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J Appl Physiol 98: 234-241, 2005. First published August 27, 2004; doi:10.1152/japplphysiol.00574.2004
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Active and passive components in the length-dependent stiffness of tracheal smooth muscle during isotonic shortening

Richard A. Meiss1 and Ramana M. Pidaparti2

1Departments of Obstetrics and Gynecology and Cellular and Integrative Physiology, Indiana University School of Medicine, Indianapolis; and 2Department of Mechanical Engineering, Purdue School of Engineering and Technology, Indiana University-Purdue University Indianapolis, Columbus, Indiana

Submitted 14 June 2004 ; accepted in final form 20 August 2004


   ABSTRACT
TOP
 ABSTRACT
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
Contraction of smooth muscle tissue involves interactions between active and passive structures within the cells and in the extracellular matrix. This study focused on a defined mechanical behavior (shortening-dependent stiffness) of canine tracheal smooth muscle tissues to evaluate active and passive contributions to tissue behavior. Two approaches were used. In one, mechanical measurements were made over a range of temperatures to identify those functions whose temperature sensitivity (Q10) identified them as either active or passive. Isotonic shortening velocity and rate of isometric force development had high Q10 values (2.54 and 2.13, respectively); isometric stiffness showed Q10 values near unity. The shape of the curve relating stiffness to isotonic shortening lengths was unchanged by temperature. In the other approach, muscle contractility was reduced by applying a sudden shortening step during the rise of isometric tension. Control contractions began with the muscle at the stepped length so that properties were measured over comparable length ranges. Under isometric conditions, redeveloped isometric force was reduced, but the ratio between force and stiffness did not change. Under isotonic conditions beginning during force redevelopment at the stepped length, initial shortening velocity and the extent of shortening were reduced, whereas the rate of relaxation was increased. The shape of the curve relating stiffness to isotonic shortening lengths was unchanged, despite the step-induced changes in muscle contractility. Both sets of findings were analyzed in the context of a quasi-structural model describing the shortening-dependent stiffness of lightly loaded tracheal muscle strips.

muscle mechanics; models; temperature; contractility

THE OBSERVED MECHANICAL BEHAVIOR of vertebrate smooth muscle tissue represents an interplay between its active elements, the contractile cells, and its passive elements, the connective tissue and extracellular matrix in which the cells are embedded. The fundamental mechanical activities of the cells, i.e., the generation of force and shortening, are strongly influenced by the passive tissue elements and by the ways in which the tissue is assembled and its components are integrated. Attempts to infer cellular properties by making measurements on intact tissues suffer from the uncertainties caused by tissue architecture. If cells are isolated for mechanical study by disassembly of the tissue, they are perforce placed in a mechanical environment far different from their normal situation, and their function may be correspondingly altered in significant ways. For example, the contractile apparatus in a cell embedded in a tissue is attached to the surrounding cells and connective tissue at numerous points via membrane-associated dense bodies (4) along its entire length, rather than just at its ends. A cell isolated for experimental manipulation is usually attached only at its ends or along one side. The resulting distortions of cellular geometry are likely to modify mechanical function in significant ways.

A possible approach to this problem would be to construct a conceptual model of tissue architecture and cell-tissue interactions. Such a model, if based on known structural and mechanical relationships within a tissue, could permit a better understanding of cellular function, despite (and in view of) the constraints provided by its mechanical environment. A model of this sort has been under investigation in this laboratory for some time (13, 17, 19), and the present study seeks to address some specific features of the model’s formulation with a series of mechanical and thermal experiments.

The model in question has been termed the "radial constraint hypothesis" (16, 19). It holds that an activated strip of smooth muscle tissue, under a very light (approaching zero) isotonic load, will shorten at constant volume and will reach an equilibrium length. As the extreme of shortening is approached, the tissue must expand significantly in a radial direction to preserve the constant-volume condition. Such expansion would be counteracted by forces developed in connective tissue structures arranged in a radial direction. This strained connective tissue would serve as a load on the contractile apparatus (the force being transferred through the incompressible cells and extracellular matrix), and this would cause shortening to be limited. It would also cause the axial stiffness of the muscle strip to rise as more cross bridges are recruited in response to the reduced internal shortening velocity. This larger population would bear the additional internal load, while the external load would remain constant. By using the measured axial stiffness of the tissue as an approximate measure of the number of active cross bridges, estimates can be made of the magnitude and direction of the opposing internal forces. Details of the hypothesis, as well as some validation of its predictions, have been given in the publications cited above. A key feature of the hypothesis is that the shortening-dependent increase in stiffness is considered to be due primarily to extracellular arrangements and not to a specific increase in the stiffness of cells themselves. The present study seeks to address this question by using techniques intended to differentiate between active and passive elements within the tissue. Some of the results to be reported here have been presented in abstract form (17, 18).

