Extra calcium on shortening in barnacle muscle. Is the decrease in calcium binding related to decreased cross-bridge attachment,force, or length?

Barnacle single muscle fibers were microinjected with the calcium-specific photoprotein aequorin. We have previously shown (Ridgway, E. B., and A. M. Gordon, 1984, Journal of General Physiology, 83:75-104) that when barnacle fibers are stimulated under voltage clamp and length control and allowed to shorten during the declining phase of the calcium transient, extra myoplasmic calcium is observed. The time course of the extra calcium for shortening steps at different times during the calcium transient is intermediate between those of free calcium and muscle force. Furthermore, the amplitude increases with an increased stimulus, calcium transient, and force. Therefore, the extra calcium probably comes from the activating sites on the myofilaments, possibly as a result of changes in calcium binding by the activating sites. The change in calcium binding may be due, in turn, to the change in muscle length and/or muscle force and/or cross-bridge attachment per se. In the present article, we show that the amount of the extra calcium depends on the initial muscle length, declining at shorter lengths. This suggests length-dependent calcium binding. The relation between initial length and extra calcium, however, parallels that between initial length and peak active force. The ratio of extra calcium to active force is therefore virtually independent of initial length. These data do not distinguish between a direct effect of length on calcium binding and an indirect effect owing to changes in cross-bridge attachment and force through some geometrical factor. The amount of extra calcium increases with the size of the shortening step, tending toward saturation for steps of greater than or equal to 10%. This experiment suggests that calcium binding depends on muscle force or cross-bridge attachment, not just length (if at all). There is much less extra calcium seen with shortening steps at high force when the high force results from stretch of the active muscle than when it results from increased stimulation of muscle.(ABSTRACT TRUNCATED AT 400 WORDS)     

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.     

Muscle calcium transient. Effect of post-stimulus length changes in single fibers

We examined the effects of post-stimulus length changes on voltage-clamped, aequorin-injected single muscle fibers from the barnacle Balanus nubilus. Extra light (extra calcium) is seen when the fiber is allowed to shorten (a small percentage) during the declining phase of the calcium transient. The opposite is observed when the fiber is stretched. Increasing the extent of shortening increases the amount of extra calcium, as does decreasing the temperature. The extra calcium probably comes from the myofilaments and not from the sarcoplasmic reticulum because (a) there is a strong correlation between the extra calcium and the level of activation; (b) there is a strong correlation between the extra calcium and the amount of force redeveloped after a length change; and (c) the time course of the appearance of the extra calcium is intermediate between that of the free calcium concentration and that of force. We suggest (a) that the calcium binding to the activating myofibrillar proteins is sensitive to muscle length or muscle force, and (b) that there is a pool of bound calcium (activating calcium) that waxes and wanes with a time course intermediate between the free calcium concentration and force.     

Cross-bridge attachment during high-speed active shortening of skinned fibers of the rabbit psoas muscle: implications for cross-bridge action during maximum velocity of filament sliding

To characterize the kinetics of cross-bridge attachment to actin during unloaded contraction (maximum velocity of filament sliding), ramp-shaped stretches with different stretch-velocities (2-40,000 nm per half-sarcomere per s) were applied to actively contracting skinned fibers of the rabbit psoas muscle. Apparent fiber stiffness observed during such stretches was plotted versus the speed of the imposed stretch (stiffness-speed relation) to derive the rate constants for cross-bridge dissociation from actin. The stiffness-speed relation obtained for unloaded shortening conditions was shifted by about two orders of magnitude to faster stretch velocities compared to isometric conditions and was almost identical to the stiffness-speed relation observed in the presence of MgATPgammaS at high Ca(2+) concentrations, i.e., under conditions where cross-bridges are weakly attached to the fully Ca(2+) activated thin filaments. These data together with several control experiments suggest that, in contrast to previous assumptions, most of the fiber stiffness observed during high-speed shortening results from weak cross-bridge attachment to actin. The fraction of strongly attached cross-bridges during unloaded shortening appears to be as low as some 1-5% of the fraction present during isometric contraction. This is about an order of magnitude less than previous estimates in which contribution of weak cross-bridge attachment to observed fiber stiffness was not considered. Our findings imply that 1) the interaction distance of strongly attached cross-bridges during high-speed shortening is well within the range consistent with conventional cross-bridge models, i.e., that no repetitive power strokes need to be assumed, and 2) that a significant part of the negative forces that limit the maximum speed of filament sliding might originate from weak cross-bridge interactions with actin.     

