Modeling rigor cross-bridge patterns in muscle I. Initial studies of the rigor lattice of insect flight muscle.

We have undertaken some computer modeling studies of the cross-bridge observed by Reedy in insect flight muscle so that we investigate the geometric parameters that influence the attachment patterns of cross-bridges to actin filaments. We find that the appearance of double chevrons along an actin filament indicates that the cross-bridges are able to reach 10--14 nm axially, and about 90 degrees around the actin filament. Between three and five actin monomers are therefore available along each turn of one strand of actin helix for labeling by cross-bridges from an adjacent myosin filament. Reedy's flared X of four bridges, which appears rotated 60 degrees at successive levels on the thick filament, depends on the orientation of the actin filaments in the whole lattice as well as on the range of movement in each cross-bridge. Fairly accurate chevrons and flared X groupings can be modeled with a six-stranded myosin surface lattice. The 116-nm long repeat appears in our models as "beating" of the 14.5-nm myosin repeat and the 38.5-nm actin period. Fourier transforms of the labeled actin filaments indicate that the cross-bridges attach to each actin filament on average of 14.5 nm apart. The transform is sensitive to changes in the ease with which the cross-bridge can be distorted in different directions.     

Strain-dependent cross-bridge cycle for muscle.

The cross-bridge cycle for actin, S1 myosin, and nucleotides in solution is applied to the sliding filament model for fully activated striated muscle. The cycle has attached and rotated isomers of each actomyosin state. It is assumed that these forms have different zero-strain conformations with respect to the filament and that strain-free rate constants are the nominal solution values. Only one S1 unit of heavy meromyosin is considered. Transition-state theory is used to predict the strain dependences of S1 binding to actin, the force-generating transition to rotated states, and the release/binding of nucleotide and phosphate. We propose that ADP release and ATP binding are blocked by positive strain and phosphate release by negative strain. At large strains, rapid dissociation of S1 nucleotide from actin is expected when the compliant element of the cross-bridge is strained in either direction beyond its elastic limits. The dynamical behavior of this model of muscle contraction is discussed in general terms. Its computed steady-state properties are presented in an accompanying paper.     

Ion-dependence of Z-line and M-line response to calcium in striated muscle fibres in rigor.

The calcium-dependent contraction of vertebrate skeletal muscle is thought to be primarily controlled through the interaction of the thick and thin filaments. Through measurement of the Donnan potential, we have shown that an electrical switching mechanism (sensitive to both anions and cations) is present in both A- and I-bands [1]. Here we show that this mechanism is not confined to the contractile apparatus and report for the first time the presence of M-line potentials. The Z-line responds to Ca2+ ions in a similar manner to the A-band under the same solution conditions (phosphate-chloride and imidazole buffers), even though it has no reported Ca2+ binding sites. Z-line potentials were not observed in tris-acetate buffer. The M-line has a markedly different response to any of the other subsarcomeric regions, however, and can only be detected in the phosphate-chloride buffer. Preliminary observations of the M-line potential in creatine kinase-deficient mouse muscle (phosphate-chloride buffer) reveal significant differences in the calcium-induced transitions between two of the genotypes and demonstrate definitively that it is the M-line potential that is being recorded. From these results, it seems likely that the charge response of the Z-line and M-line is being mediated by titin in an anion-dependent manner. Our evidence comes from several observations. First, the similarity between the response of the Z-line potentials to the A-band potentials, where titin is the only link between these structures and second, the differential observation of M-line and Z-line potentials in a range of buffers containing different anion(s). Both Z-line and M-line potentials were seen in phosphate-chloride buffer, but only the Z-line potentials could be detected in chloride-only (imidazole) buffer and neither was observed in the acetate buffer. The latter observations can be attributed to two sources. The first is the effect of acetate buffer on the conformation of myosin [2]; the second is the absence of binding of the M-line protein, myomesin, to titin in the absence of phosphate ions [3].     

Muscle cross-bridge kinetics in rigor and in the presence of ATP analogues.

