by modulation of crossbridge kinetics.

	Materials and Methods

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Preparation of Trabeculae
Two- to 3-month-old female Sprague-Dawley rats (200 to 350 g) were injected with sodium heparin (1000 U IP) and anesthetized with sodium pentobarbital (30 mg/kg IP). The heart was rapidly excised and perfused in a retrograde fashion via the proximal aorta for several minutes with low-calcium, high-potassium modified Ringer's solution at 22°C, which both arrested the heart and cleared the vasculature of blood. Thin, uniform, unbranched trabeculae were then dissected from the right ventricular free wall and transferred to relaxing solution containing 1% ultrapure Triton X-100 (Pierce Chemical Co) for 45 to 60 minutes at room temperature to permeabilize the muscle and remove adherent lipid membrane.

Solutions
The modified Ringer's solution contained (mmol/L) NaCl 130, KCl 15, MgCl₂ 1.2, NaH₂PO₄ 2.0, HEPES 10, glucose 10, sodium acetate 4, and CaCl₂ 0.05; pH was adjusted to 7.4. Relaxing and activating solutions contained (mmol/L) ATP 4, free Mg²⁺ 1, imidazole 7, EGTA 7, creatine phosphate 7, and sufficient KCl to adjust ionic strength to 180 mmol/L; pH was adjusted to 7.0. Free calcium concentrations were varied from 10^-9 mol/L (relaxing solution) to 10^-4.5 mol/L (maximally activating solution) by addition of CaCl₂ and are expressed as pCa (-log₁₀[Ca²⁺]). A computer program was used to determine the concentrations of metals and ligands in the relaxing and activating solutions.¹⁴ Chemicals were obtained from Sigma Chemical Co.

Experimental Apparatus
The skinned trabeculae were mounted between a force transducer (model 403, Cambridge Technology, Inc; sensitivity, 20 V/g; resonant frequency, 600 Hz) and a DC torque motor (model 300, Cambridge Technology) in an experimental apparatus mounted on an inverted microscope (model IMT-2, Olympus Instrument Co), similar to that previously used in our laboratory for skeletal muscle fibers.¹⁵ Briefly, the ends of the trabeculae were placed in troughs constructed from 25-gauge stainless steel tubing, which were attached to a stylus from the motor arm and another that extended from the active element of the force transducer. The trabecula was secured by overlaying each end with a 0.5-mm length of 4-0 monofilament nylon suture, which was then tied into the trough with two pieces of 10-0 monofilament nylon suture. This attachment minimized the end compliance of the muscle. Both the force transducer and motor were mounted on three-way micromanipulators, allowing adjustment of muscle position and length. The bath system consisted of a series of glass-floored wells (800-µL volume) in a stainless steel plate that could be manually translated under the muscle, allowing rapid transfer from relaxing to activating solutions. The experimental apparatus was cooled to 15°C using peltier devices (Cambion Thermoelectric Devices), which were in turn cooled by a circulating water heat sink. Force, muscle length, and sarcomere length (as described below) were digitized at 1000 Hz using a 12-bit A/D convertor (AT-MIO-16F-5, National Instruments Corp), and each was displayed and stored on a personal computer using custom software (LABVIEW for Windows, National Instruments Corp). Muscle length was changed during the experimental protocol by voltage commands to the torque motor, a process that was controlled by the computer via a 12-bit D/A convertor (AT-MIO-16F-5, National Instruments Corp) using custom software as described below.

Sarcomere Length Measurement
Sarcomere length was measured by laser diffraction using a system similar to the one previously described in detail by de Tombe and ter Keurs.¹⁶ Briefly, the trabecula was illuminated by a perpendicular helium-neon laser beam (model 05-LHP151, Melles Griot; 5-mW output, 632.8-nm wavelength), and the position of the first-order diffraction line was monitored with a 512-element photodiode array (model RC 105, Reticon) that was scanned electronically every 0.5 millisecond. A glass coverslip was placed over the well containing the trabeculae to eliminate scattering of the first-order diffraction line by the fluid meniscus of the activating solutions. Median sarcomere length was computed by an analog computer (Biomedical Technical Support Centre, University of Calgary [Canada]) calibrated using glass diffraction gratings of known spacing. Sarcomere length was also measured visually (magnification x1000) at the beginning of each experiment to confirm the calibration of the system.

