Cross-bridge scheme and force per cross-bridge state in skinned rabbit psoas muscle fibers.

The rate and association constants (kinetic constants) which comprise a seven state cross-bridge scheme were deduced by sinusoidal analysis in chemically skinned rabbit psoas muscle fibers at 20 degrees C, 200 mM ionic strength, and during maximal Ca2+ activation (pCa 4.54-4.82). The kinetic constants were then used to calculate the steady state probability of cross-bridges in each state as the function of MgATP, MgADP, and phosphate (Pi) concentrations. This calculation showed that 72% of available cross-bridges were (strongly) attached during our control activation (5 mM MgATP, 8 mM Pi), which agreed approximately with the stiffness ratio (active:rigor, 69 +/- 3%); active stiffness was measured during the control activation, and rigor stiffness after an induction of the rigor state. By assuming that isometric tension is a linear combination of probabilities of cross-bridges in each state, and by measuring tension as the function of MgATP, MgADP, and Pi concentrations, we deduced the force associated with each cross-bridge state. Data from the osmotic compression of muscle fibers by dextran T500 were used to deduce the force associated with one of the cross-bridge states. Our results show that force is highest in the AM*ADP.Pi state (A = actin, M = myosin). Since the state which leads into the AM*ADP.Pi state is the weakly attached AM.ADP.Pi state, we confirm that the force development occurs on Pi isomerization (AM.ADP.Pi --> AM*ADP.Pi). Our results also show that a minimal force change occurs with the release of Pi or MgADP, and that force declines gradually with ADP isomerization (AM*ADP -->AM.ADP), ATP isomerization (AM+ATP-->AM*ATP), and with cross-bridge detachment. Force of the AM state agreed well with force measured after induction of the rigor state, indicating that the AM state is a close approximation of the rigor state. The stiffness results obtained as functions of MgATP, MgADP, and Pi concentrations were generally consistent with the cross-bridge scheme.     

Effects of MgATP, MgADP, and Pi on actin movement by smooth muscle myosin.

To test the idea that the in vitro motility assay is a simplified model system for muscle contraction, the MgATP-dependent movement of actin filaments by thiophosphorylated smooth muscle myosin was characterized in the presence of the products MgADP and inorganic phosphate. The dependence of actin filament velocity on MgATP concentration was hyperbolic with a maximum velocity of 0.6 micron/s and an apparent Km = 40 microM (30 degrees C). MgADP competitively inhibited actin movement by MgATP with a Ki = 0.25 mM. Inorganic phosphate did not affect actin filament velocity in the presence of 1 mM MgATP, but competitively inhibited movement in the presence of 50 microM MgATP with a Ki = 9.5 mM. The effects of ADP and Pi on velocity agree with fiber mechanical studies, confirming that the motility assay is an excellent system to investigate the molecular mechanisms of force generation and shortening in smooth muscle. The rate at which rigor cross-bridges can be recruited to move actin filaments was observed by initiating cross-bridge cycling from rigor by flash photolysis of caged MgATP. Following the flash, which results in a rapid increase in MgATP concentration, actin filaments experienced a MgATP-dependent delay prior to achieving steady state velocity. The delay at low MgATP concentrations was interpreted as evidence that motion generating cross-bridges are slowed by a load due to a transiently high percentage of rigor cross-bridges immediately following MgATP release.     

Cross-bridge kinetics, cooperativity, and negatively strained cross- bridges in vertebrate smooth muscle. A laser-flash photolysis study