The temperature sensitivity of dynamic processes in biological systems has long been used to gain insight into their underlying mechanisms (24). In general, those phenomena with a biochemical basis have a high temperature sensitivity, whereas those whose basis lies in physical properties or structure have a lower temperature sensitivity. Often the measure used to characterize a process in question is the Q10, which is the ratio of the rates of the process(es) at two temperatures 10°C apart (2). Although the technique is most rigorously applied to isolated or identifiable chemical reactions, it can also be used to shed light on more complex behaviors if suitable means of quantification are available. In the present situation, this method will be used in an attempt to separate out aspects of the dynamic behavior of tracheal smooth muscle that are represented as elements in the radial constraint hypothesis. High Q10 values will be assumed to identify active cellular processes, whereas Q10 values close to unity will be assumed to arise from aspects of the behavior due to extracellular structural components of the tissue.

The other approach to be reported here involves temporary modifications of smooth muscle contractility by specific mechanical interventions. A number of studies have demonstrated that sudden shortening steps applied early in contraction have a significant effect on mechanical performance later in that contraction (3, 5, 14, 21, 28, 29). These effects appeared to be confined to the single contraction in which the intervention was performed and had no lasting effect over several contractions. If these changes affect only active elements of the model, then those properties attributable to passive elements should remain unchanged, and the pattern of the increase in stiffness with decreasing isotonic length should likewise be unchanged.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
Most of the methods and equipment used, with the exception of those involved in the temperature studies, have been previously described in detail (13, 25), and only summaries will be presented here. All use of animals was in conformance with guidelines established by the Institutional Animal Care and Use Committee of the Indiana University School of Medicine.

Muscle preparations.   All of these experiments were carried out on isolated strips of tracheal muscle from mongrel dogs. The animals were anesthetized with pentobarbital sodium. A 10- to 15-cm-long segment of extrathoracic trachea was quickly removed and placed in a physiological saline solution of the following composition (in mM): 125 NaCl, 4.7 KC1, 2.5 CaC12, 1.2 MgSO4, 15.5 NaHCO3, 1.2 KH2PO4, and 11.5 glucose. The solution was bubbled throughout the experiment with 95% O2-5% CO2 to maintain a physiological pH. The cartilaginous rings of the trachea were cut at both sides, the preparation was pinned out in a dissecting dish, and the muscle area was cleaned of epithelial and adventitial tissue. Small strips of muscle tissue (~0.75 mm diameter and 8–12 mm long) were cut from the muscle sheet, following the natural division of the tissue into discrete fiber bundles. To ensure a low-compliance attachment to the experimental apparatus, the ends of the strip were clamped in aluminum foil cylinders, as previously described (11).

After the tissue was mounted to the extension arms of the apparatus, it was extended by adjusting the position of the force transducer until a small force (~1–2% of the anticipated maximum) was recorded. This length was designated rest length (Lr) and was ~10% less than the length for maximal isometric tension development (usually defined as Lo). This procedure was followed because the experimental protocols required that passive force be kept to a minimum. After the tissue was mounted, the muscle bath, borne on a rack-and-pinion assembly, was elevated to immerse the muscle in circulating, temperature-controlled, and oxygenated physiological saline solution. Muscles were stimulated by using platinum electrodes along either side of the tissue, with supramaximal voltage pulses of alternating polarity at a frequency and voltage previously determined to produce a maximal mechanical response. The interval between stimuli was consistently 5 min.

Temperature control.   The bathing solution was pumped past one side of a thermoelectric (Peltier effect) device (Cambion) that was connected to a thermal controller. According to the requirements of the experiment, the controller adjusted the polarity and current of the driving voltage to produce the desired temperature. A feedback circuit maintained the temperature to within >1°C, and a new stable temperature could be attained within the 5-min between-contractions interval. Temperature was read visually with a remote thermometer, and the temperature controller also recorded its temperature measurement continuously on the chart recorder.

