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.     

Smooth muscle myosin: regulation and properties

The relationship of the biochemical states to the mechanical events in contraction of smooth muscle cross-bridges is reviewed. These studies use direct measurements of the kinetics of Pi and ADP release. The rate of release of Pi from thiophosphorylated cycling cross-bridges held isometric was biphasic with turnovers of 1.8 s-1 and 0.3 s-1, reflecting properties and forces directly acting on cross-bridges through mechanisms such as positive strain and inhibition by high-affinity MgADP binding. Fluorescent transients reporting release of an ADP analogue 3'-deac-edaADP were significantly faster in phasic than in tonic smooth muscles. Thiophosphorylation of myosin regulatory light chains (RLCs) increased and positive strain decreased the release rate around twofold. The rates of ADP release from rigor cross-bridges and the steady-state Pi release from cycling isometric cross-bridges are similar, indicating that the ADP-release step or an isomerization preceding it may limit the ATPase rate. Thus ADP release in phasic and tonic smooth muscles is a regulated step with strain- and dephosphorylation-dependence. High affinity of cross-bridges for ADP and slow ADP release prolong the fraction of the duty cycle occupied by strongly bound AM.ADP state(s) and contribute to the high economy of force that is characteristic of smooth muscle. RLC thiophosphorylation led to structural changes in smooth muscle cross-bridges consistent with our findings that thiophosphorylation and strain modulate product release.     

Effect of temperature on residual force enhancement in single skeletal muscle fibers

It is well accepted that the steady-state isometric force following active stretching of a muscle is greater than the steady-state isometric force obtained in a purely isometric contraction at the same length. This property of skeletal muscle has been called residual force enhancement (FE). Despite decades of research the mechanisms responsible for FE have remained largely unknown. Based on previous studies showing increases in FE in fibers in which cross-bridges were biased towards weakly bound states, we hypothesized that FE might be associated with a stretch-induced facilitation of transitioning from weakly to strongly bound cross-bridges. In order to test this hypothesis, single fibers (n=11) from the lumbrical muscles of frog (Rana pipiens) were used to determine FE at temperatures of 7 and 20 degrees C. At the cold temperature, cross-bridges are biased towards weakly bound states, therefore we expected FE to be greater at 7 degrees C compared to 20 degrees C. The average FE was significantly greater at 7 degrees C (11.5+/-1.1%) than at 20 degrees C (7.8+/-1.0%), as expected. The enhancement of force/stiffness was also significantly greater at the low (13.3+/-1.4%) compared to the high temperature (5.6+/-1.7%), indicating an increased conversion from weakly to strongly bound cross-bridges at the low temperature. We conclude from the results of this study that muscle preparations that are biased towards weakly bound cross-bridge states show increased FE for given stretch conditions, thereby supporting the idea that FE might be caused, in part, by a stretch-induced facilitation of the conversion of weakly to strongly bound cross-bridges.     

Calcium-independent activation of skinned cardiac muscle by secophalloidin

Thin filament regulation of muscle contraction is believed to be mediated by both Ca2+ and strongly bound myosin cross-bridges. We found that secophalloidin (SPH, 5-8 mM) activates cross-bridge cycling without Ca2+ causing isometric force comparable to that induced by Ca2+. At saturated [SPH], Ca2+ further increased force by 20%. SPH-induced force was reversible upon washing with a relaxing solution. However, there was more than 30% irreversible loss in subsequent Ca2+-activated force. We hypothesize that SPH activates muscle via strongly bound cross-bridges. SPH-activated contraction provides a new model for studying the role of Ca2+ and cross-bridges in muscle regulation.     

Calcium dynamics and vasomotion in arteries subject to isometric, isobaric, and isotonic conditions

In vitro, different techniques are used to study the smooth muscle cells’ calcium dynamics and contraction/relaxation mechanisms on arteries. Most experimental studies use either an isometric or an isobaric setup. However, in vivo, a blood vessel is neither isobaric nor isometric nor isotonic, as it is continuously submitted to intraluminal pressure variations arising from heart beat. We use a theoretical model of the smooth muscle calcium and arterial radius dynamics to determine whether results may be considerably different depending on the experimental conditions (isometric, isobaric, isotonic, or cyclic pressure variations). We show that isobaric conditions appear to be more realistic than isometric or isotonic situations, as the calcium dynamics is similar under cyclic intraluminal pressure variations (in vivo-like situation) and under a constant pressure (isobaric situation). The arterial contraction is less pronounced in isotonic than in isobaric conditions, and the vasoconstrictor sensitivity higher in isometric than isobaric or isotonic conditions, in agreement with experimental observations. Interestingly, the model predicts that isometric conditions may generate artifacts like the coexistence of multiple stable states. We have verified this model prediction experimentally using rat mesenteric arteries mounted on a wire myograph and stimulated with phenylephrine.     