Experimental Protocol
The kinetics of tension development were assessed using a modification of the procedure originally described by Brenner and Eisenberg⁹ designed to mechanically disrupt force-generating crossbridges in tonically activated permeabilized muscle. The trabecula was transferred from relaxing to activating solution, and tension was allowed to develop to a plateau. Subsequently, slack equivalent to 20% of original muscle length was rapidly introduced at one end of the muscle by the torque motor, and this was followed by a brief (25-millisecond) period of unloaded shortening. Unloaded shortening has been shown to reduce dynamic stiffness (which was used as an index of the proportion of attached crossbridges) in rat myocardium to 12% of that measured during an isometric contraction.¹⁷ Dissociation of most of the remaining crossbridges was accomplished by rapidly restretching the muscle to the original length. Tension redevelopment following this maneuver results from reattachment of crossbridges to the thin filament and redistribution of crossbridges into force-generating states.

It is necessary to maintain constant sarcomere length during tension redevelopment, since sarcomere shortening in the central portion of the muscle because of end compliance leads to underestimation of k_tr.^{9 10 11 12} The sarcomere length signal obtained from cardiac trabeculae is noisier and of lower intensity than that obtained from skeletal muscle fibers, a phenomenon that presumably is secondary to increased scattering of incident laser light resulting from the greater heterogeneity of sarcomere lengths in activated cardiac muscle and the extracellular connective tissue present in multicellular cardiac preparations. Consequently, we used an adaptive rather than an instantaneous feedback system to control sarcomere length. This approach was feasible in our experiments because the slack/restretch maneuver could be performed repetitively during the same activation without altering steady-state activated force or the kinetics of tension redevelopment. A proportional error and proportional error-squared feedback control algorithm was implemented with custom software (LABVIEW) using a 25-Hz finite impulse response low-pass digital filter for the sarcomere length signal (corrected for a linear phase delay). Sarcomere length was clamped during tension redevelopment to ±8 nm per half sarcomere within three to four iterations, as illustrated in Fig 2. Further iterations did not improve feedback control, which was ultimately limited by noise in the sarcomere length signal.

View larger version (18K): [in this window] [in a new window]   Figure 2. Tracings show motor position, sarcomere length, and tension and illustrate the method of sarcomere length control. Sarcomere length was clamped to ±15 nm per half sarcomere during tension redevelopment following the length release/restretch procedure using an iterative feedback control system. The root-mean-square error of the controlled sarcomere length signal during tension redevelopment for all experiments was 0.005±0.002 µm. Sarcomere length control in most cases both increased the rate of tension redevelopment and decreased the residual tension present immediately after the length release/restretch, as illustrated in this example in which ktr increased from 2.57 s-1 in the absence of control to 3.99 s-1 in the final controlled iteration. Likewise, in this example the residual tension present before force redevelopment decreased from 45% to 24% of activated tension when sarcomere length control was imposed (experiment 1/17/94, pCa 5.9).

Data and Statistical Analyses
In all cases, tension redevelopment following the length release/restretch maneuver was well fit by a single exponential function

where F_ss is steady-state force, F is force at time t, and k_tr is the rate constant of tension redevelopment. F_res represents the small residual force present immediately after the length release/restretch maneuver. Possible sensitivity of k_tr to calcium concentration was assessed using multivariate linear regression implementation of ANOVA. Curve fitting and statistical analysis were performed using commercial software (SYSTAT). Data are presented as mean±SD.

	Results

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Trabeculae Characteristics
We measured steady-state force and the rate of tension redevelopment in seven trabeculae during maximal activation (pCa 4.5) and at varying submaximally activating calcium concentrations. The use of very small trabeculae was necessary to obtain a clearly discernible first-order diffraction line during activation, although on maximal activation the first-order diffraction line invariably broadened and decreased in intensity (Fig 3). Preparations were discarded if a first-order laser diffraction line could not be resolved during maximal activation, and as a result we obtained one suitable preparation for approximately every six rat hearts dissected. The length and width of our preparations were 1.01±0.27 mm and 114.6±12.9 µm, respectively. The depth of the trabeculae was not measured in each case but typically was less than 70 µm.