Mechanical instrumentation.   All experimental contractions were made in a digitally controlled force-clamp servo system (13, 25). This system was capable of producing both isometric (length-controlled) and isotonic (force-controlled) conditions and switching rapidly between them under manual or computer control. In addition, special mechanical conditions, such as sudden shortening, could be produced. The continuous measurement of dynamic stiffness, under both isometric and isotonic conditions, was done by applying a very small (<0.5% Lr) sinusoidal length oscillation (usually at 80 Hz) to one end of the preparation and recording and analyzing the resulting force oscillation. These oscillations, superimposed on the length and force traces, were removed and quantified by a digitally controlled set of band-pass, notch, and low-pass filters. The in-phase component of the stiffness was computed as isotonic stiffness (dF/dL) and expressed in units of milli-Newtons per micrometer. The stiffness-measuring oscillations were kept small enough so that they had no observable effect on the contractile events (11).

Experimental protocols.   The basic sequence of events in an individual experimental contraction was the following. With the muscle set at the selected length (near Lr), an electrical stimulus was applied, and isometric force began to develop. At a chosen level of force (or at a specific time), the clamp circuitry was switched into the isotonic (force-control) mode, with a very small afterload being applied. The muscle was allowed to shorten fully. Resulting changes in muscle length and stiffness were then recorded and analyzed. After the contraction was completed, the servo system slowly stretched the muscle back to its original length.

All of the temperature experiments were carried out at Lr, with one or more contractions being made at each temperature. No particular direction was chosen for the sequence of temperatures to be applied. In some instances, both an ascending and a descending sequence were used, and the results were essentially independent of the direction. The interval between contractions was sufficient for thermal equilibrium to be reached within the muscle, but no attempt was made to allow the muscle to come to metabolic equilibrium at each temperature. With the light loads and isometric contractions employed, the metabolic cost of a single contraction did not appear to affect a subsequent test contraction at that temperature.

The specific protocol for the length-step experiments is given in RESULTS. All contractions in which velocity was measured consisted of an isometric portion followed by a lightly loaded isotonic shortening. In the test contractions, a sudden length step was applied during the development of isotonic force, whereas, in the control contractions, the length remained constant while force developed.

Data recording and analysis.   All experimental data traces (force, length, and force and length perturbation amplitudes) were digitized during each contraction and were stored for later processing and analysis. Each contraction event was sampled 500 times over its duration from 20 to 45 s. For convenient reference, paper chart records were made on a Gould 2600 ink-writing recorder. The digitized data were analyzed by using software developed in the laboratory, along with the curve-fitting routines from SigmaPlot software (Systat Software). Statistical comparisons were made by using appropriate t-tests with either SigmaPlot or SigmaStat (Systat Software).


   RESULTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
Effects of temperature on contractile mechanics.   In a series of 12 runs on 10 muscle preparations, contractions were carried out over a wide range of bath temperatures. The lowest temperature in the overall data set was 19.6°C, whereas the highest was 38.7°C. Each run consisted of contractions at at least three temperatures (sometimes five), and each run covered a range of at least 10°C; the range for comparison was 24–34°C, because this range was experienced by every preparation. A typical set of contractions is shown in Fig. 1, along with numerical data derived from them. A contraction consisted of an initial isometric portion that was followed by a step change to lightly loaded isotonic conditions, and the muscle was allowed to shorten to equilibrium while the stimulus was maintained. Stiffness (dF/dL) was measured continuously throughout the contraction. The peak velocity of shortening was taken as the initial rate of shortening immediately following the length transient associated with the step change in force, and the equilibrium isotonic length was recorded as the maximal shortening. For the isometric phase of the contraction, the rate of rise of force (dF/dt) was computed, and the peak value was recorded. The isometric stiffness was plotted as a function of the muscle force; for analysis, the range considered for comparison was limited by the lowest force development (at 24°C in this case) to ensure that any curvature in the relationship would affect all contractions equally. Linear regression analysis yielded a straight line of the form dF/dt = (k x F) + C, where k and C are constants with units of µm–1 and mN/µm, respectively, and F is force. Because the value of the slope k was insensitive to inaccuracies in determining resting force, it was used as the parameter for comparison among contractions.



