The mechanochemistry of force production in muscle

The working stroke upon myosin-nucleotide complexes binding to actin

For many years, it has been known that myosin binds to actin tightly, but it had not been possible to devise a muscle fiber experiment to determine whether this binding energy is directly coupled to the working stroke of the actomyosin crossbridge cycle. Addressing the question at the single-molecule level with optical tweezers allows the problem to be resolved. We have compared the working stroke on the binding of four myosin complexes (myosin, myosin-ADP, myosin-pyrophosphate, and myosin-adenyl-5'yl imidodiphosphate) with that observed while hydrolyzing ATP. None of the four was observed to give a working stroke significantly different from zero. A working stroke (5.4 nm) was observed only with ATP, which indicates that the other states bind to actin in a rigor-like conformation and that myosin products (M.ADP.Pi), the state that binds to actin during ATPase activity, binds in a different, prestroke conformation. We conclude that myosin, while dissociated from actin, must be able to take up at least two mechanical conformations and show that our results are consistent with these conformations corresponding to the two states characterized at high resolution, which are commonly referred to in terms of having open and closed nucleotide binding pockets.

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.

Kinetic and thermodynamic studies of the cross-bridge cycle in rabbit psoas muscle fibers

The effect of temperature on elementary steps of the cross-bridge cycle was investigated with sinusoidal analysis technique in skinned rabbit psoas fibers. We studied the effect of MgATP on exponential process (C) to characterize the MgATP binding step and cross-bridge detachment step at six different temperatures in the range 5-30 degrees C. Similarly, we studied the effect of MgADP on exponential process (C) to characterize the MgADP binding step. We also studied the effect of phosphate (Pi) on exponential process (B) to characterize the force generation step and Pi-release step. From the results of these studies, we deduced the temperature dependence of the kinetic constants of the elementary steps and their thermodynamic properties. We found that the MgADP association constant (K0) and the MgATP association constant (K1) significantly decreased when the temperature was increased from 5 to 20 degrees C, implying that nucleotide binding became weaker at higher temperatures. K0 and K1 did not change much in the 20-30 degree C range. The association constant of Pi to cross-bridges (K5) did not change much with temperature. We found that Q10 for the cross-bridge detachment step (k2) was 2.6, and for its reversal step (k-2) was 3.0. We found that Q10 for the force generation step (Pi-isomerization step, k4) was 6.8, and its reversal step (k-4) was 1.6. The equilibrium constant of the detachment step (K2) was not affected much by temperature, whereas the equilibrium constant of the force generation step (K4) increased significantly with temperature increase. Thus, the force generation step consists of an endothermic reaction. The rate constant of the rate-limiting step (k6) did not change much with temperature, whereas the ATP hydrolysis rate increased significantly with temperature increase. We found that the force generation step accompanies a large entropy increase and a small free energy change; hence, this step is an entropy-driven reaction. These observations are consistent with the hypothesis that the hydrophobic interaction between residues of actin and myosin underlies the mechanism of force generation. We conclude that the force generation step is the most temperature-sensitive step among elementary steps of the cross-bridge cycle, which explains increased isometric tension at high temperatures in rabbit psoas fibers.

Inferences concerning crossbridges from work on insect muscle

This paper presents a number of separate results concerning crossbridge attachment: [1] X-ray diffraction from live bumble bee flight muscle shows a set of layer lines distinct from that of relaxed Lethocerus, in which the apparent myosin helix is shorter than that of the actin. [2] Rigor crossbridges of Lethocerus are not rotatable by stretch. [3] Rabbit and Lethocerus fibres in rigor relaxed by ATP at -35 degrees C show evidence of non-rigor crossbridge attachment.

