Characterization of cross-bridge elasticity and kinetics of cross-bridge cycling during force development in single smooth muscle cells

Force development in smooth muscle, as in skeletal muscle, is believed to reflect recruitment of force-generating myosin cross-bridges. However, little is known about the events underlying cross-bridge recruitment as the muscle cell approaches peak isometric force and then enters a period of tension maintenance. In the present studies on single smooth muscle cells isolated from the toad (Bufo marinus) stomach muscularis, active muscle stiffness, calculated from the force response to small sinusoidal length changes (0.5% cell length, 250 Hz), was utilized to estimate the relative number of attached cross-bridges. By comparing stiffness during initial force development to stiffness during force redevelopment immediately after a quick release imposed at peak force, we propose that the instantaneous active stiffness of the cell reflects both a linearly elastic cross-bridge element having 1.5 times the compliance of the cross-bridge in frog skeletal muscle and a series elastic component having an exponential length-force relationship. At the onset of force development, the ratio of stiffness to force was 2.5 times greater than at peak isometric force. These data suggest that, upon activation, cross-bridges attach in at least two states (i.e., low-force-producing and high-force-producing) and redistribute to a steady state distribution at peak isometric force. The possibility that the cross-bridge cycling rate was modulated with time was also investigated by analyzing the time course of tension recovery to small, rapid step length changes (0.5% cell length in 2.5 ms) imposed during initial force development, at peak force, and after 15 s of tension maintenance. The rate of tension recovery slowed continuously throughout force development following activation and slowed further as force was maintained. Our results suggest that the kinetics of force production in smooth muscle may involve a redistribution of cross-bridge populations between two attached states and that the average cycling rate of these cross-bridges becomes slower with time during contraction.     

Force-velocity constants in smooth muscle: afterloaded isotonic and quick-release methods

In using pharmacologic stimuli, force-velocity (FV) curves are usually obtained by the method of quick release (QR) and redevelopment of shortening at peak tetanic tension; the advantage of the method being that the active state is at maximum. However, the QR may itself reduce the intensity of the active state and result in reduced values of FV constants. We tested this by delineating FV curves in canine tracheal smooth muscle using both conventional afterloaded isotonic contractions (ALI), and redevelopment of shortening after QR methods. For both these studies a supramaximal tetanizing electrical stimulus was used. The analysis of 11 experiments revealed that the latter method resulted in statistically significant reductions of all FV constants except for Po (maximum isometric tetanic tension). The means and standard errors for the sets of constants for the ALI and QR, respectively, are as follows: Vmax (maximum velocity of shortening) = 0.275 lo (optimal muscle length)/s +/- 0.024 (SE), and 0.216 lo/s + 0.023; a (hyperbolic constant with units of force) = 294 g/cm2 +/- 35 and 236 g/cm2 +/- 32; b (hyperbolic constant with units of velocity) = 0.059 lo +/- 0.004 and 0.039 lo/s +/- 0.005; a/Po = 0.214 +/- 0.028 and 0.182 +/- 0.026; and Po = 1.362 kg/cm2 +/- 0.106 and 1.294 kg/cm2 +/- 0.097. These data clearly show that the quick-release method for measuring force-velocity relationships in canine smooth muscle results in significant underestimates of muscle shortening properties.     

Muscular force production after concentric contraction

The steady-state force following active shortening does not reach the maximum isometric force associated with the final length. Isolated extensor digitorum longus and soleus muscles from mice (NMRI strain) were used to investigate the force produced by a muscle, and some parameters hypothetically influencing this shortening-induced force depression. The muscles were pre-stimulated at fixed length, shortened and then held isometrically to give maximum post-shortening forces, before de-stimulation. The shortening magnitude was 0.18, 0.36 or 0.72mm (about 2-7% of optimal length), time of shortening was chosen as 0.03, 0.06 and 0.12s, and final length as +0.72, 0 and -0.72mm, related to optimal length. The mechanical work during active shortening was evaluated by integrating the product of force and shortening velocity over the shortening period. The results show a positive correlation between the force depression and the mechanical work, whereas the force depression was not correlated to the velocity of shortening. Depression of the passive force component was also observed following all stimulations. Experiments show that the fully stimulated redevelopment of isometric force following concentric contraction follows a time function similar to the creation of force when isometric muscle is initially stimulated. The conclusion is that the isometric force development after active shortening can be well described by an asymptotic force which is decided by the produced work, and the initial isometric time constant.     

