Effects of ramp shortening during linear phase of relaxation on [Ca2+]i in intact skeletal muscle fibers

Yandong Jiang and Fred J. Julian

Department of Anesthesia Research Laboratories, Brigham and Women's Hospital, Boston, Massachusetts 02115

    ABSTRACT
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Abstract
Introduction
Methods
Results
Discussion
References

The effects of shortening distance at Vu, the unloaded shortening speed, and filament overlap on the amount of extra Ca2+ released during relaxation in muscle, as indicated by the bump area, were studied. Single, intact frog skeletal muscle fibers at 3°C were used. The myoplasmic free Ca2+ concentration ([Ca2+]i) was estimated by using fura 2 salt injected into the myoplasm. Ramps were applied, either at full overlap with different sizes or at varying overlaps with a fixed size, in the linear phase of relaxation. At full overlap, a plot of bump area vs. ramp size was fit by using a sigmoidal curve with one-half of the bump area equal to 25.9 nm. With a fixed ramp size of 100 nm/half-sarcomere, the plot of bump area vs. mean sarcomere length (SLm) was fit by a straight line intersecting the SLm axis at ~3.5 µm, close to just no overlap. The results suggest that the transition in the distribution of attached cross bridges from the isometric case to one appropriate for unloaded shortening at Vu is completed within 50 nm/half-sarcomere and support the view that attached cross bridges in the overlap zone influence the affinity of Ca2+ for troponin C in the thin filament.

cross bridges; calcium; cooperative interactions; regulation of contraction; fura 2; frog

    INTRODUCTION
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Abstract
Introduction
Methods
Results
Discussion
References

IN SKELETAL MUSCLE, the relaxation phase of contraction, particularly after a tetanus, shows two distinct phases (10, 16). First, there is a slow, nearly linear phase of force decline ending with a so-called shoulder, and this is followed by a rapid, quasi-exponential decline of force to baseline. The shoulder coincides with the onset of small amounts of sarcomere shortening throughout most of the muscle fiber, with similar amounts of lengthening at the ends, so that overall the muscle length is constant (8, 16). Later, it was shown that the shoulder coincides with the onset of a small reduction in the rate of decline of the aequorin luminescence signal, suggesting a reduction in the rate of decline of myoplasmic free Ca2+ concentration ([Ca2+]i) (5). These findings are commonly explained by assuming that the onset of the quasi-exponential phase of relaxation indicates an acceleration of cross-bridge detachment and turnover (16) and that this leads to a reduction in the binding constant of troponin C (TnC) for Ca2+ (25). Thus the affinity of Ca2+ for TnC decreases rapidly, causing the rate of release of Ca2+ to increase, leading to a decrease in the rate of decline of [Ca2+]i, which is in accordance with previous discussions (1, 12, 13, 21).

Further studies using a fluorescent dye to measure [Ca2+]i showed very prominent "natural" bumps after the onset of the shoulder during relaxation in single frog muscle fibers (6). Length-shortening ramps were also applied during the linear phase of relaxation in frog fibers to show that the release of Ca2+ is accelerated during these "artificial" bumps (6).

Recently, we have published extensive results from studies of intact cardiac muscle using the same kind of methodology to create artificial bumps during relaxation by applying appropriate shortening ramps (18). These results indicate that both naturally occurring and artificially induced bumps exist in both cardiac and skeletal muscle. Here, we extend this approach to the study of single frog skeletal muscle fibers, for which it is much easier to control and change sarcomere length. We quantitatively examine how the bump area varies with ramp size at full overlap and how the bump area varies with reduced overlap at fixed ramp size. Our results can be explained by cross-bridge transitions from isometric to unloaded shortening at Vu, greatly diminishing the Ca2+ affinity for TnC in the thin filament, and by the overlap zone most strongly influencing this affinity.

    METHODS
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Abstract
Introduction
Methods
Results
Discussion
References

A great deal of the basic methodology used in these experiments has already been well described in several recent publications from this laboratory (7, 18, 23), and these papers should be consulted for details of the procedures used here. Basically, single, intact muscle fibers were obtained from the tibialis anterior muscles of the frog Rana temporaria. The salt form of the fluorescent dye fura 2 was microinjected by iontophoresis into the myoplasm to estimate [Ca2+]i. All experiments were carried out at 3 ± 0.1°C. The mean sarcomere length (SLm) was determined from photographs of a passive fiber taken at different positions along the fiber. No attempt was made to use a feedback control device to maintain SLm constant during a contraction. However, fibers were not stretched beyond an SLm of 3.0 µm to minimize variations in sarcomere length along a fiber during contraction.