Recently we reported preliminary mechanical experiments on freshly skinned rabbit psoas fibers that suggested that while almost all of the cross-bridges are attached to actin in the presence of 4 mM adenyl-5'-yl-imidodiphosphate (AMP-PNP) (ionic strength, 0.13 M), there is an equilibrium between the attached and detached states, so that, in the presence of 4 mM AMP-PNP, fibers should not be able to maintain tension (Schoenberg, et al., 1984, in Contractile Mechanisms in Muscle, Pollack and Sugi, editors., Plenum Publishing Corp., NY). Since this suggestion was at variance with published results of Clarke and Tregear (1982, FEBS [Fed. Eur. Biochem. Soc.] Lett, 143:217), we reinvestigated the ability of rabbit psoas fibers to support tension following a 2-nm stretch in rigor and in the presence of the nucleotide analogues, PPi and AMP-PNP, for analogue concentrations ranging from 0.25 to 4 mM. We find that, whereas in rigor there is very little tension decay following a stretch, in 4 mM nucleotide analogue solution, the force generated by stretch quickly decays to zero. The force decay is not exponential; rather, it can be described by rate constants that range from approximately 0.1 to 100 s-1 in 4 mM PPi, and 0.01 to 10 s-1 in 4 mM AMP-PNP. This large range of decay rate constants may be partially related to the dependence of either analogue binding or cross-bridge dissociation upon strain, since we find that the rate constants for force decay decrease with decreasing size of stretch or with decrease of analogue concentration below the maximum studied (4 mM).(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

Transients in orientation of a fluorescent cross-bridge probe following photolysis of caged nucleotides in skeletal muscle fibres.

In muscle fibres labelled with iodoacetamidotetramethylrhodamine at Cys707 of the myosin heavy chain, the probes have been reported to change orientation when the fibre is activated, relaxed or put into rigor. In order to test whether these motions are indications of the cross-bridge power stroke, we monitored tension and linear dichroism of the probes in single glycerol-extracted fibres of rabbit psoas muscle during mechanical transients initiated by laser pulse photolysis of caged ATP and caged ADP. In rigor dichroism is negative, indicating average probe absorption dipole moments oriented more than 54.7 degrees away from the fibre axis. During activation from rigor induced by photoliberation of ATP from caged ATP in the presence of calcium, the dichroism reversed sign promptly (half-time 12.5 ms for 500 microM-ATP) upon release of ATP, but then changed only slightly during tension development 20 to 100 milliseconds later. During the onset of rigor following transfer of the fibre from an ATP-containing relaxing solution to a rigor medium lacking ATP, force generation preceded the change in dichroism. The dichroism change occurred slowly (half-time 47 s), because binding of ADP to sites within the muscle fibre limited its rate of diffusion out of the fibre. When ADP was introduced or removed, the dichroism transient was similar in time course and magnitude to that obtained after the introduction or removal of ATP. Neither adding nor removing ADP produced substantial changes in force. These results demonstrate that orientation of the rhodamine probes on the myosin head reflects mainly structural changes linked to nucleotide binding and release, rather than rotation of the cross-bridge during force generation.     

Temperature-dependence of local melting in the myosin subfragment-2 region of the rigor cross-bridge

We have used alpha-chymotrypsin as an enzyme-probe to detect local melting in the subfragment-2 region of the cross-bridges of rigor myofibrils and glycerinated psoas fibers. The kinetics of proteolysis and the sites of cleavage were determined at various temperatures over the range 5 to 40 degrees C by following the decay of the myosin heavy chain and the rates of appearance of light meromyosin fragments, using electrophoresis on sodium dodecyl sulfate-containing polyacrylamide gels. Cleavage occurs primarily at the 72,000 Mr and 64,000 Mr (per polypeptide chain from the C terminus of myosin) sites within the light meromyosin-heavy meromyosin hinge domain of the subfragment-2 region, under all experimental conditions. At pH 8.2 to 8.3 and at low divalent metal ion (0.1 mM), where the actin-bound cross-bridges are thought to be released from the thick filament surface, the intrinsic cleavage rate constant (k) increases markedly as the temperature is raised. This suggests substantial thermal destabilization of the released cross-bridge in the intact contractile apparatus. Addition of divalent metal ion (10 mM) lowers the cleavage rate and shifts the k versus temperature profile to higher temperatures. Normalized rate constants for chymotryptic cleavage within the subfragment-2 hinge region of released cross-bridges (pH 8.2, low divalent metal) of rigor fibers were markedly lower than activated fibers at all temperatures investigated (5 to 40 degrees C). Results show that conformational melting within the subfragment-2 hinge region is amplified on activation and is well above that observed when the actin-attached rigor bridge is passively released from the thick filament surface.     

