Effects of length oscillation on the subsequent force development in swine tracheal smooth muscle.

It has been shown that deep inspiration (DI) taken before application of bronchoconstricting stimuli causes a reduction in the subsequent bronchoconstriction; a fast DI has a greater inhibitory effect than a slow DI. We hypothesize that periodic length changes imposed on a relaxed airway smooth muscle (ASM) would attenuate subsequent bronchoconstriction by disrupting the organization of the contractile apparatus, and this could be an important mechanism for the observed bronchoprotective effect of DI and tidal breathing. Length oscillations of different amplitude, frequency, and duration were applied to a relaxed muscle. The effects of such perturbations on force development were then assessed. Results show that oscillations reduce the subsequent force generation and that the magnitude of force reduction is proportional to amplitude and duration of the length oscillation. After the oscillation, isometric force recovered to the preoscillation level in a series of isometric contractions, and the rate of recovery was facilitated by frequent stimulation. The in vitro behavior of ASM found in this study could account for the observed temporary reduction in bronchoconstriction subsequent to a DI.     

Responsiveness of the isolated airway during simulated deep inspirations: effect of airway smooth muscle stiffness and strain.

In vivo, breathing movements, including tidal and deep inspirations (DIs), exert a number of beneficial effects on respiratory system responsiveness in healthy humans that are diminished or lost in asthma, possibly as a result of reduced distension (strain) of airway smooth muscle (ASM). We used bronchial segments from pigs to assess airway responsiveness under static conditions and during simulated tidal volume oscillations with and without DI and to determine the roles of airway stiffness and ASM strain on responsiveness. To simulate airway dilations during breathing, we cycled the luminal volume of liquid-filled segments. Volume oscillations (15 cycles/min) were set so that, in relaxed airways, they produced a transmural pressure increase of approximately 5-10 cmH(2)O for tidal maneuvers and approximately 5-30 cmH(2)O for DIs. ACh dose-response curves (10(-7)-3 x 10(-3) M) were constructed under static and dynamic conditions, and maximal response and sensitivity were determined. Airway stiffness was measured from tidal trough-to-peak pressure and volume cycles. ASM strain produced by DI was estimated from luminal volume, airway length, and inner wall area. DIs produced substantial ( approximately 40-50%) dilation, reflected by a decrease in maximal response (P < 0.001) and sensitivity (P < 0.05). However, the magnitude of bronchodilation decreased significantly in proportion to airway stiffening caused by contractile activation and an associated reduction in ASM strain. Tidal oscillations, in comparison, had little effect on responsiveness. We conclude that DI regulates airway responsiveness at the airway level, but this is limited by airway stiffness due to reduced ASM strain.     

The effects of pH on force and stiffness development in mouse muscles

Changes in force and stiffness during contractions of mouse extensor digitorum longus and soleus muscles were measured over a range of extracellular pH from 6.4 to 7.4. Muscle stiffness was measured using small amplitude (less than 0.1% of muscle length), high frequency (1.5 kHz) oscillations in length. Twitch force was not significantly affected by changes in pH, but the peak force during repetitive stimulation (2, 3, and 20 pulses) was decreased significantly as the pH was reduced. Changes in muscle stiffness with pH were in the same direction, but smaller in extent. If the number of attached cross-bridges in the muscle can be determined from the measurement of small amplitude, high frequency muscle stiffness, then these findings suggest that (a) the number of cross-bridges between thick and thin filaments declines in low pH and (b) the average force per cross-bridge also declines in low pH. The decline in force per cross-bridge could arise from a reduction in the ability of cross-bridges to generate force during their state of active force production and (or) in an increased percentage of bonds in a low force, "rigor" state.     

Latrunculin B increases force fluctuation-induced relengthening of ACh-contracted, isotonically shortened canine tracheal smooth muscle.