Millisecond-scale biochemical response to change in strain

Muscle fiber contraction involves the cyclical interaction of myosin cross-bridges with actin filaments, linked to hydrolysis of ATP that provides the required energy. We show here the relationship between cross-bridge states, force generation, and Pi release during ramp stretches of active mammalian skeletal muscle fibers at 20°C. The results show that force and Pi release respond quickly to the application of stretch: force rises rapidly, whereas the rate of Pi release decreases abruptly and remains low for the duration of the stretch. These measurements show that biochemical change on the millisecond timescale accompanies the mechanical and structural responses in active muscle fibers. A cross-bridge model is used to simulate the effect of stretch on the distribution of actomyosin cross-bridges, force, and Pi release, with explicit inclusion of ATP, ADP, and Pi in the biochemical states and length-dependence of transitions. In the simulation, stretch causes rapid detachment and reattachment of cross-bridges without release of Pi or ATP hydrolysis.     

Cross-bridge induced force enhancement?

When a muscle is stretched while activated, its steady-state isometric force following stretch is greater than the corresponding purely isometric force. This so-called residual force enhancement (RFE) has been observed for half a century, yet its mechanism remains unknown. Recent experiments suggest that RFE is not caused by non-uniformities in sarcomere lengths, as had been assumed for a long time, and cannot be explained primarily with increases in passive force, but is directly related to the kinetics of the cross-bridge cycle. Specifically, it has been suggested that stretching an attached cross-bridge increases its dwell time and duty ratio; therefore, the proportion of attached cross-bridges in a muscle would be increased by stretch, thereby causing RFE. A three bead laser trap setup was used for testing single cross-bridge (myosin II) interactions with actin. Upon attachment of a cross-bridge, a stretch or shortening of the cross-bridge was applied with a force of about 1.0 pN. The hypothesis that stretching a single cross-bridge increases its dwell time and duty ratio was rejected. However, stretching caused an increase in the average steady-state force per cross-bridge (3.4±0.4 pN; n=433) compared to shortening (1.9±0.3 pN; n=689). Therefore, based on the results of this study, RFE cannot be explained by an increased duty ratio and the associated increase in proportion of attached cross-bridges, but might be associated with an increased force per cross-bridge.     

Cross-bridge cycling theories cannot explain high-speed lengthening behavior in frog muscle.

The Huxley 1957 model of cross-bridge cycling accounts for the shortening force-velocity curve of striated muscle with great precision. For forced lengthening, however, the model diverges from experimental results. This paper examines whether it is possible to bring the model into better agreement with experiments, and if so what must be assumed about the mechanical capabilities of cross-bridges. Of particular interest is how introduction of a maximum allowable cross-bridge strain, as has been suggested by some experiments, affects the predictions of the model. Because some differences in the models are apparent only at high stretch velocities, we acquired new force-velocity data to permit a comparison with experiment. Using whole, isolated frog sartorius muscles at 2 degrees C, we stretched active muscle at speeds up to and exceeding 2 Vmax. Force during stretch was always greater than the peak isometric level, even during the fastest stretches, and was approximately independent of velocity for stretches faster than 0.5 Vmax. Although certain modifications to the model brought it into closer correspondence with the experiments, the accompanying requirements on cross-bridge extensibility were unreasonable. We suggest (both in this paper and the one that follows) that sarcomere inhomogeneities, which have been implicated in such phenomena as "tension creep" and "permanent extra tension," may also play an important role in determining the basic force-velocity characteristics of muscle.     