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  		Fig. 1. Effects of temperature on contractile mechanics. Top left: initial (isometric) portions of 3 contractions, recorded at the temperatures indicated, are superimposed. Top center: the relationship between isometric force and stiffness during the isometric phase of the same contractions. Slopes of the curves (the parameter k; see below) were determined by fitting straight lines to each curve; the range of data used in each case was the same, being limited by the force range of the smallest contraction (at 24°C). Top right: isotonic shortening curves for the 3 contractions, at the indicated temperatures. The curve not marked is the one made at 28.9°C. Bottom: data points derived from the contractions shown above. Data for each curve were normalized to the parameter value measured at 24°C. The best-fitting straight line was used to compute the parameter value at 34°C, and the ratio of the rates of the process at 2 temperatures 10°C apart (Q10) was calculated over the range of 24–34°C. dF/dt, maximal rate of rise; dF/dL, isotonic stiffness.

 
The data derived from the three contractions shown were normalized relative to their 24°C values and were plotted as a function of temperature. From the least squares fit to each parameter set, the relative value at 34°C was computed. This yielded the Q10 values shown in Fig. 1. Pooled data from the entire data set are shown in Fig. 2. The plots of velocity, dF/dt, and isometric stiffness are as in Fig. 1 (the dF/dL plot will be elaborated below). In this display, values in each individual experiment were normalized to their parameter value at 24°C and then pooled. The value of Q10 was derived from the slope of the regression line for the population. This compared closely with the average of the individually determined Q10 values for each experiment but had the advantage of giving more nearly equal weight to every determination. As may be seen, processes closely related to biochemical reactions had a high Q10, whereas those likely due to passive elements within the muscle showed little temperature sensitivity.



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  		Fig. 2. Variation in mechanical parameters as a function of temperature. The overall data set is derived from 9 temperature runs on 6 muscle strips, a total of 32 measurements. In each panel, the plotted data are normalized to the parameter value at 24°C for each individual experimental run. Top left: initial (peak) shortening velocity from isotonic portion of contractions. Bottom left: dF/dt of isometric force. Top right: values of the constant k, derived from the best fits to the stiffness vs. force plots. Bottom right: dF/dL at the end of shortening. See text and Fig. 3 for further details of this plot.

 
The shortening-dependent stiffness ("isotonic stiffness" in Fig. 2) did not lend itself to a "single-parameter" analysis, so the method shown in Fig. 3 was adopted. Here the stiffness during isometric shortening at each of the three temperatures in the run was plotted as a function of the muscle length during shortening. To assess the homogeneity of the response, the curves were analyzed at three stages of shortening. The greatest amount of shortening that was common to all three curves was taken as "100% shortening," and on this basis the lengths corresponding to 75 and 50% shortening were defined. At each of these points, the dF/dL at each temperature was measured and analyzed as a function of temperature. The data set consisted of nine temperature runs on six muscle preparations.



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  		Fig. 3. Effect of temperature on shortening-dependent stiffness. Plot is shown of muscle stiffness as a function of length during very lightly loaded shortening. Curves obtained at 24.0, 28.9, and 33.8°C are superimposed. For clarity, only every 5th data point is displayed. Labeled horizontal lines mark the individual extents of shortening, and vertical lines mark the muscle lengths as percentages of total shortening; data were compared at these points. Inset: complete normalized data set at the 100% shortening point (compare with Fig. 2). Solid circles, data from the experiment illustrated here. As with the 50 and 75% shortening data, the slope was not significantly different from 0.

 
In all cases but one, the slope of the relationship between stiffness and temperature was not significantly different from zero, and the computed Q10 values did not reliably reflect a possible temperature dependence. For this reason, a normalized population analysis (as described above) was used. These results, for 100% shortening, are shown in Fig. 3, inset; they indicate no temperature-dependent difference between the stiffness vs. shortening curves at this point. The population Q10 values (from 41 data points) were 0.999 (0.0706 SD) at 100% shortening, 0.977 (0.2915 SD) at 75%, and 0.948 (0.421 SD) at 50%. None of these values were significantly different from 1.0, indicating that the shapes of the stiffness vs. shortening curves were not sensitive to temperature.