View larger version (87K): [in this window] [in a new window]   Figure 3. Photomicrographs show the central portion of a trabecula in relaxing solution (A, pCa 9.0, 0.49 mg tension) and maximally activating solution (B, pCa 4.5, 20.49 mg tension). Corresponding first-order laser diffraction patterns are shown on the left (C and D). Very small, uniform trabeculae were used (width, 78 µm in this example) to obtain discernible first-order laser diffraction lines at maximal activation. Sarcomere length of the relaxed fiber was 2.19 µm, whereas sarcomere length of the maximally activated fiber was 2.13 µm, demonstrating a low-compliance attachment, which was necessary for effective sarcomere length control. The increased heterogeneity of sarcomere length evident with maximal activation corresponds with a broader and lower-intensity first-order laser diffraction line than that seen in the relaxed fiber (experiment 5/23/94).

Sarcomere Length and Isometric Tension
We found that a low compliance attachment of the trabeculae to the experimental apparatus was necessary to implement sarcomere length control. Sarcomere length was set initially in the relaxed trabeculae to approximately 2.15 µm, yielding a passive tension of just 1.6±1.4 mg. Mean sarcomere length was 2.09±0.04 µm during measurements of active tension. Maximally activated tension was 62.3±62.5 mg for the seven trabeculae. The large SD for measurements of maximally activated tension was primarily due to one trabecula that was substantially larger in width and depth than the other six. The pCa resulting in half-maximal tension (pCa₅₀), as determined by the Hill transformation,¹⁸ was 5.68±0.06, and the Hill coefficient was 4.05±1.80.

Rate of Tension Redevelopment
In each trabecula, the rate of tension redevelopment increased with increasing calcium concentration (Fig 4 and Table). The rate constant of tension redevelopment (k_tr) was 3.57±0.82 s^-1 at the lowest calcium concentration studied (pCa 5.9) and increased to 9.51±1.29 s^-1 during maximal activation (pCa 4.5). The relation between k_tr and calcium concentration was generally sigmoidal and was highly significant as assessed by ANOVA (P<.001). A similar relation was found even in the absence of sarcomere length control, although k_tr values were an average of 12% lower compared with determinations in which sarcomere length was controlled. The pCa for half-maximal k_tr as determined by the Hill transformation was 5.75±0.18, and the Hill coefficient was 2.88±2.29. As demonstrated in Fig 5, the relation between relative k_tr and relative steady-state active tension was approximately linear (r²=.94, P<.001) over a range of relative tensions from 5% to 100% maximal. Extrapolation of k_tr to zero active tension on the basis of this relation yielded a baseline value that was 18.9% of maximal.

View larger version (22K): [in this window] [in a new window]   Figure 4. Effect of calcium on the rate of tension redevelopment in a representative trabecula. As evident in A, B, and C, both steady-state tension and the rate of tension redevelopment following a rapid release/restretch maneuver increased with calcium concentration. In this example (experiment 4/1/94b), active tension increased from 10.6 mg at pCa 5.7 to 31.2 mg with maximal activation. Likewise, ktr increased from 2.17 to 8.24 s-1 over the same range of calcium concentrations. Tension in C is normalized to maximal.

View this table: [in this window] [in a new window]   Table 1. Relative Tension (P/Po) and the Time Constant of Tension Redevelopment (ktr) at Increasing Calcium Concentrations

View larger version (13K): [in this window] [in a new window]   Figure 5. Scatterplot shows relative ktr as a function of relative tension for all seven trabeculae. We found the relation between relative tension (tension at any given pCa normalized to the maximally activated tension for that muscle) and relative ktr (again normalized to the ktr at maximal activation for each muscle) to be approximately linear (r2=.94).

Some degree of residual tension was invariably present immediately following the slack/restretch maneuver just before tension redevelopment (see Fig 2). The source of this residual tension, which was 36.9±14.3% of steady-state force without sarcomere length control, is not known, but it has also been observed in skeletal muscle fiber preparations.^{11 12 13} It is not likely caused by passive viscous or viscoelastic elements because its amplitude exceeds by an order of magnitude the tension overshoot present following an identical slack/restretch maneuver in relaxed trabeculae (data not shown). The residual tension declined to 22.3±12.3% of steady-state tension when sarcomere length control was imposed, suggesting that more than a third of the residual tension results from a viscosity related to end compliance in the activated muscle.

