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Journal of Physiology (2002), 543.2, pp. 555-566
© Copyright 2002 The Physiological Society
DOI: 10.1113/jphysiol.2002.022673
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ABSTRACT |
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We tested the hypothesis that force-velocity history modulates thin filament activation, as assessed by the rate of force redevelopment after shortening (+dF/dtR). The influence of isotonic force on +dF/dtR was assessed by imposing uniform amplitude (2.55 to 2.15 µm sarcomere-1) but different speed releases to intact frog muscle fibres during fused tetani. Each release consisted of a contiguous ramp- and step-change in length. Ramp speed was changed from release to release to vary fibre shortening speed from 1.00 (2.76 ± 0.11 µm half-sarcomere-1 s-1) to 0.30 of maximum unloaded shortening velocity (Vu), thereby modulating isotonic force from 0 to 0.34 Fo, respectively. The step zeroed force and allowed the fibre to shorten unloaded for a brief period of time prior to force redevelopment. Although peak force redevelopment after different releases was similar, +dF/dtR increased by 81 ± 6 % (P < 0.05) as fibre shortening speed was reduced from 1.00 Vu. The +dF/dtR after different releases was strongly correlated with the preceding isotonic force (r = 0.99, P < 0.001). Results from additional experiments showed that the slope of slack test plots produced by systematically increasing the step size that followed each ramp were similar. Thus, isotonic force did not influence Vu (mean: 2.84 ± 0.10 µm half-sarcomere-1 s-1, P < 0.05). We conclude that isotonic force modulates +dF/dtR independent of change in Vu, an outcome consistent with a cooperative influence of attached cross-bridges on thin filament activation that increases cross-bridge attachment rate without alteration to cross-bridge detachment rate.
(Resubmitted 19 April 2002; accepted after revision 25 June 2002)
Corresponding author G. C. Sieck: Department of Anesthesiology, Mayo Foundation, Rochester, MN 55902, USA. Email: sieck.gary{at}mayo.edu
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INTRODUCTION |
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The myosin molecule of vertebrate striated muscle is a molecular motor, transducing the free energy of ATP hydrolysis into mechanical work. This chemomechanical coupling is regulated by calcium (Ca2+) binding to the troponin C (TnC) subunit of the regulatory protein complex, a reaction that catalyses myosin motor activity by 'activating' the thin filament, i.e. by increasing the availability of myosin cross-bridge binding sites on actin (Ford, 1991). In turn, cooperative interactions between attached cross-bridges and the regulatory protein complex provide a positive feedback signal that further increases thin filament activation by increasing cross-bridge access to previously unavailable sites (Millar & Homsher, 1991; Swartz & Moss, 1992, 2001; Morris et al. 2001). This positive feedback effect may be mediated through an effect of attached cross-bridges on tropomyosin state ('open' vs. 'closed') (McKillop & Geeves, 1993) and/or on the Ca2+ affinity of TnC (Guth & Potter, 1987; Zot & Potter, 1989; Swartz et al. 1996).
One of the implications of a cross-bridge based cooperative mediation of regulatory protein function is that filament sliding during shortening may reduce thin filament activation. Compared to the isometric, shortening reduces the number of actin bound cross-bridges, an effect that increases with shortening speed (Julian & Sollins, 1975; Ford et al. 1985). Because of the positive feedback effect exerted by attached cross-bridges, reductions in this number might be expected to diminish the cooperative aspects of thin filament activation, thus modulating thin filament activation commensurate with the load on the contractile apparatus. Indeed, a force-velocity history mediated modulation of thin filament activation provides a mechanistic explanation for the deactivating effect that shortening has on muscle force development, a phenomenon known as shortening-induced deactivation (Edman, 1975). For example, although peak force is not affected, shortening steps applied during a fused tetanus reduces the rate of force redevelopment of frog skeletal fibres in proportion to unloaded shortening distance (Edman, 1980; Vandenboom et al. 1998). It has been proposed that shortening-deactivation is due to a reduced Ca2+ occupancy of TnC brought about by filament sliding (Edman, 1980) or to the effect that a reduced population of attached cross-bridges has on tropomyosin state (Gordon et al. 2000). However, to be entirely consistent with either hypothesis, it might be expected that the rate of force redevelopment after shortening should, in addition to shortening distance, also be altered by shortening speed dependent variations in attached cross-bridge number.
