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Krannert Institute of Cardiology, Indiana University School of Medicine, Indianapolis, Indiana 46202
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Force-velocity curves measured at different times during tetani of sheep trachealis muscle were analyzed to assess whether velocity slowing could be explained by thick-filament lengthening. Such lengthening increases force by placing more cross bridges in parallel on longer filaments and decreases velocity by reducing the number of filaments spanning muscle length. From 2 s after the onset of stimulation, when force had achieved 42% of it final value, to 28 s, when force had been at its tetanic plateau for ~15 s, velocity decreases were exactly matched by force increases when force was adjusted for changes in activation, as assessed from the maximum power value in the force-velocity curves. A twofold change in velocity could be quantitatively explained by a series-to-parallel change in the filament lattice without any need to postulate a change in cross-bridge cycling rate.
sheep; smooth muscle activation; smooth muscle contraction; muscle velocity; myosin
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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THERE IS CONTROVERSIAL EVIDENCE that thick filaments of smooth muscle are evanescent, dissolving partially during relaxation and reforming on activation (see DISCUSSION). The differing conclusions from anatomic studies suggest that another approach might profitably guide further structural investigations. Thus we undertook the present study as a search for functional alterations expected to result from changes in filament structure. The work was suggested, in part, by our previous study, which indicated that smooth muscle adapts to different muscle lengths by varying the number of contractile units in series (24). Because such plasticity would be facilitated by thick-filament evanescence, it seemed reasonable to look for functional evidence of filament reformation.
If thick filaments reform during activation, they are likely to
lengthen (31, 32). Such lengthening will cause a
series-to-parallel transition, as aggregates of cross bridges in series
on short thick filaments are realigned to a parallel orientation on
long thick filaments, as illustrated in Fig.
1. This transition will decrease velocity
and increase force in exactly the same proportion. Such functional
changes were anticipated by Huxley and Niedergerke (14) in
their original description of filament sliding. They postulated that
muscles with long sarcomeres would generate more force, whereas muscles
with short sarcomeres would have higher velocities. In support of their
hypothesis, they cited the work of Jasper and Pezard (17),
which showed that the velocities of arthropod muscles, which have
different sarcomere lengths, were inversely related to sarcomere
length. Additional support for this hypothesis has since been provided
by Jahromi and Atwood (16), who showed that isometric
force varied directly, and shortening velocity varied inversely, with
sarcomere length in arthropod muscle. The present study was undertaken
to determine whether similar correlations could be detected within the
same muscle.
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It is well known that the velocity of smooth muscle declines during the rise in force (5, 6, 18, 19, 28); therefore, the question addressed here is not whether such slowing occurs but whether an exact proportionality exists between the velocity decline and the force increase. Although this question is relatively straightforward, it is complicated by the rise, and possible later fall, of activation of the muscle. The force-velocity data must, therefore, be adjusted for changes in activation. To make this adjustment, maximum power was used to signal changes in activation (7). The force-velocity data were corrected by multiplying isotonic forces by the ratio of the maximum power at a reference time to the maximum power at other times. The rationale for these corrections is explained in the DISCUSSION.
Finally, two important and related points, discussed below, should be emphasized. First, the time course of velocity changes described here is substantially faster than that reported in some other tissues, for which other mechanisms for the slowing have been proposed (5, 6, 19). Second, the results presented are specific for the conditions used here in trachealis muscle. One anatomic study has shown that thick-filament density increases during tetani are highly tissue specific (32), suggesting that the mechanisms of velocity slowing may also be tissue specific.
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METHODS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Force-velocity properties were defined with the same apparatus and methods used in our previous study (24). The force transducer had a resonant frequency of 12 kHz. The servomotor made steps from isometric length to isotonic loads complete within 1-3 ms. A single isotonic force-velocity point was obtained from one tetanus. Velocity was measured by fitting a tangent to the length record between 50 and 115 ms after the release to the isotonic load.