The effects of laser-flash photolytic release of ATP from caged ATP [P3-1(2-nitrophenyl)ethyladenosine-5'-triphosphate] on stiffness and tension transients were studied in permeabilized guinea pig protal vein smooth muscle. During rigor, induced by removing ATP from the relaxed or contracting muscles, stiffness was greater than in relaxed muscle, and electron microscopy showed cross-bridges attached to actin filaments at an approximately 45 degree angle. In the absence of Ca2+, liberation of ATP (0.1-1 mM) into muscles in rigor caused relaxation, with kinetics indicating cooperative reattachment of some cross-bridges. Inorganic phosphate (Pi; 20 mM) accelerated relaxation. A rapid phase of force development, accompanied by a decline in stiffness and unaffected by 20 mM Pi, was observed upon liberation of ATP in muscles that were released by 0.5-1.0% just before the laser pulse. This force increment observed upon detachment suggests that the cross-bridges can bear a negative tension. The second-order rate constant for detachment of rigor cross-bridges by ATP, in the absence of Ca2+, was estimated to be 0.1-2.5 X 10(5) M-1s-1, which indicates that this reaction is too fast to limit the rate of ATP hydrolysis during physiological contractions. In the presence of Ca2+, force development occurred at a rate (0.4 s-1) similar to that of intact, electrically stimulated tissue. The rate of force development was an order of magnitude faster in muscles that had been thiophosphorylated with ATP gamma S before the photochemical liberation of ATP, which indicates that under physiological conditions, in non-thiophosphorylated muscles, light-chain phosphorylation, rather than intrinsic properties of the actomyosin cross-bridges, limits the rate of force development. The release of micromolar ATP or CTP from caged ATP or caged CTP caused force development of up to 40% of maximal active tension in the absence of Ca2+, consistent with cooperative attachment of cross-bridges. Cooperative reattachment of dephosphorylated cross-bridges may contribute to force maintenance at low energy cost and low cross-bridge cycling rates in smooth muscle.     

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.     

The smooth muscle cross-bridge cycle studied using sinusoidal length perturbations

The mechanical characteristics of smooth muscle can be broadly defined as either phasic, or fast contracting, and tonic, or slow contracting (, Pharmacol. Rev. 20:197-272). To determine if differences in the cross-bridge cycle and/or distribution of the cross-bridge states could contribute to differences in the mechanical properties of smooth muscle, we determined force and stiffness as a function of frequency in Triton-permeabilized strips of rabbit portal vein (phasic) and aorta (tonic). Permeabilized muscle strips were mounted between a piezoelectric length driver and a piezoresistive force transducer. Muscle length was oscillated from 1 to 100 Hz, and the stiffness was determined as a function of frequency from the resulting force response. During calcium activation (pCa 4, 5 mM MgATP), force and stiffness increased to steady-state levels consistent with the attachment of actively cycling cross-bridges. In smooth muscle, because the cross-bridge states involved in force production have yet to be elucidated, the effects of elevation of inorganic phosphate (P(i)) and MgADP on steady-state force and stiffness were examined. When portal vein strips were transferred from activating solution (pCa 4, 5 mM MgATP) to activating solution with 12 mM P(i), force and stiffness decreased proportionally, suggesting that cross-bridge attachment is associated with P(i) release. For the aorta, elevating P(i) decreased force more than stiffness, suggesting the existence of an attached, low-force actin-myosin-ADP- P(i) state. When portal vein strips were transferred from activating solution (pCa 4, 5 mM MgATP) to activating solution with 5 mM MgADP, force remained relatively constant, while stiffness decreased approximately 50%. For the aorta, elevating MgADP decreased force and stiffness proportionally, suggesting for tonic smooth muscle that a significant portion of force production is associated with ADP release. These data suggest that in the portal vein, force is produced either concurrently with or after P(i) release but before MgADP release, whereas in aorta, MgADP release is associated with a portion of the cross-bridge powerstroke. These differences in cross-bridge properties could contribute to the mechanical differences in properties of phasic and tonic smooth muscle.     

Suppression of muscle contraction by vanadate. Mechanical and ligand binding studies on glycerol-extracted rabbit fibers

The suppression of tension development by orthovanadate (Vi) was studied in mechanical experiments and by measuring the binding of radioactive Vi and nucleotides to glycerol-extracted rabbit muscle fibers. During active contractions, Vi bound to the cross-bridges and suppressed tension with an apparent second-order rate constant of 1.34 X 10(3) M-1s-1. The half-saturation concentration for tension suppression was 94 microM Vi. The incubation of fibers in Vi relaxing or rigor solutions prior to initiation of active contractions had little effect on the initial rise of active tension. The addition of adenosine diphosphate (ADP) and Vi to fibers in rigor did not cause relaxation. Suppression of tension only developed during cross-bridge cycling. After slow relaxation from rigor in 1 mM Vi and low (50 microM) MgATP concentration (0 Ca2+), radioactive Vi and ADP were trapped within the fiber. This finding indicated the formation of a stable myosin X ADP X Vi complex, as has been reported in biochemical experiments with isolated myosin. Vi and ADP trapped within the fibers were released only by subsequent cross-bridge attachment. Vi and ADP were preferentially trapped under conditions of cross-bridge cycling in the presence of ATP rather than in relaxed fibers or in rigor with ADP. These results indicate that in the normal cross-bridge cycle, inorganic phosphate (Pi) is released from actomyosin before ADP. The resulting actomyosin X ADP intermediate can bind Vi and Pi. This intermediate probably supports force. Vi behaves as a close analogue of Pi in muscle fibers, as it does with isolated actomyosin.     