Effect of Ca2+ on weak cross-bridge interaction with actin in the presence of adenosine 5'-[gamma-thio]triphosphate)

In the presence of the nucleotide analog adenosine 5'-[gamma-thio]triphosphate (ATP[gamma S]), effects of Ca2+ on stiffness and equatorial x-ray diffraction patterns of single skinned fibers of the rabbit psoas muscle were studied. It is shown that cross-bridges in the presence of ATP[gamma S] have properties of the weak-binding states of the ATP hydrolysis cycle. Raising the Ca2+ concentration up to pCa 4.5 has little effect on actin affinity of cross-bridges in the presence of ATP[gamma S]. However, the rate constants for cross-bridge dissociation and reassociation from and to actin are reduced by about 2 orders of magnitude. In addition, nucleotide affinity of the cross-bridge is much smaller at high Ca2+ concentrations. Implications for interpretation of fiber stiffness recorded during isotonic shortening and the rising phase of a tetanus are discussed.

X-ray diffraction and electron microscopy from Lethocerus flight muscle partially relaxed by adenylylimidodiphosphate and ethylene glycol

The low-angle X-ray diffraction pattern from Lethocerus flight muscle fibres was recorded in rigor or under two conditions that modify crossbridge structure and behaviour, aqueous adenylylimidodiphosphate (AMPPNP) and AMPPNP + calcium in an ethylene glycol-water mixture. The effects on the 38.7 nm layer-line peaks (hk.6) of the diffraction patterns were studied in detail. In aqueous AMPPNP at room temperature, a condition in which rigor tension drops to half without loss of stiffness, the peaks remained nearly as intense as in rigor except for the 10.6, which dropped to half. In 20% (v/v) ethylene glycol-AMPPNP + 100 microM-Ca2+ at 23 degrees C (gly + pnp + Ca), a condition which removed muscle tension but left stiffness close to the rigor value, the 10.6 and 11.6 peaks greatly decreased but the 31.6 remained relatively high. The 14.5 nm meridional peak (00.16) became stronger on addition of AMPPNP and again on adding glycol + calcium. Considered in terms of constructively interfering filaments and crossbridges, the X-ray data indicated a transfer of diffracting crossbridge mass towards the thick filament as relaxation proceeds. We compared the X-ray diffraction patterns and crossbridge structure seen with electron microscopy (EM) under the same chemical conditions. EM and X-ray observations were mutually quite consistent overall. However, X-ray data indicated that more crossbridge mass was stereospecifically related to actin before fixation in the partially relaxed state (gly + pnp + Ca) than was suggested by the disordered crossbridge profiles seen by EM. We conclude that myosin heads at the start of the power stroke may both be closely related to their thick filament origins and form actin-determined attachments to the thin filament.

Effect of adenosine triphosphate analogues on skeletal muscle fibers in rigor

It is commonly believed, for both vertebrate striated and insect flight muscle, that when the ATP analogue adenyl-5'-yl imidodiphosphate (AMPPNP) is added to the muscle fiber in rigor, it causes the fiber to lengthen by 0.15%. This has been interpretated (Marston S.B., C.D. Roger, and R.T. Tregear. 1976. J. Mol. Biol. 104:263-267) as suggesting (a) that in rigor the crossbridge is fixed to, i.e., almost never detaches from the actin filament; (b), that the crossbridge remains fixed to the actin filament after AMPPNP addition; and (c) that the ability of AMPPNP to cause apparent lengthening of a muscle fiber is due to its ability to cause a conformational change in the myosin crossbridge that has an axial component of approximately 1.6 nm/half-sarcomere. The present study, done only on chemically-skinned rabbit psoas fibers, confirms that AMPPNP can cause muscle fibers to lengthen by 0.15% but only for a narrow set of experimental conditions. When experimental conditions are varied over a wider range, it becomes apparent that the extent of lengthening of a rigor muscle fiber upon AMPPNP addition depends almost entirely on the strain present in the rigor fiber before AMPPNP addition. Addition of AMPPNP to an unstrained rigor fiber (one supporting zero tension), induces zero length change while addition of AMPPNP to very highly strained rigor fibers induces length changes greater than 0.15%. The data thus do not support the hypotheses that the crossbridges remain fixed to the actin filament after AMPPNP addition and that the size of the apparent length change induced by AMPPNP is related to the size of the axial component of a conformational change. Instead, the data support the idea that the ability of AMPPNP to cause lengthening of a rigor muscle fiber is related to its ability to accelerate the rate at which strained crossbridges detach from actin and reattach in positions in lesser strain. The data do not rule out a conformational change upon AMPPNP binding, they simply make clear that any attempt to measure a force response conceivably due to a conformational change, would be more than obscured by the force changes due to crossbridges detaching and reattaching in positions of lesser strain.