Strain-dependent modulation of phosphate transients in rabbit skeletal muscle fibers.

When inorganic phosphate (Pi) is photogenerated from caged Pi during isometric contractions of glycerinated rabbit psoas muscle fibers, the released Pi binds to cross-bridges and reverses the working stroke of cross-bridges. The consequent force decline, the Pi-transient, is exponential and probes the kinetics of the power-stroke and Pi release. During muscle shortening, the fraction of attached cross-bridges and the average strain on them decreases (Ford, L. E., A.F. Huxley, and R.M. Simmons, 1977. Tension responses to sudden length change in stimulated frog muscle fibers near slack length. J. Physiol. (Lond.). 269:441-515; Ford, L. E., A. F. Huxley, and R.M. Simmons, 1985. Tension transients during steady state shortening of frog muscle fibers. J. Physiol. (Lond.). 361:131-150. To learn to what extent the Pi transient is strain dependent, muscle fibers were activated and shortened or lengthened at a fixed velocity during the photogeneration of Pi. The Pi transients observed during changes in muscle length showed three primary characteristics: 1) during shortening the Pi transient rate, Kpi, increased and its amplitude decreased with shortening velocity; Kpi increased linearly with velocity to > 110 s-1 at 0.3 muscle lengths per second (ML/s). 2) At a specific shortening velocity, increases in [Pi] produce increases in Kpi that are nonlinear with [Pi] and approach an asymptote. 3) During forced lengthening Kpi and the amplitude of the Pi transient are little different from the isometric contractions. These data can be approximated by a strain-dependent three-state cross-bridge model. The results show that the power stroke's rate is strain-dependent, and are consistent with biochemical studies indicating that the rate-limiting step at low strains is a transition from a weakly to a strongly bound cross-bridge state.     

History-dependent properties of skeletal muscle myofibrils contracting along the ascending limb of the force–length relationship

There is a history dependence of skeletal muscle contraction: stretching activated muscles induces a long-lasting force enhancement, while shortening activated muscles induces a long-lasting force depression. These history-dependent properties cannot be explained by the current model of muscle contraction, and its mechanism is unknown. The purposes of this study were (i) to evaluate if force enhancement and force depression are present at short lengths (the ascending limb of the force–length (FL) relationship), (ii) to evaluate if the history-dependent properties are associated with sarcomere length (SL) non-uniformity and (iii) to determine the effects of cross-bridge (de)activation on force depression. Rabbit psoas myofibrils were isolated and attached between two microneedles for force measurements. Images of the myofibrils were projected onto a linear photodiode array for measurements of SL. Myofibrils were activated by either Ca²⁺ or MgADP; the latter induces cross-bridge attachment to actin independently of Ca²⁺. Activated myofibrils were subjected to three stretches or shortenings (approx. 4% SL at approx. 0.07 µm s⁻¹ sarcomere⁻¹) along the ascending limb of the FL relationship separated by periods (approx. 5 s) of isometric contraction. Force after stretch was higher than force after shortening at similar SLs. The differences in force could not be explained by SL non-uniformity. The FL relationship produced by Ca²⁺- and MgADP-activated myofibrils were similar in stretch experiments, but after shortening MgADP activation produced forces that were higher than Ca²⁺ activation. Since MgADP induces the formation of strongly bound cross-bridges, this result suggests that force depression following shortening is associated with cross-bridge deactivation.     

Force enhancement without changes in cross-bridge turnover kinetics: the effect of EMD 57033.