We have not been able to calibrate completely the response of the intracellular fura 2 ratio (R) signal to [Ca2+]; this inability is in contrast to our results with intact cardiac muscle (18). The main problem encountered in skeletal muscle fibers is the inability to control [Ca2+]i over a wide range of values, thus allowing a curve fit to determine Kdbeta . However, we have been able to obtain reliable estimates for Rmax and Rmin, thus allowing our results to be expressed in the dimensionless form [Ca2+]i/Kdbeta . In this case, although the absolute [Ca2+]i remains unknown, Kdbeta merely plays the role of a scale factor and the major nonlinearity in the fura 2 R signal is removed by using the relation [Ca2+]i/Kdbeta  = (R - Rmin)/(Rmax - R). R is obtained by dividing the fluorescent light (510 nm) produced by excitation at 344 nm (F344) by that produced by excitation at 380 nm (F380). Before forming R, the background and autofluorescence were first subtracted, as is necessary, but this is a minor correction for skeletal muscle compared with the correction for cardiac muscle (18).

The following comment concerns our use of the terms artificial and natural to describe the bumps observed during relaxation in muscle. A natural bump is one observed in an ordinary fixed-length relaxation after a tetanic contraction without any imposed length change. In contrast, an artificial bump is one caused by applying an external length change (always in the shortening direction in this work) at a point in time preceding the occurrence of the natural bump. In this work, the applied length decrease was always a ramp of slope Vu, the unloaded shortening speed of a muscle fiber, 3 µm · HS-1 · s-1, where HS is half-sarcomere, at 3°C. The ramps were applied during the linear phase of relaxation after a tetanus with duration of 0.5 s, so that they followed the cessation of stimulation and were close to but preceding the "shoulder" signaling onset of internal sarcomeric motion. At full overlap, the ramp sizes chosen were 12.5, 25, 50, 75, 100, and 125 nm/HS. These required 5, 9, 17, 25, 33, and 41 ms, respectively, between the beginning and end of the ramp. SLm was varied by stretching passive fibers from 2.2 to 3.0 µm in increments of 0.2 µm/HS. In all cases of varying SLm, a fixed ramp size of 100 nm/HS was used.

To calculate the bump area, the R signal was first transformed into [Ca2+]/Kdbeta . Then, by fitting the segments in the decay phase of [Ca2+]/Kdbeta flanking but not including the bump, a smooth, continuous curve with values at all time points equivalent to the original signal with the bump was obtained. This was done by using SigmaPlot (SPSS); a single, modified three-parameter exponential-decay transform was used to obtain values for the parameters a, b, and c for use in the equation y = a · exp[b/(x + c)]. (An example of such an operation is shown in Fig. 2D, which shows both the original fluorescence trace and the "curve fit without bump.") A difference curve was obtained by subtraction of the curve fit without bump from the curve fit with bump. [Examples of this are shown in Fig. 3, A and C, where it should be noted that difference curves always begin (and end) with the amplitude equal to 0.0.] The area under the difference curve, equal to the bump area, was obtained by using the area under the transform from SigmaPlot. This procedure is very similar to the one that we have described elsewhere (18). This method was accurate to analyze the natural bump and the ramp-induced bump as long as the ramp size was equal to or larger than 50 nm/HS. However, when smaller ramp sizes (12.5 or 25 nm/HS) were applied, the resulting total bumps were complex and included contributions from natural and artificial processes. This made it necessary to analyze the bumps in another way, namely, by using PeakFit software (SPSS) designed for peak separation and analysis. The total area under the difference curve of the complex bump could be obtained in SigmaPlot, but the separate areas under each peak could not. To do this, the complex difference signal was exported to PeakFit, where a curve was fit to the complex bump with the constraint that only two peaks were present. In PeakFit, it was possible to obtain the areas under the two separate peaks. The sum of these two areas was calculated and compared to the total area under the two peaks obtained by SigmaPlot, and these two areas never differed by more than ±1%. In contrast, all ramps of other sizes and the isometric case produced bumps that were obviously composed of a single peak.