Effect of inorganic phosphate on the force and number of myosin cross-bridges during the isometric contraction of permeabilized muscle fibers from rabbit psoas

The relation between the chemical and mechanical steps of the myosin-actin ATPase reaction that leads to generation of isometric force in fast skeletal muscle was investigated in demembranated fibers of rabbit psoas muscle by determining the effect of the concentration of inorganic phosphate (Pi) on the stiffness of the half-sarcomere (hs) during transient and steady-state conditions of the isometric contraction (temperature 12°C, sarcomere length 2.5 μm). Changes in the hs strain were measured by imposing length steps or small 4 kHz oscillations on the fibers in control solution (without added Pi) and in solution with 3-20 mM added Pi. At the plateau of the isometric contraction in control solution, the hs stiffness is 22.8 ± 1.1 kPa nm⁻¹. Taking the filament compliance into account, the total stiffness of the array of myosin cross-bridges in the hs (e) is 40.7 ± 3.7 kPa nm⁻¹. An increase in [Pi] decreases the stiffness of the cross-bridge array in proportion to the isometric force, indicating that the force of the cross-bridge remains constant independently of [Pi]. The rate constant of isometric force development after a period of unloaded shortening (r_F) is 23.5 ± 1.0 s⁻¹ in control solution and increases monotonically with [Pi], attaining a maximum value of 48.6 ± 0.9 s⁻¹ at 20 mM [Pi], in agreement with the idea that Pi release is a relatively fast step after force generation by the myosin cross-bridge. During isometric force development at any [Pi], e and thus the number of attached cross-bridges increase in proportion to the force, indicating that, independently of the speed of the process that leads to myosin attachment to actin, there is no significant (>1 ms) delay between generation of stiffness and generation of force by the cross-bridges.     

Muscle cross-bridges bound to actin are disordered in the presence of 2,3-butanedione monoxime.

Electron paramagnetic resonance spectroscopy was used to monitor the orientation of muscle cross-bridges attached to actin in a low force and high stiffness state that may occur before force generation in the actomyosin cycle of interactions. 2,3-butanedione monoxime (BDM) has been shown to act as an uncompetitive inhibitor of the myosin ATPase that stabilizes a myosin.ADP.P(i) complex. Such a complex is thought to attach to actin at the beginning of the powerstroke. Addition of 25 mM BDM decreases tension by 90%, although stiffness remains high, 40-50% of control, showing that cross-bridges are attached to actin but generate little or no force. Active cross-bridge orientation was monitored via electron paramagnetic resonance spectroscopy of a maleimide spin probe rigidly attached to cys-707 (SH-1) on the myosin head. A new labeling procedure was used that showed improved specificity of labeling. In 25 mM BDM, the probes have an almost isotropic angular distribution, indicating that cross-bridges are highly disordered. We conclude that in the pre-powerstroke state stabilized by BDM, cross-bridges are attached to actin, generating little force, with a large portion of the catalytic domain of the myosin heads disordered.     

Nonlinear Cross-Bridge Elasticity and Post-Power-Stroke Events in Fast Skeletal Muscle Actomyosin

Generation of force and movement by actomyosin cross-bridges is the molecular basis of muscle contraction, but generally accepted ideas about cross-bridge properties have recently been questioned. Of the utmost significance, evidence for nonlinear cross-bridge elasticity has been presented. We here investigate how this and other newly discovered or postulated phenomena would modify cross-bridge operation, with focus on post-power-stroke events. First, as an experimental basis, we present evidence for a hyperbolic [MgATP]-velocity relationship of heavy-meromyosin-propelled actin filaments in the in vitro motility assay using fast rabbit skeletal muscle myosin (28–29°C). As the hyperbolic [MgATP]-velocity relationship was not consistent with interhead cooperativity, we developed a cross-bridge model with independent myosin heads and strain-dependent interstate transition rates. The model, implemented with inclusion of MgATP-independent detachment from the rigor state, as suggested by previous single-molecule mechanics experiments, accounts well for the [MgATP]-velocity relationship if nonlinear cross-bridge elasticity is assumed, but not if linear cross-bridge elasticity is assumed. In addition, a better fit is obtained with load-independent than with load-dependent MgATP-induced detachment rate. We discuss our results in relation to previous data showing a nonhyperbolic [MgATP]-velocity relationship when actin filaments are propelled by myosin subfragment 1 or full-length myosin. We also consider the implications of our results for characterization of the cross-bridge elasticity in the filament lattice of muscle.     

