Cross-bridge behavior in rigor muscle

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

A model of flagellar movement based on cooperative dynamics of dynein-tubulin cross-bridges

A theoretical model based on molecular mechanisms of both dynein cross-bridges and radial spokes is used to study bend propagation by eukaryotic flagella. Though nine outer doublets are arranged within an axoneme, a simplified model with four doublets is constructed on the assumption that cross-bridges between two of the four doublets are opposed to those between the other two, corresponding to the geometric array of cross-bridges on the 6-9 and the 1-4 doublets in the axoneme. We also assume that external viscosity is zero, whereas internal viscosity is non-zero in order to reduce numerical complexity. For demonstrating flagellar movement, computer simulations are available by dividing a long flagellum into many straight segments. Considering the fact that dynein cross-bridge spacing is almost equal to attachment site spacing, we may use a localized cross-bridge distribution along attachment sites in each straight segment. Dynamics of cross-bridges are determined by a three-state model, and effects of radial spokes are represented by a periodic mechanical potential whose periodicity is considered to be a stroke distance of the radial spoke. First of all, we examine the model of a short segment to know basic properties of the system. Changing parameters relating to "activation" of cross-bridges, our model demonstrates various phenomena; for example "excitable properties with threshold phenomena" and "limit cycle oscillation". Here, "activation" and "inactivation" (i.e. switching mechanisms) between a pair of oppositely-directed cross-bridges are essential for generation of excitable or oscillatory properties. Next, the model for a flagellar segment is incorporated into a flagellum with a whole length to show bending movement. When excitable properties of cross-bridges, not oscillatory properties, are provided along the length of the flagellum and elastic links between filaments are presented at the base, then our model can demonstrate self-organization of bending waves as well as wave propagation without special feedback control by the curvature of the flagellum. Here, "cooperative interaction" between adjacent short segments, based on "cooperative dynamics" of cross-bridges, is important for wave propagation.     

Equilibrium muscle cross-bridge behavior. Theoretical considerations.

We have developed a model for the equilibrium attachment and detachment of myosin cross-bridges to actin that takes into account the possibility that a given cross-bridge can bind to one of a number of actin monomers, as seems likely, rather than to a site on only a single actin monomer, as is often assumed. The behavior of this multiple site model in response to constant velocity, as well as instantaneous stretches, was studied and the influence of system parameters on the force response explored. It was found that in the multiple site model the detachment rate constant has considerably greater influence on the mechanical response than the attachment rate constant. It is shown that one can obtain information about the detachment rate constants either by examining the relationship between the apparent stiffness and duration of stretch for constant velocity stretches or by examining the force-decay rate constants following an instantaneous stretch. The main effect of the attachment rate constant is to scale the mechanical response by influencing the number of attached cross-bridges. The significance of the modeling for the interpretation of experimental results is discussed.     

The effects of force inhibition by sodium vanadate on cross-bridge binding, force redevelopment, and Ca2+ activation in cardiac muscle

Strongly bound, force-generating myosin cross-bridges play an important role as allosteric activators of cardiac thin filaments. Sodium vanadate (Vi) is a phosphate analog that inhibits force by preventing cross-bridge transition into force-producing states. This study characterizes the mechanical state of cross-bridges with bound Vi as a tool to examine the contribution of cross-bridges to cardiac contractile activation. The K(i) of force inhibition by Vi was approximately 40 microM. Sinusoidal stiffness was inhibited with Vi, although to a lesser extent than force. We used chord stiffness measurements to monitor Vi-induced changes in cross-bridge attachment/detachment kinetics at saturating [Ca(2+)]. Vi decreased chord stiffness at the fastest rates of stretch, whereas at slow rates chord stiffness actually increased. This suggests a shift in cross-bridge population toward low force states with very slow attachment/detachment kinetics. Low angle x-ray diffraction measurements indicate that with Vi cross-bridge mass shifted away from thin filaments, implying decreased cross-bridge/thin filament interaction. The combined x-ray and mechanical data suggest at least two cross-bridge populations with Vi; one characteristic of normal cycling cross-bridges, and a population of weak-binding cross-bridges with bound Vi and slow attachment/detachment kinetics. The Ca(2+) sensitivity of force (pCa(50)) and force redevelopment kinetics (k(TR)) were measured to study the effects of Vi on contractile activation. When maximal force was inhibited by 40% with Vi pCa(50) decreased, but greater force inhibition at higher [Vi] did not further alter pCa(50). In contrast, the Ca(2+) sensitivity of k(TR) was unaffected by Vi. Interestingly, when force was inhibited by Vi k(TR) increased at submaximal levels of Ca(2+)-activated force. Additionally, k(TR) is faster at saturating Ca(2+) at [Vi] that inhibit force by > approximately 70%. The effects of Vi on k(TR) imply that k(TR) is determined not only by the intrinsic properties of the cross-bridge cycle, but also by cross-bridge contribution to thin filament activation.     