    RESULTS
Top
Abstract
Introduction
Methods
Results
Discussion
References

The most basic assumption here is that the bump area observed during the decaying phase of the [Ca2+]i obtained by using fura 2 during relaxation is linearly related to the amount of Ca2+ suddenly liberated into the myoplasm. A problem arises because strictly speaking the bump area has the units of micromolar × seconds, or, as in this case, is obtained by multiplying [Ca2+]i/Kdbeta by the time in seconds; in either case the units are not the same as those of the amount of Ca2+. To clarify whether bump area is proportional to the extra amount of [Ca2+]i released during relaxation, simple modeling was done by using the program Stella (High Performance Systems, Hanover, NH), which allows construction of a model by drawing a block diagram consisting of stocks and flows. This model is similar to one recently described (20), which was, in turn, modified from one already presented (26). Briefly, a central compartment simulating the myoplasm was established. Initially, the compartment contained a known amount of Ca2+. The compartment was drained by a "pump" similar to that previously described (20), and Ca2+ could be added in brief pulses via a separate "input" channel. These model results, not shown, indicate that a nearly linear relationship between bump area and the amount of Ca2+ pulsed into the myoplasm exists, and this supports the idea that the bump area can be used as a valid index of the amount of Ca2+.

A major concern in all experiments involving the use of a fluorescent dye to report [Ca2+]i, particularly in contracting muscle fibers, is the occurrence of so-called "motion artifacts." In this case, these are changes in fluorescence intensity caused by translation or rotation of a fiber or by movement of a fiber relative to the focal plane of the microscope. These kinds of artifacts can be greatly minimized by using the dual-wavelength dye fura 2 in the ratiometric mode (11). Experimental verification that motion artifacts do not play an important role in these experiments is shown in Fig. 1. Here, the passive (Fig. 1A) and active (Fig. 1B) responses of a single fiber stretched to an SLm of 2.8 µm to 100 nm/HS shortening ramps are shown. In Fig. 1A, the shortening ramp clearly causes upward deflections in both F344 and F380, most likely produced by movement into the field of more fiber, thus increasing the level of fluorescence. Note, however, that the R signal contains nearly perfect cancellation, since no sign of the deflections observed below in F344 and F380 at the time of the ramp was present. This is in contrast to the situation observed in Fig. 1B. Here, after electrical stimulation, large changes are seen in opposite directions, in both F344 and F380, as a consequence of the rise in [Ca2+]i. When stimulation was stopped and a ramp was applied during the linear phase of relaxation, a prominent artificial bump in the R signal, which is clearly associated with opposite-going deflections in F344 and F380, was observed. These opposite-going deflections in F344 and F380 indicate a true rise in [Ca2+]i caused by the ramp; it is most unlikely that they are caused by artifacts. The results in Fig. 1 strongly indicate that motion artifacts are canceled in the R signal, and true changes in [Ca2+]i are preserved.


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Fig. 1.   Effects of ramp releases on F344, F380, and the R signal in a passive and active fiber. A: a passive fiber was stretched to mean sarcomere length (SLm) of 2.8 µm. A ramp of 100 nm/half-sarcomere (HS) amplitude with slope equal to unloaded shortening speed (Vu) was then applied to reduce SLm to 2.6 µm. At time of the ramp, both F344 and F380 showed in-phase increases in fluorescence intensity (double-headed arrow), but there was no corresponding change in the R signal, a typical example of ratiometric cancellation in the R signal of motion artifact-induced changes in F344 and F380. B: Same fiber under same conditions as in A except that the ramp was applied while the fiber was active. The R signal, in top trace of B, shows a stimulus-locked oscillation followed by a distinct artificial bump (arrow) in response to the applied shortening ramp. However, for the F344 and F380 signals (bottom traces) there are now distinct out-of-phase components (double-headed arrow) in the opposite direction, in contrast to the results shown in A. This result strongly indicates that motion artifact-caused variations in F344 and F380 are well canceled by ratioing, while true changes induced by changes in [Ca2+]i are preserved. In A and B, the units of the ordinate axes are arbitrary, and the ramp has been compressed and shifted to follow well-separated paths. The levels of the R, F344, and F380 signals were chosen for clarity. In B, the R signal was compressed by a factor of 4, F344 and F380 were compressed by a factor of 2, and the ordinate scale was expanded by a factor of 2 to allow presentation of all traces conveniently.