Preparation
Sheep tracheas were obtained from a US Department of Agriculture-approved abattoir and were kept at 4°C in physiological salt solution for up to 2 days before strips of muscle (~4 mm long × 0.3 mm wide × 0.1 mm thick) were dissected and attached by aluminum foil clips (8) to a mechanical apparatus for measuring contractile properties.Solutions
Muscles were studied at 37°C and pH 7.4 in a physiological salt solution equilibrated with 95% O2-5% CO2 and containing (in mM concentrations) 118 NaCl, 5 KCl, 1.2 NaH2PO4, 2 MgSO4, 22 NaHCo3, 2 CaCl2, and 5.6 glucose. The tracheas were stored and dissected in the same solution at 4°C. Dissections were done at room temperature.Procedures
The muscles were stimulated to produce tetani at 4.5-m intervals. The main variable in the present experiments was the time after the onset of stimulation, when force-velocity properties were measured. Electrical stimulation continued until the end of the period of isotonic shortening and was then stopped. Force-velocity properties were measured from eight or nine data points obtained in as many separate contractions.Protocols
Measurements made when tetanic force was judged to have just reached its plateau value, at 11-14.5 s, were used as references to which other measurements were compared. A single protocol, which took 2-4 h, consisted of a set of measurements at the reference time and one or two other times. Only one test time was studied when it was greater than the reference time. Two test times were studied when they were less than the reference. Two of these protocols were usually done in each muscle, yielding three or four sets of measurements at different test intervals. The reason for making measurements in two sets was that tetanic force declined somewhat over the course of the experiment, and the effects of this decline were minimized in the shorter protocols.To compensate for the effect of long-term changes in tetanic force, comparable measurements were made sequentially at the test and reference times. In addition, the order of the time intervals was reversed in each sequence to minimize any alterations caused by the duration of the preceding tetanus. Thus a typical sequence of measurements consisted of six tetani carried out in the following order: reference, test 1, test 2, test 2, test 1, reference, with the isotonic load changed only slightly between the 2-s test measurements. In this way, the first three contractions in the series were preceded by longer tetani, whereas the last three were preceded by shorter tetani.
Rapid shortening at a low isotonic load frequently reduced tetanic force in the next contraction by 3-5%. To minimize this effect, a full-duration isometric tetanus was sometimes interposed between each contraction when low-isotonic loads were being applied.
Control Observations
All of the data presented here were obtained from 30 protocols in 16 muscles. The isometric force measured in the last reference contraction of the protocol averaged 93.6 ± 2.1 (SE)% of the isometric force measured in the first reference contraction. To assess the constancy of the time course of force production, the signal-averaged tetanic force records for the first and last contractions in each of the 30 protocols were examined. In Fig. 2, the averaged force record for the last contraction was fitted by a single exponent over the period when force rose from 50 to 100% of its final value. Only the second half of the force rise was fitted because the time course of force onset was unclear, but, as shown, in addition to giving a good description of the later force rise, the curve passes through most of the earlier data points as well. Figure 2 also shows the fitted curve scaled up to superimpose on the signal-averaged record for the first contractions. This scaled curve also passes very close to all of the data points, except for a slight deviation, equivalent to a maximum of 1% of isometric force, over the period from 4 to 10 s after the onset of stimulation. The observation that the same curve could be scaled in amplitude to describe both records indicates that the force decline during the protocols was not associated with a change in time course. This absence of a change in time course was further demonstrated by fitting the individual force records from the first and last contractions with a single exponent and comparing the time constants. The time constant for this exponent averaged 2.3 s in the first contraction, and it increased by an average of 0.04 s. A paired t-test showed this increase to be insignificant (P > 0.1).
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To compensate for small variations among muscles in the rise in tetanic force, data were obtained at the time when developed force had achieved specified fractions of the reference value. To simplify the presentation, we plotted the parameters of the force-velocity curves at the times corresponding to the time when force in the signal-averaged contraction achieved the same fraction of the plateau value as when the records were made.
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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The aim of these experiments was to determine whether the myofilament array undergoes a series-to-parallel transition during the rise in tetanic force. By itself, such a transition will produce exactly compensatory increases in force and decreases in velocity. The test of the hypothesis, therefore, was whether sets of force-velocity data obtained at different times during the rise in force could all be fitted with the same hyperbolic Hill (12) curve adjusted by using a single factor to scale force and velocity in opposite directions.
