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.

A model of muscle contraction based on the Langevin equation with actomyosin potentials.

We propose a muscle contraction model that is essentially a model of the motion of myosin motors as described by a Langevin equation. This model involves one-dimensional numerical calculations wherein the total force is the sum of a viscous force proportional to the myosin head velocity, a white Gaussian noise produced by random forces and other potential forces originating from the actomyosin structure and intra-molecular charges. We calculate the velocity of a single myosin on an actin filament to be 4.9-49 µm/s, depending on the viscosity between the actomyosin molecules. A myosin filament with a hundred myosin heads is used to simulate the contractions of a half-sarcomere within the skeletal muscle. The force response due to a quick release in the isometric contraction is simulated using a process wherein crossbridges are changed forcibly from one state to another. In contrast, the force response to a quick stretch is simulated using purely mechanical characteristics. We simulate the force-velocity relation and energy efficiency in the isotonic contraction and adenosine triphosphate consumption. The simulation results are in good agreement with the experimental results. We show that the Langevin equation for the actomyosin potentials can be modified statistically to become an existing muscle model that uses Maxwell elements.

A systematic muscle model covering regions from the fast ramp stretches in the muscle fibres to the relatively slow stretches in the human triceps surae.

We have proposed a muscle model which consists of two Maxwell elements and a Voigt element in parallel. The muscle model was applied on the experiment of the force responses by the fast ramp stretch in muscle fibres to determine the mechanical parameters. In the simulation, the Maxwell element with a flexible spring and a long relaxation time seemed to correspond with the force-generating state of the cross-bridges. Next, we tried the muscle model to simulate the relatively slow movement. Experimentally, we have measured torque changes by the stretch responses in the human triceps surae. In the experiments, the derivation of torque by rotation angle showed two peaks P1 and P2. The first peak P1 originated from the elastic properties of engaged cross-bridges, while the second peak P2 was due to stretch reflex signals. The model of a single-joint system simulated well with the experimental results to show a good adaptability of the muscle model.

The phenomenological model of muscle contraction with a controller to simulate the excitation-contraction (E-C) coupling.

We previously proposed a systematic motor model for muscle with two parallel Maxwell elements and a force generator P. The motor model showed the non-linear behavior of a muscle, such as the force-velocity relation and the force depression and enhancement, by using weight functions. Our newly proposed muscle model is based on the molecular mechanism of myosin cross-bridges. We assume that each parallel Maxwell element represents the mechanical properties of weak and strong binding of the myosin head to actin. Furthermore, we introduce a controller to simulate the excitation-contraction coupling of the muscle. The new muscle model satisfies all the properties obtained in our previous model and reduces the wasted energy of the viscous component to less than 5% of the total energy. The controller enables us to simulate contractions of slow and fast twitch muscles, which are driven by an artificial action potential or a processing electromyography signal despite their same mechanical components. The maximum velocities are calculated to be 3.4L(0)m/s for the fast twitch muscle model and 2.5L(0)m/s for the slow twitch muscle model, where L(0) is the initial length of the muscle model.

A new motor model representing the stretch-induced force enhancement and shortening-induced force depression in skeletal muscle.

A motor model that consists of two Maxwell elements with a force generator and one Voigt element is proposed in this paper. The motor model can achieve a hyperbolic force-velocity relation when we alter weight functions applied to the Maxwell elements and the force generator. Rate coefficients are introduced to determine the weight function and to improve the motor performance and the time course of the motor force. The weight functions are used as a controller of the motor. We assume that the mechanical impulse applied to the motor affects the rate coefficients and found that the amount of the mechanical impulse is related to the amount of force depression following motor shortening and to the amount of force enhancement following motor stretching. The time courses of the motor force following shortening and stretching quantitatively resemble those in other muscle experiments. The maximum energy efficiency of the motor that we obtained was 50% with an ATP hydrolysis type and 25% with an AC-DC motor type.

Partial specific volume and adiabatic compressibility of G-actin depend on the bound nucleotide.

We determined the partial specific volume and partial specific adiabatic compressibility of either ATP- or ADP-bound monomeric actin in the presence of Ca(2+) by measuring the density of and sound velocity in a monomeric actin solution at 18 degrees C. The partial specific volume of ATP-bound monomeric actin, equal to 0.744 cm(3)/g, which is exceptionally high among globular proteins, was reduced to 0.727 cm(3)/g when the tightly bound ATP was replaced with ADP. Associated with this, the adiabatic compressibility of ATP-bound monomeric actin, equal to 8.8 x 10(-12) cm(2)/dyne, decreased to 5.8 x 10(-12) cm(2)/dyne, which is a common value for globular proteins. These results suggested that an extraordinarily soft global conformation of ATP-bound monomeric actin is packed into a compact mass associated with the hydrolysis of bound ATP. When monomeric actin was limitedly proteolyzed at subdomain 2 with subtilisin, the nucleotide-dependent flexibility of the global conformation of monomeric actin was lost.