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1Departments of Obstetrics and Gynecology and Cellular and Integrative Physiology, Indiana University School of Medicine, and 2Department of Mechanical Engineering, Purdue School of Engineering and Technology, Indiana University-Purdue University Indianapolis, Indianapolis, Indiana 46202
Submitted 18 April 2003 ; accepted in final form 24 October 2003
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ABSTRACT |
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 TOP ABSTRACT MATERIALS AND METHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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tensegrity; isotonic shortening; length-tension curve; muscle mechanics
This paper presents an experimental analysis of the behavior of active airway smooth muscle tissue under conditions of minimal external force and consequent extreme shortening. As a framework for experimental design and analysis, a model termed the "radial constraint hypothesis" has been developed (26, 27, 29). This hypothesis holds that an activated strip of smooth muscle tissue, under a very light (or zero) isotonic load, will shorten at constant volume until it reaches 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. This expansion would be counteracted by forces developed in connective tissue arranged in a radial direction. The strained connective tissue would serve as a load on the contractile apparatus (the force being transferred by the incompressible cells and ECM), 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 were recruited in response to the reduced internal shortening velocity. This larger population would bear the additional internal load (the external load would remain constant). The working of the hypothesis is diagrammed in Fig. 1, which shows experimental data traces accompanied by diagrams of the hypothetical relationships among cells, the myofilament-cross-bridge array, connective tissue, and overall tissue dimensions.
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This hypothesis makes a number of specific predictions that can guide experiments that would test its validity. Because it posits that the equilibrium length of the shortened tissue is set by a balance between axial (cross bridge and myofilament) forces and radial (connective tissue) forces, changes in the state of either of these components should result in predictable dimensional changes in the tissue. In particular, weakening the radial elements (as by enzymatic digestion) should permit increased shortening of the tissue (2, 29) along with a reduction in axial stiffness (29). Detachment of cross bridges, on the other hand, should lead to an elongation of the active tissue in proportion to the amount of energy stored in the strained radial connective tissue. At physiological lengths, the force exerted by the contractile apparatus is balanced mainly by external loads; any imbalance results in either lengthening or shortening. At minimal lengths, however, the force exerted by the contractile apparatus (which is still capable of significant force production) is balanced only by forces set up within the tissue. 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 internal opposing forces. Previous work from this laboratory (28, 29) investigated the mechanical effects of experimentally augmenting or reducing these forces. Those experiments focused on the putative extracellular structures (connective tissue and ECM) responsible for constraining muscle shortening; the present paper will attempt to assess the contributions of active tissue elements (i.e., muscle cells and their contractile apparatus) to the mechanical behavior at short lengths. Some of the results of these studies have been presented in abstract form (30, 31).
The mechanical hypothesis under test has some features associated with the mechanical concept of tensegrity. This concept was originally developed to describe and analyze rigid mechanical structures (8, 16) and has been applied to biological structures at cellular as well as organismic levels (4, 19, 20, 48, 49). In its strictest formulation, it describes the "tensional integrity" of structures in which forces in rigid compressive elements were balanced against forces in other elements that were held in tension. In such arrangements, the overall stiffness of the structure is related to the "prestress" in the tensioned members, and removal or cutting of any element will result in the structure shifting to a new and stable size and shape. This concept has been applied, not without controversy (18), to cellular mechanics in such diverse areas as mechanotransduction (46), motility (20), development and growth (20), and resistance to external deformation (44). There has been little application of the concept to the case of soft biological tissues. Such tissues lack macroscopic rigid elements that could function in a strict formulation of the concept; it appears, however, that the incompressibility of soft tissue elements could substitute for the usual rigid struts. Ultrastructural and biochemical evidence indicates that the tensile forces within the tissue are borne by linear structures (myofilament and cross-bridge arrays, the actin cytoskeleton, and extracellular connective tissue) whose connections are localized, in part, to focal adhesion plaques at the margins of cells, across which force is transmitted by transmembrane integrin molecules. This internal "cable system" can be selectively disrupted, opening up the possibility for experimental alteration of the cable network. This could be employed as a means of assessing the degree to which the behavior of smooth muscle tissue at very short lengths can be explained as though it were a tensegrity structure. This is to be a major point of the analysis of the experiments to be presented here.
Mechanical approaches intended to test tissue tensegrity models must provide a way of both sensing internal forces and disrupting the critical elements in a specific and reproducible way. In the formulation that will be used here, one set of elements that will bear tension is the intercellular (radial) connective tissue. Previous work has shown that selective enzymatic digestion of connective tissue can affect mechanical properties in a way suggestive of a tensegrity structure (2, 29). The present paper will focus on the other tension-bearing elements, the activated myofilament array. Here, cross bridges both generate and bear tension, and they can be reversibly disrupted in a semiquantitative way by the application of large length vibrations of a magnitude sufficient to cause their detachment.