Individual data points obtained with two muscles are shown in Figs.
3 and 4.
Two sets of force-velocity measurements were made in both muscles. One,
called the reference, was made when the tetanic force had just achieved
its full value. The other, called the test, was made when force had
achieved one-half and three-quarters of its full value, respectively,
in the two muscles. The force-velocity values obtained at the two times
were first fitted with the Hill (12) hyperbola by a
nonlinear, least squares (Newton-Raphson) method (Fig. 3, A
and B). The force-velocity relations were then converted to
force-power relations by plotting the product of force times velocity
against force (Fig. 3, C and D).
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The data set depicted in Figs. 3 and 4, left, was selected as a representative example because the peaks in the force-power curves were nearly identical. As explained below, we interpreted the nearly identical maximum power as indicating that the level of activation was the same at the two times, so that no correction for variations in activation was needed. The data obtained at earlier times were then fitted with the reference curve by scaling velocity upward and force downward (leftward) by using a single "transition scaling factor" (Fig. 3E). This factor, determined by a least squares method, was used to indicate the degree of the series-to-parallel transition. The goodness of this fit was determined by examining the residuals of the fitted curves. These are plotted as a function of relative isotonic force for the reference and test curves, respectively, in Fig. 4, A and C. As shown, there is excellent agreement between the data and the fitted curves, with all of the residuals falling within the range of ±0.6% of maximum velocity with no systematic tendency of the residuals to deviate in one direction at either end of the curve.
The data in Fig. 3, A-C, were unusual in that activation at the two times was almost identical. Data pairs usually required an additional adjustment for differences in activation.
Variations in Activation
It is expected that contractile activation will rise and possibly fall partially during a tetanus. Because the level of activation is likely to affect the force-velocity relations, an adjustment was made for these changes. For reasons discussed below, maximum power was used to signal changes in activation. The data shown in Figs. 3 and 4, right, were chosen because the ratio of the maximum power of the test curve to that of the reference curve was the highest in these experiments. As shown in Fig. 3D, the peak in the test power curve was 23% higher than the peak in the reference curve. To adjust for this difference, we divided force by the ratio of the maximum powers in the two curves, to move the power points both downward and leftward, so that the peaks in the test and reference curves were the same (cf., dotted curve with solid reference curve in Fig. 3D). The same correction moves force-velocity points leftward (diamonds in Fig. 3F). These adjusted values were then fitted with the reference curve by scaling it upward and leftward by using a common transition scaling factor (Fig. 3F). The residuals plotted in Fig. 4D again show a good match of the fitted curve to the data.Goodness of Fit
To determine how well the theory accounted for the observations, the residuals of all the fitted curves were examined in a manner similar to that shown for two muscles in Fig. 4. The velocity residuals for the force-velocity curves were pooled for each 0.1 interval in relative isotonic force and plotted for three different time intervals in Fig. 5. The three time intervals in Fig. 5, A-C, were, respectively, times earlier than the reference, the reference, and times later than the reference. As shown, 26 of the 27 total average values of the residuals fell within the range of 0.5% of maximum velocity. Only 2 of the 27 average values were significantly different from zero at the 0.01 < P < 0.05 level, and there is no systematic tendency for the residuals to deviate in one direction at any time or any relative force. This close agreement between the data and the fitted curves indicates that the present analysis gives a complete and accurate description of the time dependence of the force-velocity properties of the preparation.