The purpose of this study was to test the working hypothesis that attached cross-bridge number (as reflected by isotonic force) modulates thin filament activation of intact frog skeletal fibres. Because direct measurements of thin filament activation level are not feasible with intact fibres, the hypothesis we were actually able to test was that isotonic force modulates the rate of force redevelopment after shortening (+dF/dtR). In this study we have assumed that variations in +dF/dtR reflect differences in thin filament activation, an approach justified by work showing that the rate constant for isometric force redevelopment (kTR) of permeabilized rabbit psoas muscle is influenced by thin filament activation status (Regnier et al. 1996, 1998; but see Brenner, 1988; Brenner & Chalovich, 1999). We imposed uniform releases, consisting of a ramp- and a step-change in length, to tetanized frog fibres. Isotonic force was modulated by varying ramp speed while the step reduced force to zero, a technique that allowed us to examine the effect of different isotonic forces while still measuring isometric force redevelopment rates from the same baseline. Consistent with the cooperative effects of attached cross-bridges on thin filament activation, we predicted that reductions in ramp shortening speed, and thus increased isotonic force, would increase +dF/dtR compared to after shortening at the maximal rate of unloaded shortening. We found that that the +dF/dtR of intact frog muscle fibres was modulated by shortening-speed dependent variations in isotonic force (i.e. by force-velocity history). This result demonstrates a novel aspect of shortening-induced deactivation that is consistent with a cooperative activation of the thin filament by attached cross-bridges. Aspects of this work have appeared in abstract form (Vandenboom et al. 2001, 2002).
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METHODS |
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The methods and procedures used during these experiments were approved by the Institutional Animal Care and Use Committee of Mayo Foundation. Frogs (Rana temporaria) were killed by decapitation followed by double pithing. The tibialis anterior muscle was removed and mounted in a dissecting dish containing Ringer solution (composition in mM: NaCl, 115; KCl, 2.5; CaCl2, 1.8; Na2HPO4, 2.15; NaH2PO4, 0.85; pH 7.2). Single fibres were isolated and transferred to a muscle chamber that was milled out of a Perspex block. One fibre tendon was tied (10-0 suture) to a stainless steel hook glued to a force transducer (model AE 801, Sensonor, Horten, Norway) and the other to a stainless steel hook attached to the graphite arm of a servo-motor (General Scanning, Watertown, MA, USA). Arm position and movement was controlled by computer software (LabView, National Instruments, Austin, TX, USA). Mean sarcomere length was determined optically from resting fibres prior to the start of experiments. As a result, all ramp speed and sarcomere length data reported were based on measures of fibre length after sarcomere length was set to 2.55 µm sarcomere-1. Fibres were stimulated via flanking platinum electrodes by a current pulse of 100 µs duration. Bath temperature was 3-5 °C.
Experimental protocol
A slack test was performed to determine fibre unloaded shortening velocity (Vu) (Edman, 1979). Thereafter, one or more of the following experiments was conducted. The main series of experiments was performed to determine the effect of different shortening velocities, and thus different pre-existing isotonic forces, on +dF/dtR. A second series of experiments (ramped slack tests) was then performed to test for an effect of isotonic force on fibre unloaded shortening velocity produced by the length step. These experiments were also performed to determine the effect that different step sizes had on the +dF/dtR-isotonic force relation established in the main series of experiments. The final series of experiments were controls to investigate the effect of stimulus number on the +dF/dtR associated with low and high isotonic forces.
Slack tests (n = 10)
A step-change in length was applied during the force plateau of each of several consecutive tetani. Initial sarcomere length was 2.55 µm sarcomere-1. Step amplitude was systematically increased from 0.05 to 0.35 µm sarcomere-1, in increments of 0.05 µm sarcomere-1. Step size was plotted against slack time and the data were fit by linear regression. The slope of this line yields fibre Vu while the intercept of this line with the step size axis provides an estimate of total system (fibre + mounting) compliance (Yo) (Edman, 1979). Slack times were determined using the method of Julian et al. (1986).
Fibres were treated in a similar manner during each series of experiments that followed the slack test. Fibres were initially set to a mean sarcomere length of 2.55 µm and then activated using a fixed pattern of stimulation (15-30 Hz for 1-2 s, every 150 s). After the attainment of steady-state force a single release, imposed after ~525 ms of stimulation, was applied during each tetanus. Each release consisted of a contiguous ramp- and step-change in length (e.g. Fig. 1A). The ramp component of each release was used to control fibre-shortening speed and to thus vary the isotonic force preceding isometric force redevelopment. The length step was used to zero force and allow the fibre to shorten unloaded prior to force redevelopment. This manoeuvre ensured that force redeveloped from the same baseline after each ramp.