Two attached non-rigor crossbridge forms in insect flight muscle

We have performed thin-section electron microscopy on muscle fibers fixed in different mechanically monitored states, in order to identify structural changes in myosin crossbridges associated with force production and maintenance. Tension and stiffness of fibers from glycerinated Lethocerus flight muscle were monitored during a sequence of conditions using AMPPNP and then AMPPNP plus increasing concentrations of ethylene glycol, which brought fibers through a graded sequence from rigor relaxation. Two intermediate crossbridge forms distinct from the rigor or relaxed forms were observed. The first was produced by AMPPNP at 20 degrees C, which reduced isometric tension 60 to 70% below rigor level without reducing rigor stiffness. Electron microscopy of these fibers showed that, in spite of the drop in tension, no obvious change from the 45 degrees crossbridge angle characteristic of rigor occurred. However, the thick filament ends of the crossbridges were altered from their rigor positions, so that they now marked a 14.5 nm repeat, and formed four separate origins at each crossbridge level. The bridges were also less slewed and bent than rigor bridges, as seen in transverse sections. The second crossbridge form was seen in glycol-AMPPNP at 4 degrees C, just below the glycol concentration that produced mechanical relaxation. These fibers retained 90% of rigor stiffness at 40 Hz oscillation, but would not bear sustained tension. Stiffness was also high in the presence of calcium at room temperature under similar conditions. Electron microscopy showed crossbridges projecting from the thick filaments at an angle that centered around 90 degrees, rather than the 45 degree angle familiar from rigor. This coupling of relaxed appearance with persistent stiffness suggests that the 90 degree form may represent a weakly attached crossbridge state like that proposed to precede force development in current models of the crossbridge power stroke.

A model for the interaction of muscle cross-bridges with ligands which compete with ATP

A model is presented to describe the inhibition of muscle fiber contraction by ligands that compete with MgATP. Two ligands, adenosine 5' (beta, gamma-imido) triphosphate (AMPPNP) and pyrophosphate (PPi), decrease the force developed in isometric contractions and act as weak competitive inhibitors of the maximum velocity of contraction (Pate & Cooke, 1985). These observations provide information on the energetics of actomyosin ligand states at the end of the power-stroke where MgATP dissociates the myosin cross-bridge from actin, and they are analysed in terms of a seven state model of cross-bridge kinetics. The model can reconcile the observations that these ligands bind tightly to fibers, Kd = 10(-4) M, while they are only weak inhibitors of fiber velocity, Ki = 2 X 10(-3) M. It provides a reasonable fit to the data and leads to several conclusions concerning the properties of the cross-bridge states. The states with bound ligand are shifted axially so that they occur earlier in the power-stroke than the nucleotide-free rigor state. This shift also explains the axial lengthening seen upon addition of ligands to rigor fibers. We can conclude that these ligands cause small perturbations in the cross-bridge configuration rather than large shifts. A second conclusion is that cross-bridges do not detach from actin during their power-strokes. Instead they traverse the entire length of the power stroke and are detached only at the end, leading to the suggestion that the cycling of bridges in isometric fibers is due to fluctuations in the relative positions of thick and thin filaments. With some further assumptions, the model also explains many of the rate constants and equilibrium constants of the actin-myosin-ligand interaction that have been measured in solution.