The overall findings from the temperature studies are summarized in Fig. 4. They indicate a strong temperature dependence of shortening velocity and rate of force development and a somewhat weaker dependence of the maximal isometric force development. The near-unity value of Q10 for the total shortening, especially in light of the high Q10 for initial velocity, may reflect the low-temperature dependence of the factors that limit shortening, rather than of the shortening itself. The two stiffness parameters showed essentially no temperature dependence over the range studied.



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  		Fig. 4. Comparison of Q10 values for all mechanical properties measured. The number (n) of muscle preparations involved in each parameter and the degree of significance are given. The leftmost 3 bars show high-temperature sensitivity for these parameters, whereas the rightmost 3 bars indicate a very low-temperature sensitivity. max, Maximum. See text for discussion.

 
Effects of mechanical interventions on contractile mechanics.   This portion of the study had the aim of producing a modifiable contractile state by interfering with cellular process without chemical or thermal intervention. It also sought to avoid possible (and irreversible) alterations of muscle function that might occur as a result of mechanical damage due to stretching. Therefore, the intervention chosen was that of a sudden shortening, by 10–30% of the isometric length, during the rising phase of isometric tension. As illustrated in the top two panels of Fig. 5, the length step produced a sudden fall in force that was followed by a rapid recovery. These experiments were carried out at 34–36°C.



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  		Fig. 5. Isometric effects of sudden shortening. Top: original records of length and force. Solid circles, the control record made at 7 mm. In the experimental record (solid line), the length step, from 9 to 7 mm, occurred approximately midway during the rising phase of isometric contraction, producing the corresponding fall and recovery in isometric force. Middle: pooled data from length-step experiments. There is a significant dependence of the force deficit on the size of the sudden length step. Bottom: relationship between isometric force and stiffness is not significantly (n.s.) affected by the sudden shortening.

 
The redeveloped force was compared with that from a subsequent contraction in which the length step occurred just before stimulation (control contraction). The force that was redeveloped following the length step in the experimental contraction consistently fell short of the control value. This shortfall will be termed the "force deficit." As shown in the two bottom panels, the force deficit (normalized to the control contraction in each case) was proportional to the size of the length step, more than doubling over the step range of 10–30% of the control length. Muscle stiffness fell proportionately with the force, and the ratio between force and stiffness within a contraction was unchanged. This is expressed in the bottom panel in Fig. 5. For each experimental contraction and its control, the ratio of force to stiffness was computed, and these ratios were compared for each pair. When viewed in this manner, there was no effect of step length on the relationship between force and stiffness at the peak of contraction.

Related effects were observed during isotonic contractions. Figure 6 shows a control contraction (left) and its experimental counterpart (right). The isotonic effects of the length step were a reduction in stiffness of the fully shortened muscle, a slight decrease in overall shortening, a decrease in initial velocity (with a low afterload), and an increase in the speed of relaxation. These effects were also proportional to the size of the length step as in the isometric case, although this aspect was not pursued. Pooled results from 16 muscles are shown in Fig. 7. A subset of this data pool (59 paired contractions of 10 muscle strips) was examined for evidence of length adaptation. The comparison was between two sets of contractions: in one the length was stepped from L1 to L2 immediately before stimulation at L2 (the "immediate step" set). In the other, the muscle was allowed to remain at L2 for 5 min, without stimulation, before being activated without any length change. This latter set was termed "length-adapted"; its mean shortening velocity was 91% of that of the "immediate step" value (0.9105 times, P < 0.001), whereas the relaxation velocity of the length-adapted contractions was 111.6% of that of the immediate-step set (1.1157 times, P < 0.0001). Note that these values are approximately reciprocal. There was no significant effect of the length adaptation on the total shortening of the muscles. Because the intent of this portion of the study was to modify muscle contractility as a means to an end, the length-adaptation effect was not pursued further.



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  		Fig. 6. Isotonic effects of sudden shortening. Left: control contraction at L2 (8 mm), showing the parameters of interest. Right: experimental contraction, stepped from 10 mm (L1) to 8 mm (L2), with the parameters of interest circled.

 


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  		Fig. 7. Summary of the isotonic effects of sudden shortening. All experimental contractions were paired with a control contraction immediately following, and the parameters were normalized on that basis, as the y-axis label. Values are means ± SE.