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Figure 1. Effect of ramp speed on isotonic and redeveloped force in an intact frog fibre Original length (A) and force (B) records from a representative experiment in which a different ramp speed was applied during each of a series of eight consecutive tetani. A, ramp speed was varied from 1.00 (3.21 µm half-sarcomere-1 s-1) to 0.30 Vu, in increments of 0.10 Vu (traces 1 through 8, respectively). Ramp- and step-shortening was equal to 0.35 and 0.10 µm sarcomere-1, respectively; initial and final mean sarcomere lengths are indicated. Horizontal arrow marks transition from ramp- to step-shortening (at 2.20 µm sarcomere-1). B, individual force traces corresponding to length records shown in A. Dashed vertical lines match the 0.30 Vu length record with corresponding force trace. Isotonic force during the ramp (a), zero force and unloaded shortening caused by the step (b) and isometric force redevelopment after the step (c) are indicated. C, force records of B shown expanded and time shifted to align the imposition of the length step on the x-axis (downward pointing arrow). Horizontal arrow indicates the force level (0.15 Fo) at which +dF/dtR was determined after each release. In this fibre, +dF/dtR was increased by 77 % and the time delay before force redevelopment was reduced by 30 % (upward pointing arrows) as release speed was decreased from 1.00 to 0.30 Vu (and isotonic force increased from 0 to 0.33 Fo). D, selected force records (0.30, 0.40, 0.70 and 1.00 Vu) shown differentiated and time shifted. Superimposed circles show where +dF/dtR was determined for each respective record (at 0.15 Fo). | ||
Main experiments (n = 10)
Ramp speed was varied from 1.00 to 0.30 Vu, in increments of 0.10 Vu. Ramp speeds were based upon the prior determination of fibre Vu using the slack test. The first and last releases of this series were at 1.00 Vu and these responses were averaged to control for any time-dependent change in fibre performance; all other responses were compared to this average. Although ramp speed was varied from release to release, ramp and step amplitudes were constant (mean: 0.33 and 0.07 µm sarcomere-1, respectively). Note that although these amplitudes varied somewhat from fibre to fibre, isometric force always redeveloped at the same final sarcomere length following each release in a given fibre. Because ramp speeds less than ~0.30 Vu attenuated peak redeveloped force compared to 1.00 Vu, the range of ramp speeds we tested during these experiments was limited to the range 0.30-1.00 Vu
Ramped slack tests (n = 8)
Each of the iso-velocity ramps used in these particular experiments (1.00-0.10 Vu) was followed by four different length steps (0.05, 0.11, 0.16 or 0.21 µm sarcomere-1) (e.g. Fig. 3). Ramp amplitude was 0.35 µm sarcomere-1; thus, fibres shortened from a mean initial to a mean final length of 2.55 to 2.20 µm sarcomere-1, respectively. Mean sarcomere length after the imposition of the different steps was 2.15, 2.09, 2.04 and 1.99 µm, respectively. The time delay (slack time) before isometric force redevelopment following each of the different step changes in length was plotted against step size. This plot produced independent values for Vu corresponding to the period of unloaded shortening following each ramp. The Yo associated with different releases was used to estimate total system compliance coincident with different isotonic forces.
Control experiments (n = 7)
Ramp duration was inversely proportional to ramp-speed, and thus the number of stimuli received by the fibre prior to force redevelopment was greater for slow than for fast ramps. To control for this, experiments were performed in which the start of a 1.00 Vu release was delayed compared to the start of a 0.30 Vu release. This time offset was sufficient to ensure that these respective ramps ended at the same time and that the redevelopment of isometric force occurred at similar times during the protocol, thus eliminating the effect of stimulus number on +dF/dtR. Release speed was alternated from tetanus to tetanus (n = 2 each) and the respective responses averaged.
Data analysis
Data were sampled at 10 kHz and digitally smoothed before analysis. The +dF/dtR was measured from digitally differentiated force records. The +dF/dtR was determined at a fixed load (as per cent Fo) after each of the different releases applied to a given fibre (e.g. Fig. 1C and D). However, compared to 1.00 Vu, the peak of the differentiated record tended to occur at lower force levels as the preceding ramp speed was reduced. To avoid ramp-speed dependent biases in the data that this effect may have caused, we measured +dF/dtR at the mean per cent Fo at which all differentiated records peaked (mean: 0.11 Fo, range 0.06-0.21 Fo). This procedure resulted in the +dF/dtR being measured at a percentage of Fo approximately equidistant from the peak following each different release speed.
Data are presented as means ± S.E.M. throughout. A one way ANOVA followed by a Newman-Kuels post hoc test and paired t tests were used to test for significance between means in the main and control experiments, respectively (P < 0.05).
