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.     

Cross-bridge elasticity in single smooth muscle cells

In smooth muscle, a cross-bridge mechanism is believed to be responsible for active force generation and fiber shortening. In the present studies, the viscoelastic and kinetic properties of the cross-bridge were probed by eliciting tension transients in response to small, rapid, step length changes (delta L = 0.3-1.0% Lcell in 2 ms). Tension transients were obtained in a single smooth muscle cell isolated from the toad (Bufo marinus) stomach muscularis, which was tied between a force transducer and a displacement device. To record the transients, which were of extremely small magnitude (0.1 microN), a high-frequency (400 Hz), ultrasensitive force transducer (18 mV/microN) was designed and built. The transients obtained during maximal force generation (Fmax = 2.26 microN) were characterized by a linear elastic response (Emax = 1.26 X 10(4) mN/mm2) coincident with the length step, which was followed by a biphasic tension recovery made up of two exponentials (tau fast = 5-20 ms, tau slow = 50-300 ms). During the development of force upon activation, transients were elicited. The relationship between stiffness and force was linear, which suggests that the transients originate within the cross-bridge and reflect the cross-bridge's viscoelastic and kinetic properties. The observed fiber elasticity suggests that the smooth muscle cross-bridge is considerably more compliant than in fast striated muscle. A thermodynamic model is presented that allows for an analysis of the factors contributing to the increased compliance of the smooth muscle cross-bridge.     

Cross-bridge model of muscle contraction. Quantitative analysis

We recently presented, in a qualitative manner, a cross-bridge model of muscle contraction which was based on a biochemical kinetic cycle for the actomyosin ATPase activity. This cross-bridge model consisted of two cross-bridge states detached from actin and two cross-bridge states attached to actin. In the present paper, we attempt to fit this model quantitatively to both biochemical and physiological data. We find that the resulting complete cross-bridge model is able to account reasonably well for both the isometric transient data observed when a muscle is subjected to a sudden change in length and for the relationship between the velocity of muscle contraction in vivo and the actomyosin ATPase activity in vitro. This model also illustrates the interrelationship between biochemical and physiological data necessary for the development of a complete cross-bridge model of muscle contraction.     

Length-tension relation in Limulus striated muscle

Laser diffraction techniques coupled with simultaneous tension measurements were used to determine the length-tension relation in intact, small (0.5-mm thick, 10-mm wide, 20-25-mm long) bundles of a Limulus (horseshoe crab) striated muscle, the telson levator muscle. This muscle differs from the model vertebrate systems in that the thick filaments are not of a constant length, but shorten from 4.9 to approximately 2.0 micrometers as the sarcomeres shorten from 7 to 3 micrometers. In the Limulus muscle, the length-tension relation plateaued to an average maximum tension of 0.34 N/mm2 at a sarcomere length of 6.5 micrometers (Lo) to 8.0 micrometers. In the sarcomere length range from 3.8 to 12.5 micrometers, the muscle developed 50% or more of the maximum tension. When the sarcomere lengths are normalized (expressed as L/Lo) and the Limulus data are compared to those from frog muscle, it is apparent that Limulus muscle develops tension over a relatively greater range of sarcomere lengths.     

Cross-bridge cycling theories cannot explain high-speed lengthening behavior in frog muscle.

The Huxley 1957 model of cross-bridge cycling accounts for the shortening force-velocity curve of striated muscle with great precision. For forced lengthening, however, the model diverges from experimental results. This paper examines whether it is possible to bring the model into better agreement with experiments, and if so what must be assumed about the mechanical capabilities of cross-bridges. Of particular interest is how introduction of a maximum allowable cross-bridge strain, as has been suggested by some experiments, affects the predictions of the model. Because some differences in the models are apparent only at high stretch velocities, we acquired new force-velocity data to permit a comparison with experiment. Using whole, isolated frog sartorius muscles at 2 degrees C, we stretched active muscle at speeds up to and exceeding 2 Vmax. Force during stretch was always greater than the peak isometric level, even during the fastest stretches, and was approximately independent of velocity for stretches faster than 0.5 Vmax. Although certain modifications to the model brought it into closer correspondence with the experiments, the accompanying requirements on cross-bridge extensibility were unreasonable. We suggest (both in this paper and the one that follows) that sarcomere inhomogeneities, which have been implicated in such phenomena as "tension creep" and "permanent extra tension," may also play an important role in determining the basic force-velocity characteristics of muscle.     

Regulation of Limulus skeletal muscle contraction

Skeletal muscle contraction of Limulus polyphemus, the horseshoe crab, seemed to be regulated in a dual manner, namely Ca2+ binding to the troponin complex as well phosphorylation of the myosin light chains (MLC) by a Ca2+/calmodulin-dependent myosin light chain kinase. We investigated muscle contraction in Limulus skinned fibers in the presence of Ca2+ and of Ca2+/calmodulin to find out which of the two mechanisms prevails in Limulus skeletal muscle contraction. Although skinned fibers revealed high basal MLC mono- and biphosphorylation levels (0.48 mol phosphate/mol 31 kDa MLC; 0.52 mol phosphate/mol 21 kDa MLC), the muscle fibers were fully relaxed at pCa 8. Upon C2+ or Ca2+/calmodulin activation, the fibers developed force (357+/-78.7 mN/mm2; 338+/-69.7 mN/mm2, respectively) while the MLC phosphorylation remained essentially unchanged. We conclude that Ca2+ activation is the dominant regulatory mechanism in Limulus skeletal muscle contraction.     