Other investigators have used longitudinal vibrations of different frequencies to interact with internal mechanical processes in isometrically contracting smooth muscle (23, 40) either at very low frequencies [for example, to mimic the perturbations due to breathing (6, 39)], or at higher frequencies, with the specific intent of detaching cross bridges (22). After vibration, the ability to redevelop tension is little affected (40), an indication that no permanent alteration is produced by the intervention (35, 45). In the present paper, length vibrations will be applied to smooth muscle during the course of isotonic contraction in an attempt to detach cross bridges bearing internal stress and thus to cause redistribution of internal strains. This should, in turn, lead to externally observable changes in tissue dimensions and forces.
A further key to the analysis of these experiments is the assumption that the changes in axial stiffness of muscle strips mirror changes in the number of attached cross bridges. Although a number of complicating factors limit the strict quantitative interpretation of the stiffness in terms of cross-bridge numbers, muscle stiffness is clearly related to its level of activation, and axial stiffness measurements should allow an indirect but semiquantitative measurement of radially directed internal stresses. Several lines of evidence do lend support to this concept (Refs. 7, 33, 47, and, with some caveats, Ref. 32), to the extent that it is used as a rather routine tool in mechanical studies.
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MATERIALS AND METHODS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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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 (25). Direct measurement of total system compliance, including that of the force transducer and all other mechanical components, gave a value of 0.93 µ/mN, which was equivalent to <0.5% of the muscle length at maximal force (e.g., 50 mN) at optimum length (e.g., 10 mm).
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 optimum length. 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.
Mechanical instrumentation. All experimental contractions were made in a digitally controlled force-clamp servo system (27, 38). 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 conditions of length or force (i.e., length vibrations or rapid force steps) could be simulated. The continuous measurement of dynamic stiffness was done, as previously described (25) 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.
Although the stiffness-measuring oscillations were kept small enough so that they had no observable effect on the contractile events (25), the large-amplitude vibrations used to disrupt cross-bridge attachments had profound effects on the contraction dynamics. The magnitude of these effects depended on the mode of contraction (whether isometric or isotonic) and on the amplitude, frequency, duration, and time of application of the vibration. Preliminary experiments showed that a vibration of a given amplitude (relative to the muscle length) was much more effective in disrupting isometric than isotonic contraction, and that its effect on isotonic contraction was dependent on the size of the afterload. Because the principal goal of the present study was to examine the state of the muscle under conditions of very low external forces, all vibrations were applied under isotonic conditions at very low afterload, although for comparison purposes the effects of vibration were also examined during isometric contractions. An episode of vibration was fully effective in disrupting the contraction in 1 s, with longer durations not producing further substantial changes in length, force, or stiffness. Abrupt application of vibration produced an initially large mechanical response, which reached a steady state with a time constant of 200 ms. Throughout the study, a duration of 1 s was routinely used. Over the frequency range of 20-40 Hz, the effectiveness of all vibration bursts of similar amplitudes was approximately equal, and a frequency of 34 Hz was generally used in this study.
The sinusoid used for the vibrations was generated in a conventional signal generator. After appropriate amplitude scaling, it was fed to a computer-gated linear modulator that combined it with the length command signal. The rise and fall times of the vibration burst were usually shaped exponentially (with a time constant of 56 ms) so that it did not present the muscle with a sudden maximal stretch at its onset. During the application of a vibration episode, the force clamp was temporarily switched into its isometric mode at the present length, and the length was oscillated about this mean value. Also during the vibration episode, the filter set used to extract the stiffness data was blanked out to prevent overloading the circuitry and thus to avoid the consequent recovery time after cessation of vibration. When the vibration was stopped, the control system returned the force clamp to either its isometric or isotonic mode, as the protocol in use required.
Experimental protocols. The basic sequence of events in an individual experimental contraction was the following. With the muscle set at the selected length (usually near Lr), an electrical stimulus was applied, and isometric force began to develop. At a selected level of force (or at a specific time), the clamp circuitry was switched into the isotonic (force-control) mode, with a very small afterload (termed the first afterload) being applied. The muscle was allowed to shorten fully, and then the vibration episode was applied for a set duration. After the vibration, either of two conditions was used. First, the clamp circuitry could be returned to the isotonic mode and a second afterload could be applied, whose amplitude depended on the particular experimental requirement. Resulting changes in muscle length were then recorded and analyzed. Alternatively, conditions could be made isometric at the previbration length, and changes in force could be analyzed. After the events of interest were completed, the system slowly stretched the muscle back to its original length.