	Discussion

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The major finding of the present study is that the rate of tension development in permeabilized cardiac muscle is sensitive to calcium concentration, similar to previous observations in both fast and slow skeletal muscles^{10 11 12} and in contrast to the recent suggestion that the kinetics of isometric tension development are not affected by calcium in intact cardiac muscle.¹³ Our finding is inconsistent with a simple on-off switching mechanism for crossbridge activation in myocardium and suggests that calcium has a role in regulating the kinetics of the transition or transitions between non–force-generating and force-generating crossbridge states. The significant sensitivity of k_tr to calcium demonstrated in the present study makes a compelling case for a role of crossbridge kinetics in modulating isometric force in cardiac muscle.

Differences Between Intact and Permeabilized Myocardium
The difference in results obtained in the present study and the earlier investigation by Hancock et al¹³ may possibly be explained by differences in the experimental protocol, although intrinsic differences in the mechanism of the regulation of force between intact and permeabilized muscle must also be considered. For example, the tension-pCa relation of intact cardiac muscle is apparently shifted in the direction of greater calcium sensitivity when compared with tension-pCa relations in permeabilized cardiac trabeculae.^{19 20} Whether this is due to a calcium-sensitizing cytosolic or myofibrillar constituent that is lost on detergent permeabilization or whether the activating solutions typically used with permeabilized preparations poorly reproduce the cytosolic environment is not clear, but either could potentially alter the kinetics of isometric tension development. Similarly, swelling of the myofilament lattice on skinning reduced the calcium sensitivity of tension in both skeletal²¹ and cardiac²² muscles and could potentially alter the calcium sensitivity of k_tr. The detergent (Triton X-100) used to permeabilize the trabeculae could have a direct effect on myofibrillar function. It is also possible that the difference between the two studies is related to species, since ferret ventricular myocardium contains primarily V₃ myosin²³ and rat heart contains variable proportions of the V₁ and V₃ isoforms. However, a preliminary report by Hancock et al²⁴ found no effect of calcium on the rate of tension redevelopment in Triton X-100–skinned rat myocardium. This result argues against an intrinsic difference in the mechanism of force regulation between intact and permeabilized myocardium or between species and suggests strongly that the differences between the two studies are related to differences in methods.

The methods used in the present study differ in several respects from those of Hancock et al.¹³ They performed measurements in intact ferret papillary muscles that were tetanized by high-frequency electrical stimulation after exposure to ryanodine (an inhibitor of sarcoplasmic reticulum function) rather than in tonically activated permeabilized fibers. Small force fluctuations were present in the tetanus plateaus that affected the rate of force redevelopment. Also, in earlier studies on skeletal muscle, sarcomere length was measured by laser diffraction and held constant during tension redevelopment by feedback control, because in the absence of control, k_tr is underestimated because of end compliance secondary to damage resulting from attaching the muscle preparation to the experimental apparatus.^{9 10} Sarcomere length was not directly measured by Hancock et al because of the thickness of their papillary muscle preparations. Although the central segment length of the papillary muscles was maintained constant during tension redevelopment, the heterogeneity of sarcomere lengths within the central segments could not be assessed²⁵ during sustained tetani or during tension redevelopment following length releases. In contrast, we measured the rate of tension redevelopment in very thin, detergent-permeabilized rat ventricular trabeculae and used laser diffraction techniques^{10 16} to directly measure and control sarcomere length. In this preparation, activation was steady state, and sarcomere length heterogeneity was manifest by loss of the first-order diffraction line.