We hypothesized that differences in actin filament length could influence force fluctuation-induced relengthening (FFIR) of contracted airway smooth muscle and tested this hypothesis as follows. One-hundred micromolar ACh-stimulated canine tracheal smooth muscle (TSM) strips set at optimal reference length (Lref) were allowed to shorten against 32% maximal isometric force (Fmax) steady preload, after which force oscillations of +/-16% Fmax were superimposed. Strips relengthened during force oscillations. We measured hysteresivity and calculated FFIR as the difference between muscle length before and after 20-min imposed force oscillations. Strips were relaxed by ACh removal and treated for 1 h with 30 nM latrunculin B (sequesters G-actin and promotes depolymerization) or 500 nM jasplakinolide (stabilizes actin filaments and opposes depolymerization). A second isotonic contraction protocol was then performed; FFIR and hysteresivity were again measured. Latrunculin B increased FFIR by 92.2 +/- 27.6% Lref and hysteresivity by 31.8 +/- 13.5% vs. pretreatment values. In contrast, jasplakinolide had little influence on relengthening by itself; neither FFIR nor hysteresivity was significantly affected. However, when jasplakinolide-treated tissues were then incubated with latrunculin B in the continued presence of jasplakinolide for 1 more h and a third contraction protocol performed, latrunculin B no longer substantially enhanced TSM relengthening. In TSM treated with latrunculin B + jasplakinolide, FFIR increased by only 3.03 +/- 5.2% Lref and hysteresivity by 4.14 +/- 4.9% compared with its first (pre-jasplakinolide or latrunculin B) value. These results suggest that actin filament length, in part, determines the relengthening of contracted airway smooth muscle.     

Relaxation of activated airway smooth muscle: relative potency of isoproterenol vs. tidal stretch.

Both isoproterenol and tidal fluctuations of muscle length inhibit active force development in activated airway smooth muscle. In this study, we show that length fluctuations in the range of amplitudes expected during quiet tidal breathing produce force inhibition that is equipotent with high concentrations of isoproterenol. Active force fell to 50% of its isometric value when the amplitude of the tidal stretch was 4% of muscle length. The relaxing effects of length fluctuations were insensitive to the specific contractile agonist, suggesting that the mechanism of action is largely independent of the particular signal transduction pathway and lies instead at the level of bridge dynamics. This idea is reinforced by the results of combining the relaxation effects of tidal fluctuations with those produced by isoproterenol at all but the highest concentrations studied (10(-5) M). Such a combination produces multiplicative effects, indicating largely separate modes of action. These observations suggest that the tidal muscle stretches that are attendant to spontaneous breathing comprise the first line of defense against bronchospasm and that tidal muscle stretches may be the most important of all known bronchodilating agencies.     

Inhibition of the p38 MAP kinase pathway destabilizes smooth muscle length during physiological loading

We tested the hypothesis that mechanical plasticity of airway smooth muscle may be mediated in part by the p38 mitogen-activated protein (MAP) kinase pathway. Bovine tracheal smooth muscle (TSM) strips were mounted in a muscle bath and set to their optimal length, where the active force was maximal (F(o)). Each strip was then contracted isotonically (at 0.32 F(o)) with ACh (maintained at 10(-4) M) and allowed to shorten for 180 min, by which time shortening was completed and the static equilibrium length was established. To simulate the action of breathing, we then superimposed on this steady distending force a sinusoidal force fluctuation with zero mean, at a frequency of 0.2 Hz, and measured incremental changes in muscle length. We found that TSM strips incubated in 10 microM SB-203580-HCl, an inhibitor of the p38 MAP kinase pathway, demonstrated a greater degree of fluctuation-driven lengthening than did control strips, and upon removal of the force fluctuations they remained at a greater length. We also found that the force fluctuations themselves activated the p38 MAP kinase pathway. These findings are consistent with the hypothesis that inhibition of the p38 MAP kinase pathway destabilizes muscle length during physiological loading.     

Nonlinear Compliance Modulates Dynamic Bronchoconstriction in a Multiscale Airway Model

The role of breathing and deep inspirations (DI) in modulating airway hyperresponsiveness remains poorly understood. In particular, DIs are potent bronchodilators of constricted airways in nonasthmatic subjects but not in asthmatic subjects. Additionally, length fluctuations (mimicking DIs) have been shown to reduce mean contractile force when applied to airway smooth muscle (ASM) cells and tissue strips. However, these observations are not recapitulated on application of transmural pressure (P_TM) oscillations (that mimic tidal breathing and DIs) in isolated intact airways. To shed light on this paradox, we have developed a biomechanical model of the intact airway, accounting for strain-stiffening due to collagen recruitment (a large component of the extracellular matrix (ECM)), and dynamic actomyosin-driven force generation by ASM cells. In agreement with intact airway studies, our model shows that P_TM fluctuations at particular mean transmural pressures can lead to only limited bronchodilation. However, our model predicts that moving the airway to a more compliant point on the static pressure-radius relationship (which may involve reducing mean P_TM), before applying pressure fluctuations, can generate greater bronchodilation. This difference arises from competition between passive strain-stiffening of ECM and force generation by ASM yielding a highly nonlinear relationship between effective airway stiffness and P_TM, which is modified by the presence of contractile agonist. Effectively, the airway at its most compliant may allow for greater strain to be transmitted to subcellular contractile machinery. The model predictions lead us to hypothesize that the maximum possible bronchodilation of an airway depends on its static compliance at the P_TM about which the fluctuations are applied. We suggest the design of additional experimental protocols to test this hypothesis.     