Modeling residual force enhancement with generic cross-bridge models

The interaction of actin and myosin through cross-bridges explains much of muscle behavior. However, some properties of muscle, such as residual force enhancement, cannot be explained by current cross-bridge models. There is ongoing debate whether conceptual cross-bridge models, as pioneered by Huxley (A.F. Huxley, Muscle structure and theories of contraction, Prog. Biophys. Biophys. Chem. 7 (1957) 255) could, if suitably modified, fit experimental data showing residual force enhancement. Here we prove that there are only two ways to explain residual force enhancement with these ‘traditional’ cross-bridge models: the first requires cross-bridges to become stuck on actin (the stuck cross-bridge model) while the second requires that cross-bridges that are pulled off beyond a critical strain enter a ‘new’ unbound state that leads to a new force-producing cycle (the multi-cycle model). Stuck cross-bridge models cannot fit the velocity and stretch amplitude dependence of residual force enhancement, while the multi-cycle models can. The results of this theoretical analysis demonstrate that current kinetic models of cross-bridge action cannot explain the experimentally observed residual force enhancement. Either cross-bridges in the force-enhanced state follow a different kinetic cycle than cross-bridges in a ‘normal’ force state, or the assumptions underlying traditional cross-bridge models must be violated during experiments that show residual force enhancement.     

Changes in the X-ray reflections from contracting muscle during rapid mechanical transients and their structural implications

During normal contractions of vertebrate striated muscle, it is believed that the cross-bridges which produce the sliding force undergo asynchronous cyclical changes in their structure. Thus, an X-ray diffraction diagram from a muscle under these conditions will give structural information averaged over the whole range of cross-bridge states. Such diagrams show characteristic and informative differences from those given by relaxed muscle, but can give little information about changes in the configuration of the cross-bridges at different stages of their working stroke. However, it is possible to effect a partial synchronization of these changes by applying very rapid changes in length, completed in less than one millisecond to an otherwise isometrically contracting muscle. If the amplitude of these length changes is comparable to the length of the cross-bridge stroke (say 100 A per half-sarcomere), then it should bring about a transient but significant redistribution of cross-bridge states, which would show up in the X-ray diagram. We have made use of synchrotron radiation as a high intensity X-ray source in order to record such patterns with the necessary time resolution (1 ms or less) and have found major changes in the intensity of the 143 A meridional reflection accompanying the rapid length changes of the muscle. These changes appear to arise from specific configurational changes in the cross-bridges during the working stroke. A model is suggested in which the 143 A meridional intensity in a contracting muscle arises mainly from attached cross-bridges and is generated by the part of the myosin head near the S1-S2 junction. During normal contraction, cross-bridges go through their structural cycle asynchronously with each other, since they start at different times, but if the S2 changes in length rather little, then the configurational changes in the myosin heads are synchronized with the actin filament movement in such a way that the S1-S2 junction remains relatively fixed in its axial position. In a quick release, it is suggested that bringing many S1 heads simultaneously to the end of their working strokes on actin disrupts the 143 A axial repeat of their distal ends near S2, and brings about the large decrease of the 143 A meridional reflection. This model therefore involves a large change in the position of part of the myosin head structure relative to actin during the working stroke of the cross-bridge.     

Probing cross-bridge angular transitions using multiple extrinsic reporter groups.