Perhaps the most important difference is the mechanical maneuver used to abruptly disrupt force-generating crossbridges. We used a large slack/release protocol to ensure that most force-generating crossbridges were disrupted before force redevelopment. A relatively small step release (2% to 3% of maximal muscle length) was used by Hancock et al¹³ without a period of unloaded shortening or a subsequent restretch to the original segment length. Although tension fell to zero during this maneuver, an undetermined proportion of the tension decline was likely due to release of crossbridge elasticity or end compliance without actually disrupting attached crossbridges. In fact, records of tension redevelopment in their study were well fit by a double exponential equation, with the faster component having a rate constant on the order of 1000 s^-1 and an amplitude of approximately 20%. This rapid redevelopment of tension is similar to the rate of tension redevelopment after very small (5 to 6 nm per half sarcomere) step releases in skeletal muscle fibers, which has been attributed to tension redevelopment by attached crossbridges.²⁶ Thus, such rapid tension redevelopment suggests that there was a significant population of residual attached crossbridges following the step release maneuver used in the intact papillary muscle experiments. Although the authors argue that the majority of tension recovery was likely due to reattachment of detached crossbridges, a residual population of strongly attached crossbridges could accelerate k_tr by cooperatively activating the thin filament independent of calcium concentration. Evidence supporting this idea was obtained by Swartz and Moss,²⁷ who found that N-ethylmaleimide–modified myosin subfragment 1, a rigorlike crossbridge analogue that binds tightly to actin but does not contribute to force generation, accelerates k_tr to near maximal rates even at low calcium concentrations. This observation suggests that under isometric conditions, the kinetics of crossbridge state transitions can be modulated via the cooperative activation of the thin filament by strongly bound crossbridges rather than or in addition to a direct effect of calcium.^{18 27}

Our present finding that k_tr varies with calcium concentration agrees with a report by Araujo and Walker,²⁸ which demonstrated that the rate of tension development following photolysis of caged calcium in skinned rat ventricular myocytes is influenced by calcium concentration. In contrast, frequency analysis of stiffness in intact myocardium found no effect of activation level on isometric crossbridge kinetics. Shibata et al²⁹ measured stiffness using small-amplitude sinusoidal length oscillations of varying frequencies in rabbit papillary muscles that were tonically activated with barium. The frequency of minimum stiffness, which they interpreted as a measure of crossbridge cycling rate, did not vary as a function of barium concentration. However, similar studies in permeabilized skeletal muscle have found that the frequency of minimum stiffness is also independent of calcium concentration.³⁰ Force-generating crossbridges are not disrupted by the low-amplitude length oscillations used in these types of experiments, and it is likely that the thin filaments are cooperatively activated by strongly bound crossbridges even at low calcium (barium) concentrations. As discussed above, this form of thin filament activation may mask the calcium sensitivity of crossbridge kinetics.

Differences Between Cardiac and Skeletal Muscle
The threefold to fivefold increase in k_tr over the full range of activation we observed in cardiac muscle is significantly less than that seen in fast skeletal muscle^{10 11 12} but is similar to that reported for slow skeletal muscle fibers.^{11 12} The approximately linear relation between k_tr and steady state isometric tension in cardiac muscle (Fig 5) also differs from the curvilinear relation in fast skeletal muscle, in which k_tr increases with increasing calcium only at concentrations yielding activations greater than half maximal.^{10 11 12} This observation suggests that force may be regulated differently in cardiac muscle, perhaps involving an effect of calcium concentration on both the numbers of cycling crossbridges and rate of formation of force-generating crossbridge states at low activation levels.

In addition, this difference in the kinetics of isometric tension development between heart and fast skeletal muscles could contribute to the differences in the shapes of their respective tension-pCa relations (typically less steep in cardiac muscle³¹ ). Although the molecular basis for this difference between the two forms of striated muscle is unknown, the lesser slope of the tension-pCa relation in cardiac muscle likely has important physiological implications.¹⁸ The steeper tension-pCa relation in skeletal muscle favors an all-or-none mode of contraction, whereas the shallower relation in myocardium would contribute to a more graded regulation of twitch tension and cardiac performance. Brenner¹⁰ suggested that changes in crossbridge kinetics (either f_app or g_app) could affect both the calcium sensitivity and the slope of the tension-pCa relation.¹⁰ His hypothesis is supported by several examples in skeletal muscle fibers in which acceleration of isometric crossbridge kinetics at low activation levels corresponds to a reduced slope of the tension-pCa relation. Treatment of skeletal muscle fibers with N-ethylmaleimide–modified myosin S1 increases both k_tr and isometric tension at low calcium concentrations and results in a less steep tension-pCa relation, which resembles that for cardiac muscle.²⁷ Likewise, phosphorylation of myosin light chain 2 in psoas fibers by myosin light chain kinase increases both k_tr and tension at submaximal calcium concentrations.³² These effects of N-ethylmaleimide–modified myosin S1 or myosin light chain 2 phosphorylation could also be explained on the basis of cooperative recruitment of cycling crossbridges in addition to their effects on isometric crossbridge kinetics. Nonetheless, these results from earlier studies are consistent with the idea that the sensitivity of k_tr to calcium at low activation levels may contribute to the reduced slope of the tension-pCa relation in myocardium.