Skeletal muscle myosin cross-bridge cycling is necessary for myofibrillogenesis

A major stimulus affecting myofibrillogenesis in both embryonic and mature striated muscle is contractile activity. There are two major signals associated with contractile activity: a physiological signal, the transient increase in intracellular calcium, and a physical signal, the transient increase in tension production. However, dissociating these two signals to examine their relative contributions to myofibrillogenesis has proven difficult. In this study, we have used two different myosin inhibitors to determine the importance of myosin cross-bridge cycling in sarcomere assembly. We find that the small-molecule inhibitor 2,3-butanedione monoxime (BDM), which inhibits myosin ATPase, disrupts myofibrillogenesis in amphibian myocytes, consistent with results from avian studies. However, BDM is a weak myosin inhibitor and it is non-specific; concentrations that inhibit contraction and disrupt myofibrillogenesis also disrupt calcium signaling. Therefore, we also used the recently identified skeletal muscle myosin II inhibitor, N-benzyl-p-toluenesulphonamide (BTS), which has high affinity and specificity for skeletal muscle fast myosin. BTS inhibits contraction and results in myofibrillar disruption that phenocopies our results with BDM. However, BTS does not affect either spontaneous or induced calcium transients. Furthermore, BTS is reversible and does not significantly affect the expression levels of myosin or actin. Thus, our convergent results with BDM and BTS suggest that sarcomere assembly depends on active regulation of tension in the forming myofibril.     

Active state of muscle in iodoacetate rigor

Frog sartorius muscles, equilibrated to 2 x 10(-4)M iodoacetic acid-Ringer's solution and activated by a series of twitches or a long tetanus, perform a rigor response consisting in general of a contractile change which plateaus and is then automatically reversed. Isotonic rigor shortening obeys a force-velocity relation which, with certain differences in value of the constants, accords with Hill's equation for this relation. Changes in rigidity during either isotonic or isometric rigor response show that the capacity of the rigor muscle to bear a load increases more abruptly than the corresponding onset of the ordinarily recorded response, briefly plateaus, and then decays. A quick release of about 1 mm. applied at any instant of isometric rigor output causes the tension to drop instantaneously to zero and then redevelop, the rate of redevelopment varying as does the intensity of the load-bearing capacity. These results demonstrate that rigor mechanical responses result from interaction of a passive, undamped series elastic component, and a contractile component with active state properties like those of normal contraction. Adenosinetriphosphate is known to break down in association with development of the rigor active state. This is discussed in relation to the apparent absence of ATP splitting in normal activation of the contractile component.     

Radial forces within muscle fibers in rigor

Considering the widely accepted cross-bridge model of muscle contraction (Huxley. 1969. Science [Wash. D. C.]. 164:1356-1366), one would expect that attachment of angled cross-bridges would give rise to radial as well as longitudinal forces in the muscle fiber. These forces would tend, in most instances, to draw the myofilaments together and to cause the fiber to decrease in width. Using optical techniques, we have observed significant changes in the width of mechanically skinned frog muscle fibers when the fibers are put into rigor by deleting ATP from the bathing medium. Using a high molecular weight polymer polyvinylpyrrolidone (PVP-40; number average mol. wt. (Mn) = 40,000) in the bathing solution, we were able to estimate the magnitude of the radial forces by shrinking the relaxed fiber to the width observed with rigor induction. With rigor, fiber widths decreased up to approximately 10%, with shrinking being greater at shorter sarcomere spacing and at lower PVP concentrations. At higher PVP concentrations, some fibers actually swelled slightly. Radial pressures seen with rigor in 2 and 4% PVP ranged up to 8.9 x 10(3) N/m2. Upon rigor induction, fibers exerted a longitudinal force of approximately 1 x 10(5) N/m2 that was inhibited by high PVP concentrations (greater than or equal to 13%). In very high PVP concentrations (greater than or equal to 20%), fibers exerted an anomalous force, independent of ATP, which ranged up to 6 x 10(4) N/m2 at 60% PVP. Assuming that all the radial force is the result of cross- bridge attachment, we calculated that rigor cross-bridges exert a radial force of 0.2 x 1.2 x 10(-9) N per thick filament in sarcomeres near rest length. This force is of roughly the same order of magnitude as the longitudinal force per thick filament in rigor contraction or in maximal (calcium-activated) contraction of skinned fibers in ATP- containing solutions. Inasmuch as widths of fibers stretched well beyond overlap of thick and thin filaments decreased with rigor, other radially directed forces may be operating in parallel with cross-bridge forces.     