The results from one of four experiments are shown in Fig. 2 to illustrate the way in which results were obtained at full overlap, SLm = 2.2 µm, in response to variously sized ramps. In Fig. 2A, the ramps are shown as a function of time. The topmost trace is for the isometric case; also shown are 12.5-, 25-, 50-, 75-, 100-, and 125-nm ramps. In Fig. 2B, the associated force responses are shown. Note that in the topmost isometric case it is apparent that the ramps are being applied late in the linear phase of relaxation, but their onset clearly precedes the shoulder in force, which can just be identified near the right edge. Note also that the 12.5- and 25-nm ramps do not drop the force to zero but that the 50-, 75-, 100-, and 125-nm ramps do, a finding which has important consequences in this work. In Fig. 2C, the [Ca2+]i/Kdbeta signals are shown on the same time base as those in Fig. 2, A and B. For the isometric case, the lowest [Ca2+]i/Kdbeta signal in Fig. 2C, the beginning of the natural response can just be observed at the right edge. The artificial responses clearly begin sooner, and those due to the 12.5-, and 25-nm ramps, the next two above the isometric response, obviously show signs of a complex response involving both artificial and natural components. The bumps produced by the next four larger-sized ramps, the 50-, 75-, 100-, and 125-nm ramps, are more nearly similar to single-peak responses. Thus the natural response is suppressed by applied ramps of large size. Finally, in Fig. 2D, only the [Ca2+]i/Kdbeta signal in response to the 100-nm ramp is shown. Also shown is the smooth curve fit obtained by using the SigmaPlot single, modified three-parameter exponential-decay transform, but omitting the points contained within the bump. The bump area is equal to the area under the difference curve obtained from the bump-containing and fitted smooth curves.


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Fig. 2.   Typical responses of force and myoplasmic free Ca2+ concentration ([Ca2+]i) to length ramps of various sizes at fixed full overlap (SLm = 2.2 µm). A: time course and extent of each applied ramp with constant slope of Vu. The curve labeled 0 indicates the isometric case with no ramp, and the other labels give ramp sizes in nm/HS. B: accompanying force responses. Again, the curve labeled 0 indicates the isometric case. Amount of force regenerated at termination of the ramp was variable, with a maximum at 12.5 nm and very little at 125 nm. C: composite of the artificial bump responses, with the largest bump corresponding to the ramp of 125 nm, as indicated. The isometric case is indicated by the curve labeled 0, and the beginning of the natural bump in this case is just detectable at the right edge of the panel. D: only the [Ca2+]i/Kdbeta signal in response to the 100-nm ramp is shown. Also shown is smooth curve fit with the SigmaPlot single, modified 3-parameter exponential decay transform, but with points contained within bump omitted. The curve was obtained by using an equation of the form y = a · exp[b/(x + c)], where a = 0.0513, b = 0.4446, and c = -0.4542. The difference between the raw curve and the fitted curve is used to compute the bump area.

The results shown in Fig. 3 are concerned with an issue raised in METHODS, where it was mentioned that natural bumps and most bumps caused by artificial ramps could be fit by using a single peak. However, this was not the case for the 12.5- and 25-nm ramps. An example of a difference curve for the total bump caused by a 12.5-nm ramp is shown in Fig. 3A. The total bump is obviously not a single peak. The most likely explanation is that the initial part of the bump is caused by the applied ramp, whereas the following part is a "contamination" due to a contribution from the natural bump. It was necessary to separate these contributions in a rigorous way. This was done by exporting the difference curve obtained in SigmaPlot (noisy curve in Fig. 3A) to PeakFit, where a smooth curve was fit to the raw difference curve (thin, smooth line in Fig. 3A), with the constraint that only two peaks be present. The resulting two peaks produced by PeakFit are shown in Fig. 3B. In all of the four different fibers for which the 12.5-nm ramp was used, a similar situation was encountered, i.e., a pair of peaks with the first being smaller than the second. As a useful control, the total area under the raw difference curve shown in Fig. 3A was computed with SigmaPlot. Then, the sum of the areas under the two peaks generated by PeakFit was also computed. The total areas generated by these two methods always agreed to within ±1%, thus substantiating the idea that the decomposition into two peaks made by PeakFit was valid. In all cases, the total bump response to the 25-nm ramp (not shown) also consisted of a complex response not easily associated with a single peak. Here, the two peaks produced by PeakFit were more nearly equal in area, suggesting approximately equal contributions from natural and artificial processes.