Data recording and analysis. All experimental data traces (force, length, and force and length perturbation amplitudes) were digitized during each contraction and stored for later processing and analysis. Each contraction event was sampled 500 times over its duration of from 20 to 45 s; for higher resolution at critical phases, a dual-channel Nicolet model 4094 digital oscilloscope sampled the data at a time resolution of 1 ms. For quick 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 (SPSS) software. Statistical comparisons were made by using appropriate t-tests with either SigmaPlot or SigmaStat (SPSS).
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RESULTS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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50% of maximal force) disrupted the contraction in proportion to the amplitude of the vibration. Figure 2, left, shows a typical experimental record. To obtain a quantitative and normalized measure of the effects of vibration, the ratio of the force before and after the episode was compared with the same ratio for the stiffness. The effect of the vibration was approximately the same in reducing both the force and the stiffness. On an expanded time scale (Fig. 2, top right), the decreasing force response to successive length cycles may be seen to be exponential in form; the force peaks are fitted well by a single exponential function. (In this illustration, as in Fig. 5, the onset of the vibration burst was not shaped.) The parameters of this force decline were measured in a series of six muscles. Normalized values at the force peaks were fitted to the exponential function shown in the figure. No systematic deviations from an exponential relationship were observed. For a mean vibration frequency of 33.8 ± 3.2 Hz, the time constant of the decline in force was 0.2066 ± 0.031 s. On a per cycle basis, the number of cycles to reduce the force by 63% was 7.23 ± 0.37. Effects of varying several vibration parameters are shown in Fig. 2, bottom right. Whether it was the amplitude (3-40% of Lr), the frequency (5-40 Hz), or the duration of the episode (0.32-4.0 s) that was varied, the final effects on force and stiffness were similar. The response to vibration amplitude also depended on the amount of developed force (data not shown), with a given amplitude being relatively more effective in disrupting contraction at higher developed forces. The close correspondence between the effects on force and stiffness suggests that they are related to the physical disruption of force-bearing cross bridges (see DISCUSSION).
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Effects of length vibrations on contracting muscle: isotonic conditions. Applying longitudinal vibrations to muscle undergoing isotonic contraction at very low afterloads also resulted in a temporary disruption of contractile activity. In this case, the force was not affected because it was controlled by the feedback system. However, muscle stiffness again was reduced in approximate proportion to the amplitude of the vibration, as shown in Fig. 3.
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Vibration amplitude was normalized to the muscle length at which the vibration was applied; the larger vibrations involved changes in muscle length on the order of 25% of the length at which the vibration was applied. Figure 3, inset, shows the pooled results from 83 such determinations on 12 muscles. The correlation was highly significant; the pooled data were fitted with an arbitrary third-degree polynomial with an R value of 0.8863. These results again support the assumption that the effects of the vibration were related to cross-bridge detachment. In both the isometric and the isotonic cases, the disruption was only temporary. Within the same contraction, recovery was nearly complete when the stimulus was maintained, and subsequent contractions showed no residual effect. Also related to the changes in force and stiffness was the load-bearing ability (Fig. 4). In Fig. 4, right (open circles), a muscle strip was allowed to shorten fully under a very low first afterload, but no vibration was applied. When shortening was complete, the afterload was increased abruptly (second afterload), and the muscle extended. This effect was approximately linear with afterload (Fig. 4, right, bottom curve). The same muscle was then subjected to a 1-s vibration followed by an increased second afterload as before. The extension of the muscle was significantly greater, and the slope of the relationship also was greater. The figure shows the systematic effect of vibration amplitude on muscle extension. At a given vibration amplitude, the yielding of the muscle was proportional to the size of the second afterload. With larger vibration amplitudes, the muscle yielded more under a given second afterload, again suggesting that the vibration was forcibly disrupting load-bearing cross bridges. This relationship was determined on a series of 6 muscles. The slope of the load-extension curve for the effects of vibration and afterload was 2.38 ± 1.09 times as great as that for afterload steps alone. The mean difference between the slopes was 0.571 ± 0.037 (P = 0.013). The curve for afterload step alone passed through the origin (intercept = -0.0367 ± 0.038; not significantly different from 0), whereas the intercept of the vibration+load curve was significantly greater than zero (0.2713 ± 0.047).
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The foregoing results indicate, provisionally at least, that the effect of vibration was the reversible disruption of attached cross bridges. The remainder of the results presented here will deal with the use of applied length vibrations during and after isotonic shortening as a tool to investigate the accommodation of the muscle tissue dimensions to the disruption of internal force-bearing structures in a proposed tensegrity-like system.