The mechanism of muscle contraction

Knowledge of the mechanism of contraction has been obtained from studies of the interaction of actin and myosin in solution, from an elucidation of the structure of muscle fibers, and from measurements of the mechanics and energetics of fiber contraction. Many of the states and the transition rates between them have been established for the hydrolysis of ATP by actin and myosin subfragments in solution. A major goal is to now understand how the kinetics of this interaction are altered when it occurs in the organized array of the myofibril. Early work on the structure of muscle suggested that changes in the orientation of myosin cross-bridges were responsible for the generation of force. More recently, fluorescent and paramagnetic probes attached to the cross-bridges have suggested that at least some domains of the cross-bridges do not change orientation during force generation. A number of properties of active cross-bridges have been defined by measurements of steady state contractions of fibers and by the transients which follow step changes in fiber length or tension. Taken together these studies have provided firm evidence that force is generated by a cyclic interaction in which a myosin cross-bridge attaches to actin, exerts force through a "powerstroke" of 12 nm, and is then released by the binding of ATP. The mechanism of this interaction at the molecular level remains unknown.

Crossbridge kinetics in chemically skinned rabbit psoas fibres when the actin-myosin lattice spacing is altered by dextran T-500

The actin-myosin lattice spacing of chemically skinned rabbit psoas fibres was osmotically altered by dextran T500, and the transient kinetic response of tension arising from maximally cycling cross-bridges was measured by sinusoidal length perturbations. The lattice spacing was estimated from the width of the fibres measured under a light microscope. As the dextran concentration was increased, the widths during both relaxation and Ca-activation decreased monotonically. The tension increased to a maximum at 7% dextran, and decreased again at further increases in dextran. Dynamic modulus (stiffness) increased monotonically with compression by dextran; this increase is primarily due to the elastic modulus. The rate constants slightly decreased between 0% and 4% dextran, then decreased rapidly at higher concentrations. The rate of oscillatory work output stayed approximately constant between 0% and 4% dextran, and sharply decreased at higher concentrations. Apparently, two independent effects occur as the lattice is compressed by dextran: (1) a compensation for the spacing change through an increase in tension and a decrease in the rate constants (this takes place at low dextran concentrations); and (2) an alteration of the crossbridge kinetics by grossly decreasing both the tension and the rate constants (at high dextran concentrations). The first effect is interpreted as a decrease in the detachment rate, while the second effect is interpreted as a decrease in the rate of the 'power stroke' reaction.

The inhibition of muscle contraction by adenosine 5' (beta, gamma-imido) triphosphate and by pyrophosphate

We have studied the inhibition of the contraction of glycerinated rabbit psoas muscle caused by ligands that bind to the ATPase site of myosin. Two ligands, adenosine 5' (beta, gamma-imido) triphosphate (AMPPNP) and pyrophosphate (PPi), decreased the force and stiffness developed in isometric contractions and the velocity of shortening of isotonic contractions. The force exerted by isometric fibers was measured as a function of MgATP in the presence and absence of a constant concentration of the ligands. As the MgATP concentration decreased, the inhibition of tension caused by the ligand increased, reaching approximately 50% at 25 microM MgATP and either 2 mM MgPPi or 2 mM MgAMPPNP. The maximum velocity of shortening was also measured as a function of MgATP concentration in the presence of 1 and 2 mM MgPPi and 2.5 and 5 mM MgAMPPNP. Both ligands acted as pure competitive inhibitors with Ki = 3.0 mM for PPi and 5.1 mM for MgAMPPNP. These data show that both ligands are weak inhibitors of the contraction of fibers. The results provided information on the energetics of actin-myosin-ligand states that occur in the portion of the cross-bridge cycle where MgATP binds to myosin. A simple analysis of the inhibition of velocity suggests that MgAMPPNP binds to the actomyosin complex at this step of the cycle with an effective affinity constant of approximately 2 X 10(2) M-1.

The effect of MgATP on forming and breaking actin-myosin linkages in contracted skinned insect flight muscle fibres