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Fig. 3.   Analytical procedure for calculating bump area for single- and double-peaked bumps. A: difference curve (noisy trace) for a 12.5 nm/HS ramp-induced bump, as described in legend for Fig. 2, together with a curve fit by using PeakFit (smooth trace). B: decomposition by PeakFit of the total curve fit to the complex bump into 2 separate peaks. In PeakFit, it was possible to obtain the areas under the 2 separate peaks. The sum of these 2 areas was calculated and compared to the total area under the 2 peaks obtained by SigmaPlot; these 2 areas never differed by more than ±1%. In contrast, all other ramps, with sizes of 50, 100, and 125 nm, and the isometric case produced bumps that were obviously composed of a single peak. An example of this is shown (C) for a 100-nm ramp applied to a full-overlap fiber (SLm = 2.2 µm). The noisy trace in C is the original difference curve produced in SigmaPlot, whereas the thin, smooth trace is the curve fit by PeakFit. There is obviously a very strong congruence between the 2 curves. D: PeakFit-generated curve is shown alone to demonstrate that a very good fit could be obtained assuming that only 1 peak is present.

In contrast, all bumps caused by ramps of other sizes, as well as the natural bump occurring in the isometric case, could be well fit by using only a single peak. An example of this is given in Fig. 3C, which shows the difference curve (noisy trace) in response to an artificial 100-nm ramp with the curve fit by PeakFit superimposed (thin, smooth trace). In Fig. 3D, the PeakFit curve is shown alone to indicate the very close approximation obtained by using a single peak. The areas under the raw difference curve obtained by using SigmaPlot and under the smooth, single-peak curve fit by using PeakFit were nearly equal.

The average results obtained for bump area at full overlap as a function of various-sized ramps, including the isometric case, are presented in Fig. 4. Here, we plot the bump areas associated only with ramp-induced peaks and we define the ramp-induced bump area as zero for the isometric case. The area under the artificial peak was obtained by using PeakFit as previously described for the 12.5 and 25 nm/HS ramps. The data points are very well fit by a four-parameter sigmoidal curve from SigmaPlot with a half-area ramp size of 25.9 nm/HS. Note that the relative bump areas for the four largest-sized ramps, those of 50, 75, 100, and 125 nm, lie close to 1.0, and it is these ramps that cause the force to drop to zero as shown in Fig. 2. The average bump area for the four isometric cases is shown and indicates that the bump area naturally occurring without a ramp is about one-third of the maximal bump area obtained by using the largest ramp.


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Fig. 4.   Plot of the average results of the artificial bump area as a function of ramp size at full overlap (SLm = 2.2 µm). The way in which the artificial bump areas were obtained is shown in Fig. 2. The analysis for obtaining the areas is described in the legend for Fig. 3. Each point is the mean (±SE) for 4 experiments. The point for zero ramp size by definition also has zero bump area. The largest bump area induced by the 125 nm/HS ramp was normalized to 1.0, and the other bump areas were calculated with respect to this value. All points are very well fit by a 4-parameter sigmoidal curve from SigmaPlot of the form y = y0 + a/{1 + exp[-(x - x0)/b]} where a = 1.1482, b = 12.5225, x0 = 22.4712, and y0 = -0.1520. The vertical dashed line indicates the abscissa value, 25.9 nm/HS, for half-maximal bump area. Open circle with error bars indicates the mean relative bump area for the observed natural bump in the isometric controls. The value for the natural bump area relative to the artificial one produced by the 125-nm ramps is 0.34.

The foregoing sets the stage for an examination of the bump area produced by a ramp of 100 nm/HS as a function of filament overlap. This kind of experiment is fairly straightforward with skeletal muscle fibers, at least for limited ranges of decreased overlap, whereas for the cardiac muscle we used previously it is very difficult (18). The results for one of four fibers are shown in Fig. 5. In Fig. 5A, the length responses are shown, with the flat line corresponding to no ramp and the near-vertical line corresponding to the 100 nm/HS ramp used in all cases with decreasing filament overlap. Note that the bump area produced by the 100 nm/HS ramp in Fig. 4 is very near the maximal area observed at full overlap, so it is reasonable to believe that a 100 nm/HS ramp produces a bump area of maximal size, thus allowing the influence of overlap on bump area to be determined. Shown in Fig. 5B is a composite of the force responses, including the isometric, to a 100-nm ramp as SLm was increased from the control, 2.2 µm, to 2.4, 2.6, 2.8, and 3.0 µm. Finally, the SLm was returned to 2.2 µm to obtain a control response, but this is not shown as it is essentially unchanged. In Fig. 5C, the [Ca2+]i/Kdbeta signals appropriate for each of the responses presented in Fig. 5B are shown. In the isometric case, the lowest signal, the beginning of the natural response, can be seen at the right edge of the panel. The other signals are arranged on the basis of initial SLm values of 2.2, 2.4, 2.6, 2.8, and 3.0 µm, and it is obvious that the size of each of these signals is inversely proportional to filament overlap.