15N- and 2H-substituted maleimido-TEMPO spin label ([15N,2H]MTSL) and the fluorescent label 1,5-IAEDANS were used to specifically modify sulfhydryl 1 of myosin to study the orientation of myosin cross-bridges in skeletal muscle fibers. The electron paramagnetic resonance (EPR) spectrum from muscle fibers decorated with labeled myosin subfragment 1 ([15N,2H]MTSL-S1) or the fluorescence polarization spectrum from fibers directly labeled with 1,5-IAEDANS was measured from fibers in various physiological conditions. The EPR spectra from fibers with the fiber axis oriented at 90 degrees to the Zeeman field show a clear spectral shift from the rigor spectrum when the myosin cross-bridge binds MgADP. This shift is attributable to a change in the torsion angle of the spin probe from cross-bridge rotation and is observable due mainly to the improved angular resolution of the substituted probe. The EPR data from [15N,2H]MTSL-S1 decorating fibers are combined with the fluorescence polarization data from the 1,5-IAEDANS-labeled fibers to map the global angular transition of the labeled cross-bridges due to nucleotide binding by an analytical method described in the accompanying paper [Burghardt, T. P., & Ajtai, K. (1992) Biochemistry (preceding paper in this issue)]. We find that the spin and fluorescent probes are quantitatively consistent in the finding that the actin-bound cross-bridge rotates through a large angle upon binding MgADP. We also find that, if the shape of the cross-bridge is described as an ellipsoid with two equivalent minor axes, then cross-bridge rotation takes place mainly about an axis parallel to the major axis of the ellipsoid. This type of rotation may imitate the rotation motion of cross-bridges during force generation.     

The effect of the lattice spacing change on cross-bridge kinetics in chemically skinned rabbit psoas muscle fibers. II. Elementary steps affected by the spacing change.

The actin-myosin lattice spacing of rabbit psoas fibers was osmotically compressed with a dextran T-500, and its effect on the elementary steps of the cross-bridge cycle was investigated. Experiments were performed at the saturating Ca (pCa 4.5-4.9), 200 mM ionic strength, pH 7.0, and at 20 degrees C, and the results were analyzed by the following cross-bridge scheme: [formula: see text] where A = actin, M = myosin head, S = MgATP, D = MgADP, and P = Pi = phosphate. From MgATP and MgADP studies on exponential process (C) and (D), the association constants of cross-bridges to MgADP (K0), MgATP (K1a), the rate constants of the isomerization of the AM S state (k1b and k-1b), and the rate constants of the cross-bridge detachment step (k2 and k-2) were deduced. From Pi study on process (B), the rate constants of the cross-bridge attachment (power stroke) step (k4- and k-4) and the association constant of Pi ions to cross-bridges (K5) were deduced. From ATP hydrolysis measurement, the rate constant of ADP-isomerization (rate-limiting) step (k6) was deduced. These kinetic constants were studied as functions of dextran concentrations. Our results show that nucleotide binding, the ATP-isomerization, and the cross-bridge detachment steps are minimally affected by the compression. The rate constant of the reverse power stroke step (k-4) decreases with mild compression (0-6.3% dextran), presumably because of the stabilization of the attached cross-bridges in the AM*DP state. The rate constant of the power stroke step (k4) does not change with mild compression, but it decreases with higher compression (> 6.3% dextran), presumably because of an increased difficulty in performing the power stroke. These results are consistent with the observation that isometric tension increases with a low level of compression and decreases with a high level of compression. Our results also show that the association constant K5 of Pi with cross-bridge state AM*D is not changed with compression. Our result further show that the ATP hydrolysis rate decreased with compression, and that the rate constants of the ADP-isomerization step (k6) becomes progressively less with compression. The effect of compression on the power stroke step and rate-limiting step implies that a large-scale molecular rearrangement in the myosin head takes place in these two slow reaction steps.     

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.     