The extracellular matrix in hibernating myocardium - a significant factor causing structural defects and cardiac dysfunction

The time course of force generation and the time course of muscle stiffness were measured in rabbit soleus muscles during eccentric contraction to understand the underlying basis for the force loss in these muscles. Muscles were activated for 600 msec every 10 sec for 30 min. Soleus muscles contracting isometrically maintained constant tension throughout the treatment period, while muscles subjected to eccentric contraction rapidly dropped tension generation by 75% within the first few minutes and then an additional 10% by the end of 30 min. This indicated a dramatic loss in force-generating ability throughout the 30 min treatment period. To estimate the relative number of cross-bridges attached during the isometric force generation phase immediately preceding each eccentric contraction, stiffness was measured during a small stretch of a magnitude equal to 1.5% of the fiber length. Initially, muscle stiffness exceeded 1300 g/mm and, as eccentric treatment progressed, stiffness decreased to about 900 g/mm. Thus, while muscle stiffness decreased by only 30% over the 30 min treatment period, isometric force decreased by 85%. In isometrically activated muscles, stiffness remained constant throughout the treatment period. These data indicate that, while soleus muscles decreased their force generating capability significantly, there were a number of cross-bridges still attached that were not generating force. In summary, the loss of force generating capacity in the rabbit soleus muscle appears to be related to a fundamental change in myosin cross-bridge properties without the more dramatic morphological changes observed in other eccentric contraction models. These results are compared and contrasted with the observations made on muscles composed primarily of fast fibers.     

Influence of dispersion in myosin filament orientation and anisotropic filament contractions in smooth muscle

A new constitutive model for the biomechanical behaviour of smooth muscle tissue is proposed. The active muscle contraction is accomplished by the relative sliding between actin and myosin filaments, comprising contractile units in the smooth muscle cells. The orientation of the myosin filaments, and thereby the contractile units, are taken to exhibit a statistical dispersion around a preferred direction. The number of activated cross-bridges between the actin and myosin filaments governs the contractile force generated by the muscle and also the contraction speed. A strain-energy function is used to describe the mechanical behaviour of the smooth muscle tissue. Besides the active contractile apparatus, the mechanical model also incorporates a passive elastic part. The constitutive model was compared to histological and isometric tensile test results for smooth muscle tissue from swine carotid artery. In order to be able to predict the active stress at different muscle lengths, a filament dispersion significantly larger than the one observed experimentally was required. Furthermore, a comparison of the predicted active stress for a case of uniaxially oriented myosin filaments and a case of filaments with a dispersion based on the experimental histological data shows that the difference in generated stress is noticeable but limited. Thus, the results suggest that myosin filament dispersion alone cannot explain the increase in active muscle stress with increasing muscle stretch.     

Dynamic analysis of the structure and function of sarcomeres

We attempted to analyze the relationships between the steric structure of the sarcomere and its physiological functions by the use of a sarcomere model of muscle contraction, which includes the geometric arrangement of the thick and thin filaments of the sarcomere, as well as of the cross-bridges and actin sites. Motions of both cross-bridges and myofilaments were considered in terms of our three-state model of the elementary cycle under constraints caused by the steric structure of the sarcomere proposed by Huxley and Brown. Each cross-bridge moves in a molecular potential of our three-state model under the influence of the sliding motions of myofilaments. The sarcomere model described well the tension-velocity relation and isotonic transient processes quantitatively and consistently. In addition, it allowed independence of the no-load shortening velocity upon the overlap of the thick and thin filaments, although the motions of cross-bridges were not independent. Effects of the helical periodicities of the thick and thin filaments and of the number of cross-bridges upon muscle contraction were studied, and the conditions for smooth and efficient contraction of muscle were obtained.     