Shortening amplitude affects the incomplete force recovery after active shortening in mouse soleus muscle

Compared to isometric contraction, the force producing capacity of muscle is reduced (force depression, FD) after a work producing shortening phase. It has been suggested that FD results from an inhibition of cross-bridge binding. Because the rate constants of the exponential force (re)development are thought to be primarily determined by cross-bridge attachment/detachment rate, we aimed to investigate the components of force redevelopment (REDEV) after 0.6, 1.2 and 2.4 mm shortening, resulting in varying amounts of FD (from about 5% to about 16%), in mouse soleus muscle (n=11). Compared to isometric force development (DEV), the time to reach steady-state during REDEV was about 3 times longer (370 versus 1261 ms) increasing with increasing amplitude. Contrary to a single, a double exponential function with one component set equal to the rate constant of DEV (14.3 s^?1), accurately described REDEV (RMS<0.8%). The rate constant of the additional slow component decreased with increasing shortening amplitude and was associated with work delivered during shortening (R²=0.75) and FD (R²=0.77). We concluded that a work related slow exponential component is induced to the trajectory of incomplete force recovery after shortening, causing FD. These results suggest that after shortening, aside from cross-bridges with normal attachment/detachment rate, cross-bridges with reduced cycling rate are active.     

Effects of speed and distance of muscle shortening on force depression during voluntary contractions

The purpose of this study was to determine the influence of speed and distance of muscle shortening on the amount of force depression for voluntary contractions. Two experimental tests were performed. In the first test, subjects performed isometric knee extensor contractions following muscle shortening produced by isokinetic knee extensions over the range 25-50 degrees. In the second test, subjects performed isometric knee extensor contractions following muscle shortening produced by isokinetic knee extensions at two speeds: 20 and 240 degrees /s. Knee extensor moments, surface electromyographical (EMG) signals of quadriceps femoris, and interpolated twitch moments were measured during all contractions and were compared with the corresponding values obtained during purely isometric contractions. Force depression following muscle shortening for the voluntary contractions tested in this study did not depend on the distance or the speed of muscle shortening. These results are in contrast to the corresponding results in the literature obtained using artificial electrical stimulation in which force depression was always found to be directly related to the distance of shortening and inversely related to the speed of shortening. The difference in force depression as a function of the distance and speed of muscle shortening between voluntary and artificial electrical stimulation may be associated with changes in activation following the voluntary shortening contractions, whereas activation is controlled and constant in all artificial stimulation protocols.     

Dynamic and steady state characteristics of the rabbit gastrocnemius muscle determined in series measurements

1. Within the range of the given conditions of measuring static and dynamic properties of the rabbit gastrocnemius muscle the following results were obtained: a) the dependence of the maxima of isotonic shortening upon the relative length of the muscle at constant load is linear; b) the parameters of the non-linear dependence of the passive elastic force of the muscle upon its relative length (measured in series) were identified using asymptotic regression; c) the time course of isotonic contractions (at an interval from 0 to 0.3 s after the beginning of stimulation) could be satisfactorily approximated by responses of a linear system to a step-function; d) the time course of isometric contractions (at an interval from 0 to 0.3 s after the beginning of stimulation) could be closely approximated by responses of a linear system to a step-function. 2. The time constants of isotonic and isometric contractions were determined as the parameters of the corresponding linear systems. 3. The maximum rates of the isometric and isotonic contractions were determined as maxima of the first derivatives of the responses of the corresponding models. 4. The experimental set-up made it possible to compare the values of the parameters concomitantly followed at various muscle lengths and at various loads.     