Nonlinear Cross-Bridge Elasticity and Post-Power-Stroke Events in Fast Skeletal Muscle Actomyosin

Generation of force and movement by actomyosin cross-bridges is the molecular basis of muscle contraction, but generally accepted ideas about cross-bridge properties have recently been questioned. Of the utmost significance, evidence for nonlinear cross-bridge elasticity has been presented. We here investigate how this and other newly discovered or postulated phenomena would modify cross-bridge operation, with focus on post-power-stroke events. First, as an experimental basis, we present evidence for a hyperbolic [MgATP]-velocity relationship of heavy-meromyosin-propelled actin filaments in the in vitro motility assay using fast rabbit skeletal muscle myosin (28–29°C). As the hyperbolic [MgATP]-velocity relationship was not consistent with interhead cooperativity, we developed a cross-bridge model with independent myosin heads and strain-dependent interstate transition rates. The model, implemented with inclusion of MgATP-independent detachment from the rigor state, as suggested by previous single-molecule mechanics experiments, accounts well for the [MgATP]-velocity relationship if nonlinear cross-bridge elasticity is assumed, but not if linear cross-bridge elasticity is assumed. In addition, a better fit is obtained with load-independent than with load-dependent MgATP-induced detachment rate. We discuss our results in relation to previous data showing a nonhyperbolic [MgATP]-velocity relationship when actin filaments are propelled by myosin subfragment 1 or full-length myosin. We also consider the implications of our results for characterization of the cross-bridge elasticity in the filament lattice of muscle.     

Effects of Ca2+ on the kinetics of phosphate release in skeletal muscle.

The process of phosphate dissociation during the muscle cross-bridge cycle has been investigated by photoliberation of inorganic phosphate (Pi) within skinned fibers of rabbit psoas muscle. This permitted a test of the idea that Ca2+ controls muscle contraction by regulating the Pi release step of the cycle. Photoliberation of Pi from structurally distinct "caged" Pi precursors initiated a rapid tension decline of up to 12% of active tension, and this was followed by a slower tension decline. The apparent rate constant of the fast phase, kPi, depended on both [Pi] and [Ca2+], whereas the slow phase generally occurred at 2-4 s-1. At maximal Ca2+, kPi increased in a nonlinear manner from 43 +/- 2 s-1 to 118 +/- 7 s-1, as Pi was raised from 0.9 to 12 mM. This was analyzed in terms of a three-state kinetic model in which a force-generating transition is coupled to Pi dissociation from the cross-bridge. As Ca(2+)-activated tension was reduced from maximal (Pmax) to 0.1 Pmax, (i) kPi decreased by up to 2.5-fold, (ii) the relative amplitude of the rapid phase increased 2-fold, and (iii) the relative amplitude of the slow phase increased about 6-fold. Changes in the rapid phase are compatible with Ca2+ influencing an apparent equilibrium constant for the force-generating transition. By comparison, kPi was faster than the rate constant of tension redevelopment, ktr, and was influenced less by Ca2+. Ca2+ effects on the caged Pi transient cannot account for the large effects of Ca2+ on actomyosin ATPase rates or cross-bridge cycling kinetics but may be a manifestation of reciprocal interactions between the thin filament and force-generating cross-bridges, and may represent Ca2+ regulation of the distribution of cross-bridges between non-force-and force-generating states.     