The thiadiazinon derivative EMD 57033 has been found previously in cardiac muscle to increase isometric force generation without a proportional increase in fiber ATPase, thus causing a reduction in tension cost. To analyze the mechanism by which EMD 57033 affects the contractile system, we studied its effects on isometric force, isometric fiber ATPase, the rate constant of force redevelopment (k(redev)), active fiber stiffness, and its effect on Fo, which is the force contribution of a cross-bridge in the force-generating states. We used chemically skinned fibers of the rabbit psoas muscle. It was found that with 50 microM EMD 57033, isometric force increases by more than 50%, whereas Kredev, active stiffness, and isometric fiber ATPase increase by at most 10%. The results show that EMD 57033 causes no changes in cross-bridge turnover kinetics and no changes in active fiber stiffness that would result in a large enough increase in occupancy of the force-generating states to account for the increase in active force. However, plots of force versus length change recorded during stretches and releases (T plots) indicate that in the presence of EMD 57033 the y(o) value (x axis intercept) for the cross-bridges becomes more negative while its absolute value increases. This might suggest a larger cross-bridge strain as the basis for increased active force. Analysis of T plots with and without EMD 57033 shows that the increase in cross-bridge strain is not due to a redistribution of cross-bridges among different force-generating states favoring states of larger strain. Instead, it reflects an increased cross-bridge strain in the main force-generating state. The direct effect of EMD 57033 on the force contribution of cross-bridges in the force-generating states represents an alternative mechanism for a positive inotropic intervention.     

Perturbed equilibria of myosin binding in airway smooth muscle: bond-length distributions, mechanics, and ATP metabolism

We carried out a detailed mathematical analysis of the effects of length fluctuations on the dynamically evolving cross-bridge distributions, simulating those that occur in airway smooth muscle during breathing. We used the latch regulation scheme of Hai and Murphy (Am. J. Physiol. Cell Physiol. 255:C86-C94, 1988) integrated with Huxley's sliding filament theory of muscle contraction. This analysis showed that imposed length fluctuations decrease the mean number of attached bridges, depress muscle force and stiffness, and increase force-length hysteresis. At frequencies >0.1 Hz, the bond-length distribution of slowly cycling latch bridges changed little over the stretch cycle and contributed almost elastically to muscle force, but the rapidly cycling cross-bridge distribution changed substantially and dominated the hysteresis. By contrast, at frequencies <0.033 Hz this behavior was reversed: the rapid cycling cross-bridge distribution changed little, effectively functioning as a constant force generator, while the latch bridge bond distribution changed substantially and dominated the stiffness and hysteresis. The analysis showed the dissociation of force/length hysteresis and cross-bridge cycling rates when strain amplitude exceeds 3%; that is, there is only a weak coupling between net external mechanical work and the ATP consumption required for cycling cross-bridges during the oscillatory steady state. Although these results are specific to airway smooth muscle, the approach generalizes to other smooth muscles subjected to cyclic length fluctuations.     

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.     

Activation dependence of stretch activation in mouse skinned myocardium: implications for ventricular function

Recent evidence suggests that ventricular ejection is partly powered by a delayed development of force, i.e., stretch activation, in regions of the ventricular wall due to stretch resulting from torsional twist of the ventricle around the apex-to-base axis. Given the potential importance of stretch activation in cardiac function, we characterized the stretch activation response and its Ca2+ dependence in murine skinned myocardium at 22 degrees C in solutions of varying Ca2+ concentrations. Stretch activation was induced by suddenly imposing a stretch of 0.5-2.5% of initial length to the isometrically contracting muscle and then holding the muscle at the new length. The force response to stretch was multiphasic: force initially increased in proportion to the amount of stretch, reached a peak, and then declined to a minimum before redeveloping to a new steady level. This last phase of the response is the delayed force characteristic of myocardial stretch activation and is presumably due to increased attachment of cross-bridges as a consequence of stretch. The amplitude and rate of stretch activation varied with Ca2+ concentration and more specifically with the level of isometric force prior to the stretch. Since myocardial force is regulated both by Ca2+ binding to troponin-C and cross-bridge binding to thin filaments, we explored the role of cross-bridge binding in the stretch activation response using NEM-S1, a strong-binding, non-force-generating derivative of myosin subfragment 1. NEM-S1 treatment at submaximal Ca2+-activated isometric forces significantly accelerated the rate of the stretch activation response and reduced its amplitude. These data show that the rate and amplitude of myocardial stretch activation vary with the level of activation and that stretch activation involves cooperative binding of cross-bridges to the thin filament. Such a mechanism would contribute to increased systolic ejection in response to increased delivery of activator Ca2+ during excitation-contraction coupling.     