Kinetics of thin filament activation probed by fluorescence of N-((2-(Iodoacetoxy)ethyl)-N-methyl)amino-7-nitrobenz-2-oxa-1, 3-diazole-labeled troponin I incorporated into skinned fibers of rabbit psoas muscle: implications for regulation of muscle contraction

Making use of troponin with fluorescently labeled troponin I subunit (N-((2-(iodoacetoxy)ethyl)-N-methyl)amino-7-nitrobenz-2-oxa-1, 3-diazole-troponin I, IANBD-TnI) that had previously been described in solution studies as a probe for thin filament activation (. Proc. Natl. Acad. Sci. 77:7209-7213), we present a new approach that allows the kinetics of thin filament activation to be studied in skinned muscle fibers. After the exchange of native troponin for fluorescently labeled troponin, the fluorescence intensity is sensitive to both changes in calcium concentration and actin attachment of cross-bridges in their strong binding states (. Biophys. J. 77:000-000). Imposing rapid changes in the fraction of strongly attached cross-bridges, e.g., by switching from isometric contraction to high-speed shortening, causes changes in thin filament activation at fixed Ca(2+) concentrations that can be followed by recording fluorescence intensity. Upon changing to high-speed shortening we observed small (<20%) changes in fluorescence that became faster at higher Ca(2+) concentrations. At all Ca(2+) concentrations, these changes are more than 10-fold faster than force redevelopment subsequent to the period of unloaded shortening. We interpret this as an indication that equilibration among different states of the thin filament is rapid and becomes faster as Ca(2+) is raised. Fast equilibration suggests that the rate constant of force redevelopment is not limited by changes in the activation level of thin filaments induced by the isotonic contraction before force redevelopment. Instead, our modeling shows that, in agreement with our previous proposal for the regulation of muscle contraction, a rapid and Ca(2+)-dependent equilibration among different states of the thin filament can fully account for the Ca(2+) dependence of force redevelopment and the fluorescence changes described in this study.     

Active and passive components in the length-dependent stiffness of tracheal smooth muscle during isotonic shortening.

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 (Q(10)) identified them as either active or passive. Isotonic shortening velocity and rate of isometric force development had high Q(10) values (2.54 and 2.13, respectively); isometric stiffness showed Q(10) 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.     

Tension recovery in permeabilized rat soleus muscle fibers after rapid shortening and restretch

Permeabilized rat soleus muscle fibers were subjected to rapid shortening/restretch protocols (20% muscle length, 20 ms duration) in solutions with pCa values ranging from 6.5 to 4.5. Force redeveloped after each restretch but temporarily exceeded the steady-state isometric tension reaching a maximum value approximately 2.5 s after relengthening. The relative size of the overshoot was <5% in pCa 6.5 and pCa 4.5 solutions but equaled 17% +/- 4% at pCa 6.0 (approximately half-maximal Ca2+ activation). Muscle stiffness was estimated during pCa 6.0 activations by imposing length steps at different time intervals after repeated shortening/restretch perturbations. Relative stiffness and relative tension were correlated (p < 0.001) during recovery, suggesting that tension overshoots reflect a temporary increase in the number of attached cross-bridges. Rates of tension recovery (k(tr)) correlated (p < 0.001) with the relative residual force prevailing immediately after restretch. Force also recovered to the isometric value more quickly at 5.7 < or = pCa < or = 5.9 than at pCa 4.5 (ANOVA, p < 0.05). These results show that k(tr) measurements underestimate the rate of isometric force development during submaximal Ca2+ activations and suggest that the rate of tension recovery is limited primarily by the availability of actin binding sites.     