Force enhancement and relaxation rates after stretch of activated muscle fibres

The residual force enhancement following muscle stretch might be associated with an increase in the proportion of attached cross-bridges, as supported by stiffness measurements. In this case, it could be caused by an increase in the attachment or a decrease in the detachment rate of cross-bridges, or a combination of the two. The purpose of this study was to investigate if the stretch-induced force enhancement is related to cross-bridge attachment/detachment kinetics. Single muscle fibres dissected from the lumbrical muscle of frog were place at a length approximately 20% longer than the plateau of the force-length relationship; they were maximally activated, and after full isometric force was reached, ramp stretches were imposed with amplitudes of 5 and 10% fibre length, at a speed of 40% fibre length s(-1). Experiments were performed in Ringer's solution, and with the addition of 2, 5 and 10 nM of 2,3-butanedione monoxime (BDM), a drug that places cross-bridges in a pre-power-stroke, state, inhibiting force production. The total force following stretch was higher than the corresponding force measured after isometric contraction at the corresponding length. This residual force enhancement was accompanied by an increase relaxation time. BDM, which decreases force production during isometric contractions, considerably increased the relative levels of force enhancement. BDM also increased relaxation times after stretch, beyond the levels observed during reference contractions in Ringer's solution, and beyond isometric control tests at the corresponding BDM concentrations. Together, these results support the idea that force enhancement is caused, at least in part, by a decrease in cross-bridge detachment rates, as manifested by the increased relaxation times following fibre stretch.     

A continuum model for skeletal muscle contraction at homogeneous finite deformations

The contractile force in skeletal muscle models is commonly postulated to be the isometric force multiplied by a set of experimentally motivated functions which account for the muscle’s active properties. Although both flexible and simple, this approach does not automatically guarantee a thermodynamically consistent behavior. In contrast, the continuum mechanical model proposed herein is derived from fundamental principles in mechanics and guarantees a dissipative behavior. Further, the contractile force is associated with a friction clutch which provides a simple and well-defined macroscopic model for cycling cross-bridges. To show the performance of the model, it is specialized to standard experiments for rabbit tibialis anterior muscle. The results show that the model is able to capture important characteristics of skeletal muscle.     

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.     

Cross-bridge behavior in rigor muscle

Properties of the rigor state in muscle can be explained by a simple cross-bridge model, of the type which has been suggested for active muscle, in which detachment of cross-bridges by ATP is excluded. Two attached cross-bridge states, with distinct force vs. distortion relationships, are required, in addition to a detached state, but the attached cross-bridge states in rigor muscle appear to differ significantly from the attached cross-bridge states in active muscle. The stability of the rigor force maintained in muscle under isometric conditions does not require exceptional stability of the attached cross-bridges, if the positions in which attachment of cross-bridges is allowed are limited so that the attachment of cross-bridges in positions which have minimum free energy is excluded. This explanation of the stability of the rigor state may also be applicable to the maintenance of stable rigor waves on flagella.     

A theory of contraction and a mathematical model of striated muscle

A theory of contraction and an associated model of striated muscle are presented, based on the assumption that chemical energy is being converted into electrical energy which, in turn, is being converted into mechanical energy and heat.The model, set up for the frog sartorius muscle, is able to predict the “rowing” motion of the cross-bridges, the force-velocity relation, the tension-length curve, the isometric force, all energy rates (heat and work rates), the metabolic rates and all known features of the stretched, stimulated muscle (no ATP-splitting, stretching tension higher than isometric tension, etc.). It also offers an alternative explanation for Hill's thermoelastic effect. The significance of Hill's force-velocity equation in the context of this theory is also discussed in detail.     

A mathematical model of muscle containing heterogeneous half-sarcomeres exhibits residual force enhancement

A skeletal muscle fiber that is stimulated to contract and then stretched from L₁ to L₂ produces more force after the initial transient decays than if it is stimulated at L₂. This behavior has been well studied experimentally, and is known as residual force enhancement. The underlying mechanism remains controversial. We hypothesized that residual force enhancement could reflect mechanical interactions between heterogeneous half-sarcomeres. To test this hypothesis, we subjected a computational model of interacting heterogeneous half-sarcomeres to the same activation and stretch protocols that produce residual force enhancement in real preparations. Following a transient period of elevated force associated with active stretching, the model predicted a slowly decaying force enhancement lasting >30 seconds after stretch. Enhancement was on the order of 13% above isometric tension at the post-stretch muscle length, which agrees well with experimental measurements. Force enhancement in the model was proportional to stretch magnitude but did not depend strongly on the velocity of stretch, also in agreement with experiments. Even small variability in the strength of half-sarcomeres (2.1% standard deviation, normally distributed) was sufficient to produce a 5% force enhancement over isometric tension. Analysis of the model suggests that heterogeneity in half-sarcomeres leads to residual force enhancement by storing strain energy introduced during active stretch in distributions of bound cross-bridges. Complex interactions between the heterogeneous half-sarcomeres then dissipate this stored energy at a rate much slower than isolated cross-bridges would cycle. Given the variations in half-sarcomere length that have been observed in real muscle preparations and the stochastic variability inherent in all biological systems, half-sarcomere heterogeneity cannot be excluded as a contributing source of residual force enhancement.     