Cooperative turning on of myosin subfragment 1 adenosinetriphosphatase activity by the troponin-tropomyosin-actin complex

In the field of muscle regulation, there is still controversy as to whether Ca2+, alone, is able to shift muscle from the relaxed to the fully active state or whether cross-bridge binding also contributes to turning on muscle contraction. Our previous studies on the binding of myosin subfragment 1 (S-1) to the troponin-tropomyosin-actin complex (regulated actin) in the absence of ATP suggested that, even in Ca2+, the binding of rigor cross-bridges is necessary to turn on regulated actin fully. In the present study, we demonstrate that this is also the case for the turning on of the acto.S-1 ATPase activity. By itself, Ca2+ does not fully turn on the acto.S-1 ATPase activity; at low actin concentration, there is almost a 10-fold increase in ATPase activity when the regulated actin is fully turned on by the binding of rigor cross-bridges in the presence of Ca2+. This large increase in ATPase activity does not occur because the binding of S-1.ATP to actin is increased; the binding of S-1.ATP is almost the same to maximally turned-off and maximally turned-on regulated actin. The increase in ATPase activity occurs because of a marked increase in the rate of Pi release so that when the regulated actin is fully turned on, Pi release becomes so rapid that the rate-limiting step precedes the Pi release step. These results suggest that, while Ca2+, alone, does not fully turn on the regulated actin filament in solution, the binding of rigor cross-bridges can turn it on fully. If force-producing cross-bridges play the same role in vivo as rigor cross-bridges in vitro, there may be a synergistic effect of Ca2+ and cross-bridge binding in turning on muscle contraction which could greatly sharpen the response of the muscle fiber to Ca2+.     

Elementary steps of the cross-bridge cycle in bovine myocardium with and without regulatory proteins.

The role of regulatory proteins in the elementary steps of the cross-bridge cycle in bovine myocardium was investigated. The thin filament was selectively removed by gelsolin and the actin filament was reconstituted without tropomyosin or troponin. Further reconstitution was achieved by adding tropomyosin and troponin. The effects of MgATP and phosphate (Pi) on the rate constants of exponential processes were studied in control, actin filament-reconstituted, and thin filament-reconstituted myocardium at pCa < or = 4.66, pH 7.00, 25 degrees C. In control myocardium, the MgATP association constant was 9.1 +/- 1.3 mM(-1), and the Pi association constant 0.14 +/- 0.04 mM(-1). The equilibrium constant of the cross-bridge detachment step was 2.6 +/- 0.4, and the equilibrium constant of the force generation step was 0.59 +/- 0.04. In actin filament-reconstituted myocardium without regulatory proteins, the MgATP association constant was approximately the same, and the Pi association constant increased to 2.8x. The equilibrium constant of cross-bridge detachment decreased to 0.2x, but the equilibrium constant of the force generation step increased to 4x. These kinetic constants regained control values after reconstitution of the thin filament. These results indicate that tension/cross-bridge in the presence of regulatory proteins is approximately 1.5-1.7x of that in the absence of regulatory proteins. These results further indicate that regulatory proteins promote detachment of cross-bridges.     

The effect of partial extraction of troponin C on the elementary steps of the cross-bridge cycle in rabbit psoas muscle fibers.

The elementary steps of the cross-bridge cycle in which troponin C (TnC) was partially extracted were investigated by sinusoidal analysis in rabbit psoas muscle fibers. The effects of MgATP and phosphate on the rate constants of exponential processes were studied at 200 mM ionic strength, pCa 4.20, pH 7.00, and at 20 degrees C. The results were analyzed with the following cross-bridge scheme: [formula: see text] where A is actin, M is myosin, S is MgATP, D is MgADP, and P is phosphate (Pi). When TnC was extracted so that the average remaining tension was 11% (range 8-15%), K1 (MgATP association constant) increased to 7x, k2 (rate constant of cross-bridge detachment) increased to 1.55x, k-2 (reversal of detachment) decreased to 0.27x, and K2 (= k2/k-2: equilibrium constant of cross-bridge detachment) increased to 6.6x, k4 (rate constant of force generation) decreased to 0.4x, k-4 (reversal of force generation) increased to 2x, K4 (= k4/k-4) decreased to 0.17x, and K5 (Pi association constant) did not change. The activation factor alpha, which represents the fraction of cross-bridges participating in the cycling, decreased from 1 to 0.14 with TnC extraction. The fact that K1 increased with TnC extraction implies that the condition of the thin filament modifies the contour of the substrate binding site on the myosin head and is consistent with the Fenn effect. The fact that alpha decreased to 0.14 is consistent with the steric blocking mechanism (recruitment hypothesis) and indicates that some of the cross-bridges disappear from the active cycling pool. The fact that the equilibrium constants changed is consistent with the cooperative activation mechanism (graded activation hypothesis) among thin-filament regulatory units that consist of troponin (TnC, Tnl, TnT), tropomyosin, and seven actin molecules, and possibly include cross-bridges.     