Muscle responses during and after oscillatory vibration. Figure 5 shows the typical events surrounding a vibration episode applied at the extreme of isotonic shortening. Of particular interest here is the behavior of the muscle during the vibration. The vibration began after the muscle had shortened to equilibrium under a very small afterload (to a length of 3.2 mm, with force at 1.0 mN); recall that, during the vibration episode, the muscle was under length control, whereas it was under force control during the isotonic shortening. Note that at this length the vibration (amplitude 1.1 mm peak to peak) caused both tension and compression in the muscle (Fig. 5, middle left). The length-tension behavior of the preparation during vibration is shown in Fig. 5, bottom right. The response, nearly symmetrical in form, deviated from linearity at its extremes, and the loops were slightly open. As was the case for the isometrically contracting muscle (Fig. 2), the force amplitude progressively fell in an exponential fashion with each successive vibration peak. When a similar vibration was applied to the resting muscle (at the same length), there was virtually no corresponding force response (see Fig. 5), indicating that the responses of the stimulated muscle arose from active structures within the muscle and not merely from external compression of the tissue.
When the vibration episode was terminated and the system was returned to force control, the muscle assumed a new equilibrium length that was somewhat longer than that before the vibration episode, although the afterload force was the same. This indicated that the muscle had reextended itself or had been reextended by the small afterload (cf. Fig. 4). The muscle was also significantly less stiff (Fig. 4, bottom left). As long as the stimulus was maintained, the muscle tended to reshorten back to its previbration length. Insight into this behavior is provided by Fig. 6. Figure 6, right, shows recordings of representative individual events with increasing afterload, which is associated with the postvibration behavior. Because of the importance of this finding in testing the working hypothesis, similar measurements were made on a series of muscle preparations. Determinations made on 10 separate muscle strips (mean Lr 7.50 ± 0.53 mm) showed no exceptions to the nonzero intercept value. The effect of the second afterload was approximately linear, but the most significant finding was that the intercept of the relationship was much greater than zero. Compared with the length immediately before the vibration, the zero-load extension was 11.93 ± 2.59% of the muscle length at which the vibration began. A t-test showed this value to be highly significant (t = 14.55; P < 0.00001).
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Comparison of isotonic and isometric postvibration responses. The two consecutive contractions shown in Fig. 7 show related responses that depended on the postvibration conditions of contraction. Figure 7, left, shows an isotonic contraction with a vibration imposed at the end of shortening; immediately after the cessation of the vibration episode, isotonic conditions were reestablished. As the detailed plot with expanded axes shows, the muscle underwent a 0.4-mm extension and then began a monotonic recovery at the small afterload force that it had been bearing just before the vibration. On the subsequent contraction, postvibration conditions were held isometric at the length the muscle had reached just before the vibration. In this case, the muscle exerted a force against the transducer; i.e., the force was negative, and then it began to increase to its former value. This force recoil, like its length counterpart, was sensitive to the amplitude of the vibration that disrupted the contraction.
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Figure 8 shows that there were significant differences in the pattern of the postvibrational responses. The initial extent of the isotonic recoil (Fig. 8, left) was directly related to vibration amplitude, and the recovery pathway was monotonically upward. By contrast, the isometric recoil (Fig. 8, right) was more complex. The amount of initial negative force depended on vibration in a complex way, and for the lower amplitudes it recovered quickly and steadily after the vibration episode; but for the larger vibration amplitudes, the initial negative force was less, and recovery was increasingly delayed. After the larger vibrations, there was a distinct latent period during which the force remained negative and steady. Another significant observation was in the pattern of stiffness recovery. In Fig. 8, bottom, the small open circles show the recovery of stiffness (both plotted with same vertical axis, 0-0.6 mN/µm, not shown). Note that in both cases, the stiffness increases monotonically, without any latent period as was the case for the force recovery.
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These patterns are summarized in Fig. 9. Figure 9, top and middle, shows the results of averaging postvibration recovery data from 16 muscles. For each muscle, both isotonic and isometric measurements were made, and the recovery data from the largest-used vibration amplitude pair for each muscle were averaged point by point. The data are shown as mean values, along with their 95% confidence intervals. In these averaged traces, the differences illustrated in Fig. 9 are preserved; the force latency is a bit blurred but is still evident, as indicated. For a better estimate of this parameter, it was measured directly for each of the 16 muscles by fitting a straight line to the linear portion of the force recovery and determining at which time point it intersected the horizontal line at the greatest negative force. This approach gave a mean latency of 0.650 s with a 95% confidence interval of ±0.127, which corresponds well with the value determined from the averaged traces. Measurements (not shown) of the phase angle between the length and force sinusoids used to measure the stiffness showed it to be almost zero, and there was no change in the phase angle as the sign of the recovery force changed from negative to positive.