Cross-bridge mechanism of residual force enhancement after stretching in a skeletal muscle

A muscle model that uses a modified Langevin equation with actomyosin potentials was used to describe the residual force enhancement after active stretching. Considering that the new model uses cross-bridge theory to describe the residual force enhancement, it is different from other models that use passive stretching elements. Residual force enhancement was simulated using a half sarcomere comprising 100 myosin molecules. In this paper, impulse is defined as the integral of an excess force from the steady isometric force over the time interval for which a stretch is applied. The impulse was calculated from the force response due to fast and slow muscle stretches to demonstrate the viscoelastic property of the cross-bridges. A cross-bridge mechanism was proposed as a way to describe the residual force enhancement on the basis of the impulse results with reference to the compliance of the actin filament. It was assumed that the period of the actin potential increased by 0.5% and the amplitude of the potential decreased by 0.5% when the half sarcomere was stretched by 10%. The residual force enhancement after 21.0% sarcomere stretching was 6.9% of the maximum isometric force of the muscle; this value was due to the increase in the number of cross-bridges.     

Shortening induced effects on force (re)development in pig urinary smooth muscle

INTRODUCTION: When muscle is allowed to shorten during an active contraction, the maximum force that redevelops after shortening is smaller than the isometric force at the same muscle length without prior shortening. We studied the course of force redevelopment after shortening in smooth muscle to unravel the mechanism responsible for this deactivation. METHOD: In a first series of measurements the shortening velocity was varied resulting in different shortening amplitudes. In a second series, the duration of stimulation before shortening (shortening delay) was varied. In a third series, the stimulation was interrupted for a certain duration immediately after shortening. Force, muscle length and stimulation were continuously recorded. Time constants were calculated to describe the rate of force development before and after shortening. RESULTS: With increasing shortening amplitude and with increasing shortening delay, force redevelopment decreased. Redevelopment increased with an increase in the interruption time. After stimulus interruption force redeveloped mono-exponentially with a time constant similar to that of isometric contractions (approximately 3s). Without the interruption of stimulation, the redevelopment of force immediately after shortening was best described by two time constants; one similar to and one about 3-5 times faster than the isometric time constant. DISCUSSION: Force (re)development is caused by a cascade of events leading to the cycling of cross-bridges. In smooth muscle, isometric force development is described by a time constant of about 3s. Force redevelopment immediately after shortening involves a second process which takes place at a faster rate (time constant about 1s). We assume that this process is faster due to the immediate availability of cytoplasmic calcium released during active shortening. Deactivation presumably is caused by disorganization of filaments during shortening.     

Structural features of cross-bridges in isometrically contracting skeletal muscle

Two-dimensional x-ray diffraction was used to investigate structural features of cross-bridges that generate force in isometrically contracting skeletal muscle. Diffraction patterns were recorded from arrays of single, chemically skinned rabbit psoas muscle fibers during isometric force generation, under relaxation, and in rigor. In isometric contraction, a rather prominent intensification of the actin layer lines at 5.9 and 5.1 nm and of the first actin layer line at 37 nm was found compared with those under relaxing conditions. Surprisingly, during isometric contraction, the intensity profile of the 5.9-nm actin layer line was shifted toward the meridian, but the resulting intensity profile was different from that observed in rigor. We particularly addressed the question whether the differences seen between rigor and active contraction might be due to a rigor-like configuration of both myosin heads in the absence of nucleotide (rigor), whereas during active contraction only one head of each myosin molecule is in a rigor-like configuration and the second head is weakly bound. To investigate this question, we created different mixtures of weak binding myosin heads and rigor-like actomyosin complexes by titrating MgATPgammaS at saturating [Ca2+] into arrays of single muscle fibers. The resulting diffraction patterns were different in several respects from patterns recorded under isometric contraction, particularly in the intensity distribution along the 5.9-nm actin layer line. This result indicates that cross-bridges present during isometric force generation are not simply a mixture of weakly bound and single-headed rigor-like complexes but are rather distinctly different from the rigor-like cross-bridge. Experiments with myosin-S1 and truncated S1 (motor domain) support the idea that for a force generating cross-bridge, disorder due to elastic distortion might involve a larger part of the myosin head than for a nucleotide free, rigor cross-bridge.     