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Parameters of the Fitted Hyperbolas
The reference force-velocity data were fitted with the Hill (12) hyperbola
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(1) |
Extrapolation of Force-Velocity Curves to Zero Force
In Fig. 3, the curves fitted to the data over the range in which force was less than or equal to the developed force are plotted as solid curves, with the extrapolation to zero velocity represented by dashed curves. The length of this extrapolation was 25% of the isometric intercept when force had risen to one-half of its reference value. A point to be discussed below is that, in contrast to striated muscle, these extrapolations are short because shortening velocity is relatively low during afterloaded contractions imposed during the rise in force.Time Course of Contractile Parameters
The time course of maximum power and scale factor are superimposed on the signal-averaged isometric force record in Fig. 6, A and B, respectively. Reference values, to which other values in Fig. 6 are normalized, are given in Table 1. The earliest measurements were made when force reached 42% of its reference value, 2 s after the onset of stimulation in the signal-averaged contraction. By this time, the scale factor, which indicates changes in velocity, had reached its highest value, 1.56 times the reference value. It remained at this level for another two measurement times, whereas force rose to 67% of its final value ~3.5 s after the onset of stimulation and then fell quasi-exponentially to its reference value.
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Maximum power rose rapidly to a peak value of ~1.17 times its reference value at 3.5 s and remained at this peak until ~5 s, after which it declined to the reference level. Both scale factor and maximum power fell progressively to 87% of their reference values at the end of the longest period of stimulation, 28 s after the onset of the tetanus, whereas force rose by 3.5%.
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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These experiments suggest that all force-velocity changes during a 28-s tetanus of airway smooth muscle can be explained by changes in activation accompanied by a series-to-parallel transition in the filament lattice. The agreement between theory and experiment further suggests that no other factors are required to account for the data. In particular, it is not necessary to postulate a slowing of cross-bridge cycling to account for the well-known slowing of shortening velocity, at least during a brief tetanus of trachealis muscle. All of the velocity decline can be explained by a modest increase in thick-filament length. Although the present experiments did not attempt to exclude other possible explanations of the slowing, the discussion below suggests that some of the expectations of the other theories are inconsistent with the present data. Before discussing these other possibilities, we will describe the basis of the present analysis.
Rationale for the Present Analysis
Series-to-parallel transition. The force produced by a muscle is proportional to the number of cross bridges acting in parallel. Because all cross bridges in each half-filament act in parallel, the force per filament will be proportional to the length of the filament. Thus the force generated by the muscle will be the product of the length of the filaments multiplied by the number of filaments in the cross section. On the other hand, because all of the cross bridges within one filament are physically connected, they must move along the thin filaments at the same rate (Fig. 1). The sliding velocity of single filaments is, therefore, independent of their length, but the overall muscle velocity is proportional to the number of filaments in series and contributing to the overall shortening. If filaments grow longer, there will be fewer filaments arranged in series within the muscle length but more cross bridges acting in parallel on the individual filaments (Fig. 1). To the extent that the total number of cross bridges remains constant, filament lengthening is expected to produce exactly compensatory decreases in velocity and increases in force, as described here.
Adjustment for activation. If changes in activation simply alter the number of active cross bridges on each filament, these changes will alter force without varying maximum shortening velocity. There have been some controversial suggestions that changes in activation also alter maximum velocity [see review by Podolin and Ford (22)], but the best current evidence is that maximum velocity is entirely independent of activation (23), at least when there is no internal load (7). This consideration led to the rationale for adjusting the force-velocity points by scaling isotonic force inversely to the relative level of activation.
Maximum power as an index of activation. The use of maximum power to signal changes in activation derives from the consideration that each cross bridge contributes to the muscle power, irrespective of whether it is in series or in parallel with other cross bridges. Bridges added in parallel contribute to power by increasing force, whereas bridges added in series increase power by increasing velocity. When loading is optimized so that the average bridge produces its maximum power output, the maximum power output of the muscle will reflect the number of bridges that are active (7).
Afterloaded velocities. Striated muscle that shortens when developed force rises to match an afterload achieves a high velocity immediately, and force-velocity curves derived early in a tetanus must be extrapolated for a long distance to reach the zero-velocity baseline. For example, force-velocity curves obtained when force was one-half of its full value had to be extended by 62% of developed force in single skeletal fibers (2) and by 74% in whole cardiac muscle (4). This phenomenon is predicted by the cross-bridge theory (13), which postulates that the relatively slow rise in isometric force is due to the slow approach of isometric cross bridges to their steady state. The rapid shortening in afterloaded contractions is then due to the cross bridges being driven to their steady isotonic state by the shortening.
