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 arrangements in Limulus muscle

X-ray diffraction patterns show Limulus muscle to have a structure in rigor similar to that of insect flight muscle, except that the thick filaments are staggered. Myosin filaments in relaxed muscle bear a highly ordered helical array of cross-bridges which, however, is very labile. The array undergoes a reversible transition between order and disorder in response to changes in ionic strength.     

Cross-bridge duty cycle in isometric contraction of skeletal myofibrils

During interaction of actin with myosin, cross-bridges impart mechanical impulses to thin filaments resulting in rotations of actin monomers. Impulses are delivered on the average every tc seconds. A cross-bridge spends a fraction of this time (ts) strongly attached to actin, during which it generates force. The "duty cycle" (DC), defined as the fraction of the total cross-bridge cycle that myosin spends attached to actin in a force generating state (ts/ tc), is small for cross-bridges acting against zero load, like freely shortening muscle, and increases as the load rises. Here we report, for the first time, an attempt to measure DC of a single cross-bridge in muscle. A single actin molecule in a half-sarcomere was labeled with fluorescent phalloidin. Its orientation was measured by monitoring intensity of the polarized TIRF images. Actin changed orientation when a cross-bridge bound to it. During isometric contraction, but not during rigor, actin orientation oscillated between two values, corresponding to the actin-bound and actin-free state of the cross-bridge. The average ts and tc were 3.4 and 6 s, respectively. These results suggest that, in isometrically working muscle, cross-bridges spend about half of the cycle time attached to actin. The fact that 1/ tc was much smaller than the ATPase rate suggests that the bulk of the energy of ATP hydrolysis is used for purposes other than performance of mechanical work.     

The sliding filament model of muscle contraction. III. Stability analysis and sinusoidal perturbations

A theoretical model of the energy transducing part of a single sarcomere, which has previously accounted for most of the steady state energetic and dynamical properties of striated muscle, is subjected to stability analysis. The steady states of isotonic and isometric contraction turn out to be stable and the magnitudes of the characteristic roots allow accurate reduction of the original seven state theory to a four state theory. Both versions possess a complex pair of roots giving a damped oscillatory character to the contraction velocity, the tension generated and the populations of the crossbridge states.     

An energetic model of muscle contraction

Initial energy utilization in the twitch is visualized as the result of the activity of two distinct processes. The first is the calcium-pumping activity of the sarcoplasmic reticulum, which has a constant energy requirement under normal conditions. The second is the chemomechanical transduction process consisting of a variable number of quantal contractile events, each with a fixed enthalpy equal to the molecular enthalpy of adenosine triphosphate (ATP) hydrolysis in vivo. This enthalpy appears either as heat or as contractile element work. Total enthalpy varies according to the number of quantal contractile events that occur in the twitch cycle. The basis of the variation is suggested to be velocity-dependent activity of the actomyosin ATPase, allowing more quantal events to occur in a contraction cycle when shortening occurs. The classical designation “activation heat” is held to be appropriate for the first process. The partition of the enthalpy of the second process that is currently in vogue is held to be misleading and a new formulation is suggested in which the properties of the quantal contractile event are reflected in general terms. The formulation of the proposed transduction model represents a conceptual return to the viscoelastic theory, but at a quantal level. The model can explain the results of the preceding paper and is adaptable to different muscles without having to postulate fundamental differences in energy utilization.     

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.     

Kinetic model of a single muscle contraction

A model of single muscle contraction is proposed. The kinetics of two reactions have been used: interaction between the excitation mediator and the muscle membrane receptor, and the reaction of enzymatic mediator splitting. The muscle contraction parameters have been correlated with the concentration of the mediator-receptor complex.     

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.     

A dynamic model of smooth muscle contraction

A dynamic model of smooth muscle contraction is presented and is compared with the mechanical properties of vascular smooth muscle in the rat portal vein. The model is based on the sliding filament theory and the assumption that force is produced by cross-bridges extending from the myosin to the actin filaments. Thus, the fundamental aspects of the model are also potentially applicable to skeletal muscle. The main concept of the model is that the transfer of energy via the cross-bridges can be described as a 'friction clutch' mechanism. It is shown that a mathematical formulation of this concept gives rise to a model that agrees well with experimental observations on smooth muscle mechanics under isotonic as well as isometric conditions. It is noted that the model, without any ad hoc assumptions, displays a nonhyperbolic force-velocity relationship in its high-force portion and that it is able to maintain isometric force in conditions of reduced maximum contraction velocity. Both these findings are consistent with new experimental observations on smooth muscle mechanics cannot be accounted for by the classical Hill model.     

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.     

Theory of muscle contraction II. Isotonic contraction

The theory of muscle contraction developed in Part I is extended to non-isometric cases. The basic feature of the approach is the strong viscous coupling of the movement of the counterionic (K⁺) layer with the movement of I-filaments. The surface conductance of the K⁺ layer governs the flux of H⁺ along the I-filaments which in turns regulates the rate of ATP hydrolysis. The energy output of the muscle becomes the function of its mechanical activity. By assuming linear dependence of the K⁺ layer's surface conductance on the velocity of shortening Hill's equation has been derived. With a set of reasonably chosen values of the basic parameters of the theory the values of Hill's constants have been computed. The theory has been also shown to provide the observed dependence of the isometric tension on the degree of the myofilamental overlap.     

Modelling concentric contraction of muscle using an improved cross-bridge model.

Despite its overwhelming acceptance in muscle research, the cross-bridge theory does not account for all phenomena observed during muscular contractions. A phenomenon which has received much attention in the biomechanics literature, but has evaded convincing explanation and is not accounted for in the formulation of the classic cross-bridge theory, is the persistent aftereffects of muscular length changes on force production. For example, following muscle shortening, the isometric force of a muscle is depressed for a long time period ( > 5 s) compared to the corresponding isometric force following no length change. In the present study, the classic cross-bridge model was modified in two ways in an attempt to account for the force depressions following muscle shortening. First, the steady-state force depressions following shortening were described by a single scalar variable: the work performed by the muscle during shortening; and second, the dynamic, history-dependent cross-bridge properties were described using a fading memory function. The proposed model was developed and tested for shortening of the cat soleus at constant speeds ranging from 4 to 32 mm/s, for shortening at changing speeds, and for shortening of different magnitudes ranging from 2 to 10 mm. The history-dependent forces during shortening and the steady-state force depressions following shortening were well captured with the modified cross-bridge model. The present model contains two mathematically simple adaptations to the classic cross-bridge model, and is the first such model to account for the long-lasting force depressions following muscle shortening using a single scalar variable.