Myosin regulatory light chain phosphorylation and strain modulate adenosine diphosphate release from smooth muscle Myosin

The effects of myosin regulatory light chain (RLC) phosphorylation and strain on adenosine diphosphate (ADP) release from cross-bridges in phasic (rabbit bladder (Rbl)) and tonic (femoral artery (Rfa)) smooth muscle were determined by monitoring fluorescence transients of the novel ADP analog, 3'-deac-eda-ADP (deac-edaADP). Fluorescence transients reporting release of 3'-deac-eda-ADP were significantly faster in phasic (0.57 +/- 0.06 s(-1)) than tonic (0.29 +/- 0.03 s(-1)) smooth muscles. Thiophosphorylation of regulatory light chains increased and strain decreased the release rate approximately twofold. The calculated (k-ADP/k+ADP) dissociation constant, Kd of unstrained, unphosphorylated cross-bridges for ADP was 0.6 microM for rabbit bladder and 0.3 microM for femoral artery. The rates of ADP release from rigor bridges and reported values of Pi release (corresponding to the steady-state adenosine triphosphatase (ATPase) rate of actomyosin (AM)) from cross-bridges during a maintained isometric contraction are similar, indicating that the ADP-release step or an isomerization preceding it may be limiting the adenosine triphosphatase rate. We conclude that the strain- and dephosphorylation-dependent high affinity for and slow ADP release from smooth muscle myosin prolongs the fraction of the duty cycle occupied by strongly bound actomyosin.ADP state(s) and contributes to the high economy of force.     

Shortening-induced force depression is primarily caused by cross-bridges in strongly bound states

The steady-state isometric force following active muscle shortening is smaller than the corresponding force obtained for purely isometric contractions. This so-called residual force depression has been observed consistently for more than half a century, however its mechanism remains a matter of scientific debate. [Maréchal, G., Plaghki, L., 1979. The deficit of the isometric tetanic tension redeveloped after a release of frog muscle at a constant velocity. J. Gen. Physiol. 73, 453–467] suggested that force depression might be caused by alterations in the cross-bridge kinetics following muscle shortening, but there is no research studying force depression systematically for altered cross-bridge kinetic conditions. The purpose of this study was to investigate if force depression affects so-called weakly and strongly bound cross-bridges to the same degree. In order to achieve this aim, we modified the ratio of weakly to strongly bound cross-bridges with 2,3-butanedione monoxime (BDM) in single frog fibers. BDM inhibits the formation of strongly bound cross-bridges in a dose-dependent manner, thus the ratio of weakly to strongly bound cross-bridges could be altered in a systematic way. We found that the absolute amount of force depression was decreased by 50% while the relative amount was decreased by 12% in BDM exposed fibers compared to fibers in normal Ringer's solution. Furthermore, force depression was accompanied by a decrease in stiffness that was much greater in normal compared to BDM exposed fibers, leading to the conclusion that force depression was caused by an inhibition of cross-bridge attachment following fiber shortening and that this inhibition primarily affected cross-bridges in the strongly bound states.     

An expanded latch-bridge model of protein kinase C-mediated smooth muscle contraction.

A thin-filament-regulated latch-bridge model of smooth muscle contraction is proposed to integrate thin-filament-based inhibition of actomyosin ATPase activity with myosin phosphorylation in the regulation of smooth muscle mechanics. The model included two latch-bridge cycles, one of which was identical to the four-state model as proposed by Hai and Murphy (Am J Physiol Cell Physiol 255: C86-C94, 1988), whereas the ultraslow cross-bridge cycle has lower cross-bridge cycling rates. The model-fitted phorbol ester induced slow contractions at constant myosin phosphorylation and predicted steeper dependence of force on myosin phosphorylation in phorbol ester-stimulated smooth muscle. By shifting cross bridges between the two latch-bridge cycles, the model predicts that a smooth muscle cell can either maintain force at extremely low-energy cost or change its contractile state rapidly, if necessary. Depending on the fraction of cross bridges engaged in the ultraslow latch-bridge cycle, the model predicted biphasic kinetics of smooth muscle mechanics and variable steady-state dependencies of force and shortening velocity on myosin phosphorylation. These results suggest that thin-filament-based regulatory proteins may function as tuners of actomyosin ATPase activity, thus allowing a smooth muscle cell to have two discrete cross-bridge cycles with different cross-bridge cycling rates.