Effects of oxidation on the power of chemically skinned rat soleus fibres

Oxidation alters calcium sensitivity, and decreases maximum isometric force (Po) and shortening velocity (Vmax) of single muscle fibres. To examine the effect of oxidation on the curvature of the force-velocity relationship, which determines muscle power in addition to Po and Vmax, skinned rat type I fibres were maximally activated at 15°C in a solution with pCa 4.5 and subjected to isotonic contractions before and after 4-min incubation in 50 mM H?O? (n=10) or normal relaxing solution (n=3). In five oxidised and four control fibres the rate of force redevelopment (ktr), following a rapid release and re-stretch, was measured. This gives a measure of the sum of the rate constants for cross-bridge attachment (f) and detachment (g?): (f+g?). H?O? reduced Po, Vmax and ktr by 19%, 21% and 24% respectively (P<0.001), while the shape of the force-velocity relationship was unchanged. Fitting data to the Huxley cross-bridge model suggested that oxidation decreased both the rate constant for cross-bridge attachment (f), and detachment of negatively strained cross-bridges (g?), similar to the effect of reduced activation. This suggests that oxidative modification is a possible cause of the variation in contractile properties between muscle fibres of the same type.     

Activation of skinned trabeculae of the guinea pig induced by laser photolysis of caged ATP.

The kinetics of force production in chemically skinned trabeculae from the guinea pig were studied by laser photolysis of caged ATP in the presence of Ca2+. Preincubation of the tissue during rigor with the enzyme apyrase was used to reduce the population of MgADP-bound cross-bridges (Martin and Barsotti, 1994). In untreated tissue, tension remained constant or dipped slightly below the rigor level immediately after ATP release, before increasing to the maximum measured in pCa 4.5 and 5 mM MgATP. The in-phase component stiffness, which is a measure of cross-bridge attachment, exhibited a large decrease before increasing to 55% of that measured in rigor. Neither the rate of the decline nor of the rise in tension was sensitive to the concentration of photolytically released ATP. The rate of the decline in stiffness was found to be dependent on [ATP]: 1.8 x 10(4) M-1/s-1, a value more than four times higher than that previously measured in similar experiments in the absence of Ca2+. The rate of tension development averaged 14.9 +/- 2.5 s-1. Preincubation with apyrase altered the mechanical characteristics of the early phase of the contraction. The rate and amplitude of the initial drop in both tension and stiffness after caged ATP photolysis increased and became dependent on [ATP]. The second-order rate constants measured for the initial drop in tension and stiffness were 8.4 x 10(4) M-1 s-1 and 1.5 x 10(5) M-1 s-1. These rates are more than two times faster than those previously measured in the absence of Ca2+. The effects of apyrase incubation on the time course of tension and stiffness were consistent with the hypothesis that during rigor, skinned trabeculae retain a significant population of MgADP-bound cross-bridges. These in turn act to attenuate the initial drop in tension after caged ATP photolysis and slow the apparent rate of rigor cross-bridge detachment. The results also show that Ca2+ increases the rate of cross-bridge detachment in both untreated and apyrase-treated tissue, but the effect is larger in untreated tissue. This suggests that in cardiac muscle Ca2+ modulates the rate of cross-bridge detachment.     

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.     

Measurements of the cross-bridge attachment/detachment process within intact sarcomeres by surface plasmon resonance.

We have developed a surface plasmon resonance (SPR) system to monitor the cross-bridge attachment/detachment process within intact sarcomeres from mouse heart muscle. SPR occurs when laser light energy is transferred to surface plasmons that are resonantly excited in a metal (gold) film. This resonance manifests itself as a minimum in the reflection of the incident laser light and occurs at a characteristic angle. The angle of the SPR occurrence depends on the dielectric permittivity of the sample medium adjacent to the gold film. Purified sarcomeric preparations are immobilized onto the gold film in the presence of a relaxing solution. Replacement of the relaxing solution with increasing Ca(2+) concentration solution activates the cross-bridge interaction and produces an increase in the SPR angle. These results imply that the interaction of myosin heads with actin within an intact sarcomere changes the dielectric permittivity of the sarcomeric structure. In addition, we further verify that SPR measurements can detect the changes in the population of the attached cross-bridges with altered concentrations of phosphate, 2,3-butanedione monoxime, or adenosine triphosphate at a fixed calcium concentration, which have been shown to reduce the force and increase the cross-bridge population in attached state. Thus, our data provide the first evidence that the SPR technique allows the monitoring of the cross-bridge attachment/detachment process within intact sarcomeres.     

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

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

Altered kinetics of contraction in skeletal muscle fibers containing a mutant myosin regulatory light chain with reduced divalent cation binding.