Attenuated fatigue in slow twitch skeletal muscle during isotonic exercise in rats with chronic heart failure

During isometric contractions, slow twitch soleus muscles (SOL) from rats with chronic heart failure (chf) are more fatigable than those of sham animals. However, a muscle normally shortens during activity and fatigue development is highly task dependent. Therefore, we examined the development of skeletal muscle fatigue during shortening (isotonic) contractions in chf and sham-operated rats. Six weeks following coronary artery ligation, infarcted animals were classified as failing (chf) if left ventricle end diastolic pressure was >15 mmHg. During isoflurane anaesthesia, SOL with intact blood supply was stimulated (1s on 1s off) at 30 Hz for 15 min and allowed to shorten isotonically against a constant afterload. Muscle temperature was maintained at 37°C. In resting muscle, maximum isometric force (F(max)) and the concentrations of ATP and CrP were not different in the two groups. During stimulation, F(max) and the concentrations declined in parallel sham and chf. Fatigue, which was evident as reduced shortening during stimulation, was also not different in the two groups. The isometric force decline was fitted to a bi-exponential decay equation. Both time constants increased transiently and returned to initial values after approximately 200 s of the fatigue protocol. This resulted in a transient rise in baseline tension between stimulations, although this effect which was less prominent in chf than sham. Myosin light chain 2s phosphorylation declined in both groups after 100 s of isotonic contractions, and remained at this level throughout 15 min of stimulation. In spite of higher energy demand during isotonic than isometric contractions, both shortening capacity and rate of isometric force decline were as well or better preserved in fatigued SOL from chf rats than in sham. This observation is in striking contrast to previous reports which have employed isometric contractions to induce fatigue.     

A model of force production that explains the lag between crossbridge attachment and force after electrical stimulation of striated muscle fibers.

Whereas the mechanical behavior of fully activated fibers can be explained by assuming that attached force-producing crossbridges exist in at least two configurations, one exerting more force than the other (Huxley A. F., and R. M. Simmons. 1971. Nature [Lond.]. 233:533-538), and the behavior of relaxed fibers can be explained by assuming a single population of weakly binding rapid-equilibrium crossbridges (Schoenberg, M. 1988. Biophys. J. 54:135-148), it has not been possible to explain the transition between rest and activation in these terms. The difficulty in explaining why, after electrical stimulation of resting intact frog skeletal muscle fibers at 1-5 degrees C, force development lags stiffness development by more than 15 ms has led a number of investigators to postulate additional crossbridge states. However, postulation of an additional crossbridge state will not explain the following three observations: (a) Although the lag between force and stiffness is very different after stimulation, during the redevelopment of force after an extended period of high velocity shortening, and during relaxation of a tetanus, nonetheless, the plots of force versus stiffness in each of these cases are approximately the same. (b) When the lag between stiffness and force during the rising phase of a twitch is changed nearly fourfold by changing temperature, again the plot of force versus stiffness remains essentially unchanged. (c) When a muscle fiber is subjected to a small quick length change, the rate constant for the isometric force recovery is faster when the length change is applied during the rising phase of a tenanus than when it is applied on the plateau. We have been able to explain all the above findings using a model for force production that is similar to the 1971 model of Huxley and Simmons, but which makes the additional assumption that the force-producing transition envisioned by them is a cooperative one, with the back rate constant of the force-producing transition decreasing as more crossbridges attach.     

Activation in a Skeletal Muscle Contraction Model with a Modification for Insect Fibrillar Muscle

A sliding filament model for muscle contraction is extended by including an activation mechanism based on the hypothesis that the binding of calcium by a regulating protein in the myofibrils must occur before the rate constant governing the making of interactions between cross-bridges and thin filament sites can take on nonzero values. The magnitude of the rate constant is proportional to the amount of bound calcium. The model's isometric twitch and rise of force in an isometric tetanus are similar to the curves produced by real muscles. It redevelops force after a quick release in an isometric tetanus faster than the initial rise. Quick release experiments on the model during an isometric twitch show that the “active state” curve produced is different from the postulated calcium binding curve. The force developed by the model can be increased by a small quick stretch delivered soon after activation to values near the maximum generated in an isometric tetanus. Following the quick stretch, the force remains near the tetanic maximum for a long time even though the calcium binding curve rises to a peak and subsequently decays by about 50%. The model satisfies the constraint of shortening with a constant velocity under a constant load. Modifications can be made in the model so that it produces the delayed force changes following step length changes characteristic of insect fibrillar muscle.     