Physiological Significance
Although the mechanical perturbation used in this study to index isometric crossbridge kinetics differs from the loading imposed on myofibrils in situ, it is likely that regulation of isometric crossbridge cycling would affect in vivo cardiac performance. The systolic calcium transient, measured using the calcium indicators aequorin^{33 34} and fura 2,³⁵ is brief relative to the duration of the twitch. Similarly, the kinetics of calcium binding to the thin filament are rapid³⁶ relative to the kinetics of crossbridge attachment and force generation determined in this study. Thus, k_tr may reflect the subcellular processes limiting the rate and extent of pressure rise in the intact ventricle, particularly early in the cardiac cycle, when contraction is isovolumetric.

Potential Limitations
Because of the heterogeneity of sarcomere lengths in activated cardiac trabeculae relative to skeletal muscle fibers (see Fig 2), the sarcomere length signal was noisier and had less temporal resolution than that typically obtained in studies of skeletal muscle. Consequently, an adaptive rather than an instantaneous approach to sarcomere length control was used, and the degree of control that could be achieved was less than in skeletal fibers. Despite low-pass filtering of the sarcomere length signal, some of this noise was invariably transmitted through the feedback control system and resulted in small force transients during tension redevelopment (Figs 2 and 4). The difficulties in obtaining sarcomere length measurements by laser diffraction in maximally activated cardiac trabeculae have been noted by other authors.^{37 38} We meticulously selected very thin and homogeneous trabeculae and obtained very low compliance attachments to the experimental apparatus, so it is unlikely that the first-order diffraction line and subsequently sarcomere length control could be improved. Furthermore, since tension recovery rates were sensitive to calcium in both the presence and absence of sarcomere length control, it is unlikely that this limitation affected our overall conclusions.

	Acknowledgments

 
We gratefully acknowledge the excellent technical assistance of Scott Stoker and Valtino Afonso and thank Dr Pieter de Tombe for his assistance in implementing the sarcomere length control algorithm.

	Footnotes

 
Reprint requests to Matthew R. Wolff, MD, H6/316, Clinical Science Center, 600 Highland Ave, Madison, WI 53793.

Received August 1, 1994; accepted October 12, 1994.

	References

Top Abstract Introduction Materials and Methods Results Discussion References

 
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12. Metzger JM, Moss RL. pH modulation of the kinetics of a Ca²⁺-sensitive cross-bridge state transition in mammalian single skeletal muscle fibers. J Physiol (Lond). 1990;428:754-764.

13. Hancock WO, Martyn DA, Huntsman LL. Ca²⁺ and segment length dependence of isometric force kinetics in intact ferret cardiac muscle. Circ Res. 1993;73:603-611. [Abstract/Free Full Text]

14. Fabiato A. Computer programs for calculating total from specified free or specified total ionic concentration in aqueous solutions containing multiple metals and ligands. Methods Enzymol. 1988;157:378-417. [Medline] [Order article via Infotrieve]

15. Moss RL, Gullian GG, Greaser ML. Effects of EDTA treatment upon the protein subunit composition and mechanical properties of mammalian single skeletal muscle fibers. J Cell Biol. 1983;96:970-978. [Abstract/Free Full Text]

16. de Tombe PP, ter Keurs HEDJ. Force and velocity of sarcomere shortening in trabeculae from rat heart: effects of temperature. Circ Res. 1990;66:1239-1254. [Abstract/Free Full Text]

17. de Tombe PP, ter Keurs HEDJ. An internal viscous element limits unloaded shortening velocity of sarcomere shortening in rat myocardium. J Physiol (Lond). 1992;454:619-642. [Abstract/Free Full Text]

18. Moss RL. Ca²⁺ regulation of mechanical properties of striated muscle: mechanistic studies using extraction and replacement of regulatory proteins. Circ Res. 1992;70:865-883. [Abstract/Free Full Text]

19. Yue DT, Marban E, Wier WG. Relationship between force and intracellular [Ca²⁺] in tetanized mammalian heart muscle. J Gen Physiol. 1986;87:223-242. [Abstract/Free Full Text]

20. Gao WD, Backx PH, Azan-Backz M, Marban E. Myofilament Ca²⁺ sensitivity in intact versus skinned rat ventricular muscle. Circ Res. 1994;74:408-415. [Abstract/Free Full Text]

21. Godt RE, Maughan DW. Swelling of skinned muscle fibers of the frog: experimental observations. Biophys J. 1977;19:103-116.[Medline] [Order article via Infotrieve]

22. McDonald KS, Moss RL. Osmotic compression of single cardiac myocytes reversed the reduction in Ca²⁺ sensitivity of tension observed at short sarcomere length. Biophys J. 1994;66:A404. Abstract.