We examined the kinetic properties of rabbit skinned skeletal muscle fibers in which the endogenous myosin regulatory light chain (RLC) was partially replaced with a mutant RLC (D47A) containing a point mutation within the Ca2+/Mg2+ binding site that severely reduced its affinity for divalent cations. We found that when approximately 50% of the endogenous RLC was replaced by the mutant, maximum tension declined to approximately 60% of control and the rate constant of active tension redevelopment (ktr) after mechanical disruption of cross-bridges was reduced to approximately 70% of control. This reduction in ktr was not an indirect effect on kinetics due to a reduced number of strongly bound myosin heads, because when the strongly binding cross-bridge analog N-ethylmaleimide-modified myosin subfragment1 (NEM-S1) was added to the fibers, there was no effect upon maximum ktr. Fiber stiffness declined after D47A exchange in a manner indicative of a decrease in the number of strongly bound cross-bridges, suggesting that the force per cross-bridge was not significantly affected by the presence of D47A RLC. In contrast to the effects on ktr, the rate of tension relaxation in steadily activated fibers after flash photolysis of the Ca2+ chelator diazo-2 increased by nearly twofold after D47A exchange. We conclude that the incorporation of the nondivalent cation-binding mutant of myosin RLC decreases the proportion of cycling cross-bridges in a force-generating state by decreasing the rate of formation of force-generating bridges and increasing the rate of detachment. These results suggest that divalent cation binding to myosin RLC plays an important role in modulating the kinetics of cross-bridge attachment and detachment.     

A modified distance variable for the Hill formalism for kinetic models of muscle contraction

The distance variable of the Hill formalism for kinetic models of muscle contraction is compared to a modified distance variable. Instead of measuring the distance from a fixed point on the myosin filament to a neighboring actin, the modified variable measures the deviation of the myosin cross-bridge from its equilibrium position. Although for attached cross-bridges the two definitions are equivalent, the new variable is an index of cross-bridge conformation for cross-bridges of all states. The modified variable may be used to complement the use of the Hill variable, or to replace it. The utility of the modified variable is illustrated by an example which matches cross-bridge structures to biochemical kinetic data and to the free energy functions necessary for the design of a kinetic model.     

Effects of antibodies against dynein and tubulin on the stiffness of flagellar axonemes

Antidynein antibodies, previously shown to inhibit flagellar oscillation and active sliding of axonemal microtubules, increase the bending resistance of axonemes measured under relaxing conditions, but not the bending resistance of axonemes measured under rigor conditions. These observations suggest that antidynein antibodies can stabilize rigor cross-bridges between outer-doublet microtubules, by interfering with ATP-induced cross-bridge detachment. Stabilization of a small number of cross-bridge appears to be sufficient to cause substantial inhibition of the frequency of flagellar oscillation. Antitubulin antibodies, previously shown to inhibit flagellar oscillation without inhibiting active sliding of axonemal microtubules, do not increase the static bending resistance of axonemes. However, we observed a viscoelastic effect, corresponding to a large increase in the immediate bending resistance. This immediate bending resistance increase may be sufficient to explain inhibition of flagellar oscillation; but several alternative explanations cannot yet be excluded.     

Effects of MgATP and MgADP on the cross-bridge kinetics of rabbit soleus slow-twitch muscle fibers.

The elementary steps surrounding the nucleotide binding step in the cross-bridge cycle were investigated with sinusoidal analysis in rabbit soleus slow-twitch muscle fibers. The single-fiber preparations were activated at pCa 4.40, ionic strength 180 mM, 20 degrees C, and the effects of MgATP (S) and MgADP (D) concentrations on three exponential processes B, C, and D were studied. Our results demonstrate that all apparent (measured) rate constants increased and saturated hyperbolically as the MgATP concentration was increased. These results are consistent with the following cross-bridge scheme: [cross-bridge scheme: see text] where A = actin, M = myosin, S = MgATP, and D = MgADP. AM+S is a collision complex, and AM*S is its isomerized form. From our studies, we obtained K0 = 18 +/- 4 mM-1 (MgADP association constant, N = 7, average +/- sem), K1a = 1.2 +/- 0.3 mM-1 (MgATP association constant, N = 8 hereafter), k1b = 90 +/- 20 s-1 (rate constant of ATP isomerization), k-1b = 100 +/- 9 s-1 (rate constant of reverse isomerization), K1b = 1.0 +/- 0.2 (equilibrium constant of isomerization), k2 = 21 +/- 3 s-1 (rate constant of cross-bridge detachment), k-2 = 14.1 +/- 1.0 s-1 (rate constant of reversal of detachment), and K2 = 1.6 +/- 0.3 (equilibrium constant of detachment). K0 is 8 times and K1a is 2.2 times those in rabbit psoas, indicating that nucleotides bind to cross-bridges more tightly in soleus slow-twitch muscle fibers than in psoas fast-twitch muscle fibers. These results indicate that cross-bridges of slow-twitch fibers are more resistant to ATP depletion than those of fast-twitch fibers. The rate constants of ATP isomerization and cross-bridge detachment steps are, in general, one-tenth to one-thirtieth of those in psoas.     