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To summarize the population data for the recovery process, the most salient features of the isotonic and isometric responses were chosen. For isotonic recovery, the initial postvibration extension was considered as a function of the prior vibration amplitude in contractions without significant afterload (cf. Figs. 4 and 6). For 40 measurements on 6 muscle strips (Fig. 9, bottom left), the relation showed a highly significant correlation. The feature used to summarize the isometric recovery was the duration of the latent period (Fig. 6, bottom right). This time period was determined as outlined in the paragraph above.
Despite some approximations inherent in this method, there was a very strong correlation between the delay in force recovery and the amplitude of the prior vibration.
Axial stiffness as a predictor of internal strain. The previous measurements of length recoil were all made at the peak of isotonic shortening and hence at the peak of axial stiffness. To test for a more complete association between axial stiffness and the strain of internal elastic elements, a series of measurements was made during the rise of the axial stiffness. Figure 10, top left, shows the record of the development of axial stiffness over the time course of isotonic shortening. The solid line shows the relationship measured continuously during a single contraction. The open circles are taken from a series of six consecutive contractions. They represent the stiffness just before a 1-s vibration episode, immediately after which the rapid extension of the muscle was measured as before. The recoil measurements are shown as the solid circles in Fig. 10, top right, plotted as a function of the muscle length just preceding the application of vibration. Also shown are the initial stiffness points from Fig. 10, top left, as well as the shortening-dependent stiffness for a single contraction. All of these quantities show the same dependence on muscle length, an observation that is emphasized in the plot in Fig. 10, bottom left, which shows a very high correlation between the prior stiffness and the recoil extension. This finding was further supported by pooling similar results from nine muscle strips (a total of 88 data measurements). The data were normalized to make them more directly comparable, because the absolute values of stiffness and shortening varied significantly from strip to strip. The recoil extension was normalized to the length just before the vibration episode, and the stiffness was normalized to the value at the maximal extent of isotonic shortening (e.g., the 10-s point in Fig. 10, top left). Linear regression analysis yielded a slope of 1.039 ± 0.106, an intercept of -0.1356 ± 0.0723, and a correlation coefficient of 0.7253. The P value for the slope was <0.0001. This correlation was highly significant, and no systematic deviation from linearity was detected.
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DISCUSSION |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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The hypothesis views the final length attained by a fully shortened, externally unloaded, smooth muscle strip as resulting from an equilibrium between forces causing shortening and those opposing it. Detaching strained structures in either direction should allow the overall tissue dimensions to adjust in such a way as to reestablish the equilibrium between the two sets of forces. The previous work (see introduction) involving enzymatic digestion of active tissue revealed an increase in shortening and a decrease in axial stiffness, indicating that radial forces were diminished. The experimental aim in this paper was to disrupt cross-bridge connections, which act in the longitudinal direction, so that a new equilibrium of internal forces could be established. For this reason, the first part of RESULTS presented evidence that active cross-bridge interactions can be reversibly disrupted by the application of cyclic stretches and releases (longitudinal vibrations) to contracting smooth muscle.
Cross-bridge detachment by length vibration. Contracting muscle undergoes obvious progressive mechanical changes during and after the large stretches and releases of an applied vibration. The use of longitudinal vibrations to interrupt an active contraction has been employed in the past to study the kinetics of isometric force recovery (21, 22, 34) in bladder smooth muscle. In that case (as in the present paper) the frequency of the vibrations was very high compared with the inherent cycling time of cross bridges, because the aim in both cases was to disrupt ongoing contraction as a means to an experimental end. Other workers (6, 12) have also employed length oscillations to contracting muscle at lower frequencies (to mimic the tidal effects of breathing). Such low-frequency oscillations also disrupt cross-bridge interactions, but in this case there is a complex interaction between the perturbing frequency and the cross-bridge dynamics that does not result in a sudden and large-scale detachment of active bridges. In both cases, however, there is good evidence that the external perturbations were having a direct effect on the integrity of cross-bridge interactions.