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RESULTS |
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The purpose of the main set of experiments was to test the effect of isotonic force on +dF/dtR using intact frog skeletal muscle fibres. Length and force records from a representative experiment are shown in Fig. 1A and illustrate the effect of the imposed ramp- and step-length change on force. The ramp caused an initial rapid decline in force before reaching an isotonic value that was inversely related to fibre shortening speed. The range of isotonic forces produced in this way corresponded to the lower portion of the force-velocity relation (0-0.34 Fo, Table 1). The step imposed after each ramp quickly reduced isotonic force to zero. After a brief period of unloaded shortening the fibre redeveloped force under isometric conditions. Because release amplitudes were uniform, isometric force always redeveloped at the same final sarcomere length. Consistent with this, peak force redevelopment was similar for all releases (Table 1, Fig. 1A).
The force records of Fig. 1B are shown on a slower time scale and time-shifted in Fig. 1C. A comparison of the different slopes of the individual force traces clearly illustrates the effect that decreasing shortening speed, and increasing isotonic force, had on the rate that force redeveloped. The association between shortening speed and +dF/dtR is summarized in Fig. 2A. The dependence of +dF/dtR on the preceding isotonic force is shown in Fig. 2B. Because isotonic force is a function of both the number of attached cross-bridges as well as the mean force per cross-bridge (Ford et al. 1985), the linear relation between +dF/dtR and isotonic force suggests that thin filament activation coincident with isometric force redevelopment was related to an effect of cross-bridge binding to actin during ramp-shortening.
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Figure 2 A, relation between fibre shortening speed and +dF/dtR. Plot of +dF/dtR after ramp- and step-shortening vs. fibre shortening speed during the ramp. Fibre shortening speed expressed relative to the fastest ramp (1.00 Vu, 2.76 ± 0.11 µm half-sarcomere-1 s-1). The +dF/dtR is normalized to the value obtained after a 1.00 Vu release. Curve fitted to data is a double exponential. B, direct relation between preceding isotonic force and +dF/dtR. Plot of +dF/dtR (normalized to 1.00 Vu) measured after different releases vs. isotonic force measured during different ramps. Data are fit by linear regression (r = 0.99, P < 0.001). Extrapolation of the straight line to 95 % Fo yields a 3.5-fold increase in +dF/dtR compared to 1.00 Vu. Data plotted in A and B are means ± S.E.M. (n = 10). | ||
Selected force records of Fig. 1C, shown differentiated in Fig. 1D, show that force redevelopment did not occur at a constant rate following any release and that the complexity of these records decreased as isotonic force increased. For example, there was a secondary peak in the differentiated record after the faster releases. Also note that, because we measured +dF/dtR at a constant load +dF/dtR was measured at slightly different times on each trace (i.e. 15 and 5 ms after isometric force redevelopment following 1.00 and 0.30 Vu releases, respectively) (Fig. 1B and C).
Ramped slack tests
In addition to an increased +dF/dtR, the force records shown in Fig. 1C also reveal that the slack time before force redevelopment decreased as pre-release isotonic force increased. The slack time decreased approximately linearly with increasing isotonic force and was reduced by 30 ± 5 % after shortening at 0.30 vs. 1.00 Vu (Table 1), indicating an apparent increase in unloaded shortening speed. Thus, it was considered that unloaded cross-bridge cycling rate was increased by the preceding isotonic force, a modulation that would also account for the increased +dF/dtR we observed under the same conditions. Alternatively, the decreased slack time could have been due to an isotonic force-dependent increase in recoil of the series elastic component (SEC). Accordingly, a series of experiments, illustrated in Fig. 3, was performed in order to distinguish between these two possibilities by assessing the effect of length step size on slack time for different isotonic forces. In most regards these experiments were similar to the main set of experiments except that the amplitude of the final length step was systematically increased from 0.05 to 0.21 µm sarcomere-1 and this was plotted against the resulting slack times for each isotonic force tested. The ramp speeds tested and corresponding isotonic forces (as per cent Fo) were 1.00 (0.01 ± 0.01), 0.75 (0.04 ± 0.01), 0.45 (0.16 ± 0.02), 0.25 (0.39 ± 0.03) and 0.10 (0.72 ± 0.04) Vu. Although decreasing ramp speed progressively decreased the slack time corresponding to the smallest length step, the increase in slack times for longer steps at each isotonic force was relatively uniform compared to the smallest step. Thus, although increasing length step size increased slack time for each isotonic force tested, individual regression lines had similar slopes (mean: 2.82 ± 0.11 µm half-sarcomere-1 s-1), indicating that Vu was similar for all conditions (Fig. 4A). Based on this neither the increased +dF/dtR nor the decreased slack time could be attributed to an increased cross-bridge cycling rate during unloaded shortening. Compared to a ramp at 1.00 Vu, increasing isotonic force did however cause a progressive leftward shift in the step size-slack time relation, increasing Yo independent of change in Vu.