Myosin cross-bridge orientation in rigor and in the presence of nucleotide studied by electron spin resonance.

The tilt series electron spin resonance (ESR) spectrum from muscle fibers decorated with spin labeled myosin subfragment 1 (S1) was measured from fibers in rigor and in the presence of MgADP. ESR spectra were measured at low amplitude modulation of the static magnetic field to insure that a minimum of spectral lineshape distortion occurs. Ten tilt series ESR data sets were fitted simultaneously by the model-independent methodology described in the accompanying paper (Burghardt, T. P., and A. R. French, 1989. Biophys. J. 56:525-534). By this method the average and standard error in the mean of order parameters for the probe angular distribution were calculated for the two states of the fiber investigated. The average order parameters were used to reconstruct the probe angular distribution in two dimensions, one angular dimension corresponding to a polar angle measured relative to the fiber axis, and the other a torsional angular degree of freedom of the probe. We find that the probe angular distributions for the rigor and MgADP states of the fiber differ such that the rigor distribution is broader and shifted relative to the distribution in the presence of MgADP. The shape of the rigor distribution suggests the presence of two probe orientations, one similar to that in the presence of MgADP, and another at a different orientation. The shape of the distribution in the presence of MgADP suggests that the binding of the nucleotide to the rigor cross-bridge shifts the spin population into a more homogeneous one by causing a cross-bridge rotation.     

The Z-band lattice in skeletal muscle in rigor

Previous work with tetanized and relaxed muscle has shown a correlation between active tension and the structure of the Z-band. This suggests that there is a correlation between the cross-bridge binding in the A-band and the structure of the Z-band. Using electron microscopy and optical diffraction we have examined this correlation in glycerinated muscle in rigor and in unstimulated intact muscle. We have found that the Z-bands of muscles in rigor always show the basketweave form, while those of the unstimulated muscles always show the small square form. The basketweave form found in rigor muscles is similar in form and dimension to that found in tetanized muscle. Thus it appears that the small square form of the Z-band is found in physiological states with little cross-bridge binding and the basketweave form is found in states with a high degree of cross-bridge binding.     

Resting myosin cross-bridge configuration in frog muscle thick filaments

Clear images of myosin filaments have been seen in shadowed freeze-fracture replicas of single fibers of relaxed frog semitendinosus muscles rapidly frozen using a dual propane jet freezing device. These images have been analyzed by optical diffraction and computer averaging and have been modelled to reveal details of the myosin head configuration on the right-handed, three-stranded helix of cross-bridges. Both the characteristic 430-A and 140-150-A repeats of the myosin cross-bridge array could be seen. The measured filament backbone diameter was 140-160 A, and the outer diameter of the cross-bridge array was 300 A. Evidence is presented that suggests that the observed images are consistent with a model in which both of the heads of one myosin molecule tilt in the same direction at an angle of approximately 50-70 degrees to the normal to the filament long axis and are slewed so that they lie alongside each other and their radially projected density lies along the three right-handed helical tracks. Any perturbation of the myosin heads away from their ideal lattice sites needed to account for x-ray reflections not predicted for a perfect helix must be essentially along the three helical tracks of cross-bridges. Little trace of the presence of non-myosin proteins could be seen.