The extrapolations required to reach the zero-force intercept of the force-velocity curves were substantially less than those seen in striated muscle for the same level of tetanic force development. When isometric force had achieved one-half of its full value, isotonic force had to be extrapolated by only 25% to reach the zero velocity (Fig. 3A), which is ~40% of the comparable value in striated muscle. Such low afterloaded velocities can be expected by the cross bridges being closer to their final, isometric distribution. The slow rise in force late in a tetanus would then be due less to the slow approach of cross bridges to their steady-state distribution, as in striated muscle, and more to the postulated filament transition.Relationship to Earlier Work
Tissue differences. It should be emphasized that the results presented here are specifically for trachealis muscle and that there are likely to be substantial differences when other tissues are compared. For example, structural studies of anococcygeus show an increase in the density of thick filaments associated with stimulation, whereas the same observations of taenia coli muscle show no change in filament density (32). Similarly, the slowing of bladder smooth muscle (18) is substantially greater than that for tracheal smooth muscle, both as described here and as described by Seow and Stephens (28). Finally, the velocity slowing described here occurs over a substantially shorter interval than that associated with a decrease in phosphorylation in porcine carotid artery (5, 6) and bovine trachealis (19). These differences in velocity changes may result from mechanisms different from that proposed here.
Thick-filament evanescence. This was first postulated by Schoenberg (26) and by Rice et al. (25) because thick filaments were more abundant when the muscles were prepared for electron microscopy either at low pH (20) or in high-divalent cations (26). Because both conditions are obtained during activation and because the thick filaments were often very much diminished in smooth muscle fixed at rest, it seemed possible that they dissolved during relaxation and formed on activation. Although it was found later that some fixation conditions will always yield thick filaments in electron micrographs [see review by Somlyo and Somlyo (29)], there have also been continuing reports that the amount of myosin incorporated into thick filaments increases during activation and is diminished during relaxation (9, 10, 31, 32).
Whereas the amount of myosin in thick filaments appears to diminish during relaxation, in all of the recent studies quoted thick filaments do not disappear entirely. Such partial dissolution of the filaments might be much more difficult to recognize in electron micrographs and would require extensive quantitative measurements of filament lengths and numbers. This was a major reason for undertaking the present functional studies. The results provide a good estimate of the time course and extent of filament lengthening. Now that this is known, a more directed search for the anticipated morphological changes can be made. Finally, the thick-filament lengthening required to slow velocity during the rise in tetanic force, ~55%, is in good agreement with the 60% increase in thick-filament density seen by Godfrain-Debecker and Gillis (10) after correction for fiber shrinkage and is greater than the 25% increase in filament density found by Xu et al. (32). As in the present experiments, the increased filament density seen by Godfrain-Debecker and Gillis (10) also occurred in association with a late rise in force during a sustained contraction.Changes in contractile parameters during the tetanus. It is well known that smooth muscle velocity declines during a tetanus (5, 6, 18, 19, 28), but there are differences in the way this slowing is reported to occur. Kamm and Stull (19) described a significant decline in a/Fo associated with the velocity slowing. Dillon et al. (5) and Dillon and Murphy (6) reported only a slight decline, whereas Seow and Stephens (28) reported an increase. The finding in the present study that a/Fo was unchanged is thus in keeping with the average conclusion from these earlier reports. It should be stated, however, that a is determined by a long extrapolation and is, therefore, liable to substantial error. The present conclusion, that a/Fo remains constant, is not based on an estimation of a but on a direct comparison derived from interpolation of the curves.
Changes in muscle stiffness during the tetanus. In the absence of any compliance in series with the cross bridges, the proposed mechanism would increase muscle stiffness out of proportion to force during the time that the filaments are lengthening. As calculated by Mijailovich et al. (21), however, compliance in series with the cross bridges reduces relative changes in overall muscle stiffness to such an extent that conclusions drawn from the measurements are likely to be unreliable, at least until length changes in the series elements can be estimated. There are four possible sources of compliance in series with the bridges: tissue at ends of the muscle preparation, cell-to-cell connections, dense bodies connecting the thin filaments, and the filaments themselves. Each should be assumed to contribute at least a small amount to the measured muscle compliance, and evidence for substantial filament compliance for skeletal muscle has accumulated in the last decade (1, 11, 15, 30). Until similar estimates are available in smooth muscle and until some measurement of overall series elastic element compliance can be made, it would not be fruitful to assess the proposed mechanism from stiffness measurements.