Muscle force and stiffness during activation and relaxation. Implications for the actomyosin ATPase

Isolated skinned frog skeletal muscle fibers were activated (increasing [Ca2+]) and then relaxed (decreasing [Ca2+]) with solution changes, and muscle force and stiffness were recorded during the steady state. To investigate the actomyosin cycle, the biochemical species were changed (lowering [MgATP] and elevating [H2PO4-]) to populate different states in the actomyosin ATPase cycle. In solutions with 200 microM [MgATP], compared with physiological [MgATP], the slope of the plot of relative steady state muscle force vs. stiffness was decreased. At low [MgATP], cross-bridge dissociation from actin should be reduced, increasing the population of the last cross-bridge state before dissociation. These data imply that the last cross-bridge state before dissociation could be an attached low-force-producing or non-force-producing state. In solutions with 10 mM total Pi, compared to normal levels of MgATP, the maximally activated muscle force was reduced more than muscle stiffness, and the slope of the plot of relative steady state muscle force vs. stiffness was reduced. Assuming that in elevated Pi, Pi release from the cross-bridge is reversed, the state(s) before Pi release would be populated. These data are consistent with the conclusion that the cross-bridges are strongly bound to actin before Pi release. In addition, if Ca2+ activates the ATPase by allowing for the strong attachment of the myosin to actin in an A.M.ADP.Pi state, it could do so before Pi release. The calcium sensitivity of muscle force and stiffness in solutions with 4 mM [MgATP] was bracketed by that measured in solutions with 200 microM [MgATP], where muscle force and stiffness were more sensitive to calcium, and 10 mM total Pi, where muscle force and stiffness were less sensitive to calcium. The changes in calcium sensitivity were explained using a model in which force-producing and rigor cross-bridges can affect Ca2+ binding or promote the attachment of other cross-bridges to alter calcium sensitivity.     

Role of MgATP and MgADP in the cross-bridge kinetics in chemically skinned rabbit psoas fibers. Study of a fast exponential process (C)

The role of the substrate (MgATP) and product (MgADP) molecules in cross-bridge kinetics is investigated by small amplitude length oscillations (peak to peak: 3 nm/cross-bridge) and by following amplitude change and phase shift in tension time courses. The range of discrete frequencies used for this investigation is 0.25-250 Hz, which corresponds to 0.6-600 ms in time domain. This report investigates the identity of the high frequency exponential advance (process C), which is equivalent to "phase 2" of step analysis. The experiments are performed in maximally activated (pCa 4.5-5.0) single fibers from chemically skinned rabbit psoas fibers at 20 degrees C and at the ionic strength 195 mM. The rate constant 2 pi c deduced from process (C) increases and saturates hyperbolically with an increase in MgATP concentration, whereas the same rate constant decreases monotonically with an increase in MgADP concentration. The effects of MgATP and MgADP are opposite in all respects we have studied. These observations are consistent with a cross-bridge scheme in which MgATP and MgADP are in rapid equilibria with rigorlike cross-bridges, and they compete for the substrate site on myosin heads. From our measurements, the association constants are found to be 1.4 mM-1 for MgATP and 2.8 mM-1 for MgADP. We further deduced that the composite second order rate constant of MgATP binding to cross-bridges and subsequent isomerization/dissociation reaction to be 0.57 x 10(6)M-1s-1.