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Fig. 5.   Typical responses of force and [Ca2+]i at fixed ramp size to various overlaps. A: 2 length traces are shown, the isometric case (labeled 0) and the 100 nm/HS length ramp, since the length ramp was identical for all values of SLm. B: composite of the force responses. A total of 6 traces are shown. One, labeled 0, is for the isometric case. There are 5 additional traces, each showing the response to the 100 nm/HS ramp at SLm values of 2.2, 2.4, 2.6, 2.8, and 3.0 µm. Note that as the SLm was increased the steady force value preceding the ramp dropped as expected. Force regeneration at the end of the ramp was small, with the maximum at SLm = 2.2 µm. C: composite of the artificial bump responses generated by the applied ramps (5 traces with that for an SLm of 2.2 µm at top). Bottom trace (No ramp) applies to the isometric case, and it is apparent that there was no obvious bump during most of the time courses of the artificial bumps. However, at far right of bottom trace, the beginning of the natural response can be seen. The way in which the artificial bump areas were determined is described in legend for Fig. 3.

Finally, in Fig. 6, the average results from all four fibers are shown in a plot of normalized artificial bump area as a function of sarcomere length. The linear regression curve produced by SigmaPlot was constrained to pass through point pair (2.2, 1.0). The intersection of the straight line and the sarcomere length axis falls very close to an SLm of 3.5 µm, which is very near to just no overlap for fibers obtained from the tibialis anterior of R. temporaria (2). Thus these results strongly support the idea that the bump area produced by a large-amplitude ramp shortening applied during the linear phase of relaxation decreases linearly to approach zero as filament overlap and cross-bridge interaction vanish.


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Fig. 6.   Plot of bump areas, obtained at fixed ramp size, as a function of SLm. The analysis for obtaining the bump areas is described in the legends for Figs. 2 and 3. Each point is the mean (±SE) for 4 experiments. The SLm took on values of 2.2, 2.4, 2.6, 2.8, and 3.0 µm, and the fixed ramp size was 100 nm/HS for all SLm values. The bump area produced by the ramp at full overlap, 2.2 µm, was used to normalize all bump areas. The linear regression, performed by SigmaPlot, had the equation y = b(0) + b(1) · x, where b(0) = 1.0 (constrained to pass through origin) and b(1) = -0.778. Note the intersection of the line and the abscissa, near SLm = 3.5 µm, or near just no overlap for fibers from the tibialis anterior muscle of Rana temporaria. The value for the postcontrol full-overlap bump area (not shown) was very nearly the same as the precontrol value shown.

    DISCUSSION
Top
Abstract
Introduction
Methods
Results
Discussion
References

The major emphasis in this work is on the transient rise in [Ca2+]i, or bump, usually observed during relaxation after the cessation of stimulation; the bump follows the shoulder in the force record during ordinary fixed-end relaxation in normal skeletal muscle fibers, usually from the frog (6, 20). The bump is observed after stimulation ceases, so that the high [Ca2+]i associated with the activation of contraction declines rapidly toward baseline, thus making it much easier to detect small changes in [Ca2+]i by using a suitable intracellular reporter (fura 2 in these experiments). We have chosen here, and in our previous work with cardiac muscle (18), to use the bump area as an indicator of the amount of Ca2+ released during either a natural or artificial bump. As mentioned in RESULTS, the bump area does not have units of micromolar. However, the results from a simple model for the release and uptake processes for Ca2+ in the myoplasm, as discussed in RESULTS, lend support to the view that the bump area is a valid indicator of the amount of Ca2+ released into the myoplasm.