Metabolic mechanisms. In general, it has been presumed that the slowing of smooth muscle velocity is due to a slowing of cross-bridge cycling. Such slowing might be caused by a metabolic alteration secondary to a change in the concentration of a metabolite or to an alteration of the bridges themselves. A specific variant of this latter mechanism is the latch bridge hypothesis (6), which suggests that dephosphorylated cross bridges cycle more slowly. These dephosphorylated bridges are analogous to the "catch" bridges of the anterior byssal retractor muscle of Mytelus, which allows the mollusk to cling to a rock with very little energy expenditure. The present experiments suggest an alternative explanation for the early velocity slowing during the rise in isometric tension, which is entirely different from the general class of mechanisms requiring metabolic slowing. One observation in the present experiments argues against the metabolic mechanisms, at least in the preparation studied under the conditions used.
The cross-bridge theory (13) suggests that the cross-bridge detachment rate determines maximum shortening velocity. The postulated slowly cycling latch bridge would thus be expected to be slow in detaching. When both normal and latch bridges are present, these slower bridges would impose an internal load on the more rapidly cycling bridges. This internal load is expected to increase a/Fo and decrease the curvature of the force-velocity curve. (see Ref. 7 for discussion). The absence of such a change thus mitigates against a partial population of slowly cycling bridges. In conclusion, the present work suggests a series-to-parallel change in the smooth-muscle filament lattice during the development of a tetanus. Such a transition would be expected if thick filaments elongate during the tetanus. The present work is thus in keeping with the findings that thick-filament abundance increases during activation. It also suggests a mechanism by which smooth muscle is converted from a shortening organ to a force maintenance structure with little change in metabolic rate. Furthermore, our earlier study, which showed that the number of contractile units in series varies with adapted muscle length, suggests a reason for this evanescence: it facilitates plastic changes that allow the muscle to adapt to different lengths by varying the number of filaments arrayed in series. This mechanism would explain why smooth muscle is smooth, i.e., why it does not have striations: the lattice is constantly changing.| |
ACKNOWLEDGEMENTS |
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Special thanks to Dr. Jeffrey J. Fredberg for suggestion of the schematic diagram shown in Fig. 1 and helpful comments on the manuscript.
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FOOTNOTES |
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This work was supported by National Heart, Lung, and Blood Institute Grant HL-52760 (to L. E. Ford and C. Y. Seow) and Medical Research Council of Canada Grant MT-13271 (to C. Y. Seow).
Present addresses: V. R. Pratusevich, Institut Biotechnol., 8 Nauchny Prospekt, Moscow, Russia 107246; C. Y. Seow, Departments of Pharmacology/Therapeutics and Anatomy, University of British Columbia, 2176 Health Sciences Mall, Vancouver, BC, Canada V6T 1Z3.
Address for reprint requests and other correspondence: C. Y. Seow, Dept. of Pharmacology/Therapeutics, Univ. of British Columbia, 2176 Health Sciences Mall, Vancouver, BC, Canada V6T 1Z3 (E-mail: cseow{at}interchange.ubc.ca).
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.
Received 24 March 2000; accepted in final form 21 April 2000.
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REFERENCES |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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). Curves are the
signal averages of the 1st (top curve) and last
(bottom curve) reference contraction in each of the 30 protocols. A single exponential (solid curve) was fitted to the
bottom record over the time between 2.1 and 14 s when
force was rising from 50 to 100% of its final value. This same curve
was then scaled up to superimpose on the top record.
) normalized to maximum
velocity (Vmax)] vs. relative isotonic force
[isotonic force (F) divided by isometric force (Fo)] for
the reference data (A and B) and test data
(C and D) for the 2 muscles illustrated in Fig.