 
The parameter of special interest in this portion of the study was the effect of the length step on the shape of the dF/dL vs. shortening curves. Paired isotonic contractions were analyzed in the same way as the temperature experiments (see Fig. 3) previously described. Comparisons were made, as indicated in the example in Fig. 8, top, at the three length points. The results, normalized to the control curve values at each length, are shown in Fig. 8, bottom. At none of the test lengths was there a significant difference between the curves, indicating that the factors responsible for reducing contractility did not affect the increase in stiffness associated with low-afterload isotonic shortening.



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  		Fig. 8. Effect of sudden shortening on shortening-dependent stiffness. Top: stiffness vs. length curves from an experimental (poststep) contraction and its control. As in the case of the temperature experiments (compare with Fig. 3), the curves were compared at 3 stages of shortening. Bottom: comparisons at the 3 stages, as measured in 16 muscle preparations, show that the curves do not differ as a result of the prior length step.

 

   DISCUSSION
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
The experiments reported here were done in an attempt to distinguish between the active and passive contributions to the pattern of stiffness changes that occur during the shortening of tracheal smooth muscle. An underlying assumption was that the passive contributions would be relatively insensitive, both to the environmental temperature and to contractility changes induced by mechanical interventions. These two means of producing contractile alterations were chosen because, although their presumed locus of operation is intracellular, they should have their effects through distinctly different mechanisms. A necessary part of the experimental work involved characterizing the overall response, active as well as passive, to the experimental manipulations, and then relating that response to the known features of smooth muscle contraction.

The presence of a length-dependent axial stiffness increase during isotonic contraction is a central feature of the radial constraint hypothesis. While the hypothesis holds that this stiffness is due to extracellular forces localized in radially oriented connective tissue structures, the possibility of an intracellular locus must be considered. The use of two independent experimental approaches, both designed to exert their effects intracellularly, was an attempt to address the possibility that active structures within the cells were responsible for the increase in stiffness that accompanied the later stages of isotonic shortening. In a study of the stiffness of isotonically contracting tracheal muscle, Seow and Stephens (26) also found an approximately linear increase in stiffness with decreasing length, although their experiments were confined to lengths greater than ~50% of the resting length. In the present study (see, e.g., Fig. 3), the muscle strips shortened to ≤25% of the starting length, and the increase was highly nonlinear, with most of the stiffness increase occurring in the last 25% of the shortening. The Seow and Stephens analysis of the stress-strain curves of a theoretical series elastic element suggested that this element became functionally shorter during isotonic shortening, although they did not suggest a mechanism for this change. Later work in skeletal muscle [see Higuchi et al. (8) and references therein] demonstrated that compliance of the myofilaments added significantly to the total muscle compliance. These workers (8) were able to demonstrate that the stiffness of single isolated muscle fibers was correlated with the length of the nonoverlap zone (i.e., the I band); as the muscle shortened, the overlap decreased, and the stiffness increased proportionally. The presence of this phenomenon, and their ability to measure its effects, depended on the high degree of regularity of the striated muscle fiber. In addition, their isolated fibers were freed from the constraints of neighboring cells and connective tissue.

There are many uncertainties in extrapolating the skeletal muscle results to the case of smooth muscle, with its much less regular cellular and tissue structure. Given the current state of knowledge of the detailed organization of the smooth muscle contractile apparatus [see Gunst and Tang (4) for a recent review], it is apparent that there is no compelling evidence for a length-dependent nonoverlap zone in which thin-filament compliance could dominate the overall muscle elasticity. Using amphibian stomach smooth muscle, Harris and Warshaw (6) measured the length-dependent stiffness of isolated muscle cells and found that it decreased as the length decreased, a change that they attributed to a reduction in cross-bridge formation. In this case, as for the skeletal muscle measurements cited above, the cells were freed from the physical constraints associated with tissue structure. This implies that the stiffness increase observed while intact tissue shortens is associated with the overall structure of the tissue (with cells and connective tissue interacting) and not to some intracellular mechanism(s).

