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

Abstract 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.