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Figure 3. Effect of length step size on force redevelopment of an intact frog fibre Original length (a) and force (b) records from representative ramped slack test experiment in which an isotonic ramp was followed by different length steps. In each panel, the length and force records from four separate releases incorporating the same ramp but different length steps are shown. The ramp speeds used for this fibre are indicated in each panel. Ramp amplitude was 0.35 while the length step sizes used in conjunction with each ramp were 0.05, 0.11, 0.16 and 0.21 µm sarcomere-1, respectively. Final sarcomere length after each respective release was thus 2.15, 2.09, 2.04 and 1.99 µm (top to bottom length traces in each panel). Force redevelopment at these different sarcomere lengths and the corresponding slack times are labelled 1, 2, 3 and 4, respectively, in each panel. Double-headed arrow in panel A marks the ramp to step transition (at 2.20 µm sarcomere-1) from which slack time was measured. Isotonic forces corresponding to ramps depicted in panels A-E were 0, 0.02, 0.23, 0.42 and 0.76 Fo, respectively. Only the final 100 ms of the 0.11 Vu ramp is depicted. Vertical bar at top right in panel A calibrates the largest release amplitude (i.e. 2.55 to 1.99 µm sarcomere-1. Same fibre as Fig. 1. | ||
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Figure 4. Effect of isotonic force on Vu and Yo A, plot of step size vs. slack time when 4 length steps of increasing amplitude were imposed at the end of each of 5 different ramps (open circles, 0.10; filled circles, 0.25; open squares, 0.45; filled squares, 0.75; triangles, 1.00 Vu). Individual regression lines had similar slopes (Vu, range: 2.80 ± 0.10-2.86 ± 0.10 µm sarcomere-1 s-1) but different intercepts with the step size axis (Yo). Vu and Yo determined using a standard slack test were 2.92 ± 0.13 µm sarcomere-1 s-1 and 0.018 ± 0.002 µm sarcomere-1 (arrow), respectively. B, biphasic decrease in total system compliance with decreasing isotonic force. Ramp speed corresponding to each force level is indicated. Linear regression was performed on data representing high (1.00 and 0.75 Vu) and low (0.45-0 Vu) ramp speeds. Data points in A and B are means ± S.E.M. (n = 8). | ||
Another purpose of the experiments illustrated in Fig. 3 was to test the effect that increasing the amplitude of the final step-change in length had on the relation between +dF/dtR and isotonic force (Fig. 2B). Although in these experiments the final sarcomere length varied depending upon length step size isometric force always redeveloped on the plateau of the length-tension relation for frog skeletal muscle fibres (Gordon et al. 1966). This eliminated the possibility that variations in +dF/dtR observed after different ramp speed and length step combinations were due to differences in sarcomere length. Data plotted in Fig. 5A show the effect of increasing step size on the relationship between +dF/dtR and isotonic force during the preceding ramp. As step size increased, the slope of this relationship decreased, indicating less dependence of +dF/dtR on preceding force. When plotted as a function of the slack time associated with the different length steps, there was a tendency for the extinction rate of +dF/dtR (Fig. 5B) to decrease as preceding isotonic force was decreased. For example, the half-time for the decay of +dF/dtR shown in Fig. 5B was increased from 9.2 ± 1.2 to 18.5 ± 1.6 ms as isotonic force decreased from 0.39 ± 0.03 to 0.01 ± 0.01 Fo. Thus, the +dF/dtR measured after a ramp- and step-change in length is a complex function of both the preceding isotonic force and the amount of unloaded shortening beforehand.
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Figure 5. Effect of length step-size on +dF/dtR A, effect of step size on the +dF/dtR-isotonic force relation when +dF/dtR is normalized to the largest length step size applied after each ramp. Each data set fit by linear regression corresponds to a different step size (in micrometres per sarcomere) (filled circles, 0.05; open circles, 0.11; filled squares, 0.16-0.21). Data for 0.16 and 0.21 µm sarcomere-1 steps were similar and pooled for clarity. B, relation between slack time and +dF/dtR (normalized to longest step). Each data set is fitted by a double exponential and corresponds to a different speed of applied ramp (filled circles, 0.25; open circles, 0.45; filled squares, 0.75-1.00 Vu). Data for 0.75 and 1.00 Vu ramps were similar and pooled for clarity. Data points in A and B are means ± S.E.M. (n = 7-8). | ||
Control experiments
Because all ramps were of a similar amplitude, ramp duration increased with decreasing ramp speed. Thus the redevelopment of isometric force occurred at different times during tetanic stimulation depending upon ramp speed (range: 600-740 ms for 1.00 and 0.30 Vu, respectively). This raised the possibility that +dF/dtR was influenced by differences in stimulation time, and not ramp speed, per se. To control for this difference we performed experiments, illustrated in Fig. 6, in which the start time of the 1.00 Vu release was delayed to ensure that it ended at the same time as a 0.30 Vu ramp. The +dF/dtR was increased by 70 ± 7 % (P < 0.05, n = 7) after a 0.30 vs. a 1.00 Vu release, an increase equal to 95 % of the increase in +dF/dtR measured from the same subset of fibres when releases were not offset. Thus stimulus number had little effect and the main influence on +dF/dtR was the preceding isotonic force.