Effects of temperature.   A number of laboratories have studied the temperature dependencies of smooth muscle mechanics (7, 9, 12, 20, 22, 23, 27, 30). In some of these cases, chemically skinned preparations were used to avoid problems associated with temperature-dependent activation processes. The results from measurements of a wide variety of tissues, including rabbit urinary bladder (7), rat portal vein (10, 22), dog and rat tracheal muscle (23, 27), and guinea pig taenia coli (9, 20), have all shown a similar pattern. In general, the highest Q10 values were obtained for dF/dt and for Vmax, the maximal unloaded shortening velocity. Which of these two parameters had the higher value varied from study to study; in the present paper, the difference between these two Q10 values was not statistically significant. It is the measurement of Vmax that is likely to be the most closely associated with events of the cross-bridge cycle, because the load on the contractile system is constant, whereas, in an isometric contraction, the load (and hence the events of the cross-bridge cycle) varies continuously as force is being developed. In all of the studies cited, and in the present one as well, the temperature dependence of the maximal isometric force was less than the two other measures. This is a reasonable finding, because the peak of isometric force represents a quasi-steady state whose value is less dependent on a single rate-determining process.

Another consistent finding was a low-temperature dependence for the series elastic component, as measured by a variety of methods. Stephens et al. (27) found a Q10 of ~0.75 for this parameter, whereas Peiper et al. (22) found an average value of 0.85. Hellstrand and Johansson (7) found a value of 1.0 for rabbit urinary bladder, and Yamakawa et al. (30) found a value of 1.2 in isolated toad stomach muscle cells. In general, and in the present study as well, the active stiffness of smooth muscle becomes slightly less as temperature increases. However, the overall value of the Q10 was around unity, indicating that this parameter does not depend heavily on temperature-sensitive rate processes. This suggests either that the locus of this elastic element is in passive extracellular structures that are more compliant than the cross bridges to which they are ultimately connected, or that the stiffness of the cross-bridge array depends very little on temperature and much more on the number of attached cross bridges. This is borne out by the single-cell measurements of Yamakawa et al., as cited above.

Effects of length steps.   A number of people have demonstrated changes in smooth muscle contractility following decreases in length imposed during active contraction (3, 5, 14, 21, 28, 29). While the mechanisms underlying these changes are likely to involve a number of factors, the final result is a reversible state of decreased shortening or force production. The results obtained in the present study are quite similar to those from a more extensive study of the behavior of ovarian ligament muscle (14), in which evidence was presented of cross-bridge detachment (and subsequent reattachment) following either controlled (isotonic) or abrupt shortening steps. Similar interpretations were applied to data arising from experiments involving guinea pig taenia coli (1), rat tracheal muscle (23), and single toad stomach muscle cells (30). Stiffness measurements (14, 23, 30) indicated that the effects were confined to changes in the cross-bridge population and not in connective tissue or its attachments.

Taken as a whole, the mechanical interventions cited above and employed in this paper appear to act selectively on the contractile mechanism, principally by promoting detachment of cross bridges, and not on its passive supporting components, such as parts of the extracellular matrix. The repeatability of the interventions also argues against physical damage of the supporting structures. Similarly, the pattern of mechanical changes that occur as functions of temperature indicates an active locus for the reported effects. The apparent degree of selectivity shown by these two separate approaches argues for their use in attempting to identify components of the tissue that are involved in the working of the radial constraint hypothesis. Of primary significance in this report was the finding that the shape of the curve defining the shortening-dependent stiffness was independent both of the temperature and of the state of muscle contractility. A parameter sensitivity analysis of the radial constraint model (15) showed that the shape of the measured axial stiffness curve should be highly sensitive to changes in radial connective tissue parameters and quite insensitive to changes in active tissue elements. The lack of temperature or contractility sensitivity shown by the length-stiffness curves in the present study lends support to the hypothesis that the pattern of shortening-dependent stiffness is primarily a consequence of tissue architecture, not of some property inherent in the cells or in the contractile mechanism. These present findings are consistent with the predictions made within the framework of the hypothesis in other mechanical situations (16, 19), which further support the assignment of the roles of active and passive components as identified in the present study.


   GRANTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
ACKNOWLEDGMENTS
 REFERENCES
 
This work was supported by National Science Foundation Grant IBN-9904610.


   ACKNOWLEDGMENTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
REFERENCES
 
We thank Drs. Susan Gunst and Wiltz Wagner for providing experimental tissue.


   FOOTNOTES
 

Address for reprint requests and other correspondence: R. A. Meiss, Dept. of Obstetrics and Gynecology, Indiana Univ. School of Medicine, IB 356, 975 West Walnut St., Indianapolis, IN 46202 (E-mail: igeq100{at}iupui.edu)

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. Section 1734 solely to indicate this fact.


   REFERENCES
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 

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