A simple model with myofilament compliance predicts activation-dependent crossbridge kinetics in skinned skeletal fibers

The contribution of thick and thin filaments to skeletal muscle fiber compliance has been shown to be significant. If similar to the compliance of cycling cross-bridges, myofilament compliance could explain the difference in time course of stiffness and force during the rise of tension in a tetanus as well as the difference in Ca(2+) sensitivity of force and stiffness and more rapid phase 2 tension recovery (r) at low Ca(2+) activation. To characterize the contribution of myofilament compliance to sarcomere compliance and isometric force kinetics, the Ca(2+)-activation dependence of sarcomere compliance in single glycerinated rabbit psoas fibers, in the presence of ATP (5.0 mM), was measured using rapid length steps. At steady sarcomere length, the dependence of sarcomere compliance on the level of Ca(2+)-activated force was similar in form to that observed for fibers in rigor where force was varied by changing length. Additionally, the ratio of stiffness/force was elevated at lower force (low [Ca(2+)]) and r was faster, compared with maximum activation. A simple series mechanical model of myofilament and cross-bridge compliance in which only strong cross-bridge binding was activation dependent was used to describe the data. The model fit the data and predicted that the observed activation dependence of r can be explained if myofilament compliance contributes 60-70% of the total fiber compliance, with no requirement that actomyosin kinetics be [Ca(2+)] dependent or that cooperative interactions contribute to strong cross-bridge binding.     

Parallel inhibition of active force and relaxed fiber stiffness by caldesmon fragments at physiological ionic strength and temperature conditions: additional evidence that weak cross-bridge binding to actin is an essential intermediate for force generation.

Previously we showed that stiffness of relaxed fibers and active force generated in single skinned fibers of rabbit psoas muscle are inhibited in parallel by actin-binding fragments of caldesmon, an actin-associated protein of smooth muscle, under conditions in which a large fraction of cross-bridges is weakly attached to actin (ionic strength of 50 mM and temperature of 5 degrees C). These results suggested that weak cross-bridge attachment to actin is essential for force generation. The present study provides evidence that this is also true for physiological ionic strength (170 mM) at temperatures up to 30 degrees C, suggesting that weak cross-bridge binding to actin is generally required for force generation. In addition, we show that the inhibition of active force is not a result of changes in cross-bridge cycling kinetics but apparently results from selective inhibition of weak cross-bridge binding to actin. Together with our previous biochemical, mechanical, and structural studies, these findings support the proposal that weak cross-bridge attachment to actin is an essential intermediate on the path to force generation and are consistent with the concept that isometric force mainly results from an increase in strain of the attached cross-bridge as a result of a structural change associated with the transition from a weakly bound to a strongly bound actomyosin complex. This mechanism is different from the processes responsible for quick tension recovery that were proposed by Huxley and Simmons (Proposed mechanism of force generation in striated muscle. Nature. 233:533-538.) to represent the elementary mechanism of force generation.     

MgADP promotes a catch-like state developed through force-calcium hysteresis in tonic smooth muscle.