Cross-bridge mechanism of residual force enhancement after stretching in a skeletal muscle

A muscle model that uses a modified Langevin equation with actomyosin potentials was used to describe the residual force enhancement after active stretching. Considering that the new model uses cross-bridge theory to describe the residual force enhancement, it is different from other models that use passive stretching elements. Residual force enhancement was simulated using a half sarcomere comprising 100 myosin molecules. In this paper, impulse is defined as the integral of an excess force from the steady isometric force over the time interval for which a stretch is applied. The impulse was calculated from the force response due to fast and slow muscle stretches to demonstrate the viscoelastic property of the cross-bridges. A cross-bridge mechanism was proposed as a way to describe the residual force enhancement on the basis of the impulse results with reference to the compliance of the actin filament. It was assumed that the period of the actin potential increased by 0.5% and the amplitude of the potential decreased by 0.5% when the half sarcomere was stretched by 10%. The residual force enhancement after 21.0% sarcomere stretching was 6.9% of the maximum isometric force of the muscle; this value was due to the increase in the number of cross-bridges.     

Changes in thick filament length in Limulus striated muscle

Here we describe the change in thick filament length in striated muscle of Limulus, the horseshoe crab. Long thick filaments (4.0 microns) are isolated from living, unstimulated Limulus striated muscle while those isolated from either electrically or K+-stimulated fibers are significantly shorter (3.1 microns) (P less than 0.001). Filaments isolated from muscle glycerinated at long sarcomere lengths are long (4.4 microns) while those isolated from muscle glycerinated at short sarcomere lengths are short (2.9 microns) and the difference is significant (P less than 0.001). Thin filaments are 2.4 microns in length. The shortening of thick filaments is related to the wide range of sarcomere lengths exhibited by Limulus telson striated muscle.     

Cross-bridge movements during a slow length change of active muscle.

Tension changes caused by slow stretch or release of actively contracting muscle are accompanied by axial displacements of myosin heads (i.e., cross-bridges) from the positions characteristic of isometric contraction. The direction of the axial displacement appears to affect the rate of cross-bridge detachment or reattachment during muscle-length changes.     

Structure of Limulus telson muscle thick filaments

Computer analysis of electron micrographs of negatively stained thick filaments isolated from the telson levator muscle of the horseshoe crab (Limulus polyphemus) has shown that they have a four-stranded helical structure. The repeating units along each helix have a bent extended shape (measuring approximately 20 nm × 8 nm × 8 nm) and are inclined at an angle of about 30 ° to the helical path. At the resolution of this study, it was difficult to establish the exact size of the surface subunits, but our results are probably more consistent with each unit representing the two heads of a single myosin molecule rather than larger aggregates.     

Cross-bridge orientation in skeletal muscle measured by linear dichroism of an extrinsic chromophore

Linear dichroism of chromophoric labels attached to myosin heads has been used to establish cross-bridge orientation in myofibrils and muscle fibers. Generalized expressions were obtained for the dichroic ratio of a circularly symmetrical assembly of chromophores viewed through high apertures. The theoretical expressions were used to estimate the angle Θ of the absorption dipole of the dye relative to the myofibrillar axis. Myosin subfragment-1 has been labeled with tetramethyl rhodamine and diffused into the I-band of myofibrils; endogenous muscle myosin has been labeled directly. Dichroism has been measured from these preparations in the absence (rigor) and presence of MgATP and its analogs. In rigor, angle Θ was 80 °. Relaxed and contracted preparations displayed no dichroism, suggesting a high degree of cross-bridge disorder. MgAMP-PNP² and MgPP_i imposed on the cross-bridges a distribution intermediate between rigor and relaxation. In the presence of MgADP the preparations showed strong dichroism of the opposite direction to that present in rigor. No detachment of the cross-bridges occurred under these conditions and the effect was not due to the rotational displacement of the attached dye by the nucleotide. It is concluded that the formation of a ternary complex myosin-MgADP-actin makes it possible to detect a large local deformation imposed on the cross-bridge by nucleotide binding, which results in a change of the spatial attitude of the mobile region of the protein by about 40 °.     

Structure of short thick filaments from Limulus muscle

Shortened Limulus thick filaments, isolated from stimulated muscle, are structurally similar to long filaments, isolated from unstimulated muscle, except for length. Both have 3-fold screw symmetry with a helical repeat at approximately 43 nm, axial spacing of 14.5 nm between successive crowns of crossbridges and 4-fold rotational symmetry as estimated from the Bessel argument, by analysis of optical transforms of electron micrograph negatives of negatively stained samples. Both short and long filaments also have similar radii for the location of their crossbridges, thus similar diameters. Equal numbers of subunits/helical strand are also apparent on images of metal-shadowed long and short filaments. Since these data argue against molecular reorganization during filament shortening, it is suggested that the change in length of Limulus thick filaments may occur by reversible disaggregation of constituent protein molecules.     

Cross-bridge mechanisms underlying the history-dependent properties of muscle spindles and stretch reflexes

The effects of prior movement on the force responses of skeletal muscle are compared with the effects of movement history on the changes in firing rate of muscle spindle receptors. Prior release results in the linearization of the mechanical properties of skeletal muscles, which can be provisionally explained by cross-bridge models of muscular contraction. The history-dependence of responses of muscle spindle receptors in unanesthetized decerebrate preparations appears to result from the kinetics of cycling and noncycling cross-bridges. The results of this comparison indicate that the integration of mechanical properties of muscle and spindle receptor promotes stiffness regulation.     

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.