Compliant realignment of binding sites in muscle: transient behavior and mechanical tuning.

The presence of compliance in the lattice of filaments in muscle raises a number of concerns about how one accounts for force generation in the context of the cross-bridge cycle--binding site motions and coupling between cross-bridges confound more traditional analyses. To explore these issues, we developed a spatially explicit, mechanochemical model of skeletal muscle contraction. With a simple three-state model of the cross-bridge cycle, we used a Monte Carlo simulation to compute the instantaneous balance of forces throughout the filament lattice, accounting for both thin and thick filament distortions in response to cross-bridge forces. This approach is compared to more traditional mass action kinetic models (in the form of coupled partial differential equations) that assume filament inextensibility. We also monitored instantaneous force generation, ATP utilization, and the dynamics of the cross-bridge cycle in simulations of step changes in length and variations in shortening velocity. Three critical results emerge from our analyses: 1) there is a significant realignment of actin-binding sites in response to cross-bridge forces, 2) this realignment recruits additional cross-bridge binding, and 3) we predict mechanical behaviors that are consistent with experimental results for velocity and length transients. Binding site realignment depends on the relative compliance of the filament lattice and cross-bridges, and within the measured range of these parameters, gives rise to a sharply tuned peak for force generation. Such mechanical tuning at the molecular level is the result of mechanical coupling between individual cross-bridges, mediated by thick filament deformations, and the resultant realignment of binding sites on the thin filament.     

Considerations on the history dependence of muscle contraction.

When a skeletal muscle that is actively producing force is shortened or stretched, the resulting steady-state isometric force after the dynamic phase is smaller or greater, respectively, than the purely isometric force obtained at the corresponding final length. The cross-bridge model of muscle contraction does not readily explain this history dependence of force production. The most accepted proposal to explain both, force depression after shortening and force enhancement after stretch, is a nonuniform behavior of sarcomeres that develops during and after length changes. This hypothesis is based on the idea of instability of sarcomere lengths on the descending limb of the force-length relationship. However, recent evidence suggests that skeletal muscles may be stable over the entire range of active force production, including the descending limb of the force-length relationship. The purpose of this review was to critically evaluate hypotheses aimed at explaining the history dependence of force production and to provide some novel insight into the possible mechanisms underlying these phenomena. It is concluded that the sarcomere nonuniformity hypothesis cannot always explain the total force enhancement observed after stretch and likely does not cause all of the force depression after shortening. There is evidence that force depression after shortening is associated with a reduction in the proportion of attached cross bridges, which, in turn, might be related to a stress-induced inhibition of cross-bridge attachment in the myofilament overlap zone. Furthermore, we suggest that force enhancement is not associated with instability of sarcomeres on the descending limb of the force-length relationship and that force enhancement has an active and a passive component. Force depression after shortening and force enhancement after stretch are likely to have different origins.     

Evidence for increased low force cross-bridge population in shortening skinned skeletal muscle fibers: implications for actomyosin kinetics.