Tonic rabbit femoral artery and phasic rabbit ileum smooth muscles permeabilized with Triton X-100 were activated either by increasing [Ca2+] from pCa > 8.0 to pCa 6.0 (calcium-ascending protocol) or contracted at pCa 6.0 before lowering [Ca2+] (calcium-descending protocol). The effects of, respectively, high [MgATP]/low [MgADP] [10 mM MgATP + creatine phosphate (CP) + creatine kinase (CK)] or low [MgATP]/[MgADP] (2 mM MgATP, 0 CP, 0 CK) on the "force-[Ca]" relationships were determined. In femoral artery at low, but not at high, [MgATP]/[MgADP] the force and the ratio of stiffness/force at pCa 7.2 were significantly higher under the calcium-descending than calcium-ascending protocols (54% vs. 3% of Po, the force at pCa 6.0) (force hysteresis); the levels of regulatory myosin light chain (MLC20) phosphorylation (9 +/- 2% vs. 10 +/- 2%) and the velocities of unloaded shortening V0 (0.02 +/- 0.004 l/s with both protocols) were not significantly different. No significant force hysteresis was detected in rabbit ileum under either of these experimental conditions. [MgADP], measured in extracts of permeabilized femoral artery strips by two methods, was 130-140 microM during maintained force under the calcium-descending protocol. Exogenous CP (10 mM) applied during the descending protocol reduced endogenous [MgADP] to 46 +/- 10 microM and abolished force hysteresis: residual force at low [Ca2+] was 17 +/- 5% of maximal force. We conclude that the proportion of force-generating nonphosphorylated (AMdp) relative to phosphorylated cross-bridges is higher on the Ca2+-descending than on the Ca2+-ascending force curve in tonic smooth muscle, that this population of positively strained dephosphorylated cross-bridges has a high affinity for MgADP, and that the dephosphorylated AMdp . MgADP state makes a significant contribution to force maintenance at low levels of MLC20 phosphorylation.     

Mathematical simulation of muscle cross-bridge cycle and force-velocity relationship

Muscle contraction underlies many essential functions such as breathing, heart beating, locomotion, regulation of blood pressure, and airway resistance. Active shortening of muscle is the result of cycling of myosin cross-bridges that leads to sliding of myosin filaments relative to actin filaments. In this study, we have developed a computer program that allows us to alter the rates of transitions between any cross-bridge-states in a stochastic cycle. The cross-bridge states within the cycle are divided into six attached (between myosin cross-bridges and actin filaments) states and one detached state. The population of cross-bridges in each of the states is determined by the transition rates throughout the cycle; differential equations describing the transitions are set up as a cyclic matrix. A method for rapidly obtaining steady-state exact solutions for the cyclic matrix has been developed to reduce computation time and avoid the divergence problem associated with numerical solutions. In the seven-state model, two power strokes are assumed for each cross-bridge cycle, one before the release of inorganic phosphate, and one after. The characteristic hyperbolic force-velocity relationship observed in muscle contraction can be reproduced by the model. Deviation from the single hyperbolic behavior at low velocities can be mimicked by allowing the rate of cross-bridge-attachment to vary with velocity. The effects of [ATP], [ADP], and [P(i)] are simulated by changing transition rates between specific states. The model has revealed new insights on how the force-velocity characteristics are related to the state transitions in the cross-bridge cycle.     

Two step mechanism of phosphate release and the mechanism of force generation in chemically skinned fibers of rabbit psoas muscle.

The elementary steps of contraction in rabbit fast twitch muscle fibers were investigated with particular emphasis on the mechanism of phosphate (Pi) binding/release, the mechanism of force generation, and the relation between them. We monitor the rate constant 2 pi b of a macroscopic exponential process (B) by imposing sinusoidal length oscillations. We find that the plot of 2 pi b vs. Pi concentration is curved. From this observation we infer that Pi released is a two step phenomenon: an isomerization followed by the actual Pi release. Our results fit well to the kinetic scheme: [formula: see text] where A = actin, M = myosin, S = MgATP (substrate), D = MgADP, P = phosphate, and Det is a composite of all the detached and weakly attached states. For our data to be consistent with this scheme, it is also necessary that step 4 (isomerization) is observed in process (B). By fitting this scheme to our data, we obtained the following kinetic constants: k4 = 56 s-1, k-4 = 129 s-1, and K5 = 0.069 mM-1, assuming that K2 = 4.9. Experiments were performed at pCa 4.82, pH 7.00, MgATP 5 mM, free ATP 5 mM, ionic strength 200 mM in K propionate medium, and at 20 degrees C. Based on these kinetic constants, we calculated the probability of each cross-bridge state as a function of Pi, and correlated this with the isometric tension. Our results indicate that all attached cross-bridges support equal amount of tension. From this, we infer that the force is generated at step 4. Detailed balance indicates that 50-65% of the free energy available from ATP hydrolysis is transformed to work at this step. For our data to be consistent with the above scheme, step 6 must be the slowest step of the cross-bridge cycle (the rate limiting step). Further, AM*D is a distinctly different state from the AMD state that is formed by adding D to the bathing solution. From our earlier ATP hydrolysis data, we estimated k6 to be 9 s-1.     

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.