Isoproterenol attenuates myosin phosphorylation and contraction of tracheal muscle

The effects of isoproterenol on isometric force, unloaded shortening velocity, and myosin phosphorylation were examined in thin muscle bundles (0.1-0.2 mm diam) dissected from lamb tracheal smooth muscle. Methacholine (10(-6) M) induced rapid increases in isometric force and in phosphorylation of the 20,000-Da myosin light chain. Myosin phosphorylation remained elevated during steady-state maintenance of isometric force. The shortening velocity peaked at 15 s after stimulation with methacholine and then declined to approximately 45% of the maximal value by 3 min. Isoproterenol pretreatment inhibited methacholine-stimulated myosin light chain phosphorylation, shortening velocity, and force during the early stages of force generation. However, the inhibitory effect of isoproterenol on force and myosin phosphorylation is proportionally greater than that on shortening velocity. Isoproterenol pretreatment also caused a rightward non-parallel shift in the methacholine dose-response curves for both isometric tension and myosin light chain phosphorylation. These data demonstrate that isoproterenol attenuates the contractile properties of airway smooth muscles by affecting the rate and extent of myosin light chain phosphorylation, perhaps through a mechanism that involves the synergistic interaction of myosin light chain kinase phosphorylation and Ca2+ metabolism.     

The effect of shortening history on isometric and dynamic muscle function

Despite numerous reports on isometric force depression, few reports have quantified force depression during active muscle shortening (dynamic force depression). The purpose of this investigation was to determine the influence of shortening history on isometric force following active shortening, force during isokinetic shortening, and velocity during isotonic shortening. The soleus muscles of four cats were subjected to a series of isokinetic contractions at three shortening velocities and isotonic contractions under three loads. Muscle excursions initiated from three different muscle lengths but terminated at a constant length. Isometric force produced subsequent to active shortening, and force or shortening velocity produced at a specific muscle length during shortening, were compared across all three conditions. Results indicated that shortening history altered isometric force by up to 5%, force during isokinetic shortening up to 30% and shortening velocity during isotonic contractions by up to 63%. Furthermore, there was a load by excursion interaction during isotonic contractions such that excursion had the most influence on shortening velocity when the loads were the greatest. There was not a velocity by excursion interaction during isokinetic contractions. Isokinetic and isotonic power–velocity relationships displayed a downward shift in power as excursions increased. Thus, to discuss force depression based on differences in isometric force subsequent to active shortening may underestimate its importance during dynamic contractions. The presence of dynamic force depression should be realized in sport performance, motor control modeling and when controlling paralyzed limbs through artificial stimulation.     

Myosin light chain phosphorylation and evidence for latchbridge formation in norepinephrine stimulated canine veins

The role of 20000 dalton myosin light chain phosphorylation in mediating venous smooth muscle contraction was studied in isolated preparations of canine jugular and femoral vein. One min 10(-5) M norepinephrine-induced contraction was accompanied by significant increases in phosphorylation (jugular - 21 to 46%; femoral - 19 to 54%) which were reversed within 10 min after agonist washout. During 40 min stimulation, phosphorylation and isometric force redevelopment rates declined to near basal levels while force was maintained. These findings implicate light chain phosphorylation as a prerequisite for initial tension development by crossbridge cycling in venous smooth muscle. However, long term tension can be maintained through a process similar to the latchbridge state in tracheal and arterial smooth muscle.     

Mechanical properties of human bronchial smooth muscle in vitro.

The in vitro mechanical properties of smooth muscle strips from 10 human main stem bronchi obtained immediately after pneumonectomy were evaluated. Maximal active isometric and isotonic responses were obtained at varying lengths by use of electrical field stimulation (EFS). At the length (Lmax) producing maximal force (Pmax), resting tension was very high (60.0 +/- 8.8% Pmax). Maximal fractional muscle shortening was 25.0 +/- 9.0% at a length of 75% Lmax, whereas less shortening occurred at Lmax (12.2 +/- 2.7%). The addition of increasing elastic loads produced an exponential decrease in the shortening and velocity of shortening but increased tension generation of muscle strips stimulated by EFS. Morphometric analysis revealed that muscle accounted for 8.7 +/- 1.5% of the total cross-sectional tissue area. Evaluation of two human tracheal smooth muscle preparations revealed mechanics similar to the bronchial preparations. Passive tension at Lmax was 10-fold greater and maximal active shortening was threefold less than that previously demonstrated for porcine trachealis by us of the same apparatus. We attribute the limited shortening of human bronchial and tracheal smooth muscle to the larger load presumably provided by a connective tissue parallel elastic component within the evaluated tissues, which must be overcome for shortening to occur. We suggest that a decrease in airway wall elastance could increase smooth muscle shortening, leading to excessive responses to contractile agonists, as seen in airway hyperresponsiveness.     