A potential problem in fluorescence work, particularly in contracting and shortening muscles, is the possibility that results could be seriously contaminated by motion artifacts. However, the results shown in Fig. 1 clearly do not indicate a contribution of any serious magnitude from such artifactual processes. Instead, the results shown in Fig. 1 indicate that artifactual motion-induced changes are very well canceled by forming the R signal, whereas the ability to respond to true changes in [Ca2+]i is well preserved. Thus there should be no serious concern about such possible contaminant influences. The contributions of changes in background and autofluorescence may be of concern because these contributions must first be subtracted from the raw fluorescence signals obtained by alternate excitation at 344 and 380 nm before the ratio, or R, signal can be formed. Fortunately, in this work, the contributions from both background and autofluorescence were small and constant. This is quite different from what is found for autofluorescence from cardiac muscle when fura 2 is used to determine [Ca2+]i (18).

The key question concerns the cause of this transient elevation in [Ca2+]i during relaxation, since it can be routinely and clearly observed, particularly in isolated frog skeletal fibers. For cardiac muscle, we have argued that this phenomenon is most likely the result of a reversal during relaxation of a strong cooperation between Ca2+ binding to TnC and cross-bridge attachment (18). This interpretation was not easy to accept in cardiac muscle, since in this case powerful Ca2+ transporters exist, in addition to the sarcoplasmic reticulum (SR); the actions of these transporters might conceiveably result in a transient change in [Ca2+]i during relaxation. In skeletal muscle, there seems to be little doubt that the transient rise in [Ca2+]i observed during relaxation and after the shoulder is best explained on the basis of reduced affinity of Ca2+ for TnC owing to a reduction in the number of attached cross bridges (6). The reduction in the number of attached cross bridges, after the shoulder, follows from arguments presented in the introduction to this study, indicating that the shoulder coincides with the onset of small amounts of sarcomere shortening and subsequent cross-bridge turnover throughout most of an isolated muscle fiber. The important assumption here is that the transient rise in [Ca2+]i does, indeed, reflect a change in the binding affinity of Ca2+ to TnC in the thin filamental, though this has never been directly proved, to the best of our knowledge. It then becomes a question of how best to exploit this change to shed new light on the workings of the contractile machinery in an intact fiber.

We believe we have found a way to do this by applying external rapid ramp shortenings to create artificial bumps before the occurrence of the natural ones, or in place of them (18). The property is studied during relaxation when [Ca2+]i is falling rapidly toward baseline levels, so the problem of detecting small changes in [Ca2+]i against a background of greatly elevated [Ca2+]i is avoided (23). The fraction of attached cross bridges does not decrease much during the slow, linear phase of isometric force relaxation while [Ca2+]i approaches low levels; thus, the nature of the bumps is more easily revealed. In our view, the usual pattern of behavior after the shoulder in skeletal muscle fibers is closely simulated by the applied ramps. In the normal, fixed-end case, the usual internal rearrangement of sarcomere lengths owing to nonuniform relaxation at the time of the shoulder leads to cross-bridge cycling and turnover, with a consequent decrease in the number of attached cross bridges, which, in turn, leads to a decrease in the affinity of Ca2+ for TnC, and this causes a natural bump. The slow, linear phase of relaxation would be the ideal time to impose an external length decrease to cause a result essentially similar to that described above for the natural case, that is, cross-bridge cycling and turnover with a consequent reduction in the number of attached cross bridges. This would then lead to the production of a repeatable artificial bump that would be closely time locked to the length change.

The way in which data were obtained under conditions of varying ramp size at full overlap is shown in Fig. 2. The complication caused by complex bumps produced by the 12.5 and 25 nm/HS ramps was treated as described in the legend for Fig. 3. It is noteworthy that the ramps with the four largest amplitudes associated with drop of force to near zero, and its maintenance there as a consequence of shortening at near Vu, are the ones that are mainly in the plateau region of the dose-response curve shown in Fig. 4. This suggests that the dominant process in producing the bump is the transition from a cross-bridge distribution appropriate for isometric contraction to a distribution appropriate for shortening at Vu, with a much-reduced number of attached cross bridges. At ramp sizes smaller than 50 nm/HS, the force did not drop to zero and the bump area was smaller than that induced by ramps of larger sizes. Because the fibers were shortening at the same speed regardless of the sizes of the ramps, it most likely is the size of the ramp that limits the amount of force fall, the fraction of cross bridges detached, and the size of the associated bump.