The precise relationship between muscle stiffness and the state of the cross-bridge population is a matter of some controversy, especially in investigations of the fundamental mechanism of contraction. For the purposes of this study, the exact constant of proportionality is not of major importance, because it is relative changes that are of interest. Although other compliant structures within the muscle may modify its overall response, a fully relaxed muscle (with most cross bridges unattached) is also in its most compliant state, and a fully contracted muscle (with maximal cross-bridge attachment) is at its stiffest. Between these extremes, an approximate proportionality must exist. Thus the low stiffness during unloaded (low force) isotonic shortening implies a relatively small population of attached cross bridges, whereas the sudden increase in stiffness near the end of the shortening implies a rapid increase in the population size, a change associated with the recruitment of a length-dependent internal load.
In the present experiments, the postvibration stiffness under isometric conditions was reduced in direct proportion to the reduction in force (Fig. 2), regardless of the parameters of the vibration. This implies that the individual force generators (cross bridges) are also responsible for the stiffness of the muscle. The exponential decline in peak force during a vibration episode (Figs. 2 and 5) may be explained, on the basis of cross-bridge mechanisms, as follows. Because the muscle cells are small compared with the overall tissue dimensions, their force (and external forces applied to them) must be transmitted through the active cells, the same ones whose cross bridges are generating force. Individual cross bridges would detach when the shearing forces to which they were subjected were greater than they could support, and the population of attached bridges would become smaller. Given the close relationships among force, stiffness, and cross-bridge numbers, this would result in an increase in the overall compliance of the tissue (i.e., a reduction in stiffness). The next cycle of stretch in the longitudinal vibration would be delivered to (and through) a more compliant tissue, one less able to cause individual cross bridges to become overstressed, and fewer would be broken during that cycle. However, the muscle compliance would still be increasing in proportion to the (somewhat smaller) number of bridges broken. Thus each subsequent cycle would be less effective in breaking cross bridges until a steady state was reached. Increasing the vibration amplitude at this point would lead to another exponential decline and a subsequent (lower) steady-state force response (unpublished observations). Because the effectiveness in detaching cross bridges would depend on how many are still attached, this process would inherently lead to the observed exponential decline in the cyclic force response to a constant-amplitude applied vibration. At the steady state (Fig. 5), the oscillatory relationship between force and length shows somewhat open loops, implying a background viscosity on which the active responses are superimposed.
Other factors favoring a cross bridge-based explanation include the parallel changes in isometric force and stiffness during the recovery from a vibration episode (cf. Fig. 9, top left), the increased extensibility (i.e., reduction in force-bearing ability; cf. Fig. 6), and the rapid recovery of force and stiffness after the episode. The behavior in subsequent contractions appears to be independent of, and undiminished by, the previous mechanical history and the elapsed time between contractions.
Although the basis of the change in stiffness after large vibrations is most likely to be found in "classical" cross-bridge interactions, other possibilities may exist. It has been shown that resting skeletal muscle exhibits the property of thixotropy (36), in which the short-range elastic component of the muscle suddenly yields after a small amount of stretch. Active smooth muscle shows a similar behavior (24) that has also been attributed to cross-bridge interaction. There is also the possibility, however, that the behavior may be due to the mechanical properties of the colloidal gel that is present in the ECM, i.e., a material property. In particular, the application of sudden shearing forces to the ECM could result in a rapid decrease in its viscosity, a property found in a number of natural and synthetic gels. Although such a phenomenon might be invoked to explain some of the vibration-induced changes in stiffness that are the result of large vibrations, it is difficult to relate the stability and shape of the isotonic length-stiffness curve to a material property rather than to discrete elements such as cross bridges, myofilaments, and connective tissue. This latter view is most strongly supported by the results reported here.
A question also arises regarding the independent contribution of intracellular structures (in addition to cross bridges) to the measured stiffness of the tracheal muscle strips. At moderate lengths (near Lr), the axial stiffness is clearly related to cross-bridge activity, as outlined above. There are apparently no published data regarding transverse tissue stiffness at these lengths, and it is presumably not a major factor in the mechanical response. There is the possibility, however, that at the very short lengths studied here, there may be a cellular component to the radial (transverse) stiffness. Measurements of the stiffness of cultured tracheal smooth muscle cells (1) have shown changes in cell stiffness that are related to the level of contractile activation. The contractile response is also related to the level of actin polymerization; this observation implicates cytoskeletal elements in the development of cell stiffness. A direct comparison between isolated cells and cells constrained within a tissue is difficult, however, because cells in a tissue possess a high degree of imposed longitudinal order, whereas individual cells in culture have a much more varied orientation of their contractile activity, as shown by the multiple orientations of cytoskeletal elements (1). There is also evidence that the cytoskeletal structures are subject to remodeling during the course of a contraction (13) and that there are changes in contractile function (force development) associated with the remodeling. Whether such cytoskeletal changes would also result in an increase in transverse stiffness of a isolated cell during isotonic contraction has not been approached experimentally. Studies of freely shortening isolated tracheal muscle cells (5) have shown that these cells are capable of large amounts of shortening (at scaled velocities higher than those measured in intact tissue) and that maximally shortened cells showed little tendency to reelongate after agonist was removed. Isolated cells (by definition) do not have mechanical connections to the contractile systems of their neighbors, and it is likely that they shorten under quite different contractile system configurations than do tissue-bound cells. It may be that development of radial stiffness (and the storage of elastic energy) is not possible in isolated cells, or it may imply that the structures, which could bear such tension, were sensitive to the level of activation. Given these considerations, the possibility of an intracellular contribution to the observed transverse tissue stiffness at short lengths cannot be dismissed, but the evidence presented here and earlier (29) indicates that its role is likely to be less important than the architecturally based tissue forces.