Could an increase in airway smooth muscle shortening velocity cause airway hyperresponsiveness?

Airway hyperresponsiveness (AHR) is a characteristic feature of asthma. It has been proposed that an increase in the shortening velocity of airway smooth muscle (ASM) could contribute to AHR. To address this possibility, we tested whether an increase in the isotonic shortening velocity of ASM is associated with an increase in the rate and total amount of shortening when ASM is subjected to an oscillating load, as occurs during breathing. Experiments were performed in vitro using 27 rat tracheal ASM strips supramaximally stimulated with methacholine. Isotonic velocity at 20% isometric force (Fiso) was measured, and then the load on the muscle was varied sinusoidally (0.33 ± 0.25 Fiso, 1.2 Hz) for 20 min, while muscle length was measured. A large amplitude oscillation was applied every 4 min to simulate a deep breath. We found that: 1) ASM strips with a higher isotonic velocity shortened more quickly during the force oscillations, both initially (P < 0.001) and after the simulated deep breaths (P = 0.002); 2) ASM strips with a higher isotonic velocity exhibited a greater total shortening during the force oscillation protocol (P < 0.005); and 3) the effect of an increase in isotonic velocity was at least comparable in magnitude to the effect of a proportional increase in ASM force-generating capacity. A cross-bridge model showed that an increase in the total amount of shortening with increased isotonic velocity could be explained by a change in either the cycling rate of phosphorylated cross bridges or the rate of myosin light chain phosphorylation. We conclude that, if asthma involves an increase in ASM velocity, this could be an important factor in the associated AHR.     

Myosin filament polymerization and depolymerization in a model of partial length adaptation in airway smooth muscle

Length adaptation in airway smooth muscle (ASM) is attributed to reorganization of the cytoskeleton, and in particular the contractile elements. However, a constantly changing lung volume with tidal breathing (hence changing ASM length) is likely to restrict full adaptation of ASM for force generation. There is likely to be continuous length adaptation of ASM between states of incomplete or partial length adaption. We propose a new model that assimilates findings on myosin filament polymerization/depolymerization, partial length adaptation, isometric force, and shortening velocity to describe this continuous length adaptation process. In this model, the ASM adapts to an optimal force-generating capacity in a repeating cycle of events. Initially the myosin filament, shortened by prior length changes, associates with two longer actin filaments. The actin filaments are located adjacent to the myosin filaments, such that all myosin heads overlap with actin to permit maximal cross-bridge cycling. Since in this model the actin filaments are usually longer than myosin filaments, the excess length of the actin filament is located randomly with respect to the myosin filament. Once activated, the myosin filament elongates by polymerization along the actin filaments, with the growth limited by the overlap of the actin filaments. During relaxation, the myosin filaments dissociate from the actin filaments, and then the cycle repeats. This process causes a gradual adaptation of force and instantaneous adaptation of shortening velocity. Good agreement is found between model simulations and the experimental data depicting the relationship between force development, myosin filament density, or shortening velocity and length.     

Mechanisms for the mechanical response of airway smooth muscle to length oscillation

Shen, X., M. F. Wu, R. S. Tepper, and S. J. Gunst. Mechanisms for the mechanical response ofairway smooth muscle to length oscillation. J. Appl.Physiol. 83(3): 731-738, 1997.Airway smoothmuscle tone in vitro is profoundly affected by oscillations in musclelength, suggesting that the effects of lung volume changes on airwaytone result from direct effects of stretch on the airway smooth muscle.We analyzed the effect of length oscillation on active force andlength-force hysteresis in canine tracheal smooth muscle at differentoscillation rates and amplitudes during contraction with acetylcholine.During the shortening phase of the length oscillation cycle, the activeforce generated by the smooth muscle decreased markedly below theisometric force but returned to isometric force as the muscle waslengthened. Results indicate that at rates comparable to those duringtidal breathing, active shortening and yielding of contractile elementscontributes to the modulation of force during length oscillation;however, the depression of force during shortening cannot be accountedfor by cross-bridge properties, shortening-induced cross-bridgedeactivation, or active relaxation. We conclude that the depression ofcontractility may be a function of the plasticity of the cellularorganization of contractile filaments, which enables contractileelement length to be reset in relation to smooth muscle cell length asa result of smooth muscle stretch.