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Figure 6. Effect of release speed on isometric force redevelopment of a frog muscle fibre when releases are offset to finish at the same time during a tetanus Length (A), force (B) and differentiated force (C) records from a representative control experiment in which the start of a 1.00 Vu ramp (thin line) was delayed by ~160 ms in order to ensure that this ramp ended at the same time during tetanic stimulation as a 0.30 Vu ramp (thick line). Ramp and step amplitudes were similar (0.35 and 0.10 µm sarcomere-1, respectively). Initial and final mean sarcomere lengths indicated; horizontal arrow marks the ramp to step transition (at 2.20 µm sarcomere-1). Compared to 1.00 Vu, +dF/dtR was increased by 67 % after the 0.30 Vu release (87 % of the increase when releases were not offset). Note that the differentiated records in C are not aligned with the records of A and B. Differentiated records are truncated to start at the conclusion of the ramp and thus show the delay in force redevelopment after the fast compared to the slow release. Each length and force record is the average of two separate sweeps. Same fibre shown in Figs 1 and 3. | ||
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DISCUSSION |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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The working hypothesis for these experiments was that thin filament activation of an intact frog muscle fibre is modulated by the number of cross-bridges bound to actin (as reflected by isotonic force) during shortening. In support of this hypothesis, we found that +dF/dtR was inversely related to fibre shortening speed and directly related to the preceding isotonic force during ramp shortening. The isotonic force dependence of +dF/dtR could not be attributed to an increased rate of cross-bridge cycling, as fibre Vu was unaffected by isotonic force. This force-velocity history or memory effect of isotonic force on +dF/dtR reveals a novel aspect of shortening-induced deactivation consistent with proposed cooperative effects of attached cross-bridges on thin filament activation (Gordon et al. 2000).
Rate of isometric force redevelopment
Because fibres redeveloped isometric force at the same sarcomere length after each release, the isotonic force dependent variations in +dF/dtR were independent of differences in either final sarcomere length or peak redeveloped force after shortening. Also, because fibres were stimulated throughout each contraction, intracellular Ca2+ concentration ([Ca2+]i) was likely to be maintained at saturating levels throughout shortening and force redevelopment. Consequently, the increased +dF/dtR we observed with increasing isotonic force was independent of the availability of Ca2+ binding to TnC. Because variations in +dF/dtR may reflect differences in thin filament activation, our results indicate that, by decreasing ramp speed and increasing isotonic force, thin filament activation was increased independently of [Ca2+]i (Bremel & Weber, 1972; Colomo et al. 1986; Millar & Homsher, 1991; Swartz & Moss, 1992).
One explanation for the strong correlation between isotonic force and +dF/dtR shown in Fig. 2B is that thin filament activation is modulated by the number of actin bound cross-bridges during ramp shortening. A memory effect of attached cross-bridges on +dF/dtR is however only possible if the decay in this cooperative state lags cross-bridge detachment. Solution studies using fluorescence probes bound to troponin I have shown that this may indeed be the case. For example, Ishii & Lehrer (1993) showed that the half-time of decay of thin filament activation induced by detachment of myosin S-1 from regulated thin filaments in solution (25 °C) is in the order of tens of milliseconds. The length steps we used to zero force prior to redevelopment produced slack times in the order of ~10 ms, a value close to the lower limit for the time-dependent decay of thin filament activation suggested by Ishii & Lehrer (1993). Thus, it follows that the variations in +dF/dtR we observed may have been due to the resulting differences in the cooperative state of thin filament activation resulting from different ramp speeds. The decrease in the slope of the individual +dF/dtR- isotonic force regression lines shown in Fig. 5A is explained by a proportionality between unloaded shortening distance and thin filament deactivation after each ramp, as would be expected if there was a time-dependent decay in this cooperative state. The changing relation between +dF/dtR and slack time associated with different isotonic ramps (Fig. 5B) supports this idea and also shows that the rate of this decay was proportional to the preceding isotonic force. Indeed, when the temperature differences between the two studies are considered, the range of values for the time-dependent extinction of +dF/dtR we found accord with the values for the half-time of thin filament deactivation provided by Ishii & Lehrer (1993).