Vibration-induced changes in tissue dimensions and subsequent recovery. Recent work from this laboratory (unpublished experiments and Refs. 30, 31) has emphasized that, even at very short lengths, the contractile mechanism is still capable of generating considerable force. Because stiffness is still appreciable at these short lengths, an important axial force-transmission pathway must be directly from cell to cell through a very stiff mechanical connection, which would permit external length changes to affect cross-bridge interactions. According to the working hypothesis, breaking cross bridges should result in a change of the shape (i.e., lengthening) of the highly shortened muscle as strained radial elastic elements recoil. This change should be independent of external forces and should bear a definite relationship to the extent of the cross-bridge breaking and, hence to the amplitude of the vibration. Relevant observations are shown in Figs. 4, 5, 6, 7, 8, 9. The findings illustrated in Fig. 6 (and associated text), with its strongly nonzero intercept, effectively rule out the possibility that the observed lengthening (at near-zero force) was due to external (afterload) forces. Although the dimension directly measured was the tissue length (with a mean change of 11.9%; see RESULTS), the change in tissue diameter (calculated to be on the order of a 5% decrease) can be directly inferred, even though current instrumentation did not allow a direct measurement. Postvibration recovery of the length change was associated with a monotonic decrease in length and a similar steady increase in stiffness, implying that the driving force for the reshortening was the progressive reattachment and cycling of cross bridges previously uncoupled by the vibration. It also implied that the cells (i.e., the axial elements) were never completely unloaded. From a tissue-geometry standpoint, the internal redistribution of forces during isotonic recovery is quite similar to that which had taken place during the initial isotonic shortening.
Under isometric postvibration conditions, preventing the muscle from elongating by the presence of fixed end attachments should result in a force being applied to the transducer by the muscle, a behavior that is the analog of the isotonic extension discussed above. That this negative force would be supplied by passive tissue elements, and not by unusual cross-bridge activity, is supported by the monotonic increase in stiffness during recovery, even while external force is negative. The lack of changes in the stiffness phase angle during the transition from negative to positive recovery forces also supports the idea that, from the perspective of the myofilament/cross-bridge array, forces are always positive (i.e., tension producing). In the isometric recovery case, the complex time-course of force recovery would reflect the complex geometric relationships between cross-bridge and radial forces during the reattachment process and the redistribution of internal strain.
Toward a proposed internal architecture for tracheal muscle tissue. The present study, along with previous work, supports the concept that the length-dependent stiffness behavior is the result of the actions of sets of anatomically discrete components. The role of the cross-bridge/myofilament component is supported by the results of the experiments designed to detach cross bridges and to follow their subsequent reattachment (cf. Figs. 7, 8, 9). Besides some electron microscopic evidence (9-11), the presence of passive radial connective tissue elements is supported by previous work that has demonstrated the stability of the shape of the isotonic force-stiffness relationship (27, 29). Interventions that would be expected to have significant effects on cross-bridge function (i.e., temperature changes, partial activation, prior contraction history, starting length) have minimal effect on the shape of the curve describing the dependence of stiffness on instantaneous length during isotonic shortening. Given the present state of knowledge, both anatomic and functional, about the behavior of smooth muscle at very short lengths, it may be useful to examine the degree to which the radial constraint hypothesis is in accord with the phenomenon of tensegrity as its biological application is currently understood (17).