     

Smooth muscle molecular mechanics in airway hyperresponsiveness and asthma

Asthma is a respiratory disorder characterized by airway inflammation and hyperresponsiveness associated with reversible airway obstruction. The relative contributions of airway hyperresponsiveness and inflammation are still debated, but ultimately, airway narrowing mediated by airway smooth muscle contraction is the final pathway to asthma. Considerable effort has been devoted towards identifying the factors that lead to the airway smooth muscle hypercontractility observed in asthma, and this will be the focus of this review. Airway remodeling has been observed in severe and fatal asthma. However, it is unclear whether remodeling plays a protective role or worsens airway responsiveness. Smooth muscle plasticity is a mechanism likely implicated in asthma, whereby contractile filament rearrangements lead to maximal force production, independent of muscle length. Increased smooth muscle rate of shortening via altered signaling pathways or altered contractile protein expression has been demonstrated in asthma and in numerous models of airway hyperresponsiveness. Increased rate of shortening is implicated in counteracting the relaxing effect of tidal breathing and deep inspirations, thereby creating a contracted airway smooth muscle steady-state. Further studies are therefore required to understand the numerous mechanisms leading to the airway hyperresponsiveness observed in asthma as well as their multiple interactions.     

Dynamic equilibration of airway smooth muscle contraction during physiological loading.

Airway smooth muscle contraction is the central event in acute airway narrowing in asthma. Most studies of isolated muscle have focused on statically equilibrated contractile states that arise from isometric or isotonic contractions. It has recently been established, however, that muscle length is determined by a dynamically equilibrated state of the muscle in which small tidal stretches associated with the ongoing action of breathing act to perturb the binding of myosin to actin. To further investigate this phenomenon, we describe in this report an experimental method for subjecting isolated muscle to a dynamic microenvironment designed to closely approximate that experienced in vivo. Unlike previous methods that used either time-varying length control, force control, or time-invariant auxotonic loads, this method uses transpulmonary pressure as the controlled variable, with both muscle force and muscle length free to adjust as they would in vivo. The method was implemented by using a servo-controlled lever arm to load activated airway smooth muscle strips with transpulmonary pressure fluctuations of increasing amplitude, simulating the action of breathing. The results are not consistent with classical ideas of airway narrowing, which rest on the assumption of a statically equilibrated contractile state; they are consistent, however, with the theory of perturbed equilibria of myosin binding. This experimental method will allow for quantitative experimental evaluation of factors that were previously outside of experimental control, including sensitivity of muscle length to changes of tidal volume, changes of lung volume, shape of the load characteristic, loss of parenchymal support and inflammatory thickening of airway wall compartments.     

Fading memory model for airway smooth muscle dynamic response

This work presents the application of a fading memory model to describe the behavior of contracted airway smooth muscle (ASM) for two biophysical cases: finite duration length steps and longitudinal sinusoidal oscillations. The model parameters were initially determined from literature data on transient step length change response and subsequently the model was applied to the two cases. Results were compared with previously published experimental data on ASM oscillations. The model confirms a trend observed in the experimental data which shows that: (i) the value of tissue length change is the most important factor to determine the degree of cross-bridge detachment and (ii) a strong correlation exists between increasing frequency and declining stiffness until a certain frequency (∼25 Hz) beyond which frequency dependence is negligible. Although the model was not intended to simulate biophysical events individually, the data could be explained by cross-bridge cycling rates. As the frequency increases, cross-bridge reattachment becomes less likely, until no further cross-bridge attachment is possible.     

Effect of Loading History on Airway Smooth Muscle Cell-Matrix Adhesions

Integrin-mediated adhesions between airway smooth muscle (ASM) cells and the extracellular matrix (ECM) regulate how contractile forces generated within the cell are transmitted to its external environment. Environmental cues are known to influence the formation, size, and survival of cell-matrix adhesions, but it is not yet known how they are affected by dynamic fluctuations associated with tidal breathing in the intact airway. Here, we develop two closely related theoretical models to study adhesion dynamics in response to oscillatory loading of the ECM, representing the dynamic environment of ASM cells in vivo. Using a discrete stochastic-elastic model, we simulate individual integrin binding and rupture events and observe two stable regimes in which either bond formation or bond rupture dominate, depending on the amplitude of the oscillatory loading. These regimes have either a high or low fraction of persistent adhesions, which could affect the level of strain transmission between contracted ASM cells and the airway tissue. For intermediate loading, we observe a region of bistability and hysteresis due to shared loading between existing bonds; the level of adhesion depends on the loading history. These findings are replicated in a related continuum model, which we use to investigate the effect of perturbations mimicking deep inspirations (DIs). Because of the bistability, a DI applied to the high adhesion state could either induce a permanent switch to a lower adhesion state or allow a return of the system to the high adhesion state. Transitions between states are further influenced by the frequency of oscillations, cytoskeletal or ECM stiffnesses, and binding affinities, which modify the magnitudes of the stable adhesion states as well as the region of bistability. These findings could explain (in part) the transient bronchodilatory effect of a DI observed in asthmatics compared to a more sustained effect in normal subjects.     