The single parameter used to characterize the plot was the abscissal value for ramp size coinciding with one-half the maximal bump area, 25.9 nm/HS, as shown in Fig. 4. This value is clearly less than the repeat distance along the thick filament for cross bridges attaching to the thin filament in the same plane, 42.9 nm/HS, although it is larger than the repeat distance for cross bridges in all planes, 14.3 nm/HS (3). It is now believed that ~50% of the sarcomere compliance resides in the thin filaments (17, 24), and there is no doubt that substantial series mounting compliance exists in our fibers, typically near 18 nm/HS, when used for determining Vu by the slack test when no attempt was made to hold SLm constant (23). However, the presence of additional compliance in our system would lead to our value of 25.9 nm/HS for one-half maximal bump area being revised downward, although it is not known for certain whether it would approach the cross-bridge repeat distance of 14.3 nm/HS. Thus our curve of bump area vs. ramp size in Fig. 4 shows that the attachment transition from the isometric to the isotonic case at Vu is completed when the fiber shortens by ~50 nm/HS without taking account of mounting or thin-filament compliance, so the fraction of attached cross bridges most likely decreases rapidly within this distance. This supports the view that the cross-bridge cycling distance is <25.9 nm/HS, rather than near 60 nm/HS (27) or 40 nm/HS (14).

The way in which data were obtained under conditions of varying overlap with a single large-amplitude ramp being used to obtain a maximal bump is shown in Fig. 5. The average data obtained from four experiments are plotted in Fig. 6. In order to evaluate the results properly, it must be kept in mind that the SLm at just no overlap in fibers obtained from the tibialis anterior muscle of R. temporaria, such as the ones used here, is very near 3.5 µm (2). Remarkably, the linear regression fit to the average data in Fig. 6 intersects the abscissa at very near an SLm of 3.5 µm. The implications of this finding are quite substantial. This clearly shows that in an intact muscle system the artificial bump area caused by a large, saturating ramp applied during the linear phase of relaxation could be extrapolated to a value near zero as the amount of overlap vanishes. In other words, when the size of a ramp of slope Vu is large enough to produce a bump area of maximal size, it is the amount of overlap that determines the size of the bump area. The amount of overlap is simply proportional to the number of attached cross bridges in an active fiber. Most likely, the large applied ramp induced a transition from a cross-bridge distribution appropriate for isometric contraction to one appropriate for shortening at Vu, as argued above. The stiffness at Vu is about one-third of the isometric value (9, 19), and this implies that even fractionally fewer cross bridges are attached if the new thin-filament compliance measurements are taken into account and it is assumed that all cross bridges are attached in rigor (15). Therefore, the influence of the ramp most likely caused a cross-bridge distribution change from an isometric one in the linear phase of relaxation to one appropriate for shortening at Vu with a much-reduced number of attached cross bridges. This, in turn, could cause a bump if it reduced very much the affinity of Ca2+ for TnC, as pointed out in the introduction to this study. The effect would be maximal at full overlap, or SLm = 2.2 µm, where the number of cross bridges attached during the linear phase of relaxation would be greatest. As SLm was increased, with a consequent decrease in overlap, the bump area would tend to zero just as active force development does, and this was strongly substantiated by the finding that the intersection of the linear regression and the abscissa in Fig. 6 is very close to 3.5 µm.

These are new and important results, since they show that it is the overlap zone, or zone of cross-bridge attachment, that controls the bump area. Our results support the hypothesis that cross bridges attached to actin in the overlap zone control the affinity of Ca2+ for TnC. Our findings are in agreement with the view that "regional," i.e., overlap, interactions predominate in controlling changes in the affinity between Ca2+ and the thin filament (22), rather than supporting the view that the thin filament is involved along its entire length (4). If the attached cross-bridge number is suddenly reduced, this most likely decreases the affinity of Ca2+ for TnC in the overlap zone, thus liberating Ca2+ into the myoplasm. The magnitude of this effect will depend on both the number of cross bridges attached before the sudden ramp occurs and how much the fiber shortens to change the cross-bridge attachment distribution from nearly isometric to one appropriate for isotonic shortening at Vu.

    ACKNOWLEDGEMENTS

This work was supported by National Institutes of Health Grant HL-35032 (to F. J. Julian).

    FOOTNOTES

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.

Address for reprint requests: F. J. Julian, Department of Anesthesia Research Laboratories, Brigham and Women's Hospital, 75 Francis St., Boston, MA 02115.

Received 19 May 1998; accepted in final form 17 September 1998.

    REFERENCES
Top
Abstract
Introduction
Methods
Results
Discussion
References

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