The secondary peak observed in differentiated records after the fastest ramps was likely to be due to the positive feedback effect of newly attached cross-bridges on thin filament activation. This secondary peak might be expected to be absent when force redevelops after slow releases because in this case more cross-bridges are attached during shortening and because of the positive effect that these cross-bridges exert on thin filament activation as compared to fast releases.
Molecular mechanism
The isotonic force dependence of +dF/dtR and independence of Vu is consistent with an effect of attached cross-bridges on thin filament activation that increased the probability for cross-bridge re-attachment after shortening without altering cross-bridge detachment rate. However, our results shed no light upon the molecular mechanism(s) responsible for this effect. One possibility is that of an increased Ca2+ activation of the thin filament mediated through an allosteric effect of attached cross-bridges on the Ca2+ affinity, and thus the Ca2+ occupancy, of TnC. Support for cross-bridge mediated influences on the Ca2+ affinity of TnC that may modulate thin filament activation come from both skinned (Guth & Potter, 1987; Zot & Potter, 1989; Cantino et al. 1993; Swartz et al. 1996) and intact frog muscle fibres (Vandenboom et al. 1998). Consistent with this, the kTR of skinned skeletal fibres is Ca2+ sensitive (Brenner, 1988; Metzger & Moss, 1990; Hannon et al.1993; Chase et al. 1994; Regnier et al. 1996, 1998). The lack of effect of this mechanism on Vu is consistent with studies showing that the shortening speed of intact mouse and frog muscle fibres is insensitive to experimental interventions aimed at reducing [Ca2+] (and presumably the Ca2+ occupancy of TnC) (Edman, 1979; Westerblad et al. 1998).
McKillop & Geeves (1993) have presented a three-state model for thin filament activation in which Ca2+ binding to TnC shifts tropomyosin from a 'blocked' to a 'closed' state, a transition that allows only weak cross-bridge binding to actin. The presence of weakly bound cross-bridges more fully activates the thin filament by shifting tropomyosin into an 'open' state, a configuration that permits strong cross-bridge binding and force development (McKillop & Geeves, 1993). Within this framework, an alternative explanation for the history effect of isotonic force on +dF/dtR is that the decay rate of the 'open' to the 'blocked' or 'closed' tropomyosin state(s) is influenced by the number of strongly-bound, force-generating cross-bridges that were present prior to detachment (Gordon et al. 2000).
Relation to previous studies
A controversy regarding the molecular mechanism for the regulation of isometric force redevelopment centres upon whether it is governed by Ca2+ control over cross-bridge access to the thin filament (recruitment) or by Ca2+ control over cross-bridge cycling rate (kinetics). Based largely on data showing no effect of isotonic force, Brenner and co-workers have suggested that the Ca2+ dependence of kTR is mediated by direct control of Ca2+ over cross-bridge cycling rate and not thin filament activation (Brenner, 1988; Brenner & Chalovich, 1999). In contrast, kTR at submaximal Ca2+ activation is increased by calmidazolium and by dATP, two compounds believed to increase thin filament activation (Regnier et al. 1996, 1998). Also, calmidazolium did not increase kTR at maximal Ca2+ activation although dATP did increase maximal kTR slightly, suggesting that although maximal Ca2+ activated kTR is determined by both cross-bridge cycling rate and thin filament activation, submaximal Ca2+ activated kTR is influenced mainly by activation of the thin filament. The present results are thus in agreement with the findings of Regnier et al. (1996, 1998) in that they suggest that the thin filament was less than maximally activated during shortening and that the extent of thin filament activation affects +dF/dtR. However, in the present study, the extent of thin filament activation was modulated by controlling shortening speed, and thus the number of attached cross-bridges, rather than by [Ca2+]. Also, our data extend previous results by identifying a memory effect of attached cross-bridges on thin filament activation.
The linear dependence of +dF/dtR on preceding isotonic force contrasts with the curvelinear kTR:force relationship presented found for permeabilized rabbit psoas fibres. In these studies, the kTR:force relationship is linear at low (< 0.50 Fo) forces but curves upward at higher forces (> 0.50 Fo) (Regnier et al. 1996, 1998; Morris et al. 2001). This discrepancy may be due to the relatively low levels of isotonic force tested; higher forces may have changed the +dF/dtR-isotonic force relationship.
Slack time
The finding that slack time decreased as isotonic force increased is consistent with studies showing that shortening speed of skinned rabbit psoas muscle fibres is modulated by isotonic force (Iwamoto, 1998). It is also consistent with the finding that the strong binding analogue N-ethyl-maleimide myosin subfragment-1 (NEM-S1) increases the low-velocity phase of unloaded shortening at submaximal Ca2+activation, although in this study the high-velocity phase was unaffected (Swartz & Moss, 2001). However, in our study, the relationship between slack time and step size after different ramp speeds had similar slopes, indicating that steady-state cross-bridge cycling rate during unloaded shortening was not influenced by isotonic force. However, it is also possible that we failed to detect such a change because of an inability of the slack test to detect short-lived modulations of Vu (Martyn et al. 1994).