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.     

Cyclic stretch enhances reorientation and differentiation of 3-D culture model of human airway smooth muscle

Activation of airway smooth muscle (ASM) cells plays a central role in the pathophysiology of asthma. Because ASM is an important therapeutic target in asthma, it is beneficial to develop bioengineered ASM models available for assessing physiological and biophysical properties of ASM cells. In the physiological condition in vivo, ASM cells are surrounded by extracellular matrix (ECM) and exposed to mechanical stresses such as cyclic stretch. We utilized a 3-D culture model of human ASM cells embedded in type-I collagen gel. We further examined the effects of cyclic mechanical stretch, which mimics tidal breathing, on cell orientation and expression of contractile proteins of ASM cells within the 3-D gel. ASM cells in type-I collagen exhibited a tissue-like structure with actin stress fiber formation and intracellular Ca²⁺ mobilization in response to methacholine. Uniaxial cyclic stretching enhanced alignment of nuclei and actin stress fibers of ASM cells. Moreover, expression of mRNAs for contractile proteins such as α-smooth muscle actin, calponin, myosin heavy chain 11, and transgelin of stretched ASM cells was significantly higher than that under the static condition. Our findings suggest that mechanical force and interaction with ECM affects development of the ASM tissue-like construct and differentiation to the contractile phenotype in a 3-D culture model.     

A maturational model for the study of airway smooth muscle adaptation to mechanical oscillation

It has been shown that mechanical stretches imposed on airway smooth muscle (ASM) by deep inspiration reduce the subsequent contractile response of the ASM. This passive maneuver of lengthening and retraction of the muscle is beneficial in normal subjects to counteract bronchospasm. However, it is detrimental to hyperresponsive airways because it triggers further bronchoconstriction. Although the exact mechanisms for this contrary response by normal and hyperresponsive airways are unclear, it has been suggested that the phenomenon is related to changes in ASM adaptability to mechanical oscillation. Healthy immature airways of both human and animal exhibit hyperresponsiveness, but whether the adaptative properties of hyperresponsive airway differ from normal is still unknown. In this article, we review the phenomenon of ASM adaptation to mechanical oscillation and its relevance and implication to airway hyperresponsiveness. We demonstrate that the age-specific expression of ASM adaptation is prominent using an established maturational animal model developed in our laboratory. Our data on immature ASM showed potentiated contractile force shortly after a length oscillation compared with the maximum force generated before oscillation. Several potential mechanisms such as myogenic response, changes in actin polymerization, or changes in the quantity of the cytoskeletal regulatory proteins plectin and vimentin, which may underlie this age-specific force potentiation, are discussed. We suggest a working model of the structure of smooth muscle associated with force transmission, which may help to elucidate the mechanisms responsible for the age-specific expression of smooth muscle adaptation. It is important to study the maturational profile of ASM adaptation as it could contribute to juvenile hyperresponsiveness.     

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.     

Breathing pattern of anesthetized humans during pancuronium-induced partial paralysis

We investigated the breathing patterns of 17 subjects anesthetized with enflurane before and after partial muscle paralysis produced by pancuronium bromide. In the face of significant muscle weakness produced by pancuronium, breathing patterns are characterized by decreases in both tidal volume and respiratory frequency. The decreased tidal volume corresponded to the decrease in occlusion pressure, indicating that the decreased tidal volume results solely from a decreased contractile force of the respiratory muscles. The decreased respiratory frequency was due to prolongation of both inspiratory and expiratory time without changing the ratio of the inspiratory time to the total breath time. Withdrawal of phasic vagal influence by airway occlusion before partial muscle paralysis revealed that an active Breuer-Hering inflation reflex was operative in only 8 of all 17 subjects. Since the contribution of the Breuer-Hering inflation reflex alone does not seem to account for the consistent decrease in respiratory frequency, some other mechanisms modulating respiratory frequency might be involved in the characteristic breathing patterns during partial muscle paralysis under enflurane anesthesia.     

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.