Estimates of cellular mechanics in an arterial smooth muscle.

Estimates of force generation or shortening obtained from smooth muscle tissues are valid for individual cells only if each cell is contracting homogeneously and if cells anatomically arranged in series are mechanically coupled. These two assumptions were tested and shown to be valid for the pig carotid media under certain conditions. Homogeneity of cellular responses in carotid strips was estimated from the motion of markers on the tissue during K+ -induced isometric contractions. When tissues were stretched to L0 (the optimum length for force generation), there was little marker movement on stimulation. However, considerable marker movement was observed on stimulation at shorter muscle lengths, reflecting localized shortening or stretching. The mechanical coupling of the very small cells in the media was determined by measuring the dependence of cell length on tissue length. Tissues were fixed with glutaraldehyde during isometric contractions at various tissue lengths (0.4--1.1 x L0). The fixed tissues were macerated with acid and the lengths of the dispersed cells were measured. Cell lengths were broadly distributed at all muscle lengths. However, the direct proportionality between mean cell length and muscle length (as a fraction of L0) indicated that cells which are anatomically in series are coupled force-transmitting structures. We conclude that valid estimates of cellular mechanical function in this preparation can be obtained from tissue measurements at lengths greater than about 0.9L0.     

Mechanical work as predictor of force enhancement and force depression

The steady-state force following active muscle shortening or stretch differs from the maximum isometric force associated with the final length. This phenomenon proves that the isometric force production is not only dependent on current muscle length and length time derivative, but depends on the preceding contraction history. Isolated extensor digitorum longus and soleus muscles from mice (NMRI strain) were used to investigate the force produced by a muscle, and some parameters hypothetically influencing this history-dependent force modification. The muscles were pre-stimulated at a fixed length, then different stretch/shortening episodes were introduced, whereafter changes of the active force were recorded while the muscles were held isometrically to approach a steady-state force before de-stimulation. The mechanical work during active stretch and shortening was evaluated by integrating the product of force and ramp velocity over the length-varying period. The results show a negative linear correlation between the force modification and the mechanical work produced on or by the muscle, continuous between shortening and stretch. A corresponding modification of the passive force component following each stimulation was also observed. The conclusion is that the isometric force attained after stretch or shortening is well described by an asymptotic force which is determined by the mechanical work.     

Kinetics of force redevelopment in isolated intact frog fibers in solutions of varied osmolarity.

Isolated intact frog muscle fibers, while shortening with the intrinsic maximal speed, were stretched back to the original length to measure the kinetics of force redevelopment. These kinetics give information on the attachment rate constant in the cross-bridge cycle in vivo, and a value of approximately 25.6 s-1 (0 degree C) is found in the present study. We find that these kinetics were slightly less sensitive to temperature than was the unloaded shortening speed. The effect of hyperosmolarity on force redevelopment was also measured in solutions with added sucrose or KCl. The rate constant was nearly halved with 120 mM sucrose, but there was practically no effect with isosmotic (60 mM) KCl. These results indicate that the rate constant of force redevelopment is insensitive to raised intracellular ionic strength. In sucrose, the fiber width was also compressed, and the attenuation of the rate constant of force redevelopment in this case is consequently attributed to the decrease in interfilament space. The order of magnitude of the rate constant found in this study suggests that tension transduction by a cross-bridge, during each turnover cycle, requires a series of elementary steps following the attachment.