Most of the work on the biological implications of tensegrity has concerned itself with cellular phenomena (15, 41, 43). Although there is significant controversy in the field (e.g., see Ref. 18), some of it concerned with definitions of the terms involved, there appear to be some features that are agreed to be essential to demonstrating the operation of a tensegrity system (4, 43). There must be discrete elements under continuous tension, and this tension must be balanced by compression elsewhere in the system. This is usually taken to mean that there should be some sort of rigid struts bearing the compressive force, and in isolated cells microtubules have been suggested for this role (42, 43); significant experimental evidence indicates that this may be the case in a number of situations. The role of cables (tensile members) is played by cytoskeletal (actin) filaments anchored at focal adhesion plaques at the margins of the cells (37, 46); these also serve as cellular attachment points to a relatively stiff substrate. This attachment also allows for the required presence of "prestress," a background level of tension and compression that causes the structure to have a definite shape (42, 43). Application of the tensegrity concept to the next higher level of organization, in this case smooth muscle tissue, would require that the same (or analogous) structures and forces be present.
In the case of the tracheal muscle preparations studied here, the behavior of interest occurred only at the shortest lengths, where the putative radial forces were maximal. At this extreme shortening, the direct experimental evidence for the nature of the stressed members consisted of the observed longitudinal stiffness increase in the absence of significant external loading, the forced extension after vibration, and the force response during the vibration itself. The presence of two orientations of internal strain existing in the unperturbed tissue is an inference that is supported by behavior like that shown in Fig. 10, where the amount of recoil (which could be manifested as either a length or force adjustment) was related to the prior stiffness in a rather direct and quantitative way. In particular, increased axial stiffness (interpreted as arising from cross bridges opposing radially disposed reactive forces) is manifested as a correspondingly increased amount of postvibration extension or negative force. Note also that the length-tension behavior during vibration (cf. Fig. 5) was quite symmetrical even though highly nonlinear. This symmetry argues for the quantitative similarity of the two opposing sets of elastic elements when the length is oscillated about its natural equilibrium point at the end of its active shortening.
The foregoing discussion is also related to the question of prestress, another aspect of a tensegrity structure (42). This refers to the proportional increase of the stiffness of a structure as stress is applied. In the present case, the observed rapid increase in stiffness as the muscle approaches its equilibrium length is interpreted as the result of the internal forces applied by the contractile apparatus. Although this force is implied rather than directly measured, its reality is demonstrated by the fact that the postvibration muscle exerted a significant force against the rigid tension transducer (Figs. 7, 8, 9), indicating that the radial connective tissue had been bearing an actual tensile force. Had the muscle been given a more compliant attachment against which to extend itself after vibration, it would have been possible to express the internally stored mechanical energy in quantitative terms. Given the validity of these inferences, the proportionality shown in Fig. 10 between prior stiffness and the extent of forced extension (as a proxy for the internally applied prestress) indicates indirectly that this criterion for a tensegrity structure was met.
A further requirement of a tensegrity model is that the tension-bearing members must be structurally discrete. There is now ample evidence (12, 14) to support the concept that the contractile apparatus is organized in discrete filamentous actinmyosin interactions whose connection to the adjacent cells (or connective tissue) is made via integrin molecules organized into localized patches along the cell margins. Likewise, collagen filaments of various orientations, some in a radial direction, are present to serve as cables bearing tensile forces opposed to those generated by the contractile apparatus. The domain of the anatomic tension-bearing elements of the tensegrity structure is thereby extended from the individual cells to the tissue as a whole.
What remains is the question of the compression-bearing members in the structure. Evidence indicates that at the cellular level, microtubules are capable of supporting compression (43). In smooth muscle, at the tissue level, discrete "struts" are apparently lacking; however, the incompressibility and resistance to flow of both the extracellular and intracellular contents could provide a virtual "fulcrum" across which the discrete radial and axial forces are balanced. It would thus serve as a distributed, rather than a discrete, component for supporting the compressive forces. In earlier work from this laboratory (27), it was demonstrated that, for the same muscle, osmotic adjustments of the tissue volume (the virtual strut) were correlated with changes in the stiffness at a common length. Reductions in tissue volume could be considered analogous to removing supporting members, reducing the prestress, and thereby making the system less stiff.
At some point, the question becomes one of definitions. We have shown that predictable changes in the tissue shape can be explained as the response to changes in the internal balance of forces, both of tension and compression. In this regard, the system could be regarded as tensegrity-like, although it does not meet the formal requirement of having discrete compression-bearing structural elements. Regardless of the formal definition employed, the empirical evidence presented here supports the radial constraint hypothesis as a structurally based mechanism that can account for tissue dimensional changes in a consistent way that suggests numerous experimental opportunities for investigating the functional architecture and the physiological function of an important class of biological tissues.
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, Data points from the 4 events at the right. Inset: nonzero distribution of the y-intercepts from the 10 individual experiments in the data pool.
, Associated stiffness traces (both with a 0.0-0.6 mN/µm y-axis, not shown) are shown at bottom.