The dynamic characteristics of the low force myosin cross-bridges were determined in fully calcium-activated skinned rabbit psoas muscle fibers shortening under constant loads (0.04-0.7 x full isometric tension Po). The shortening was interrupted at various times by a ramp stretch (duration, 10 ms; amplitude, up to 1.8% fiber length) and the resulting tension response was recorded. Except for the earlier period of velocity transients, the tension response showed nonlinear dependence on stretch amplitude; i.e., the magnitude of the tension response started to rise disproportionately as the stretch exceeded a critical amplitude, as in the presence of inorganic phosphate (Pi). This result, as well as the result of stiffness measurement, suggests that the low force cross-bridges similar to those observed in the presence of Pi (presumably A.M.ADP.Pi) are significantly populated during shortening. The critical amplitude of the shortening fibers was greater than that of isometrically contracting fibers, suggesting that the low force cross-bridges are more negatively strained during shortening. As the load was reduced from 0.3 to 0.04 P0, the shortening velocity increased more than twofold, but the amount of the negative strain stayed remarkably constant (approximately 3 nm). This This insensitiveness of the negative strain to velocity is best explained if the dissociation of the low force cross-bridges is accelerated approximately in proportion to velocity. Along with previous reports, the results suggest that the actomyosin ATPase cycle in muscle fibers has at least two key reaction steps in which rate constants are sensitively regulated by shortening velocity and that one of them is the dissociation of the low force A.M.ADP.Pi cross-bridges. This step may virtually limit the rate of actomyosin ATPase turnover and help increase efficiency in fibers shortening at high velocities.     

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.     

Changes in force and stiffness during stretch of skeletal muscle fibers, effects of hypertonicity.

Slow stretch ramps (velocity: 0.17 fiber lengths s-1) were imposed during fused tetanic contractions of intact muscle fibers of the frog (1.4-3.0 degrees C; sarcomere length: 2.12-2.21 microns). Instantaneous force-extension relations were derived both under isometric conditions and during slow stretch by applying fast (0.2 ms) length steps to the fiber. An increase in tonicity (98 mM sucrose added to control Ringer solution) led to significant reduction of the maximum isometric tension but at the same time to marked increase in the force enhancement during slow stretch. The maximum force level reached during the stretch was affected very little. Experiments on relaxed fibers showed that recruitment of passive parallel elastic components were of no relevance for these effects. Hypertonicity slightly increased the instantaneous stiffness of the active fiber both in the presence and in the absence of stretch. The total extension of the undamped fiber elasticity was considerably reduced by increased tonicity under isometric conditions but was only slightly affected during slow stretch. The change in length of the undamped cross-bride elasticity upon stretch was thus greater in the hypertonic than in the normotonic solution suggesting a greater increase in force per cross-bridge in the hypertonic medium. The contractile effects are consistent with the assumptions that hypertonicity reduces the capability of the individual cross-bridge to produce active force and, furthermore, that hypertonicity has only minor effects on the number of attached cross-bridges and the maximum load-bearing capacity of the individual bridge.     

The frequency response of smooth muscle stiffness during Ca2+-activated contraction

To investigate the mechanism of smooth muscle contraction, the frequency response of the muscle stiffness of single beta-escin permeabilized smooth muscle cells in the relaxed state was studied. Also, the response was continuously monitored for 3 min from the beginning of the exchange of relaxing solution to activating solution, and then at 5-min intervals for up to 20 min. The frequency response (30 Hz bandwidth, 0.33 Hz (or 0.2 Hz) resolution) was calculated from the Fourier-transformed force and length sampled during a 3-s (or 5-s) constant-amplitude length perturbation of increasing-frequency (1-32 Hz) sine waves. In the relaxed state, a large negative phase angle was observed, which suggests the existence of attached energy generating cross-bridges. As the activation progressed, the muscle stiffness and phase angle steadily increased; these increases gradually extended to higher frequencies, and reached a steady state by 100 s after activation or approximately 40 s after stiffness began to increase. The results suggest that a fixed distribution of cross-bridge states was reached after 40 s of Ca2+ activation and the cross-bridge cycling rate did not change during the period of force maintenance.     

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.