At neutral pH, fully Ca2+ -activated glycerinated dorsal longitudinal fibre bundles from Lethocerus indicus contract under isometric conditions and respond to release by deactivation, i.e. quick release causes a delayed tension fall. At slightly alkaline pH, the release-induced deactivation becomes a transient phenomenon, i.e. a delayed tension fall is followed by a slow tension recovery. This enabled us to study the effect of MgATP concentration on the phases of deactivation and slow recovery. Reduction of the MgATP concentration slows down the tension response to a quick length change and increases the time constants of the delayed deactivation phase and of the slow recovery phase. The rate constants depend on the ATP concentration according to the Michaelis-Menten law yielding apparent dissociation constants (Km) of 2 mM and 0.09 mM and maximal rate constants of 700 s-1 and 20 s-1 for the deactivation phase (crossbridge detachment) and slow recovery phase (crossbridge reattachment) respectively. The rate of MgATP hydrolysis is also hyperbolically related to the MgATP concentration (Km = 0.14 mM, maximal MgATP turnover rate 1.2 s-1. It is concluded that the effect of MgATP on the deactivation phase, in which crossbridges dissociate strain dependent from the actin, is controlled by at least two mechanisms: (1) fast equilibrium transitions within attached crossbridge states which augment MgATP dissociation from crossbridges with discharged elastic elements; and (2) a crossbridge strain-dependent isomerization of the ternary actin-myosin-MgATP complex which determines crossbridge detachment from the actin.

The effect of the ATP analogue AMPPNP on the structure of crossbridges in vertebrate skeletal muscles: X-ray diffraction and mechanical studies

Adenylylimidodiphosphate (AMPPNP), a nonhydrolysable analogue of ATP, has been used to arrest the crossbridge cycle of muscular contraction in one of its hypothetical intermediate states. Whole frog sartorius muscles were chemically demembranated, and it was found possible to cycle such skinned muscles reversibly between the relaxed and rigor states. The effect of binding of AMPPNP on the structure and spatial arrangement of the crossbridges of such muscles was studied using low-angle X-ray diffraction, with simultaneous recording of the mechanical effects, starting from the rigor state. Saturating concentrations of MgAMPPNP produce a characteristic decrease of about 50% in the original rigor isometric tension with a concomitant increase in muscle length by 0.13%. The equatorial X-ray diffraction pattern is modified in the following way: the lattice dimensions and the intensity of the (10) equatorial reflection do not change, while the intensity of the (11) equatorial reflection increases slightly. These observations of very small equatorial changes could be explained by assuming that in these muscles (as distinct from others such as rabbit psoas) the analogue does not produce a significant degree of detachment of crossbridges; that is, there are only AMPPNP-modified attached ones. The changes in the meridional X-ray diffraction pattern are more pronounced: the meridional reflection at 14.5 nm decreases in intensity, and the meridional reflection at 7.2 nm increases considerably: the intensity of all the actin-based off-meridional layer-lines decreases. There are no signs of the characteristic relaxed layer-lines, and the changes in the layer-line intensities are probably due to there being a single population of AMPPNP-modified attached crossbridges, rather than a mixture of attached and detached crossbridges. Thus the AMPPNP X-ray pattern, both equatorially and meridionally, is somewhat similar to the rigor one, indicating that most of the crossbridges remain attached. On the other hand, the fact that there are some changes in the layer-line intensities of the AMPPNP frog pattern, without the appearance of any signs of a relaxed equatorial pattern, indicates that the attached crossbridges are in a structural state that is different from rigor, one is not seeing, apparently, simply a mixture of rigor and relaxed states. Our tentative interpretation of this result is that there may be a structural change in the crossbridge near to the junction with S2, with less significant changes occurring in the parts of the crossbridge close to actin.

Cross-bridge states in invertebrate muscles

Arguments are presented for doubting whether the effect of AMPPNP on insect flight muscle in rigor signals a reversion of the power stroke of attached cross-bridges. Instead, the effect of this nucleotide on insect and other muscles may be better explained in terms of the behavior of detached bridges. Knowledge of events in the detached half of the contractile cycle may nevertheless be relevant to understanding the mechanism of energy transduction.

The kinetics of cross-bridge attachment and detachment studied by high frequency stiffness measurements

Muscle fiber stiffness, supposedly an indication of attached cross-bridges, was measured throughout tetanic contraction and subsequent relaxation. Stiffness increased at a rate faster than the development of force during the rise of tetanic contraction and decreased more slowly than force during relaxation. One explanation for these results is that long-lived cross-bridge states may exist between attachment, force generation and detachment.