The most likely mechanism for the decreased slack time we observed with increasing isotonic force is an increased recoil of the SEC. For example, the increase in Yo shown in Fig. 4B suggests an isotonic force dependent increase in the length of the SEC, a change that would increase the series elastic recoil, and thus the speed of fibre shortening, independent of cross-bridge cycling rate. This effect of increasing isotonic force may have lead to a more rapid shortening of the series elastic component at the transition from ramp- to step-shortening, thus increasing the rate of fibre shortening not attributable to cross-bridge cycling. In the intact frog fibre at low temperatures, the speed of shortening attributed to passive tension is several times greater than Vu (Claflin et al. 1989), thus explaining why the slack times measured after slow ramps were shorter than could be accounted for on the basis of fibre Vu alone (Fig. 1C). However, since a period of zero force preceded force redevelopment, it seems unlikely that differences in recoil of the SEC directly affected +dF/dtR.
Control experiments
We demonstrated that neither total stimulus number nor ramp duration affected the basic relationship between isotonic force and +dF/dtR. Thus, it appears unlikely that this relationship was due to any mechanism involving an accumulation of metabolic byproducts of ATP hydrolysis. Yet this possibility cannot be totally excluded. For example, it has been shown that an increased concentration of inorganic phosphate [Pi] increases kTR in skinned muscle fibres (Regnier et al. 1995). With increasing stimulus duration, an elevation in [Pi] may have occurred. If so +dF/dtR should have increased with increasing stimulation duration, independent of ramp speed, something that was not observed. It has also been shown that an increase in ADP, another ATPase byproduct, reduces the Vu of both skinned (Cooke & Pate, 1985) and intact muscle fibres (Westerblad et al. 1998). If increasing stimulus duration was accompanied by an increase in ADP concentration, a reduction in Vu should have occurred, again, something that was not observed. Finally, if mediated by an increased Pi, the +dF/dtR-shortening speed relation should perhaps mirror the relation between ATPase rate and shortening speed, which peaks at approximately 0.30 Vu. However, in our experiments +dF/dtR continued to increase when fibre shortening speed was reduced as low as 0.10 Vu (data not shown). Thus, it appears unlikely that an accumulation of ATPase byproducts accounted for the increased +dF/dtR.
Limitations
Because we made no attempt to monitor or control sarcomere length, the possibility should be considered that there were differences in the amount of internal shortening that occurred with different release speeds (Brenner & Eisenberg, 1986). However, the step-change in length we imposed after each isotonic ramp should have unstressed the SEC to similar degrees after each different ramp, thus making +dF/dtR independent of differences in the amount of internal shortening that may have occurred. Also, when unloaded, the shortening of sarcomeres along the length of an intact frog fibre is uniform; however, when loaded, sarcomere shortening is non-uniform (Julian & Morgan, 1979). In intact frog fibres, non-uniform sarcomere shortening has been demonstrated to reduce the peak of redeveloped tension at shortening speeds < 0.30 Vu (Edman et al. 1993). However, peak redeveloped isometric force was similar after each release, indicating that non-uniform sarcomere shortening was not a problem at the shortening speeds examined in the present study.
Ramp shortening at moderate to high speeds expands the radial spacing between myofilaments while isometric tension regeneration after shortening recompresses it (Cecchi et al. 1990; Ashley et al. 1999). Thus, it must be considered that variations in the rate of isometric force redevelopment at the same sarcomere length could be due to shortening-speed dependent variations in myofilament lattice spacing. Under such a situation, force redevelopment after slower ramp shortening would occur at a myofilament lattice spacing closer to an optimal for isometric force redevelopment, whereas ramp shortening at 1.00 Vu would cause myofilament lattice spacing to depart from optimal. This possibility cannot be excluded by the present results.
Summary
The rate of isometric force redevelopment after ramp- and step-shortening is proportional to isotonic force in the intact frog muscle fibre. This force-velocity history effect demonstrates a novel aspect of shortening-induced deactivation and suggests that attached cross-bridges modulate thin filament activation. Because Vu was not altered, the isotonic force dependence of +dF/dtR is explained by a cross-bridge mediated activation of the thin filament that influences cross-bridge attachment rate independent of change to cross-bridge detachment rate.
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Acknowledgements
This work was supported by National Institute of Health Grants HL 37680 and HL 34817 to G. C. Sieck and the Mayo Foundation. We would also like to thank Dr D. R. Claflin, Dr D. L. Morgan and Dr S. R. Taylor for helpful discussions regarding these experiments.
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