23. Book CBS, Wilson RP, Ng YC. Cardiac hypertrophy in the ferret increases expression of the Na⁺-K⁺-ATPase ₁- but not ₃-isoform. Am J Physiol. 1994;266:H1221-H1227. [Abstract/Free Full Text]

24. Hancock WO, Huntsman LL, Martyn DA, Gordon AM. Isometric force kinetics are unaffected by Ca²⁺ in skinned rat ventricular myocardium. Biophys J. 1994;66:A404. Abstract.

25. Huntsman LL, Joseph DS, Oiye MY, Nichols GL. Auxotonic contractions in cardiac muscle segments. Am J Physiol. 1979;237:H131-H138.

26. Huxley AF, Simmons RM. Proposed mechanism of force generation in striated muscle. Nature. 1971;233:533-538. [Medline] [Order article via Infotrieve]

27. Swartz DR, Moss RL. Influence of a strong-binding myosin analogue on calcium sensitive mechanical properties of skinned skeletal muscle fibers. J Biol Chem. 1992;267:20497-20506. [Abstract/Free Full Text]

28. Araujo A, Walker JW. Kinetics of tension development in skinned cardiac myocytes measured by photorelease of Ca²⁺. Am J Physiol. In press.

29. Shibata T, Hunter WC, Yang A, Sagawa K. Dynamic stiffness measured in central segment of excised rabbit papillary muscles during barium contracture. Circ Res. 1987;60:756-769. [Abstract/Free Full Text]

30. Kawai M, Cox RN, Brandt PW. Effect of Ca ion concentration on crossbridge kinetics in rabbit psoas fibers: evidence for the presence of two Ca-activated states of thin filament. Biophys J. 1981;35:375-384. [Medline] [Order article via Infotrieve]

31. Sweitzer NK, Moss RL. The effect of altered temperature on Ca²⁺-sensitive force in permeabilized myocardium and skeletal muscle. J Gen Physiol. 1990;96:1221-1245. [Abstract/Free Full Text]

32. Metzger JM, Greaser ML, Moss RL. Variations in cross-bridge attachment rate and tension with phosphorylation of myosin in mammalian skinned skeletal muscle fibers: implications for twitch potentiation in intact muscle. J Gen Physiol. 1989;93:855-882. [Abstract/Free Full Text]

33. Allen DG, Blinks JR. Calcium transients in aequorin-injected frog cardiac muscle. Nature. 1978;273:509-513. [Medline] [Order article via Infotrieve]

34. Allen DG, Kurihara S. The effects of muscle length on intracellular calcium transients in mammalian ventricular muscle. J Physiol (Lond). 1982;327:79-94. [Abstract/Free Full Text]

35. Backx PH, ter Keurs HEDJ. Fluorescent properties of rat cardiac trabeculae microinjected with fura-2 salt. Am J Physiol. 1993;264:H1098-H1110. [Abstract/Free Full Text]

36. Robertson SP, Johnson JD, Potter JD. The time-course of Ca²⁺ exchange with calmodulin, troponin, parvalbumin, and myosin in response to transient increases in Ca²⁺. Biophys J. 1981;34:559-569. [Medline] [Order article via Infotrieve]

37. Kentish JC, ter Keurs HEDJ, Ricciardi L, Bucx JJJ, Noble MIM. Comparison between sarcomere length-force relations of intact and skinned trabeculae from the rat right ventricle. Circ Res. 1986;58:755-768. [Abstract/Free Full Text]

38. Kentish JC, Stienen GJM. Differential effects of length on maximum force production and myofibrillar ATPase activity in rat skinned cardiac muscle. J Physiol (Lond). 1994;475:175-184.[Abstract/Free Full Text]

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